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Water transport in proton exchange membranes Castañón, Tatiana Romero 2008

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WATER TRANSPORT IN PROTON EXCHANGE MEMBRANES by Tatiana Romero Castafión  Ing. QuImica, Universidad Popular Autónoma del Edo. de Puebla, 1996 M. EnergIa Solar (Hons), Universidad Nacional Autónoma de Mexico, 1999  A THESIS SUBMITTED iN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY in  THE FACULTY OF GRADUATE STUDIES (Mechanical Engineering)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) October 2008 © Tatiana Romero Castaflón, 2008  Abstract Water transport across Nafion membranes was investigated under activity gradients at atmospheric pressure. The activity gradients across the membrane were controlled by exposing one side of the membrane to dry gas under laminar flow, while maintaining liquid or vapour equilibrium with water on the other side of the membrane. The measurements were made under steady state and transient conditions. The main objective was to identify the rate limiting mechanism among the three major water transport processes in Nafion: diffusion in the bulk, and sorption across both interfaces. The proposed hypothesis was to represent the overall water transport across the membrane as the sum of resistances across the membrane bulk and interfaces. The experimental implementation required new hardware and techniques. A dual chamber cell with temperature, humidity, and pressure control was designed with a gated valve to control the initial starting time for transient measurements. Unlike previously reported work, this design enabled the individual control of membrane thickness, temperature, pressure, relative humidity, and dry gas flow rate in each chamber. The ability to control these variables made the experimental results amenable to theoretical simulations. Two phenomenological models were proposed to separate the contributions of bulk transport and sorption processes. The Varying Diffusion Coefficient model (VDC) was a preliminary effort to generate mass transport coefficients. The Vaporization-Exchange Model (VEM) provided an approximation for the steady state and transient water transport data through the definition of a novel boundary condition that describes the kinetics at the interface, while diffusion is described by Fick’ s law.  11  The VEM yielded interfacial water transport rates:  0.75 cm& 1 for liquid-, and  k= 0.63 cms’ for vapour-equilibrated membranes. Such results contribute to fill the gap for the membrane interfacial kinetics in the fuel cell literature. The analysis with the VEM revealed that interfacial water transport became rate limiting at membrane thickness below Ca. 100 pm. Analysis of transient data with VEM generated bulk diffusivity coefficients: D27x 10b0 m s’, for liquid equilibrated membranes at 30-70°C, which agreed with literature 2 data. 2 composite membranes to study the A case study is presented for Nafion-Si0 effect of the membrane water content, by addition of silicon dioxide to Nafion membranes. The status of water in the membrane was characterized with long-established techniques, such as vapour sorption, scanning calorimetry, and water uptake measurements. Information from these measurements was coupled with measurements from the dual chamber cell. Experimental results indicated a threshold at 16 wt% of silicon dioxide above which the water transport properties of the composite differed significantly from additive-free Nafion. Analysis with the VEM suggested that the addition of the composite produced structural changes to the polymer matrix.  111  Table of Contents Abstract  .  ii  Table of Contents  iv  List of Tables  vi  List of Figures  vii  Acknowledgements  Xvi 1  Introduction  1  1.1 Proton Exchange Membrane Fuel Cells 1 1.2 Water Management in PEMFCs  3  1.2. Proton Exchange Membranes 1.2.1 Perfluoro sulfonic acid membranes  5 6 10 13  1.2.2 Alternative Membranes Composite Membranes  1.3 2.  17  Literature Review 2.1 Structure of Nafion membranes  17  2.2 Water Transport Properties in PFSA membranes  20  2.3 Theoretical Studies of Water Transport in Nafion Membranes  23  2.3.1 2.3.2 2.3.4 2.3.5  Water diffusion Transport in porous media Vapour sorption and desorption Transport through the membrane’s bulk and interfaces: diffusion, and  2.4 Experimental determination of Mass Transfer coefficients 2.4.1. Diffusion coefficient 2.4.2 Interfacial mass transport coefficients 2.4.3 Aims of this research 3.  14  Research Outline  sorption  24 25 27 28  29 29 33 39  Experimental Methods  41  3.1 Membrane Preparation  41  3.1.1 Membrane activation 3.1.2 Nafion 115- silicon dioxide composite membranes  41 42  3.2 Water Transport Experimental Concept  43  3.3 Permeability Cell  45  3.3.1. Experimental set up, instruments and sensors 3.3.3 Activity gradient  3.4 Water Transport Experimental Protocols  49 54  56  iv  [Original document was missing page v]  List of Tables Table 1.1 Physicochemical characteristics of perfluorinated sulfonic acid (pfsa) membranes. [25-281  7  Table 1.2. Properties of alternative proton exchange membranes in comparison to nafion. Modified from [25,44,45]  12  Table 1.3 Thesis overview  16  Table 2.1. Diffusion coefficients, experimental tecimiques  32  Table 2.2. Summary of relevant interfacial mass transfer coefficient reported values  36  Table 2.3. Summary of the most relevant experimental approaches related to this thesis 38 Table 3.1. Properties of Nafion 11 5/SiO composite membranes [45]  43  Table 3.2. Illustrative example of the effect of varying the gas flow rate on the water activity  55  Table 3.3. Coefficient values [89] for apour pressure Equation (3.7)  57  Table 3.4. Water uptake, water content and weight of wet membrane data for Nafion 115 and Nafion 115/ 5i0 2 membranes under fully saturation at 25°C  66  Table 3.5. Enthalpy of fusion measured by DSC for Nafion 115 and Nafion 115/ Si0 2 membranes  69  Table 4.1. Activation energy for Nafion 115 membranes equilibrated with liquid and vapour water  77  Table 5.1. Summary of diffusion and surface transfer coefficients from model for liquid equilibrated Nafion 112 and 117 at different temperatures. The best 0 fit is shown for each experiment Table 5.2. Steady state response from analysis with VEM  99 103  Table 5.3. Bulk permeability DCmax and interfacial k of nafion in LE and VE Nafion at 50°C  105  Table 5.4. Summary of Diffusivity coefficient (D), water concentration in the membrane  (Cax)  and the corresponding dimensionless vaporization rate (y)  110  Table 6.1 Properties of Nafion 11 5/5i0 2 composite membranes  113  Table 6.2 Descriptors of Equation 6.1 components  127  vi  List of Figures Figure 1. 1 Proton Exchange Membrane Fuel Cell  1  Figure 1.2 Water dynamics in proton exchange membrane fuel cell  5  Figure 1.3 Polymeric chemical structure of Nafion (m1; x5-13.5; n=2; yl)  7  Figure 1.4. Schematic illustration of Nafion microstructure from Li [15]  8  Figure 2.1. Model by Gierke of spherical ionic clusters. Adopted from Gierke [53]  18  Figure 2.2. Model by Weber and Newman. Modified from [55]  19  Figure 2.4. Diffusion coefficient as a function of membrane water content. Adapted from Motupally et al. [19] Figure 3.1. Setup for water transport experiments  31 44  Figure 3.2. The gate valve is pneumatically controlled to connect/disconnect the membrane with the wet chamber  45  Figure 3.3. The wet and dry chambers were separated by a membrane holder  46  Figure 3.5. Top isometric view of the permeability cell  48  Figure 3.6. Membrane assembly process  49  Figure 3.7 Complete experimental setup for water transport measurements  51  Figure 3.8. The vapour pressure was measured at different helium flows and temperatures  57  Figure 3.9. For each experiment, the steady state vapour pressure was obtained from the plateau and plotted as a function of helium flow rate  58  Figure 3.10. (a) Flux from steady state water transport for LE Nafion 117 at 30, 50 and 70°C  60  Figure 3.11 Measured time response to relative humidity step change from vaisala® dew point sensor  62  Figure 3.12. Typical transient water transport signal  64  Figure 3.13. DSC thermograms  68  Figure 3.14. Vapour sorption and desorption kinetics resulting from varying the atmospheric relative humidity  70  Figure 3.15. Membrane water content vs. Water activity for Nafion 115 and Nafion 117 71  vii  Figure 4.1. Measured steady-state water flux was measured  74  Figure 4.2. The measured flux across Nafion 115 is shown at atmospheric pressure for varying the temperature  76  Figure 4.3. Measured steady state flux of water across Nafion 115 membranes comparing isothermal (solid) and non- isothermal (hollow) conditionss Figure 4.4. Calculated resistance to water transport for Nafion 115  79 80  Figure 4.5. The water concentration corresponding to fully saturated gas mixtures at different temperatures Figure 4.6. Comparison of water flux across membranes with different thicknesses  82 84  Figure 4.7. Comparison of water fluxes at 50°C from three different thicknesses: 51:127:183 jim in their expanded form  86  Figure 4.8. Comparison of physical state of water in contact with the membrane during transient water transport  88  Figure 4.9. The flux derivative is compared for a Nafion 117 membrane in LE and VE conditions  89  Figure 4.10. The acceleration of the flux across the membrane as a function of time  91  Figure 4.11. Measured times in LE Nafion 112 and 117 membranes  93  Figure 5.1. Experimental vs. simulated transient data for initially dry membranes  97  Figure 5.2. Experiment vs. simulation transport flux across Nafion 112 (left), and Nafion 117(right) Figure 5.3. Measurements of (l-RH)/RH as a function of the gas velocity  98 104  Figure 5.4. Linear fits of the slopes from Figure 5.3 vs. Nafion lix thickness in liquid and vapour equilibrated membranes Figure 5.5. Representative linear fit of long-time response. LE Nafion 117  104 108  Figure 5.6. Simulation (lines) and experimental (dots) data in the short-time for LE Nafion 117 at 30, 50, and 70°C  109  2 composite membranes at 25°C Figure 6.1. Vapour water isotherms for Nafion ii 5/Si0 117 Figure 6.2. Rate of change for sorption  118  Figure 6.3. The state of water as a function of Si0 2 content in Nafion 115 membranes. 119  vii’  ), 2 Figure 6.4. Steady state water transport fluxes in unmodified Nafion 115 (0 wt% Si0 2 and NafionISiO  122  2 Figure 6.5. Thickness dependency for steady state water transport across NafionISiO composite membranes Figure 6.6. Fitting lines for measured (1-RH)/RH data vs. gas velocity  124 125  2 wt% for LE Figure 6.7. The slopes from Figure 6.6 are plotted against the content of Si0 and VE composite Nafion membranes  126  Figure 6.8. A one-dimensional, steady state approximation with continuous water concentration profiles Figure A. 1: Control volume in the dry chamber of the permeability cell  129 145  Figure C. 1 :Setup for dew point temperature sensor cross-reference. A saturated atmosphere was kept during measurements  159  Figure D. 1. Membrane water content vs. Water activity for Nafion 115 and Nafion 117 at different temperatures, from different sources  163  Figure D.2 The effective water diffusivity for le (left) and vapor-gas equilibrated membranes (right) from permeation measurements  165  ix  [Original document was missing pages x-xi]  Nomenclature  a  Dimensionless water activity in chamber  a  3 in the membrane (Only in section 5.1) Concentration of SO  3 mol SO 3m  A  Membrane superficial area  2 m  Cm  Max. membrane water concentration  mol / cm 3  c  Concentration of water  mol / cm 3  Diffusion coefficient of water  /s 2 m  Dc  Effective diffusivity  /s 2 m  e  Electrons  F  Faraday constant  2 H  Hydrogen  H+  Protons  0 2 H  Water  I  Current density  02  Oxygen  coulomb / mol  2 A/m  Flux of water across the membrane  mol / m 2s  ka  Absorption mass transfer coefficient  m/s  kd  Desorption mass transfer coefficient  m/s  k  Effective hydraulic permeability coefficient  2 cm  k  Interfacial mass transport rate for liquid and vapour equilibrated  m/s  membranes L  Membrane thickness  m  , 13 Md  Molecular weight of dry Nafion  gr / mol  True gas flow  mol / s  3 so  Moles of SO 3 species  mol  Pagm  Atmospheric pressure  bar  FL  Partial pressure of water  kPa  P  Pressure in chamber  bar  xii  P  Vapor pressure  bar  psat  Saturation pressure  bar  r  Pore radius  cm  Q  Equivalent weight  gr dry Nafion / mol SO 3  R  Ideal gas constant  J / K mol  RH  Relative humidity  T  Chamber temperature  x  Membrane thickness  X  Water mole fraction  V  Chamber volume  3 cm  (Partial) molar volume of water  3 / mol cm  Gas flow rate  min 3 cm 1  Wb  Bound water weight in the membrane  g  Wnb  Non-bound water weight in the membrane  g  W  Total water weight in the membrane  g  a  Mass transport coefficient  J cm s 2 mol  A  Difference  V  Gradient  1/length  Viscosity of water  Pa s  2  Membrane water content  mol H 0/mol S0 2 3  y  Surface tension of water (Only in Eq. 2.7)  N / cm  y  Dimensionless vaporization rate  jim  Greek  U  Chemical potential  J / mol  Internal contact angle (Only in Eq. 2.7)  deg  xiii  0 0 Pd  Dimensionless concentration dimensionless steady-state concentration Density of dry Nafion  gr / m 3  Dimensionless electro-osmotic drag coefficient Time domain  Subscript and Superscript  1,2  Chamber side (l=wet chamber, 2=dry chamber)  A  absorption  D  desorption  C  Capillary  G  Gas phase  He  Helium Protons  mt  Interfacial  L  Liquid phase  max  Maximum  Nil 5/Si0 2  Composite membrane (Nafion 115 doped with Si0 ) 2  sat  Saturation  3 SO  Sulfonic ion groups  ss  Steady state  t  Time  V  Vapour phase  v  Vaporization  w  Water  xiv  Abbreviations  AFM  Atomic Force Microscopy  BT  Back Transport  EOD  Electro-osmotic Drag  EW  Equivalent Weight  FTIR  Fourier Transform Infrared Spectroscopy  IFCI  Institute for Fuel Cell Innovation  LE  Liquid Equilibrated  MRI  Magnetic Resonance Imaging  NMR  Nuclear Magnetic Resonance  NRC  National Research Council  ODE  Ordinary Differential Equation  PEM  Proton Exchange Membrane  PEMFC  Proton Exchange Membrane Fuel Cell  PFSGE  Pulsed Field Gradient Spin-Echo  SANS  Small Angle Neutron Scattering  VDC  Varying Diffusion Coefficient  VE  Vapour Equilibrated  VEM  Vaporization-Exchange Model  WT  Water Transport  xv  Acknowledgements I would like to start thanking my supervisor, Dr. Walter Mérida for his support and outstanding mentorship during this project.  I want to thank the members of my committee Dr. David Wilkinson, Dr. Michael Eikerling and Dr. Bryan Wetton for the insightful discussions throughout these years and for reviewing this thesis in spite of their busy agendas.  I thank Dr. Charles Monroe for many insightful discussions, which helped to enlarge my vision of science.  Thanks to Dr. Titichai Navessin, Dr. Steven Holdcroft ant the MEA group at NRC-IFCI for their help in sample preparation, support, and advice regarding this research.  I would like to thank the previous and present members of Dr. Mérida’s group: Robbie, Ignacio, Chris, Saul, Peter, Amir, Galvin, Omar, David, Ed, Shensheng, and Michael, for their friendship and motivational discussions throughout these years. I was very lucky to be part of this group.  I thank my proof readers, Edward McCarthy, Mario Delgado, and David Kadylak,. My special gratitude is to my friend Edgard Neudorf, who not only did an exhaustive work proofreading this thesis but was also a constant source of encouragement during the writing process.  I was fortunate to share these academic years with people who enriched this experience with inspirational discussions and warm friendship. My sincere thanks to Dr. Olivera Kesler, and fellows Ignacio Valenzuela, Peter Cave, and Makoto Adachi for these years of priceless memories.  xvi  I could have not been able to finish this thesis without balancing it with good times and good friends. Thanks to Monica Danon-Schaffer and Scwist members for being good mentors and friends. Thank you to my friend José Alberto Felix for his moral support in the last years. Thanks to all members of my futbol team for their support and encouragement in the good and hard times.  I would like to express my deepest gratitude to my parents: Rosa Luz and Salvador, for their unconditional love and the sacrifices they have made for me throughout my study life. I thank my siblings Gabriela, Salvador, and Estela for their encouragement and understanding during my unavailable times in the last years. My gratitude is also for my beloved godparents, Pablo (rip) and Eva Castañón who encouraged me to pursue my dreams. (Gracias familia por apoyarme una vez más)  Finally, I want to profoundly thank to Ruben, my husband, who has been my pillar throughout these years. This journey is much his as it is mine. Without his patient love and care I would not have been able to accomplish it. (Gracias Ruben por tus cuidados cariflo, y paciencia).  xvii  1. Introduction 1.1 Proton Exchange Membrane Fuel Cells Proton Exchange Membrane Fuel Cells (PEMFCs) are electrochemical reactors that generate electrical energy from a continuous supply of fuel and oxidant gases, being these in the most general case, hydrogen and air, respectively. PEMFCs comprise two electrodes; a cathode, and an anode, and a solid membrane, which acts as ionic conductor (see Figure 1.1). Current PEMFC technology, using hydrogen as fuel, offers power generation ranging from 10.1 to  W with lower CO 2 emissions and higher efficiencies  than combustion engines. These advantages have motivated its broad application for powering from portable to transportation systems.  External circuit (e) -  Humidified Fuel supply +H (H 0 2 )  I  j  —I  1  “ii  -  F:.’  -  Electrolyte/Membrane  Oxidant supply (Air or 02)  ‘  Produced H 0 2  (+%O H i 9 ( 2  —*  HO(€)  <100°C  Figure 1. 1 Proton Exchange Membrane Fuel Cell  1  Despite their advantages, the commercialization of PEMFCs is still limited mainly due to the limited hydrogen supply infrastructure. Also, the availability of pure hydrogen, required to maintain a free of emissions- life cycle, is restricted to expensive technology that is not widely spread in the industrial world, such as elecotrolysis. Instead, industrial hydrogen production relies on extraction from fossil fuels which disrupts the zero-emission-technology concept. Other limitations to the massive commercialization of PEMFCs are high manufacturing cost, limited components lifetime, reliability, and the need to simplifr the support sub-systems [1].  Gas compression, power conditioning, cooling, and water  management are examples of the required subsystems of a fuel cell. The work presented here addresses the fundamental processes related to the water management approaches. Proper water management is indispensable for optimal PEMFC operation. The membrane must be hydrated to enable protonic conduction, but water in other regions (most notably the electrode layers) can hinder the access of reactants to the active sites at the membrane-catalyst interface. As a result, modem membrane electrode assemblies (MEA5)  incorporate  advanced water  management  schemes  including  reactant  humidification [2,3], hydrophobic treatment of the electrode substrates [4] and multi layer MEA structures incorporating micro-porous materials [5,6]. Faulty water management is the main cause for flooding and dryness in the cell, two of the most common failure modes of PEMFCs. During such failures, fundamental reaction pathways are affected, leading to decreased performance and lifetime.  2  1.1.2 Water Management in PEMFCs  Failure can be prevented by suitable water management strategies[2,3,7-lO] which in many situations have relied on trial and error practices for optimisation. A more rational optimization process requires a clear understanding of the water transport mechanisms in PEMFCs. Two main transport mechanisms move the water across the membrane: Back Transport (BT), and Electro-osmotic drag (EOD) towards the cathode[11-14].  The  balance of these two processes determines the activity gradient of water across the membrane. During operation, cathodic reactions produce water at the membrane-electrode interface. Evaporation takes place and the water is partly convected out with the reactant gas; the rest is transported trough the membrane towards the anode. As protons cross the membrane, a shell of solvating water molecules surrounding the positive ion travels with it to the cathode, creating the so called EOD effect, which is a function of the current load as shown in Equation (1.1) [15]:  0 N  (Oj;  (1.1)  where, Neo is the flux of water due to EOD; a, is the EOD coefficient, i.e. the number of water molecules accompanying the proton, and NH+, is the flux of protons as a function of current density [16-181. This EOD coefficient is not constant; it has been proven that this value is a functiOn of the number of ionic sites in the membrane, the porosity of the  3  membrane, the operation temperature, the water activity, and of the current density. As shown in Equation (1.1), an increase in current produces an increase in the flux of water to the cathode side of the membrane. On the opposite direction, BT of water to the anode, results from the concentration gradient formed across the membrane when water is produced at the cathode. BT can also be induced through application of a pressure gradient across the membrane-electrode assembly. A common approach to study this phenomenon is through Fick’s first law of diffusion, which describes the proportional flux of water due to the water concentration gradient in the membrane [19]:  BT  = _DeBVCw(2)  (1.2)  where Deff is the diffusion coefficient of water, and c is the water concentration.. D. has also been reported to be a function of the membrane hydration level (2). As the current load increases, the EOD flux overcomes BT, resulting in a net transport of water from anode to cathode. This excess water content can cause flooding on the cathode side. As a consequence of the flooding, the gas diffusion layer (GDL) pores are blocked [20], impeding the passage of reactants to the triple-phase zone in the catalyst layer [6,9,21], contributing to mass transport limitations. Flooding also reduces the availability of electroactive surface, increasing the activation overpotential of the cathodic half-reaction. Additionally, due to the effect of EOD, the anode side may be dehydrated, increasing the resistivity of the membrane and leading to steep ohmic drops in current-voltage plots.  4  In practical PEMFC applications, it is common to use humidified reactant gases to prevent membrane dehydration [22,231. Usually, humid hydrogen is fed to the anode to keep it hydrated. Meanwhile, at the cathode side, a temperature increaseof the fuel cell can vaporise the water produced by the cathodic reaction. As a result, the membrane is in contact on one side, with liquid water and vapour on the other, and the water uptake rate consequently differs on each side of the membrane. This also impacts, BT and EOD[24]. Figure 1.2 illustrates the water dynamics in the membrane-electrode assembly. Humidified H 2 gas  0 Exhausted 2 H  •A  •1  Humidified 0: gas  Figure 1.2 Water dynamics in Proton Exchange Membrane Fuel Cell  1.2. Proton Exchange Membranes Proton exchange membranes (PEM5) play an essential role as ion conductors and gas separators in PEMFCs. In order to be used as electrolytes in fuel cells they must comply with main requirements[ 15]: •  chemical stability  •  mechanical stability  •  impermeable to gas  5  •  resistance to dehydration  •  high proton conductivity  •  low production cost  ( 0.1  Scm’)  Usually, PEMs are thin films (<100 pm) of solid polymer electrolytes with ionic functional groups (i.e., sulfonic acid groups) acting as protons.  1.2.1 Perfluoro sulfonic acid membranes  The chemical structure of PEMs consists typically of fluoroethylene backbone with sulphonated-terminated, perfluorinated vinyl-ether branches which allow proton exchange between the polymer networks created. Gore and Nafion have been considered the standard membranes for commercial TM fuel cell (PEMFC) technology. Other commercial brands are FlemionTM, and Aciplex (See Table 1.1). Nafion membranes are the focus of the present study. Even though Gore is currently considered the standard membrane for commercial fuel cells (more than Nafion), its availability is limited for industrial applications only. Its use for research projects is not easily granted and very little information is publically available. Nafion is the commercial name from Dupont; its introduction to the market started with the space programs in the 1960’s The  Nafion  structure  is  formed  by  the  copolymerization  of  poiy  tetrafluoroethylene (PTFE) and polysulfonyl fluoride vinyl ether. The incorporation of these two polymers provides Nafion with two phases: a hydrophobic Teflon-type backbone, and a hydrophilic phase associated to the vinyl ether side chains with sulfonic acid groups terminations.  6  Table 1.1 Physicochemical characteristics of perfluorinated sulfonic acid (PFSA) membranes. [25-281 Proton Equivalent Water Thickness Structure parameters Trademark Type Membrane  Nafion 112  Dupont  Weight  Uptake  Conductivity  j 3 (g molSO  (wt %)  (S cm ) 1  1100  36  (urn)  m=1x=5-13.5;n=2;y=1  51  b 0071  (shown in Figure 1.3) 1100  127  Nafion 115  0.la  25  0.0043 0066 • 0 b  1100  183  Nafion 117  34  0.0133c d 009  Asashi  25-100  1000-1200  43  0.108  m0;n2;x3.6-10  50:125:250  800-900  54  0.114  m0; n1-5  50:80:120  1000  Aciplex  m=0; n2-5;x1.5-14  Dow  Flemion  Chemicals Dow Chemical’ Asashi Glass C a Not commercially available. Conditioned in water at 100°C, water at 25°C, 1 00%RH at 30°C,  d  100%RH at 25°C  A representation of the chemical structure of Nafion monomer is shown in Figure 1.3.  2 ((CF  —  ) 2 CF  —  2 (CF  —  CF))_ (0  — CF)m 2 CE  0  —  ) 2 (CF  H 3 SO  3 CF  Figure 1.3 Polymeric chemical structure of Nafion (m=1; x=5-13.5; n=2;y=1)  7  Nafion chemical stability and mechanical strength is provided by the strong Teflon-type backbone (See Figure 1.4). The hydrophilic phase is flexible enough to swell and absorb water to increase the weight of the dry membrane as much as 50% (or up to 100% when it is contact with liquid water){ 15]. The association of water will then depend largely on the number of acid groups associated per gram of dry polymer, i.e., Ionexchange capacity.  Fluorocarbon backbone material  0  -  SO  ®  H  •  0 2 H  Figure 1.4. Schematic illustration of Nafion microstructure with the hydrophilic side chains and hydrophobic backbone structure. Modified from Li [15].  The measure of ionic content in the polymeric membrane can also be represented by the Equivalent Weight ( EW 1000/ IEC):  8  Equivalent Weight (EW)  =  g  dry Naflon mol 3 SO  (1.3)  It has been reported that water content influences proton and water transport properties of Nafion[ 17,29-311. The water content  (?) is reported as the number of water  molecules present in the polymer in terms of the number of ionic sites:  2  O 2 molH 3 molSO  (1.4)  In practical applications for PEMFC, the membrane equivalent weight ranges between 800-1500 EW [321. For Nafion, the most common EW is of 1100. Thus, the number of water molecules associated to each ionic site would depend on the relative amount of water absorbed by the membrane in terms of its dry weight (i.e., water content, 2. See Equation 2.1 in Section 2.2). Section 2.2 includes an overview of the current discussion in the literature of fuel cells regarding the quantification of water content in Nafion membranes. The membrane undergoes recurring shrinking and swelling cycles due to water content fluctuations [33-35]. The swelling pressure is counterbalanced by elastic pressure exerted by the polymer matrix which prevents dissolution of the membrane in polar solvents. Because the chemical stability of Nafion is compromised above its glass transition temperature (1 10°C), PEMFCs systems operate at approximately 80°C to prevent irreversible damage to the chemical structure by keeping water in its liquid phase. Even though this temperature lies below the boiling point, the temperature is high enough to maintain a two phase water system. The need for constant humidification and low temperatures for water management restrict operating regimes of fuel cells significantly.  9  Research efforts towards the use of high temperature [36-3 8] and low humidity [3,8,39,40] operation in PEMFCs could render humidification obsolete or unnecessary, but current designs still rely on humidified reactants. Despite significant advances in polymer design and manufacturing techniques [25,41-43] Nafion continues to provide a useful standard for commercial PEMFC applications. Nafion membranes have been studied from different perspectives to understand their dual performance as proton conductors and water transport media. The membrane requires humidity to conduct ions and poor water management therefore decreases the accessibility of the reactants to the ionic sites, decreasing the system performance and lifetime. 1.2.2  Alternative Membranes  The mechanical and chemical stability of PEMs become compromised at high temperature and low humidity. Another challenge for the PEMs is their frequent volume change due to swelling and shrinking. A membrane that does not swell would represent a solution for stable and long lasting seals in PEMFCs, a common source of mechanical failure. These disadvantages of Nafion have increased research interest to produce alternative materials that operate in environments above 120°C and below 50%RH, and are less prone to swelling. Table 1.2 shows the current classification of alternative membranes. The table shows some of their physical properties and performance in comparison to perfluorosulfonic acid (PFSA) membranes. The scarcity of factual information is due to the variability of material combinations found in the literature which makes it difficult to present a consistent comparison between material properties.  10  With temperatures above 100°C, water transport would occur in a single vapour phase domain. However, high temperature opens up another challenge: the need for more robust ionic conductors than Nafion, such as composite membranes.  11  Table 1.2. Properties of alternative proton exchange membranes in comparison to Nafion Modified from [25,44,45]. .  Category  Structure  Physico- chemical  Thickness  Proton  (j.tm)  Conductivity  Characteristics  (S cm’) Partially  Fluorocarbon base  Fluorinated  with hydrocarbon  • Mechanically stronger  25-200  10’  • Less durable and less  aromatic side chain Non  Fluorinated  chemically stable  Hydrocarbon base  • Mechanically stronger  10.1 —1 0  with polar groups  Hydrocarbon  a  • Lower chemical and  thermal stability Non Fluorinated Aromatic  Aromatic base with  • Mechanically stronger 2  10  • Polar  • Chemical and thermal  • Sulfonic acid  stability at temps. up to 300°C  group Acid-Base polymer  • Improved water uptake  10  Acid into  • Thermally and  alkaline polymer  chemically stable  base  • Improved dimensional  stability. Durability to be proven. Modified  PFSA:  Reinforced  Nafion impregnation  50-76  into PTFE  [45]  10  --  . 300-2000 MPa (Young’s  modulus)  membranes:  • Dimensionally stable  • Modified PFSA Composite doping  .Nafion doped  10  b  lv -4  c  -  .-  50% less water uptake 20% higher water uptake  with Si0 2 • Nafion doped with Zirconium phosphate • Nafion doped with  ‘U  phosphoric acid aat 20-140°C b  at 120°C & 40%RH C  at 60°C (vs 1 0 for Nafion same conditions)  dat  175°C  12 Composite Membranes Hygroscopic inorganic composite membranes are reported to offer improved thermal and chemical stability at temperatures above 100°C. By sol-gel reactions, Nafion membranes 2 and Si0 2 are examples of can be modified with addition of inorganic nanoparticles. Ti0 additive materials that sustain chemical stability at high temperatures and maintain good proton conductivity under such conditions. -Nafion membranes have shown improved water content and proton 2 Si0 conductivity due to the hygroscopic properties of the silica [42,46-48]. The addition of the composite provides higher water retention for the membrane and conductivity at high temperatures. Proton conductivity in composite Nafion has been reported in the order of i0 to i0 Scm’ at 100°C.In Nafion, sol-gel reactions occur in the polar clusters inside the membrane, generating Si0 2 nanoparticles which fill in clusters associated with the ionic S0 3 sites [49]. Researchers have targeted Si0 -Nafion membranes to produce self-humidifying 2 membranes in order to eliminate PEMFCs’ current dependence on humidification systems. In spite of the interest, a clear explanation of how the membrane performs in relation to its water transport has not been presented. Changes of mechanical properties such as coefficients of volume expansion, pore-size distributions, and shear or bulk moduli, after the addition of Si0 , may be associated with the improved performance of 2 the composite membranes in the fuel cell. Alternative membranes, is a topic of increasing research interest. In the search for optimization of water management and reduction of support subsystems in PEMFCs, alternative membranes offer a viable solution. Improved proton conductivity at higher  13  temperatures, longer lifetime, and manufacturing cost reduction are the current research interests.  1.3 Research Outline Chapter 1 centers on the motivation for the study of water transport mechanisms in proton exchange membranes based on the demand for proper water management in PEMFCs. Chapter 2 describes the evolution of water transport in Nafion membranes in the last 20 years from the more qualitative studies to the more fundamental by incorporation of the surrounding effects to the material water transport properties. The use of spectroscopic techniques (i.e., NMR, FTIR) have allowed isolated membrane studies to outline the morphology and main characteristics of the polymer in the presence of water. It also explains how the research interest of this thesis lies on correlating environmental, membrane structure and water transport mechanisms. The experimental approach used on this thesis focused on overall empirical environmental variables, such as temperature, humidity, pressure, composition, and gas flow rate, rather than on physical changes in the membrane. Chapter 3 describes the experimental work: membrane preparation, the permeability cell designed to measure water crossover across PEMs, and the protocols to measure and analyze water transport under steady state and transient conditions (Sections 3.1 to 3.2). Other complementary and existing techniques used for characterization of water transport properties are described in Sections 3.3 to 3.5. The focus of this work is on the investigation of Nafion water transport within the range of operational conditions and parameters common to fuel cell systems. The effect of the activity gradient acting as a  14  mass transport driving force, and the water phase in contact with the membrane were explored under experimental conditions. Chapter 4 presents experimental results from the measurements with the permeability cell under steady and transient state. Isothermal and non-isothermal experiments generated results that provided insight on the importance of the interfaces for the mechanisms of water transport. Thickness and temperature measurements under steady state and transient regimes guided the development of two phenomenological models to describe the role of the interfaces during water transport. Chapter 5 describes both models based on a resistance in series configuration to accounting for the bulk and interfacial mass transport. The firs model, the Varying Diffusion Coefficient (VDC) model analyzed  transient water transport data as a  preliminary exercise to deconvolute interfacial sorption from bulk diffusion. The second model, the Vaporization-Exchange Model (VEM) analyzed the steady state and transient water transport and considered a dynamic boundary condition to describe a bidirectional flux resulting from the reaction kinetics of water vaporization at the membrane surface. The VEM allowed deconvolution of individual contributions to the overall water transport; it provided simultaneous information about the mass transport rates for the membrane-gas interface and diffusivity coefficients for the bulk. In Chapter 6, a study of water transport is presented for Nafion-composite membranes and the effect of increasing the membrane water content on the structural and water transport properties of the membrane is discussed. The analysis included permeability measurements and various membrane characterization techniques. Table 1.3 shows the thesis content overview.  15  Table 1.3 Thesis overview Objective: Investigate the mass transport mechanisms of water in Nafion membranes by  including boundary effects under typical operating conditions of PEM Fuel Cells Justification: Current models fail to represent precisely the differing water transport mechanisms in the bulk and across boundaries under the effect of external driving forces Tasks accomplished: Ch. 1 Introduction  •  Motivation for this research  Ch. 2 Literature Review  •  Evolution of water transport research in Nafion  Ch. 3 Experimental  •  Developed analysis tool to characterize water transport in PEM: •  Designed permeability cell with individual temperature control and time zero control  •  Measured water transport across Nafion membranes under steady state and transient conditions  •  Investigated effect of membrane water content in water transport: Si0 -Nafion membranes 2  •  Compared water transport performance in Nafion and -Nafion membranes 2 Si0  •  Characterized composite-membranes for water uptake, vapour sorption and desorption, and differential scanning calorimetry  Ch. 4 Results and Discussions  •  Found evidence of the importance of interfacial mass transport in steady state and transient water transport.  Ch. 5 Mathematical Models  •  Identified interfacial and bulk mass transfer rate constants from steady state permeability.  • Confirmed diffusivity coefficients from transient water permeability Ch. 6 A case study: water transport dependency on water content in Nafion/composite membranes  •  Determined effect of increased water content in mechanisms of water transport  Ch. 7. Conclusions  16  2. Literature Review The structure and water transport properties of Nafion have been studied under different schemas. Experimental and mathematical modeling have widely described the polymeric membrane. In the same way, the water transport phenomena across Nafion have been analyzed under the effects of diverse gradients acting as driving forces. Each approach has partially described the complexity of Nafion, its water uptake, and transport capacity for better understanding and application in PEMFCs. In Section 2.1 a review of the most significant transport mechanisms of water inside Nafion membranes is provided. Transport is described in terms of diffusion, permeability, and interfacial mass transfer mechanisms. In section 2.2, the experimental techniques to calculate diffusion and mass transfer coefficients are summarized. In section 2.3, a review of the physical models that have described the membrane structure is presented.  2.1 Structure of Nafion membranes The morphology of Nafion has been modeled with the help of a wide variety of scattering methods: small angle x-ray scattering, and small angle neutron scattering.{50-52]. Through these measurements, Nafion has been identified as a two-phase material with certain cristalinity that disappears with increasing water content. The low crystalinity of the material makes the characterization of Nafion a challenge even for state-of-the-art techniques.  17  A model proposed by Gierke et al. [53] was the first to describe the complex morphology of Nafion as a cluster network. Based on X-Ray Scattering studies, it was proposed that Nafion is formed by random network of spherical clusters of 40  A,  organized as inverted micelles. These clusters are connected by channels of  A  10  diameter, as shown in Figure 2.1.  Figure 2.1. Model by Gierke of spherical ionic clusters. Adopted from Gierke [53]  Several other models presented proposals to explain the microstrucutre of Nafion. Yeager and Steck, and Gebel and collaborators [34,54], proposed hydrophilic pores of cylindrical shape surrounded by hydrophobic domains. Gebel used small angle scattering data to explain the shape shift from isolated spherical to cylindrical interconnected ionic clusters due to the swelling and dissolution processes during water uptake. Above 50 wt% water content, Gebel found a structural inversion resulting in acid groups outside the rod-like micellar structures, which created a hydrophilic surface.  The model from Weber and Newman [55], represented in Figure 2.2, describes the structural changes of the membrane as a function of the water content. The dry membrane absorbs water and solvate the acid groups. The further the addition of water, it causes the water to form clusters around the ions, so that inverted micelles are formed  18  and connect within each other. In the last stages, interconnections of water channels form the hydrophilic paths; this situation is expected for membranes saturated with water vapour (2=14)  ,  and fully saturated membranes (i.e., 2=22), as shown on the right of  Figure 2.2.  •  do° •  0  • .  • • •  0• 0  .  2=0  .  0  0  •  .  2=l4  .<2  Figure 2.2. Model by Weber and Newman structure as a function of the water content the black  00.0.  •0  0  • •  .0 0.. 00  0 0  .  2=22  Modified from [55]. The evolution of the membrane  (k). The background represents the fluorocarbon matrix,  is the polymer side chain, the gray is the liquid water, and the dotted line is a collapsed  channel.  Scbmidt-Rohr and Chen [52] simulated small angle X-ray scattering data and fitted it to different contemporary models. The authors found the best data fit with an array of parallel cylindrical channels of inverted micelles with polymer backbone on the outside, as represented in Figure 2.3. The model describes channels with diameters of ca. 2.4 nm. (spherical models calculate diameters  <  1.2 nm). According to the authors, this  ionic continuity explains the bulk-like water diffusivity under freezing temperatures across the membrane as the narrower channels will remain full.  19  Inverted micelle  T 50 nm  / 0 2 H  Crystallite  Figure 2.3. Model of parallel cylindrical nanochannels in Nafion. The inverted micelle cylinder with Teflon backbone on the outside and the ionic side groups in the channel (left). On the right, hexagonal packing of several cylinders. Modified from [52].  2.2 Water Transport Properties in PFSA membranes Proton and water transport in Nafion are the most documented properties in the literature of fuel cells. This review, however, focuses on water transport properties only, such as diffusivity, mass transport coefficients, water content, etc. Water sorption measurements have been used to characterize Nafion water uptake in liquid and vapour environments. Several authors [11,56] reported on the difference in equilibrium water contçnt under liquid- and vapour-saturated environments, with 2=22 for the former and 2= 14 for the latter. In the fuel cell literature, the term “Schroeder’s paradox” is frequently used to describe this discrepancy. It is paradox, because in both  20  cases, the thermodynamic water activity is unity (a=]), but the equilibrium water uptake is higher for the membranes in contact with liquid.. The majority of the investigations agree that this difference is related to the physical structure of the membrane. Zawodzinski ët al. [57] reported contact angle measurements and demonstrated that the membrane’s top layer behaves hydrophobic when the surrounding environment is water vapour and it behaves as a vapourequilibrated membrane even though it has been only recently removed from immersion in liquid water. Yet, it is believed its interior water content will remain high. The authors explained the phenomena as a reorganization of the surface to balance out the dielectric properties of the membrane with the environment. The phase inversion has also been observed by FTIR surface spectroscopy measurements [58]. Gottesfeld et al. and Futerko and Hsing [59,60] agreed that the membrane remains in a stable thermodynamic state when it its equilibrated with vapour. When the membrane is in contact with liquid, the thermodynamic equilibrium is interrupted by the membrane swelling in order to accept more molecules. All the reports based on gravimetric measurements found a difference between liquid and vapour water uptake. Varied physical explanations have contributed to the debate on whether the membrane changes its structural properties due to the chemical potential of the environment. Futerko and Hsing [60] proposed an explanation for the paradox based on the Flory-Huggins model based on the heat of mixing and entropy during the water kinetics. The model explains that at higher entropies and exothermic heat of mixing, the water uptake decreases, which explains the lower water content for saturated vapour equilibrated membranes. For the liquid case, the model found that the  21  polymer matrix surrounding the sulphonic acid groups has a strong interaction with the water molecules which generates an endothermic heat of mixing. As a result, the membrane increases its water uptake. The model agreed well with experimental observations of surface changes in the polymer matrix, which became hydrophilic when the membrane was in contact with liquid water [57,59]. Similarly, McLean et al. [611 studied the ionic domains on or near the surface of K type Nafion membranes at room temperature and humidity using atomic force microscopy (AFM). They discovered that the membrane showed a thin hydrophobic layer of ca. 5  A on the surface. The formation of a hydrophobic layer has been proposed by  Majsztrik et al. [62] as an explanation for the lower water uptake in vapour sorption and permeation experiments. Choi and Datta [63] explained the water uptake difference from vapour and liquid using the force equilibrium between the swelling pressure and the elastic deformation of the polymer. The model included details on the solvent polarity, the hydrophobic ratio in the polymer and the chemistry of the ionic groups. Accordingly, the liquid equilibrated membrane generates a chemical potential which accounts for the difference in water uptake. The thermal history of the membrane has been related to the difference between vapour and liquid water uptake in perfluorsulphonic membranes.  Hinatsu et al. [56]  observed that the thermal history defines the polymer structure and hence the water uptake capacity. More recently, Onishi and collaborators [64] completed long term measurements on water sorption where the membrane-vapour system was left to reach equilibrium for up to two months. The data compared liquid and vapour water uptake  22  [Original document was missing pages 23-25]  This analysis assumes the membrane to be homogeneously saturated, neglecting concentration gradients. In sorption experiments concentration gradients tend to be large, so Equation 2.4 is a better approximation than 2.5.  According to Eikerling and collaborators [121, considering the Nafion membrane as a nanoporous material can drive to an alternative two-phase analysis in porous media, where contact angle (6), surface tension (y) and pore radius (r) define a capillary pressure by: PPGPL  cos 0 r  (2.6)  Since the capillary pressure balances out the advance of water inside the pores, this pressure can be considered the driving force for the liquid transport flux through the porous media by the expression: j  =——---(VpC+VpG) Vp  (27)  When the system is under uniform gas pressure, VPG is neglected. In this way, k is the permeability rate in a saturated medium. Eikerling et al. and Weber and Newman [66,711 proposed a hybrid model based on the concentrated solution theory and a porous media treatment for the membrane. These models attempted to bridge the gap between one- and two-dimensional models and allowed the analysis within the range of vapour to liquid. The model incorporated a dependency of polymer structural change on water content based, on capillary  26  phenomena. It described the evolution of the formation of channels and interconnections between them with the increase of water uptake.  2.3.4 Vapour sorption and desorption  A frequent approach in the analysis of Nafion water transport is done through the mechanisms of sorption and desorption in transient mode, described by the continuity of water in the membrane: dc dt  -*c ax  (2.8)  Using boundary conditions that assume Henry’s law, the water uptake is calculated in terms of the net change in membrane mass as it equilibrates with the ambient water vapour pressure. Some kinetic studies have calculated mass transfer and diffusion coefficients in Nafion in this way; under steady state conditions water-sorption isotherms have been derived [72-74]. Futerko [60] developed a model to calculate the absorption of water derived from the Flory-Huggins thermodynamic model. His analysis was focused on differentiating the water uptake from liquid and vapour, and found this difference to be correlated with the structure of the polymer. Krtil et al. [75] defined vapour transport from inside to outside the ion clusters as the dominating mechanism for thinner membranes. In membranes thicker than 10 tim, the dominating mechanism of transport was described as conventional Fickian diffusion.  27  Choi et a!. [76] applied the thermodynamic analysis from Flory-Hugins theory and coupled it with Freger’s elastic model to account for the swelling effects caused by vapour sorption. They found a correlation between sorption and the elastic deformation and acid concentration variation during swelling. A recent model claimed a mechanism for water in Nafion [77] that contradicts Fick’s law of diffusion. The model fitted to experimental vapour sorption and desorption data assumed two-stage transport mechanism, where polymer swelling and relaxation became the rate limiting process during the water uptake, i.e., when the concentration gradient became negligible.  2.3.5 Transport through the membrane’s bulk and interfaces: diffusion, and sorption  Ge and collaborators [78] described a water transport model for a fuel cell that set the basis for a novel analysis of water transport in Nafion within an electrode-membrane assembly. The model comprises the transport of water inside the bulk of the membrane and transport in and out through the membrane-electrode interfaces. The bulk transport was defined as Fickian diffusion; and the surface mechanisms, as absorption and desorption. Results from this analysis demonstrated that absorption of vapour water is slower than desorption across the membrane-electrode interface. Majztrik et al. [62] reported an analysis based on the three-step-mechanism transport model proposed by Ge.  The authors faced the challenge to decouple the  individual contributions from surface and bulk mechanisms due to the nature of the steady state permeation experiments. The authors assumed a constant flux within and  28  across the membrane bulk and interface. The result provided an estimation of effective interfacial mass transport coefficients and a coupled component for diffusion and water concentration in the membrane,  CmaxD,  which the authors could not deconvolute into  individual values for the diffusivity coefficient, D, and the water concentration in the membrane,  Cm.  2.4 Experimental determination of Mass Transfer coefficients  Several experimental methods have been used to quantif’ bulk and interfacial properties. The techniques will be discussed below.  2.4.1. Diffusion coefficient  Through gravimetric water uptake measurements, Yeo and Eisenberg [79] defined the temperature dependence for diffusion coefficient based on water sorption measurements. After this effort, advances in the experimental techniques for the calculation of the water diffusivity in Nafion have progressed until the use of state of the art methodologies (NMR, FTIR, etc). The use of isotopes to determine the diffusion coefficient is common in liquid equilibrated membranes. Zelsmann et al. [80] proposed a procedure to determine water diffusivity through the use of isotopes in the vapor state with Far IR Spectroscopy. The 1 with this technique. s 2 value of the diffusion coefficient averaged 1 .5x1 0b0 m The self-diffusion coefficient of water through partially hydrated membranes has been characterized in detail through Nuclear Magnetic Resonance (NMR). The technique  29  works by means of correlating the ‘H interdiffusion with the intra-(or self-) diffusion coefficient of water [29]. Later, the same research group lead by Gottesfeld [29], reported experiments for a fully hydrated Nafion 117 membrane, combining imaging sequence with pulsed—field-gradient-spin-echo (PFGSE) NMR technique. The value of the selfdiffusion coefficient found at 25°C was 5.5 and 7.5 x10’° m , for vapour- and liquid1 s 2 equilibrated Nafion, respectively. The use of the PFSGE NMR technique has been traditionally used to study diffusion and flow in porous media. The way the self-diffusion coefficient is determined reflects the molecular diffusion of a solute, in this case water, in a solvent media of the same composition, which is not the case of water in Nafion membrane. Thus, the term self-diffusion is not appropriate for water diffusion measured in Nafion. Independently of the misleading terminology, PFSGE NMR, has characterized the diffusivity of water in the absence of activity gradients. As a consequence, these results are not fully applicable to situations with large gradients such as those found in a working fuel cell under current load. The variability of the diffusion coefficient from different techniques is illustrated in the graph of Figure 2.4, as reported by Motupally and collaborators [19]. The common finding in these results is the dependence on water content for the diffusion coefficient. From Figure 2.4, Zawodzinski’s results [29] from NMR studies showed the diffusion coefficient as function of the water content with a maximum, after which it decreased at higher hydration. In Fuller’s experimental analysis [81], a linear correspondence between the diffusion coefficient and the membrane water content was reported. Nguyen reported similar results with a linear dependency on water content [82].  30  Fickian Diffusion Coefficient vs. Water Content at 303K 2  I  I  Zawocinski Data (1991) -Fufler( 992) N9uyenet at (1993) [_—Zawockinski. (1991) via Metupafly et ai 30O  1.8  —  -  —  I  Lb  —  1.4 -  /  E 2  -4-  12  /  II  I 0.8  -.  / -  -  Ij’  I o  1,.  0.4  /‘--a Water Content [mal H OlmoI SO 2 ] 3  Figure 2.4: Diffusion Coefficient as a function of membrane water content. Adapted from Motupally et al. [19]  In spite of the variability of self diffusion coefficients results, and the questions about their applicability to fuel cell membranes, Motupally and collaborators [19] found self diffusion coefficients from experimental water permeation fluxes in a fuel cell that agreed with the results from Zawodzinski’s NMR. The authors used activity gradients controlled by the gas flow rate and pressure in the fuel cell to associate the crossover flux and the driving force. Ge et al. [78] used activity gradients to gain insight on the interfacial resistance to water transport. Their work incorporated three associated mechanisms in the overall transport process: absorption and desorption at gas/membrane interfaces, and diffusion of water in the polymer. The diffusion coefficient found from the analysis of water permeation was described as water content dependant with a maximum value of 8 x10’° and 11.5 x10’° m , at 323 and 353 K, respectively. 1 s 2  31  Apparent diffusion coefficients have been reported from vapour sorption experiments [74]. Result from desorption data generated a value of 2.6 x l012 m s’ 2 compared to 7.7 x 1 013 2 m from sorption data. The difference comes from an observed 1 s faster desorption rate through Fickian analysis. The authors concluded that sorption kinetic information could not provide reliable diffusion coefficients due to the coupling of mass transport with boundary layer effects and non-isothermal conditions in the membrane. To address these limitations, Rivin et al. proposed steady state permeation coupled to solubility measurements to define effective diffusion coefficients, Deff, that increased monotonically with water concentration. Values for Deff ranged from 0.126 to 2.35 x 1010 m 1 from 0.2 to 1 activity gradient, correspondingly; and 3.07 x10’° m s 2 1 s 2 for membranes equilibrated with liquid water. Table 2.1 summarizes results from diffusion coefficient values obtained from the methodologies described above.  Table 2.1. Diffusion coefficients, experimental techniques Diffusion Nafion Technique Coefficient Conditions Type 1010 m 2 s’ 1155  Reference  1.8-2.2  30°C ?=22 30°C .=2-14 30°C 7=22 25°C ?.=2-14 27°C  2006, Suresh etal. [83]  0.026-0.07  Desorption-sorption  2006, Rivin et al. [74]  0.13-3.1  ?2-22  2006,Rivinetal. [74]  Water Uptake  2.1  117  NMR  0.6-5.5  117  NMR  7.5  117  Steady State Permeation  1.4-9.8  117  Tritium Tagged Water Vapour Sorption  1977, Yeo and Eisenberg [79] 1991, Zawodzinski et a!. [29] 1993, Zawodzinski et a!. [11] 1992, Fuller [81]  Steady State Permeation 112,115,117  +  Solubility  32  Results in Table 2.1, show a wide range of values for the diffusivity coefficient in Nafion membranes at temperatures below 3 0°C. The dependency on water content is observed for NMR and Steady State Permeation; however, this dependency varies from linear to non-linear, as shown in Figure 2.4. Because each technique studies the water diffusivity under a different driving force schema, the results are not comparable. NMR applies no activity gradient to the membrane. The water uptake and vapour sorption gravimetric measurements provide a homogenous water environment, where there is no activity gradient. It has been discussed above that in the gravimetric techniques; it is the polymeric elastic force the acting limit mechanism for water transport. Contrarily, permeability measurements apply an activity gradient across the membrane acting as the main driving force for the water transport through the membrane bulk and interfaces.  2.4.2 Interfacial mass transport coefficients  Progress in fuel cell modeling relies on transport parameters to simulate the mass transport mechanisms at the membrane surface. Fuel cell literature shows little sensible physical information on water transport across the interface. The importance of the mass transfer across the gas-membrane interface has been addressed before [11,74]; ever since, interfacial mass transfer coefficients in Nafion have started to appear in analyses of water transport. However, due to the novelty of this idea, these interfacial coefficients are less well represented in the literature than diffusion coefficients.  33  From the mechanism-in-series for water transport model, first described by Ge et al. [78], mass transfer coefficients of water were reported for a membrane-electrode assembly. The authors described the transport processes at the interfaces as absorption and desorption. The model described the interfacial transport dependency on the activation energy proposed by Yeo and Swee[79], it assumed a water volume fraction in the membrane. The coefficients showed values in the range of iO cms 1 The analysis showed water content dependency for the interfacial mass transfer coefficients for VE and LE membranes. Most fuel cell models rely on experimental data to fit parameters by trial and error [84-86]. A common approach is to define a boundary condition for the flux based on Henry’s law: boundary =  (2.9)  from where an iterative solution is commonly applied to identify the interfacial mass transfer coefficient, k 1 [62,68,77]. In order to relate the water concentration in the membrane with the water content in the gas, the use of equilibrium isotherms has been proposed.[68]. Following similar procedures, modelers have reported on water transfer coefficients within the range of 0.1 to 10 xl 0 cms’. However, the application of Henry’s law to describe equilibrium at the gas-membrane interface is flawed for systems where a kinetic process is present across the membrane surface. From permeability measurements on Nafion membranes, a recent analysis presented by Majzstrik and collaborators [62] attempted to describe mass transport coefficients for the surface and bulk water transport. The authors reported a water flux,  34  which they called “effective transport coefficient”, that in effect is nothing more than a fudge factor. The analysis is incorrect, as the authors defined the flux at the boundary using Henry’s law (Equation 2.10), assuming incorrectly equilibrium across the membrane-gas interface. Futerko and Sing [601 also reported on an effective interfacial transport coefficient that was the result of fitting water flux values into a PEMFC water transport model. Satterfield et al. [77] reported interfacial mass transport coefficients from vapour uptake measurements. The authors described a boundary flux from a variation of Henry’s law where the transport phenomena at the interface and in the bulk were related by: D  —  ãx  =  1 (Cmax k  —  c)  (2.10)  The limitation of their model lies in the neglected interaction between the membrane and the surrounding vapour pressure. The model failed to include the possibility of water accumulation in the gas. Table 2.2 summarizes the most relevant reports on interfacial mass transfer coefficients. The wide variability in the reported values for the interfacial mass transfer coefficients is evident in Table 2.2. Comparison between these results is not duable because of the different assumptions each approach made. The results from Berg et al. and Okada et al. correspond to the fit between mathematical models with experimental data from full fuel cell testing. Therefore, the whole membrane-electrode-assembly system adds complexity and contributes with two more boundary resistances to water transport from the membrane-catalyst, catalyst-gas diffusion layer, and gas diffusion layer- gas interfaces. In the case of Satterfield and Benziger, the main flaw of their  35  mathematical model is the assumed equilibrium between the membrane and the humidity of the adjacent gas. The possible kinetic or convective process across the membrane surface created by the gas was not considered in the analysis.  Table 2.2. Summary of relevant interfacial mass transfer coefficient reported values. Interfacial Mass transfer coefficient Technique Authors 3 cms’ x10 Berg et al.  0.57 (80°C)  Fit between experiments and  Okada et al.  1 (50-80°C)  water transport model of a fuel cell  Ge et al.  sorption: 0.1— 0.8  @ X=1-9  desorption: 0.45-3.25  @ =l-9  Permeability measurement in MEAs  Satterfield and  2.8 (Nafion 1 12)  Gravimetric measurements  Benziger  10.2 (Nafion 1 15)  from vapour uptake  10.6 (Nafion 1110) 7.6 (Nafion 1123)  A complete physical and mathematical representation of the membrane boundary conditions typical to fuel cells is not available in the literature.  Most experimental  methods simulate equilibrium conditions, instead of representing the dynamics across the membrane surface. Even more, when the experimental techniques achieve to reproduce the typical conditions within a PEMFC, the mathematical models were not able to address the boundary process due to the membrane-flowing gas interaction. Table 2.3 shows the summary of the most relevant experimental techniques that have addressed the study of water transport phenomena in proton exchange membranes. Those analyses show the advance on the phenomenological understanding of the mass  36  transport across Nafion membranes. As shown, gravimetric techniques for vapour and liquid uptake have dominated the research of water transport across Nafion membranes. Even though these techniques offered a partial solution to the objective of this thesis research; they were not chosen as the primary research tool because the transport mechanisms occurring during water uptake are not representative of the ones driven by activity gradients. Water sorption experiments involve a well-mixed medium that entirely surrounds the membrane. In the last two years, new approaches have emerged to incorporate imaging techniques in the identification of water content profiles across the MEA in functional fuel cells. The images analysis from Magnetic Resonance Imaging (MRI) [110, 111], for example, have provided information on the localization of water accumulation and dehydration inside the membrane. However, due to the early stages of these techniques, further improvement in the corresponding phenomenological models are required to extend the comprehension of water transport mechanisms across the membrane. Therefore, in this work, water content distribution imaging techniques were not discussed in extent.  37  Table 2. 3 .Summary of the most relevant experimental approaches related to this thesis  T  Technique  -__  I.DI  —  .  .  .  o  .  Remarks  Id)  Sorption Gravimetry Yeo and Eisenberg, 1 977[451 Water immersion Gravimetry Takamatsu et a!.. 1979  •  NMR Spectroscopy Zawodzinski et al 1993 [54]  •  Water transport Motupally et al. 2000 [48]  •  Quartz-Microbalance Sorption Gravimetry Ktril et al. 2001 [40]  •  Hydrogen pumping cell Ye and Wang 2007 [6] Water transport Majsztrik et al. 2007[27]  Measured water uptake in Nafion in long time experiments. Obtained Diffusion Coefficient D=f(T), and Activation Energy.  •  Measured water uptake. Obtained Apparent i Diffusion Coefficients. Long time experiment  •  •  Obtained Self Diffusion Coefficients as function of water content for Nafion.  •  •  Measured Permeability Flux. Found Fickian Diffusivity in MEAs  •  Measured Sorption, Desorption Rate. Obtained Diffusion Coefficient from transients and Vapour Isotherms from steady state data for Nafion. Measured Boundary Layer Resistances. Obtained Effective Diffusivity and Sorption Isotherms in Nafion. Measured Permeability Rate. Calculated Nominal Diffusivity in Nafion as nominal concentration was used. Measured Permeability Flux. Obtained Fickian Diffusivity, Absorption, and Desorption Mass Transfer Coefficients in MEA with microporous layer in an active PEMFC Measured Water Concentration Profile in long time experiments. Calculated Fickian Diffusion Coefficient in a Fuel Cell. Measured Permeability Flux. Found Bulk effective diffusivity: C D, and Effective mass 1 transfer coefficient at gas/membrane interface. C’,. and D were not individually calculated. Measured water uptake. Found interfacial mass transfer coefficient in Nafion  •  •  •  •  •  •  •  •  I  Vapour sorption Rivin et al. 2001 [39]  Water transport Rivin et al. 2001 [39] Water transport Ge et a!. 2005[43]  •  •  •  •  •  •  •  •  •  •  •  •  •  -  —  Vapour Sorption Majsztrik et al. 2007[27], Satterfield et al. 2008 [42]  •  •  •  —  LJ  Water Transport Romero, 2008 (this work)  •  •  •  •  •  •  •  Measured Permeability Flux in short time experiments Calculated inteifacril mass transfer rates, k,, and individual values for Diffusivity coefficient, D, and water concentration C’,,, in Nafion. Characterized water transport for composite/Nafiori membranes.  38  2.4.3 Aims of this research  Prior to this research, in-situ (fuel cell) water balance techniques were considered a viable way to identify the effects of the driving forces created by operational conditions, i.e., gas flow, temperature, pressure, and humidity. Nevertheless, the disadvantage of such approach was the added complexity of boundary effects from the membrane-catalyst layer, catalyst-gas diffusion layer, and gas diffusion layer-gas, each one representing a complete independent system. Instead, the interest for this research lies on a more fundamental characterization of water transport in the membrane bulk and membrane-gas interface. In order to distinguish the mechanisms of water transport across the bulk and the interfaces of Nafion membranes, the interest focused on observing the effects of activity gradients as the main water transport driving force. A total resistance to the main water transport processes in Nafion was proposed by means of a resistance in series analogy, as illustrated in Equation 2.11. This equation describes the sum of the resistances to interfacial sorption and bulk diffusion: 1 1 d resistances=—+——+—, ka lcd D  (211)  where the transport rate at the interfaces, for sorption and desorption, and in the bulk (of thickness ci) are described by ka, kd, and D, correspondingly. The experimental interest was to isolate the mechanisms that dominate the transport in a passive membrane, where the mechanisms of proton mobility and water generation were negligible. For this purpose, a new experimental design was required to allow the incorporation of operational conditions common to fuel cell systems. A new water  39  transport testing rig and experimental protocols were proposed to accomplish this objective. The following chapter (Chapter 3) describes the proposed water transport experiment concept used to characterize PEMs. It includes the experimental protocol for the steady state and transient measurements. It also includes the description of pre-established techniques to complete the analysis of water transport in Nafion and composite-Nafion membranes.  40  3. Experimental Methods This chapter describes the methodologies to characterize water transport in Nafion membranes. Section 3.1 addresses sample preparation for Nafion and composite-Nafion membranes. Sections 3.2 and 3.3 are focused on the water transport experimental concept, design of the permeability cell, and experimental protocols for steady state and transient measurements are addressed in section 3.4. The second part of this chapter centers on the description of pre-established techniques for the investigation of membrane properties related to water transport. The procedures for water content, differential scanning calorimetry, and dynamic vapour sorption techniques are described in sections 3.5.1 to 3.5.3.  3.1 Membrane Preparation 3.1.1 Membrane activation  Nafion membranes fabricated by Dupont® were used for all experiments. The series of Nafion 112, 115 and 117 membrane was chosen in order to keep the same Equivalent Weight (1100 g dry Nafion/mol S03) and to be able to vary the thickness from: 51 to 127 to 183 .tm, correspondingly (measured at 23°C and 50% RH).  Prior to all experiments, the membranes were chemically pretreated by full immersion in 3 wt% H 0 aqueous solution (at 8 0°C) for 2 hours, followed by repeated 2 rinsing in de-ionized Milli-Q water (Millipore) at room temperature, immersion in 1.0 M  41  S0 (aq) for another 2 hours (at 80°C), and finally repeated rinsing in de-ionized Milli 2 H 4  Q  water (Millipore) at room temperature. The membranes were stored in de-ionized  water for at least 24 hours to ensure full hydration. Prior to the assembly into the gated cell, the membranes were pat-dried with tissue paper to remove the excess water taking care that the membrane was not pressed to avoid excessive dehydration. For each experiment, the membrane was exchanged to start with a fresh membrane.  3.1.2 Nafion 115- silicon dioxide composite membranes  In order to modify the water content of Nafion membranes, we used Nafion 115 membranes doped with Si0 2 nanoparticles. The membranes were supplied by the MEA group in NRC-IFCI. The membranes were prepared by the sol-gel method as reported in [45].  The  weight  content  of Si0 2  was  controlled  by  immersion  time  in  tetraethylorthosilicate solution to produce samples with 10, 16 and 33 wt% of silicon dioxide (Si0 ) nanoparticles. Reports suggest that the sol-gel reactions in Nafion occur in 2 the polar clusters inside the membrane generating Si0 2 nanoparticles which fill in the clusters associated to the ionic S0 3 sites [49]. X-ray analysis showed a homogeneous distribution of the silica nanoparticles across and along the membrane samples [45]. After the sol-gel preparation, the membranes were chemically pretreated as described in 3.1.1, and stored with de-ionized water. Prior to the analysis, smaller area samples were cut off from the originally prepared membranes. The hygroscopic properties of silica increased the water uptake capacity of the membrane [45,87]. The Equivalent Weight of the composite membranes changed due to the incorporation of the 2 Si0 as described in Equation (3.1):  42  S,sEo 1 EWNI  =  S + EWNll 1 EWNI 5  wt%J 2 SiO (3.1)  2 wt% A summary of the membrane properties changes as a function of the Si0 content is presented in Table 3.1. Table 3.1. 2 S10 wt %  a  2 composite membranes [45] Properties of Nafion 115/Si0 Dry Membrane  Liquid equilibrated Membraneb  Equivalent Weight  Thickness, mm  Thickness Gain, %  3 g dry membrane/mol S0  [45]  [45]  This work  oa  0.132  14  16  1100.0  10  0.15  12  11  1222.5  16  0.142  8.9  15  1310.6  33  0.171  8  13  1642.0  Pure Nafion 115, °under 25 °C  Cfrom  C  Eqn. (3.1)  3.2 Water Transport Experimental Concept The water transport experiments in Nafion membranes required a cell design that allowed the membrane to be compressed between two environments with independent temperature, pressure and humidity control. The thin membrane ( 50 to 1 80pm) required high-quality sealing in order to achieve total separation of the environments. Figure 3.1 illustrates the experimental concept. The setup comprises a two compartment-cell where either liquid or vapour would provide the water supply on one side of the membrane, and a dry gas to evaporate the water from the membrane surface on the other side. Figures 3.1 show a schematic cross section of the design setup: a Nation membrane sample placed in a circular holder to create two cylindrical chambers: wet and dry. Figure 3.1 a shows the liquid equilibrated  43  1 from the (LE) experiment setup, the membrane separated liquid water at temperature T . For the vapour-equilibrated (VE) membrane experiments 2 dry chamber at temperature T (Fig.3. ib), the Nafion sample is kept in contact with a constant volume of fully saturated air on the wet side of the cell (the conditions on the wet and dry sides were identified with the subscripts 1 and 2, respectively).  (a)  (b)  humid gas  dry gas  Ii  Pneumatic gate  I,  humid  vent  H,O (g)  IA? level  2 T  gas  Figure 3.1. Setup for water transport experiments: (a) liquid equilibrated membrane; (b) vapour equilibrated membrane.  The original feature of the permeability cell design is the gate valve that allows isolation of the membrane from the wet environment (Figure 3 .2a). This gate valve allowed the reproducibility of transient water transport measurements. During measurements, the gate valve is maintained open (Figure 3.2b), so equilibrium between the stagnant fluid (wet) and the membrane is maintained.  44  (b)  (a)  Open Gate  Closed Gate  Wet  Dry  Wet  Dry  Figure 3.2. The gate valve is pneumatically controlled to connect/disconnect the membrane with the wet chamber. (a) closed-gate configuration, (b) open-gate configuration.  Unlike typical transient gravimetric measurements [74,77,82], our experiments generated known boundary conditions on both sides of the membrane by controlling the gas flow rate on one surface, and keeping a stagnant volume of liquid or vapour water on the other side of the membrane. In this way, the boundary layer resistance can be neglected on the wet side. The mixing between the gas and the water vapour, promoted by the gas stream, also reduces the possibility of a boundary layer resistance on the dry membrane surface.  3.3 Permeability Cell In order to control temperature, pressure and humidity in both chambers, the permeability cell had to accommodate temperature, and humidity sensors; as well as gas and water supply, and exhaust lines. Finally, a fast and easy assembly was an important design factor in order to improve testing time during sample exchanges. In several attempts the designed cells’ prototypes presented challenges to align and seal the membrane sample within the cell, and the procedure took longer than 30  45  minutes. The final design achieved all previous requirements, and included a novel feature to control the initial time of the measurement, through a gated-valve. Figure 3.3 shows the cell including details on the sensor positions and the cell components: dry and wet chambers, water jackets, membrane holder, and gated valve. The figure includes connections to the water baths that controlled the temperatures ). 2 around the environmental chambers (Tj and T  Figure 3.3. The wet and dry chambers were separated by a membrane holder. The inset shows an enlarged schematic of the dry chamber (including sensor locations).  The dry chamber manifold was designed in such a way that the gas flow rate at the inlet is withdrawn at the same velocity from the cell. When the gas enters the cell, it is directed to the wall where it is splits and mixes quickly. The larger the flow rates, the more enhanced is the stirring, and then gas to gas diffusion can be neglected [88]. Figure  3.4 outlines the distribution of the inlet, outlet ports and sensors in the dry chamber.  46  Figure 3.4. Schematic distribution of the gas manifolds and sensors in the dry cell.  The dew point sensor measures an averaged temperature as result of the enhanced mixing in the chamber. Because the nozzles of the inlet and exhaust are small compared to the membrane area and are oriented far away from each other, good mixing is ensured. In order to prevent formation of steady convective flows, the vents are orientated away from the membrane. Reynolds number calculations confirmed the absence of turbulent flows (See Appendix A). The assumption of good mixing is based on the fast gas diffusivity known in vapour water; however, further physical evidence to probe this assumption right is required. The cylindrical chambers with total volumes of approximately 125 cm 3 were separated by 2 cm 2 of exposed membrane on either side. The stainless steel chambers had a double wall to circulate hot water. The final cell design was manufactured by Tandem Technologies Ltd. Technical specifications are included in Appendix B. The photos in Figure 3.5 show the cell from an isometric view (left), and the cells’s main body with the membrane holder in place (right).  47  Figure 3.5. Top isometric view of the permeability cell (left); (right) dry chamber disconnected from cell’s body to assemble the membrane.  Placement of the membrane into the sample holder first and then into the cell’s body is shown in Figures 3.6. A wet membrane (pat-dried) is first assembled between two flat silicon seals (of thickness 1.55 mm) cut to the same size as the internal diameter of the holder. The holder is tightened up with four bolts with equal torque to seal the membrane evenly and to prevent leaks (Figure 3.6a). In Figure 3.6b, the gated valve is closed during insertion of the sample holder into the cell’s body, which prevents contact between the membrane and the wet chamber, previously filled with water. The speed of the sample assembly was reduced to a total of 2-5 minutes.  48  (a)  (b)  Figure 3.6. Membrane assembly process: (a) the wet membrane and silicon gaskets are placed into the sample holder; (b) the sample holder is placed into the water transport cell. The gate, made of acrylic is closed in the picture to restrict the water to the wet chamber during the assembly.  3.3.1. Experimental set up, instruments and sensors  For all water transport measurements, we used the permeability cell within the experimental setup illustrated in Figure 3.7. Mass Flow Controllers (Alicat®, 0-500 sccm, ±0.4% of reading + 0.2% of full scale) supplied nitrogen, and helium gas to the cell. When higher flow rates were required, the MFCs were connected in parallel arrays min Nitrogen was used for vapour equilibrated 3 cm . to supply up to 1000 STP 1 experiments to enhance water vaporization by bubbling gas into a water volume inside the wet chamber. In the dry chamber, helium was invariably used as the carrier gas due to its light molecular weight which enhances mixing in the chamber, reducing the flight time to reach the sensor. Two water baths (Haake®, 23OVAC, 50Hz, 5L) circulated hot water through the cell’s water jackets. For the bath operation, we used the temperature provided by the thermocouple readings inside the cell chambers.  49  Fine wire K-type thermocouples (Omega® 5TC-TT-K-30-36, ±1 °C or 0.4% of reading value) and pressure transducers (Omega® PX1O5-015G5V, 0-15 psig) were used to monitor temperature and pressure within the chambers. The relative humidity was monitored via dew point temperature measurements with a composite, thermallycontrolled probe that prevented condensation (Vaisala® HMT 330, ±1% RH from 0 to 90% RH, and ±1.7% RH from 90 to 100% RH) [89]. The dew point temperature sensor was cross-referenced with an RGA—Mass Spectrometer (Hiden TM HPR-20) to quantify the vapour pressure of saturated gas. Appendix C shows the experimental set up for calibration of the dew point sensor and results.  50  PISTON  Nitrogen  ROTA METER —  Water Bath Exhaust  FLOW METER  Helium  FLOW METER  ED Temperature Sensor  NJ  Check Valve  ED Pressure Sensor  Manual Valve  cEJzx  Rotameter  Dew Point Sensor Mass Flow Controller  Water Pump -  Figure 3.7 Complete experimental setup for water transport measurements. The permeability cell is monitored for temperature in both chambers; and pressure and dew point in the dry side chamber. The gate’s activation mechanism and the temperature control systems are included.  51  3.3.2 Thermal effects  A possible source of error to consider in the data analysis is the heat flux due to the enthalpy of evaporation and condensation from and into the membrane. In order to quantify the error from neglecting the energy balance, the temperature drop across the membrane was calculated from the maximum water flux across the membrane, J (Calculation of the water flux is described in Section 3.4.1), and the vaporization enthalpy of water (AJi  =  36.78 kJ/mol [90]):  q=J  (3.2)  /pJvap  Using Fourier’s law: (3.3)  AT  the largest temperature change across the membrane is found by: (3.4)  LJ•AH’ AT k  where k corresponds to the thermal conductivity of Nafion in the limiting dry condition  (  0.13 W/mK, for Nafion at 50°C and 0%RH[91]), and L is the maximum membrane  thickness tested (183 pm). The analysis result showed a maximum temperature drop of 5°C for the LE, and 2.6°C for the yE. Thus, neglecting the energy balance can result in an estimated  ±  23%  error in temperature activated processes, according to an Arrhenius dependency.  52  In an attempt to corroborate the temperature drop across the membrane, thermocouples were placed on the wet and dry surface of the membrane. For these measurements, the wet chamber was filled up with liquid or vapour, accordingly. For LE, the membrane temperature showed zero gradient across the thickness of the membrane; for yE, the membrane showed a drop of 1 °C in the dry side. Care was taken to ensure the thermocouples’ tips were in direct contact with the membrane surface; even so, further temperature measurements are needed to map out the membrane surface temperature with higher control of embedding the sensor tips on the surface without perforating the sample. For the cell’s accurate temperature control, a thermocouple placed close to the membrane’s surface was used to regulate the temperature of the water baths. Independent temperature measurements showed that the temperature variation within the dry chamber could be considered negligible; the temperature distribution was measured along the horizontal axis inside the centre of the dry chamber. For these measurements, the gate was kept closed and hot water supply was maintained constant through the jacketed wall of both chambers. Four thermocouples were located along the horizontal axis and results showed a 1°C gradient from end to end of the dry chamber. However, in regular operating conditions, with the open gate and the corresponding flowing gas, the maximum temperature gradient along the horizontal axis was measured to be in +0.1°C range, this improvement in the temperature homogeneity is due to the mixing effect of the drying gas, which accounts for a negligible temperature gradient inside the chamber. This was reproducible for the temperature range of 3 0-80°C.  53  3.3.3 Activity gradient The drying effect of the varying gas flow rate over the membrane surface created a water concentration profile across its thickness. In this research, we adopted activity difference as the main driving force for water transport due to their natural occurrence in working PEM fuel cells. Much has been reported on the response on water transport to different driving forces:  pressure,  chemical  potential,  and  isotopic  concentration  gradients  [65,66,70,92,93]. Under extreme working conditions, the water and heat management designs of fuel cells can not guarantee constant or full hydration for the membrane generating activity gradients that act as the main driving force for water transport across the membrane. The activity difference across the thin membrane was calculated for water transport experiments according to: Aa=awet  1 —a , 2 dry =a  (3.5)  where a conventional definition of water activity was adopted as reported in the context of fuel cells: for liquid water vapor in fully saturated air a= i =  1,2 for unsaturated air at temperature l  (3.6)  54  This expression provides a normalized parameter for water activity on either side of the membrane, equivalent to the relative humidity in the gas phase next to the membrane surface’. Table 3.2 illustrates the effect of varying gas flow on the water activity calculated with Equation 3.6 for unsaturated air. These data correspond to a VE equilibrated Nafion 115 membrane at 30, 50, and 70°C.  Table 3.2. Illustrative example of the effect of varying the gas flow rate on the water activity Water Activity,  Pw,i  (i)  He gas flow 3 min’ (STP) cm 30°C  50°C  70°C  50  0.50  0.35  0.36  100  0.20  0.22  0.23  300  0.08  0.09  0.09  500  0.05  0.05  0.055  700  0.04  0.03  0.04  1000  0.02  0.02  0.02  1  In this work, inside the membrane and on its surfaces it is referred to the water concentration as water content, 2 mol H 0 /mol SO 2 -, instead of water activity 3  [=1  55  3.4 Water Transport Experimental Protocols  The following sections (3.3.1 and 3.3.2) describe the proposed methodology applied to PFSA membranes for water transport measurements in steady state and transient regimes using the permeability cell.  3.4.1 Steady state water transport  Once the membrane was assembled and the wet chamber reached the desired temperature and humidity with the gate closed, a constant flow rate of dry helium was established in the dry chamber upon reaching a steady state. Our experimental protocol defined steady state as the state for which the cell temperature and the dew point temperature did not vary by more than ±0.01°C under a constant helium flow rate. A small but detectable positive pressure was required to maintain the flow of helium gas. Typically, the pressure inside the chambers was less than 0.1% higher than the prevailing atmospheric pressure (i.e., AP in Figure 3.1 was between 1 o and 1 0 atm). The water vapour pressure was calculated from the dew point measurements via the relationships in Equation (3.7), and the empirical coefficients in Table 3.3 (provided by the sensor’s manufacturer for the Vaisala® HMT 330):  3  (3.7)  ’ +b 1 ln@ 4 lnP =b  56  Table 3.3. Coefficient values [89] for Vapour Pressure Equation (3.7):  0 C  0.4931358  b_,  4 -0.58002206x10  C,  2 -0.46094296x10  0 b  1 0.13914993x10  2 C  4 0.13746454x10  1 -0.48640239x10  3 C  7 -0.12743214x10  4 0.41764768x10  3 b  7 -0.14452093x10  4 b  6.5459673  Figure 3.8 provides a sample data set to illustrate the results and data treatment in the steady state experimental series. The water vapour pressure in the dry chamber, F , 2 was recorded at different temperatures and helium flow rates.  41  o 6560  1  1 li;  4  T  2  . . . . . . . . . • • • • • • • • • • •  -  z—  j:  -  -4 ‘-4 4—1  30  ------‘  &25  m 2 3 m  20  T2  15 I  —  0  100  •  I  •  200  I  300  I -  400  500  Time (s) Figure 3.8. The vapour pressure was measured at different helium flows and temperatures. For each experiment, the steady state vapour pressure was extrapolated. For clarity, the symbols were plotted every 15 data points only. At steady state, the final value for P 2 was obtained from each curve as indicated by the arrow (a).  57  The steady state P 2 values were then plotted as a function of the associated flow rate. See Figure 3.9 for several data sets on vapour pressure under different temperatures. Each point in the graph represents one individual experiment. luvu 0  10:  1•  30  0  200  400  600  800  1000  1200  Helium flow 1 min 3 (cm )  Figure 3.9. For each experiment, the steady state vapour pressure was obtained from the plateau and plotted as a function of helium flow rate.  To calculate the flux of water across the membrane, ideal gas behaviour, conservation of mass, and no water accumulation within the membrane (at steady state) was assumed. Using the corresponding helium flow rate and the molar fraction of water, , which was derived from the vapour pressure data and total pressure ratio, the flux, 2 x was defined by: i(  2 x  .  (3.8)  The details of this calculation are included in Appendix A. The typical curve from steady state data is shown at different flow rates in Figure 3.1 Oa. The graph shows the asymptotic flux increasing at higher flow rates corresponding  58  to a liquid equilibrated (LE) Nafion 117 membrane at 30, 50, and 70°C. Figure 3.llb, shows the data reproducibility from 3 experiments at each temperature. The flux data showed good reproducibility with maximum standard deviation of 0.003 and maximum standard error of ±0.001. One of the findings during the experiments was the importance of keeping the membrane wet during sealing and assembling in the sample holder. In this way, the seal between the membrane and the gaskets is maintained firm while the exposed membrane area shrinks and expands due to humidity changes in the experiment. Yet, a source of data deviation that could not be avoided with the current setup was the humidity variation in the room air. The averaged vapour pressure from experiments carried out during days with environmental conditions within the average (i.e., 39% RH and 20°C), and the vapour pressure from days of extra humidity (63%RH, 20°C) difference in the data.  showed up to 8.4 %  A further improvement in the setup would be to isolate the  experiment from the humidity of the room air.  59  70°C 50 30  A  0.06  • •  A  A  •  a  0.05.  Eo.o4.  *  0  E x  0.03  *  U h.O.02  0.01.  ‘,.w.  0  I  I  I  200  400  600  800  Helium flow (cm ) 1 3 min  I  I  I  •  I  0.06.  0.05 0  E  0.04  0  x  0.03  U I  0.02  8  0.01. ]30°C u.vu.  •  0  200  I  I  I  400  600  800  Helium flow (cm 3 min ) 1  Figure 3.10. (a) Flux from steady state water transport for LE Nafion 117 at 30, 50 and 70°C. Error bars correspond to the standard error from three experiments in each point, as shown in (b).  60  3.4.2 Transient water transport Transient measurements for Nafion 112 and 117 membranes were performed with liquidgas equilibrated membranes at 30, 50, and 70°C and atmospheric pressure (1005 mbar monthly average) with the set up as described in Figure 3.7. A set of measurements for Nafion 112 and Nafion 117 under VE at 50°C were completed at atmospheric pressure for comparison reasons; analysis on VE membranes is required. For transient measurements, the permeability cell provided high accuracy to control the initial measurement time through the sliding gated valve. The gated-valve, which separated the membrane from the wet chamber, was opened after the dry chamber had reached desired conditions of humidity and temperature. The response time of current commercial humidity sensors limited our measurements time resolution to 1 second. The time response for our primary sensor: (Vaisala® HMT 330) was measured in the cell, after opening the gated valve to the wet chamber previously saturated with vapour. The measured response time was 1 second min (STP), and 3 cm under dynamic conditions, i.e., for helium flow range 100-1000 1 30°C. Figure 3.11 shows the response time under static air and compares it with the response under dynamic conditions (above described). The sensor responded faster in the latter case due to the enhanced mixing from the flowing gas.  61  30°C 80 70 6O 5O  4o. 0 >  a,  20  —  10  °  0•—  Step Change Sensor at stagnant conditions Sensor with gas mixing I  -.  0  3  6  9  12  15  18  21  24  Time, s Figure 3.11 Measured time response to relative humidity step change from Vaisala® dew point sensor.  Prior to the experiment, the membrane pre-conditioning procedure followed was: 1) drying out the membrane at room temperature for 20 hours, 2) assembling the membrane in the dry side of the cell with the gate valve closed (to keep the membrane surface away form the wet chamber), 3) dry helium was fed into the dry chamber at the desired temperature for 5 to 6 hours. The flow was varied each hour alternatively from 100 to 500 1 min 3 cm (STP) until the dew point temperature reached a minimum steady state. In this way, the membrane’s surface was driven to a dehydrated condition that was experimentally reproducible within a maximum dew point standard deviation of ±3°C at 30, 50 and 70°C. This deviation can be explained by the relative humidity of the environment. It is probable that the air humidity diffuses through the exhaust stream into the chamber because of a water concentration gradient between the environment and chamber.  62  For a different initial condition, the same method would apply, i.e.; for a semihydrated membrane, a humid gas flow could be fed to condition the membrane to a desired relative humidity value after dehydrating it for 20 hours. When the dew point signal reached steady state, the pneumatically controlled gate valve was lifted, exposing the membrane to the wet environment and establishing a thermodynamic potential gradient to drive the water across. The time was measured until the dew point temperature reached a maximum and reached the final steady state. The dew point temperature was converted to vapour pressure and from it, the water flux was calculated to proceed with the data analysis. The dew point temperature data were converted to water flux, in the same way as described by Equation 3.8, to facilitate the data analysis. From all transient experiments, we identified a characteristic transient signal for Nafion membranes with an s-shape curve, similar to the curve of sorption experiments [74]. Figure 3.1 2a shows the flux of water as a function of time. In all graphs, a kinetic response was identified between an initial and a final steady state. The initial steady state, represented by  initial,  was  recorded from the time when the gated valve was lifted (zero time) to the start of the flux rise. After the kinetics, the second steady state, the beginning of the second plateau. Both,  tss, final,  tss,jfljtjal  and  was recorded from zero time to tss,final  are identified as the curve  inflexions in the graph of Figure 3.1 2a. In Figure 3.1 2b a comparison of the transients for LE Nafion 117 membranes at 30, 50, and 70°C is shown.  63  (a)  Nationll77O°C  Th. 2 z  0.00.  tss initial I  I  100  0  I  200 300 Time (s)  I  I  400  500  (b) a  30°C  050 C4  A70  E  g Li. ..  0.04 0.02 A  0.00 0  250 500 Time (s)  750  Figure 3.12. Typical transient water transport signal (a); transient curves for liquid equilibrated Nafion membranes at different temperatures (b).  64  3.5 Pre-established membrane characterization techniques  The following sections describe analytical techniques (i.e., water content, DSC, and DVS) applied to Nafion and Si0 -Nafion membranes as part of the case study presented 2 in Chapter 6.  3.5.1 Water content measurement To obtain the mass of the wet membrane, the membrane samples were equilibrated in liquid water at room temperature for 24 hours. Before measurement, the excess water was pat-dried and the membrane was quickly weighted to calculate the sample water content at the beginning of the experiment. The samples were driven to dehydration at 60°C and vacuumed overnight. The membrane’s dry weight was measured to calculate the water uptake according to Equation (3.9):  water  uptake  weight of wet membrane weight of dry membrane weight of dry membrane —  =  (3.9)  The number of water molecules per sulfonic group, ?, is calculated from the water uptake and the equivalent weight (EW) for Nafion 115 or the corresponding, EW, value for the composite membranes (as it is described in Section 3.1.2):  water content (2) =  water uptake EW 18  (3.10)  65  where the 18 in the denominator is the molecular weight of water. A summary of the membrane water content measurement results as a function of the Si0 2 wt % is presented in Table 3.4:  Table 3.4. Water uptake, water content and weight of wet membrane data for Nafion 115 and Nafion 115? Si0 2 membranes under liquid equilibrium at 25°C. 2 Si0  Water Uptake  Water Content (A)  Weight of wet membrane  Wt %  H 0 / g dry Nafion g2  mol H 0/mol SO 2 3  g  0  0.25±0.007  19.46  0.008± 1E-3  10  0.20±0.004  15.02  0.004± 1E-4  16  0.24±0.016  18.70  0.0047±2E-4  33  0.26±0.0 19  21.03  0.0053± 6E-5  3.5.2 Differential scanning calorimetry (DSC) Fully saturated membrane samples were characterized with a DSC QlO instrument (TA instruments®) to identify the ratio of freezable to non-freezable water present within the polymer. Non-freezable water is considered to be strongly bound to the ionic groups; meanwhile, the freezable water corresponds to the water molecules in free state with similar transport properties to bulk water.  For the purposes of this work, the non  freezable water is referred to as bound water weight (Wb), and the freezable water as non bound water weight (Wb). The sum of both is the total water weight in the membrane:  (3.11)  66  The membrane sample, of usually 4-5 mg was first equilibrated in liquid water and room temperature for 24 h before the measurement. Each sample was pat-dried and weighed in a sealed aluminum pan to avoid water loss and introduced to the temperaturecontrolled chamber to carry on the freezing and melting temperature scans using liquid nitrogen as coolant. During the test, the sample was subjected to a temperature gradient scan from 2 to -100°C to determine the enthalpy of the freezing water; and from -100 to 10°C for the melting enthalpy. A heat flow curve was plotted for each experiment as the one shown in Figure 3.13 a. The integrated area under the peak of the melting curve provided the heat of fusion for the corresponding sample. Its normalization with the heat of fusion obtained for bulk water (219 J g’) provided the mass of freezable water in the membrane. The mass of non-bound water is calculated according to Equation. (3.12):  Enthalpy of fUSOflrnnpje x weight wet membrane Wb=  Enthalpy of fusionb,,lk  (312)  The assumption that the heat of fusion for bulk water is equivalent to bound water used in this analysis is based on the discussion presented by Siu [311 on the basis of studies by Pintauro et al. [94], and Paddison et al. [95]. The authors found that the freezable water inside the pores of the membrane has the same dielectric constant to that of bulk water (within 10%). The water in the center of the pore, close to the wall, is kept in isolation from the electrostatic charge effect. Their studies estimated that 50% of the total volume of a fully hydrated pore of Nafion corresponds to liquid water, which has a similar value to the fraction of freezable water in the membrane.  67  Figure 3.13b shows the thermograms for Nafion 115 and composite-Nafion . 2 membranes with 10, 16, and 33 wt% Si0  (a)  Temperature, °C  (b) 0.1  0.0 •••“  ——  .  -0.2  2 Si0 N115+l6wt%Si0 2 2 --—N115+33wt%SiO  .100  -80  -60  -  -40  -20  0  20  Temperature, °C  Figure 3.13. DSC thermograms: (a) typical signal for Nafion 115 in its hydrated form. The area under the peaks is integrated to calculate the enthalpy of fusion and freezing, respectively. (b) thermograms for composite Nafion 115/Sb 2  68  From the measurements, the heat of ftision values are summarized in Table 3.5.  Table 3.5. Enthalpy of fusion measured by DSC for Nafion 115 and Nafion 115/ Si0 2 membranes  •  2 Si0  Enthalpy of fusion  Wt%  J/g  0  23.73±0.74  10  13.10±1.97  16  1 6.50±26  33  17.82±5.83  With the mass of total water content and the non-bound water known, from mass conservation the amount of bound (non-freezable) water is obtained. Results from these calculations will be presented in Section 6.6.  3.5.3 Dynamic vapour sorption (DVS)  In order to compare the mechanisms of sorption and desorption between pure Nafion and  membranes containing silicon dioxide (Si0 ), Dynamic Vapour Sorption (DVS) 2 measurements were performed under 25°C within the range 0 to 95% RH, using a DVS 1000 instrument (Surface measurement systems, London, UK). The DVS chamber includes temperature and humidity control, and a mass balance to record the membrane weight gain. For sorption measurements, the membrane started from a dry state. With 10% RH incremental steps in the chamber, the membrane was driven to a maximum water uptake at 95% RH. In desorption experiments, the membrane started wet, equilibrated with the chamber at 95% RH, and it was driven to a dry condition decreasing the humidity in the  69  same differential steps until 0% RH was reached. At each relative humidity step, the experiment  lasted  until  the  membrane  mass  variation  reached  a  minimum  (dmldt=0.000 1). Typical transient mass change response is shown in Figure 3.14, for sorption and desorption. The mass change along the plateaus of the sorption curves (Figure 3.14) was averaged to generate the steady state data set. The steady state mass uptake data was then converted into water content (2) according to Equation. (3.10).  I  I  I  I  6.8  100  6.6  80  6.4 60 C)  =  ..  40 6.0  111111  0  200  400  600  800  :  C)  1000  Time, mm  Figure 3.14. Vapour Sorption and Desorption kinetics resulting from varying the atmospheric relative humidity. Figure 3.15, shows common isotherms for Nafion 115 and 117 from vapour sorption measurements, under steady state, at 25, 30, 50 and 80°C, obtained from the  literature [11,56,96] The isotherms for vapour sorption obtained in this work, for Nafion 115 and Nafion 11 5/S i0 2 composite membranes, from the DVS measurements are included in Section 6.5.  70  24 22 20 18 16 14  Nafion 115 (Soboleva & Holdcroft) 25°C o 50°C 80°C Nafion 117 0 30°C (Zawodsinski)  •  22 20  (Schoroeders Paradox)  b  18 16 14 12  12•  :8:  Activity Figure 3.15. Membrane water content vs. water activity for Nafion 115 and Nafion 117 at different temperatures, from different sources.  The following chapter discusses the results of the previously discussed experimental techniques. Results from water transport measurements are presented for Nafion membranes in Sections 4.1 and 4.2. Steady state water transport was also measured for 5i0 -Nafion membranes; results are included in Chapter 6. 2 In Chapter 6, results from DVS, DSC and water content are presented for Nafion and composite-Nafion membranes.  71  4. Results from Water Transport in Nafion Membranes This chapter summarizes the results from water transport measurements across Nafion and composite/Nafion membranes. The first section (4.1) presents results from permeability experiments in Nafion membranes under steady state. The mass transport was studied as function of the temperature, thickness, water content, and physical state of water in contact with the membrane. The contribution of the gas-membrane interfaces to the mass transport resistance became evident from non-isothermal experiments and thickness comparison under steady state. The second section (4.2) presents the analysis of water transport (WT) under transient conditions as a function of thickness, temperature and contact with vapour and liquid water. To my knowledge, transient measurements of the WT across both interfaces of Nafion under the effect of activity gradients are the first to be reported. From the dynamic flux data, the temperature and thickness comparisons suggested that surface limited mechanisms become important at high temperatures.  4.1 Steady state water transport in Nafion membranes Using the experimental set up described in Section 3.2, transport experiments were carried out with pretreated Nafion 115 membranes. The following sections present results under isothermal and non-isothermal conditions.  72  4.1.1  Isothermal conditions  The flux across the Nafion membrane was calculated as described in Section 3.3. Figures 4.1 a and 4. lb summarize the results for the experimental series: liquid equilibrated (LE) and vapour equilibrated (VE) Nafion 115 membranes, respectively. On the x-axis, the 3 min 1 (STP). The error bars accuracy from the gas mass flow controllers is ±0.6 % cm correspond to the accuracy in the dew point manufacturer’s calibration with a maximum . These are absolute errors since our experimental error 1 s 2 possible error of ±0.03 mo1m 2 was negligible: the maximum error found from reproducibility tests was ±0.001 mol m . Moreover, based on the cross-reference tests between the dew point sensor and the 1 s mass spectrometer (Appendix C), it was assumed that the flux trends observed in Figures 4.1 a and b are independent of the sensor’s accuracy, i.e. the flux dependency on the gas flow rate is expected to maintain the same profile even with a different type of humidity sensor. The calculated water fluxes for LE membranes were larger than the fluxes from VE membranes at similar temperatures and helium flow rates. For these experiments, we assumed a water content profile across the membrane. The increasing flux of water with gas flow rate supports our assumption of high absorption and diffusion rates in the membrane, and slow evaporation to the (dry) gas phase. These assumptions are based on the higher water uptake capacity of Nafion when the membrane is in contact with liquid water, compared to a lower uptake when the membrane is surrounded by saturated gas [56]. Our measured water fluxes from LE membranes agree with published values using dry gas to produce activity gradients [19].  73  (a) I  I  1 1.2x10 e C4  U)  8O°C  1 1.0x10  E 0 8.Oxl 0.2  I  I  7O°C  6.Oxl 0.2 4.Oxl 0.2  60°C  •  2.Oxl 0.2,  *  0.0.  I  I  I  0  *  4  I  I  200  400  •  5O°C  5  • *  S  I  •  30°C I  •  600  800  1000  min 3 (cm ) Helium flow 1 (b) 6.Oxl 02  I  I  •  I  I  •  5.0x10 Cl)  4.0x10  80°C  3.0x10  :+  70°C  2 2.OxlO •* * *.  j 1.0x10  I I  S.  An  0  •  I  •  200  A  *  *  A I  60°C 50°C 40°C  I  400  •  30°C  I  I  600  800  1000  Helium flow 1 min 3 (cm ) Figure 4.1. Measured steady-state water flux was measured for (a) LE and (b) VE membranes, between 30 to 80°C and atmospheric pressure. Note the difference in the scales.  74  In Figure 4. ib, for VE membranes, fluxes were lower (50%) than the values 2s 1 at 70°C and 100 1 min 3 cm observed with LE membranes (e.g., 0.046 and 0.026 molm for LE and VE membranes, respectively). Several authors have related this difference to Schroeder’s paradox. Recently, it was reported that this difference is due to membrane structural changes created by the thermal histories of the membrane prior to the tests. These studies related the change in water uptake with structural modifications produced in the polymer by thermal stresses during preparation of MEAs. Those reports concluded that thermal stresses can affect the water content and water transport in the membrane [56,64]. Contrarily, the samples used in these investigations received the same thermal treatment, and therefore, it can be assumed there was no thermal history difference associated to the higher water transport in LE compared to VE membranes. Instead, a proposed explanation is based on the Nafion surfaces changes, from hydrophobic to hydrophilic, discussed elsewhere [59,60]. The surface switch has been measured by receding and advancing contact angle of water droplets on Nafion, and found that the membrane interface switches from hydrophobic to hydrophilic when it is contacted with liquid water [35,57]. This is consistent with the model of micellar structures that provide a hydrophobic membrane surface in membranes with low water content [34,5 5]. In VE membranes at high temperatures, (Figure 4.1 b), the lower water fluxes suggest that the membrane surface dehydration gets exacerbated with high gas flow rates (Figure 4.lb). This behaviour was observed by Majsztrik and collaborators [62] and explained in terms of a hydrophobic skin layer formation. If local dehydration occurs  75  close to the membrane surface, it is possible that water dynamics are slow down due to the poor interconnections between pores and the decreased pores size. Following a temperature dependence analysis, it was found that the water transport flux is well described by Arrhenius temperature dependence. The graphs in Figure 4.2 show the curves: log of flux vs. l/T, for Nafion 115 at different gas flow rates.  I  I  I  0.5 0.0  I  c LE N115  —  30 cm 3 min 1 50  0  io v 300  E -0.5 E -1.0 —1.5  4 500 700 G 1000  ..a..:::::::;.:::.:,  20  a a P  .  P.  0  —I -3.0  0.0028 0.0029 0.0030 0.0031  0.0032 0.0033  llTemperature (K ) 1  05•  ‘  VE  0  30 cm’ min 1 50 100  V  300  0  N115  4 500 )700 G 1000  E -0.5 -1.0-  20 .0  -2.5  a)  3  0  -3.0 0.0028 0.0029 0.0030 0.0031 0.0032 0.0033  llTemperature (K ) 1  Figure 4.2. The measured flux across Nafion 115  is  shown at atmospheric pressure for varying the  temperature. Liquid water fluxes (solid symbols) and vapour fluxes (hollow symbols) are shown. The inset shows the Arrhenius dependency of the flux with temperature.  76  The graph in Figure 4.2a shows the LE case, where the slopes of the linear fit generated activation energy values that decreased with the increasing gas flow rate. In Figure 4.2 b, the VE case shows the slopes of the fitted lines increasing in a slower pace to the flow rate variation than in the LE case. Table 4.1 shows the Activation Energy (Eact) results. Table 4.1. Activation Energy for Nafion 115 membranes equilibrated with liquid and vapour water Helium Flow  Eact  min 3 cm 1  kJ mo[ 1 LE  VE  30  51.24  47.84  100  50.45  45.57  300  50.48  42.97  500  50.53  42.41  700  48.54  42.44  1000  48.07  43.56  The averaged value of Eact  for LE showed a value of 50 ±0.58 kJ  moi’  meanwhile, for VE membranes averaged 44 ±0.88 kJ mot’. Considering a 25 % error anticipated from neglecting the energy balance (Section 3.3.2), it is possible that the Eact of the VE steady state water transport approximates the enthalpy of water vaporization (zS.H” = 36.78 kJ moF’ [90]). The reason why LB shows a higher value for the Eact is not understood. It has been presented before that the interaction between water and the polymer is stronger for LE membranes. Futerko and Sing [60] explained that the structure of the membrane is altered when it is contact with liquid water, as stronger interactions are formed between the water molecules and sulfonic acid groups. The difference with a VE membrane, is that the vapour water molecules interact between each other and  77  desorption from the membrane is easier as the interaction between solvent and polymer is weak. The observations from Zawodzinski et al. [57] agreed with the concept of an stable and natural hydrophobic surface of the membrane, which suffers alterations when it is equilibrated with liquid water, switching to a hydrophilic type. Thus, it can be inferred than the higher Eact for LE may be attributed to the difficulty to detach water from the polymer in order to desorption to occur. Physical parameters of the membrane as porosity, water confinement, and connectivity of pores could be included in a further analysis to explain this observation in a phenomenological way.  4.1.2  Non-isothermal conditions  Non-isothermal conditions were applied across the membrane to enhance evaporation to the dry chamber. The temperature was increased in the dry chamber to increase the amount of water that could be present in the saturated gas mixture. Figure 4.3 compares three isothermal experiments at 30, 40 and 50°C, with their non-isothermal counterparts at a constant temperature gradient, AT  =  30°C (i.e., Ti  =  30, 40, 5 0°C, and T2  60, 70,  . 3 800C) The LE series (Fig. 4.3a) yielded monotonic increases in water flux up to moderate flow rates, exhibiting a maximum, after which the flux across the membrane decreased below the corresponding flux for isothermal conditions. The  corresponding  VE series (Fig. 4.3b) showed a maximum flux at lower flow rates than their counterparts in the LE series. These results are consistent with an evaporation rate threshold above  The case where Tl>T2 was not addressed because of the condensation problems associated. In such a case, the enhanced water flux would lead to condensation in the lower temperature chamber where the sensor was located, which would mask the membrane water transport data.  78  which the surface of the membrane experiences a deeper dehydration (from the dry gas). Conversely, the absorption rates on the humidified vapour side were possible insufficient to keep the bulk of the membrane hydrated. In this manner, the gas—membrane interface became an effective barrier for water transport moderated by the lower availability of water in the wet side, and showing higher resistance at high flow rates. In LE membranes, the gas—membrane interfacial resistance became limiting only at high flow rates.  (a)  (b)  A  0.020  0.020  A  0.015  0.015  i  E  A  T / T / ET 30/30/0 • 40/40/0 • 50/50/0 0 30/60/30 40/70/30 0 50/80/30  A  0  E xO.010  A  .  E  °  X  A  a  o •  0.005  A  •  0 •  0  0 •  •  0  A  .  8  •  •  •  U I I  10  a oos  .  100 Helium flow (cm 3 m1n ) 1  1000  0.000•  200  400  600  Helium Flow 1 min 3 (cm )  Figure 4.3. Measured steady state flux of water across Nafion 115 membranes comparing isothermal (solid) and non- isothermal (hollow) conditions for (a) LE membranes, and (b) VE membranes.  Many performance indicators for water transport across membranes have been used in the context of humidifier design. These include the water recovery ratio, humidity ratio and the deviation from full saturation [97]. A normalized relative humidity ratio, ((1 -RH)/RH), was used to characterize water transport across membrane interfaces [98].  79  Figure 4.4 shows the measured water transport for the isothermal and non-isothermal experiments. Higher temperatures in the VE membranes showed higher ratios (i.e., higher resistances to water transport) compared with the LE counterparts. These results suggest the existence of resistive interfaces at membrane surfaces under vapour equilibrium conditions.  (a)  (b)  I  120  •  oo•  A  8O• Z  o  I  30vs30 40vs40 50vs50 30vs60 40vs70 50vs80  I  •  I  —  I  I  •  I  I  80  60 D 0  0  0  60  flow ratelarea, cms’  Figure 4.4. Calculated  flow ratelarea, cms  resistance to water transport for Nafion 115 in (a) vapour, and (b) liquid  equilibrium as a function of the gas flow rate in isothermal (solid symbols), and non-isothermal conditions (hollow symbols).  80  4.1.3  Water profile across the membrane interfaces  The abrupt decrease in water flux (Figure 4.3b) provides evidence for the existence of non-linear water concentration profiles within the membrane. F. Buchi and G. Scherer [99] have reported on such water profiles across Nafion membranes under fuel cell operation. Small angle neutron scattering (SANS) data showed that the membrane can have discontinuous variations in its hydration levels. However, across the membrane interfaces, description of the water concentration profile raises different challenges. In an attempt to define the water concentration profile across the interfaces, an analysis was carried out to determine and compare the water concentration in three different phases: saturated gas, membrane and bulk water. The analysis below shows the implications when using water concentration as the normalized parameter for the water transport driving force. An approach common to the fuel cell literature was applied[15] to quantify water concentration in the membrane. Empirical material properties were used to calculate an effective water concentration:  nso2 CHO =  Vd +AV  (4.1)  1 EW(l+y)  2Pd( —  , EW= 1100 g mor’. The constant in the denominator (y = /iV/Vd) was 3 where p,= 2 gcm used to quantify the change in volume upon hydration (zlV) as a fraction of the original volume of dry membrane (Vd=O.O25). The water concentration was calculated for 81  24>2>0, and for 1>y>0. Results from this calculation are shown in Figure 4.5. The expression in Equation (4.1) is an approximation because the water is present in the hydrophilic regions only. Dividing by the total membrane volume provides an average water concentration over both hydrophobic and hydrophilic regions. Figure 4.5 compares the water concentrations calculated with Equation (4.1) and compares them with the corresponding concentrations in fully saturated air and liquid water (between 15 and 90°C). As illustrated, even for low water contents (2  <  5) the  calculated water concentration inside the membrane is much larger than the corresponding value for fully saturated air. Considering the hydrophilic regions only would make the membrane water concentrations even larger.  2. —.  1 02  2  4  6  8  10  12  14  16  18  20  22  24  26  (c)  0  E  0  =  1 02  0—1  101  101  (b)  0 4-’  Cu 4—’  ci)  10  0  :10 0  ()  (a)  10  102  C) .  io  1o’  A  Cu  10  20  30  40  50  60  70  80  90  100  Temperature (°C) Figure 4.5. The water concentration corresponding to fully saturated gas mixtures at different temperatures (a) is compared to the calculated water conceütration at different membrane water contents (b). The family of curves in (b) assumes a range of volume changes upon hydration (i.e., 0100% of the original dry volume. The concentration in liquid water (c).  82  These results contradict the prior expectation of a positive water concentration gradient, which is thought to be the main driving force for water transport across the membrane interface when it is equilibrated with saturated air (i.e., VE membrane). This inconsistency highlights the need for a normalized driving force parameter that considers thermodynamic( 1 F, RI1) and membrane physical variables  EW  p, porosity, etc.) to characterize water profiles across the interfaces. Due to the lack of a definition for the driving force across the membrane interfaces, an absolute representation of water concentration profiles is not doable. Similarly, using water activity as the normalized parameter raises inconsistencies, as both liquid water and vapour saturated have activity 1, which has lead to the mystification of an existing paradox (Schroeder’s) to explain the membrane water uptake difference, instead to promote the need for a solid explanation of the occurrences at the membranes interfaces.  83  4.1.4  Thickness dependency  The mass transport across Nafion membranes of different thicknesses was measured. Figure 4.6 summarizes the fluxes for Nafion 112, 115, and 117 with wet thicknesses equal to 51, 127, and 183 m, respectively. In all cases, the flux decreased with increasing thickness, but the difference disagreed with flux predicted by Fick’s law, as explained below.  0.03-  50°C A  A  E  0.02-  •  o  A  N-112  •  N115  Liquid  A  0  I  A  A:  0.01  (U  0  6 I  0 100  500  N-115 I Vapour N-1171  1000  1500  Helium Flow 1 min 3 (cm )  Figure 4.6. Comparison of water flux across membranes with different thicknesses, from 51 to 183 .tm, measured at 50°C,  in VE (hollow) and LE (solid)membranes.  The same data was plotted as a function of the wet membrane thickness. The graphs in Figure 4.7 show the fluxes for Naflon 112, Nafion 115, and Nafion 117. The tendency of the flux is shown to decrease with higher thickness in both data sets. The  84  graphs show the predicted flux determined by Fick’s law (i.e., inverse thickness dependency) for the flux of Nafion 112. The predicted flux for VE (Figure 4.7a) and LE (Figure 4.7b) were calculated using the flux of Nafion 117 as reference at same activity gradient, based on the thickness decrease from 183 to 51 im (used data correspond to the fluxes at activity gradient of 0.6 for yE, and 0.5 for LE). 2 molm s’ showed one order of 2 In Figure 4.7a, the predicted flux for VE: 2.4 x10 3 molm s’. In Figure 2 magnitude difference with the actual measured flux of 7.9 x10 4.7b, for the LE case, the estimated flux for Nafion 112 was 3.5 xlO  -2  s’, and the 2 molm  2 molm s’. 2 measured value showed a flux of 1.15 x10 These results suggest that diffusion is not rate dominant in thin membranes (51 tim), and that resistances at the membrane surface play an important role to the mass transport across the Nafion membranes, especially when equilibrated with vapour water. The mass flux loss is consistent with results from Majsztrik and collaborators [621 in the thickness range of 51 to 254 cm. These authors explain that resistances to mass transport dominate over diffusion resistance, yet they were not able to quantif’ the surface and bulk resistances.  85  (a)  2.4x10 2 2 2.1x10  Estimated Flux by Diffusion Dependence  2 1.8x10 E  1.5x1O’ Naficn 112 N115  .  2 E 1.2x10 x  N117 Heflow min 3 cm 30 1 0 50 A 100 v 300 0500 1 700 1000 • 50 (Prediction) 0  ‘  3 9x10  A  A  * 0  0  0  -  6x1 0 I  I  0.05  0.10  I  I  I  0.15  0.20  0.25  •  0.30  Nominal Thickness (mm) (b) •  Estimated Flux by Diffusion Dependence  A  30x10-2 He flow 0 30 1 min 3 cm 050 A 100 v300 1 500 700 0 1000 • 50 (Prediction)  E 2 E 20x10* a 1.0x10 2  0  Nafionhl2 I  0.05  •  0  0  N115  N117  I  I  0.10  0.15  I  •  0.20  0.25  0.30  Nominal Thickness (mm)  Figure 4.7. Comparison of water fluxes at 50°C from three different thicknesses: 51:127:183 jtm in their expanded form. (a) VE membranes; (b) LE membranes.  86  The Vaporization-Exchange model, included in Section 5.2, had as objective the quantification of these resistances. The analysis, successfully identified the interfacial mass transport rates and bulk diffusivity using the steady state and transient water transport data presented in this chapter. The following section describes the transient data from liquid WT experiments on Nafion.  4.2 Transient water transport Experiments on Nafion of different thicknesses were carried out between the temperature range of 30 to 70 °C in the time domain and under activity gradients. These experiments are the first report on transient water transport measurements under activity gradients. Transient data reported previously has been obtained from DVS experiments where the membrane is surrounded homogenously with saturated gas at specific relative humidity, and membrane water uptake is recorded [56,62,77]. Contrarily, in the transient water transport experiments presented here, the membrane is subjected to an activity gradient to act as the water transport driving force. Using the setup described in Section 3.5 the water crossover flux was measured as a function of time. The typical response is shown in Figure 4.8, and it shows the dynamic flux from an initially dry condition (the membrane was dried for 20 hrs in room temperature followed by conditioning under the dry chamber temperature and humidity for 5 hrs) until the final steady state. The flux data from transients were analyzed with the mathematical models included in Chapter 5.  87  0.015-  E 0.010-  0.005-  .  f  50°C VE LE  0.0000  I  •  200  I  •  •  400  600  I  •  800  I  1000  Time (s) Figure 4.8. Comparison of physical state of water in contact with the membrane during transient water transport. Flux measured experimentally at 50°C for liquid equilibrated (triangles) and vapour equilibrated (squares) Nafion 117  As an exploratory exercise, the flux derivative on time was calculated for the transient water transport flux. The following section (4.2), discuss the observations from the derivatives of the flux, from which a rate of change was obtained and a maximum value was identified. It is not the purpose of this analysis to discern the interfacial from bulk transport phenomena, but to explore the effects from the temperature and membrane thickness variation in the transient response.  L  Figure 4.9 illustrates the rate of change for fluxes (i.e.,  nd 2  derivative of the moles  of water) in vapour and liquid equilibrated membranes. The graph shows that the rate of change was faster for liquid than for vapour. The graph also shows that the maximum rate was reached for vapour faster than for liquid. This suggests a slower water transport rate across the vapour-membrane interface.  88  3x1 O  U,  4 2x10  E 0  E c..1  .  lxi 0  0 0  50  100  150  Time (s) Figure 4.9. The flux derivative is compared for a Nafion 117 membrane in LE and VE conditions.  4.2.1 Temperature and thickness effects  In order to determine the effect from temperature variation, transient measurements were carried on for Nafion 112 and Nafion 117 membranes at 30, 50 and 70°C. The concept of the derivative used here has no direct meaning on the identified mechanisms of water transport. Figure 4.1 Oa and 4.1 Ob include the derivatives of fluxes in Nafion 112 and Nafion 117, respectively. Original flux data from experiments are included in the inset plots. The major difference is observed at 70°C, with a higher maximum rate for the Nafion 112 membrane. Figure 4.1 Oc contains the summary of the derivatives of the fluxes for Nafion 112 and Nafion 117, within the thickness range: 51: 183 jim, in LE and VE conditions at  89  50°C. The maximum peaks confirmed that liquid in Nafion 112 had the highest rate among them. The slopes after the maximum for each membrane overlapped between each other. This suggests a thickness-independent mechanism taking the rate control after reaching the maximum. The graph in Figure 4.lOd compares two experiments with Nafionll7 membranes liquid equilibrated at 50°C after receiving a different pretreatment. The highest of the derivative curves corresponds to a membrane dehydrated for 20 hours prior to the testing, and it is compared to a membrane dehydrated for 72 hours. The latter showed a process slower than the former. The time to reach steady state increased 30% for the membrane with the longest drying history. The deviation between the final steady state between both membrane fluxes showed a 16% difference which falls far outside the experimental error (2% difference). Through independent weight measurements it was found that the water content of the membrane showed no change between 20 and 72 hours of drying. Whether the dehydration under atmospheric air produced membrane structural changes after the first 20 hours is not clear. Further experiments are required to explain the source of this difference.  90  (a)  (b)  .,  lxi  0.06  lxi 0  WateriNll2IDryGas  :e  f  x  0.02  0.02  E  ,—..  4 6x10  i  4 r io  0.04  4 9x10 E  WaterINll7!DryGas  0.06  E  .  0.00  4 6x10  0.00  0  250 500 lime(s)  62750 C  C.  4 3x10  750  4 3x10  U:,Jj  A  0  50  100 lime(s)  150  50  0  200  150  100  200  lime (s)  (dl  (c) 3x1 Q4 4 3x10 0  LiquidlNafion 112 LlquldINafion 117 VapourlNafionll2  0  2x1 0  Driedx2Ohrs Driedx72hrs  CM  (n  !-  E 2x1  2x10:  0  E ‘I  4 1x10 (9 (9  C  c lxlO CM  5x10 (9  117 cL 0  50  100 Time (s)  150  200  A  0  50  100  150  200  Time (s)  Figure 4.10. The acceleration of the flux across the membrane as a function of time. Temperature effect for (a) Nafion 112, and (b) Nation 117, at 30, 50, and 70°C in LE samples. (c) Comparison between liquid and vapour rate of transport in Nation 112 and Nation 117. (d) LE Nafion 117 membrane for two different water content conditions: after dehydration for 20 and 72 hours.  91  From the derivatives, the time at which the maximum rate of change occurred, tm,  corresponds to the inflection point of the dynamic water transport curve before the  final steady state.  When  tss,jfliüa/, tssfinal  and  tm  were compared for Nafion 112 and  Nafion 117, at 30, 50, and 70°C two different trends were observed, as depicted in Figures 4.lla, b, and c. In Figures 4.lla and 4.llb  tss,jfljtjal  and  tm  showed  linear response to the  temperature variation; and it was reproducible for both membrane thicknesses. Both tss,initial  and  tm  decreased with higher temperature and smaller thickness.  In Figure 4.11 c,  tssfinal  decreased with the temperature raise with higher variation  between temperatures for Nafion 117. The difference with respect to thickness became negligible at 70°C. These results suggest that bulk diffusion is overcome by a thicknessindependent mechanism at 70°C. Further analysis on this area is part of ongoing investigations in the author’s research group. The previous experimental data confirms that surface resistances are present on the membrane-gas interfaces, especially at temperatures above 50°C. In an attempt to elucidate surface and bulk diffusion processes, two models were developed to assist in the analysis of steady state and transient water transport data.  92  (a) • 0  20  15  —  Nation 112 Nation 117  0  U)  0  10  .  .  U,  .  .  5  P’I•I•I’I•  300  310  320  330  340  350  Temperature (K)  (b) I Nation 112 0 Nation 117  0  40  30  0  .  xCe E  .  20  0  . 10 p.I.I,I,I,  300  310  320  340  330  3  Temperature (K)  (c) 0  •  240  Lo  Nation 112 Nation 117  200 U)  160 U  Overlap  0  120 • 80 3Ô0  310  320  330  340  350  Temperature (K)  Figure 4.11. Measured times in LE Nafion 112 and 117 membranes: (a) time before the signal started to raise  tjnjliaI,  (b) time to reach maximum acceleration in the flux  m€1t t  and (c) time to reach the final  steady state t final.  93  5. Mathematical Models To elucidate the individual contributions from surface and bulk water transport mechanisms, the Varying Diffusion Coefficient (VDC) model, was developed to provide a first approximation on the incorporation of surface mechanisms of transport to the bulk. From this model, the quantification of the resistances was not achieved, but it gave insight on the need to describe a boundary condition to represent the membrane interface more accurately. A second phenomenological solution named the Vaporization-Exchange model (VEM) was proposed to separate the contributions to the mass transport from the surface and the bulk. The model described a dynamic membrane-gas boundary and related the gas flow rate with the resulting humidity in the chamber. Application of the model to the transient data generated values for the interfacial water transport rates: k; the diffusivity coefficients and the maximum concentration of water (DCm). These results proved the importance of the membrane boundary s in the analysis of water transport phenomena. The two models applied to the WT data are contributions from independent groups. The VDC model is an analytical solution proposed for the transient data as requested to Dr. Brian Wetton from the Department of Mathematics-UBC.  The  adaptation of the model to MATLAB language was performed by Peter Cave, a former Masters student in the Department of Mechanical Engineering. A preliminary data analysis is presented in his Master’s thesis [100]. The Vaporization-Exchange Model is an original contribution from Dr. Charles Monroe from Simon Fraser University. The model along with my experimental data have been accepted for publication elsewhere [98].  94  My contribution to these analyses lies on the proposed resistance in series analogy for water transport across the membrane, the design of the experimental setup and variables to make the data amenable to theoretical simulations, and the participation on the data analysis and phenomenological interpretation.  5.1 Mass Transfer Coefficients from Varying Diffusion Coefficient (VDC) Model A mathematical solution was applied to transient water transport data to deconvolute bulk diffusion from surface mechanisms. This model was based on the resistance in series array to account for the resistance to water transport in each stage of the overall process. Equation (5.1) includes mass transfer coefficients for the mechanisms across the surfaces and within the membrane bulk giving an overall mass transfer resistance [101,102]:  1 koverati  1  1  1  ka  ‘Dff  d  =—+-,——+-—,  (5.1)  where ka, kDf and kd correspond to mass transfer coefficient for absorption, diffusion and desorption, respectively.  The model incorporated the Fick’s diffusion  theory with a boundary condition based on Henry’s law to define the membrane water content in terms of the water sorption isotherms. The model is described in detail in Appendix E. Based on Equation (5.1), transient experimental data were used to estimate the sorption and diffusion terms in Equation (5.2):  95  J=a  1  (5.2)  L D  kd  A2 represents the water content difference across the thickness L of the membrane, and a is the concentration of sulfonate sites in the membrane, kd and D correspond to the mass transfer coefficients for desorption and diffusion, respectively. Both coefficients lead to a given steady state flux Jwritten in terms of a basis parameter 0 in (0,1). The model simulates fluxes between two boundary conditions that describe either:  a) a diffusion-limited extreme case, with 0 =0, and b) a surface-limited extreme case, with 0  =  1  The model considered water transport to obey the diffusion equation and the diffusion coefficient, D, is allowed to depend on water content in general:  d2 dt  d( dx  d2” dx)  —=—I D(2)— I  The variable diffusion coefficient is described by D(2)  (5.3)  62, where 8 is a  constant. For every Oe (0,1), values of kd and 6 were obtained that together match the steady state flux I The value of 0 that minimized the least square regression error between simulation and experimental data was used to determine final kd and 3 values. The model compared simulated signals with experimental fluxes across the membrane in different conditions. Figure 5.1 represents an example of the comparison.  96  Figure 5.1 compares transient flux data for Nafion 117 at 5 0°C, a 0 value of 0.8 m and 3 was found to minimize the least square regression error. Using a=1789 mol S0 )’ and lcd =6.097 2 ) 3 (molSO (molH s’ O 2 L=0.183 mm yields values of ö=3.l0xl0’ m x10 m 7  s.  The simulated flux showed a good fit in the short and long term of the rising  signal. xl  cJ  E 0  E  ci) -o  E  a) C’) C)  2 C.) >C D  U II)  cci  lime (s)  Figure 5.1. Experimental vs. simulated transient data for initially dry membranes. Transport flux across Nafion 117 at 50°C. Continuous lines in the background show the model simulation with 0 changing from 0.1 to 0.9 in increments of 0.1.  Figure 5.2 shows the transient data fitting for (left) Nafion 112, and (right) Nafion 117 at 30°C. The model predicted longer times for the thicker membrane which agrees with the data. The offset occurred in the long term for the thinnest membrane (left) meanwhile, for the thick membrane (left) the model over predicted the signal raise in the short term.  97  35 r== xlO’  1  x1O  1  2.5 ifnceamn9 0  —  0  50  100  Figure 5.2. Experiment at 30°C. with  150 Time (S)  200  250  300  0  100  200  300  400 500 Time (S)  600  700  800  900  vs. simulation transport flux across Nafion 112 (left), and Nafion 117 (right)  increasing from 0.1 to 0.9.  Reproducibility tests revealed that the final steady state of the water signal is highly related to the initial condition in the membrane. If the dew point had a lower initial value, the final steady signal showed variations of ±3°C. This data variability complicated the fitting process, especially in the long time. In the short time domain, the offset was believed to come from the model’s neglect of a boundary condition that describes the interaction between the gas flow rate and the evaporation of water from the surface. Table 5.1 shows the results for kd and 8 in Nafion 112 and Nafion 117 at different temperatures. The value of 0 that minimized the least square regression error between simulation and experimental data decreased with the increase of temperature and increased with thickness. The fact that increasing the temperature 0 approaches zero, it suggests that diffusion becomes the limiting mechanism at high temperature (because  0O means a diffusion-limited scenario). These results agree with observations from the transient experimental measurements.  98  Table 5.1. Summary of diffusion and surface transfer coefficients from model for liquid equilibrated Nafion 112 and 117 at different temperatures. The best 0 fit is shown for each experiment. e  Temperature  0  XIU  (m01 (mo1H,O  12  1  IdxlO  7  (m s) s  0 best fit  J Nafion 112  1.52 2.86 7.31  30 50 70  13.88 19.95 28.79 From literature: Berg et al. 80 80 Ge et al.  30 50 70  2.1 19.7 50.1 Nafion 117  0.73 0.29 0.29  1.49 6.51 44.43  0.91 0.76 0.34  57 45-325 (?=1-9)  The model calculated mass transport coefficients for desorption that agreed with results from Berg et al. and Ge et al. [78, 86]. Where the model failed was in the prediction of a constant The changing  for both thicknesses.  disagrees with its expected constant value, so that D would be a function  of 1 only (because D(%)  =  8%). The explanation for this inconsistency remains uncertain.  But may be solved by incorporating the 3-dimensional nature of the diffusion process trough a porous media: as thickness increases, the assumption of a 1 -D linear path for water becomes simplistic. One of the limitations of the model, as mentioned before, is the assumed fixed boundary condition on the dry membrane surface. The model fixed the water concentration of the dry chamber to the initial water content value during the transition time. The following section describes a phenomenological model that proposes a dynamic boundary condition, which describes more accurately the kinetics of vaporization and condensation processes at the surface.  99  5.2 Membrane Bulk and Boundaries. Analysis of Water Transport with  the Vaporization-Exchange Model 5.2.1 Description of the Vaporization-Exchange Model (VEM) The experimental water transport data from this work raised interest for solving the contributions from interfacial and bulk resistances in Nafion. A different approach to account for the membrane interfacial phenomena was proposed with the VaporizationExchange model [98] using the steady state and transient measurements. The model described the dynamic transport of water across the membrane bulk and interface due to the vapour pressure gradient across the interface. The problem was translated to a dimensionless analysis, and the suggested system of governing differential equations was solved for initial and boundary conditions that represented with accuracy our experimental conditions. Traditional models for water transport in Nafion considered a fixed boundary condition described, often by the correlation between isothermal vapour pressure and membrane water content from equilibrium gravimetric measurements. The previously described VDC model for transient transport (Section 5.1) used, in this way, isothermal data for describing the gas-membrane boundary. This approach has been used in the past to link the membrane water content in equilibrium with the vapour pressure in the surroundings, where the environment provides a homogeneous activity with no external driving force. Therefore, the use of isothermal data is not appropriate for a non equilibrated gas-membrane interface. The main differences with the VDC model lie, first, on the dependency on water content for the bulk diffusivity that the VEM lacks. A second difference lies on the  100  physical description of the dynamic membrane-gas interface occurring in the experiment, contrarily to the assumed equilibrium the VDC model considered. The VEM, instead, assumed a flux boundary where evaporation and condensation across the gas-membrane interface occurred indistinctly as a function of the gas flow. The vapour accumulation in the chamber was expressed mathematically as a mass balance in time domain leading to a steady state at long times. This flux boundary represents the effect of the gas flow velocity where the flux direction is a function of the flowing gas velocity in the dry chamber. Fitting to this model with steady state water transport data revealed values the interfacial water transport rates, k. Using transient water transport data, values for the bulk permeability component were determined: the diffusivity coefficient D, and the maximum water concentration for liquid- and vapour-equilibrated membranes: c and c respectively. ,  The VEM incorporated a term for bulk diffusion and water evaporation and condensation across the gas-membrane surface represented in the overall water balance: V dp cit  r —  t  1  V  +  AJ t  (53)  Within the membrane, the transport of water was described by Fick’ s law. The water flux across the membrane-gas interface is given by:  J(t) = —D  ôz t,L  (5.4)  101  Liquid-equilibrated membranes The LE case describes the membrane in contact, one surface, with liquid water, and the other surface exposed to the flowing gas. Since the model describes the transient transport in the gated cell, initial conditions are describes as:  0Z  (o) = Pm  c(0, z) =  and  (5.5)  After the gate is opened the concentration at the membrane-water interface is defined by the boundary condition: c(t,0) = c  (5.6)  The boundary condition at the membrane-gas interface was described as follows:  —  D  =  [peq (cQ, L)) POUj —  1,  (5.7)  where D, refers to the Fick’s diffusion coefficient for the internal transport, and k represents the rate of mass transfer across the interface. Equation (5.7) represents the flux across the interface. The equilibrium vapour pressure, Peq, is linked to the water content c(t,L) (in zL) according to the vapour sorption isotherm. Vaporization and condensation are represented by the last term on the right. This term refers to an activated process controlled by Gibbs free energy of water sorption, which determines Peq (c(t, L)). Condensation is a purely kinetic process with a rate proportional to the actual vapour pressure Pout. For the model, the description of Peq is reduced to a simplified version of the equilibrium vapour sorption from isothermal measurements to a linear relationship:  102  peq(C(t,L))  —c(t,L),  (5.8)  max  This expression of Henry’s law assumes a constant proportionality coefficient independent of the membrane water content to make governing equations easier to solve analytically. The formulation of the governing system and its solution is presented in detail in Appendix F.  Vapour-equilibrated membranes The main differences when describing VE is the definition of the water concentration at the membrane-vapour interface (in  z=  0), in this case: c, which  replaces c’ax; and the new boundary condition (at z=L) described by:  —  D  1.0  =  [psai  —  Peq (cQ, L))]  kvP.sat  [i  c(t0)] —  5.2.2 Application of the VEM to steady state water transport data Solutions to the governing e4uations system (See Appendix F) are summarized in Table 5.2  Table 5.2. Steady  state response from analysis with VEM Slope  of linear: (1-RH)/RH v.  LE  1 mLE =  VE  m  k  2 =  k  +  Psat L RTDCax  +  Psat L RTDCax  V A (5.10)  (5.11)  103  From our LE steady state water transport measurements, the vapour pressure data were plotted as: in (1-RH/RH) vs. gas flow velocity, for Nafion of different thickness, as shown in Figure 5.3. 30 25 Vapour  20 I  15  10 5  Liquid  0  I  ,.i.,.i.i.i.  0  2  1  3  4  5  6  7  Flow ratelArea, cms  Figure 5.3. Measurements of (1-RH)/RH as a function of the gas velocity show a good fitting with the VE model. The slopes obtained from the fitting lines in Figure 5.3 were plotted against the thickness variation of Nafion membranes, as shown in Figure 5.4.  o •  Vapour Liquid  4 0 0  °  E  03 Cl,  a,  22  .•  1 0  I  0.005  0.010  0.015  0.020  Thickness, cm Figure 5.4. Linear fits of the slopes from Figure 5.3  vs. Nafion lix thickness in Liquid and Vapour  equilibrated membranes.  104  The graph, slope vs. thickness, in Figure 5.4 showed a good linear approximation 0.96 for VE and R 2 =0.99 for LE). Through the 2 between the three thicknesses data (R ,  intercept and slope of the LE line, values for the bulk permeability component: DCmax, and the interfacial mass transfer: k were obtained provided that they fulfilled Equation (5.10). The same approach was followed with the slope and intercept of the VE linear fit of Figure 5.4 The values of k and DCm were obtained for vapour equilibrated Nafion through Equation (5.11). The mass transfer and diffusivity coefficients values found for Nafion are summarized in Table 5.3.  Results of k for LE and VE showed similar rates. This  counters the expectation of a higher permeability for LE membranes. However, it is rational to conclude that the vaporization-exchange rate is similar for LE and VE membranes if the main sources of error along the analysis are considered: the error in the linear fit can be as high as 20%, membrane swelling can produce a thickness variation of up to 8% in thickness, and the neglect of the energy balance adds in a 25% error in Icy. Therefore, these results can be considered a qualitative verification of the vaporizationexchange model. More analysis and variation of more membrane thicknesses are needed to obtain quantitative results. Table 5.3. Bulk permeability DCm and interfacial k of Nation  kv*  *  in LE and VE Nation at 50°C.  Dcmax  (ms’)  s’) 1 (molm  Nafion  3 x10  5 x10  LE  7.5  1.0  YE  6.3  1.5  The estimated error for k ranges in ± 23% according to the thermal losses effects from Section 3.3.2.  105  Current models in the literature have not been able to identify individual values for D and  Cmax  from water transport measurements [19,62,78,81]. Some authors, [78,811  used water concentration from isothermal data and Fick’s law analysis for determining D. Motupally’s model [19] used self diffusion coefficients from NMR measurements and isothermal data to calculate water fluxes. Similar to the VEM, Majztrik and collaborators found a range value of 18-39 x10 5 molm’s’ for the permeability, Dc, component which related diffusivity and what the authors assumed an equilibrium water concentration in 5 the membrane. The main difference with the values obtained in this work: 1-1.5 xl0 molm’s’ (Table 5.3) lies on the erroneous assumption of an equilibrium between the membrane and the surrounding of Majztrik et al. approach, they did not include the effect from the adjacent gas on the water content of the membrane, as the VEM did. In addition, their model was not able to separate the product into individual values for D and c. In the following section, the application of the Vaporization-Exchange model to the LE transient water transport data is described. It shows a successful procedure to determine the individual values for D, and corresponding maximum water concentration, Cax  in the membrane.  106  5.2.3 Fitting the vaporization-exchange model to transient water transport data  The measured transient water transport data were analyzed with the solutions proposed for the VEM. A pair of transformed Laplace equations accounted for the solution to the long- and short-time water transport measurements. Based on an iterative solution with both equations, values for D and  Cax  were individually determined.  Transient measurements from Nafion 117 in LE were used for the analysis. The initial experimental conditions described an initially dry concentration for the membrane: Orn (o, ) = 0; and zero vapour pressure in the gas chamber: &, (o) = 0. Boundary conditions outlined a relative humidity gradient across the membrane: on the wet side, saturation was fixed as constant. On the dry side, the dynamic vaporization-condensation regime described a flux across the interface. Assuming an initially dry membrane,  (çt’ =  0), the long- time solution expression  was simplified to:  6(v) lim—=1—e r>>1  (512)  I  and for the short-time, the simplification led to  (i.T exp(i1  limO (v)=yi (1+2r) erfcl  L  —==  —.,j—  v  ir  4v)JII  ——  ‘.  (5.13)  107  Solving Equation (5.12), the slope of the fitted line of the curve of ln(1-RH(t)/RH(ss)) vs. time in the long-time data generated the value for the exponential decay, lcj. See Figure 5.5. Figure 5.5 is a representative set of data for Nafion 117 and its corresponding linear fit in the long-time range. Similarly, the lineal fit was done for the data at 30, 50 and 70°C. The line adjustment was kept conservatively below 400s, since all experiments showed steady state below 300s. Moreover, the data dispersion became significant above 400s.  \\xPeñmenaIdaExPeñmentaIda  i: 0  100  200  300  400  Time (s) Figure 5.5. Representative linear fit of long-time response. LE Nafion 117.  From the fitted line, the slope was equivalent to Icj, which corresponds to the exponential term in Equation 5.12 and it is defined by Equation. 5.14. With k , the first 1 approximation for D was calculated:  108  =  [  RH(ss)+ (i  +  +  —  (5.14)  RH(ss))1  Using Dcmax from steady state (Table 5.3), preliminary individual values for D and c in the long term were calculated. These were used to simulate the short-time response with Equation (5.15). Assuming an initial dry condition for the membrane (çt’  =  0), the equation for the short-time is reduced to: limO  r  fr)  = y  (l erfc I I ‘J4v)  + Zr)  ;: —  —  L  ij  V  2Z  ( l1  exp I  —  II  4r,ij  —  (5.15)  Comparison of the simulated and experimental short time data is shown in Figure 5.6.  I  0.10  • •  70°C 50°C 30°C  I’  .  •  /  0.08 •  a.  /  *  0.06 7’  ô.E 0.04  A...  ‘  /  0.02 • A  0.00 0  I  I  I  10  20  30  •  I  40  Time, s Figure 5.6. Simulation (lines) and experimental (dots) data in the  short-time for LE Nafion 117 at 30,  50, and 70°C.  Final D and c were obtained from the best fit between simulation and experimental data in the short time response. The same procedure was applied for Nafion  109  117 data under 30, 50 and 70°C. Table 5.4 shows the results and the corresponding dimensionless vaporization rate, y. The values for diffusion coefficient compared closely to reports from the literature for liquid equilibrated membranes. However, it is worth to mention that the dependency on water content for the diffusivity coefficient has not been addressed in this work; therefore, comparison is only applicable to the limiting case of a . 3 fully saturated membrane with water content ranging 22 mol/S0 For the analysis of the maximum water concentration in the membrane, c, was reported in accordance with fully saturated membranes presenting values below 55 M, as shown in Table 5.4. This agrees with the concept of a fully saturated membrane region assumed to be close to the liquid-membrane interface. Values for y confirmed that interfacial mass transfer rates become significant with temperature increasing.  Table 5.4. Summary of diffusivity coefficient (D), water concentration in the membrane ( C ) and the corresponding dimensionless vaporization rate (‘y). Liquid Temperature °C  Equilibrated Membrane  y  10  D x 10 4 s 1 m  mol L 1  Type Nafion 117 30  N115  2.0537  48.69  1.957  50  N115  3.7649  26.56  1.067  70  N115  6.6815  14.97  0.601  From literature at 30°C: 10  Authors  Type  Yeo and Eisenberg  Ni 155  2.1  Water Uptake  Zawodzinski et al.  Ni 17  7.5  NMR  Suresh Ct al.  Ni 17  1.8-2.2  Fuller  N117  1.4  D x 10  s 2 m  Technique  Tritium Tagged Water Steady State Permeation  110  The Arrhenius-dependency for diffusion coefficients from Table 5.4 showed activation energy of 24 kJmor’. This value compared similar to the activation energy (25—31 kJmor’) found from desorption experiments [77J, but lower (Ca. 50%) than the activation energy calculated from steady state measurements (see Section 4.1 .1). The transient water transport data are the result of the driving force effect of a large water concentration gradient. The water concentration profile, at the moment of lifting the gate valve, can be outlined as a steep slope between the two membrane surfaces, one of which is in contact with liquid water, and the opposite in contact with dry gas, is in severe dehydration. The influence of this extreme water concentration gradient acting as driving force, could explain the reduced energy demand for water transport in the short time.  111  6. A case study: Water transport dependency on membrane water content This chapter investigates the relation between membrane water content and its transport properties by means of comparing pristine Nafion membranes with modified composite 2 composite membranes Nafion membranes. Results from Nafioni 15 and Nafioni 15/Si0 were compared for water transport, vapour sorption and desorption, and differential 2 increased the water uptake scanning calorimetry. The hygroscopic properties of Si0 capacity of the membrane, and with it, its water transport properties were investigated. Results presented here are preliminary for an in-process journal publication  This section of the thesis explored the effects of the water content over the transport 2 properties of modified Nafion. We used Nafion membranes modified with Si0 nanoparticles to investigate how the addition of hygroscopic silica influences the water uptake and the membrane transport properties. 2 ,prepared atNRC-IFCI Nafion 115-Si0 2 membranes with 10, 16 and 33 wt% of Si0 by M. Rodgers [45], were compared with unmodified Nafion 115 by measurements of: a) steady state water transport at 80°C in liquid-gas and vapour-gas equilibrium b) vapour water sorption and desorption at 25°C from 0 to 95% RH, and c) differential scanning calorimetry in liquid saturated membranes at 25°C.  112  6.1 Water content measurements from full saturation with liquid  Membrane samples were fully immersed in liquid water at room temperature. Results from water uptake and thickness change measurements for Nafion  115 and  2 composite membranes are included in Table 6.1. The data from this work NafionllS/Si0 and from [45] correspond to membranes from the same batch prepared by M. Rodgers.  2 composite membranes. Table 6.1 Properties of Nafion l15ISiO Liquid equilibrated Membrane” Dry Membrane 2 Si0 wt %  Thickness, mm [45]  [45]  This work  [45]  This work  oa  0.132  14  16  23  23.7  10  0.15  12  11  25  20.5  16  0.142  8.9  15  28  26  0.171  8  13  28  26  33 a  Thickness Gain,% Water Content, wt%  Unmodifieu Nafion 115;  °  under 25 °C  Table 6.1 includes in the first column the thickness measurements of the dry samples. The results confirm that the addition of Si0 2 increased the membrane thickness. On the second set of columns, the data shows the results from thickness gain  (%) and  water content (wt%) of the samples under liquid saturation. On the one hand, it was found that the thickness gain decreased with the increase of silica, which suggests that the addition of Si0 2 lowered the membrane swelling capacity. On the other hand, the water content increase stopped at 16 wt% SiO , which implies that the easiness to absorb water 2 provided by the early addition of silica was counterbalanced after 16 wt% Si0 . 2 In the measurements of Young’s modulus with membranes from the same batch as those used here, Rodgers [45] found that the membrane became stiff with addition of 2 (from 0 to 33 wt%). The explanation for a membrane switch to a rigid configuration Si0 113  was explained by the theory of scaffolding formation proposed by Yang [103] and Rodgers [45] in composite membranes. Young’s modulus measurements have confirmed 2 the membranes maintain the same flexibility as that for that below 10 wt% Si0 unmodified Nafion [104]. It can be explained that the scaffolding occurred somewhere after 1 Owt % of Si0 2 and this is what caused swelling stoppage and water uptake increase at 16 wt % of Si0 2 in the present study.  6.2 Water Content from Vapour Water Sorption and Desorption Isotherms from sorption and desorption experiments were obtained at 25°C from 0 to 0.95 activity using the DVS procedure (Section 3.4). Figure 6.1 shows the water content for the membrane series including pristine Nafion 115 and Nafion 11 5/SiO from 10, 16, and 33 wt% Si0 . 2 The water content of composite membranes increased with increasing water activity, in the same way as that for the unmodified Nafion (0%). Similar dependency was found for Nafion!Si0 2 at 90°C [105]. In terms of the amount of water uptake, at 120°C,  Miyake et al. found the unmodified Nafion showed noticeable lower water  uptake than silica-modified-Nafion [87]; below 90°C, the water content difference was slightly higher for the composite than the pure Nafion, agreeing with the results at 25°C presented here. In the sorption isotherm, Figure 6.1(a), the water content of composite membranes presented higher values than unmodified Nafion 115, with the highest value for 16 wt% of silica.  A similar trend was found with water content data measured in liquid  equilibrated membranes (Section 4.5.4). However, Miyake et al. [87] concluded that for  114  composite membranes prepared with Nafion 117, with 5 to 26 wt% content of silica, the isothermal sorption presented the same water content to unmodified Nafion at 25°C. This discrepancy may be explained by the thickness difference between Nafion 115 (this work) and Nafion 117 if we consider that the thickness increase with Nafion 117 can be translated into a water transport mechanism dominated by the bulk. We described already that higher membrane thickness decreases the flux crossover (section 4.1.4). Desorption isotherms, in Figure 6.1(b), show the membrane water content driven from a saturated condition to a dry environment. The graph is presented from low to high activities to facilitate the comparison with the sorption graph. Better water retention was observed for unmodified Nafion 115 compared to composite membranes between 0 to 0.7 water activity. The presence of silicon dioxide slightly reduced the water retention capacity compared to unmodified Nafion in the low and intermediate activity range. Desorption of water from composite membranes has been described as a temperature dependant process [1041 requiring higher temperatures to desorb the bound water. Further testing is required to confirm that higher temperatures would improve desorption of water from composite membranes over unfilled Nafion.  115  (a)  20  lOwt % SiO 16wt% 0 33wt%  Sorption  0  Co 0  10.  C  5  o  Q  C.) Q  o. 0.0  I  I  0.2  0.4  I  I  0.6  0.8  •  1.0  Water activity, PwlPsat  (b)  I  20  • A  •  I  •  Desorption  1 Owt % Si0 2 l6wt% 33wt%  A  15  I  A  (0 >  ,10 A  A  (0  4-  ‘ft  0  C) a, 4-  I  I  I  (0” •  •  0.0  0.2  0.4  I  0.6  •  0.8  1.0  Water activity, PwlPsat  2 composite membranes at 25°C for (a) Figure 6.1. Vapour water isotherms for Naflon 115/Si0 sorption, and (b) desorption.  116  Transient records from isothermal measurements were used to calculate the rate of sorption and desorption for each membrane sample. Figure 6.2 compares the derivatives of the mass variation with respect to time vs. the water activity. In both cases, sorption and desorption, the rate of change from unmodified Nafion showed a constant rate (1.3 4 mgs’) with the increasing activity. Contrarily, composite Nafion showed an x10 increasing rate of sorption (Figure 6.2a) with addition of silica that was exacerbated at 0.8 activity. On the desorption graph (Figure 6.2b), the rate of change for composite and unmodified Nafion presented a similar value (1 xl 0 mgs’) in the range 0.1 to 0.7 activity, but a threshold occurred at 0.8 activity, from where the composite Nafion increased the transport rate with the addition of silica. The desorption rate for composite membranes was higher (ca. 2x) than for sorption. Contrarily, the unmodified Nafion membrane showed a constant rate for sorption and desorption along the activity variation.  117  (a) 0.010 0.008  G  2 0%wtSiO  •  10 16 33  • A  0.006  A I  0.004 ‘.0.002 o  (I)  A  I  I  A  0  0.000 0.1  •  .  0  0.2  0.3  (b)  A  A  A A  0.4  0.5  0.6  0  0  0  0.7  0.8  0.9  Water Activity ‘w’sat)  -0.016  I  •  c o  -0.012  0%wtSiO 10 16  E -0.008 C  0  -0.004 U) 0  C  p  0.000  1’  •  0.1  0.2  0.3  •  a  a  •  I  •  0.4  0.5  0.6  0.7  0.8  0.9  Water Activity  wsat  Figure 6.2. Rate of change for sorption (a) and desorption (b) of vapour water in unmodified Nafion 2 membranes. 115 and composite N115/Si0  118  6.3 State of Water in Liquid Saturated Membranes  The state of water in liquid saturated membranes was characterized by thermal calorimetry using the technique described in Section 3.5.2. The water content in the membrane was classified as bound and non-bound according to its endothermic and exothermic energy when it was subjected to a temperature scan. 2 to Nafion Figure 6.3 shows the change of water with the addition of Si0 membranes for total, bound, and non-bound water. Continuous lines show the data for 2 wt% variation. The error bars have the same value for composite membranes with Si0 bound and non-bound water because the water content ratio is derived from their difference with respect to the total water. Independent symbols on the left correspond to unmodified Nafion 115 data.  water ratio  40 Unmodified Nafion 115  —  30  —-___  60o Total water  ç  45..  .—  •  Bound water  C2O  30 Non-Bound water  10  —  _—  I  Bound/Non-Bound water ratio  0  0  1.0  0  5  10  15  20  25  30  35  2 content (wt %) Si0  2 content in Naflon 115 membranes. Data at Figure 6.3. The state of water as a function of Si0  o wt% corresponds to unmodified Nafion.  119  The bound to total water ratio decreased with increasing silica content from 10 to 33 wt%. However, at 0 wt%, the corresponding value for unmodified Nafion membrane was low compared to the composite membranes. The bound water showed a maximum at 16 Si0 2 wt % and decreased with Si0 2 wt% increasing. Conversely, the non-bound, or free-water presented an upward trend with the addition of silica. These results indicate, that on the one hand, the membrane total water content is enhanced by the addition of silica, but it is limited by probable scaffolding formation, and on the other hand, that the bound water switches to bulk type water with the further addition of Si0 . This suggests a change in microstructure in the polymer morphology at 2 16 Si0 2 wt%. Summarizing the previous results, it was found that the membrane increased water content with silica addition but it reduced its ability to swell, indicating that nanoparticles 2 wt %, the water may occupy interstitial spaces between ionic clusters. From 0 to 16 Si0 content increased; but stayed constant with further silica content. The 16 Si0 2 wt% content marked a possible change in the material morphology. This is supported by the observations from the vapour sorption measurements, pointing to a more hydrophilic membrane at 16 Si0 2 wt%. Calorimetry results suggest that the addition of silica may cause some structural changes in the cluster domain of water liberating water molecules with the further addition of silica. Addition of silicon dioxide to Nafion was analyzed with water transport under steady state conditions. The following  section describes  preliminary results with the permeability cell.  120  2 Composite Membranes 6.4 Steady State Water Transport in Nafion 115/Si0  2 and unfilled Nafion The water transport across membrane samples for Nafion 1 15-Si0 115 was examined under steady state conditions at 8 0°C. This selected temperature was considered to be a balance between the operational temperatures of PEMFCs and the limits of the test rig accuracy. Figure 6.4 shows the crossover flux as a function of the gas flow rate for VE and LE membranes. Similarly to unmodified Nafion (section 4.1.1), silica composite membranes’ fluxes responded with an increase regarding the driving force applied (i.e., gas flow rate) in the low range. At higher flow rates, LE membranes showed higher fluxes than yE. Comparing the fluxes obtained from Nafion 115 at 80°C in Section 4.1 .1, we found the value of the flux to be dependent upon the type of sweeping gas used. In the analysis of composite membranes, Nitrogen was used as the carrier gas instead of Helium. It was found that Nitrogen generated lower dew point temperature data than Helium. Further analysis is required in this area, but a possible explanation is that due to the heavier molecule weight, Nitrogen reduced the mixing time between gas and vapour in the dry chamber, thus affecting the dew point temperature measurements. Figure 6.4a shows the vapour transport flux. Along the activity gradient (i.e., Nitrogen flow rate), the fluxes for the composite membranes were comparable with unfilled Nafion. The fluxes increased with the gas flow in the low regime, and decreased at higher driving forces. This flux decay is explained by a faster evaporation threshold at higher flows. The composite membranes behaved similarly to unfilled Nafion that neither prevented dehydration of the membrane surface at higher gas velocities.  121  (a) 0.030 0.027 V •0.024 E  x  0  T  zO.021  0  LI..  7  I  0.018  •  0.015  010 16 v 33  0  0  SiO,wt%  111•1•1  200  0  400  600  800  1000  Nitrogen flow 1 min 3 (qg) )  (b) 0.075  7  V  4  0.060  a  o E  0  0  0  D0.045  *  I  0  H  OnO,wt%  L  0.030  V33  ‘  1•11’1•1•  0  200  400  600  800  1000  Nitrogen flow 1 min 3 (cm )  ), and 2 Figure 6.4. Steady state water transport fluxes in unmodified Nafion 115 (0 wt% Si0 , at 80°C; a) in yE, and b) LE 2 2 composite membranes with 10, 16 and 33 wt % S10 NafionISiO conditions.  122  Composite membranes from the same batch as the one previously analyzed for vapour-vapour-transmission by M. Rodgers [45], showed no difference in performance , under a 0.6 activity gradient (the nature of 2 between samples, from 0 to 33 wt% Si0 those experiments did not allow the specification of the sweeping gas flow rate used). The activity gradient was calculated in a similar fashion as explained in Section 3.2.1. The activity at the wet side is considered 1, and the activity at the dry side, is calculated from the environment vapour pressure and saturation pressure ratio, as described by Equation 3.5 and 3.6. The vapour transmission rate calculated from Rodger’s experiments s’. This rate agreed with our flux range found in our 2 ranged from 0.024 to 0.031 molm vapour-gas WT experiments, within 0.018 to 0.026 molms’. The graph for LE membranes, in Figure 6.4b, shows an increased flux with the addition of silicon dioxide. The transport flux under high activity (gas flow above 500 3 min’) for 16 and 33 silica wt% composite membranes exceeded Nafion’s transport cm fluxes. Figure 6.5 compares the flux vs. membrane thickness for the two sets: composite ; and unmodified Nafion with Nafion 112, 2 membranes with 0, 10, 16, and 33 wt % Si0 Nafion 115 and Nafion 117. The graph shows a decreasing trend for unmodified Nafion membranes with increasing thickness. On the contrary, composite membranes showed little variation with the thickness.  123  0.05  8.Oxl 02  0.15  0.10  0.20  II  2 ç 6.0x1O  —  x  0.25  0.30  liii  ;  2 N115+Si0  4.0x10 ••  it  x  2 2.0x10  0.05  Unmodified Nafion  0  g 0.10  0.15  0.20  0.25  0.30  Membrane thickness, mm 2 composite Figure 6.5. Thickness dependency for steady state water transport across Nafion/Si0 membranes (solid symbols) and unmodified Nafion 115 (hollow symbols) at 80°C and 50°C, respectively, measured in liquid equilibrated samples. The varying symbols (squares to triangles) mi&’. 3 correspond to increasing gas flow rate from 30 to 1000 cm  The comparison between Nafion and composite membranes suggest a material . The difference in the scale 2 transport property change caused by the addition of Si0 between fluxes for composite and unmodified membranes in Figure 6.5 is due to the difference in testing temperature, 80 and 50°C, accordingly. It is assumed that the addition of silicon dioxide produces structural changes in the membrane, creating and maintaining better connected pathways, facilitating the transport across the bulk. To understand how this improved performance may be related to surface or bulk phenomena we applied the Vaporization-Exchange Model to determine the values of the interfacial mass transfer coefficient and bulk permeability. The following section describes the analysis.  124  6.5 Analysis of Composite Nafion Membranes using the VEM.  Using the vapour pressure data from the WT measurements and thickness records from , the Vaporization-Exchange Model was applied following a similar 2 the addition of Si0 procedure to that explained in Section 5.2.2. From vapour pressure data measured at 80°C, the relative humidity ratio ((12 in LE and RH)/RH) was calculated for unmodified Nafion 115, and composite Nil 5/Si0 VE samples. Figure 6.6 shows the linear fit from the vapour and liquid water transport measurements.  I I  cc  4  5  Gas velocity, cm  Figure 6.6. Fitting lines for measured (1-RH)IRH data vs. gas velocity for composite/Nafion 115 membranes with 0, 10, 16 and 33% Si0 , and Nafion 115 (0% Si0 2 ). 2  The slopes of the straight lines obtained from Figure 6.6 were used to graph Figure 6.7 The slopes vs. the Si0 2 wt% content are shown for VE and LE. In VE and LE, the slopes showed little variability with the increase of silica content. The averaged slope value for VE appears higher (ca. 200%) than its counterpart in LE. This difference points to a higher resistance to water transport for VE than for LE membranes, but gives no insight about the effect on the mechanisms of water transport with the addition of silica. 125  10  0 Vapour Equilibrated  •  9,  Liquid Equilibrated  8 E (I,  6  ‘5 0. .2 4 U) 3  .  1  2 I 0  I  0  5  10  15  20  25  30  35  2 content, wt % Si0 Figure 6.7. The slopes from Figure 6.6 are plotted against the content of Si0 2 wt% for LE and VE composite Nafion membranes.  Based on the resistance in series model, the slope represents the sum of the individual water transport mechanisms (i.e., resistances) across the membrane, and it is equal to the total resistance according to the analogy of resistance in series analogy. The Equation 2.11 is rewritten for LE and VE as:  m  =  resistance =  1  +  —  ()  v  1  +  —  v  (2)  L —  (3)  (6.1) mLE =  resistance =  + v  (1)  01(2) + (3)  According to the proposed analogy, the individual resistances are described in Table 6.2:  126  Table 6.2 Descriptors of Equation 6.1 components Individual  Description  Resistance  1  kinetic resistance at membrane/gas interface  V  (1)  1  kinetic resistance at the membrane/stagnant fluid interface (2)  L ) 3 D(  bulk resistance  For composite Nafion membranes, L, and D are expected to be a function of the 2 wt% content. Si0 Any quantitative conclusion for the transport resistances would be speculation. It was expected that the slope would provide information on the effect of silica addition in the increase/reduction of resistance to water transport. However, the slopes for VE and LE in Figure 6.7, shows no visible effect on the net total resistance with the addition of silica. This contradicts the observations from water transport and water uptake characterization, where it was found that the silica content enhances both overall mechanisms. This suggests that the VEM is not able to represent the polymer structural changes originated in the Nafion membrane by the silica addition. In order to characterize PEM membranes with the VEM, the model will need to include the change in morphology due . 2 to the increased water content promoted by the Si0  127  6.6 Polymer Structure and Water Transport in PEM.  The water transport investigations carried out for this thesis highlighted the importance of interfacial kinetics in the water transport studies, and also revealed that membrane water content and its interaction with the polymer structure influence the mechanisms of water transport. Therefore, further experimental and modeling work are required to define the dependence of water transport on polymer structure. A proposed approach is described below. Figure 6.8 shows the water content profile across a LE and VE membrane during steady state water transport experiments. Bear in mind that a normalized parameter that encloses physical and environmental parameters is in need to describe the effective transport driving force. In the LE case (left), the wet surface shows a higher water penetration; meanwhile, in the VE (right) membrane, the wet surface shows higher water transport resistance with a thinner water penetration layer. Regions with varying water concentration were outlined in both cases. These regions differentiate water saturation levels within the bulk due to the water activity gradient created by the flowing gas on one surface, and the stagnant fluid in contact with the opposite surface. Within these regions, the mechanisms of water transport can be assumed to be different from each other. This assumption is valid under the basis of Weber and Newman model [55] of polymer structural variations as a function of water content (described in Figure 2.2, section 2.1). In regions of low water concentration (thickness=L-cf), it is assumed that water is transported via diffusion through a structure of low porosity (corresponding to low water content 2<14). Contrarily, water transport in  128  highly saturated regions (thickness=d) is assumed to occur via hydraulic permeation through an expanded channels structure based on the continuous pore-like structure described by Weber an Newman. Quantification of diffusivity coefficients in the membrane bulk reported by Volino and Diat [1061 have shown that water diffusivity in saturated membranes, of 2> 10, show similar values to the bulk water diffusivity.  Wet  VE  (1)  (2)  \  E  0  d  L  0  d  L  Figure 6.8. A one-dimensional, steady state approximation with continuous water concentration profiles inside the bulk and across the interface. The profile inside the bulk shows discontinuity due to dehydration of the top layer close to the membrane-gas interface. The profile across the watermembrane interface shows continuity across the LE interface (left), and discontinuity on the VE interface (right).  Figure 6.8 also describes water content profiles across the interfaces. For LE (left), the membrane-stagnant fluid interface is represented with a continuous profile. Contrarily, for VE membranes (right), the interface is considered to show discontinuity. This is based on the lower water uptake for VE membranes reported elsewhere [11,56], and from permeability measurements with VE membranes presented in this work.  129  According to the resistance in series analogy for water transport, it is likely that the resistances within the bulk can be represented as a function of the water content, according to:  1 1 L-d d resistance=—+—+ + D(1) D(2) k k  where D(]) and D(2)  ‘62  will depend on the lower and higher water content regions,  respectively.  130  7. Conclusions and Recommendations 7.1 Conclusions A comprehensive experimental study on water transport phenomena was carried out on proton exchange membranes under activity gradients in steady state and transient regimes. Experiments looked for evidence on the importance of interfacial processes in controlling the overall water transport.  Experimental conditions were kept in accordance with typical conditions of membranes in PEM fuel cells without the incorporation of electric work, i.e., passive condition.  A dual chamber cell was designed to measure water transport across membranes with independent control of temperature, pressure, relative humidity, composition, and gas flow rate. The cell’s novel feature was a gated-valve to allow reproducibility of transient water transport measurements across the membrane.  Experimental results, from steady state water transport measurements, showed that vapour-membrane interfaces are more resistive than their liquid-membrane counterparts. The water fluxes observed in LE membranes were roughly 2x higher than their VE counterparts. Non-isothermal experiments supported the assumption that exacerbated membrane dehydration acts as a barrier to water transport.  131  Transient water transport data motivated the design of two phenomenological models, the Varying Diffusion Coefficient model (VDC) and the Vaporization Exchange Model (VEM). The VDC model considered a linear dependence of the diffusivity coefficient on water content; it was a preliminary effort to quantify interfacial water transport resistances. The VEM incorporated the effect of the membrane adjacent gas into the water transport mechanisms across the membrane bulk and boundaries. The model successfully 1 for LE, and generated values for the interfacial mass transport coefficient, k: 0.75 cm s 0.63 cm s 1 for VE membranes. The model calculated that interfacial mass transport phenomena are rate limiting below a membrane critical thickness of 100 tm.  Transient water transport data were coupled with the VEM. The analysis generated , which 1 s 2 values for diffusivity coefficients, D, for LE membranes in the range of 1 0b0 m is consistent with results from NIvIR measurements. A dimensionless vaporization rate showed that interfacial mass transfer rates become significant with increasing temperature.  • Temperature dependence for steady state water transport data agreed with Arrhenius’ temperature dependence. The activation energy for LE showed Eact=SO kJ mor’ and 44 kJ  mor’ for VE membranes. The possibility that the Eact from VE steady state water transport approximates the enthalpy of water (AH ’ = 36.78 kJ/mol) was considered. t The higher Eact for LE was explained under the basis of stronger interactions between  132  liquid water and the polymer, which not only alter the natural hydrophobic surface of the membrane but also induce a higher resistive water desorption process.  From transient liquid water transport, the activation energy, Eact, of the diffusivity coefficient showed a value of 25 kJmor’. This Eact is 50% less than the Eact found from the LE steady state measurements. This suggested that the larger the activity gradient, the lower the energy demand for water transport across the membrane.  The effect of the water content on the water transport properties of the proton -Nafion composite 2 exchange membranes was experimentally investigated through Si0 membranes. The addition of silicon dioxide into Nafion increased the water content of the membrane and decreased the membrane capacity to swell.  2 modified membranes showed no effect on the net vapour water transport Si0 compared to unmodified Nafion, but showed improved performance in the liquid water transport at high gas flow rates.  Results from vapour sorption, and water uptake measurements indicated that the 2 wt % marked a change in the morphology of Nafion. Scanning membrane with 16 Si0 2 wt%, the membrane water content calorimetry measurements showed that above 16 Si0 reached a threshold and a partial volume of water switched from bound to a free condition within the bulk.  133  The VEM was applied to the steady state water transport data from composite/Nafion membranes at 80°C. The analysis showed no change in the water transport total resistance with the addition of Si0 . This analysis highlighted the need to include polymer structural 2 parameters as a function of the water content into the analysis of water transport.  It is my hope that the experimental setup, protocols and analytical tools presented here become the basis for future more ambitious research projects.  7.2 Recommendations for future work In order to complete the study of water transport in PEMs, considerable work still remains. Cell Design: •  A faster humidity sensor could be used to monitor the transient water transport in thin membranes. One of the challenges of the current setup is to decrease the sample area/chamber volume ratio to improve the water signal resolution in low humidity testing.  •  To complete the operational conditions of a membrane within a PEM fuel cell, the incorporation of current load will allow the identification of the electro-osmotic drag and back transport fluxes in the membrane. For this, the dual chamber cell needs to be redesigned to incorporate electrical contacts on both sides of the sample with an external connection to a current load. Also, the sample holder will need to be redesigned to be able to include the gas diffusion layers and current collectors.  134  Experiments: •  Measurements with different chamber volumes and variation of the sensor position within the chamber are suggested to validate the assumption of good mixing in the dry chamber with laminar flow.  •  Measurements at higher pressure are needed in order to eliminate the environmental humidity noise at low testing temperature and to incorporate the pressure driving force effect on water transport.  •  Variations in the relative humidity inside the gas chamber are recommended to analyze the effect of surface dehydration and allow quantification of the dehydrated layer penetration.  •  A clear explanation on the transient water transport signal difference for membranes dried for different time periods has to be determined. Structural analysis is required to confirm possible changes on the membrane surface occurring by exposition to the ambient air.  •  VE transient measurements are to be completed. The analysis of transients with vapour water will allow the quantification of the resistance to transport across the vapour-membrane boundary.  •  More steady state water transport tests for more membrane thicknesses are required in order to complete a quantitative analysis of the Vaporization Exchange Model.  •  -Nafion membrane preparation 2 Measures for reproducibility control of the Si0 should be taken in consideration.  135  •  2 doped Nafion membranes is required to The structural characterization of Si0 carry out the complete interpretation of the empirical results presented in this work. 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Qwater bath  m gas,in iflw,2,  2 h in gas ,out , m w,1,  1 h  •  membrane  Q wafer bath Figure A.1: Control volume in the dry chamber of the permeability cell  Based on a mass balance, the exhaust flux in the control volume is composed by the gas flux and the water flux across the membrane: mTouf = rn gas out + rnw2  (A.1)  145  where, =  (A.2)  2 m,  and 2 x’  2 m =  1— X  mg  (A.3)  where =  2 P  (A.4) Tote!  assuming  ‘o1aI =  F, the flux of water across the membrane is calculated according to: 2 rmoil m J=__=[_ij  (A.5)  Gas Flow Regime The Reynolds number was calculated based on the cell dimensions, helium density and dynamic viscosity at 25°C using the gas flow rate used in the dry chamber: 30 to 1000 /min (STP): 3 cm  Table A. 2. Reynolds Number  for the gas flow rate calculated for the dry cell configuration Re  Cell component  Inlet Tubing Exposed Membrane  Diameter, q iO m  3.17 15.95  =  O V  /t  x 30  3  1.8 0.36  mill_i  mini 3 1000 cm  60 12  146  The results from Table A.2 suggest a low Reynolds number along the gas flow rate range applied during experiments. Thus, it was considered that neglecting forced convective effects of the sweeping on the dry membrane surface was a good approximation. Similarly, the boundary layer resistance was neglected due to the fast mixing of the gas creating a non-parallel flow with respect to the membrane surface.  147  Appendix B. Technical drawings. Design of the permeability cell  Description  Qty.  Material  # Drawing  2  Chamber  S.S.  1,2  2  External sealing flange  SS.  3  2  0-Ring  FPR encap.silicon  4  2  Gasket  Silicon  5  I  Sample Holder  Polycarbonate  6  2  Gas, Water and Sensors manifold  S.S  7  1  Gated Valve Piston  S.S.  8  9  Gated Valve  Polycarbonate  9  148  This figure has been removed due to Copyright reasons. The drawing shows the cell gate subassembly.  149  This figure has been removed due to Copyright reasons. The drawing shows the sample chamber-sample side.  150  This figure has been removed due to Copyright reasons. The drawing shows the gate valve cover.  151  This figure has been removed due to Copyright reasons. The drawing shows the cell’s gate.  152  This figure has been removed due to Copyright reasons. The drawing shows the gate valve-gate carrier.  153  This figure has been removed due to Copyright reasons. The drawing shows the gated cell-stand.  154  This figure has been removed due to Copyright reasons. The drawing shows the sample carrier- 1.  155  This figure has been removed due to Copyright reasons. The drawing shows the sample carrier subassembly.  156  This figure has been removed due to Copyright reasons. The drawing shows ported end cap.  157  This figure has been removed due to Copyright reasons. The drawing shows the retaining ring.  158  Appendix C. Dew Point Temperature sensor: cross-reference with Mass Spectrometer Dew point sensor  Vent  Isothermal Water Bath  Check valve  I  2 N Mass Flow controller  Figure Cl: Setup for dew point temperature sensor cross-reference. A saturated atmosphere was kept during measurements.  Results from both techniques are shown in Table C. 1, and compared with theoretical saturation pressure calculated from Hyland and Wexier expression [107] at each saturation temperature.  159  Table Cl. Vapour Pressure (mbar) data. Results from cross-reference analysis: dew point temperature (VaisalaTM), RGA-MS(Hiden 9, and HyJand and Wexier Equation. T 30°C  Techniques Hyland & Wexler Equation (Our Reference) RGA-Mass Spectrometer (HidenTM) Dew Point T. Sensor ) TM (Vaisala  I  40°C  I  I  50°C 60°C Pw (mbar)  I  70°C  I  80°C  0.042  0.073  0.122  0.198  0.310  0.471  0.044  0.073  0.124  0.198  0.33 1  0.485  0.043  0.075  0.124  0.202  0.313  0.464  The dew point temperature sensor (Vaisala TM ) showed smaller error (max. 2.7%) than the Mass Spectrometer (max. 6.7%) with respect to the reference in the whole temperature testing. The Mass Spectrometer showed larger deviation from the reference at temperatures  60°C, while the dew point temperature sensor showed less variability in  the whole temperature range.  160  Appendix D. Effective Diffusivity from steady state coefficients Most of the reported analyses for Nafion membranes are based on an effective diffusion coefficient, which embodies the lack of information on the microscopic topology. This coefficient is a function of the chemical species, their environment, and the local geometry. Most of the reported work simplifies the analysis by considering only its dependence on water content, and by incorporating material properties like the density of dry Nafion, Pd, and the equivalent weight. With these simplifications, the molar flux of water in a membrane can be calculated according to first Fick’s law of diffusion:  J  =  —D(2)VcffQ  (D.1)  Following expressions based on first Fick’s law, Motupally et al. derived diffusion coefficients for Nafion membranes by assuming one dimensional Fickian transport at steady state [19]: )=_JE1+7) 2 D(  (a  (D.2)  We assumed a linear water concentration as illustrated in Figure 4.5 with possible discontinuities across the interfaces. Although similar diagrams have been used to describe water transport in Nafion [62], we emphasize that the exact variation of water activity or concentration across the membrane is not known.  161  In general, the variation of water content with distance across the membrane (i.e., the exact form of A(x) in the range 0  <  x  <  L  is unknown. Considering the very  simplified case of a linear profile:  (J  I  ((A(L+xL)—t(0)) i=C L+AL  1=1  ãx)  (D.3)  2 is constant, and ilL is the change in membrane thickness upon hydration (at C steady state). We calculated the approximate values for 2(0) and 2(L+zlL) based on our experimental values for vapour pressure, the measured membrane thickness, and the empirical absorption isotherms.  The membrane surface water content, (2(0)), was calculated from isothermal data and the linear profiles supported by the works of Scharfer and Ge et al. [78,108]. We used the empirical absorption isotherms (Figure D.1) reported by Zawodsinski [ill, and Hinatsu [56], and recent data from Soboleva and Holdcroft (for Nafion 1 15)[96], to calculate the values of water content on the membrane surface (2(L))based on our calculated activity values generated by the gas flow rate.  162  24  22 20 18 16 14  24  Nafion 115 (Soboleva & Holdcroft) o 25°C 0 50°C 80°C Nafion 117 30°C (Zawodsinski)  •  22  20 (Schoroeders Paradox) q-j  12  18 16 14 12  10  hEoo!6.oo  Activity Figure D.1. Membrane water content vs. water activity for Nafion 115 and Nafion 117 at different temperatures, from different sources  We used the conventional defmition of water activity to describe the relative humidity in the gas phase next to the membrane surface. From the isotherm in Figure D. 1, for each water activity on the dry surface, the water content, (L+AL), was calculated from correlating our experimental vapour pressure data with the isothermal sorption data. The measured change in membrane thickness, (L+ziL), for the liquid-gas and vapor-gas equilibrated membranes in our experimental series was approximately 30% and 21% of the original membrane thickness, respectively. The water content at the wet surface, 2(0), was given a value of 22 and 14 3 O/molSO for liquid and vapour 2 molH equilibration, respectively.  The effective diffusivity coefficient for Nafion 115 was calculated under the assumptions of one-dimensional transport are included in Table D. 1, for 30, 50 and 70°C, with helium flow rate maintained at 100 cm /min (STP) in all cases. 3  163  Table D.1. Effective diffusivities for water in Nafion 115 membrane equilibrated with liquid-gas and vapour-gas at different temperatures  Deffeclive Temperature  Vapour  Liquid  x 1010 m 2s 30 40 50 60 70 80 Eactivation ( kJmol)  0.25 0.56 0.79 1.25 2.21 3.55 45  0.26 0.47 0.85 1.50 2.83 4.30 51  The increasing diffusivity with the temperature rise compared well with published data [78,811. The activation energy calculated from liquid diffusivity showed 51 kJmor’; followed closely by 45 kJmor’, from vapour diffusivity.  The diffusivity showed low dependency on the water phase (liquid or vapour) in contact with the membrane. We emphasize that the transition from the experimental measurements to the calculated diffusivities depends on several assumptions whose validity can be questioned. Assuming a linear concentration profile within the membrane is the first weakness in this type of analysis. Different methodologies and assumptions in this process amongst different authors contribute to the variability in reported diffusion coefficients.  Figure D.2 is a representation of the diffusivity coefficient dependency on the activity gradient acting as the driving force. The maximum and decay of Deff shows the limited effect of the driving force when it is overcome by interfacial resistance. This  164  evidences the need of more information on the kinetics of the interfacial phenomena in order to decouple bulk from surface transport.  4 4.0x10 6.OxlO°  0 30°C 040°C 50°C eo°c 1 70°C E°80°C  5.OxlO°  4.0x10  4 3.0x10  Co  E  Co  3.0x10  2.01(10  -°  E  2.OxlO°  V 7 W  V  V 1.0x10°  V  .  0  V oc0 0  0.0  I  I  I  0.1  0.2  0.3  I  0.4  0.5  0.6  I  0.7  0.8  I  0.9  to  “IIIIIII••  0.0  0.1  0.2  0.3  0.4  05  0.6  0.7  0.8  0.9  Figure D.2 The effective water diffusivity for LE (left) and vapor-gas equilibrated membranes (right) from permeation measurements.  165  1.0  Appendix E. Varying Coefficient Diffusion Model Using the form proposed in [1091, the following relationships at the boundary are assumed: J  where  =  =  Q is the concentration of sulfonate  Q kd (IxL  (El)  —  sites in the membrane and kd is the desorption  coefficient. Given an initial water content profile 2(x, 0) and inlet flow parameters that determine 2 and )4, and J(t) can be predicted numerically. By comparing the transient model prediction to experimental data, estimates of 8 and kd can be determined.  We consider briefly the case of constant diffusivity, D, at the beginning of this paragraph for illustrative purposes. At steady state, the following result comes from the model after a straightforward calculation:  J=QF—%)  (E2)  where F defines the resistance in series neglecting Ic,:  F=  (E3)  1/rd +L/D  166  With a fuiiy hydrated membrane surface we assumed fast sorption rates and resistance across this surface is neglected.  From the steady state computations, the relative size of D and kd cannot be determined. The parameter kd has a minimum possible value:  kdmin  =  Q(2_ ,e)  (E4)  The values of D and kd that lead to a given steady state flux J can be written in terms of a basis parameter 6 in (0,1). Two equations can be established:  lcd  D  =  dij  0  = Lkdmin  (E5)  (E6)  This basis parameter is nothing more than a modified form of the Biot dimensionless number for mass transfer, relating the ratio of diffusion resistance to convection resistance. For our case of interest, where D is not constant but has a linear  167  dependency on water content with parameter ô, the same general procedure can be used. However, the analogue of Eqn. (E6 ) is mathematically more complex. At steady state,  =  —Q8A(x)  d2(x) (E7)  Rearranging this equation gives, d2 2J 22—=—-—— dx Qö  Noting that 2,-=  d(22)  and thatJ =Qkd(2 2  (E8)  —%),  d(22)2kçl,  _A;)  Integrating both sides with respect to x from 0 to L, with boundary conditions 2(0)  (E9)  11q 2  and 2(L) =22, 2jq —2 =2B(2 2 —A)  (ElO)  Where by definition Lkd  B=—  (Eli)  2 +2B% 2 _(2q +2B2)=O  (E12)  Rewrite Eqn.(E10),  And finding the positive root, =  B+/B2  +(2q +2B2)  (E13)  168  Then (E14)  Now with kd given via Equation (E3) and J known from the experimental data, Equation (E14) becomes an implicit equation for B, which was solved with a root finding technique. With B and kd known, 8 can be found from the definition of B (Equation (Eli)).  169  Appendix F. Dimensionless solution to the governing equation system of the Vaporization-Exchange Model. The following dimensionless variables were defined: =  where  e,, (r, )  =  L  L  ,  =  o(z)  and  0 C C  = POUt  Psat  represents position in the membrane, r time,  1 —P  ,  (F.1)  Pin  em water concentration in the  membrane, and O, vapour pressure of water in the dry chamber. If the inlet gas is dry, then ps,, = 0. Thus, 8 becomes the relative humidity of the outlet gas, RH. The ratio of interface to bulk rate processes is defined by the parameter a, which can be described as equivalent to a Biot number:  — Lkvpsat(a—RHin)  a—  (F2)  )RT 0 D(Cm —c  where RH 5 / p 1 p defines relative humidity in the inlet stream, and  C  stands for the  initial water concentration in the membrane. Instead of expressing the typical convection by the flowing gas, as a Biot or Sherwood number would, a represents the scale of diffusional resistance over the scale of the kinetic resistance to vaporization exchange: a is small when vaporization exchange limits the flux and large when mass transfer through the membrane is rate limiting. Three dimensionless parameters may be controlled experimentally: COP:iat C  0 — pIfl ( /c )— RH,  (Psat  =  -  Pn)  l RII,  =  kAL 2 DV  ,  and ci  =  DV  (F.3)  170  The governing equations become  dr  =  —q56  —  a r,l  ‘  =  and  ãOm  8r  (F.4)  the initial conditions simplify to  e(o)=o  &(o,)=o,  and  (F.5)  And the boundary conditions on the membrane are 0,,, (v,o)  1  and  a  ,i  =  a[8,, (r) 0,,, —  (, i)+ ‘(i o,,, (r,1))J. —  (F.6)  Steady State Response.- The governing system is solved by the method of Laplace transformation with respect to time. This employs the initial conditions immediately, reduces gas continuity to an algebraic relation, and simplifies water continuity in the membrane to an ordinary differential equation (ODE) in  .  The ODE can be solved  directly, after which one can isolate the dependent variables. In terms of the Laplace variable s, =  +  y + s)cosh(J)+ a(i  -  +  s)sinh(iJ /  (F7)  The steady state vapour pressure,  =  1im() limsOv  =  r y+q5[1+a(1— çv)j1  (F.8)  171  Upon a return to the original, dimensional experimental parameters, this rearranges to:  l—8°  = (i  —  O°  +  Lp sat  “IV V I— = m — A RTDCmax)A  (F.9)  Transient Response.- Solving Equation (F.7) for sO, O, was converted in a sum of two terms and the denominator was replaced by their second-order Maclaurin series, inversion yields  _yIe2T  lim  r>>1  9,,  (F.1O)  ,  with constants  [±  1 k  +  __-&,°  +  and  —  +  =  = (k 1  —  (F.11)  An expansion of Equation (F.7) for large s yields an expression valid for small r. By inversion, the following equation is derived limO  ()=  +  2r) erfc[-_i==J  —  exp  1)] + 7VT 4r  (F.12)  172  Appendix G. Collaborative work terms Many challenges needed to be overcome to ensure the success of this project. The main challenges were a lack of lab facilities, testing instruments, and project setup. Once these constraints were overcome, however, the design of the testing rig, its corresponding thermodynamic analysis, as well as control and instrumentation proceeded successfully. I carried these out under the supervision of Professor Walter Mérida. Furthermore, I am also the primary contributor to the experimental protocols, measurements, data analysis and results interpretation presented in this thesis. A version of Sections 4.1 and 4.2 will be submitted for publication. Romero, T. and Mérida, W. “Liquid and vapour water transport in Nafion membranes”. The significant results this thesis produced could not have been achieved without 3 generated an the collaborative efforts of the following people. Professor Bryan Wetton analytical solution (Section 5.1) to my proposed resistance in series water transport configuration. Professor Michael Eikerling 5 and Dr. Charles Monroe ’ 4 2 proposed the vaporization-exchange model (included in Section 5.2) to fit my experimental data. The application of this model combined with my data analysis resulted in acceptance for journal publication. Monroe, Ch. ; Romero, T.; Mérida, W. and Eikerling, M. (2008) A vaporization-exchange model for water sorption and flux in Nafion, Journal of Membrane Science, 324 (2008) 1. Professor Steve Holcroft 3 and the Membrane Electrode Assembly (MEA) team ’ 2 3 provided equipment, training, and membrane samples which I used for analysis of Department of Mathematics, University of British Columbia, Vancouver, Canada, V6T lZ4 Department of Chemistry, Simon Fraser University, Vancouver, Canada, V5A 1 S6 National Research Council (NRC) Institute for Fuel Cell Innovation (IFCI), Vancouver, Canada, V6T 1 W5  ‘  -  173  composite membranes. Chapter 6 includes the results of this analysis. On these terms, the following journal publication is in preparation: Romero, T.; Adachi, M.; Titichai, N., - Nafion 2 Mërida, W., and Hodlcroft, S. The nature of water transport in composite Si0 membranes.  174  


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