N M R Study of P F ~ Doped Polypyrrole: A Potential Candidate for Artificial Muscles by Chien-Hsin Tso B.Sc, Tsing Hua University, Taiwan, 2001 A THESIS SUBMITTED IN PARTIAL F U L F I L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF Master of Science in The Faculty of Graduate Studies (Physics) The University Of British Columbia August 2, 2006 © Chien-Hsin Tso2006 11 Abstract Conducting polymer actuators, such as polypyrrole, are promising materials for novel applications because they are more muscle-like and potentially less expensive than common motors. A variety of N M R techniques are employed to examine the ion content and dynamics of PFg doped polypyrrole films in different oxidation states. The ion content decreases linearly with decreasing electrochemical potential, directly confirming the ion insertion mechanism of polymer actuation. With known ion content and deposition current, a doping level (dopant ion/pyrrole) of 0.26 was determined for the as-grown film. A Ti relaxation study reveals that the rotational correlation time of PFg ions in the oxidized film (10.76 ps) is similar to that in the solvent (8.08 ps), suggesting the ions are located inside solvent pockets rather than at stable sites in the polymer matrix. ID Nuclear Overhauser Effect (NOE) difference experiments confirm the solvated ion environment in oxidized films, but reveal a drastic decrease in the NOE enhancement factor in reduced films, implying that polypyrrole undergoes a significant structural change when reduced. This change leads to a much less solvated environment as experienced by the dopant ions in the reduced state. Translational motion of the PFg ions in the oxidized films at two orientations is probed via self-diffusion coefficient measurements made using pulsed-field gradient (PFG) N M R . The D values obtained at different diffusion times range from 3 x 1 0 cm /s to 5 x 10~ cm /s. The echo attenuation obtained by P F G . N M R experiments not only gives direct information on ionic diffusion but also serves "as a potential tool to explore the pore morphology of doped polypyrrole films. - 8 2 9 2 Ill Contents Abstract ii Contents iii List of Tables . . v List of Figures vi Acknowledgements 1 Introduction 1.1 Introductory Remarks . 1.2 A n Introduction to Nuclear Magnetic Resonance (NMR) 1.3 Principles of N M R . . . • 1.4 Effects of Pulses 1.5 Ti, T Relaxation Times 1.6 N M R Spectroscopy: FID Signal and the Fourier Transform 1.7 Internal Spin interactions 1.7.1 Chemical shift < 1.7.2 J-couplings 1.7.3 Dipole-dipole couplings 2 2 3 An 2.1 2.2 2.3 viii '. . Introduction to P F g Doped Polypyrrole PFg Doped Polypyrrole Belongs to the Class of Conducting Polymer . . PFg Doped Polypyrrole as Muscle-Like Actuators Comparison between Conducting Polymer Actuators and Other Actuation Technologies 2.4 Synthesis of PFg Doped Polypyrrole 2.4.1 Electrodeposition 2.4.2 Electrochemical Reduction 2.4.3 Conductivity Measurement 1 1 2 2 6 7 8 9 9 10 11 12 12 14 15 16 16 18 18 P F g Ion Content in the P P y Films as a Function of Oxidation States 20 3.1 Experimental Method . . : 20 3.1.1 ID P Spectroscopy 20 3 1 Contents 3.2 3.3 4 iv Results Discussion 20 22 Rotational M o t i o n s of PFg Ions i n the P P y F i l m s 4.1 Relaxation Theory 4.2 Experimental Method 4.2.1 Relaxation Measurements 4.3 Results 4.4 Discussion 24 24 28 28 29 31 5 Solvent Accessibility of PFg Ions i n the P P y F i l m s 5.1 Nuclear Overhauser Effect (NOE) 5.2 Experimental Method 5.2.1 ID N O E Difference Spectroscopy . 5.3 Results 5.4 Discussion 33 33 34 34 34 35 6 37 37 40 42 42 48 49 7 Translational M o t i o n s of P F g Ions i n the P P y F i l m s 6.1 Pulsed-Field Gradient (PFG) N M R 6.1.1 Self-Diffusion in Restricted Geometries 6.2 Experimental Method 6.2.1 Pulsed-Field Gradient N M R Measurement 6.3 Results 6.4 Discussion Conclusion References . , 53 55 V List of Tables 1.1 Properties of most common nuclei for N M R studies 6 3.1 Doping levels as a function of oxidation state 4.1 4.2 4.3 4.4 23 Ti relaxation times and the rotational correlation times r of two solvent samples ~ P Ti relaxation times as a function of temperature of PPy sample Si~S . T i relaxation times and the rotational correlation times T of two PPy samples: S and S at room temperature T relaxation times of three PPy samples: Si~S c 3 1 3 c t 2 2 3 5.1 N O E enhancement factor rj of the five samples 6.1 6.2 6.3 30 31 31 31 35 Spectra width Au from one-D image gradient calibration at gradient amplitude x (0-1) and the corresponding gradient strength. 46 Self-diffusion coefficients of solvent samples 48 Diffusion coefficients of the oxidized S and the less oxidized S PPy sample. 5 0 1 2 vi List of Figures 1.1 1.2 1.3 1.4 1.5 1.6 Energy levels of spin 1/2 nucleus in the presence of the magnetic field. . . Spin precession Schematic descriptions of N M R phenomenon The magnetization is tipped down by 6 by a R F pulse with duration t . . Internal spin interactions for spin 1/2 Line splitting for a two spin 1/2 system (AX) with J-coupiing constant J - 3 4 5 7 10 10 2.1 2.2 2.3 2.4 Chemical structure of some common conducing polymers Conductivities of polypyrrole relative to other materials Redox reaction of PPy in the presence of PFg anions Volume changes in PFg doped polypyrrole when it is subjected to a redox reaction Chemical structures of T E A P , P C and pyrrole monomer Polypyrrole deposition setup and synthesis conditions Time response of reduction current during potentiostatic discharging of PPy films 13 13 14 2.5 2.6 2.7 p AX 15 17 17 18 3.1 3.2 ID P spectrum of doped PPy films along with KH2PO4 standard solution. 21 Number of PFg ions per unit mass of PPy films at different oxidation states. 22 4.1 4.2 Modulation of the local dipolar field by molecular rotations The spin-lattice relaxation time as a function of rotational correlation time for dipolar relaxations Inversion-recovery pulse sequence for Ti measurement. Spin echo pulse sequence for T measurement The effect of temperature on T depends on the the location of r with respect, to the 7\ minimum P Ti relaxation times as functions of temperature of P P y sample S S . 30 32 5.1 5.2 Pulse sequences for steady state N O E difference spectroscopy N O E enhancement factor rj of the five samples. 35 36 6.1 6.2 Pulse field gradient spin-echo sequence (PFGSE) . Features of molecule motions when undergoing free diffusion and restricted diffusion Expected behaviors of D vs. A in free diffusion and restricted diffusions. 37 4.3 4.4 4.5 4.6 6.3 3 1 2 x 25 28 28 29 c 3 1 r 3 40 41 List of Figures A gradient coil set designed for higher coil constant and better gradient profile 6.5 Signal attenuation of E intensity in H 0 for gradient strength calibration. 6.6 One-D image gradient calibration 6.7 Pulse sequences for diffusion measurements 6.8 Echo attenuation with respect to gradient strength g of 0.05M P C sample. 6.9 Diffusion coefficients measured by P F G N M R experiment 6.10 The sheets of P P y thin films were stacked either parallel or perpendicular to B field 6.11 Signal attenuation 1(g) from S[ oxidized P P y sample at A=50 ms and 3s. vii 6.4 X 2 43 44 45 47 48 49 49 51 Vlll Acknowledgements I gratefully thank my advisor Dr. Carl Michal, from whom I really have learned a lot in this research project. I also thank my fellow grad students in the N M R lab: Xiang Li, Phil Eles and Tom Depew for being there whenever I've needed help. Many thanks go to Mya Warren and Dr. John Madden for sharing their experience in the synthesis and the electrochemical experiments of polypyrrole. 1 Chapter 1 Introduction 1 . 1 I n t r o d u c t o r y R e m a r k s Materials scientists have long sought to develop lightweight materials that grow and shrink significantly in length or volume when subjected to electric stimulation. Such substances could serve as drivers for novel motion-generating devices, (generally called actuators) possible replacements for the ubiquitous electric motor, which is often too bulky and heavy for smaller-scale applications. Electroactive polymers are a promising alternative to materials commonly used for existing actuators because they display sufficient physical response to electrical excitation to power new classes of actuators. Polypyrrole (PPy) is one of the most studied electroactive polymers due to its environmental stability, ease of fabrication and high conductivity when doped. [1] Because PPy films expand and contract in response to applied electrochemical potentials, PPy has been proposed for use as a soft actuator material. [2] Although many research groups have had success in developing real applications of PPy actuators [3, 4, 5], the relationships between microscopic structural changes and macroscopic movements are still not fully understood, partly due to the difficulties in investigating the insoluble and structurally disordered conductive P P y films [6]. H and C solid-state N M R have been applied to PPy [7, 8, 9], however, low spectral resolution from overlapping broad lines limits the information available from such studies. Cross-polarization/magic angle spinning (CPMAS) can improve the resolution somewhat,[10, 11] but requires films to be mechanically ground into fine powders, raising concerns about changes to the material structure. Dopant ions inside P P y films are believed to play an important role in both the macroscopic and microscopic behavior of actuators as actuation is generally attributed to dopant ion insertion/expulsion into or out of the bulk polymer films. [12] There appears to be little research reported to date in the literature directly investigating the ions in P P y films. In this thesis we have employed N M R techniques to study PFg ions inside polypyrrole as a function of oxidation state, with the aims of understanding the microscopic details of the actuation, as well as elucidating the structure of the material. The fundamentals of N M R as well as the operation of Fourier spectroscopy are briefly reviewed in the introduction chapter, followed by an introduction to the material under study, PFg doped polypyrrole. Chapter 2 presents quantitative measurements of PFg doping levels as a function of oxidation state by ID P NMR, which provides direct evidence of the ion insertion actuation mechanism. Chapter 3 explores the rotational mobility of PFg ions by measuring their T\ relaxation time constant. 1 1 3 3 1 Chapter 1. 2 Introduction In chapter 4, nuclear Overhauser effect (NOE) experiments are performed to reveal the solvent accessibility of PFg ions in the polymer films. Chapters 3 and 4 provide a picture of the environment in which the ions reside. Chapter 5 deals with measuring translational motion of dopant ions inside polypyrrole by pulsed-field gradient (PFG) NMR. The diffusion coefficient of ions, a critical quantity in predicting actuator behavior, can be readily obtained without the need for parameter fitting via some intermediate modeling process. Lastly, findings presented in the preceding chapters are summarized in the conclusion chapter. 1 . 2 A n I n t r o d u c t i o n R e s o n a n c e ( N M t o R N u c l e a r M a g n e t i c ) Nuclear magnetic resonance spectroscopy is one of the most versatile and informative tools in many areas of science today. Often N M R readily provides difficult to acquire or otherwise unobtainable information. There are two essential features that have rendered its power. First, it uses built-in atomic labels directly from the sample. Second, it is selective and noninvasive. In addition, new N M R techniques have continued to proliferate, and commercially available instrumentation has reached the state of the art in terms of sensitivity, flexibility, and computational power. As examples of the diversity of the techniques of N M R consider magnetic resonance imaging, which has become a major clinical diagnostic tool, and the use of multi-dimensional solution state N M R for solving the structures of proteins. 1 . 3 P r i n c i p l e s o f N M R Each nucleus carries an intrinsic nuclear spin / , (which may be 0) and has its own nuclear magnetic moment ~jt according to Equation 1.1, where 7 is the gyromagnetic ratio. jt = j 7 (1.1) When the nuclear magnetic moment is placed in an external magnetic field ~§, the different spin states acquire different magnetic potential energies. In the presence of the static magnetic field B, an N M R sample, which normally involves a huge number of spins, produces a small amount of spin polarization (net magnetization) in equilibrium. A radio frequency (RF) signal of proper frequency can induce a transition between spin states, leading to a nuclear magnetic resonance. If the radio frequency is switched off, then the spins will relax back to equilibrium producing a measurable amount of R F signal at the resonant frequency associated with the spin flip. Take a spin 1/2 nucleus as an example: a spin 1/2 nucleus has two spin states, |f) spin up and \[) spin down. The Hamiltonian for a magnetic moment in the presence of Chapter 1. Introduction 3 m= -1/2 B m=l/2, -1/2 A E m= -1/2 No magnetic field Magnetic field Figure 1.1: Energy levels of spin 1/2 nucleus in the presence of the magnetic field. magnetic magnetic field ~B* = B'z is given in Equation 1.2: H=---ft-~S. (1.2) For positive 7 , spins parallel to the magnetic field have lower energy than spins that are anti-parallel to the magnetic field. By plugging Equation 1.1 into Equation 1.2, we find: H = - 7 T • ~B* = -jBI (1.3) z where H and I are quantum mechanical operators. Evaluating the energies of the spin states, we find: z E = (ip I H I ip) —-yBIz = (tp I I ip) = (ip I —jBmh (p) — I mhuiL, (1-4) in which E is the potential energy of the spin 1/2 in the magnetic field, | <p) is its spin state, U>L is the Larmor frequency defined as U>L = —7-6, and m is the z-component quantum number, which can be 1/2 or —1/2 for a spin 1/2 nucleus (see Figure 1.1). Nuclei with different 7 values lead to different observation frequencies for different nuclei on a particular spectrometer. For an ensemble of spins 1/2 in the static ~~§ field, the distribution of nuclei in the two energy states ±1/2HUL in equilibrium is given by the Boltzmann distribution, with the lower energy state more populated than the upper: AT -E /kT p !Hl - 1 ~ -E /kT N e t h ~ p e -(E -Ei)/h!r _ ~ —AE/kT h e _ - -hw /kT L e ' / , r\ ^ ' where Nh and Ni are the numbers of spins in the higher and lower energy states respectively. It is the small excess number of spins in the lower energy state (around 1 0 - 4 Chapter (a) 1. (b) B 4 Introduction B A AA M M oo, Figure 1.2: The behavior of M (a) at equilibrium, and (b) after perturbation after a pulse. or less) that gives the system a net magnetization M", and it is the net magnetization that determines the N M R signal. In thermal equilibrium, the net magnetization will be aligned with the static ~~§ field (Figure 1.2 (a)) and will stay there unless the system is disturbed in some way. If we somehow misalign the induced magnetization from the applied field (e.g. by applying a radio frequency pulse, as described in Section 1.4), then the Zeeman Hamiltonian (Equation 1.3) will cause the system to time evolve according to: | ip(t)) = exp (—ijrt) \ (p), and the expectation values of I will be functions of cosujit and sinuj t. Physically this means that the net magnetization precesses around the z-axis. Once the magnetization has been moved away from the positive z-direction, the static magnetic field causes it to rotate at its Larmor frequency (Figure 1.2 (b)). This motion is known as Larmor precession. A simple N M R experiment then consists of two steps, first a radio frequency (RF) pulse that is oscillating at an appropriate frequency is applied to disturb the system, transitions between the energy levels will be induced, ie, the nuclear spin system will "resonate." After the perturbation, the system will relax back to thermal equilibrium. If we were to wind a coil of wire around the axis perpendicular to the B* field, the component of the precessing magnetization in the x-y plane would induce an oscillating current in the coil which then generates a signal known as a free induction decay (FID). The resulting FID contains a wealth of information about the spin system, and the Fourier transform of the FID is the desired frequency domain N M R spectrum ready for subsequent analysis. The N M R phenomenon is shown schematically in Figure 1.3. We can also write down the classical description of the equation of motion of the net macroscopic magnetization, the Bloch Equations: x>y L ^ - = jA4x~t1 dt (1.6) K ' The evolution of the spin magnetization in principle can be fully described by the quantum mechanical formalism if the spin Hamiltonian is written down. However the classical treatment of the spin system can often be useful to provide an intuitive understanding, and for simple N M R experiments the classical treatment provides a complete 5 Chapter 1. Introduction (a) (b) z X (d) z (c) z x z (f) . ( e ) AB Volts Intensity Figure 1.3: Schematic descriptions of N M R phenomenon, (a) In equilibrium, the net magnetization from an N M R sample is along the static field, (b) The N M R experiment consists of disturbing this equilibrium, generally with a burst of radio frequency energy, (c) The spins dephase according to their chemical shifts and spin-spin interactions, (d) The spin system strives to re-establish its equilibrium via spin-spin and spin lattice processes, (e) Meanwhile, the induced voltage is monitored in the x-y plane by a resonant radio frequency coil. This signal is the free induction decay (FID), (f) The FID is then Fourier transformed to give the desired frequency-domain spectrum. 6 Chapter 1. Introduction Table 1.1: Properties of most common nuclei for N M R studies. Nucleus H H 1 2 13 1 5 C N 19 F 31p Natural Abundance (%) 99.98 0.0156 1.108 .0.365 100 100 Spin Quantum Number (/) 1/2 1 1/2 ' 1/2 1/2 1/2 and accurate picture of the phenomenon. common nuclei in N M R studies. 1.4 7 (lOW/Ts) 26.7520 4.1067 6.7265 -2.7108 25.167 10.829 Table 1.3 lists the properties of the most Effects of Pulses It has been pointed out earlier that if the magnetization can be moved away from its equilibrium position, then precession occurs and a signalmay be detected. The excitation is produced by a second magnetic field B\, which oscillates at the appropriate radio frequency. This field is created by a current in a coil wound perpendicular to £?. The coil is often the same coil in which the signal is received, and by convention we define the coil axis as the x axis. If the excitation frequency Ui is equal to the Lamor frequency UL, U)I=U) L = jB. (1.7) The field Bi interacts with the magnetization A? to produce a torque which moves the magnetization towards the x-y plane. The magnetization will precess around the R F field at an angular frequency 7 B 1 . At the same time, it is precessing about the magnetic field at a frequency jB. This rather complicated motion, simultaneous precession about two axes, is referred to as a nutation. The final position of the magnetization will depend upon the length of time for which the radio frequency is applied. (See Figure 1.4) The B\ field is applied as a pulse of duration t , which usually lasts for a few microseconds. The tip angle 6 which the magnetization is tipped from the z axis is easily calculated as: p 0 = lB t x p (1.8) We can determine the relationship between the pulse width and the tip angle by varying the duration and examining the resulting signal intensity. The signal will be a maximum for a tip angle of ir/2, a null at ir, a negative maximum at 37r/2, and return to a null at 2n with the magnetization back along the z axis. 7 Chapter 1. Introduction z M(t ) p M s y X Figure 1.4: The magnetization is tipped down by 9 by a R F pulse with duration t . p 1.5 T i , T Relaxation Times 2 The nuclear spin relaxation times (Ti and T ) refer to characteristic time scales for spin magnetization to regain equilibrium after an R F pulse perturbation. Relaxation times probe molecular dynamics because molecular motions will generate fluctuating magnetic fields at the site of the nuclear spins, causing transitions in the spin states and thus bringing the system back to thermal equilibrium. The spin relaxation times Ti and T are essential parameters in the N M R experiments because not only do they provide valuable information as to motion and dynamics, but they also set time scales over which various aspects of the spin system stay coherent after being disturbed from equilibrium. Ti is the spin-lattice or longitudinal relaxation time, and is a measure of how fast the magnetization relaxes back along the z-axis. T is the spin-spin or transverse relaxation time, and is a measure of how fast the magnetization dephases in the transverse(x-y) plane. Phenomenologically, the time dependence of macroscopic magnetization, having components M , My, and M , during the relaxation is described as 2 2 2 x z M (t) M + M {t) M (0)cos(uj t)e~% (1.10) My(t) M (0) sm(u t)e 2 (1.11) z x 0 x (M (0)-M )e-^ z 0 0 T y 0 (1.9) (1.12) where M is the equilibrium magnetization. The Bloch equations including relaxation 0 Chapter 1. Introduction 8 can then be written as: dA4 7A? x ~B* - R(tf - (1.13) My) R 1 . 6 N M R S p e c t r o s c o p y : F o u r i e r F I D S i g n a l a n d t h e T r a n s f o r m Once an R F pulse with spectrometer reference frequency w / is applied to disturb the spin system from equilibrium, the magnetization relaxes towards equilibrium, and an oscillating current (FID) is induced in the coil. This signal is amplified, filtered, and captured by analogue-to-digital converters to allow for processing and analysis on a computer. Because the signals oscillate as quickly as several hundred MHz, the quadrature receiver combines the N M R signal, which oscillates at the Larmor frequency UJQ, with the reference signal to generate a new signal with the relative Larmor frequency Q.Q. re ^0 — ^0 ~ (1.14) ^ref The range of f2 values is typically in the kHz range, reducing the speed requirements of the analogue-to-digital converters, and reducing the amount of data that must be collected and processed. Depending on the exact value of co f, there may be some signals with oscillation frequencies larger than to f, and some with oscillation frequencies smaller than u> f due to chemical and other resonance shifts. In order to separate frequencies above u f from those below, the receiver supplies two output signals, which for exponentially decaying resonances, are of the form: 0 re re re re s (t) oc c o s ( £ V ) e " t / T 2 s (t) oc sin(f2 t)e" t/:r2 A B (1.15) 0 The two signals can be combined into a complex signal s(t), s(t) = s^(£) + is sit) and positive and negative values of Qo can then be distinguished. Note that a more general 5 form of s(t) is s(t) = because normally the N M R signal is a superposition of signals with different relative Larmor frequencies in the system. The time domain signal s(t) can then be converted into a frequency spectrum by Fourier transformation, X^'(0> (1.16) if we substitute s(i) into Equation 1.16, we obtain: S (tt) = a L ( Q ; Q ) t J ; (1.17) 9 Chapter 1. Introduction Q;) caled a; where L(Q; is the complex Lorentzian, and is the amplitude. The real part of L(Q; Cli) is called the absorption Lorentzian Re{L(f2; fij)}: Re{L(fi;fi ' = (i7wr|^ <> )} 118 and the imaginary part is called the dispersion Lorentzian Im{L(f2; Qi)}: •i-Wn=ft)}- J ( ^ ^ , (!•") The full-width-at-half-height (FWHH) of the absorption Lorentzian is just ^ Hz, with the important implication that a fast signal decay leads to a broad peak and a slow signal decay leads to a narrow peak. 1 . 7 I n t e r n a l S p i n i n t e r a c t i o n s The external spin interactions involve the interaction with the magnetic field generated by the external static B field' and an oscillating Bi field which is perpendicular to it. The internal spin interactions involve interaction with the magnetic and electric fields generated by the sample itself. The internal spin interactions are the interactions we are interested in because they encode information (eg. distances, angles, bonding) about the spin system. For spin 1/2 nuclei, the relevant internal spin interactions are chemical shift, J-couplings, and dipole-dipole couplings. A l l of these interactions result in small perturbations of the resonance away from the Larmor frequency. The effect of each internal spin interaction is described below. 1.7.1 Chemical shift Nuclei of the same type can achieve the resonance condition at different frequencies because the local field each nucleus experiences is affected by its electronic environment. These bond-dependent shifts are known as chemical shifts. When a static field B* is applied, the ~S field will induce electron currents that produce small magnetic fields opposed to B*. (See Figure 1.5 (a)) As a result, the local magnetic field felt by each nucleus is given by: Blocal = B(l - o) (1.20) where a is the screening or shielding constant and o depends on the details of the electron wavefunctions in the vicinity of the nucleus. A chemical shift can be expressed as a frequency differences in Hertz with respect to a reference signal from a standard solution, but since it will depend on the ~~§ field, chemical shift is typically reported in ppm (parts per million): . . Chemical shift WP™) = Chemical shift from reference Spectrometer frequency 6 X ° ( } Chapter 1. 10 Introduction (a) shielding Figure 1.5: Internal spin interactions for spin 1/2. (a) Chemical shift (b) J-couplings (c) Direct dipole-dipole couplings. f A JAX fx J A X -*• Figure 1.6: Line splitting for a two spin 1/2 system ( A X ) with J-coupling constant JAX- 1.7.2 J-couplings The J-coupling between nuclear spins arises from the influence of the bonding electrons on the magnetic fields created by the nuclear spins.(See Figure 1.5 (b)) While the chemical shift indicates the local electronic environment, the J-coupling provides a direct spectral manifestation of the chemical bond. If two spins 1/2, A and X , are coupled to each other with a coupling constant J Hz, and if J is larger than the linewidths, then the peaks of A and X will each be split into two peaks separated by J Hz. (See Figure 1.6) The peak of A in system A X will be split to 2nl + 1 lines if there are n spins of X interacting with the nucleus A . The value of the coupling constant depend on the molecular geometry and the number of bonds between coupled nuclei. For protons in organic materials, three-bond J-couplings are typically around 7 Hz. One-bond J-couplings between *H and C are typically around 135 Hz, while one-bond J-couplings between directly-bonded C spins are usually around 50 Hz. In solid state, J-coupling typically does not result in a clear separation of line splitting because typical linewidths obtained in the solid state (100Hz - 10's of kHz) are often greater than the J-coupling. n 1 3 1 3 11 Chapter 1. Introduction 1.7.3 Dipole-dipole couplings Dipole-dipole couplings represent the direct magnetic interactions of nuclear spins with each other. Since each nuclear spin represents a magnetic moment, it generates a magnetic field Bi i, looping around in the surrounding space according to the direction of the spin magnetic moment. A second nuclear spin interacts with this magnetic field. (See Figure 1.5) The local field Bi i at a nucleus I, generated by a nucleus S (in the high field approximation where only the secular part of the dipole field is retained) is given oca oca = * < / " W -'> IS (1.22) R where p is the magnetic moment of S, rjs is the internuclear distance, and 9 is the angle between the internuclear vector and the ^ field. Thus the dipolar Hamiltonian is given by: s H = ~^7j (3cos .g fi2 D 2 /s - 1)7,5, (1.23) where po is the permeability constant. The constant term in front of Equation 1.23 corresponds to the magnitude of the dipolar interaction which is: d I8 =i p ^ ' (1-24) Equation 1.24 provides the through-space coupling in units of Hz. For example, two H spins separated by a distance of 2 A experience an interaction djs = —15 kHz. The interaction goes down according to the inverse cube of internuclear distance, and scales linearly with the gyromagnetic ratio of each interacting spins. Note that the dipolar Hamiltonian in Equation 1.23 is orientation-dependent, and since the 6 changes as the molecule rotates the consequence is that in an isotropic liquid where molecules can rotate freely, the intramolecular dipolar-dipole couplings will average to zero. 1 12 Chapter 2 A n Introduction to P F Polypyrrole 2 . 1 P F g D o p e d C o n d u c t i n g P o l y p y r r o l e 6 Doped B e l o n g s t o t h e C l a s s o f P o l y m e r Conducting polymers are conjugated polymers, namely organic compounds that have continuous overlapping IT orbitals, resulting in delocalized bonds along the polymer backbone that create a band structure similar to that found in semiconductors. Chemical structures of some common conducting polymers including polypyrrole are shown in Figure 2.1. When electrons or holes are introduced to the polymer chains, a process called doping, those positive charge carriers (holes) and negative charge carriers (electrons) enable electric conduction. The typical range of the electrical conductivity of P P y relative to other materials is shown in Figure 2.2. The electronic states of the polymers can be reversibly controlled by doping (oxidation-reduction processes), and the oxidation state is related to tunable changes in properties: structural, mechanical or optical, which leads to the use of conducting polymers in a host of applications including actuators, electrochromatic devices, and supercapacitors. In electrochemical doping, the conducting polymer is in electrical contact with an electrode in an electrochemical cell. Electrons are added to or removed from the polymer via the electrode, thereby changing the oxidation state. The oxidation process leads to extra holes or electrons on the polymer chains (called p-doping or n-doping), which are balanced by the flux of ions to or from the electrolyte to maintain the electroneutrality. These ions are referred to as dopants or counterions. PFg doped polypyrrole in this study is prepared electro chemically and is a p-doped conjugated polymer when oxidized. PFg dopant ions are incorporated inside the polymer to balance the charge. (See Figure 2.3) The doping level of the oxidized state (as-grown state, see experimental section) reaches one dopant ion for every three to four monomers. Electrical conductivity of polypyrrole in the oxidized state is typically 3 ~ 4 x 10 S/m compared to ~ 1 x 10 S/m in the fully reduced state. 4 1 Chapter 2. An Introduction to PF Doped Polypyrrole 6 Polypyrrole C Ts/cm) Vlty '° 6 ,Ox Re ^ 10"' v IP' 10"'° 10' 3 ^ s Figure 2.2: Conductivities of polypyrrole relative to other materials. 13 Chapter 2. An Introduction to P F g Doped Polypyrrole PPy + PF oxidation PPy (PF ) + + 6 6 14 e" reduction + (PF ) 6 0 + ne Figure 2.3: Redox reaction of PPy in the presence of P F 2 . 2 P F 6 D o p e d P o l y p y r r o l e a s n 6 anions. M u s c l e - L i k e A c t u a t o r s As noted above, many properties of technological interest related to conducting polymers result from oxidation-reduction (redox) processes. When a neutral conducting polymer is electrochemically oxidized by applying sufficient potential in an electrolyte, positive charges (holes) are generated along the backbone and solvated counterions (dopant ions) are forced to enter the polymer to maintain electroneutrality. This promotes the opening of the polymeric structure and a significant increase in free volume. (See Figure 2.4) Opposite processes occur during reduction: electrons are injected into the polymer, positive charges are eliminated, and the dopant ions and solvent molecules are expelled into the solution. The redox properties of conducting polymers that are responsible for reversible and controllable changes in volume open new possibilities for the development of actuators often referred to as artificial muscles. PFg doped polypyrrole is one of the most promising polymer actuators for artificial muscles because it can attain moderate strain (~ 2%) at low working potential. It is believed that the actuation is due to the dimensional changes produced by electrochemically inserting PFg ions into the polymer electrode. The cations in normal cases are selected to be big enough to prevent then from entering the polymer, so that the volume changes are attributed to dopant ions only. Chapter An Introduction 2. Figure 2.4: Volume changes in P F reaction. 2 . 3 C o m p a r i s o n A c t u a t o r s 6 6 Doped Polypyrrole 15 doped polypyrrole when it is subjected to a redox b e t w e e n a n d to PF O t h e r C o n d u c t i n g A c t u a t i o n P o l y m e r T e c h n o l o g i e s Nature's skeletal muscles demonstrate the most impressive actuator that engineers have been trying to mimic. They provide billions of work cycles involving contraction of more than 20%, generate stresses of ~ 0.35 MPa, and contract at 50% per second with maximum efficiency of ~ 40% [13]. State-of-the-art conducting polymer actuators operate at voltages of a few volts and can generate high strains (~ 26%), high strain rates (~ 12%/s ), and stresses up to 100 times greater than those of mammalian muscles (~ 34 MPa) [13]. However, the drawbacks related to conducting polymers are: (1) the need for encapsulation: they generally need to be wet and so must be sealed within flexible coatings; (2) low energy conversion efficiency: typically < 1%; (3) relatively short cycle life: the actuator performance usually degrades after several thousand cycles [14, 15]. While ionic electroactive polymers (EAPs), including conducting polymers work on the basis of electrochemistry - the mobility or diffusion of charged ions; there are other types of EAPs that are driven by electric fields such as dielectric elastomers . Actuation of dielectric elastomers is mainly caused by Maxwell stress, which results from the attraction between charges on opposite electrodes and the repulsion between like charges. These systems can generate strains of 120%, stresses of 3.4 MPa, and a peak strain rate of 34000%/s for 12% strain [13]. The major shortcoming of dielectric elastomers is the requirement of high activation voltage - typically 1 — 5 kV, which limits their use in the mobile devices. Some other common materials for actuation besides EAPs are piezoelectric ceramics and shape memory alloys. In piezoelectric materials, mechanical stress causes crystals to electrically polarize and vice versa. When a voltage is applied across a piezoelectric material, it will deform. The efficiency of piezoelectric materials are very high, up to Chapter 2. An Introduction to PF Doped Polypyrrole 6 16 90%, and the response is fast. The disadvantage is the small strain of less than 1%, yet they have found use in producing motions on the order of nm in the control of scanning tunneling microscopes. Shape memory alloys (SMA) actuate through phase changes in crystal structures. A temperature difference of only about 10°C is necessary to initiate this phase change. These materials can generate strains of up to 8%, stress of up to 200 MPa but require the inefficient conversion from thermal energy to mechanical energy. [13, 16] There are many other types actuators around which are reviewed in Madden et al. [13]. A l l of these actuators have their advantages and disadvantages, and efforts are being made to improve their performance. Because polymer actuator can generally be small, light and cheap in addition to its low operating voltages and high stress, many future actuator applications are expected to be based on polymer materials. 2 . 4 S y n t h e s i s o f D o p e d P F g P o l y p y r r o l e The conditions during synthesis of PPy determine the physical properties of the resulting polymer to a great extent. In this work we follow the methods of Yamaura et al. [17] for synthesizing PPy, and the subsequent electrochemical experiments are done by methods developed in collaborator Dr. John Madden's lab. 2.4.1 Electrodeposition The oxidative polymerization of polypyrrole (PPy) was carried out galvanostatically at a current density of 0.125 m A / c m at —30°C from a solution of 0.6 M purified pyrrole, 0.05 M tetraethylammonium hexafluorophosphate (C^Hs^N+PFg (TEAP) and 1% distilled water by volume in propylene carbonate C 4 H 0 3 (PC). The chemical structures of T E A P , P C , and pyrrole monomers are shown in Figure 2.5. The electrolyte was deoxygenated with nitrogen before use. Polypyrrole was deposited onto a polished glassy carbon substrate for a duration of 8 hours, resulting in nominal film thickness of approximately 16 pm ~ 26 pm and density of ~ 1.5 g/cm . A copper sheet is used as counter electrode. Nonconducting Kapton tape is spirally wound to mask the glassy carbon crucible's surface, so that strips of polypyrrole films with a width of 1 cm can be produced. The as-grown film from the above experimental conditions is in its oxidized state with an equilibrium electrochemical potential ~ 0.4 V vs. Ag/AgC104, and ~ 0.5 V vs A g / A g C l in different depositions. Figure 2.6 shows the schematic deposition setup and the synthesis conditions. Note that in the ion content experiment, all potentials are reported against Ag/AgC104- However we found that the potential of the Ag/AgC10 reference electrode drifts on a time scale of weeks, thus in all other experiments the potentials are reported against Ag/AgCl. 2 6 3 4 Chapter 2. An Introduction to P F 6 Doped Polypyrrole Pyrrole Molecular Formula C H N Molecular Weight 67.09 Density 0.967 g/ml 4 5 TEAP Molecular Formula q Molecular Weight 275.22 F NP Molecular Formula Molecular Weight C H 0 102.09 g CH 4 6 3 I 0 3 / O Figure 2.5: Chemical structures of T E A P , P C and pyrrole monomer. •> Galvanostatic depostion at 0.125 mA/cm Deposition electrolyte: 0.05M TEAP, 0.6M pyrrole, and 1% water in PC Working electrode: Glassy Carbon .> Counter electrode: Copper sheet -> Polypyrrole thin film Figure 2.6: Polypyrrole deposition setup and synthesis conditions. 17 Chapter 2. An Introduction to PF Doped Polypyrrole e 0.02 r -0.1 I -0.12 1 0 ' 500 ' 1000 Time (s) 1 1500 18 1 2000 Figure 2.7: Time response of reduction current during potentiostatic discharging of PPy films. 2.4.2 Electrochemical Reduction Subsequent reductions of the as-grown film were done potentiostatically in a threeelectrode cell at several potentials in P C containing 0.05 M T E A P . For the ion content study, samples S2, S 3 , and S4 were reduced to potentials of E = 0.2 V , —0.2 V , and —0.4 V vs Ag/AgClC>4 respectively. For the other studies, sample S -S' were reduced to E — 0.25 V , -0.2 V , -0.4 V vs Ag/AgCl. Different oxidation states of polymer films refer to their open circuit potentials vs a reference electrode. As-grown P F g doped films are reduced directly on the glass carbon crucible to achieve the best electrical contact between the working electrode and the polymer. Carbon fiber paper is used as counter electrode to maximize the electrode surface area. When each potentiostatic discharging had reached its equilibrium (See Figure 2.7), a strip of polypyrrole film with area 1 cmx4 cm was peeled off the glassy carbon surface and rinsed thoroughly with propylene carbonate. For the ion content experiment, the films were left in ambient environment for two days and flattened into sheets to make them easier to handle. For all the other measurements, the films were soaked in P C containing 0.05M T E A P for two days and rinsed with pure P C immediately before use. 2 2.4.3 4 Conductivity Measurement The electronic properties of conducting polymer films were characterized through conductivity measurements. It is advantageous to have high conductivity since it reduces the IR drop (potential difference) along the polymer. The conductivity is measured using a four-point probe method to avoid contact resistance. Four thin copper wires are Chapter 2. An Introduction to PF Doped Polypyrrole 19 6 forced to contact the two ends of the polymer strip and are directly connected to an HP multimeter for four-point measurement. Conductivity o is then calculated based on: R - l - l - L - (2.1) where I is the length of the film between the center two probes, w is the width and t is the thickness of the film. Since conductivity is achieved by percolation of charge carriers through ordered regions, it is dependent upon microscopic polymer morphology, and therefore is extremely sensitive to various experimental parameters, for example, the electrode preparation, deposition current density, and temperature. The maximal conductivity of our as-grown film is obtained to be 323 S/cm. 20 Chapter 3 PFg Ion Content in the PPy Films as a Function of Oxidation States - 3 . 1 E x p e r i m e n t a l 3.1.1 M e t h o d ID P Spectroscopy 31 Our ID P N M R experiments were performed on a homebuilt N M R spectrometer working at 8.4 T with a solid state probe tuned for phosphorus at 147 MHz. Sheets of PPy films were placed neatly inside the sample tube and oriented so that the sheets' normal was always perpendicular to the R F coil axis to minimize the R F loading of the probe's resonant circuit, which manifests itself as a lowering of the quality factor (Q) of the probe. The ID N M R phosphorous spectra of P P y films were obtained by single 7r/2 pulse excitation and were referenced to an external potassium phosphate ( K H 2 P O 4 ) standard solution in order to obtain quantitative information of the film samples. The P peak in K H 2 P O 4 is well separated from the P peak in T E A P allowing correct intensity integration. The time between each acquisition was always >5 times longer than the longest Ti to ensure full relaxation. 3 1 3 1 3 1 3 . 2 R e s u l t s Four pieces of PFg doped P P y (Si to 5 4 ) were prepared in four different oxidation states at E — 0.43 V, 0.2 V, -0.2 V, -0.4 V vs Ag/AgC10 . Each piece, along with a capillary of the standard solution KH2PO4 was placed in an N M R tube. Figure 3.1 shows a typical ID P spectrum of the sample. The sharp peak near 1 ppm corresponds to the phosphorus of K H P 0 . The broad peak is due to PFg ions inside the P P y film. The N M R line from PFg ions in the P C solvent showed the expected J-splitting pattern, but when in the films, an additional broadening masks the J-splittings. The lineshape of ions in the films can be reproduced from the J-split line observed in the solvent by convoluting with a 600 Hz F W H M Gaussian function. Relaxation measurements, described in Chapter 4, reveal that the ions tumble rapidly, suggesting that this 600 Hz broadening is likely due either to couplings to other spins inside the films or to magnetic field inhomogeneity rather than intramolecular P-F dipolar couplings. Because the number of K H 2 P O 4 molecules in the standard is known, the number of 4 3 1 2 4 Chapter 3. PF Ion Content in the PPy Films as a Function of Oxidation States 21 6 50 -50 0 -100 -150 -200 -250 Chemical shift (ppm) Figure 3.1: The broad peak is the P P y peak and the sharp peak is KH2PO4 peak. P F ions in the films can be obtained from a comparison of the integrated intensity of the peaks according to 6 Number of P in P F J ions Integrated area of P P y peak Number of P in K H P 0 ~ Integrated area of KH2PO4 peak 3 1 (3-1) 3 1 2 4 The number of dopant ions divided by the film's initial mass (mass of the film before reduction) is plotted against the electrochemical potential E in Figure 3.2, and the four points can be fit into a straight line. The result provides direct evidence for ion insertion mechanism of actuation since the number of dopant ions increases linearly with increasing oxidation potential. With known total deposition charges spent, sample weight, and number of PFg ions in each sample, the number of pyrroles and solvent molecules in each sample can be extracted from Equations 3.2 and 3.3, where Q is the total deposition charge, N , Ni, N i are the number of pyrroles, PFg ions, and solvent molecules, and m is the total mass. (3.2) Q 2N + Ni p so P m = Nm p p + Ni'nii + N sol m aol (3-3) Chapter 3. P F Ion Content in the PPy Films as a Function of Oxidation States 22 6 7e+17 linear fit too 6e+17 CO OO c3 .2 "3 5e+17 4e+17 a 3e+17 PL, 2e+17 4) 1 le+17 s 0 -0.6 -0.4 -0.2 0 E(V) vs Ag/Ag 0.4 0.2 0.6 + Figure 3.2: Number of P F ions per unit mass of PPy films at different oxidation states. 6 The doping level (expressed in terms of ion to pyrrole ratio, Ni/N ), as well as solvent molecule to pyrrole ratio (N i/N ) as functions of oxidation state are shown in Table 3.1. Conductivity information of each sample is also included in Table 3.1 for reference. p so 3 . 3 p D i s c u s s i o n Previous investigations regarding doping levels of doped conducting polymer have relied on elemental analysis and X-ray photoelectron (XPS) spectroscopy to measure dopant concentration [18, 19], but both techniques are destructive and insensitive to chemical environment, and X P S also suffers from the fact that only a thin layer of the polymer is probed. ID P N M R is a noninvasive tool used here to measure PFg ion content, and because P is only contained in PFg ions, selective information can be obtained without any ambiguity. To the best of our knowledge, systematic measurements on doping level vs. oxidation state have not been carried out previously. Our experiments have shown that the ion content increases in a linear fashion with the electrochemical potential of the polymer,, directly confirming the ion intercalation mechanism of actuation. With known ion content, the number of pyrroles and solvent molecules per unit mass can be easily extracted. The obtained doping level for the asgrown (S-L) sample (Ni/N = 1/3.83 = 0.26) is consistent with previously determined values which is 0.25 [20, 21] and 0.27 [22] in the literature. This suggests that all the 3 1 3 1 p Chapter 3. PF Ion Content in the PPy Films as a Function of Oxidation States 23 6 Table 3.1: Doping levels of samples S1-S4 in terms of ion to pyrrole ratio (Ni/N )and solvent molecule to pyrrole ratio (N i/N ). Conductivities are determined by a four point probe method. P so PFg doped PPy samples Si (as-grown) s2 S Si 3 P E(V) vs Ag/Ag+ Conductivity (S / cm) 250 189 13 0.23 0.43 0.2 -0.2 -0.4 Ni/Np 1/3.83 1/6.23 1/10.63 1/21.26 N /N sol P 1/0.67 1/0.92 1/0.63 1/0.74 ions are detected, and examining ion content via ID P N M R spectroscopy seems to be a reliable and straightforward method. The ion concentration inside the oxidized film is calculated to be at least 2 M (number of moles of PFg ions divided by the film volume). Note that we assume a uniform deposition in this ion content analysis and it is believed that the cation (tetraethylammonium, N(C2H )^") is unable to enter the films because it is much larger than PFg ion [22, 23]. In addition, doped polypyrrole resembles a capacitor in a way that the amount of charge can be stored in relation to the strength of the applied potential ( Q oc V), but charge does not accumulate on two conductors separated by a dielectric. Instead the charge accumulates inside the polymer film, at interfaces between the polymer and the enclosed solvent. Because of the porous nature of the films, they have a high surface area and thus a high capacitance. 3 1 5 24 Chapter 4 Rotational Motions of P F ^ Ions in the PPy Films 4 . 1 R e l a x a t i o n T h e o r y Because the relaxation of P in PFg ions is due to the dipolar couplings from F that are modulated by the rotation of the ions, the rotational motions of PFg ions in the P P y films can be accessed by measuring the P Ti relaxation time. Before describing the experimental results, we begin by presenting a brief introduction to relaxation theory and the analytical relations between the rotational dynamics and the Ti relaxation. The most important relaxation mechanism for spins l/2 is often the through-space dipolar coupling. There are intramolecular dipolar interactions inside a molecule and the intermolecular dipolar interaction among spins of different molecules. In the interior of a molecule, the variation of dipolar coupling of spins arises almost uniquely from the rotation of the molecule, the variation of the distance between the spins due to vibrations being negligible. (See Figure 4.1) We will discuss the case of intramolecular interaction only as it is the case of P relaxation in PFg ions. The general approach to relaxation theory we will pursue involves the spin density matrix. We shall describe the framework of this semi-classical relaxation theory below and show how the T i and rotational correlation time r are linked together in the spin-1/2 case. For details of the derivation we refer to Abragam [24]. We consider a spin system of Hamiltonian H = H + Hi(i), where H is the main static Hamiltonian, and Hi(t) represents all of the fluctuating interactions responsible for relaxation. The density matrix operator a contains all of the physically significant information about the ensemble of spins. We can write the equation of the evolution of the density matrix (evolution of the spin system): 3 1 1 9 3 1 : 3 1 c 0 da •i[{H + Hyl<x]. Q ~dt 0 (4.1) We can isolate the effect of the fluctuating Hamiltonian by switching to the Heisenberg picture, in which it is the observables that vary with time. In the Heisenberg picture, we consider a(t) = exp(iH t)a exp(—iH t). Equation 4.1 becomes: 0 0 da ~dt = -^(0,5], (4.2) Chapter 4. Rotational Motions of PF Ions in the PPy Films 6 25 Local Dipolar Field Molecular Tumbling Figure 4.1: Modulation of the local dipolar field by molecular rotations. By integrating Equation 4.2 and taking its average over all identical molecules of the sample (represented by the bar), we obtain: o{t) = ?(0) - i f [H\(t'),a(t')]dt! Jo (4.3) An approximate solution to Equation 4.3 can be found by iteration: o{t) = o{Q)-i Jo [H^MVW - dt' Jo df[W (t),[H (t''),o(0)}} + .-. 1 Jo 1 (4.4) The first integral on the right hand side vanishes because the dipolar coupling averages to zero in solution, so the leading non-zero term becomes: o(t) - o(0) = - f dt' f dt''[%(t),[%{t"),d{0)]\ Jo Jo (4.5) To deal with this integration, we assume the fluctuating Hamiltonian H\(t) takes the form: H {t) = Y,V F (t) x a a (4.6) a where the V is the spin operators and the F are random functions. The autocorrelation function of the random function F is defined as: a a a F (t)F;(l') a = G (\t-t'\) aP (4.7) Chapter 4. Rotational Motions of PF 6 Ions in the PPy Films 26 Equation 4.5 can be written in the following form: a f dt' f Jo Jo dt"G {\t'-t/'^e^ '-^"^ (4.8) 1 a0 The integral in Equation 4.8 is exactly the Fourier transform of the autocorrelation function G p, which can be represented by a spectral density function J (cj): a a/3 roo J p(w)= a / Jo G a P (\t-t'\)eM-iu\t-t'\)d(t-t') (4.9) It can be shown that the dominant contributions to Equation 4.8 are the terms where a. — P, therefore from now on we retain only the relevant terms, and will denote the function J by J . With the assumption that o(t)—o(0) is small, we have approximately: aa a a{t) - o(0) ^ do t dt Equation 4.8 becomes : do = dt ( - °e )]]J M. ? (4.11) a q This is the master equation for the evolution of the density matrix under the effect of a random perturbation. The expectation value of the physical observable Q in an ensemble can be obtained from (Q) = Tr(Qo), therefore the master equation for the relaxation of a physical variable is the following: = - J > K ) { ( [ [ Q , V ] ,V2]> - <[[Q, V ], V^]) } a ^ a a (4.12) eq In the case of dipolar relaxation between two spins of 1/2, the dipolar Hamiltonian takes the form: H, = -^{t.t-3I 1 2 l z I 2 z } (4.13) where r is the distance between I\ and I . In order to perform relaxation calculations, we must express E\ as a sum of products of spin operators and random field operators. By expressing the I\, I in spherical coordinates, we obtain the proper representation for the dipolar Hamiltonian where 9 and (p are random functions of time: 2 2 2 //i, = 2 -^53F*((?^)r (/ / ) m 1> 2 . (4.14) Chapter 4. Rotational Motions of PF Ions in the PPy e 27 Films with F = y|(3cos 0-l) F±i = sin 9 cos 9 F = 0 ±2 ± 2 exp(±i(p) 3/2sin <9cos6>exp(±i0) 2 To =• T±i T (4.15) 2 = = -j=(3h I z-t-t) z 2 Tl/2(/i±/ , + l/2/ / hzh±) 2 1 ± 2 ± In principle, once we have the Hamiltonian in the appropriate representation, then we can evaluate the evolution of the desired observable I using the master equation (Equation 4.12). We now show the results for longitudinal relaxation (Ti) in the case of two spins 1/2, by substituting I , the longitudinal spin operator, in place of Q in Equation 4.12 and simplifying. We find: z z d(Iu) - (hzU) - Pcross{{hz) - -Pl({hz) = dt (hz)e ) (4.16) q with Pi = 1 1 7i 7 fi 2 2 { 2 2 10 P C T 0 S S 3 1 r-6 ° \ 1 + o;?r T _ 17 ^ % ~ 10 T T-6 c f c \ l + 1+ ( 2 + 6 - u; ) r 2 Wl 2 a 1 + 1 + (( + c u 1+ ( ; )2 2 2 r Wl \ +w)r ) 2 Wl 2 2 c \ 1 6 (( ; 2 _ ^ 2 { ' (Am J where pi corresponds to the longitudinal relaxation rate 1/T and to\ and u are the Larmor frequencies of spin 1 and spin 2 ( i i , i ) . r is a time scale that characterizes the decay time of the autocorrelation function G(\ t — t |) and is referred to the rotational correlation time in the case of two spin 1/2 dipolar relaxation. Through Equation 4.17, we are able to probe the rotational correlation time r of the nucleus by measuring T i . If we plot the longitudinal time constant Ti against the rotational correlation time r , typically we get the curve shown in Figure 4.2. Molecules in gases have the lowest correlation times at room temperature, followed by small molecules in non-viscous liquids. Notice that there also exists a cross-relaxation between the longitudinal magnetization of the spin i i with that of i in Equation 4.17. This coupling is the basis of the Overhauser effect, described in Chapter 5. 1; 2 c c c 2 2 \ Chapter 4. Rotational Motions of P F 6 Ions in the PPy Films 28 Figure 4.2: The spin-lattice relaxation time as a function of rotational correlation time for dipolar relaxations. pi pi/2 Figure 4.3: Inversion-recovery pulse sequence for Ti measurement. 4 . 2 E x p e r i m e n t a l 4.2.1 M e t h o d Relaxation Measurements P relaxation measurements were performed on a homebuilt N M R spectrometer working at 8.4T with a variable temperature probe tuned for phosphorus at 147MHz. A commonly used pulse sequence for measuring Ti is called inversion-recovery. It is given by 7r — r — | — AQ.(See Figure 4.3) The first pulse in the sequence is a IT pulse which tips the equilibrium magnetization M down to —M . The magnetization relaxes back towards thermal equilibrium during the interval r, and the process is monitored by the second pulse, which projects the net magnetization into the x-y plane. The signal intensity is therefore r dependent and can be fit with the function J(r) = IQ(\ — 2e i ) to extract T i . T relaxation can arise from numerous mechanisms and often cannot be correlated as easily to a single motional parameter. It does however give some measure of the motion of the spins. The faster the motion and the more homogeneous the spin's environment, 3 1 z z T 2 Chapter 4. Rotational Motions of PF 6 29 Ions in the PPy Films pi pi/2 111 « 1 / > ft A 2 Figure 4.4: Spin echo pulse sequence for T measurement. 2 the longer the T . The T measurement is routinely done by the spin echo sequence | — | — 7r — | — y4Q.(See Figure 4.4) The first | pulse tips the magnetization down to the x-y plane, and spins will start to dephase during the | period. Then a TT pulse refocuses the magnetization producing an echo signal. The experiment is arrayed with different^r, and the corresponding peak intensity is an exponential decay with r via I(T) = I§e 2 . 2 2 T 4 . 3 R e s u l t s In the case of the PFg ion, we assume that the dominant mechanism for phosphorus relaxation is the P — F intramolecular dipolar interaction from the isotropic rotation of ions. Neglecting the contributions from distant fluorines (not directly bonded), the Ti relaxation equation that describes the interactions of the 6 neighboring fluorines on phosphorus is given by Equation 4.19 if the motions of the fluorines are uncorrelated with that of the phosphorus. In the PFg ion, the motions are clearly correlated, but Equation 4.19is a good approxamation nevertheless [24]. 1 Ti = n F m\ 2 1 YpT h- U J 10 r F 6 3 Jprl 1 + (up 1+ - W ) T* F 2 (uj + upfrl (4.19) P where np is the number of directly bonded F to P . We examined the P Ti relaxation times on three wet P P y samples 5 -5 along with two P C solvent samples containing 0.05 M and 2 M TEAP-respectively. Because in solution state the molecules are tumbling quickly, they are in a fast motion regime where OJ T^ <C 1, the relationship between rotational correlation time r and Ti can be reduced to a simple form: 1 9 , 3 1 3 1 , 1 3 2 c i //A)\ 2 ipiW r can then be extracted easily from Equation 4.20. Results from the two solvent samples at room temperature are shown in Table 4.1. c Chapter 4. Rotational Motions of PF Ions in the PPy Films 6 30 Table 4.1: T i relaxation times and the rotational correlation times r of two solvent samples. c Sample 0.05M P C 2M P C 3 1 P Ti 4.10 4.10 (s) (PS) Tc 8.08 8.08 T, Figure 4.5: The effect of temperature on Ti depends on the the location of r with respect to the Ti minimum. c As for probing rotational motions of PFg in the films, it is insufficient to only measure Ti at room temperature because one Ti corresponds to two rotational correlation times according to Figure 4.2. Therefore, Ti of three PPy samples are measured as functions of temperature, because the effect of temperature on T depends on the the location of r with respect to the Ti minimum. (See Figure 4.5) For systems having long correlation times, warming the sample (reducing the correlation time) reduces Ti; for systems with short correlation times, warming the sample generally increases T\. The spin-lattice relaxation time constants as functions of temperature for three P P y samples that are in different oxidation states (Sj-S ) are shown in Table 4.2 and plotted in Figure 4.6. Ti of the oxidized sample S and the less oxidized sample S increase with temperature, suggesting that PFg ions are in the short correlation time limit. The reduced sample S has a nearly constant Ti over much of the temperature range. This plateau in Ti vs. temperature suggest that there may be additional relaxation processes. Since the PFg ions of samples S i and S are in the fast motion regime and the P Ti relaxation is due to the rotational motions of the PFg ion, we are able to obtain r of PFg ions in S[ and S' samples at room temperatures through Equation 4.20. Results are shown in Table 4.3. We have also measured T of both F and P in the film samples. Results are shown x c 3 x 2 3 3 1 2 c 2 1 9 2 3 1 Chapter 4. Rotational Motions of PF Ions in the PPy Films 6 Table 4.2: 3 1 31 P Ti relaxation times as a function of temperature of P P y sample S[-S' . 3 Temperature (°c) -30 -15 (-20 for S ) 0 22 40 3 1 2 P Ti of S[ (s) 2.02 2.22 2.70 3.08 3.36 3 1 P Ti of S (s) 1.80 1.78 2.27 2.96 3.37 . 2 3 1 PTiofS (s) ' 1.32 1.03 1.72 1.72 1.72 3 Table 4.3: Ti relaxation times and the rotational correlation times T of two P P y samples: S[ and S at room temperature. c 2 Sample s[ . s2 3 1 P Ti (s) 3.08 2.96 (PS) 10.76 11.19 Tc in Table 4.4. 4.4 D i s c u s s i o n The rotational correlation times of PFg ions observed in the as-grown sample S[ (10.76 ps) and the less oxidized sample S' (11.19 ps) are not very different from the rotational correlation time of ions found in the solvent (8.08 ps). This suggests that ions are contained in liquid pockets containing solvent molecules instead of at stable positions within the polymer matrix. Therefore, we believe the dopant ions reside in pores of the amorphous region of polypyrrole. The reduction of r in the reduced sample S is not so straight-forward as multiple relaxation mechanisms are possibly involved. However we suspect the rotational tumbling is further slowed down such that in this case the ions are on the slow motion side of the T l minimum (See Figure 4.2). The fact that each relaxation measurement is well fit by a single Ti relaxation constant indicates that either the motion of ions in the entire PPy sample is homogenous, or that 2 c 3 Table 4.4: T relaxation times of three P P y samples: S[-S' . 2 3 Sample s[ S s'3 2 3 1 P T (ms) 1.88 1.78 0.19 2 1 9 F T (ms) 0.79 0.58 0.10 2 32 Chapter 4. Rotational Motions of PF Ions in the PPy Films 6 PFg ions located in different pools communicate rapidly compared to T\. It is worth mentioning that the rotational correlation time of molecules traditionally can be derived from the Debye equation: T < - T ¥ V (4 - 21) with known solvent viscosity r] and estimated Stokes radius r . The calculated r of PFg ions in solvent from Debye equation at room temperature is 7.71 ps by using r vis s c s .= 2.08 A. (1.579+0.5, bond length of P-F plus the atomic radius of F) [25] which is in agreement with the r (8.08 ps) determined from the relaxation study. However the conditions of applying Debye equation to calculate r of ions in films are not well defined, therefore the use of Debye equation is not suitable for the studying rotational correlation times here. Discussions regarding T measurements are integrated into the discussion of Chapter 6. c c 2 33 Chapter 5 Solvent Accessibility of PF^~ Ions in the P P y Films 5 . 1 N u c l e a r O v e r h a u s e r E f f e c t ( N O E ) Nuclear spin cross-relaxation in liquids is caused by mutual spin flips (transitions between spin states) of dipolar-coupled spins which are induced by motional processes. Cross-relaxation leads to a transfer of magnetization between the spins, known as the nuclear Overhauser effect(NOE). The NOE is extremely important in the determination of molecular structure because it provides constraints on the distances between various nuclei. These constraints allow the complete determination of the 3D structure of large biomolecules. From the above relaxation section, we've already arrived at the equation that describes how I\ of the two-spin system evolves with time. The most striking manifestation of the Overhauser effect is the steady state value of (I\ ) when the spin I is saturated, so that (I ) = 0. To satisfy the steady state condition, we have = 0, then Equation 4.17 becomes: z z 2z 2z d ^ dt = 0 = - ((I ) I u ) Pl - (I ) ) + p oss(hz)e lz (hz) = (hz)e eq CT q + —(hzU q I T lz (5-2) Pi \ l i (5-1) (hz) eq I e rcross where rj is the N O E enhancement factor. Due to the cross relaxation, the signal of spin 1 is enhanced by a factor of 1 + r\ when saturating spin 2. The NOE enhancement factor depends on the correlation time, hence the motion of the molecules. In the limit of very rapid molecular motion (small r ), becomes: c (/l ) 2 = (/lz)e {l+^} = (/l,)e [l + ^ } 9 g (5-3) with the equilibrium magnetization being proportional to the gyromagnetic ratios. Here we see a rather disappointing result that the NOE enhancement factor rj is predicted to Chapter 5. Solvent Accessibility of PF 34 Ions in the PPy Films 6 be independent of r, however this applies only for the completely artificial circumstance of two dipoles totally isolated from all other sources of relaxation. In a reality, two- spin system may show distance and correlation time dependent NOE enhancement: (5.4) ' ncc^ when other competing sources of relaxation are present. This is the basis for using the N O E to compare internuclear distances in different molecules. Cross-relaxation and nuclear Overhauser effects can be studied by ID Nuclear Overhauser Difference Spectroscopy where N O E enhancement is obtained by selectively saturating one spin while observing the intensity changes in other spins. 5 . 2 E x p e r i m e n t a l 5.2.1 M e t h o d ID NOE Difference Spectroscopy In measuring the NOE enhancement between solvent proton H and P in PFg ions, we saturate the solvent H resonance with a long train of weak 7r/2 pulses and then compare the intensity of P with its equilibrium value. This can be simply done by integrating the P peak with and without H radiation, and then taking the difference. The actual pulse sequences used are (See Figure 5.1): (1) [ f ( H) - r ^ — " _ - f ( P) - AQ. (2) [f OH) — — r — f ( P) — AQ where n = 50 is the number of repeats and T\ — 2 ms, r = 248 ms, which are arbitrarily chosen as long as they are <C T i of H . Note that the pulses tuned to the solvent protons are weak enough to significantly affect only the *H in P C but not any protons attached to a more rigid polymer backbone. Sequence (1) is equivalent to a simple | pulse on P , and Sequence (2) is the same as (1) except for the additional H radiation. The N O E difference can be found by subtracting the perturbed and unperturbed spectra. Identical experimental conditions are ensured in both sequences in order to obtain the correct difference intensity. a 3 1 1 3 1 3 1 1 : 31 T 2 T l j P ° w e r - 31 o n 2 : 2 3 1 l 5 . 3 R e s u l t s ID N O E difference experiments are done on three wet PPy samples S' S' at E == 0.53 V, 0.25 V , -0.2 V vs A g / A g C l and on two P C samples containing 0.05 M T E A P , 2 M T E A P respectively in order to perform a comparative study among them. H radiation on protons of P C (C4H 03) is expected to affect the population distribution of F of PFg ions if they are close enough in space to relax each other. The fluctuating fields from the F will then in turn relax their neighboring P. If the relaxation processes involve relevant transition pathways which are correlation time r and the distance r dependent, a positive P signal increase will be observed due to H saturation. In order to compare the N O E results unambiguously, two solvent samples are used as control experiments, r 3 : 1 9 6 1 9 3 1 c 3 1 J Chapter 5. Solvent Accessibility of P F Ions in the PPy Films 35 6 r P i / 2 Figure 5.1: Pulse sequences for steady state N O E difference spectroscopy. Table 5.1: N O E enhancement factor 77 of the five samples. NOE 77 0.107 ±0.02 0.163 ±0.004 0.163 ±0.006 0.17 ± 0 . 0 2 -0.035 ± 0 . 0 3 Sample 0.05M P C 2M P C ' s[ S' 2 s'3 and identical experimental conditions are applied. The N O E enhancement factor 77 of P is calculated from Equation 5.5. 3 1 (Perturbed — Unperturbed) P peak intensity 31 01 . . (^D.Oj Unperturbed P peak intensity Results from the 5 samples are shown in Table 5.1 and Figure 5.2. 5.4 D i s c u s s i o n Samples S[ and S' exhibit similar 77 values to those of the solvent samples, implying that ions in the oxidized films are surrounded by solvent molecules in an environment similar to the free solvent. The much smaller (consistent with zero) N O E enhancement 2 Chapter 5. Solvent Accessibility of P F 6 Ions in the PPy Films 36 of the reduced sample S' seems to indicate that PFg ions in the reduced sample are more tightly coupled to the P P y backbone, and are not contact with the solvent.(see Figure 5.2). This could suggest that between the oxidation state 0.25V and —0.2V, the films may undergo some significant structural changes, causing ions in S to reside in a much less solvated environment than ions in Si and S . 3 7 3 2 0.05M PC Figure 5.2: NOE enhancement factor rj of the five samples. 37 Chapter 6 Translational Motions of PF^~ Ions in the P P y Films 6 . 1 P u l s e d - F i e l d G r a d i e n t ( P F G ) N M R The use of pulsed-field gradient N M R to study translational self-diffusion originating from Brownian motions was first suggested by McCall, Douglass and Anderson[26] and first demonstrated by Stejskal and Tanner in 1965[27]. The Stejskal and Tanner pulse sequence (pulsed gradient spin echo sequence) involves a spin echo plus two magnetic field gradient pulses:| - T(PFG) - IT - T(PFG) (Figure 6.1). By imposing two gradient pulses separated by A with amplitude g and duration S in a spin echo sequence, spins are labeled spatially as their local Larmor frequency becomes u>(r) = jB + jg • f. In the absence of a gradient, there is no loss of phase coherence in the N M R signal following the | pulse. At the time of the first gradient pulse, there is a position-dependent phase shift, which may be said to record the spin's position along g. Following the gradient pulse, this phase shift persists until it is inverted by the IT pulse. A second phase change occurs at the time of the second gradient pulse. For nuclei that have not moved between the gradient pulses (during A , the interpulse separation), the phase shift of the second gradient pulse completely reverses the phase shift of the first gradient pulse, and the magnetization refocuses perfectly. Net motion results in incomplete refocusing at the end of the spin echo sequence, leading to an attenuated echo signal. Figure 6.1: Pulse field gradient spin-echo sequence (PFGSE). Chapter 6. Translational Motions of PF Ions in the PPy Films 6 38 Here we'll show how one can correlate the echo attenuation with diffusion in the case of free diffusion using the macroscopic approach, starting from the Bloch equations (Equation 1.13) containing diffusion terms: ^ = MxB-fi(M-M„) + flv M 2 7 (6.1) where D is the spin diffusion coefficient and the B field now is ~$ = (0,0,5 + ^ ( i ) ~(?(t) is 0 except during, the gradient pulses. If we define the transverse magnetization as m = M + iM , and plug it into Equation 6.1, we obtain: x y dm — Ot m = -iLU m, - xj(g 0 • r). - 2 — + DV m, (6.2) ±2 In the absence of diffusion (D = 0), m relaxes exponentially with a time constant T , and may be expressed as m = ip - >ot-t/T2 ^ r ^ j t h precessing magnetization unaffected by the transverse relaxation. If we substitute rn, into Equation 6.2, we have: 2 e iu w n e dip — e s e ' = -iy(g (6.3) • r)lp The simplified equation can be solved in two parts. Between the | pulse (/; = 0) and the 7r pulse (t = r) ip is given by ip = A exp(—ijf • F) (6.4) where 7 t y ) = f g(i)dt (6.5) Jo A corresponds to the value of I/J immediately following the | pulse. During the period from the f to 7r pulse each spin acquires a position dependent phase — jf • F. Because the effect of the TX pulse is to set back the phase of ip by twice the amount that it has advanced, in the period following the TT pulse we have: ip = Aexpi-i-yr • (F - 2/)) (6.6) where / = F ( r ) . We may use a single expression to represent the behavior of ip from the | pulse to the echo: ip{r,t) = Aexp{-iyr-(F-2H(t-T)f)) (6.7) where H is the unit step function H(t — r) = 0 when t < T, H(t — r) = l when t > r. We can now consider the solution of 'ip in the presence of diffusion by allowing A to be a function of t. By substituting tp(r, t) into: ^ = -ij(g • r)iP + DV vb 2 (6.8) Chapter 6. Translational Motions of P F 6 Ions in the PPy Films 39 We find. d A ® _ 2 _2H(t-T)f] A(t) ' 2 dt = J D[F Integrating Equation 6.9 from t = 0 to t = 2T, the echo attenuation E — Stejskal and Tanner pulse sequence can be obtained. ln[^] = = F dt-±f 2 ( 2 from the + jT'-j D[F - 2jfdt ln[E}= j*—?DF*dt - 7D (6.9) T Fdt + Afr) (6.10) 0 The calculation of the echo attenuation (Equation 6.10) is quite straightforward but rather tedious. For example, using the time dependence of g(t) in Figure 6.1, the integral of F(t) from t '= 0 to t = 2r is calculated as follows, F(t) = Odt-r / J0 gdt+ Jti Jti+S 0dt+ . gdt Jti+A = g(t + 6 - ti - A ) (6.11) And according to the definition / = F ( r ) , f is / = F(T)= fg(t)dt Jo = / 0dt+ Jo Jti gdt+ 0dt = g5 Jti+5 (6.12) After performing the symbolic algebra analysis, we obtain the relationship between signal attenuation and the diffusion coefficient for free diffusion (Equation 6.13). l n [ ^ ] = H E { 9 > A ) ]= - ^ W ( A - |). (6.13) The term | accounts for the finite width of the gradient pulse. Rearranging Equation 6.13, we find: A(2T) = A(0) exp[- V D^ (A - |)] 2 7 J (6.14) From the Bloch equations including the diffusion of magnetization, we can derive the necessary relationship analytically as shown in Equation 6.13. However, in the case of restricted diffusion the macroscopic approach becomes impossible to formulate, and a ' propagator formalism may be used to describe the result of the P F G N M R experiment. Chapter 6. Translational Motions of P F Time scale Free diffusion 40 Ions in the PPy Films 6 Restricted diffusion Figure 6.2: Features of molecule motions when undergoing free diffusion and restricted diffusion. 6.1.1 Self-Diffusion in Restricted Geometries In the P F G experiment, we probe the particle's motion by taking a measurement at time t = ti and a second measurement at time t = t\ + A . The key point is that in the P F G experiment the echo attenuation gives information on the displacement along the gradient axis that has occurred during the period A , and this displacement can be related to the diffusion coefficient. If a particle is diffusing within a restricted environment, the displacement along the z-axis will be a function of A , the diffusion coefficient, and the size and shape of the restricting geometry. Consequently, if the boundary effects are not taken into account and we analyze the data using the equation for free diffusion, we will get an apparent diffusion coefficient D , that is in general smaller- than the actual diffusion coefficient. Considering molecules diffusing inside a single pore of diameter a (characteristic length of the geometry), the observed motion will be strongly dependent on the time scale (see Figure 6.2). For short diffusion times A <§C a jD the diffusion will appear to be unrestricted because molecules have not diffused far enough to feel the effect of boundary. The diffusion coefficient determined will be the same as that observed for freely diffusing molecules. For long diffusion times A 3> a /D, because maximum mean displacement is limited by the pore diameter a, the root mean displacement ((n — r ) } becomes time-independent (where we have defined r as the starting position of a given molecule, and r\ its position a time A later), therefore the diffusion coefficient will be proportional to 1/A. At intermediate timescales (A « a j'D) the behavior may be quite difficult to characterize. Because at this time scale, Dart of the molecule's diffusion is app 2 2 2 0 0 2 41 Chapter 6. Translational Motions of PF Ions in the PPy Films 6 (a) Free diffusion (b) Restricted diffusion (isolated pores) • (c) A Restricted diffusion (connected pores) A • A Figure 6.3: Expected behaviors of D vs. A in free diffusion and restricted diffusions. restricted by the barrier and the mean squared displacement will not scale linearly with A , thus the measured diffusion coefficient (D ) will appear to be time dependent. For diffusion in connected pores, one can imagine the long time behavior will be different from that in isolated diffusion because the maximum mean displacement is no longer limited by the pore diameter. Therefore the observed diffusion coefficient at long times will not decrease as 1/A. Figure 6.3 shows the expected behaviors of D vs. A in free diffusion, diffusion in isolated pores, and diffusion in connected pores. To understand restricted diffusion' in P F G experiments, it is convenient to use a propagator formalism approach. One needs to consider the quantity P(ro | f i , A), the conditional probability of a molecule moving from position r to r in the time A . P ( r | r A) is often termed the diffusion propagator and it also obeys Fick's second law of diffusion [28], app 0 ap „jn,A ( r x ) = 0 D v 2 f , ( r n | r i | A l 5 ) ( 6 l 5 ) In the case of unrestricted Brownian motion, the solution of P(r \ ri, A) is a Gaussian distribution over molecular displacement, with a distribution width which expands with time: 0 P(r 0 | r i > A) = ( 4 7 r D i ) - 3 / 2 exp ( - ( n 'jf^j (6.16) The echo attenuation measured by the P F G experiment is just the Fourier transform of ) Chapter 6. Translational Motions of PF 6 Ions in the PPy Films 42 the diffusion propagator: E(g, A) = f [ p(r ,0)P(r 0 0 | r A) x exp (ijSg • (n - r )) dr dr u 0 0 (6.17) x where p(r , 0) is the starting molecular density (spin density). If we substitute Equation 6.16 into Equation 6.17, we retain the expected echo attenuation equation as in Equation 6.13. In the case of restricted diffusion, the solution of Equation 6.15 which is the diffusion propagator will deviate from its classic Gaussian form because different boundary conditions are imposed. We have to substitute the relevant p(ro,0) and P(r \ ri, A) in order to evaluate the corresponding echo attenuation equation. By understanding the the influence of restrictions on the form of the propagator, and hence the echo attenuation function in a P F G experiment, one can extract information not only about the motions of the molecules but also the geometry of the boundaries and thus about the pore morphology of the surrounding medium. However P(ro | r\, A) tends to be difficult to obtain for nontrivial geometries. 0 0 6 . 2 6.2.1 E x p e r i m e n t a l M e t h o d Pulsed-Field Gradient N M R Measurement A l l P F G N M R experiments were performed on a homebuilt N M R spectrometer working at 8.4 T with a diffusion probe tuned for fluorine F at 342 MHz. Measurements of signal intensity A(2T) are made with several values of gradient strength g, then fit to Equation 6.14 for given A , 7, 5 to extract the diffusion coefficient D. The diffusion coefficient can then be obtained as a function of diffusion time A by performing the same measurement at different A's. 1 9 Gradient C o i l Design The gradient coil design of the gradient probe used here is inspired by Cory's design [29] which was developed for solid state studies where diffusion coefficients are small. A Maxwell pair of coils is generally employed for producing gradients along the z direction in superconducting magnets because it is simple to construct, and good gradient profiles can be obtained with very few turns. A Maxwell pair consists of a set of circular loops with currents of equal amplitudes but opposite directions. This configuration generates magnetic field gradients symmetric about the mid-plane and about the central axis. The gradient profile and the gradient coil constant (defined as the gradient strength per unit current: T/m-A) in principle can be calculated via the Biot-Savart Law. In order to obtain larger coil constant and better gradient linearity, a gradient set is constructed from two building blocks. Figure 6.4 shows the configuration where 12 copper wires are wound on the inner side that is close to the sample, and 84 wires are wound on the outer side. The predicted coil constant is 0.27 T/m-A. Chapter 6. Translational Motions of P F 6 Ions in the PPy Films 43 3.5 cm 0.5 cm 1 "CZJD" Figure 6.4: A gradient coil set designed for higher coil constant and better gradient profile. The winding direction of upper two sets is opposite with the lower two sets. The total dimension is 3.5 cm x 4.5 cm. Gradient Calibration The gradient strength needs to be carefully calibrated to obtain an accurate diffusion coefficient D from a fit to Equation 6.13. Two methods were used on the home-built diffusion probe: (1) back-calculation of the coil constant from a diffusion experiment on H 0 using D = 2.3 x 1CT cm /s for pure H 0 at 25°C [30]; (2) a spin-echo experiment with P F G turned on between | and ir pulse during the acquisition, which gives a ID image of the sample and the effective gradient across it. The back-calculation method relies on the correct D value of the standard compound. All recent results in the literature are consistent with the value of D = 2.3 x 10~ cm /s for pure H 0 at 25°C, however since the N M R probe temperature inside the magnet may be as low as 18 — 21°C, we estimate D to be 2.03 x I O cm /s at 20°C according to [31]. The H signal intensity of H 0 is obtained as a function of unknown gradient strength g (g = gmax% where x is gradient amplitude from 0 to 1), and is fit to Equation 6.14 for g , given that A,j,5, and D (2.03 x 10~ cm /s) are known. (See Figure 6.5) The instrumental maximum gradient strength using the back calculation method is determined to be 480 G/cm. A cylinder sample filled with pure water was also used for ID image calibration. Fourier transforms return images of the sample cross-sections with respect to the gradient direction. For a cylinder sample with its long axis perpendicular 5 2 2 2 5 2 2 - 5 2 1 2 5 2 m a x to the gradient direction (z), we obtained a half circular image. (See Figure 6.6) The width of the spectrum Au is related to the sample radius r and the gradient strength g via: Au = ^ (6.18) Table 6.1 shows the results of Au at different gradient amplitude x (0-1) and the cor- Chapter 6. Translational Motions of P F 1 — r i i 6 Ions in the PPy Films i i 1 I ' 44 fit - - \ \ \ - \ \ \ - \ \ \ \ - \ \ \ \ - \ \ 0 1 1 0.1 1 0.2 0.3 N N. 1 0.4 1 0.5 ^_ -++ 0.6 - 0.7 0.8 0.9 Gradient amplitude x Figure 6.5: Signal attenuation of H intensity in H 2 O for gradient strength calibration. 1 responding g values calculated from Equation 6.18. From the fit of the data g(x), we obtained the gradient strength as g = 485.53 • x + 1.22 (G/cm), yielding a maximum g of 488 G/cm. We note that the maximum gradient strength based on the predicted coil constant of 27 G/cm-A and the maximum gradient current supplied 15.2 Amp (<?max = 27 x 15.2 = 410.2 G/cm) is in reasonable agreement with both of the empirical 5max values. Since the ID image calibration is the more direct method, along with the fact that we don't have a firm empirical value for D of water at the sample temperature, we will use the ID calibration result. Pulse Sequences for Diffusion Measurements The first and the most simple pulse sequence for measuring diffusion is the Stejskal and Tanner sequence, also known as the pulsed field gradient spin-echo (PFGSE) sequence: ^ — T(PFG)—7T — T(PFG) (See Figure 6.1). There have been many other pulse sequences developed since then to specifically meet different experimental needs, for example, to eliminate eddy current effects, and to deal with imperfection of gradient pulses etc. One commonly employed pulse sequence is the stimulated echo pulse sequence (PFGSTE): f - TI(PFG) - \ - r - § - n(PFG) - AQ (see Figure 6.7(a)). This sequence was designed to avoid T relaxation effects by storing the magnetization along the z axis during r , so that the relaxation depends primarily on T i , which is usually much longer than X for macromolecules. Longer diffusion times (A) can then be used. 2 2 2 2 45 Chapter 6. Translational Motions of PF Ions in the PPy Films 6 1 Figure 6.6: One-D image gradient calibration. A longitudinal encode-decode (LED) pulse sequence was proposed by Gibbs and Johnson [32] to ease eddy current effects by delaying the acquisition until the effects have dissipated. Eddy currents are inevitably generated in the surrounding conducting surfaces around the gradient coils due to the rapid rise of the gradient pulses, causing amplitude or phase distortion of the echo. These effects often lead to a spurious extra echo attenuation which can be easily misinterpreted as a higher diffusion coefficient. Many such sequences are based on STE, as in the following: § - (PFG)-§ -r -f -r (PFG)-\-T -\-AQ where T is the settling time.(See Figure 6.7(b)) However the L E D P F G sequence does not solve the problem of the eddy current tail from the first gradient pulse extending to the second transverse evolution period, therefore another method involving a self-compensating bipolar pulse pair (BPP) is employed [33, 34]. Each regular gradient pulse is replaced by a pair of pulses having different polarities and separated by IT pulses. The eddy currents caused by two gradient pulses with identical areas but different polarities will tend to cancel each other. Finally, the pulse sequence used in this work to determine the diffusion coefficient is a stimulated echo L E D sequence incorporating bipolar gradient pulses (BPP-LED pulse sequence) shown in Figure 6.7(c). This sequence was tested extensively on H 0 and a P C sample containing 0.05 M T E A P to ensure that reliable D at relevant A time scales is obtained (where the eddy current effects are not present). Similar to the simple P F G S E sequence, the signal attenuation j?f.) due to diffusion is given by the following equation: Tl 2 x e e 2 A A(2r) = ,4(0) e x p [ - < / - W ( A /2)\ 2 7 Tg (6.19) Chapter 6. Translational Motions of PF Ions in the PPy Films 6 46 Table 6.1: Spectra width Ais from one-D image gradient calibration at gradient amplitude x (0-1) and the corresponding gradient strength. Gradient amplitude x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 (kHz) 84 168 252 334 418 498 580 664 748 832 Gradient strength g (G/cm) 49.31 98.63 147.94 196.10 245.42 292.44 340.60 389.91 439.23 488.54 where T is the time separation between a bipolar pair. A 16 step phase cycle for the B P P - L E D pulse sequence is adopted from Johnson et al. [35]. g Chapter 6. Translational Motions of PF Ions in the PPy Films 6 (a) pi/2 47 pi/2 pi/2 Tl 5 i A (b) pi/2 pi/2 pi/2 pi/2 n Ti pi/2 T e r-i 11 pi/2 pi pi/2 pi/2 pi pi/2 pi/2 T H 5/2 H 5/2 H T 1 1 1 •4 H Tg : T e V • 1 • -4 ; • A Figure 6.7: (a) Stimulated echo(PFGSTE) pulse sequence. (b)A longitudinal eddycurrent delay(LED) pulse sequence, (c) A bipolar pulse pair(BPP) L E D pulse sequence. Chapter 6. Translational Motions of PFg Ions in the PPy Films 1 *~ — 1 1 1 1 1 1 fit «~ Kg) * s % \ \ \ \ V \ X % X X. X X • I I 1 0 50 1 I 1 I 1 I 100 150 200 1 ~ l _ 250 I 1 I 1 I I I 300 350 400 450 500 Gradient strength g (G/cm) Figure 6.8: Echo attenuation with respect to gradient strength g of 0.05M P C sample. 6 . 3 R e s u l t s The diffusion coefficient D of two wet P P y samples S[ and S' at E = 0.53 V , 0.25 V vs A g / A g C l and two P C samples containing 0.05 M , 2 M T E A P are measured by a stimulated echo L E D sequence incorporating bipolar gradient pulses. Solvent samples again were used for control experiments. We optimized the three experimental parameters S, T , T under the constraint of T i , T relaxation, and then kept them fixed in all diffusion measurements. The numbers are '5 = 300 ps, T = 100 /is, T = 100 ms. Figure 6.8 shows the P F G signal intensities 1(g) at A = 50 ms of sample 0.05 M P C , and the diffusion coefficient of PFg is determined through fitting to Equation 6.19. The same fitting process was repeated for all samples at different diffusion times (A's). Self-diffusion coefficients of the 0.05 M and 2 M P C samples measured over different observation times (A) are shown in Table 6.2 and plotted in Figure 6.9 (a). 2 g e 2 g e Table 6.2: Self-diffusion coefficients of solvent samples. Sample 0.05 P C 2 D(50 ms) 3.50 x 10~ ± 1.7% £>(50 ms) 1.99 x 1 0 " ± 3.6% 6 2M P C D(A) (cm /s) D(100 ms) D(500 ms) 3.43 x 10~ ± 1.4% 3.48 x 10~ ± 2,1% L>(500 ms) L>(1000 ms) 1.59 x 10~ ± 2.5% 1.73 x 10" ± 1.1% 6 6 6 6 6 Diffusion coefficients were measured from the most oxidized sample S[ (see Table 6.3, 48 Chapter 6. Translational Motions of P F (b) (a) xlO 0.2 0.4 0.6 0.8 1 1.2 6 Ions in the PPy Films 49 xlO 0.5 1 1.5 2 2.5 Diffusion time A (s) Diffusion time A (s) Figure 6.9: (a) D of 0.05M,2M P C samples and (b)D of the oxidized PPy sample S[ over different observation times A . NMR tube Polypyrrole films Horizontal orientation Vertical orientation Figure 6.10: The sheets of PPy thin films were stacked either parallel or perpendicular to B field. Figure 6.9 (b)) with films oriented in two directions, once with film's normal perpendicular to the static B field axis (S[ V) and once perpendicular ( ^ H ) , so that diffusion in both planes can be sampled. (See Figure 6.10) For sample S' , partly because there are fewer ions in the less oxidized films (smaller signal to noise ratio), data points suffer from intrinsic noise, yielding D with large errors. The D obtained under these circumstance may lack of credibility; nevertheless experimental values are given below: D =(3.51 x 1 0 ± 77%) cm /s at A = l s, and (6.76 x 10~ ± 63%) cm /s at A=1.5 s. Diffusion measurements on sample S are not feasible due to its short T (97ps), signals basically decay away before the acquisition. 2 app app -9 2 app 9 2 3 2 6 . 4 D i s c u s s i o n When we use the P F G method to measure diffusion in free solution, the length of the observation time we choose (A) should not affect the value of the diffusion coefficient Chapter 6. Translational Motions of PF Ions in the PPy Films 6 Table 6.3: Diffusion coefficients of the oxidized S[ and the less oxidized S' P P y sample. Films are oriented parallel (H) and perpendicular (V) to the magnetic field. 2 Sample D(A) (cm /s) D(100 ms) 1.24 x 10" ± 32.1% 2 7J(50 ms) 2.57 x l O " ±29.9% £>(1500 ms) 4.66 x l O " ± 12.3% D(50 ms) £>(500 ms) 4.57 x l O " ±47.8% 1.04 x 10" ± 21.1% D(1500 ms) D(2000 ms) 4.31 x 10" ± 24.8% 4.76 x 10" ± 27.5% £>(1000 ms) D(1500 ms) 3.51 x l O " ± 77% 6.76 x 10~ ± 63% 8 8 D(1000 ms) 4.47 x 10" ± 14.2% 9 9 5 V 2 8 8 9 9 9 9 D(1000ms) 4.98 x 10" ± 25.4% D(3000 ms) 6.35 x 10" ± 11.2% 9 9 extracted from the measurement. This is what we observed in the solvent samples; the diffusion coefficients of both samples are essentially the same from A=50 ms to 1 s. From the solvent measurements, we. are confident that the D values beginning from 50 ms are not affected by the disturbance of the eddy current effect. Measurements made at A < 50 ms may bear the influence of the eddy current effect (even though the pulse sequence used is devoted to overcome this problem), and also suffer from the fact that very little echo attenuation is produced, if the diffusion coefficient is small, according to Equation 6.19. This results in a less accurate determination of D values. Figure 6.11 shows the signal attenuation data from S oxidized P P y sample at A=50 ms and 3 s. One can see that due to the slow translational motions of PFg ions in the films and short diffusion time A , only little attenuation is achieved. We can however try implementing stronger gradients, thereby increasing the degree of signal attenuation. The fact that D<xpp over a range of A's is not distinctly different between the two oriented S samples, suggests that the films are homogeneous in morphology, at least on the length scales probed here (~ 1.4/im). If there were large oriented crystalline regions inside the films, then we should have observed dissimilar behaviors in terms of diffusion coefficients as a function of A . 1 l The D values measured from P F G experiments can be compared to. the D values from the numerical fitting of impedance spectroscopy data. Impedance analysis based on diffusion models yields values of diffusion coefficients as large as 10~ cm /s for CIO4 ions in P P y / P C [36]and 10~ cm /s for PFg ions in P P y / P C [37]which are believed rather high for diffusion of ionic species in solids. These high values have been explained in terms of solvent ingress, effectively assisting the ionic diffusion progress [38, 39]. Our D value for PFg in PPy films (~ 5 x 10~ cm /s)' is two order of magnitude slower than that typically obtained from the impedance data, and we believe reflects ionic motions app 7 8 2 9 2 2 50 Chapter 6. Translational Motions of PF Ions in the PPy Films 6 (a) 2.1 S, Oxidized PPy A =50ms fit 1(g) 3 i=r 1.9 (3 0 50 100 150 200 250 300 350 400 450 500 0 50 100 Gradient strength g (G/cm) 150 200 250 300 350 400 450 500 Gradient strength g (G/cm) Figure 6.11: Signal attenuation 1(g) from S[ oxidized PPy sample at A=50 ms and 3s. in the polymer/electrolyte matrix in steady state. As seen in Figure 6.9 (b) the A dependence of D of 5 films appears to be an indication of restricted diffusion. The diffusion coefficient begins to drop quickly from 50 ms, implying that at least some of ions are already "feeling" the boundaries. We can conjecture an upper limit of pore size a by plugging D(50 ms) and A== 50 ms into D = The upper limit of the characteristic length scale (pore size) a in S[ is determined to be ~ 0.4 pm. At longer times, diffusing molecules probe the connectivity of the pore space. The diffusion coefficient reaches a plateau at 2-3 s instead of decreasing with inverse time, suggesting that the pores are interconnected rather than being isolated voids inside the polymer. The data from sample S' provides a higher bound of the diffusion coefficient in that oxidation state (E = 0.25 V vs Ag/AgCl), D must be < 1 0 cm /s. Because if the diffusion coefficient of diffusion for the ions was greater, we would have observed a greater echo attenuation. The short F T of the reduced S sample in Table 4.4 that impeded us from measuring the diffusion coefficient actually serves as an index as far as how F spins are being relaxed. Generally speaking the stronger the spin coupling to the environment, the shorter the T (this also reflects on the peak linewidth). We have found that the T values of F and P in the reduced film sample S' are much shorter than in the two oxidized samples (S[ and S' ). This dramatic difference in T would be consistent with a structure in the reduced state in which the dopant ions interact more strongly, with the polymer backbone, whereas at high doping levels (e.g. the oxidized state) the interactions with the solvent dominate. This picture is consistent with the results from the Ti relaxation study and ID N O E difference experiments that suggest the existence, of an abrupt structural change between oxidation states 0.25V and — 0.2V vs Ag/AgCl. app : 2 -8 2 1 9 2 3 1 9 2 1 9 3 1 2 3 2 2 51 Chapter 6. Translational Motions of PF Ions in the PPy Films 6 The same conclusion has also been suggested from an impedance study on PFg doped PPy in various states of oxidation as the impedance characteristics of the oxidized and reduced PPy are distinctively different [40]. 52 53 Chapter 7 Conclusion We have demonstrated that N M R spectroscopy is a versatile tool for the study of dopant ions in polymer systems. Advantages of N M R over other techniques lie in its selectivity, which is employed to determine the ion content, and its ability to detect motions in different time scales, which enable us to probe the rotational and translational motions of PFg inside the P P y films. By investigating these quantities systematically as a function of oxidization state, it is possible to relate the microscopic structural changes to macroscopic material behaviors. The ion content decreases linearly with decreasing electrochemical potential (E), directly confirming the ion insertion mechanism of polymer actuation. With known ion content, sample mass and deposition current, the pyrrole/ion and pyrrole/solvent ratios can be determined. The obtained doping level for the as-grown (Si) sample (Ni/N = 1/3.83) is consistent with the literature [20, 21, 22]. This suggests that all the ions are detected, and examining ion content via ID P N M R spectroscopy seems to be a reliable and straightforward method. PFg doped polypyrrole, as fabricated using the described electrodeposition method, are found to be porous in nature. P relaxation and ID N O E difference experiments showed that PFg ions in the oxidized films (S[) and less oxidized films (S ) are located inside pores containing propylene carbonate solvent molecules. As the PPy films are reduced, PFg ions that remained inside the films became less splvated, -possibly because the pores are literally smaller. However we believe that there are still many solvent molecules inside the reduced PPy films according to the solvent molecule to pyrrole ratio (N i/Np) in Table 3.1. Those results were based on dry samples, and are likely underestimates of the true solvent content of wet films. P F G N M R experiments provide direct measurements regarding the self-diffusion coefficient of PFg ions inside polypyrrole films. The D values of PFg in P P y films from the P F G study (~ 10~ cm /s) appear to reflect ionic motions in the polymer/electrolyte matrix in steady state without any external perturbations, and can be used in PPy actuator modeling, and thus in predicting its behaviour. The time-scale dependence of D of the oxidized films (5 ) at short times had let us conjecture an upper limit of pore size a of ~ 0.4/-4 m, and the values at longer times enables us to probe the connectivity of the pore space. Data suggests that the pores are interconnected rather than being isolated voids inside the polymer. Suggested experiments for the future include: (1) further investigate the T i vs. temperature behavior of the reduced P P y sample as other relaxation mechanisms (rather than ionic rotations) may provide information on the polymeric environment that ions p 3 1 3 1 2 so 9 2 app X Chapter 7. Conclusion 54 experience in the reduced state. (2) improve the instrumental limits of the P F G experiments, for example, to increase the gradient strength (reduce the gradient duration) to overcome the short F T problem so that extensive P F G experiments can be performed in the less oxidized and reduced films as well. A shielded magnetic gradient coil system in the N M R probe head would prevent the gradient pulse from affecting the region outside the gradient coils, thereby reducing the generation of eddy currents. 1 9 2 55 References [1] T.A. Skotheim, R.L. Elsenbaumer, and J.R. Reynolds eds. The Handbook ducting Polymers. Mercel-Dekker, New York, second edition, 1977. [2] P.I. Lazarev ed. Molecular [3] E.J. Smela. Micromech. Electronics. Microeng., of Con- Kluwer Academic Publishers, Boston, 1991. 9:1-18, 1999. [4] J.D.W. Madden, B. Schmid, M . Hechinger, S.R. Lafontaine, P G . A . Madden, F.S. Hover, R. Kimball, and I. Hunter. IEEE Journal of Oceanic Engineering, 24:199201, 2004. [5] S. Hara, T. Zama, W. Takashima, and K . Kaneto. Synthetic 2005. [6] Y . Nogani, J . P Pouget, and T. Ishiguro. Synthetic Metals, Metals, 149:199-201, 62:257-263, 1994. [7] X . G . Li, L.X. Wang, M.R. Huang, Y.Q. Lu, M.F. Zhu, A. Menner, and J. Springer. Polymer, 42:6095-6105, 2001. [8] O. Cakmak, M . Basturkmen, and D. Kisakurek. Polymer, 45:5451-5458, 2004. [9] F. Devreux, G. Bidan, A.A. Syed, and C.J. Tsintavis. Physique, 46:1595-1601, 1985. [10] B. Wehrle, H.H. Limbach, J. Mortensen, and J. Heinze. Synthetic 298, 1990. Metals, 38:293- [11] T.C. Clarke, J.C. Scott, and G.B. Street. IBM J Res Develope, 27:313-320, 1983. [12] O. Inganas and Q. Pei. Solid state ionics, 60:161-166, 1993. [13] J.D.W. Madderi, N.A. Vandesteeg, P A . Anquetil, P G . A . Madden, A. Takshi, R.Z. Pytel, S.R. Lafontaine, P.A. Wieringa, and I.W. Hunter. IEEE Engineering, Journal 29:706-728, 2004. [14] T.F. Otero and J.M. Sansinera. Bioelectrochem. Bioenerg., 38:411-414, 1995. [15] G . M . Spinks, B. X i , D. Zhou, V . Truong, and G.G. Wallace. Synthetic 273-280, 2004. [16] R. H. Baughman. Nature, 308:63-65, 2005. of Oceanic - Metals, 140: References 56 [17] M . Yamaura, T. Hagiwara, and K . Iwata. Synthetic Metals, 26:209-224, 1988. [18] H. Okuzaki, T. Kondo, and T. Kunigi. Polymer, 40:995-1000, 1999. [19] E. Naudin, P. Dabo, D. Guay, and D. Belanger. Synthetic Metals, 132:71-79, 2002. [20] M . Salmon, A . F . Diaz, A . J . Logan, M . Krounby, and J. Bargon. Mol. Crys. Liq. Crys., 83:1297-1308, 1982. [21] H . Zhao, W.E. Price, C O . Too, and G . G . Wallace. J. Membr. Sci., 119:199-212, 1996. [22] M . Yamaura, K . Sato, T. Hagiwara, and K . Iwata. Synthetic Metals, 48:337-354, 1992. [23] P G . A . Madden, J.D.W. Madden, P A . Anquetil, N.A. Vandesteeg, A . Takshi, R.Z. Pytel, and I.W. Hunter. IEEE Journal of Oceanic Engineering, 29:696-705, 2004. [24] A. Abragam. The Principles of Nuclear Magnetism. Oxford University Press, London, 1961. [25] W. F. Kuhs and G. Mattern. Acta Cryst, B50:741-746, 1994. [26] D. W. McCall, D.C. Douglass, and E.W. Anderson. Ber. Busenges. Phys. Chem., 67:336, 1963. [27] E.O. Stejskal and J.E. Tanner. J. Chem. Phys., 42:228-292, 1965. [28] E.O. Stejskal. J. Chem. Phys., 43:3597-3603, 1965. [29] W. Zhang and D.G. Cory. J. Magn. Reson, 132:144-149, 1998. [30] H. Weingartner. Z. Phys. Chem., 132:129-149, 1982. [31] F. Franks ed. Water - A comprehensive Treatise. Plenum Press, London, 1972. [32] S.J. Gibbs and C.S. Jonson Jr. J. Magn. Reson, 93:395-402, 1991. [33] R.F. Karlicek and I.J. Lowe. J. Magn. Reson, 37:75-91, 1980. [34] R . M . Cotts, M.J.R. Hoch, T. Sun, and J.T. Marker. J. Magn. Reson, 83:252-266, 1989. [35] D. Wu, A. Chen, and C.S. Johnson Jr. J. Magn. Reson A, 115:260-264, 1995. [36] K . West, M.A. Careem, and S. Skaarup. Solid State Ionics, 60:153-159, 1993. [37] J.D. Madden. Doctoral Dissertation. Massachusetts Institute of Technology, Boston, 2000. References 57 [38] B.W. Johnson, D.C. Read, R Christensen, A . Hamnett, and R.D. Armstrong. 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NMR study of PF₆̄ doped polypyrrole : a potential candidate for artificial muscles Tso, Chien-Hsin 2006
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Title | NMR study of PF₆̄ doped polypyrrole : a potential candidate for artificial muscles |
Creator |
Tso, Chien-Hsin |
Date Issued | 2006 |
Description | Conducting polymer actuators, such as polypyrrole, are promising materials for novel applications because they are more muscle-like and potentially less expensive than common motors. A variety of NMR techniques are employed to examine the ion content and dynamics of PF-₆, doped polypyrrole films in different oxidation states. The ion content decreases linearly with decreasing electrochemical potential, directly confirming the ion insertion mechanism of polymer actuation. With known ion content and deposition current, a doping level (dopant ion/pyrrole) of 0.26 was determined for the as-grown film. A T₁ relaxation study reveals that the rotational correlation time of PF-₆ ions in the oxidized film (10.76 ps) is similar to that in the solvent (8.08 ps), suggesting the ions are located inside solvent pockets rather than at stable sites in the polymer matrix. 1D Nuclear Overhauser Effect (NOE) difference experiments confirm the solvated ion environment in oxidized films, but reveal a drastic decrease in the NOE enhancement factor in reduced films, implying that polypyrrole undergoes a significant structural change when reduced. This change leads to a much less solvated environment as experienced by the dopant ions in the reduced state. Translational motion of the PF-₆ ions in the oxidized films at two orientations is probed via self-diffusion coefficient measurements made using pulsed-field gradient (PFG) NMR. The D values obtained at different diffusion times range from 3 x 10-⁸̄ cm²/s to 5 x 10-⁹ cm²/s. The echo attenuation obtained by PFG NMR experiments not only gives direct information on ionic diffusion but also serves as a potential tool to explore the pore morphology of doped polypyrrole films. |
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Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2010-01-16 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0085182 |
URI | http://hdl.handle.net/2429/18177 |
Degree |
Master of Science - MSc |
Program |
Physics |
Affiliation |
Science, Faculty of Physics and Astronomy, Department of |
Degree Grantor | University of British Columbia |
Graduation Date | 2006-11 |
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UBCV |
Scholarly Level | Graduate |
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