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Alpha-T-T and T-T-alpha-T diagrams in intelligent processing of thermosetting composites Osinski, Barbara 1993

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ALPHA -T-T and T-T-ALPHA-T DIAGRAMSIN INTELLIGENT PROCESSING OF THERMOSETTING COMPOSITESBarbara OsinskiM.Sc. (Ceramics) University of Mining and Metallurgy, Krakow, PolandA THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THEREQUIREMENTS FORTHE DEGREE OF MASTER OF APPLIED SCIENCEinTHE FACULTY OF GRADUATE STUDIESMETALS AND MATERIALS ENGINEERINGWe accept these thesis as conforming to the requested standardTHE UNIVERSITY OF BRITISH COLUMBIAApril 1993© Barbara OsinskiIn presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature) METALS & MATERIALS ENGINEERINGDepartment ofThe University of British ColumbiaVancouver, CanadaDate ^DE-6 (2/88)11ABSTRACTThe majority of existing models for processing in thermoset matrix composites concentrate nearlyexclusively on heat and mass transfer problems and account for material-related aspects in a verysimplified manner The objective of this work is to provide that missing element by proposing aclearly defined system which yields all the information of Gillham' s T-T-T diagram but can beused for non-isothermal curing cycles. To build the system, three elements are needed: the gelationand vitrification curves, expressed as functions of degree of conversion; the kinetic model ofconversion; and a diagram combining all complex information provided by the system. The proposedsystem for the Narmco 5208 resin incorporates a recently developed mechanistic model for thekinetics of conversion.The algorithm calculates and graphically presents the progress of thermosetprocessing using the developed diagrams which re-introduce time as an independent variable. Themost important part of the system is its graphical output: a-T-T diagrams, originally developed inthis work. Their role is to enhance the understanding of the process by providing the rheologicalinformation.Practical applications of the system, with an increasing degree of its sophistication, are presentedusing four examples. The first case demonstrates the basic value offered by the diagrams - predictionof the moment of gelation and vitrification in advance; the second application shows the advantageof the system in thick composite processing; the third is the generation of the T-T-T diagram forthe Narmco resin based on the kinetic model of conversion; the fourth application, where the systemis used in the reverse mode, in a new capability - the search for an optimum curing cycle in the RTPmethod.iiiIn experimental part of the work, the kinetic model of conversion incorporated into the systemwas verified using the Differential Scanning Calorimetry (DSC) technique, and the rheology ofthe resin was investigated using the Rheometric Dynamic Analyser (RDA) and DSC apparatus.ivTABLE OF CONTENTSPageABSTRACT^ iiTABLE OF CONTENTS^ ivTABLES viFIGURES^ viNOMENCLATURE^ xABBREVATIONS xiiACKNOWLEDGEMENTS xiii1. INTRODUCTION^ 11.1^Scope of the Work 52. CHEMICAL SYSTEM OF EPDXY RESIN^ 72.1^Introduction^ 72.2^Reaction Mechanism and Kinetics of Narmco Resin^ 103. MODELLING OF KINETICS OF CONVERSION 123.1^Introduction^ 123.2^Degree of Cure 133.3^Review of Existing Models^ 143.4^Conversion of Epoxide Groups 203.5^Experimental Verification of Cole's Model^ 223.6^Results and Discussion^ 233.7^Contribution of the Author 234. CHEMORHEOLOGICAL CHANGES DURING CURE^ 354.1^Theory^ 354.1.1^Viscosity 384.1.2^Gelation 424.1.3^Vitrification^ 484.2^Experiments 514.2.1^Introduction 51v4.2.2^Review of Techniques for Rheological Characterization^524.2.3^Determination of Gelation and Vitrification Point Using 57RDA Technique4.2.4^Discussion of the Results^ 634.2.5^Determination of Vitrification Point on the Basis of the DSC^65measurements4.3^Contribution of the Author^ 655. CURE DIAGRAMS AS A METHOD OF DISPLAYING INFORMATION OF 90RHEOLOGICAL CHANGES IN MATERIAL UNDER PROCESSING5.1^Gillham's T-T-T and C-H-T Diagrams^ 905.2^a-T-T Diagram - the Concept^ 945.3^Structure and Operation of the Developed "System"^ 955.4^Interaction of the Proposed System With a Thermal Model of^98Composite Processing5.5^a-T-T and T-T-a-T Diagrams - the Graphical Output^100of the System5.6.^Applications^ 1045.6.1^RDA Tests 1045.6.2^a-T-T Diagram in Processing of Thick Composites^ 1305.6.3^Generation of T-T-T Diagram for Narmco Resin 1335.7^Contribution of the Author^ 1356. APPLICATION OF ALPHA-T-T DIAGRAM TO RTP METHOD^1366.1^Contribution of the Author^ 1377. CONCLUSIONS^ 1398. REFERENCES 143viTABLESPage:1. Gelation Point - Experimental Data^ 842. Vitrification - Experimental and Theoretical Data^ 853. List of RDA Tests^ 104LIST OF FIGURESPage1. Schematic of prepreg lay-up 12. The principal events occuring during a cure cycle 23. Epoxy group 74. Schematic form of a typical epoxy reaction 75. Network formation in epoxy resin 96. Main reactions in a cure of Narmco resin 117. Isothermal DSC curve obtained at temperature 130°C. 258. Isothermal DSC curve obtained at temperature 170°C. 269. Isothermal DSC curve obtained at temperature 190°C. 2710. Dynamic DSC curve obtained at heating rate 3°/min. 2811. Dynamic DSC curve obtained at heating rate 5°/min. 2912. Calibration curve for dynamic tests 3013. Verification of conversion kinetic model - isothermal 130°C. 3114. Verification of conversion kinetic model - isothermal 170°C. 3215. Verification of conversion kinetic model - dynamic 3°/min 33vii16. Verification of conversion kinetic model - dynamic 5°/min. 3417. Schematic representation of the cure of a thermoset 3718. Measurement of viscosity 3919. Types of amine units 4420. Possible configurations for TGDDM-DDS system 4521. Specific volume as a function of temperature 4922. Time dependence of the stress and strain during a test 5323. Rheometrics Dynamic Analyzer 5824a. RDA record of processing - 140 °C/30 min. 6624b. Degree of conversion for experiment 140°C/30 min. 6725a. RDA record of processing - 170/140 °C/180 min. 6825b. Degree of conversion for experiment 180/140°C/180 min. 6926a. RDA record of processing - 170°C/60 min. (A). 7026b. Degree of conversion for experiment 170°C/60 min (A). 7127a. RDA record of processing - 170 °C/60 min. (B) 7227b. Degree of conversion for experiment 170°C/60 min. (B) 7328a. RDA record of processing - 170°C/120 min. (A). 7428b. Degree of conversion for experiment 170°C/120 min. (A). 7529a. RDA record of processing - 170°C/120 min. (B). 7629b. Degree of conversion for experiment 170°C/120 min. (B). 7730a. RDA record of processing - 190°C/180 min (A). 7830b. Degree of conversion for experiment 190°C/180 min. (A). 7931a. RDA record of processing - 190°C/180 min. (B). 8031b. Degree of conversion for experiment 190°C/180 min. (B). 81viii32a. RDA record torsion mode 8232b. RDA record torsion mode 8333. DSC record, rate of temperature increase 10°/min 8634. DSC record, rate of temperature increase 10°/min. 8735. DSC record, rate of temperature increase 5°/min. 8836. DSC record, rate of temperature increase 5°/min. 8937. TTT cure diagram 9238 CHT cure diagram 9339. Structure of the system 9740. Interaction of the system with a thermal model 9941. Comprehensive a-T-T diagram 10142. T-T-a-T diagram 10243. T-T-a-T diagram without surfaces of gelation and vitrification 10344a. Temperature cycle in test 140°C/30 min. 10644b. History of degree of conversion 10744c. a-T-T diagram 10845a. Temperature cycle in test 170°C/140°C/180 min. 10945b. History of degree of conversion 11045c. a-T-T diagram 11146a. Temperature cycle in test 170°C/60 min (A). 11246b. History of degree of conversion 11346c. a-T-T diagram 11447a. Temperature cycle in test 170°C/60 min.(B). 11547b. History of degree of conversion 116ix47c. a-T-T diagram 11748a. Temperature cycle in test 170°C/120 min (A) 11848b. History of degree of conversion 11948c. a-T-T diagram 12049a. Temperature cycle in test 170°C/120 min (B). 12149b. History of degree of conversion 12249c. a-T-T diagram 12350a. Temperature cycle in test 190°C/180 min.(A). 12450b. History of degree of conversion 12550c. a-T-T diagram 12651a. Temperature cycle in test 190°C/180 min.(B). 12751b. History of degree of conversion 12851c. a-T-T diagram 12952. a-T-T diagram in thick composite processing 13153. T-T-a-T diagram in thick composite processing 13254. T-T-T diagram for Narmco resin 13455. a-T-T diagram in RTP processing 138NOMENCLATUREB^= initial ratio of primary amine N-H bonds to epoxide groupD^= diffusivityE^= activation energyE'^= storage moduliE"^= loss moduliF^= structure factorf^= fractional free volumefe^= functionality of epoxy groupfa^= functionality of hardenerG'^= storage modulusG"^= loss modulusg^= gyration factorHt^= heat developed during the reaction between the starting point anda time (t)Rot^= total heat developed during the cureMa^= moles of epoxyMe^= moles of hardenerxiIVI,^= weight-average molecular weightPe^= fraction of epoxy active groupPa^= fraction of hardener active groupr^= initial ratio of hardener to epoxy groupsR^= gas constant (8314.4 J kmo1-1)T^= temperatureTgo^= glass transition temperature at a=0t^= timeTgoo^= maximum glass transition temperaturea^= fractional degree of conversion of epoxide groupsR^= fraction of amine N-H bonds which have reacted7^= rate of shear8^= shear stressc^= tensile strain= friction factorTI.^= complex viscosityT1'^= dynamic viscosityTr^= imaginary viscosityxii= branching coefficientco^= frequency of oscillations in dynamic testinga^= tensile strainABBREVIATIONSDMA Dynamic Mechanical AnalyzerDSC Differential Scanning CalorimeterRTP Rapid Thermoset ProcessingTBA Torsional Braid AnalyzerTMA Thermal Mechanical AnalyzerACKNOWLEDGEMENTSI would like to extend special thanks to Professor K. Gillham of Princeton University from whosework my idea is conceived. Professor's Gillham diagrams served not only as a starting point butalso as a continuous standard for my Thesis throughout its development. His encouragement andinspiration are deeply appreciated.I would also like to express my gratitude to Professor B. Hawbolt and Professor P. Steiner ofUniversity of British Columbia for their support, constructive criticism, and helpfulrecommendations.Special thanks are also due to Professor G. Springer of Stanford University for his time spentdiscussing my work and for his hospitality.Finally I would like to thank Mr. A. Russell of National Defence Research and Professor P. Steinerfrom University of British Columbia for giving me an opportunity to work on their equipment, aswell as Dr. K. Cole National Research Council of Canada and Mr. D. Wilson Bombardier Inc. forsupplying the materials essential to the completion of my work.I am also deeply indebted to the Government of Canada for providing the financial support for mywork in a form of a student loan.11. INTRODUCTIONDuring the last few years great progress has been made in the development of high-performancecomposites. Most are fabricated using carbon or aromatic fibers with an epoxy matrix based ontetraglycidyl diamino diphenyl sulphone (TGDDM-DDS) formulations. The laminates are generallyproduced by the Autoclave/Vacuum Degassing Laminating Process where the polymerizationreactions of the thermoset matrix are activated and the composite is consolidated. In this process,prepreg plies of desired shape are laid up in a prescribed orientation to form a laminate. The laminateis placed upon a smooth metal tool surface and covered with successive layers of an absorbentmaterial (bleeder), a fluorinated film to prevent sticking, and finally a vacuum bag. The entiresystem is placed into an autoclave, vacuum is applied to the bag, and the temperature is increasedit a constant rate in order to promote the resin flow and polymerization. Figure 1 43 represents asimple lay-up 42.43 The principal physical events occurring during such a cure cycle are illustratedn Figure 2. 4°Figure 1. Schematic of the prepreg lay-up.2Figure 2. The principal events occuring during a cure cycleThe processing conditions in the autoclave are dictated by the chemoreological properties of theepoxy matrix and by heat transfer characteristics of the composite-tool-autoclave system. Therelative rates of heat generation and of heat transfer determine the values of the advancement ofthe reaction and the viscosity through the thickness of the laminate. The processing of a polymericcomposite based on thermoset matrices, requires the optimization of the cure cycle parameters aswell as an adequate rheological characterization of the reacting system Z9•°3The mentioned optimization of the cure cyle may be attempted on the basis of a mathematicalmodel of the process. Unfortunately, the existing models for processing of thermoset matrix3composites are poorly suited for the task. To some extent, the existing knowledge on the materialunder processing is responsible for this fact; it does not provide all of the information necessary fora full optimization in the quantitive form required for algorithmization. However, the existingmodels of the old generation fail to provide the essential information even if this information maybe generated on the basis of the existing knowledge. They account typically for three aspects of theprocess: heat transfer, fluid flow, and kinetics of resin conversion, concentrating nearly exclusivelyon the first two and using simplified, experimentally-determined expressions for the third. The heattransfer model, combined with the model of conversion are to ensure that the temperature in anylocation of the material during processing does not exceed the value, liberally assumed as theacceptable maximum, and that the degree of conversion of the material at the end of processingdoes reach a value liberally assumed as the acceptable minimum. The resin flow model is to ensurethe proper level of material compaction reached before the resin becomes too visous to flow. It alsomay be used, to some extent, to control the behaviour of gaseous discontinuities in the processedmaterial. The element missing in those models is a model of rheological behaviour of the resin.Yet, rheological transformations taking place during processing have a serious impact either on theprocess itself, or on the final properties of the product. The phenomenon of gelation marks the endof resin flow and carries a special meaning for the precipitation of an additional phase in the caseof toughened resin processing. Vitrification not only defines the moment when a material acquiresmechanical properties of a solid, but causes the diffusion-controlled slow-down of the conversionreaction and may determine the final degree of conversion obtained in the product. It also maydetermine the density of cross-linking, specific volume, and final contraction of the material - theproperties of the semi-finished product. In cases when these parameters vary from location tolocation, additional stresses, and eventual deformations may be generated. In fact, the stresses maybe generated simply because vitrification does not occur at different locations simultanously.This study is an attempt to fill the existing gap in the modelling of thermoset-based compositeprocessing by developing an additional model segment representing material behavior. The4segment accounts for the kinetics of resin conversion, as well as for rheological transformationsof the material, and could be used as a part of a comprehensive model of composite processing, asa stand-alone model of resin behaviour or combined with a thermal model, to simulate the processingof a non-reinforced resin system. The advanced kinetics of conversion expressions utilized in thesegment are of the mechanistic approach reported by Cole.A very specific problem resulting from the kinetics of conversion application is the complexity ofthe produced information. At any moment of processing there are three variables involved: time,temperature and degree of conversion, as well as at least three phenomena: gelation, initialvitrification, and final vitrification. If a heat transfer model is additionally employed, for thick, ornon-uniformly shaped material under processing, the complexity is amplified by a number ofcharacteristic locations at which the mentioned variables must be monitored. This complexity callsfor especially effective means of conveying the produced information to the user of the model in acomprehensive and transparent form. The perfect example of a well-suited form for the applicationare Gillham's Time-Temperature-Transformation (TTT) diagrams . 23 ' 51 ' 53 '7° The diagrams, however,are built for, and can be applied to isothermal curing only, while in industrial practice, especiallyin case of thick materials, the processing cycles are non-isothermal. The concept of the diagramspresented in this study which could be applied to any processing cycle stems from the fact that thepoint of gelation and the point of final vitrification, for a resin system, can be quite easily expressedas a function of the degree of conversion and temperature 67 . Gelation is expected to occur at aconstant value of conversion, while the point of vitrification is described by the DiBenedetto equation54. Both curves may be plotted on the grid of the degree of conversion versus temperature ofprocessing. In order to place the point of processing in the same figure, its coordinates - themomentary temperature of processing and the degree of conversion must be determined. The lattercan be calculated if the kinetic model of conversion is available.5The objective of this study was to create an algorithm based on the presented concept and to developdiagrams comprehensively displaying the complex information produced. The algorithm consistsof different elements, and is therefore called a 'system'. The elements of the system are:material-dependent gelation, initial vitrification, and final vitrification; material - and - cycle -dependent kinetics of conversion; and the original alpha-T-T and T-T-alpha-T diagrams, whichprovide a comprehensive characterization of processing by displaying all the information producedby the system graphically. The diagrams are the most valuable and innovative part of the system.The system itself is limited to the well-known aspects of material behavior and does not addressall the problems involved in optimization of the processing cycle. However, it creates the basis onwhich further efforts leading in this direction can be made by providing a basis for a comprehensiveunderstanding of the process.The best way to understand and to assess the real value of the system, and the diagrams, is to studythe examples of their practical application. The presented applications include amanufacturer-suggested processing cycle, followed by the cycles applied in Rheometrics DynamicAnalyser (RDA) experiments, and reproduction of the Gillham diagram. An original method ofRapid Thermoset Processing (RTP) takes a distinctive place among these applications, proving theextensive potential capabilities of the concept presented in this study.1.1 Scope of the workOf the three elements of the ' system' - kinetics of conversion, rheological characteristics of thematerial, and the diagrams - the kinetics of conversion is investigated first. After reviewing typicalmodels of the kinetics of conversion a decision was made to use an approach developed by Colespecifically for the resin system under consideration. This excellent kinetics expression for theconversion reaction was incorporated into the computer code of the model of conversion. The model6is verified by comparing its results with the results of experiments conducted on the same resinsystem using Differential Scanning Calorimetry (DSC) technique, with either isothermal or linearlyincreasing temperature cycles.The second objective of the work is to measure/verify rheological parameters of the resin systemrelated to gelation and vitrification phenomena. The suitability of different techniques fordetermination of rheological parameters was assessed. The moment of gelation is determined usingthe RDA apparatus, the vitrificaton is investigated using RDA and DSC techniques.Since the original alpha-T-T and T-alpha-T-T diagrams, proposed by the author, cannot stand alone,but are generated by the system for each specific temperature cycle, both, the system and the diagramsare developed and presented simultanously. It is important to realize that the diagram concept hasgrown out of Gilham' s T-T-T diagrams. The T-T-T diagrams, however, are for a specific type ofa thermal cycle (isothermal, or linear temperature increase), and contain the kinetics of conversionwithin, while the proposed diagrams may be applied to any temperature cycle, no matter howcomplex, and require the support of the system. The main problem of the proposed diagrams is thatthere are three variables to be shown simultanously: time, temperature and degree of conversion.To deal with this problem, either a special arrangement of three different graphs is employed (a-T-Tdiagram), or a 3-dimensional graph is used (T-a-T-T diagram) 51 '52 .A number of examples of the diagrams application are presented. These are either for thetemperature cycle as suggested by the manufacturer of the resin, or for temperature cycles used inthe investigation of the rheological properties of the resin. An interesting, although hypotheticalexercise, was conducted by using the system to generate Gillham' s diagram for isothermalprocessing. Another interesting application of the diagrams and the system is demonstrated for thenewly developed RTP method 9 '52 . The system provides the necessary information for this processingmethod to allow for its optimization.72. CHEMICAL SYSTEM OF EPDXY RESIN2.1 Introduction Thermosetting epoxy resin is a synthetic organic polymers that cures to a solid infusible mass byforming a three dimensional network of covalent chemical bonds. These network polymers possessa variety of useful properties, including high chemical and solvent resistance, outstanding adhesionto many substrates, low shrinkage on cure, good impact resistance, flexibility, and good electricalproperties. As a result, epoxy resins have gained wide acceptance in composite materials fordemanding structural application.The key to the excellent performance of epoxy resins is the chemistry involved in network formation.The epoxy resins (also known as epoxide resins and occasionally as ethoxyline resins) arecharacterized by the possession of more than one epoxy group per molecule (Figure 3). Thethree-membered epoxy ring is highly reactive to many substances, particularly with proton donors,so that reactions of the schematic form can occur (Figure 4).0^ 0^ OH—CH—CH— + HXFigure 3.^ Figure 4.Epoxy group^Schematic form of a typical epoxy reaction.8Such reactions allow chain extension and/or crosslinking to occur without elimination of smallmolecules such as water. As a consequence, these materials exhibit a lower curing shrinkage thanmany other types of thermosetting plastics. The non-epoxy part of the molecule may be aliphatic,cycloaliphatic, or highly aromatic hydrocarbon or it may be non-hydrocarbon. Similar remarks alsoapply to the chain extension/cross linking agents so that cross-linked products of great diversitymay be obtained. In practice, however, the commercial scene is dominated by the diglycidyl etherof bisphenol A (BPA) and its higher homologs. The glycidyl ethers of various novolac resins arethe second most important class of epoxy resins. The glycidyl novolacs are characterized by betterelevated-temperature performance than BPA-based resin.The cross-linking of epoxy resins may be carried out either through the epoxy groups or the hydroxygroups. Three chemical reactions are of major importance to the curing of epoxy composite matrices:the amine/epoxide reaction, the anhydride/epoxide reaction, and the Lewis acid-catalyzed epoxidehomopolymerization. The most common curing agents are the amines, in which each of theamino-hydrogens reacts with an epoxide group (Figure 5). Depending on the number of aminohydrogens on the curing agent, their reactivity, the number of epoxide group per resin molecules,and the supporting structures of each, a wide variety of mechanical properties can be obtained andvarious laminating processes can be used. Chain extension and crosslinking of epoxy resins dependon the reaction of epoxy groups with themselves and with the hydrogen of donor compounds. Thereaction may be promoted by heat, by catalysts, or by agents which chemically interact with theepoxide. The rate of cure of the epoxy system is significantly increased by agents such as borontrifluoride complexes, organic sulphides or tertiary amines.9CH2-7CHCH2'oOCH2CIHCH2OHCH3o A c1CH3OCH2CH —CH 2\o/nDIFUNCTIONAL+H1H—N CH2HIN—H• ANHYDRIDES.• LEWIS ACIDS,• 3° AMINESALSO CURETETRAFUNCTIONAL f . 41OHI-^^-^"'"CH2 —CH —CH2 \N•zwv`CH2—CH— CH2/OHCH2OH1,CH2 —CH—CH2N\CH2 —CH—CH2..wv•IOHFigure 5.Network Formation In Epoxy Resin102.2 Reaction Mechanism and Kinetics of Narmco ResinThe Narmco Rigidite 5208 epoxy resin, which was chosen for this study, basically consists ofTetraglycidyl Diamino Diphenyl Methane (TGDDM) and Diamino Diphenyl Sulphone (DDS)curing agent. The third component of the Narmco resin is based on a bisphenol A Novolac. TheTGDDM-DDS system is widely used in the manufacture of graphite fiber reinforced structuralcomposites for aerospace application. The chemistry involved in the Narmco curing process iscomplex. The epoxy amine reaction produces hydroxyl groups which have two effects: (1) theycatalyze the reaction which produces them, and (2) they themselves react with epoxy rings to formether linkages. 6 ' 34 ' 47 Therefore, the reaction mechanism is both a stepwise (epoxide-amine addition)and chain (etherification) polymerization. The sequence of main reactions presented in Figure 6was suggested in the literature. 5'34'47Figure 6.Main Reactions In The Cure of Narmco Resins123. MODELLING OF KINETICS OF CONVERSION3.1 Introduction: The first step for the development of an intelligent system leading to the design optimization andcontrol of the processing of high performance composites is to obtain adequate information aboutthe reaction kinetics of the epoxy matrix. The polymerization of a thermoset polymer generallyinvolves the transition of a fluid resin into a rubber, and then into a solid glass, as a result of thechemical reaction between active groups present in the system, which develop a progressivelydenser polymeric network. The reaction kinetics of thermoset matrices is strongly dependent onthe physical properties characterizing the different stages of the curing process. The dependency isstrong near vitrification where a cessation of the reaction is generally observed although the reactionis not complete. The rate of chemical reactions in condensed systems is controlled by the reactivityof functional groups and by their mobility. The reaction rate is controlled by the chemical reactivityof groups according to the mass action law, based on the average concentration of reactive groupsand the Arrhenius dependence of the rate constant on temperature. This case is observed if the rateof displacement of the group (diffusion) is much faster than the formation of the chemical bonditself. If, however, the mobility of the medium is reduced, the control by chemical reactivity (kineticcontrol) is accompanied by control of the reaction rate by diffusion (diffusion control).The diffusion control may be of two types: (a) specific, when the apparent reactivity depends onthe diffusion coefficient of the species (molecules) to which it is attached, and (b) overall, whenthe mobility of all groups is hindered by the reduced mobility of the medium. The specific diffusioncontrol is typical for fast reactions, such as chain polymerization, whereas, the overall diffusioncontrol is typical for polymer system where in the course of the reaction the system passes into aglassy state. This latter phenomenon is quite common in the curing of epoxy resins, when the glass13transition temperature Tg, increases so much that it approaches the reaction temperature T cure.The reaction is known to still continue at Tcure Tg, but the reaction rate decreases considerablyuntil it stops completely. When the reaction is quenched by vitrification, a subsequent exposure totemperature greater than the cure temperature could result in further reaction. 23,27,34,423.2 Degree of CureThe progress of the curing reaction is expressed quantitatively in terms of the fractional degree ofconversion of epoxide groups (a). Mathematically, it is described with a dimensionless numberranging from zero for an uncured resin to one for a fully cured resin. The degree of conversionvaries accordingly to resin kinetics and applied conditions. Initially the resin has a zero degree ofconversion meaning none of the resin component (amine and epoxy) has reacted. At the end of acure cycle, if all component have reacted, the resin has a degree of conversion of one. Since thepolymerization reaction of the epoxy system is exothermic the generic degree of conversion isdefined as:Fita = tot(1)where H, is the heat developed during the reaction between the starting point and a time (t), and1-1,0t is the total heat developed during the cure.daIn a kinetic model, an expression —dt f(a, T) must be derived where T is a temperature ofprocessing.2,16,47143.3 Review of Existing ModelsThe most common and one of the simplest models corresponds to an empirical n-th order of reaction,first proposed for epoxy resins by Kenny and Apicella. 40d cc= K (1 a)nwhere K is the temperature-dependent kinetic constant (Arrhenius Equation),K = A exp RTn is the reaction order, and a is the degree of conversion.This simple approach does not reflect an autocatalytic character of conversion and it does notaccount for the diffusion controlled phenomena.Assuming that the reactivity towards epoxy groups is the same for the primary amine groups initiallypresent and for the secondary amine groups formed during the reaction, Horie 37 has proposed thefollowing equation:d aTit = (K/ +K2a)(1 — a) (B — a) (4)where K 1 is a rate constant for the reaction catalyzed by groups initially present in the resin, K2 isa rate constant for the reaction catalyzed by newly-formed hydroxyl group, and B is the initial ratioof amine N-H bonds to epoxide rings. This equation takes into account the autocatalytic characterof the epoxy-amine reaction but it does not account for the possibility of an etherification reaction.(2)(3)15For the epoxy-amine system with a significant excess of epoxy with respect to amine and for asystem containing aromatic amines, where etherification reaction is important, the Horie equationis not adequate. The diffusion control is not included in the reaction.Kamal 38 ' 39 has proposed a semi-empirical equation:dot— = (K1 + K2 (0(1– ardt (5)The model includes an element responsible fo'r an autocatalytic behavior of epoxy systems and theequation provides a good fit to experimental data by introducing the variable m and n exponents,but it does not provide a description of the chemistry of the curing process. Additionally, the m,n,exponents are temperature-dependent (according to Arrhenius) and this dependency must bedetermined.Springer and Loos 43 have proposed two different patterns of behavior for the a divided by acritical value of a= 0.3.dadt = (K1+ K2a) (1 – a) ((3 - a)(6)d aTit = K3 (1 - a)16It is assumed that in the beginning (a< 0.3) the epoxide-amine reaction is prevailing and must beconsidered. When the epoxide-amine reaction is completed, the epoxide hydroxyl reaction takesover, and the reaction is assumed to be of first order. This equation gives a reasonably good fit tothe experimental data but again it does not provide a description of the network formation.Sanford and McCullough 61 have proposed a more advanced model for the epoxy-amine curereaction. They assumed a stoichiometric mixture of epoxy-amine, and described the autocatalyticreaction by:dadt = {K1+ K2(1— a)}a2 (7)where K1 and K2 have an Arrhenius temperature dependence.The equation describes correctly the early stages of the cure. As the cure progresses and the resincrosslinks, the glass transition temperature Tg of the system rises. When it approaches the curingtemperature, the resin passes from a rubbery to a glassy state, the mobility of the reactivity groupis hindered, and the reaction is controlled by diffusion rather than by chemical factors. If Equation7 was to remain correct also for advanced stages, the diffusional effect must be incorporated intoit. Following the approach of Huguenin and Klein 61 , the reaction rate may be modified via theRabinowitch equation yielding:EaA, exp(--i7Ki —^1 + (8 ) exp(--,Eawhere D is diffusivity, 8 essentially includes the vibration frequency and geometric factor, Ea isthe activation energy in the Arrhenius equation, and A, is the frequency factor in the Arrheniusequation.(8)17The diffusivity D is a function of temperature, as well as a, and may be described by free-volumetheory. Using Macedo and Litovitz approach 61 , which accounts for both, the activation andsegmental mobility, the diffusivity may be expressed as:Ed^bdD =Do exp(–R—T)exp(--f )^ (9)where Do is a constant, Ed is an activation energy of diffusivity, bd is a constant accounting forcritical free volume for motion, and f is a fractional free-volume.Combining Equations 7 ,8 and 9:Al exp(--Ea, )da ^RT— +dt80^Ed^Ea,1 +(7) exp(- 17 ) exp(- 2bf )exp(--RT)EntA2 exp(-- ) (1 – a)RT +^8^Ed^bd^Ea21 + ( D0) exp(- 77-, )exp(--f )exp(--1-?7, )1a2 (10)It should be noted that the fractional free volume(f) in Equation 9 and 10 is a function of an actualtemperature and the glass transition temperature of a material and is therefore also a function of a.f = fg + af(T – Tg )^ (11)where fg is a fractional free volume at Tg, of is a thermal expansion coefficient of the free volume,and Tg is a glass transition temperature described by the DiBenedetto equation.If Equation 11 is substitued into Equation 9:18bD =Do exp(– RiE exp(- 14 + af[T d_ Tg(0)]}^(12)A new mechanistic approach to modelling the cure kinetics of epoxy-amine thermosetting resinswas recently (1991) proposed by Cole. 15,16 The model is based on the model proposed by Horie,but it takes into account both the epoxide-amine reactions and the subsequent etherification reaction[Figure 6]. The kinetics is completely described by three rate constants of the Arrhenius type. Theeffect of the diffusion control is included and described by a simple equation. The model providesan excellent prediction of the degree of conversion over the whole range of cure (160°C-200°C)without introducing empirical parameters or making approximations such as separating the reactioninto distinct regimes. The constants were derived specifically for the Narmco 5208 epoxy-aminesystem.The basic assumptions inherent in the model are: (1) the epoxide-amine reactions arehydroxyl-catalyzed, (2) the secondary amine groups have the same reactivity with respect to epoxideas the primary amine groups, (3) the etherification reaction is first order with respect to epoxideconcentration, and may also involve hydroxyl groups, tertiary amine groups, or both. The progressof the polymerization is described in terms of two parameters a and (3. The first (a) is the overalldegree of conversion as expressed in terms of the fraction of epoxide groups reacted. The second((3) is the fraction of amine N-H bonds which have reacted. 15,16—d 13 = [(K1 + BK2 (3) (1 –13)] • (1 – a) • f(a, T)^ (13)dtda =dt [B(Ki + BK2(3) (1 – (i)+ K3 0 3] • ( 1 - a) -f(a, T) (14)19The diffusion control factor f(oc, T) is given by:f(a, T) = [1 + exp(30.1 a + 4.06 — 0.1617T)I 1^(15)The diffusion control factorf(a,T) was based on a semi-empirical relationship based on free volumeconsiderations. When the degree of cure reaches the critical value a„ diffusion control takes overand the diffusion-controlled rate constant kd is given by:Kd = IC exp[—C(a — as )]^ (16)where kc is the rate constant for chemical kinetics, and C is a constant.The equation corresponds to a rather sudden onset of diffusion control at a = a s . In reality, theonset is gradual and there is a region where both chemical and diffusional control are significant.According to Rabinowitch, the overall effective rate constant IC can be expressed:11^1_lc Kd IC (17)Combining Equation 16 and Equation 17, the diffusion control factor f(a) can be defined:IC ^1 f(a) — Kc — 1+ exp[C (a— ac )]The effective reaction rate is equal to the chemical reaction rate multiplied by the diffusion factor.For values of a significantly lower than as , f(a) is approximately equal to 1 and diffusion controlis negligible. When a approaches a„f(a) begins to decrease, reaching 0.5 when a = a,. Beyondthis point it continues to decrease, eventually approaching zero, so that the reaction becomes veryslow and finally stops.15'16(18)203.4 Conversion of Epoxide GroupsIn order to compare empirically determined parameters in the kinetic modelling, it is necessary toaccurately measure the conversion of functional groups. Three methods may be used for followingthe extent of reaction in an epoxide-amine system: titration, infra-red spectroscopy, and thermalanalysis.The classical method for monitoring the extent of reaction in epoxy-amine system is chemicaltitration. The most commonly used titration technique is based on the addition of a hydrogen halideto the epoxide group* 6/0\^OHI^I- C—C- + fa --* -C C-I^I I^IXThe difference between the amount of acid added and the amount unconsumed determined by backtitration with standard base, is a measure of the epoxy content.Infra-red spectroscopy has also been used to analyze the conversion of epoxy resin with amine Themethod is based on the fact that change in the IR absorbance band at a frequency associated witha certain functional group are related to changes in the concentration of that particular group in thesample. The infra-red spectroscopy technique for monitoring the extent of reaction has severaladvantages. The disappearance and formation of all the types of functional groups which occurduring the cure reaction can be monitored. It is also possible to determine conversion for samples21in the pre- and post-gel regions. However, there are limitations involving the application of infra-redspectroscopy to quantitative analysis . One of the primary difficulties associated with this methodconcerns the complexity of the IR spectra and the sensitivity of the equipment, which enhance theprobability of the overlap of absorbance peaks. Severe inaccuracies in the determination of thedegree of cure can result by overlap of new bands which appears during the reaction."'Differential Scanning Calorimetry (DSC) is the third, and probably the best, method which can beused to determine the extent of reaction in thermosetting systems. It measures the rate of enthalpychange as a sample is cured. It is assumed that the heat evolved during the reaction is proportionalto the conversion of functional group [Equation 1]. Equation 1 assumes that the extent of the reactionat the end of the cure cycle is 100%. Ideally, 1-1,0, is equal to the heat corresponding to the totalconversion of all reactive groups. Equation 1 also assumes that a single type of reaction occursduring the cure or that the heat evolved during different reactions is the same. 17223.5 Experimental Verification of Cole's ModelThe Narmco 5208 resin used in this study was provided compliments of Canadair Inc. The resinwas in the form of a partially polymerized film. The actual initial degree of polymerization (a) inthe received sample was 0.03, according to Narmco Inc.The applicability of Cole's model to the above resin system was verified in the experimental portionof the work. The experimental process utilized to perform such a verification was conducted on aDifferential Scanning Calorimeter (Du Pont 2910 module) under the conditions of nitrogenenvironment in accordance with the following procedural guidelines. The verification included bothisothermal and non-isothermal tests. Isothermal DSC tests were performed to eliminate the eventualdependency on temperature of two types of reactions with different rates, occurring simultaneouslyduring the cure of TGDDM-DDS system.Approximately 10 mg samples of the material in question were placed in unsealed aluminum pans.The basic calibration process was conducted accordingly to the instrument operating manual.Isothermal runs were performed at three different temperature; 130°C, 170°C, and 190°C. Theexperimental results of these tests are visually depicted in Figures 7-10.In the dynamic mode the samples were heated from room temperatures to 300°C and two heatingrates 3 °/min and 5°/min were used to obtain the results shown in Figure 10 and 11. In the dynamicmode, the accuracy of the results was additionally verified by introducing an extra procedure.Following the basic experiments each sample was heated for a short time interval at 300°C to assurea complete cure reaction. The sample was then cooled within the equipment and re-heated again at23the same heating conditions. The DSC record obtained during the re-heating contains nothing butthat characteristic of the equipment and could be used as a calibration curve for a main experiment(Figure 12).3.6 Results and DiscussionOn the basis of Cole's kinetic model a computer program was developed which numericallyintegrates the rate of conversion as a function of time for a given temperature history.The examples of the DSC records, plotted against the ones predicted from the model are presentedin the Figures 13-16.An excellent agreement between results predicted from Cole,s model (smooth lines) and theexperimental data (lines marked with circles) can be found. In the case of dynamic heating with therate 5°C/min [Figure 16] there is virtually no difference between the predicted curve and theexperimental data up to a temperature of 210°C.Small differences are observed for a low temperature isothermal test (130°C) and for dynamic testsfor temperature exceeding 200°C. It should be remembered, however, that the validity of the modelwas defined by Cole as 140°C-190°C. At 130°C the rate of the reaction is very slow and the sensitivityof the equipment is not sufficient to draw any conclusion.243.7 Contribution of the AuthorThe authors own contribution within Chapter 3 consists of:(1) Development of a computer program for Cole's model of kinetics of conversion.(2) Verification of Cole's model, using the DSC technique.Neither of the mentioned tasks contain an element of originality; Cole's model has been presented15,16 as a complete package, including all related constants, and the DSC is a technique routinelyapplied for investigation of the kinetics of thermoset conversion. 17 The computer program of thekinetics model developed by the author employs the commonly used method of numericalintegration. Using an assumed temperature history the code calculates and integrates the rate ofconversion for consecutive time increments, producing a history of conversion as an output.25Figure 7.Isothermal DSC curve obtained at temperature 130 °C.0.140.12o . 10of 00.080 .06Legend:T - temperatureC - DSC curve0.040.020.00 17—^--r—20 40 6b-r-^1^ -r-BO 100 120^140^160^180^0Time (min) General V4.1C DuPont 2000Legend:1^T - temperatureC - DSC curve300— 250—200300)c.— 150 n4-)^aE0)I-- 100—500.40.0 I020^40^60^80^160^120^140Time (min)^ General V4.1C DuPont 2000000000)LzU)E4-3cn01—■U.cooo• .•••(C-f)yin• •••••4Ccl••=6`"3bA -FL)CCI•.040 0CI)C.)Ecd3001.21.0—250Legend:T - temperatureC - DSC curve0.8—200-Ei)x 0.6—04.,1500.4—1000.2—0.0—50—0.220 25 30Time (min)035^40^45General V4.IC DuPont 20000.300.28-Legend:T - temperatureC - DSC curve300- 250I0.26--a-200F.,00.24- - 1500.22- - 1000.20- - 500.18 0 10^20^30^4^6^60 0Time (min) General V4.1C DuPont 20000.050.043..§ 0.040Z 0.0350a5 0.030CCw> 0.025Z0C.)^0.020U.0 0.015LLI<I—^0.010CC0.0050.00031RATE OF CONVERSION-Legend:calculatedexperimental_0 0 ---,...........,......_e0^60^120 180^240^300 36TIME (MIN)Figure 13.Verification of conversion kinetic model.Isothermal 130°C.32RATE OF CONVERSION0.160.140.1200.10CCL1J> 0.080• 0.06LL00.04I-<CC 0.020.00Legend:- calculated0^ 0 0 - experimenter0^30^60^90^120 150 180TIME (MIN)Figure 14.Verification of conversion kinetic model.Isothermal 170°C.0.500.4513k- 0.40Z 0.35O0.30CCw> 0.25Z0O 0.20U_O 0.15IliI--^0.10CC<0.050.0033RATE OF CONVERSION/ALegend:- calculatedo o 0^- experimentale0^10 20^30^40 50^60^70^80^91TIME (MIN)Figure 15.Verification of conversion kinetic model.Dynamic 3°/min1.21.1.3)^1k**0.9O 0.8(7)cc 0.7w> 0.6O 0.50U- 0.40w 0.3I-< 0.2CC0.1034RATE OF CONVERSION/Legend:calculated- experimentalAii•/o e0^5 10 15 20 25 30 35 40 4!TIME (MIN)Figure 16.Verification of conversion kinetic model.Dynamic 5°/min.354. CHEMORHEOLOGICAL CHANGES DURING CURE4.1 TheoryDespite the widespread use of polymer composite materials there are still many technical problemsto be solved. One of the major issues is processing of high performance thermoset composites withimproved material quality and reliability. Todays choice of processing parameters is primarily basedon extensive testing. This approach is not only costly but additionally, if the prepreg material orgeometry of the parts is changed, the testing results are usually not applicable. Instead, a scientificapproach can be used which is based on an understanding of the fundamental chemical and physicalevents characterizing the behavior of the composite during processing. This approach allows for abetter choice of processing conditions and decreases the experimental work needed to determinethe proper cure cycle. From a material point of view, not only chemistry but also the processingconditions should be selected to give the most uniform and reliable cure obtained in the shortestpossible time. The characteristics of the curing process and the final properties are stronglydependent upon the chemorheological properties. 2,4,14,41,60The knowledge of the chemorheological characteristics is extremely important in the fabricationof advanced polymeric composites which requires precise resin cure control. This part of the workis focussed on the principal rheological phenomena governing the behavior of thermosets duringtheir processing. 31 '45 '55Generally, the processing of thermoset matrix composites (curing process) involves a transition ofthe polymer from the liquid to the solid state as illustrated in Figure 17 6 . In the case of an epoxy36matrix a liquid consists of epoxy oligomers, a curing agent and often catalysts. The cure begins asa consequence of stepwise polymerization with simultaneous linear growth and branching of thechain. Whether branching or linear growth occurs faster depends on the relative rate of the epoxidewith the primary or secondary amine hydrogens. As the reaction proceeds, the molecular weightincreases rapidly, and eventually several chains become linked together into a network ofsemi-infinite molecular weight. The sudden and irreversible transformation from viscous liquid toan insoluble gel is known as the gel point. At the gelation point, small molecules are also presentand often the majority of the reactive groups are still unreacted. Gelation does not inhibit the curingprocess; after gelation the reaction proceeds towards the formation of one infinite network with asubstantial increase in cross-linking density, stiffness, glass transition temperature, and ultimatephysical properties. The volume contraction which occurs during the cure is a result of the exchangeof Van der Waals bonds for shorter covalent bonds. Because of increased molecular crowding theglass temperature is elevated. 24,32,34,4137Figure 17.Schematic representation of the cure of a thermoset, starting with monomers (a), proceeding viasimultaneous linear growth and branching below the gel point (b), continuing with formation of agelled but incompletely crosslinked network (c), and finally a fully cured thermoset (d).384.1.1 ViscosityFor many simple fluids, the study of rheology involves the measurement of viscosity only. For suchfluids, the viscosity depends basically upon the temperature and hydrostatic pressure. However, therheology of polymers is more complex because polymeric fluids do not show ideal behavior andtheir rheological properties depend upon the rate of shear, the molecular weight and structure ofthe polymer, the concentration of additives, and the temperature. 50 '66For ideal, Newtonian fluids :Shear stress^T T=Viscosity (11) = Rate of shear strain dY ydt(19)If the fluid is not Newtonian, a plot of shear stress T, against the rate of shear if, is not a straight linebut a curve, such as the solid line shown in Figure 18. The liquid may be Newtonian at very lowshear rates to give a limiting viscosity ri o from the initial slope of the ti versus Y curve. When the— y curve is not linear, the viscosity may be defined in two ways for any given rate of shear asillustrated in Figure 18 5° . The apparent viscosity Ti c,, is the slope of the secant line from the originalto the shear stress at the given value of shear rate, that is,tiAla = 7^ (20)The slope of the line at the chosen value of 'j' is another viscosity called the consistency l c .(21)39Figure 18.Measurement of viscosity40In the cases where the relative velocity of shearing plates is not constant but varies in a sinusoidalmanner, a complex viscosity T) . i, is measured. The complex viscosity contains an elastic componentin addition to a term similar to the ordinary steady state viscosity. The complex viscosity is definedby:1 = - ill "^(22)The dynamic viscosity ri', is related to the steady state viscosity and is the part of the complexviscosity that measures the rate of energy dissipation. The real component of viscosity ri', measuresthe dissipation of energy and is related to the loss modulus G", by:G = con'^ (23)The imaginary viscosity T) , measures the elasticity or stored energy and is related to the storagemodulus G', by5° :G = wry "^ (24)where co is the frequency of the oscillations in radians per second.The zero shear viscosity of thermoset depends on the structural build-up during polymerization,and is equal, according to Berry and Fox, to:ri = F^ (25)41where is a friction factor and F is a structure factor.The friction factor depends on local intrachain and interchain forces between neighboring segmentsin the polymer and its magnitude is given, according to Sanford, by the equation:c = co exi:(„f;, j expW^(26)where En is the activation energy, b is a constant which includes a critical free volume required formotion, and f is a frictional free volume, which equals:f = fg + a(T —Tg)^ (27)where fg is the free volume at Tg, and a is an expansion coefficient. The structural factor F, inEquation 25 may be expressed:Fccg(M,„)a^ (28)where g is a gyration factor, Mw is a weight average molecular weight, and a is a constant havinga value in range of 2.5 - 3.5.It should be noted that:g,111,,= f(a)^ (29)Tg in Equation 27 may be found from the DiBenedetto Equation 48,49 and Mw can be calculatedfrom the Macosco 44 Equation 33.424.1.2 GelationFrom a rheologic al point of view, two major phenomena occur during thermoset processing; gelationand vitrification. 19,27,40,48,53 The gelation is of great technical importance since the flow of a resinis not possible after gelation. As a consequence, void diffusion and further compaction of thecomposite can no longer occur. 2 '43 Gelation occurs at a specific point in the course of the chemicalreaction and depends on functionality, reactivity, and stoichiometry of the reactants. The criticalconversion at the gel point can be derived from the theory first proposed by Flory 25 . Flory introducedthe branching coefficient (x) defined as the probability that a given reactive group of a branchedunit of functionality greater than two is connected, via a chain of bifunctional units, to anotherbranched molecule.For a resin/hardener system, 3 '4° if Pe and Pa are the fraction of epoxy and hardener active groupswhich have reacted, respectively, the branching coefficient is given by:P 2K = P e • Pa = r Pa2 = -ir (30)where r is the ratio of the hardener (ma ), to epoxy (me ) groups initially present in the reactive mixturema faMar = -=me feMewhere fe , fa are the functionalities and Me , Ma are the moles of the epoxy resin and hardener molecules.The condition describing the incipient formation of an infinite network is derived by the theoreticaldependence of the molecular weight on the branching coefficient.(31)+43When the branching coefficient reaches its critical value ic, the network leads to an infinite molecularweight:1K —^c Ve — 1)(fa — 1) (32)For TGDDM-DDS system, weight - average molecular weight may be expressed as 7 '44 : Pa[ 1+  pe Pe ea [1 + Pe e^e ll[Al eM a_ a +Pe _ ea^Pe—e(33)ma2 + fa ± mei+(- f±1M a + Mer • faPe _ ea^r.m^ 1 d- 1 11[(f 1)M I pae+ p +p[^Pe e^e —^ae _a e _ ea +( fer pa )[( rffe a )ma+ me][P eM a +[P e (i) — 1) +[P JD — 1) pe_Pae+— peae—ea +2Pe _ e + 2Pe - eel [ 1 + 1pe _711Mel[1 — (fe — 1)[P JD — 1) +[P e (i) — 1) pe—a +pe —ea +2P e _ e + 2P e --ee][1 + Ppee- ee ]11Pe _ ea—eA4,2^ A4,3E> E E>_<EEA4,044where:f, - functionality of the TGDDM monomer = 4fa - functionality of the DDS monomer =4Ma - monomeric molecular weight of DDS = 248Me - monomeric molecular weight of TGDDM = 422r - stoichiometric ratio of epoxide groups to amino-hydrogen groupj2p.^'• weight average extent of reaction — 1 .pa,tP a , i - fraction of amine units which have i reacted sites Pa - conversion of amino-hydrogensP, - conversion of epoxide groupsPe -a 5 Pe -e 2 Pe -ea) Pe -ee - fractions of epoxide groups of EA, EE, EEA, EEE configurations, respectively(Fig. 19 and 20).A4,1 A4,2 ,^A44Figure 19.Types of amine units with 0,1,2,3, and 4 reacted sites45Schematic ^Chemical Structure^Description of Reaction /0\,%"•-CH2CH CH2 The epoxide group is completelyunreactedE 0 OH1^1cH2 CH— CH2OH1/N"\-CH2CH—CH_1 201r`IN-CH2CH— CHT-N-"-P.The epoxide group has reactedwith an amino-hydrogenEAThe epoxide group has reactedwith an amino-hydrogen and thenthe formed hydroxyl reacted withan epoxide groupH1r`l"\--CH2CH--CH-4•1..",\201"1.•- CHC11--CH2OHThe epoxide group has reactedwith a hydroxyl groupEEH1r`t\--CH2CH—CH--N...n.,\0'`r\--CH2CH--CH2,%/N-CH,CH—CH24 IOHThe epoxide group has reactedwith a hydroxyl group and thenthe newly formed hydroxylreacted with another epoxidegroupFigure 20.Possible configurations for TGDDM-DDS system46At the gel point, the weight-average molecular weight becomes infinite. 7 '44 This condition is metwhen the denominator of the last segment of Equation 33 is equal to zero:e—ea^ e —ee1— (fe — 1 )[P e (I) — 1) ±[P e (v — 1) Pe P ± Pe ea+ 2Pe—e + 2Pe—ee  Pee][1+  il= 0 (34)The above equation allows for the calculation of the critical value of conversion at the gel point.However, the procedure of calculations is not straightforward since the conversion exists in theequation in an implicit form, being represented by elementary conversion ratiosPe — alPe — e,Pe —ea , Pe — ee•In order to obtain the conversion at the gelation point, a kinetic model accounting for all mentionedelementary conversion ratios contributing to the overall conversion, must be run for the consecutivetime increments until the condition in the Equation 34 is approached.Under typical processing conditions the polymer at the critical gel point is neither a solid, sincestress in a deformed critical gel can relax to zero, nor it is a liquid, since stress during flow growsto infinity. The polymer before the gel point (sol) is soluble, while the polymer beyond the gel pointis no longer soluble. At the gel point the steady shear viscosity diverges to infinity. The steady shearmeasurements, however, can not be used in the close vicinity of the gelation point since they wouldresult in breaking an existing molecular structure, and dynamic mechanical measurements are usedinstead. In such an experiment, the evolution of G' ,G'' is measured in small amplitude oscillatoryshear as a function of extent of crosslinking, (a) .47At the gel point the dynamic moduli follow a power law 69,70:G' — G" ,---, con^(35)The loss tangent, tan 8 = G,, is independent of frequency. Therefore, two methods to determine thegel point exist:1.The gel point is reached when the loss tangent becomes independent of frequency, the methodused successfully by Holly 36 .2. For some polymers the gel point coincides with the G' — G " crossover, in experiments in whichG', G" are measured at constant frequency, co, during the evolution of the crosslinking reaction.This method can by applied for stoichiometrically balanced polymers, 6 and networks with an excesscrosslinker, at temperatures above the glass transition. 32,33,62These novel methods not only allow for the direct determination of the gel point but they also allow,by extrapolation, the prediction of the gel point when the polymer is close to gelation, but has notyet reached it.6'35'56'69'713484.1.3 VitrificationDistinct from gelation, vitrification may occur at any stage of the reaction. This transformation froma viscous liquid or elastic gel to a glass appears when the glass transition temperature of the materialreaches the cure temperature, or vice versa. Further curing in the glassy state is slow and diffusioncontrolled. Vitrification is a reversible process. Curing of vitrified material can be accelerated byheating the partially cured thermoset above its glass temperature Tg. "26'41'42,67 The glass temperatureTg, is the temperature below which a material exhibits properties typical of glass. It is usuallydefined in terms of a specific volume or enthalpy as a function of the cooling rate. At temperaturesabove the glass transition the molecular mobility is great enough for a material to rearrange rapidlyto a structure characteristic of its temperature. Upon cooling, the increase in molecular crowdingdecreases the mobility to the point where rearrangements necessary to achieve an equilibrium liquidconfiguration and chemistry can not keep up with the rate of cooling. The point of departure fromthis equilibrium state or break (abrupt decrease in slope) in the specific volume-temperature coolingcurve depends on the rate of cooling. The departure or break comes sooner at a higher temperaturewith faster cooling. At slower cooling rates the sluggish molecular rearrangements can keep upwith cooling until a lower temperature is reached. This break point is identified as a glass transitiontemperature and is a material-characterizing parameter. (Figure 21.)Aq(dCp)(b)49Tg8 TgA^TTrFigure 21.Specific volume (enthalpy) as a function of temperature: (a) for two different cooling rates (A>B)and (b) starting from a particular condition of the material in the glassy state at two different rates(A>B).50The glass transition temperature Tg, is a sensitive and practical parameter for following the cure ofa reactive thermosetting system. 27 '53 '70'67 A wide range of values of Tg is encountered during cure,and it can be measured throughout the entire range of cure. The fact that Tg increases nonlinearlywith conversion in crosslinking system, makes it even more sensitive in the later stages of reaction,when the reaction rate is slow, for example at high conversion and after vitrification (solidification).DiBenedetto 48'49 in his analysis of the crosslinking effect on the physical properties of the polymer,derived the equation relating the shift in the glass transition temperature to the extent of reaction.Ex^Fx _.Tg—Tgo E: - ( F.) a (36)Tg^1 _ ( 1 _ !F:,n )ccFx iwhere Tgo is the glass transition temperature of the system at a=0, —F s the ratio of segmentalm mobilities for a certain extent of the reaction cc,energies.Exand — is the corresponding ratio of latticeErnEnns and Gillham showed that an excellent fit of the overall experimental Tg versus a relationshipEX,E Fxcould be obtained when both 7  i were taken as adjustable parameters. Moreover, the ratio of bothparameters is given byexTge.,Tx = TgoFmwhere Tgc., is the maximum glass transition temperature obtained when a =1.(37)514.2 Experiments4.2.1 IntroductionFrom the main three rheological parameters of thermosets; viscosity, point of gelation, point ofvitrification, only the latter two are of direct interest to the study. An attempt has been made todetermine them experimentally. The objective of the experimental effort was twofold:(1) To verify the suitability of modern methods for rheological parameter determination. Some ofthe methods are novel and eventual difficulties in their application or interpretation, as well asadditional information they may provide, were of interest. It would be beneficial to suggest easyand dependable procedures for determining the necessary rheological information along withdiagrams and concepts of modelling of thermoset processing proposed in the next chapter.(2) To verify the overall accuracy of the modelling system consisting of two elements; kinetics ofconversion and rheological characteristic of the resin. The system is presented in the followingchapter.Numerical values of the parameters obtained from the experiments are of secondary importance -they could be either derived from the theoretical considerations or found in literature.524.2.2 Review of Techniques for Rheological CharacterizationDuring a cure cycle, the thermosetting material changes from liquid to a glassy solid state, and theextent of the viscoelastic modulus variation made the monitoring of the structural built-up verydifficult. While polymers in the liquid state can be characterized by steady-state viscositymeasurements, dynamic theological techniques are needed to follow the cure behavior in thepost-gel region. For thermosetting systems, dynamic measurements are generally easy to perform,and data can be collected in both the liquid and the post-gel region. 19 56,58,59,62,63,64,69In the dynamic measurement, samples of a material are subjected to oscillating forces and theresulting deformations are measured. Dynamic moduli and loss tangents are evaluated as a functionof forcing frequency, time/degree of cure, and temperature. These methods include low-frequencynonresonance and resonance methods.For an isotropic sample that is subjected to a sinusoidaly varying tensile strain E, at a frequencybelow that required to induce resonance vibration, for linear viscoelastic behavior, under steady-stateconditions, the stress a, sustained by the sample is also sinusoidal, but the stress cycle leads thestrain cycle by a phase angle 8 , as illustrated in Figure 22. 58= co cos cot (38)= ao cos(cot + 8) (39)a = a, cos 8 cos cot — as sin 8 sin cot (40)where w is the angular frequency and a o , co are the amplitudes of a and E.53tFigure 22.Time dependence t, of the stress a, and strain E, during a low-frequency (nonresonance) test.54Equation (40) demonstrates that the stress consists of two components. One component is ofmagnitude ao cos 8 and is in phase with the strain. The other component of magnitude a o sin 8 is90 ° ahead of the strain and thus in phase with the strain rate. Therefore, the material behaves partlyas an elastic solid and partly as a viscous liquid, and the stress - strain relationship is written:CY = E0E ' COS C.Ot — F.0E" sin cot^ (41)where the component moduli are given by:E =—'go cos 8Et)- aoE =— sin 8e0These equations suggest that the tensile modulus can be specified in complex form. For this purposethe strain and stress cycles are represented by the real part of :E = Eo exp(i cot)^ (44).G = Go exp[i (wt + 8)] (45)where1i = (-1)2^(46)Then:(42)(43)55* (7^Ea* GoE = –7, = —exp(i8)E E * = (-12 (cos 8 + i sin 8) = E' + i E"EoThe real part of the modulus E', which is in phase with the strain, is termed the storage modulussince it is proportional to the peak energy stored per cycle in the material. The imaginary part ofthe modulus E", which is out of phase with the strain, is proportional to the net energy dissipationper cycle and is known as the loss modulus.The ratioE= = tankE (49)is termed the loss factor or damping factor.It should be emphasized that E', E" , and tan 8E depend on the test frequency and also on temperature,and each is used to characterize dynamic mechanical properties either at a given frequency ortemperature or preferably, over a range of these variables.Although the components of E * are determined quite simply from dynamic tensile or flexural tests,it is often convenient to obtain dynamic properties for another mode of deformation - the shear. Forisotropic materials, dynamic experiments yield the components of the complex shear modulus:G G' + iG" = 01 + tan 8G )^ (50)(47)(48)where G', G " , and tan 8E , are the shear storage modulus, loss modulus, and loss factor, respectively.56Nonresonance MethodsAt low frequencies (0.01 - 100 Hz) dynamic moduli and loss factors are determined directly fromthe amplitudes of, and phase angle between, the force and displacement cycles for samples subjectedto a time-harmonic force of deformation. For polymer evaluation, the instruments working innonresonance methods include thermal mechanical analyzers, and rheometers. The idealinstrument, in this category, is the Rheometrics Dynamic Analyzer (RDA) evaluating suchviscoelastic properties as viscosity (i *), elastic modulus (G'), viscous modulus (G"), and damping( tan 5). The RDA is capable of making these measurements on a material in its liquid or solid formin dynamic shear using parallel plates, cone and plate, and torsion fixtures. The combination ofprecision stress and strain detection, makes RDA the most accurate and convenient instrumentavailable. RDA evaluates materials under an extremely broad temperature range (-150 to 600 °C).The wide dynamic range of the RDA's transducer (at least three decades) makes it ideally suitedfor thermoset characterization. Minimum viscosity, gel point, and vitrification moment of resinsand prepregs can be determined during curing. With a temperature range of 1° to 60°C per minutealmost any curing process can be simulated. 8,14,20,58,59,64Resonance Method - Torsion Pendulum, Dynamic Mechanical AnalyzerTorsional deformations are more suitable than simple shear for determining the dynamic shearproperties of rigid materials as they avoid the high force level associated with measurabledeformation. Although less versatile than nonresonance techniques, this methods allow moreaccurate measurements. Values of the elastic modulus and loss modulus can be obtained for aspecimen of known simple geometry (rectangular film or a cylindrical filament). The elastic shearmodulus G ', is calculated from the frequency and the logarithmic decrement is calculated from the57decay of a damped oscillating wave. The times to macroscopic gelation and vitrification can beassigned from the times to reach consecutive maxima in the logarithmic decrement vs. timepiot.9,24,27,47,584.2.3 Determination of Gelation and Vitrification Points Using RDA TechniqueFor the determination of the gelation point the RDA technique seems to be the most promising.Alternative methods are: solubility testing and the Torsional Braid Analyzer (TBA). Solubility tests,however, are not very exact due to the subjectivity involved in the interpretation of their results.The TBA technique was reported 23,24,27,47,70,71 to be successfully used for defining gelation but theauthor of the Thesis did not have access to the equipment. To specify the vitrification moment anumber of methods may be used: DSC 19 '7133 , TMA 20, RDA59, and TBA 23,24,27,46,47,71,72,73 Due to thecomplex behavior of thermosets only resonance techniques are commonly utilized for this purpose.However, in this work, lack of access to TBA and DMA equipments forced the author to investigatethe possibility of using RDA and DSC methods instead.The tests on the RDA apparatus (Figure 23), to which access was provided, courtesy of the DefenceResearch Establishment Pacific, were conducted by continuous monitoring of rheologicalparameters of the material undergoing a processing cycle. The applied processing cycles wereusually isothermal using the processing temperature in the range of 140 - 190 °C and consisted ofthree parts: a rather rapid ramp from room temperature to the temperature of isothermal processing,extended period of isothermal processing, and a linear decrease of the temperature at the end of thecycle. Only in one instance, in order to speed up the conversion process, the temperature of 170 °Cwas applied initially, and later returned to the temperature of processing of 140°C.58Figure 23.Rheometrics Dynamic Analyzer59In the experiments parallel plate geometry was used, with the exception of one experiment, whichwas conducted in the torsion mode. The decision to use parallel plates stemmed from the fact thatthe arrangement has been commonly used by other authors 6 ' 3342 . The choice of plate diameter (25mm) was to ensure versatility of measurements, so that both phenomena, gelation and vitrification,could be recorded in the same experiment. Smaller plates, more suitable for monitoring of advancedstages of processing, had to be ruled out due to the resin bleeding problem resulting from the verylow viscosity of the Narmco resin at low levels of conversion. If the viscosity itself were the mainobject of investigation, the larger plates (40 mm) would be advisable.The material used in the parallel plate investigations was Narmco 'B' - stage resin, while forexperiment in the torsion mode the Narmco prepreg was used. The thickness of resin placed betweenparallel plates was about 0.4 mm. The mode of test under the apparatus nomenclature was 'time/curesweep'. The frequency of oscillation in the experiments was set at 1.6 Hz. After placing the materialbetween the plates, the gap between them was fixed, not allowing for any axial movement. Thiswas necessary to avoid squeezing the resin out from the gap at an early stage of the experiment.Considering the extreme changes in material physical/mechanical properties during the processing,the 'auto' option was chosen for the strain, with a maximum value of 10% adjustable in 2% steps.The maximum allowable torque was specified as 60 g•cm. Under the mentioned mode the apparatusattempts to maintain a minimum stress which provides a satisfactory level of measured strain andstress. In the low viscosity region the strain is increased up to its specified limit to generate asufficiently strong signal representing torque. In the region of material vitrification, the maximum,specified torque is used to generate the measurable strain signal.During the experiment, the temperature of a material, storage modulus, loss modulus, and eventually,tangent of the phase angle between stress and strain (loss tangent) are recorded by the apparatus.On the basis of these records, which are presented in Figures 24a-31a, the determination of gelation60and vitrification points was carried out.The point of gelation, for a single experimental record, was identified as a place of intersection ofthe storage modulus G' and loss modulus G" curves. The more rigorous procedure of searchingfor the moment where the ratio of both moduli does not depend on the applied frequency of oscillationcould not be implemented due to time restrictions in the access to the RDA. Nonetheless, theinvestigations of other researchers 6 ' 33 ' 62 show that for frequencies in the range 1 - 10 Hz, the pointof moduli intersection yields a very good approximation of the gelation moment. It may be notedalso that the curves of both moduli in the vicinity of gelation become so steep that even if the ratioof the moduli corresponding to gelation is slightly different than 1, the resulting error in term ofgelation moment is negligible.The determination of the vitrification point from the records was difficult. In the absence of anyclear suggestion in the literature, the intention was to look for any characteristic behavior of curvesG', G", and tangent of phase shift, which may indicate the point of vitrification. The latter two(G",tangent) had to be ruled out, however, since in the vicinity of vitrification their readings wereout of the sensitivity range of the apparatus. The area of the G' curve where the vitrificationphenomena should be looked for remainded a question. The work of Gillham 24 ' 2733 suggests thatdue to the decreasing rate of conversion in the vicinity of vitrification, the moment of vitrificationis not to be expected during isothermal processing, but rather later, during final cooling. In this areaof the records, either an increase, or sudden and pronounced decrease of the storage modulus G'appears, the latter suggesting, perhaps, breaking of a material. In the interpretation of the results,with one exception, this point of rapid decrease of G' was considered as an approximate vitrificationmoment.A question may arise concerning the rationale of the assumption that the moment of materialbreaking may mark the moment of final vitrification. During thermoset processing, even under61isothermal conditions, the density of chain packing increases, leading to the shrinking of a material.This is especially true when a material approaches vitrification. The linear decrease of processingtemperature during the final stage of the experiment additionally contributes to shrinkage. At themoment of vitrification the free volume disappears, making a material more brittle. All these,combined with the fact that the gap between plates is forcefully fixed, leads to the generation ofstresses, and may lead to an eventual breaking of the material."In Figure 26a a typical record is presented. It may be seen that at a beginning of the cycle bothcurves, G' and G", drop to a very low level and remain at it for 20 - 30 minutes, responding to theapplied temperature. Later the advancement of conversion causes the curves to rise again. Thecurve of G" starts first but the rate of increase is higher for the G' curve so that the curves crosseach other after the time of about 40 minutes. The point of intersection is considered as a point ofgelation and is marked 'G' in the figure. Proceeding further, the curve of G" reaches local maximumand becomes chaotic (measurement is out of the sensitivity range). The curve of G' in the meantimeincreases at progressively decreasing rate forming a knee shape. A linear temperature decrease atthe end of processing results in an increase of G', followed by its sudden drop at the moment wherevitrification is expected.The procedure for the identification of the vitrification moment is not simple. In experiment140°C/30min (Figure 24a) no break in a material is recorded, and a vitrification point is recognizedas a moment when the curve of G' rising rapidly, reaches the high-level plateau. In experiment170°C/140 C/180min (Figure 25a), and in experiment 170°C/60min(A) (Figure 26a), a clean dropin G' curve is recorded. It may be noticed, however, in these and in the other experiments that theresin seems to never break completely. In experiment 170°C/60min(B) the G' curve recovers whenreheating is applied (Figure 27a), which is something to be expected. However, in experiment62170°C/120min(A) (Figure 28a), the curve 'recovers' during further cooling. This casts a doubt onweather the sudden drops of G' curve observed in the figures are really associated with materialbreaking, or rather with the displacement of the tool in its fixture under extensive stress.In the record of the experiment using the torsion mode, the gelation point cannot be identified.Neither can the vitrification point be determined from the storage modulus curve. However, athorough examination of the loss tangent curve shows an interesting oscillation (Figure 32b) forthe time of processing of 170 min, which corresponds to the processing temperature of about 100°C, while the vitrification is expected to take place at about 115°C . Nonetheless, since the oscillationis weak, agreement is only approximate, and on the basis of a single record no suggestion can beformulated.634.2.4 Discussion of the ResultsA major inconvenience in further evaluation of the obtained results is that the points of gelation orvitrification found on experimental records are specified in terms of time and temperature, but notin terms of the degree of conversion. It is quite natural that for different temperatures of processingthe time for gelation and vitrification to take place is different; this information, however, is notadequate for the evaluation of the results through necessary comparisons. The comparison can onlybe made on the basis of the degree of conversion and temperature. It should be recalled (Equation34) that for any resin system, gelation is expected to take place at one specific value of the degreeof conversion, and that the vitrification point can also be expressed as a function of the degree ofconversion, with the addition of temperature of processing as a secondary parameter (Equation36). In order to obtain values of the degree of conversion, the kinetics of conversion for the Narmcoresin was utilized in the work to build the model of conversion in the form of a computer code basedon numerical integration (see Chapter 3). The nature of the model allows it to be applied to anytemperature/processing cycle, producing consecutive values of conversion as a function of time.The model was used to produce a curve of conversion as a function of time for each processingcycle of the experiments (Figures 24b-31b). From these curves the degree of conversion,corresponding to the time of identified gelation and vitrification, could easily be found.In Table 1 the temperature of processing, time of processing at gelation, and degree of conversionat gelation for conducted experiments are provided. The identification of the gelation point fromexperimental records, as a point of inter-section of storage and loss modulus curves, did not createany serious problems. A minor problem may be reported in experiment 190°C/180min(B) (Figure31a), where strong oscillation of G' and G" appeared directly before gelation.64The obtained experimental values of conversion at gelation are in a very narrow range (0.31 - 0.36),which is consistent with the theoretical value of conversion at gelation of 0.33 6 '7 ' 8 . This excellentagreement proves that the RDA technique is ideally suitable for the determination of gelation. Italso strongly indicates that the theory of resin rheological behavior, combined with a high-qualitykinetics model of conversion, is able to produce results very consistent with high-precisionmeasurements.It may be noticed from Table 1 that the degree of conversion at gelation slightly increases with theincrease of the temperature of processing. This tendency, although in agreement with Serrano andi63Harran, 62 s much weaker than reported there, and its statistical significance is doubtful.In order to conveniently discuss the experimental results of vitrification, the time of vitrification,the degree of conversion at vitrification, and the temperature of vitrification, the results are presentedfor all experiments in Table 2. The temperature at vitrification may be directly compared with thelast column in the table, where temperatures of vitrification for the same values of conversion arecalculated from the DiBenedetto equation 48 '49 . The agreement is far from being perfect. Consideringthis, the spread of results, and weakness of the concept itself, the method, as it is, cannot be acceptedas a primary tool for the determination of vitrification points. However, taking into account thatdetermination of the vitrification point for some resin systems may be problematic even with theTBA technique, the tested method, may still prove to be of value as a supplementary techniqueafter further experiments. In such eventual experiments special attention should be directed at theuse of smaller plates, and utilization of readings of the indicator of axial forces.654.2.5 Determination of the Vitrification Point on the Basis of the Differential ScanningCalorimeter Measurements. The concept of the technique takes advantage of the fact that due to free volume, the enthalpy ofthe material above the vitrification temperature is expected to substantially increase. The successfuluse of the method was reported in the work of Wisanralcicit. 71 In experiments conducted in thepresented thesis, the samples of the Narmco resin were processed isothermally at 190 °C, for twohours, to the degree of conversion of about 0.9 and Tg was expected to be approximately 160 °C.The samples were later cooled and than heated again using a linear temperature increase. Resultsof the DSC are presented in Figures 33-36. Although various temperature increase rates weretested, the resulting differential heat consumption curves did not exhibit any behavior which wouldallow the identification of the vitrification moments.4.3 Contribution of the AuthorThe research effort within Chapter 4 consists of experiments conducted on RDA and DSCapparatuses and is aimed at the determination of gelation and vitrification points for variousprocessing conditions. The applied methods are quite novel and there are very few publication onthe subject.OCDIa0_660^10^20^30^40^50^60^70^80time [minutes]Legend:V - vitrification pointFigure 24a.RDA record of processing 140 °C/30 minutes00 30TIME (MIN) 24b.Degree of conversion for experiment 140 °C/30 minutes672005000 100 200 300Legend: time (minutes]68150CO10310 2io i10°1 0 - i108S0'.110CD100G - gelation pointV - vitrification pointFigure 25a.RDA record of processing 170/140°C/180 minutes.00 30 60 90 120 150 180 210 240 270TIME (MIN) 25b.Degree of conversion for experiment 170/140°/180 minutes.690COCO700^ 50^ 100^ 150Legend:^ time [minutes]G - gelation pointV - vitrification pointFigure 26a.RDA record of processing 170°C/60 minutes (A)."--21D0^30^60^90^120^151TIME (MIN)Figure 26b.Degree of conversion for experiment 170°C/60 minutes (A).00000.'10610510'1031 0210 11 00200190.5181171.5162152.5143133.5—O124114.5,10595.58676.56757.54838.52919.510E720^10^20^30^40^50^60^70^80^90^100^110time fminutesiLegend:G - gelation pointV - vitrification pointFigure 27a.RDA record of processing 170°C/60 minutes (B).00 30^60TIME (MIN) 27b.Degree of conversion for experiment 170°C/60 minutes (B).7310 310 1C_)LW740LE10210610 41010 210'10010'740^50^ 100^150^200Legend:^time [minutes)G - gelation pointV - vitrification pointFigure 28a.RDA record of processing 170°C/120 minutes (A).7510.^30^60^90^120TIME (MIN)Figure 28b.Degree of conversion for experiment 170°0120 minutes (A).150ioaCD— 105— 95.5— 86— 76.5— 67— 57.5— 48— 38.5— 29— 19.=CI)C-D(13a)(4)4-ioa200— 190.5— 181— 171.5— 162— 152.5— 143— 133.5_— 124— 114.5076o^A1 0 0^46117t tilt,Iiii ^100 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250^Legend:^ time [minutes]G - gelation pointV - vitrification pointFigure 29a.RDA record of processing 170 °C/120 minutes (B).7710.•1■■■00^30^60^90^120^150TIME (MIN)180^210Figure 29b.Degree of conversion for experiment 170 °C/120 minutes (B).10610800610595.58676.56757.54838.529Legend: time [minutes]781 0519.5I^1^I^I^I^I^I^I^I^1^I^I^I^I^I^I^I^I^I^I^I^I^I^I^I0 10 20 30 40 50 60 70 80 90 100110120130140150 160 170 180 190 200 210 220 230 240 250 2601 01 01 010 4100 10200190.5181171.5162152.51 43133.5-124C)114.5,G - gelation pointV - vitrification pointFigure 30a.RDA record of processing 190°0180 minutes (A).30^60^90^120^150TIME (MIN)180 210790.9OZ 0.8CC 0.70.600.5LL0.4^a: 0.3 ^^0.2 ^0.10Figure 30b.Degree of conversion for experiment 190°C/180 minutes (A).1500100^a'DE0)F-500^50Legend:G - gelation pointV - vitrification point100^ 150time (minutes)100 I ^t I 1^I ^0200 2508010 8 200Figure 31a.RDA record of processing 190°C1180 minutes (B).810^30 60 90 120 150 180 210 240 270TIME (MIN)Figure 31b.Degree of conversion for experiment 190°C/180 minutes (B).^ 50^ 100^ 150^ 200^ 250time [minutes]Figure 32a.RDA record, torsion mode - temperature cycle and moduli G' and G".0 50 100^ 150time (minutes]Figure 32bRDA record, torsion mode - moduli G,' G" and loss tangent.200 250o "1 0 1010gOCLCD10 0CD^7101 0 51 0 1................................................. ,.....10 010-210-38384Table 1.Gelation Point - Experimental Data.Experiment Temperature at gelation( C)Time of gelation(min)Degree of conversionat gelation140°C /30 min 140 not gelled not gelled170/140° /180 min 140 60 0.31170° /60 min (A) 170 40 0.31170° /60 min (B) 170 41 0.32170° /120 min (A) 170 40 0.31170° /120 min (B) 170 42 0.32190° /180 min (A) 190 29 0.35190° /180 min (B) 190 30 0.3685Table 2.Vitrification - Experimental and Theoretical Data.Experiment Time ofvitrification(min)Degree ofconversionTemperatureatvitrification°CTheoreticaltemperature ofvitrification°C140°C/30 min - 0.1 0 2.9170/140°C/180 min 250 0.56 76.5 73.0170°C/60 min (A) 103 0.59 108.0 79.0170°C/60 min (B) 83 0.57 95.5 74.9170°/120 min (A) 143 0.74 100.0 114.0170°C/120 min (B) 202 0.76 104.0 119.0190°C/180 min (A) 204 0.94 162.0 176.0190°C/180 min (B) 233 0.94 112.0 176.0Heat Flow (W/g)11.)^ry^ru^NO^03 Cr) OOO^aTemperature ( °C)CDaG)CD ■-•t13CD1-,Ort- 0NOO0113OO^086Figure 33.DSC record, rate of temperature increase 10°C/minute.240Legend:T - temperatureC - DSC curve-1.3- -220-1.2- 200U0- 180- 160- 140-1.710 12^14^16^18^20^22 120Time (min) General V4.1C DuPont 20000.7 250—2000.6—T. 3—1500.5——1000.4—0.310Legend:T - temperatureC - DSC curve'15^20^I25^30^35^40Time (min) General V4.IC DuPont 2000—50089(3.) adn4eJadwai0incpc) c:,in00N CU .-1 ...-11^I^ IOInt000CU0 cID 0V' CI_=CIC..)"'7>s-I(0C_0_0 C'rt 00C..-1Ea)EI-•coto1( 6 /M) mold 4eaHFigure 36.DSC record, temperature increase 5 °C/minute.905. CURE DIAGRAMSAS A METHOD OF DISPLAYING INFORMATION OFRHEOLOGICAL CHANGES IN MATERIAL UNDER PROCESSING5.1 Gilham's T-T-T and C-H-T DiagramsThere are at least four possible states of the thermoset system, depending on temperature and degreeof conversion; liquid, sol glass, gel rubber and gel glass. The transition in the state of material canbe conveniently shown in the Gillham's T-T-T and C-H-T diagrams in time of processing versustemperature coordinates. The T-T-T diagram for isothermal curing is the better known of the two.Isothermal curing ensures an unique relationship between time of processing and degree ofconversion for any temperature of processing, resulting from the kinetics of conversion implicitlyincorporated into the diagram. The time of processing also represents the degree of conversion fora given temperature. As a result the degree of conversion could be eliminated as an independentvariable, leaving only two; time and temperature.It should be stressed that the T-T-T diagram shown in Figure 37 can be read only horizontally, andthat shifting from one isotherm to another is not permissible in the diagram (unless certain additionalprocedures are employed). It may be noticed from the diagram that the gelation curve is of thedecreasing exponential type, while the curve of vitrification is roughly 'S 'shaped. It should alsobe remembered that vitrification causes a drastic slow-down of kinetics of conversion and underreal conditions of processing often marks an end to further conversion.At the beginning of processing, when the degree of conversion is low, the resin is in the liquid,ungelled state, unless the temperature is below the temperature of vitrification of an unprocessedresin, Tgo. For a low processing temperatures (below Tg gel) the vitrification comes first, before91gelation. For higher processing temperatures, the gelation comes first, leading to the formation ofan unvitrified gel (gel rubber). Further processing in this range of temperatures results in vitrificationof a resin, which occurs when the horizontal isothermal line of processing crosses the curve ofvitrification. Physically, Tg is a property of a material and in thermosets is not a constant, but afunction of the degree of conversion. With the progress of processing the Tg of a material rises,until it becomes equal to the temperature of processing. At this moment vitrification takes place.If processing continues, conversion, although very slow, still increases, and the Tg of a materialbecomes higher than the processing temperature, advancing the material deeper into the glassy state.Tg .., the upper limit to which the Tg may proceed with the progress of conversion, correspondsto a fully converted resin (a=1.). For temperatures of processing slightly below Tg ., extendedprocessing after vitrification may lead to full cure (the line of processing reaching the curve of fullprocessing in the diagram). The diagram suggest that the only way of fast processing of a materialto the level of full cure is to avoid the vitrification-related slow-down by applying (at leasttemporarily) a temperature of processing higher than Tg... However, the T-T-T diagrams show thedanger of such a procedure through an existence of yet another curve - the line of upperdevitrification. This is, in fact, the curve of material destruction, and can be reached even as a resultof extended processing below Tg ... 22,23,24,26,27,28The most important value of T-T-T diagrams is the understanding of the process that they provide.The advantage of the diagrams is that the kinetics of conversion is incorporated into the diagrams,so that the required time for processing, or time for characteristic events to occur may be readdirectly for a given temperature of isothermal processing. Moreover, the possibility of adding newfeatures was suggested by Gillham 27 '53 - the contours of iso-alpha, or iso-Tg. These contours allowthe shifting from one isotherm to another on the graph at different temperatures, making the diagramsmore universal.GEL 4,:\^ GEL GLAS -S-74.-""r`'92There is also another advantage of the diagrams related to the process of their creation. Since theuse of the TBA technique allows for the identification of the moment of gelation as well asvitrification, within one experiment involving a continuous process of isothermal curing, theexperiment conducted at any temperature level yields two characteristic points for the diagram,one belonging to gelation, the other to the vitrification curve. Using different temperatures ofprocessing, the curves of gelation and vitrification can be determined, without involving the degreeof conversion measurements, which may be difficult to determine for a slow progress of a reactionat low temperatures.LOG TIME7 \^........ ....... cU_R.......SOL/GELGLASSFigure 37.Isothermal Time Temperature Transformation (111) Cure DiagramHEATING RATE (°C/MIN)5 01g1?-".'-' :*-4 2i '^8^50 .;^a^8wldciocsd d c; dO c; 6^8 0o o:^. ,iI. i^;^; •i •^Legend:ffsAi:A^ V - curve of vitrificationi : • t& A :, I^iPiltilit i ti It: :^..:i^..1.0110 ,1 A250225 -;200175 -150125100 -,75 -,50Tgo,2^3^488c?093In order to further expand the applicability of the T-T-T diagram - the Continuous HeatingTransformation (CHT) diagram was proposed. The diagram is built in the same way as T-T-Tdiagrams, and contains the same information, except that it is valid for heating with a lineartemperature increase rather than for isothermal heating. 713233LOG TIME (MIN)Figure 38.Continuous Heating Transformation (CHT) Cure Diagram945.2 a-T-T Diagram - The ConceptDespite the mentioned advantages, the Gilham's diagram is not as suitable as an element ofmodelling of thermoset processing as it is for isothermal processing. Even if thermal cycles appliedin processing are isothermal, the resulting temperature history at locations distant from the tool maynot be isothermal. The changes in the kinetics of resin conversion are more likely to happen thanthe changes in rheology. In the case of altered kinetics, the Gilham's diagrams loose their validity,since the kinetics is a built in element of their structure. If, however, the kinetics could be somehowseparated from resin rheology in the process of diagram creation, only the kinetics would have tobe adjusted.The proposed concept of an algorithm that could be applied to any processing cycle stems from thefact that the point of gelation and the point of final vitrification for a resin system can be easilyexpressed as a function of the degree of conversion and temperature. Gelation is expected to occurat a constant value of conversion, while the point of vitrification is conveniently described by theDiBenedetto equation 49 . Both curves may be plotted on the grid of the degree of conversion versustemperature of processing. In order to place the point of processing in the same figure, its coordinates,the momentary temperature of processing and degree of conversion, must be determined. The lattercan be calculated only if the model of the kinetics of conversion is available. The method does notrequire isothermal conditions of processing, but the display it produces is inferior to Gillham'sdiagram. Due to the system of coordinates used in the diagram, the time of processing cannot beread directly from the graph produced, and the curve of upper devitrification from Gillham' s diagramcannot be easily incorporated into the graph.The objective of this work was to create an algorithm based on the presented concept, while lookingfor improved forms to comprehensively display the complex information produced. The research95effort resulted in the development of a system that calculates and graphically presents the progressof thermoset processing. The system can be applied to non-isothermal processing and accounts forthe degree of conversion as well as phase changes in a material. The newly proposed diagramsreintroduce time into their system of coordinates.5.3 Structure and Operation of the Proposed SystemIn order to build the proposed system for a new material, three elements are needed: gelation andvitrification curves, expressed as a function of the degree of conversion, alpha; the kinetic modelof conversion; and diagrams displaying the information of the two previously mentioned elementsin a clear and an efficient fashion. All these elements and their interaction are presented in Figure39. For any specific time and temperature history, the kinetic model employing numericalintegration calculates the momentary degree of conversion. The momentary temperature ofprocessing, T, provides the remaining coordinate of the point, representing the state of processingin the alpha-T coordinate system.The system presented here is developed for the Narmco resin. For this material, there exists anexcellent mathematical model of the kinetics of conversion, developed by Cole 15,16, based on amechanistic approach, which was incorporated into the system . The value of conversion at gelationand the parameters of the DiBenedetto vitrification curve were adopted from various literaturesources. 6,7,8,34,67,68 Both gelation and vitrification parameters were further verified experimentally,as presented in the previous chapter.96In order to develop the system for any other resin the parameters in the rheological element of thesystem have to be adjusted and the model of kinetics of conversion has to be replaced, perhapscompletely. They are no specific requirements concerning a model of conversion to be incorporatedinto the system. However, the accuracy of the model will affect the accuracy of the system. In theabsence of a mechanistic model of kinetics the possibility exists of experimentally fitting one ofexisting simplified expressions, using the DSC technique.97Temperature Cycle 01Processing Point inalpha-T CoordinatesModel of Kineticsof ConversionGelation and VitrificationCurvesin alpha-T CoordinatesGraphical Form:alpha-T-TandT-T-alpha-TDiagramsFigure 39.Structure of the system985.4 Interaction of the Proposed System With a Thermal Model of Composite Processing.During a curing process, a material is exposed to an elevated temperature and pressure for a specificlength of time. The modelling of composite processing consists of at least two main models: heattransfer and resin flow. In a typical processing arrangement, the temperature is applied to a heatingtool adjacent to one side of a composite, while the other side is insulated by a bleeder and a vacuumbag. Due to low thermal conductivity of a material and strong exothermic effect of the chemicalreactions, the temperature in the material differs from location to location. The most pronounceddifference is one between the temperature in the material adjacent to the heating tool and thetemperature on the far-side of the location; this difference depends on the overall thickness of thecomposite. The difference is visible even for a composite a few millimeters thick, and becomessignificant for a thicker one, thereby creating a need for modelling of this thermal phenomenon.Any thermal model requires information on the exothermic reaction of conversion and in this way,depends on material-related information. The interaction of a thermal model of composite processingand the system presented here is shown in Figure 40. The temperature cycle applied to a heatingtool provides boundary conditions for a heat transfer model, which in turn calculates the temperaturedistribution across material. A conversion kinetics model, interacting with other elements of thesystem, utilizes the temperature distribution to calculate local rates of conversion, which are usedby a heat transfer model and treated as heat sources. The conversion model numerically integratesthe rates of conversion to calculate the momentary degree of conversion for different locations inthe composite.5299T (boundary)Heat Transfer ModelAd(alpha)/dtDiagramsSYSTEMTemperatureCycleKineticsof ConversionGelationand VitrificationFigure 40.Interaction of the proposed system with a thermal model1005.5 a-T-T and T-T-alpha-T Diagrams - Graphical Output of the SystemIn Figure 41 the results of the proposed system, obtained for a temperature cycle similar to thatsuggested by the producer, are displayed. The diagrams consists of three parts. Part I displays anassumed temperature cycle. In Part II this temperature history is used by a kinetic model ofconversion to obtain the degree of conversion as a function of time. Part III presents the main partof the a-T-T diagram which contains the curve of gelation (G), the curve of vitrification (V), theline of full cure, and the curve of processing (P). The curve of processing is marked with smallcircles. The marks are drawn for approximately 10 min time intervals, as a way to introduce timeinto Part III, which otherwise uses a conversion-temperature system of coordinates. The three-partdiagram not only contains the complete information about a material under specific processingconditions, but the configuration of the graphs also provides an additional advantage. It allows forthe determination of the time of processing for any point on the processing curve. This can be doneeither by drawing a vertical line from the point to the curve of conversion below (Part II) and thenreading the time horizontally, or by drawing a horizontal line from the point on the temperaturecurve (Part I), and then reading time vertically. Usually only one of these two ways is practical.It should be noted that even if the temperature cycle is fixed, there are still three parameters ofprocessing in the diagram: time, temperature and degree of conversion. This is the reason why acomplex alpha-T-T diagram consists of three different parts. Another option for representing anequivalent amount of information is to develop a three-dimensional image, as shown in Figure 42.The 'x' and 'y' coordinates are time and temperature, so that the thermal cycle of processing canbe drawn in the base of the graph. The 'z' coordinate is the degree of conversion. The curves ofgelation and vitrification take the form of surfaces. The thermal cycle of processing shown in Figure42 is the same as that shown in Figure 41. Since surfaces of gelation and vitrification sometimes18030^60^90^120^150TIME (M N)1 1220200180 ^0 160Ui 140 ^CC120D1-100<80CCula_6040111I-200-20 ^0TEMPERATURE CYCLE/^ Part Ialpha-T-T DIAGRAMLegend:G - curve of gelationV - curve of vitrificationP - curve of processing0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ;DEGREE OF CONVERSION101obstruct the view of the processing curve, the same graph can be shown without the mentionedsurfaces. This is done in Figure 43 where the curve of processing is produced exclusively. Thenon-continuities of the curve mark its cross-section with the gelation and vitrification surfaces.Figure 41.Comprehensive a-T-T diagramfor manufacturer suggested temperature cycle.102609°2130°1""^1111011111■-111,1174- tO0 120180180 20044 OA 0. ............................^ .....z..... 1........... .................... 44:: .: ..•••%.•••••2:110?°,6 °:°::II ^1111114114:::Zigi-': --"' ,---"^-".IliCCt..)ILQi ^. 10 , 4°.1:11::::::!i:::::::::::...:.:::::s:::::::.::::.:•::::1:.11:::!:.;:.;v%ll'lii:;p:1:' -................................................................................................................................................ ......... ::::...;;;;A:itiii:;:iiiii.i:iii;;'°44,r4e ............................................................................................. ........................ 1:::1A jottitss.0•7_, ..„ ,,,,,...:14--1--"" ....................... .  Pze•-•• 0_20.413.1..............................,Stgl 0,,1••••.....4:::#04,441NSTE:04:04:Sair.044,04,1111111304eir, '42 plii4,4 ,4, ,,,.......... .:4„.00 -4,.ir-tiCt)€1▪ :▪ *0cvOLegend:G - surface of gelationV - surface of vitrificationP - curve of processingAFigure 42.T-T-a-T diagramfor manufacturer suggested temperature cycle.04 0.2SO 200.zLegend:P - curve of processing103Figure 43.T-T-oc-T diagram without surfaces of gelation and vitrification1045.6 Applications5.6.1 - RDA TestsAs it was mentioned in Chapter 4 of the Thesis, the major problem in completing RDA tests wasa limited access to the apparatus. In order to maximize the utilization of the equipment a verydetailed plan of experiments was required. This was made feasible by the use of the system anda-T-T diagrams which allowed predictions of the moment of gelation and vitrification in advance,avoiding useless experiments, and eliminating any waste of time in a single experiment. Thecomplete set of figures presenting alpha-T-T diagrams in tests is shown in Figures 44-51.Test Figure140°C/30 min in figures 44 a,b,c170/140 °C/180 min in figures 45 a,b,c170°C/60 min (A) in figures 46 a,b,c170°C/60 min (B) in figures 47 a,b,c170°C/120 min (A) in figures 48 a,b,c170°C/120 min (B) in figures 49 a,b,c190°C/180 min (A) in figures 50 a,b,c190°C/180 min (B) in figures 51 a,b,cTable 3.List of RDA experimentsIn parts 'c' of the listed figures, points of gelation and vitrification identified from experimentsare marked.A typical example of processing is presented in Figure 50. Figure 50a shows the thermal cycle usedin isothermal processing at temperature 190°C, and Figure 50c presents the progress of processing105in a - T system of coordinates. The curve of processing in figure 50c is marked with small circles.The moment of gelation is expected to occur at an intersection of the curve of processing with avertical line of gelation. However, according to RDA measurements, the gelation takes place slightlylater, at the point marked as 'G'. At an advanced stage of processing in its isothermal part, theincreasing density of circles in the curve of processing indicates a rapid slow-down of conversion,caused by the fact that the processing curve approaches the curve of vitrification. Vitrificationphenomenon is expected to occur during final cooling of the resin, when the processing curve crossesthe vitrification curve. The moment of vitrification as determined from RDA experiments, however,comes a little later. Its location on the curve of processing is marked by 'V'.Figures 44 a,b,c show that the experiment 140°C/30min was designed for the investigation ofrheological behavior of a resin at a very low level of conversion, processed at a low temperature.Consequently, no gelation phenomena is recorded, and special cooling arrangements are requiredfor resin vitrification. Figure 45 shows the processing at 170 °C/1407180m in which is supposedto reach gelation at a low temperature of processing. However, in order to accelerate the processof conversion, and to make the experiment shorter, the elevated temperature of 170 C is applied atthe beginning, and reduced later in the process, before the important transitions take place. Theseries for processing at 170 C are conducted for two different lengths of processing: 1 h (Figure47) and 2h (Figure 48) to investigate the conditions in the vicinity of the manufacturer-suggestedcycle. Finally, the experiments using the processing at 190 C for an extended period of time (Figure50 and 51) were designed to explore the behavior of a material which is being converted to a veryhigh degree with the use of very high temperature.a-T-T Diagrams provided, in advance, the information of temperature cycles, yielding a full rangeof processing conditions. Without the support of the diagrams the described variety of processingwould not be achieved in such a limited time.0 30TIME (MIN)5-220200180160Ill 140CCD 120I-< 100CCW 80EL2 60wI- 40200-20TEMPERATURE CYCLE/ ^106Figure 44a.Temperature cycle in test 140°C/30 min107DEGREE OF CONVERSION0^ 30^ 61TIME (MIN)Figure 44 b.History of degree of conversion for test 140°C/30 min. DIAGRAM220200180160140CC 120< 100CCuj 800• 60I- 40200-200^.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1DEGREE OF CONVERSIONLegend:V - experimental vitrificationFigure 44c.a-T-T diagram showing processing curve for test 140°C/30 min.109TEMPERATURE CYCLE220200180a 160140ILICC 120DQ 100CC80WQ.60wI- 40200-200^30 60 90 120 150 180 210 240 270TIME (MIN)Figure 45a.Temperature cycle for test 170°C/140°C/180 min.110DEGREE OF CONVERSION10.^30 60 90 120 150 180 210 240 270TIME (MIN)Figure 45b.History of degree of conversion in test 170°C/140°C/180 min2202001806 160III 140XD 120I-< 100CCWa_80alI—6040200-20alpha-T-T DIAGRAM1110^0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Legend: DEGREE OF CONVERSIONG - experimental gelationV - experimental vitrificationFigure 45c.a-T-T diagram showing processing curve in test 170°C/140°C/180 min.112TEMPERATURE CYCLE2202001800 160ILI 140CCD 120I-< 100CCW 80a_2 60wI— 40200-200^30^60^90^120^150TIME (MIN)Figure 46a.Temperature cycle in test 170°C/60 min (A). 30^60^90TIME (MIN)120 150113DEGREE OF CONVERSIONFigure 46b.History of degree of conversion in test 170°C/60 min (A).220200180C) 160ILI 140CCD 120Q 100CCWa.802tu601- 40200-20alpha-T-T DIAGRAM0.2 0.3 0.4 0.5 0.6 0.7 0.8-3^c 0 0 00V.4v10 0.1 0.9114DEGREE OF CONVERSIONLegend:G - experimental gelationV - experimental vitrificationFigure 46c.a-T-T diagram showing curve of processing in test 170°C/60 min (A).0^30^60TIME (MIN)115TEMPERATURE CYCLE2202001800 160W 140CCD 120I-< 100trW 80a.2 60LLII— 40200-20Figure 47a.Temperature cycle in test 170°C/60 min (B).0z o0Cl)cr ow>Z o0o o .L-0 o.wwCC 0.wCi O.0..^30^60^gn1116DEGREE OF CONVERSIONTIME (MIN)Figure 47b.History of degree of conversion in test 170°C/60 min (B).117alpha-T-T DIAGRAM2202001800 160L1.1 140CCD 120I-< 100CCW 80CL60ILII— 40200-200^0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9DEGREE OF CONVERSIONLegend:G - experimental gelationV - experimental vitrificationFigure 47c.a-T-T diagram showing processing curve in test 170°C/60 min (B).118TEMPERATURE CYCLE220200180a 160LV 140CC 120Q 100CCW 802 60I- 40200-200^30^60^90^120TIME (MIN)Figure 48a.Temperature cycle in test 170°C/120 min (A).150119DEGREE OF CONVERSION10.^30^60^90TIME (MIN)120 150Figure 48b.History of degree of conversion in test 170°C/120 min (A).10^0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 13 C^G0 0 0 0 0 0 0 0 OC 00,o120alpha-T--T DIAGRAM220200180U 160ILI 140CCD 120I-< 100CCWa_80w60/• 40200-20Legend: DEGREE OF CONVERSIONG - experimental gelationV - experimental vitrificationFigure 48c.a-T-T diagram showing processing curve in test 170°C/120 min (A).180 2100^30^60^90^120^150TIME (MIN)2202001800 160LLI 140CC 120DQ 100CCuja.802 60IllI— 40200-20TEMPERATURE CYCLENNNN/ ^121Figure 49a.Temperature cycle in test 170°C/120 min (B). 30^60^90^120^150TIME (MIN)180 210122DEGREE OF CONVERSIONFigure 49b.History of degree of conversion in test 170 °C/120 min (B).220200180160fW 140CC 120I-< 100al 802 60I- 40200-20alpha-T-T DIAGRAM1230^0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Legend: DEGREE OF CONVERSIONG - experimental gelationV - experimental vitrificationFigure 49c.a-T-T diagram showing processing curve in test 170°C/120 min (B).E...220200180160Ill 140CCD 120I-100<Cr80Wa_2 60Lli40I--200-20TEMPERATURE CYCLE180 2100^30^60^90^120^150TIME (MIN)124Figure 50a.Temperature cycle in test 190°C/180 min (A).125DEGREE OF CONVERSION10.90Z 0.8i/3cr 0.7W>Z 0.600 0.5IJ-0.4ILIWCC 0.3C9tuin 0.20.100^30^60^90^120^150^180TIME (MIN)Figure 50b.History of degree of conversion in test 190°C/180 min (A).2100000^00Goo126alpha-T-T DIAGRAM220200180C..) 160LU 140CC 120I-< 100Crula.802w601.— 40200-200^0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9DEGREE OF CONVERSIONLegend:G - experimental gelationV - experimental vitrificationFigure 50c.a-T-T diagram showing processing curve in test 190°C/180 min (A).127TEMPERATURE CYCLE2202001806 160ILI 140CCnI--120< 100CCWa_ 802w1--6040200-200^30 60 90 120 150 180 210 240 270TIME (MIN)Figure 51a.Temperature cycle in test 190°C/180 min (B).128DEGREE OF CONVERSION0^30 60 90 120 150 180 210 240 270TIME (MIN)Figure 51.History of degree of conversion in test 190°0180 min (B). 160111 140CC 1201—•:( 100CCala_802w60I— 40200-20alpha-T-T DIAGRAM10 0.1 0.80.7 0.4 0.5(^0^ 0 0 0 0010G129Legend: DEGREE OF CONVERSIONG - experimental gelationV - experimental vitrificationFigure 51c.a-T-T diagram showing processing curve in test 190°C/180 min (B).1305.6.2 a-T-T Diagram in Thick Composites ProcessingIn thick materials, different locations usually have a different temperature history and therefore adifferent degree of conversion, different glass transition temperature, and different moment ofvitrification. All these differences result in a different structure of a material and the creation ofadditional stresses. The alpha-T-T diagram provides information on which point vitrifies first andits temperature of vitrification. Figure 52 shows a diagram which was generated by combining theprocessing information from the presented system with a realistic prediction of temperature for alayer of the Narmco resin 4 5 mm thick 52 . In each part of the diagram in Figure 52 two curves arepresent - one for the location in the processed material that is adjacent to the heating tool (markedwith circles) and the other for the opposite side location (marked with triangles). Part I of the diagramshows the assumed curing cycle at the tool, and the resulting temperature cycle at the other side ofmaterial, with a high temperature peak due to the exothermic heat of conversion. The peak isresponsible for the high degree of conversion observed for the far-side location in Part II of thediagram. Finally, in Part III there are two curves of processing. The auxiliary lines connecting thecurves are drawn to connect processing points of the same processing time. When the temperatureof processing starts decreasing at the end of the cycle at a rate of 2 °C/minute, the temperature inboth locations is nearly the same. However, the far-side location obtained a higher degree ofconversion, and therefore vitrifies first at the temperature of 150°C. The material at the tool vitrifiesabout 10 minutes later at the temperature of 135 °C. As a result of the applied processing cycle, thestructure and degree of contraction of the material differs from location to location. The structureof the material at the far-side location was probably negatively affected by the temperature ofprocessing, exceeding 220°C for a period of time. It may be concluded from the diagram that themoment of gelation was reached at different times in different locations.alpha-T-T DIAGRAMTEMPERATURE CYCLEmiryipso^amimmin. Ali1/0111101111111111111/111111 11111111111101111111111•11111111111•11117.11117 Illiiii111111111111111111111W11111111111111111111111111111=11111111Part II41^I220200180160140120100806040200-20 111=111110^30^60^90^120^150^180TIME (MIN)Legend:o - location at a heating toolo - location at a centerCAm131In Figure 53 an T-T-a-T diagram containing the same cycle of processing as figure 52 is presented.Unfortunately, the surfaces of gelation and vitrification obscured the view and had to be removedfrom the graph.0^0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1DEGREE OF CONVERSIONFigure 52.a-T-T diagram in thick composite processing132• - location at a heating tool• - location at a centerFigure 53.T-T-a-T diagram in thick composite processing.1335.6.3 Generation of T-T-T DiagramThe a-T-T and T-T-a-T diagrams previously presented are supposed to contain basic informationequivalent to that of the T-T-T diagrams, but to be more universal in their applications. If this isso, it should be possible to produce the T-T-T diagrams using the proposed system. The T-T-Tdiagram may be generated by running consecutive simulations of isothermal processing for varioustemperature levels, waiting for gelation and vitrification to occur, and plotting both points in thetime-temperature system of coordinates. This exercise has been conducted for the Narmco resinand the resulting T-T-T plot is presented in Figure 54. The only technical problem which wasexperienced was a necessity for fine tuning of the variable time increments for processing, especiallyin the range of low temperature processing. In the figure, the curve of gelation, vitrification andfull cure are present; their shape is consistent with Gillham's diagrams. Discussion of thedevitrification curve is beyond the scope of this Thesis. It should be realized, however, that theproduced diagram has a limited accuracy, since the kinetics of conversion used by the system hasnever been verified for temperatures below 130°C. Also, in this specific exercise, thevitrification-related slow-down of conversion reaction was not accounted for.134190150Uwc, 110I-<ccwa. 70MLI/F-30-10TIIi1 110°1i^110' 102 109 10` 105 11Legend:^TIME (MIN)G - gelation curveV - vitrification curveF - full cure curveFigure 54.T-T-T diagram for Narmco resin.1355.7 Contribution of the AuthorChapter 5 covers the main research effort of the author:(1) the concept of the system(2) the concept of a-T-T and T-T-a-T diagrams(3) realization of the system and the diagrams in a form of a computer program for theNarmco resin(4) application of the system and diagrams for the simulation of processing, using a manufacturersuggested cycle and devised temperature cycles applied in RDA experiments(5) utilization of the system to produce a T-T-T diagram(6) application of the system and diagrams for the simulation of the processing of thickcompositesThe research is original and was performed exclusively by the author. It should be noted that theobjective of this work is to provide a modelling element representing material behavior, rather thanthe modelling of the entire process, so that the modelling of thermal phenomena of the process areout of the scope of this work. The temperature of material in a central location used in Chapter5.6.2, addressing the processing of thick composites, was re-printed from another work.521366. APPLICATION OF ALPHA-T-T DIAGRAM TO CHARACTERIZE THE RAPIDTHERMOSET PROCESSING (RTP) METHODThe RTP method, proposed by Breitigam, Bauer and May 9, partly replaces the processing in theautoclave by processing in a pre-programmed furnace, cutting the cost of production. The methodtakes advantage of the fact that initial vitrification does not cause the slow-down in the kinetics ofthe reaction of conversion, this slow-down takes place in the vicinity of the final vitrification point.As a result, in a certain range of processing parameters, the state of the material exists in whichthe resin has the stiffness of a solid, but the rate of conversion is not negatively affected. In termsof the degree of conversion-temperature coordinates (Part III of the a-T-T diagram), the curve ofprocessing in the RTP mode should be on the right side of the initial vitrification curve, but maynot approach the vicinity of the final vitrification curve.The intention of the research effort presented here was to examine the feasibility of creating aprocessing diagram which can be used as a tool to optimize the processing cycle for RTP. Theexercise is a hypothetical one, since the Narmco resin, for which the system was developed, is notvery suitable for RTP processing. It has too low a degree of conversion at gelation, a low temperatureof vitrification of B-staged resin, and the range of the verified applicability of the conversion modelincorporated into the system does not cover processing below 130°C. Yet, if this hypothetical attemptproved to be successful, the same approach could be applied to any real case.The first step in the research was to determine the shape and the analytical form of the initialvitrification curve in the a-T coordinates. This was done on the basis of the same RDA recordswhich were used for the verification of gelation and final vitrification curves. The moment of initialvitrification was recognized in the records as a midpoint of the 'knee' of the storage modulus (G')curve, with an arbitrary safety margin added. The identified curve of initial vitrification, "IN", is137shown in Part III of Figure 55. It was found that the original DiBenedetto equation, which is usedroutinely to analytically express the curve of final vitrification in a-T coordinates, can be easilyadapted to provide an analytical form of the initial vitrification curve, as well.In the second step of the investigation, an attempt was made to find the ideal trajectory of the RTPprocessing curve in a-T coordinates. In order to ensure the maximum effectiveness and,consequently, the shortest possible time of processing, the curve of processing should be paralleland run as close as possible to the initial vitrification curve. After introducing an additional safetymargin, the correct curve of processing was assumed, as shown in Part III of Figure 55. Once thiscurve was known, it was discovered that the system could be easily altered to be run in a partlyreversed mode, identifying for consecutive time increments the correct temperature cycle from theassumed processing curve in the a-T coordinates. This correct or optimum curing cycle is presentedin Part I of Figure 55 in which the temperature rises very slowly over an extended initial processingperiod, and very rapidly at the end of processing. Two inter-related aspects should be emphasizedin connection with the curve generation:(1) The only alternative way to obtain an acceptable thermal curve of processing is by performingvery laborious experiments involving the TBA technique and a trial-and-error approach.(2) Any idea of simplifying the presented thermal curve, by linearization and safe application ofeven slower rate of temperature increase may look tempting, but is, in fact, very risky. Any alterationof the presented curve requires repeated calculations involving alpha-T-T diagrams.6.1 Contribution of the AuthorThe modelling effort and resulting diagrams presented in Chapter 6 are original and performedsolely by the author. The proposed approach is the only existing one to design the RTP processfrom theoretical consideration. The practical importance of the approach, however, depends on thepractical importance of the RTP method itself.138TEMPERATURE CYCLE^alpha-T-T DIAGRAM.4%.,Vo160^ I^II--180 I^INF.AM MIN Part III140 111111111111^r20 II WIFANI^IIIt'100^ IWITAM11•21180 IVA1111/160 FM%40^W: ^_% 0.41M11120 Part Io pr/20^ I^I0^1200^240 0^3600^4800^6000TIME (MIN)11aOLegend:^ "A.aaIN - curve of initial vitrification^-IM4)F - curve of final vitrification^m 00..—. c.P - curve of processing^m"2 ita0^ Part II0a•0O----i^10^0.1 0.2 0.3 0.4 0.5 0_6 0.7 0.8 0.9 1DEGREE OF CONVERSIONFigure 55.a-T-T diagram in RTP processing.1397. CONCLUSIONSThermoset-based composites are often classified as high - performance materials. On the otherhand, they are also frequently considered as non-dependable, with a poor reproducibility of finishedproduct properties. Two factors contribute to the latter. First, thermosets are extremely sensitiveto the parameters of processing and may be easily damaged by processing errors. At the same time,the control of thermoset processing and the equipment used in the process may seem primitive,creating a deceiving impression of simplicity and promoting carelessness in production.The first generation of mathematical models was developed to eliminate processing errors.Ironically, however, the models shared the over-simplistic approach, not to the process itself, butrather to the material being processed. A situation was thus created, where numerous groups ofmaterial specialists, usually with chemical backgrounds, were making tremendous advances in theunderstanding of chemical reactions and in network structure formation (rheology). This progresswas nearly neglected by groups of scientists, usually with non-chemical backgrounds, making theirown substantial contribution in modelling of the heat and mass transfer phenomena associated withthe process. In modelling, preference was given to experimentally-based, simplified expressionsfor kinetics of conversion, rather than the complex expressions worked out by chemists. Theobjective of modelling was to ensure that a rigid prescription for correct processing, called themanufacturer-suggested processing cycle, was executed throughout the material to the greatestextent possible. The understanding of how this suggested cycle was formulated, and consequently,to which extent, and how it could be altered without causing harm to the processed material wasbeyond the scope of the modelling, excluding the possibility of modelling becoming a part of thisformulation process. Even the basic, well-known theological phenomena, such as gelation andvitrification, which do affect either the variables included in modelling (rate of heat generation,temperature), or the final properties of the product, have been neglected in the early modellingefforts.140It is not that the importance of the rheological phenomena was not recognized at all in the area ofthermoset processing. The need for occasional processing of very thick layers of resin taughtscientists to take advantage of the vitrification-induced slow-down of conversion. It was also learnedthat for a slow, linear temperature increase, the state of the material is 'sliding' along the vitrificationcurve, always slightly above the curve. There was, however, no scientific tool to visualize theseaspects of processing.Here the concept of this thesis originated. The objective was to create a modelling elementrepresenting theological information on the material under processing, and to produce the complexgenerated rheological information in a comprehensive and transparent graphical form. Themodelling element was developed in the work as the proposed system, and the graphical form isrepresented by a-T-T and T-T-a-T diagrams.The proposed system presented in the Thesis, with its graphical output as a-T-T, and T-T-a-Tdiagrams, provides full information on a material under processing. It plots the progress ofprocessing, characterized by time, temperature and the degree of conversion relative to the majormaterial transformations: gelation, initial vitrification, and final vitrification. It is capable ofpredicting a diffusion-controlled slow-down of the reaction of conversion caused by finalvitrification, the temperature of final vitrification, and the moment of initial and final vitrification.The information contained in the diagrams is enriched in the case of thick material processing, whenthe progress of processing in one characteristic location may be directly related to the progress inanother location, providing the time sequence for vitrification.The diagrams, especially the a-T-T diagram, have two roles to fulfill: to provide information andto improve understanding of the processing. One glance at the location of a processing point allowsfor determination of the state of the material and current values of the processing variables. The141choice of a degree of conversion as an abscissa in the main part of the a-T-T diagram seemsuncomfortable for a beginner, but teaches one to think in categories of material structure. Forsomeone who has become familiar with the processing diagrams, gelation is no longer a changeof physical state, but rather a certain stage in network formation. Similarly the temperature of glasstransition is no longer a temperature, but rather a property of a material related to the density of thenetwork, and naturally increasing with the progress of processing.The system, and the diagrams proposed in this work are developed from the theory of the processand no experimental proof of their validity is required. A need exists, nonetheless, to demonstratetheir eventual applications and capabilities. From this point of view, the experimental part of thework is of secondary importance, and was intended to give reality to the produced examples,providing the system with real kinetics of conversion, and real rheology of the Narmco resin. Forthe author, it was an opportunity to become familiar with experimental techniques and problemsrelated to the determination of kinetics, and rheological characterization of a resin system.The latest generation of kinetics of conversion models, represented by Cole's mechanistic model,proved to be very well suited to the kinetic requirements of the system. For real conditions ofprocessing, the range of model validity is more than sufficient. For more theoretical applications,however, it would be beneficial to ensure the validity of the model for temperatures below 130 °C.The expression for the conversion slow-down that occurs near vitrification would also have to bereexamined to be applicable for low temperatures.The RDA technique allowed for dependable and accurate identification of the gelation point.Unfortunately neither this technique nor the DSC technique used in the work were fully satisfactoryin determining vitrification. The RDA records, however, allowed for a comfortable identificationof initial vitrification phenomena.142The diagrams presented, and the proposed system, although novel today, are only the first step inequipping the existing processing models with material-related information. It is expected,however, that they will provide a solid base for other steps, and other more sophisticated applicationswhich are yet to be developed. Even within the current work, the additional element of the curveof initial vitrification was added to the basic a-T-T version. Similarly, the contours of iso-viscositymay be added as viscosity is a function of the degree of conversion.With the recent publication of the RTP method 9 an unexpected opportunity to demonstrate one ofthe future, more sophisticated applications of the diagram arose - an opportunity to utilize thediagrams as the only existing tool for the optimization of the thermal processing cycle. Theapplication of the system to the method shows a completely new perspective on the function of thediagrams. The "ideal" curve of processing, in a-T co-ordinates was determined first, and on thebasis of the curve, the system found the correct optimum temperature cycle to be applied.Today when the work is completed, modelling of the processing of thermoset-based compositesis slowly changing. There is a general acceptance of the idea to include material-related informationin models of processing, and progress is being made in this direction. It gives a great personalsatisfaction for the author to be able to state that even such modelling precursor as Professor G.Springer of Stanford University accepted the need for an element responsible for material behaviorin his work.143REFERENCES1. Adabo, H.E., Williams,R.J., J.Appl.Pol.Sci.,27,1327 (1982)2. Apicella,A.," Developments in Reinforced Plasics" Ch.5, Protchard ed.,New York (1986)3. 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