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Accelerated radiation polymerization of vinyl-divinyl comonomer systems Micko, Michal 1973-03-04

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ACCELERATED RADIATION POLYMERIZATION OF VINYL-DIVINYL COIvIONOMER' SYSTEMS by MICHAEL M. MICKO BeChem (Enq*)s Slovak Technical University, Bratislava, 1959 C.Sc* Slovak Technical University, Bratislava, 1966 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department Forestry We accept this thesis as confirming to the required standard» THE UNIVERSITY OF BRITISH COLUMBIA April, 1973 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver 8, Canada i ABSTRACT Gel-effect (Ge) acceleration in radiation polymerization of methyl methacrylate (MMA) -divinyl monomer (DVM) systems and properties of resulting polymer products have been investigated. Four methacrylate esters with variable molecular bridge length between the double bonds, i.e., ethylene glycol dimethacrylate (EGDMA), diethylene glycol dimethacrylate (DEGDMA), triethylene glycol dimethacrylate (TrEGDMA) and tetraethylene glycol dimethacry- . late (TEGDMA), were used as DVM accelerators and crosslinking agents. The course of polymerization was followed by temperature (T)-time(t) polymerization exotherm curves. A new technique was developed to determine the "Gel-Effect Point" (GEP) and individual polymerization parameters associated with gelation in crosslinked network, i.e., polymerization rate coefficient (PRC), curing time (tii^), overall curing rate (l/t^^)* and overall acceleration constant (K). The overall curing rate was found to be proportional to the volume concentration of crosslinking agent only up to 15 to 20% DVM in the system. Within this concentration interval 11 the overall acceleration constants increased with molecular distance between DVM double bonds in the following order: EGDMA (1.1 x ICT3), DEGDMA (1.5 x 10-3), TrEGDMA (1.8 x 10~3), and TEGDMA (2.4 x 10~3 rnin"^ cone.""-*). Half-time concentration values, i.e., concentration of divinyl monomer required to reduce the curing time to one-half of that for pure MMA, increased in reverse order. Numerically, half-time concentra tion values for TEGDMA, TrEGDMA, DEGDMA, and EGDMA were 3, 4, 5, and 7% respectively. The calculated overall acceleration constant allowed prediction and calculation of curing times for..,. individual comonorner mixtures. The agreement between predicted and experimentally measured values was within 5% error. The derived empirical equation for prediction of curing time was also applicable to the heat-catalyst polymerization system. All divinyl monomers studied were found to be efficient crosslinking agents and improved the thermomechanical and strength properties of the resulting copolymers. The compression stress, strain and toughness exhibited well defined maxima within 5-lC/o of divinyl monomer in the mixture. Within this concentration interval both maximal acceleration and superior mechanical properties of copolymers were obtained. The numerical value of copolymer connection number (CN ) was found to be a useful structural parameter relating mechanical and thermomechanical properties with copolymer crosslinking density. iii TABLE OF CONTENTS ceo <>«»'««« o r> f • o • * o » «• TABLE OF CONTENTS.. LIST OF TABLES..... LIST OF FIGURES... LIST OF SYMBOLS............. ACKNOWLEDGEMENTS... «• * * • • «• • o t> « • • # «• 2 © 0 LJ^II2JR./\T0 Piiz R IE V 11_ v •/» 0 ««« »• © * o &» * e © o «• » ^ « » • 2.1 Radical Chain-Growth Polymerization... « a • a 9 * • 0 0 t> o » e o * • 0 e 2.1.1 Free radicals; formation and 2.1.2 Radiation polymerization of vinyl 2.1.2.1 Kinetic considerations........ . 2.1.2.2 Overall rate of polymerization 2.1.2.3 Bulk polymerization of MMA.... 2.2 Polymerization in Gel-Phase Media........... 2.2.1 Autoacceleration; experimental evidence for gel-effect (Ge)........... 2.2.2 Acceleration within the crosslinked netv^ork; copolymerization cf vinyl-divinyl comonomer systems............. 2.2.2.1 Orosslinking and gelation; prediction of gel-effect (Ge). 2.2.2.2 Influence of divinyl monomer molecular bridge length „. PAGE i iii vi viii xi xiii I 6 6 7 9 10 11 13 15 22 23 28 PAGE 2.2.2.3 Accelerated polymerization in forming wood polymer composites ( i"/PC )....««..«. ».ooo..o..o.o... 3l 3«0 MATERIALS AND MEiHODS...»..«.•................... 36 3 o 1 Mon 0 me rSe«o.«..«o«oA0o#«o.ooeott.o«o.0.o«ooo.. 36 3.1.1 Methyl methacrylate. ••....«<»•••••...«.• • 36 3.1.2 Divinyl monomers.»....o...............« 36 3.1.3 Calculation of structural parameters... 37 3.1.4 Preparation of comonomer mixtures...... 39 3.2 Radiation Polymerization Technique........... 40 3.2.1 Definition and determination of polymerization parameters.............. 40 3.2.2 Polymerization procedure. 42 3.2.3 Reproducibility of experimental results 43 3.3 Properties of Polymer Products............ ».. 44 3.3.1 Thermomechanical properties............ 44 3.3.2 Mechanical strength properties...,.,..., 46 s n HT c»ri TOM 52 5.1 Radiation Polymerization of the M-4A-TEGDMA C onion o (no IT SystGiiu *«6f)««44«<(ti)e*o«r}aar}M«««««« 5.2 Influence of Molecular Bridge Length in ^ Divlny— Monomers* «o.......»......4.o.oo«..oo. 5.3 Prediction and Calculation of Curing Times... 61 63 5.3.1 Application of the derived equation to published results..»• 5.4 Analysis of Crosslinked Polymer Product , r Thermomechanical Curves...............100 5.5 Analysis of Polymer Product Compression S"LxGSo**o\,x*ciu. n u.xv©so & # •» o«**««* * *>«*«0 ©*«*»«* 70 V PAGE 6 tt 0 COwO.L< LIS IOl\fS ftft««94a«0£te»«QG>00Q«*eo«9C.«««O0oe>»««» 76 7.0 RECOMMENDATIONS FOR FURTHER STUDY 78 3 o 0 Lj X T H H.A. 1 LIR.E C1IED« ««M«««0«*oi>«t(ito«eot*tio«*o»»« 79 vi LIST OF TABLES TABLE PAGE 2-1. Effect of conversion level on the polymeriza tion characteristics of methyl methacrylate ^ 2-2. Some data on polymerization of dimethacrylatic esters (photoinitiator - benzoin 0,2%) (8).... ^9 3-1» Some properties of methyl methacrylate (MMA) and divinyl monomers (DVM) used in this study- 90 3- 2. Concentrations and relative viscosities of different methyl methacrylate (Mr.'A)-divinyl monomer (DVM) mixtures, .......... 4- I« Polymerization•exotherm characteristics for the' MMA-TEGDMA comonomer system (67,69)....... 92 4-2. Calculated polymerization parameters for the MMA--TEGDMA c omonomer system (67,69) ........... 93 4-3. Polymerization exotherm characteristics for MMA-EGDMA, MMA-DEGDMA and MMA~ TrEGDMA -i QA. c omon oine r sysuems »o.««..o. ?. ?. o.. ...... ' • 4-4. Calculated polymerization parameters for MMA-EGDMA, MMA-DEGDMA and MMA-TrEGDMA comonomer 4-5. Differences between measured and calculated curing times for lower concentrations of divinyl monomer (DVM) in MMA-DVM systems...... 96 4-6. Differences between measured and calculated curing times for lower concentrations of TEGDMA in the styrene (S)-TEGDMA system (70).. ' 97 4-7. Differences in calculated and published curing times for TBS.-di-and tri-vinyl comonomer systems (53)....i............. « 98 4-8. Differences in calculated and published curing times for heat-catalyst cured MMA-trimethylol propane trirnethacrylate (TMPTMA) polymeriza-u X Oil Sy S*t GHl ( 3 ) a t u p o :» i a 3 » a o « aQ4 + o«oee*i<i6&*e4o Vll PAGE 4-9. Radiation polymerization of TEGDMA at different dose 4-10. Thermomechanical properties of radiation cured poly(MMA) and crosslinked MMA-DVM polymer prOdliCtS» e«o#»«o»*oa(>Oi»4oO'jec*«>ji)i)8i)e*«»oO(«9«o» 101 4-11. Mechanical properties of radiation cured . poly(MMA) and crosslinked MMA-DVM polymer 4-12. Calculated parameters from compression stress-strain curves for radiation cured poly(MMA) and MMA-DVM polymer products. 103 viii LIST'OF FIGURES FIGURE PAGE 3-1. Solution of a typical polymerization exotherm curve includina .derivation of "Gel-Effect Point" (GEp)» "Cure" (MAX), and showing "Activation" (l) and "Acceleration" (II) ^ • 3-2, Typical thermomechanical curves for thermo plastic (l), partly crosslinked (2) and fully crosslinked (3) polymer products; and showing for (2) solutions for glass transition temperature (Tg), thermal distortion tempera ture (TDT') and slope (s) in the transition ^ 3-3. Polymer stress-strain curve nomenclature and typical curves for different types of plastics (90 79) -1-00 4-4. .tionship between t?,^x anc* volume concen tration of TEGDMA in the "MMA-TEGDMA comonomer 4-1. Relai trat — — — — — - - - ~ —— mixture (6 /,69).................o............. 4-2. Polymerization rate coefficients in "Activation" (PRCi) and "Acceleration" (PRCn) periods as functions of TEGDMA volume concen tration in the MMA-TEGDMA comonomer mixture (67 69) 1Q8 4-3. Relationship between overall curing rate (l/ts.-w) and TEGDMA volume concentration in the MMA-TEGD;- "iA comonomer mixture (67.69)...... Relationship between tMAX and divinyl monomer (DVM)'volume concentration in MMA-DVM 4-5. Relationship between tQEP and divinyl-monomer (DVM) volume concentration in MMA-DVM corn0nornGx rnixtiJXGSo*i»vtf»o*<>4o©L>»#«o<»#*e <?©«•<>*»* 4-6. Polymerization rate coefficients in "Activation" (PRCj) and "Acceleration" (PRCTJ) periods as functions of divinyl monomer (DVM } volume concentration in MMA-DVM comonomer 110 111 112 Ix FIGURE 4-7, Relationship between t^^ and tGEp for different' MMA-DVM comonomer systems and the 4-8. Relationship between overall curing rate UAr/iAx) and DVM concentration in MMA-DVM 4-9. Overall acceleration constant (K) and its reciprocal. (l/l<) as functions of divinyl monomer connection number (CNQYM* Table 3-1).. 4-10. Relationship between overall curing rate (l/tj,/^) and DVM concentration in t-butyl styrene (TBS)-DVM mixtures, Evaluation of original heat catalyst data from (53)... o o a « o 4-11. Overall curing rate (lA^vO as a function of the radiation dose rate. 4-12. Shape of thermomechanical curves for MMA-EGDMA polymer products......................... 4-13. Shape of thermomechanical curves for MMA-i EGDiviA polymex' produces......................... 4-14. Glass transition temperature (Tc.) as a func tion of copolymer connection number (CMC0) for different MMA-DVM polymer products 4-15. Thermal deformation degree (TDD) and thermal distortion temperature (TDT) as functions of copolymer connection number (CMC0) for different MMA-DVM polymer product s............. 4-16. Linear thermomechanical deformation coefficient (LTDC) as a function of divinyl monomer (DVM) volume concentration in MMA-DVM polymer products..... 4-17. Linear thermomechanical deformation coefficient (LTDC) as a function of copolymer connection number (CNco) for different MMA-DVM polymer products. 4-18. Shape of compression stress-strain curves for MMA-EGDMA polymer products......c..... X FIGURE 4-19. Shape of compression stress-strain curves for MMA-TEGDMA polymer products. OO9OO990O&O9 4-20, Compression stress-strain parameters as functions of comonomer composition. The MMA-EGDMA comonomer system............. 00000*000 4-21. Compression stress-strain parameters as functions of comonomer composition. The MMA DEGDMA comonomer system.......... QG4O00O0O0O 4-22. Compression stress-strain parameters as functions of comonomer composition. Ihe MMA TrEGDMA comonomer system......,,,. O00O00Q00 4-23. Compression stress-strain parameters as functions of comonomer composition. The MMA TEGDMA comonomer system. 4-24. Compression stress at rupture as a function copolymer connection number (CMC0) for different MMA-DVM polymer products 4-25. Relationship between area under the compres sion stress-strain curve (F) and plastic deformation for different MMA-DVM polymer products, 0OO*e««OO0O0*O9«<)«0»OO««0»OO xi LIST OF SYMBOLS a = Number of 2-way connected atoms A MA Allyl methacrylate AN = Acrylonitrile b Number of 3-way connected atoms BMA Butyl" methacrylate c = Number of 4-way connected atoms Connection number CM CNco — Copolymer connection number d = Specific gravity, g/cm3 D — Radiation dose, Mrad dp Depth of penetration, mm DP - Degree of polymerization DVB — Divinyl benzene DVM Divinyl monomer DEGDMA Diethylene glycol dimethacrylate E Modulus of elasticity, kg/cm^ EGDMA Ethylene glycol dimethacrylate Monomer functionality 0 f r - Area under the stress-strain curve, cmf-Ge — Gel-effect GEP = "Gel-Effect Point" h = Polymer sample height, mm k Sensitivity constant, mils/inch . K Overall acceleration constant, min" . conc kp = P.ropagation rate constant kt Termination rate constant LTDC Linear thermomechanical deformation coefficient, l/°C M Monomer MAX = Exotherm maximum, "Cure" mf Mole fraction M/AA = Methyl methacrylate MW Molecular weight Number of -G-CH2-CH2- units in DVM n OAC Overall acceleration constant OCR Overall curing rate 05 R Overall gelation rate P = Extent of oolycondensation reaction, % • P Dead polymer PPC Paper polymer composites PRC = Polymerization rate coefficient, °C/min PPC in "Activation" period, °C/min PRC! PRC II PRC in "Acceleration" period, °C/min poly(MMA) Poly(methyl methacrylate) poiy(S) Polystyrene xii R* = Primary radical Ri  Rate of initiation RM* = Growing polymer radical Rp  Overall rate of polymerization, /6/hr s = Slope of thermomechanical curve in transition region S = Styrene t  Time, min T = Temperature, °C TBS = t-Butyl styrene TDD = Thermal deformation degree, % TDT = Thermal distortion temperature, °C TEGDiMA = Tetraethylene glycol dimethacrylate Tg = Glass transition temperature, °C tGEP - Time to onset GEP, min ?GEP = Temperature at GEP, °C tr^AX " Time to reach exotherm maximum, min TMAX - Temperature at exotherm maximum, °C TfvlPTA = Trimethylol propane triacrylate TMPTMA = Trimethylol propane trimethacrylate TrEGDMA = Triethylene glycol dimethacrylate VA = Vinyl acetate VAD = Vinyl adipate VC  Vinyl chloride VPC = Veneer polymer composites VS  Vinyl succinate WPC = Wood polymer composites I = "Activation" period II  "Acceleration" period %xel = Relative viscosity xiii ACKNOWLEDGEMENTS I wish to acknowledge contributions of all my present and previous teachers. It has been my privilege to have been closely associated with Dr. L. Paszner, Research Associate, Faculty of Forestry and Dr. J. W. Wilson, Professor, Faculty of Forestry. I wish to express my thanks to both of them for valuable advice, constructive criticism, thoughtful considerations and helpful suggestions during the investigations and preparation of this dissertation. Their support provided over the past years is deeply appreciated. I wish to thank the University of British Columbia for Graduate Fellowships: the Faculty of Forestry for Research Fellowships and other financial support; Dr, R. V/. Wellwood and Dr. N. C. Franz for support from an NEC operating grant during final stages of thesis preparation. Appreciation is also expressed to Miss E. Budyk and technical staff; in particular, to Mr, U. Rumma and G„ Bohnenkamp for help with construction and calibration of the thermomechanical analyzer. Last but not least, I am grateful to my wife Gitka and children Michelle and Martin-Mike for their great patience and sacrifice over the many weekends devoted to this study and Its reporting. 1 INTRODUCTION Wood is a valuable material, used traditionally in its natural state. Ease of fabrication and finishing, pleasing appearance, high strength to weight ratio and low cost are characteristics contributing to its wide use. Numerous attempts have been made to improve inherent wood properties. Finishes have been developed to increase resistance to weathering and mechanical abrasion, treatments have been developed to improve dimensional stability or to impart greater resistance to decay, fire and biodegradation. One treatment of current interest is the combination of wood with polymers to form wood polymer composites (WPC). A means for producing WPC involves impregnation and in si.tu polymerization of vinyl monomers in wood structures. Among techniques available for curing WPC, radiolytic polymerization has-been much examined (4,5,30,31,49,54,55,56, 82,84,85,90,93,99). After a decade of extensive experimenta tion and development, WPC products have begun to appear in the market (30). Monomers such as methyl methacrylate (MMA) and styrene (S) are economically attractive. A major restriction imposed by most monomers employed in WPC manufacture has been long curing schedules, and 2 coxresponding high dosages, required to complete radiolytic polymerization. The requirement with S, as example, is not only beyond reasonable economics, but so large as to degrade the wood substrate. Certainly, better radiation efficiency has become a necessity to further process development. Several methods have been used to accelerate radiation polymerization of vinyl monomers incorporated in wood matrices. Addition of low molecular weight compounds, particularly carbon tetrachloride (CC14), was found to accelerate the radiation curing of various vinyl monomers (30,55,90,93). However, secondary effects caused by CC14, particularly by its function as a chain-transfer agent (22), are so disadvantageous that it is not considered for technological applications (30,82). It has been known from the theory of monomer gelation (38) that incorporation of small amounts of crosslinking agents, containing two or more vinyl groups, allows formation of three-dimensional networks which, during early stages of polymerization reactions would turn the comonomer system into a gel. Relatively little work has been done to utilize the phenomena of gelation to accelerate radiation polymerization. So far only Raff ££. al.. (84) and Kent e_fc_ ad. (55) have paid limited attention to acceleration in vinyl-divinyl comonomer systems as related to radiation processing of WPC. Recently, during quite 3 advanced stages of this work, Kenaga (53) and Duran and Meyer (33) attempted to utilize this method in randomly chosen heat-catalyst systems. A systematic study of gelation kinetics in vinyl-divinyl comonomer systems is completely lacking. Up to this point no quantitative information has been available on the following parameters: 1. differences in curing rates before and after the Gel-Effect Point (GEP), ii. the temperature profile during polymerization, iii. efficiency of different crosslinking agents, iv. the influence of molecular bridge length between double bonds of divinyl monomer on regulating the propagation and termination reactions in gelled network, and v. the relation between overall curing rate (OCR) and composition of comonomer mixtures. The primary objective of the present study was to test the hypothesis that radiation polymerization of vinyl-divinyl comonomer systems may be accelerated by forming gelled three-dimensional networks. Further,characteristics of these networks should depend on divinyl monomer (DVM) features, such as bridge length between the double bonds. This should allow predictions of the polymerization course 4 and OCR by merely considering the DVM chemical structure. Since the hypothesis involves regulation of individual elementary steps of polymerization reactions it is expected that such findings would be fully applicable to acceleration of heat-catalyst systems. Further purposes of this work were to: i. develop techniques which allow monitoring of radiation polymerization to complete conversion, determination of GEP and associated parameters, ii. investigate acceleration polymerization across wide ranges of comonomer concentration with various systems, and iii. elucidate properties of various polymer products available from the systems examined and attempt to relate these to monomer structural features. MMA was selected as the basic monomer for the study because of its present utility in WPC products and because of wide literature available on such composites. Another reason was compatibility of MMA with a commercially available homologous DVM series of glycol dimethacrylate esters. The DVM crosslinking agents were ethylene glycol dimethacrylate (EGDMA), diethylene glycol dimethacrylate (DEGDMA), triethylene glycol dimethacrylate (TrEGDMA) and tetraethylene glycol dimethacrylate (TEGDMA). To the best of the author1 s knowledge no literature relates molecular bridge length with gelation or acceleration in vinyl-divinyl comonomer systems. The source of radiationrwas gamma rays from decaying 60Qq. It was chosen on the basis -of its availability, proven effectiveness in initiation of MMA polymerization and its high penetrating power, normally required for large sections of wood composite products. 6 2.0 LITERATURE REVIEW 2.1 Radical Chain-Growth Polymerization Polymers of the type important to this study are macromolecules built up by the linking together of a large number of unsaturated molecules termed monomers. Radical chain-growth polymerization is initiated by reactive species containing unpaired electrons, i.e., free radicals. 2.1.1 Free radicals; formation and reactions Organic molecules containing one or more unpaired electrons are termed free radicals. They can be either monoatomic species or polyatomic aggregates of different chemical structure. Free radicals are generally considered to be highly unstable species because of their very short lifetime in reaction systems, particularly in homogeneous liquid or gaseous reaction media. Production of free radicals may be accomplished by either of two general reactions: i. homolytic decomposition of covalent bonds, or ii. generation by an electron transfer mechanism. Homolytic decomposition of covalent bonds into two 7 or more radical fragments may be accomplished by absorption of energy in almost any form; thermal, electromagnetic, electrical, sonic or mechanical. All these energy forms have been used for free radical production and initiation of radical chain-growth polymerization (22,36,59,60,78,106). For practical applications thermal and electromagnetic energy are the most important means by which free radicals are produced. The latter generally includes either of two major sources, ultraviolet light or high energy radiation. These are termed ionizing radiation. Free radicals take part in a variety of destructive chemical reactions, such as oxidation and thermal degradation. The most important synthetic type reactions involving free radicals are: i. addition to multiple covalent bonds, and ii. radical termination reactions. Both reactions are crucial to radical chain-growth polymerization with vinyl monomers and will be discussed later in relation to specific problems of the present study. 2»lo2 Radiation polymerization of vinyl monomers Radiation induced polymerization of vinyl monomers is a direct application of radiation chemistry. Such syntheses of high polymers have been used for more than three 8 decades and now represent well established methods for producing a variety of polymers and copolymers. Radiation polymerization is not just a laboratory curiosity, but includes industrial applications. Its application to production of wood polymer composites (WPC), for example, is currently practiced commercially and under further development (30,55,56,90). It is known that the initiation step in radical chain-growth polymerization reactions requires application of external energy. In radiation polymerization this energy is supplied by ionizing radiation from a source. Once the chain-growth reaction is started, however, the polymerization proceeds independent of the energy source according to conventional kinetic rules derived for chain-growth polymeriza tion (22,36,42). Main features of vinyl monomer radiation polymerization are basically similar to those of conventional heat-catalyzed free radical polymerization reactions. The chemical action of radiation is limited to the primary initiation step leading to production of free radicals and to a few peculiar secondary effects, such as degradation and crosslinking. Radiation polymerization mechanisms have been described by Chapiro in an excellent monograph (22), as well as by others (24,42,74). In all these studies . 9 features of radiation polymerization kinetics are discussed. In addition, the present study requires special emphasis on acceleration via gel-effect (Ge) phenomena in highly viscous and crosslinked structures. 2.1.2.1 Kinetic considerations Kinetics of chain-growth polymerization is based on interpretation of experimental results from free radical reactions. At least three types of reactions are described (22) as: i. initiation, which produces free radicals, * ii. propagation, which involves a sequence of identical reactions repeated many times, and iii. termination, which stops the chain-growth reaction. It is also possible that a single free radical may initiate formation of more than one polymer molecule through a reaction in which the active site, i.e., free radical, is transferred without loss of activity to another molecule in the system. This type of reaction is termed a chain-transfer reaction. Formation of macromoleculas containing thousands of covalentiy bonded monomer units is an overall result of the above elementary reactions. .10 2.1.2.2 Overall rate of polymerization The overall rate of vinyl monomer polymerization, i.e., the rate of monomer disappearance in the reaction system, was described (22,42) by the following kinetic scheme: Process: Rates: Initiation: X 2 R R^ <........... 0/2™l/ Propagation: R° + M > RM* RMx + M —-> RM;+1 kp/RMV'/iV ....../2-2/ Termination: RM° + RM' -> Px+y kt/RM*/2 ........./2-3/ where: X any molecule in the system, R* = primary radical, M = monomer; RM° = growing polymer chain^ P = dead polymer, = rate of initiation, kp = rate constant for propagation, and k^ = rate constant for termination. After mathematical treatment and steady state assumptions, the overall polymerization rate (Rp) is given as: -l/2m l/2 , .  . This classical equation indicates that rate oi polymerization is proportional to the square root of initiation 11 1/2 rate. The quantity k /fc, , a constant value at steady state P <* conditions, changes at higher conversion degree and accelerates the overall reaction rate. As a second consequence an increase in molecular weight (M.W), or degree of polymeriza tion (DPjjis observed. This is required by the following equation (22): "''*•* DP = k Af/2- Ril/2« M /2-5/ P t x With respect to a monomer of interest in this study, (MMA), the published results on polymerization kinetics fully confirm /2-4/ and /2-5/ (22,59,106). Bulk polymerization of MMA, especially to the high conversion degree, exhibits deviations from these theoretical predictions (6,22,64,75,87, 89,103). 2.1.2.3 Bulk polymerization of MMA Much work has been done in the area of MMA radiation polymerization. The free radical mechanism for this reaction was established by Chapiro (22). He deduced the mechanism from data which showed that polymerization was inhibited by air and benzoquinone. During initial reaction stages the polymerization process shows a characteristic Arrhenius temperature dependence, with an activation energy of 4.9 kcal/mole (3,22). The constant value of activation energy was observed over wide !2 temperature range ( -18 °C to 70 °C) with dose rates 2.3 to 2.5 x 10^ rad/hr,. In a more recent work by Lipscomb and Weber (60), who operated between -49 and -19 °C and at a dose rate of 3.7 x 105 rad/hr, the activation energy was found to be 3.85 kcal/mole. It should be pointed out, however, that the freezing point of MMA is -48;2 °C (86), which casts doubt as to validity of the data at -49 °C. The reaction controlled region is dose rate dependent. Chapiro (22) reported a dependence to the 0.5 power for low dose rates (less than 5.4 x 10^ rad/hr). Above 10^ rad/hr the reaction was said to be dose rate independent. Ballantine et al. (3) reported dose rate dependence of 0.5 up to 2.0 x 10~* rad/hr. In contrast Lipscomb and Weber (60), working at approximately the same dose rate, reported a power factor of 0.33 at both -49 °C and -19 °C. For MMA, as for other vinyl monomers, the mechanism of free radical polymerization changes drastically at high conversion degree. A special mechanism, which predominates and controls later stages of polymerization kinetics, has been attributed to Ge. Because of its particular importance to the present study, Ge phenomena are discussed in detail in a later section. Attempts to define overall reaction orders have been unsuccessful due to effects associated with Ge phenomena. 13 Nevertheless, the MMA polymerization reaction is considered to be of zero-order up to about 20% conversion (12). Rabinowitch (83) derived an expression relating reduction of the termination rate constant with the rate of diffusion for second order reactions* Vaughan (104) and later Robertson (87) tried to correlate the experimental data for MMA and styrene using the Rabinowitch equation. The result, however, was unsatisfactory. Attempts to quantify polymerization rates in the Ge region have been hampered by two major factors. Firstly, the onset of Ge does not occur at a specific conversion. Rather, conversion at which Ge begins is strongly dependent upon temperature. Secondly, experimental measurements in the Ge region are inherently difficult. Isothermal conditions are almost impossible to maintain?and analysis of the partly • plasticized material requires special experimental techniques for recovery and solution of gels and isolation of the unconverted monomer. 2.2 Polymerization in Gel-Phase Media The kinetic scheme of free radical polymerization, discussed in Section 2.1.2.2, applies only to the initial reaction stage up to approximately 5 to 10% conversion. If reactions proceed to higher conversion degrees the mobility of reactive species is reduced by a massive increase in local 14 viscosity. The rate of diffusion is significantly reducedc This phenomenon manifests itself in Ge, commonly observed in bulk polymerization of vinyl monomers, particularly with MMA (75,103)• The most important consequence of Ge is acceleration of the overall polymerization rate, as soon as some critical conversion level has been reached,, If viscosity of the reaction medium is further increased, long range diffusion of polymeric radicals is suppressed and only local mobility of polymer segments ensures limited reaction. Finally, if the system sets to glass, all polymeric radicals remain immobilized and the residual reaction, if any, results only from diffusion of small unreacted monomer molecules. Under a given set of reaction conditions various polymerization reactions may fall into any one of three cases as: i. both propagation and termination are controlled by reaction rate, ii. propagation is reaction-controlled and termination is diffusion-controlled* or iii. both propagation and termination are diffusion-controiled„ The case of diffusion-controlled propagation and reaction-controlled termination is a physical impossibility, 15 since reaction between two polymer radical segments would be favored over reaction between monomer and polymer radicals. 2.2.1 Autoacceleration; experimental evidence for gel-effect (Ge) Bulk polymerization of a number of vinyl monomers, such as MMA (6,13,62,75,87,89,103), methyl acrylate (MA) (15,64,65), butyl methacrylate (BMA) (14), S (8,39,87) and vinyl acetate (VA) (59), follow the patterns of autocatalytic reactions. The polymerization proceeds smoothly at first with constant rate, as expected from steady state kinetics /2-4/. After a critical conversion is attained the reaction rate suddenly increases several times. The reaction at this stage shows a definite autoacceleration character. For S polymerization, for example, the overall acceleration factor is 5.2 at 38% and 16.9 at 60% conversion (59). Similarly for MMA polymerization, the initial polymerization rate of 3.5%/hr increases to 15.4%/hr at 30% conversion and 24.5%/hr at 50% conversion (43) as shown in Table 2-1. Simultaneously with increase in polymerization rate, several secondary effects are evident.. These include increased MW and concomitant local temperature rise (22,36). These effects are explained by the decreased termination. It is generally accepted that reduction in the rate of termination is caused by reduced mobility of growing polymer chains in the viscous medium. 16 Measurements of individual rate constants. Table 2-1 (43)., show that the decrease in termination rate occurs at fairly low conversion, generally between 10 to 30%, On the other hand, the propagation rate is enhanced only after 50 to 60% conversion, i.e., after the reaction mixture has already gelled. This is in accordance with theoretical conclusions drawn by Rabinowitch (83). He concluded that reactions having low activation energies are more likely to become diffusion-controlled. An average activation energy for termination is 0 to 2 kcal/mole, while activation energy for propagation is*5 to 8 kcal/mole (22,23,36). A similar conclusion was reached by Vaughan (104) who calculated critical viscosities for elementary reaction steps. His critical viscosities for termination and propagation were 2.0 and 7,0 x 10~* poise, respectively. It must be emphasized, however, that the viscosity effect is not due to changes in radical reactivities. Instead, it arises from a purely physical effect caused by the diffusion barrier. Hayden and Melville (43) studied variation of several MMA polymerization parameters with conversion, including average lifetime of a kinetic chain and rate constants for both propagation and termination. They pointed out that the termination rate constant decreased by about 100,000-fold from the start of polymerization up to 50% conversion. The effect of conversion on kinetic variables has been divided into three distinct stages as*. 17 i. Stage 1^ up to 10% conversion, ii. Stage II, between 10 to 70% conversion, and iii. Stage III? over 70% conversion. In Stage I the reaction mixture changes from a mobile liquid to a viscous syrup, but the rate of polymeriza tion adheres to steady state kinetics represented by /2~4/. In Stage II the reaction mixture changes from a very viscous fluid to a soft solid. Large increases are obtained in both polymerization rate and lifetime of the kinetic chains. Both increase by approximately ten fold. In Stage III as conversion nears completion, termina tion appears to become a unimolecular process and even propagation becomes diffusion-controlled as molecules are immobilized in the gel-glassy reaction medium. Although propagation in gel is hindered, the overall effect is much smaller since kp values are smaller than k^ by a factor of 104 to 10^ (Table 2-l). Termination involves the reaction of two large polymer segments /2-3/„ while in propagation only one large polymer radical and a small monomer molecule are involved /2-2/. High viscosity affects the former much more than the latter. Therefore, the quantity , , l/2 kp/k^. changes during the polymerization process. This results, in accordance with /2-4/, in an increase of the overall polymerization rate with increasing conversion. As a second consequence, and in accordance with /'2~b/, an increase in molecular weight is obtained.. This has been verified experimentally also for numerous vinyl monomers (13,14,78). Solvents and chain-transfer agents, which directly reduce viscosity and molecular weight of polymer products, delay or even eliminate the onset of 6e, As shown by Schultz and Haborth (89), autoacceleration is completely eliminated when the reaction system is diluted with 60% of an inert solvent. Molecular weight of polymer formed in different solutions also decreases with increasing dilution. This is the result of decreased kinetic chain lifetime due to bimolecular chain termination (6,103). It was further shown that addition of an inert polymer, which increases viscosity of the reaction media, brought about a premature appearance of Ge (103). Temperature changes of reaction media were measured by several investigators. It was noted that acceleration is accompanied by considerable overheating of the system. In order to avoid additional complications, such as created by non-isothermal conditions, Schultz and Harborth (89) polymerized thin layers of MMA onto a mercury surface. Results of this experiment conclusively demonstrated that Ge acceleration is a truly kinetic phenomenon. Temperature rise at the onset of Ge-'is much more pronounced with MMA than with S (3), even at very low polymeriza tion temperatures, e.g,, -18 °C. Difunctionai methacrylates 19 and acrylates, irradiated in solid state, showed remarkable temperature rise even at -90 °C reaction temperature (22). A direct consequence of Ge in polymerization under constant rate of initiation is that the concentration of growing polymer chains increases with time Thus the poly merization system does not follow stationary kinetics due to violation of the steady state assumption. Overall polymeriza tion rate is not proportional to the square root of initiation /2-4./c Indeed, a marked departure from conventional kinetics is observed and the reaction order with respect to initiation rate rises above the theoretical 0.5 value. A complete treatment of Ge kinetics should take into account both the gradual decrease of termination rate and the concomitant increase in free radical concentration. Such a treatment is still lacking (23). Reduction in the termination step in free radical polymerization, and. consequently premature onset of Ge, can be brought about by several physical methods. All these methods are based on the principle that termination by the mutual reaction of two polymer chains can be prevented by isolating the growing polymer segments from each other. In many cases, isolation of growing polymer fragments has been accomplished by "occlusion" of the active end groups within discrete polymer particles. This phenomenon is responsible for the unusual rate behaviour observed in the following systems (59): 20 i. polymerization reactions initiated in gas pha se, ii. polymerization of a monomer in a medium which is non-solvent for the resulting polymer, termed precipitation polymerization, iii. emulsion polymerization, iv. polymerization of crystalline monomers in the solid systems, and v. polymerization within crosslinked networks, such as vinyl-divinyl comonomer systems. Systems ii, iii and v are far the most important, particularly for practical applications involving WPC, as well as paper polymer composites (PPC). If polymerization is carried out in a medium in which the resulting polymer is insoluble, the growing polymer chains separate from the solution to form a second phase by precipitation. Reaction proceeds thereafter in heterogeneous medium and usually shows a peculiar behaviour similar in many respects to Ge. Systems which behave in this manner include: i. pure monomers which do not dissolve their own polymer, for example acrylonitrile (AN) and vinyl chloride (VC), ii. monomer solutions immiscible with solvents which are precipitants for the polymer, e.g., methanol-S, methanol-MMA. hexane-VA, and 21 iii. comonomer mixtures which do not dissolve the resulting copolymer, as the AN-S comonomer system. Acceleration during early reaction, stages, a pheno menon identical with Ge, has been interpreted as impeded termination in the presence of a polymer precipitant (1,16, 22,75). Here relative conversion rate is a function of monomer/precipitant ratio. Maximum acceleration is observed at precipitant content slightly below the precipitation point where phase separation leads to a viscous, gel-like coagulate highly swollen by monomer. The overall polymerization rate, at this point, rises sharply and the reaction exhibits non-steady state kinetics. Physical state of the precipitated polymer and the extent of swelling seem to be very important factors in preparation of graft copolymers (2l). Thus., it has been reported that a highly swollen substrate is necessary to form large amounts of graft copolymers, e.g., increased grafting efficiency (21,49,57,96). The alcohol-S system has been used in applied studie for radiation cured WPC. Siau et. al_. (90) compared grafting efficiency of S on red pine (Pinus resinosg Ait.), as well as on yellow-poplar (Llriodencir.pn tulipifera L. ). Ramalingam et al. (85) evaluated effects of a three component system, methanol-S-water, on graft copolymerization efficiency. They concluded that,in addition to the observed acceleration effects, this system increased grafting efficiency. This is in accordance with theoretical conclusions drawn from radical lifetimes observed in viscous and swollen systems (21,43). 2.2.2 Acceleration within the crosslinked network; copoly merization of vinyl-divinyl comonomer systems In many copolymerization reactions divinyl compounds are used as monomeric constituents. The obvious reason for including such compounds is to obtain crosslinks between linear macromolecuies. This leads to three-dimensional net works. When divinyl monomers (DVM) are incorporated in a comonomer system, only one of the double bonds reacts//). The other is left as a pendant vinyl group. At higher conversion degree the pendant vinyl group may be involved in propagation reactions. At such stage a rather abrupt transition is experienced in passing from the liquid to gel state. If sufficient polyfunctional crosslinking agent is used, a significant departure from linearity in the overall polymeriza tion rate can be achieved during early reaction stages due to a premature onset of Ge phenomena. Increase in polymerization rate is a direct consequence of reducing the termination reaction step by isolating the growing polymer radical seg ments in crosslinked three-dimensional networks (59), 23 The formation of such a network,resulting in gelation of the comonomer mixture, generally takes place over a very narrow conversion range and varies inversely with both the amount of crosslinking agent and average DP (34,36,97,105). Flory (34) outlined a general method for determining and predicting the extent of reactions in which such a network is possible and carried out a detailed calculation,for the case of polycondensation reactions. His calculations were in good agreement with experimental results. He indicated that a similar method may be applied to addition polymerization, particularly for vinyl-divinyl comonomer systems in which all vinyl groups have the same reactivity. 2.2.2.1 Crosslinking and gelation; prediction of gel-effect (Ge) According to Flory's treatment on polycondensation reactions, Ge in monovinyl and divinyl comonomer mixtures in which all vinyl groups have the same reactivity may be calculated from the functionality equation (34): where: p = extent of reaction f = average functionality DP = degree of polymerization 24 For a very large DP, which is always the case in addition polymerization, /2-6/ reduces to: With bifunctional monomer molecules, as a consequence of /2-7/, gelation does not occur. With tri- and tetra-functional molecules gelation occurs at 66 and 50% conversion, respectively. However, practical experimental results do not correlate with predicted values. Large deviations from theoretical values were observed even for polymerization of related monomers such as VA-vinyl succinate (VS), MMA-EGDMA, or S-divinyl benzene (DVB) (97,105). Explanation of these deviations, as pointed out by Flory (36) and Walling (105), lies mostly in two factors: i. application of the condensation polymerization functionality equation to chain-growth poly merization systems, and ii. excessive occurrence of intra-molecular cross-linking before onset of Ge, where wastage of inter-molecular crosslinks in this manner is neglected by theory. • Alfrey ei. a_l„ (l) concluded that crosslinking. and subsequent gelation depends on relative reactivities of two double bonds in DVM. The point at which Ge occurs has been treated mathematically for several comonomer systems. In all 25 instances it has been assumed that DVM was present in a low concentration, since this is the case encountered in most practical applications. Generally, three cases were considered (l) according to type of crosslinking agent, as well as vinyl monomer used: io Case I? copolymerization of symmetrical DVM with a vinyl monomer of equal reactivity, ii. Case II, copolymerization of a symmetrical DVM with a vinyl monomer of different reactivity, and iii. Case III^ copolymerization of an unsymmetrical DVM with vinyl monomer of different reactivity. In Case I all double bonds have the same reactivity and chemical structure. Examples of such a system are: i. MMA-EGDMAy ii. VA-vinyl adipate (VAD), and iii. S-DVB. In Case II the reactivity and structure of double bonds in DVM differ from the double bond character in the vinyl monomer. An example of this system is S-EGDMA or MMA-DV3. Acceleration in this system was studied previously (70). 26 In Case III the two double bonds in dienes have different structures and reactivities. An example of this type is MMA-allyl methacrylate (AMA). This system is very complicated and inefficient. Allyl type double bends have generally lower reactivity, thereby crosslinking and Ge occur only after considerable conversion has been attained. In some cases reaction of one double bond in the diene results in a marked reduction in reactivity of the remaining double bond. The overall effect is a marked delay in Ge. An example of this is copolymerization of vinyl monomers with 1,3-dienes. The 1,4 polymerization of diene leads to residual 2,3 double bonds, which have lowered reactivity (l). The most studied dienes of this type are isoprene, butadiene and chloroprene (1,44,58,95). Much experimental material has been accumulated on copolymerization of symmetrical DVM with vinyl monomer of identical double bond structure (Case I). Results derived from experimental data on gelation were in good agreement with predicted values (l) only within a limited DVM concentration range. There has been some controversy about these discrepancies (9V,105). Storey (97) studied the acceleration efficiency of DVB in the S-DVB comonomer system using heat-catalyst. He found that initial polymerization rate varied linearly with 27 DVB concentration at both temperatures studied (70 °C and 87 °C). The MMA-EGDMA system was studied by Walling (105), He also examined the VA-VAD system. In all studies at higher DVM concentration agreement between expected results and those obtained was poor. The discrepancy may have arisen in part from intra-molecular chain cyclization reactions (17,18,19,38, 40,41,61,92) which prevent DVM participation in inter-molecular crosslinking. Walling (105), however, did not consider this to be a major factor. He interpreted his results in terms associated with diffusion-controlled crosslinking reaction. According to his hypothesis, rate coefficient of the cross-linking process decreases with increasing DVM concentration. Simpson et. al. (91) showed that a considerable fraction of DVM is used in the intra-molecular cyclization reaction. This resulted in delayed gelation at comparatively high conversion degrees. Subsequently, Gordon and Roe (40) examined application of the classical gelation theory to the MMA-EGDMA comonomer system. They concluded that this theory was applicable to their results only if further allowances were made for internal cyclization. Further, diffusion controlled crosslinking, as described by Walling (105), was unimportant until after Ge had been passed. Later, Holt and Simpson (48) estimated the extent of inter-molecular cyclization on a series of diallyl esters. All monomers studied gave rise to chain cyclization under 28 similar reaction conditions. The tendency of monomers to cyclize was found to be controlled by the molecular distance between double bonds in the difunctional monomer. This has not been considered as a significant factor in gelation kinetics. 2.2.2.2 Influence of divinyl monomer molecular bridge length It may be theorized that polymerization kinetics of vinyl-divinyl comonomer systems and properties of the polymer products from such systems are determined not only by the nature of reactive groups, but also by the chemical structure and dimension of the DVM molecular bridge, i.e., the molecular fragment connecting double bonds in the DVM, Divinyl monomers having considerable molecular bridge length have higher viscosities. This may have an indirect effect on diffusion processes and polymerization kinetics, particularly in. connec tion with gelation and acceleration via Ge. From experimental data collected for other purposes in (48,61) and from other studies (7,8,9,57,58,76,77) an inference can be made as to the importance of molecular distance between DVM double bonds. This is based on: i. competition between inter-molecular and intra-molecular propagation as related to the ring size3 i.e., cycllzation versus cross-linking; and 29 ii. overall polymerization kinetics, e.g., numerical values of individual rate constants, as well as overall polymerization rate. The importance of intra-molecular cyclization was emphasized when Butler and co-worker (18,19) found that radical polymerization of diallyl monomers gave soluble, non-crosslinked polymers with little or no residual unsaturation. Extensive work by Simpson and co-workers (48,91,92) has helped to show that the size of ring structure which can be formed, determines whether inter-molecular polymerization or intra molecular cyclization is the predominant reaction for a particu lar monomer. As a rule, the formation of 6-membered rings is appreciably greater than those of larger size (59,78). Contrary to expectations, however, ring structures containing as many as 11 and 17 atoms have been reported (17,33,48,61). The influence of molecular bridge length on polymerization kinetics and numerical values of individual rate constants has not been studied systematically. Only limited data are available. Recently, however, Soviet scientists (7,8,9,57,53,76) have published comprehensive studies on polymerization kinetics and properties of such polymers. Berlin (3) calculated individual rate constants of dimethacrylate esters of alkyleneglycols having the general f ormula: CHo Ch" i i CH2 = C - COO -( CH2 ) - 00C - C = CH2 where: x = 4, 6, 10. 30 The initial polymerization rate and propagation rate constants sharply increased with length between double bonds. The absolute kp value for MMA was 300 l/mole, sec and increased to 600, 1,2.00, and 1,880 l/mole. sec for monomers with x equal to 4,6, and 10 respectively (Table 2-2). At lower and average conversions, kp for these compounds exceeded kp for MMA by 5-10 times, although true MMA radical reactivity and the double bonds of methacrylate esters do not depend on the nature of glycol or ester residues (12). From Table 2-2 it is evident that the initial poly merization rate for all oligomers exceeds polymerization rate• for MMA even at 50% conversion where viscosity of the polymeriza tion mixture is much higher. The reason for higher polymerization rate is obvious from the numerical value of k^/k^^. Simple calculation of kp/k^.^^, from data at zero conversion for esters with x equal to 4, 6, and 10 gives 67, 152 and 290 x 10"^, respectively. All these values are significantly higher than the maximum value found for MMA as demonstrated in .Table 2-1 (43). Similar increase in initial polymerization rate was pointed out for polymerization of dimethacrylates and mixed allyl and carboxyallyl esters, such as (8) : Rx - 0 ~(CH2-CH2-0)I_3**R2 where: Rj_ is: CH? = C - CO-CH3 R2 is: CH2 = CH - CH2 - COO , or CH2 = CH - CH2 - 0 -31 The increased reactivity with increase in molecular bridge length between double bonds was attributed to multiple ether bonds which increased flexibility of the three-dimensional framework. Because flexibility of these molecules favours tight packing, double bonds of acrylate groups are drawn together and are arranged in a "kinetically-favourable" pattern and form "bundle associated swarms" similar to nematic forma tion in liquid crystals (8). The transformation from liquid polymerizable esters to space-regular crystalline arrangements indicates broad possibilities of directed synthesis and regulation of both polymerization kinetics and properties of the resultant polymer products. 2.2.2.3 Accelerated polymerization in forming wood polymer composites (WPC) Much work has been published in connection with application of vinyl monomers to wood and papers. Both radiation and heat catalyst techniques of polymerization have been used (4,5,30,31,33,49,53 - 56,82,84,85,90,93,96,101). This simple process converts wood into WPC, a composite material -with improved physical properties such as hardness, abrasion resis tance and compression strength. Further, dimensional stability and associated wet strength properties are improved. So far MMA and S have been the most widely used monomers for this purpose. 32 Problems with in situ radiation polymerization of vinyl monomers relate to radiation sensitivity of wood constituents, particularly cellulose. Vinyl monomers, such as S require massive dosages (10 Mrad) for complete polymeriza tion. The large dose requirements are necessary mainly because of low G-value, 0.6 (22). It i"s also expected that monomers associated with wood components require more energy for polymerization due to influence of wood components and oxygen in the wood structure. It is known (22) that chlorinated compounds, such as CCI4, accelerate radiation polymerization of vinyl monomers. The method has been used for reducing dose requirements in production of WPC (30,55,82,93). However, secondary effects caused by CCI4, particularly since it functions as a very efficient chain-transfer agent (22,42,59), are disadvantageous and limit practical value of CC14 acceleration technique (30,82). Addition of crosslinking monomers, which contain two or more vinyl groups, to common vinyl monomers allows copolymerization and formation of three-dimensional networks. In addition to improved WPC physical properties (30,66) , crosslinking agents quickly turn liquid monomers, deposited in the wood void spaces, into gels and thus: i. accelerate the polymerization via Ge, and ii. eliminate large monomer losses due to evaporation. 33 So far, only scant attention has been given to the accelerating ability of different divinyl monomer-s, A systematic study on gelation kinetics in vinyl-divinyl comon omer systems is lacking. Raff et al. (84) investigated the effect of 5% DVB on radiation polymerization of S in WPC, They found that presence of the crosslinking agent increased the conversion degree for a particular dosage. Unfortunately, other comparative data were not given, Kent et. al_. (55) proposed addition of a DVM (EGDMA) for the purpose of increasing molecular weight, as well as acceleration of radiation polymerization. EGDMA was examined as additive to MMA, However, the minor accelerating effect at 2/o concentration was not very convincing. Kenaga (53) discussed heat-catalyst polymerization with a series of vinyl-divinyl and vinyl-trivinyl comonomer systems. Effect of crosslinking agents on polymerization of t-butyl styrene (TBS) in basswood (Tilda ameripana Lt) at 90°C was followed by the time-temperature exotherm method for DVM concentrations up to 30%. Based on evidence provided by his study trimethylol propane triacrylate (TMPTA) was selected as the most effective accelerator. Several dimethacrylates were shown to be more effective than DVB. The latter contain small amounts of diethyl benzene which remained trapped in wood and caused odor problems. 34 In 1969 Paszner (79) introduced and found TEGDMA to be a very effective crosslinking agent and accelerator for radiation polymerization of MMA, and S. Dose requirements for complete polymerization, as followed by the time-temperature exotherm method, were found to be lower than that for an optimum mixture of S-AN. Subsequently, the accelerating ability of TEGDMA was tested systematically In numerous other comonomer systems (.11,25,26,52,67-71,79-81,98,99). Recently, Duran and Meyer (33) adopted a systematic approach for evaluating the accelerating ability of trimethylo/ propane trimethacrylate (TMPTMA) with MMA in basswood composites. Using maxima of time-temperature exotherm curves (3l) as indicators of reaction rates showed that time to exotherm peak decreased rapidly as percentage of crosslinking agent increased across low concentration levels (1-20%). They attributed the increase in reaction rate, i.e., the decrease in time to exotherm peak, to formation of a three-dimensional gel structure. In our laboratories, as reported earlier (68-70,79-81, 98) time-temperature exotherm curves were used for quantitative characterization of accelerating ability of crosslinking agents in radiation polymerization of vinyl-divinyl comonomer systems. The most attractive comonomer systems have been applied to fabrication of WPC, PPC and veneer polymer composites (VPC), as well as proposed for tough, highly resistant surface coatings (25,26,52,79-81,98,99). 35 In summary, much work has been done to clarify Ge acceleration phenomena in vinyl monomer homopolyrnerization. Vinyl-divinyl comonomer systems, however, have not been studied systematically. It is clear that theoretical treat ment of Ge during polymerization of vinyl-divinyl comonomer systems is more complex than that accepted for condensation polymerization. Acceleration y_ia crosslinking agents is based not only on statistical treatment of crosslink probabilities, but involves many other factors, such as intra-molecular cyclization, diffusion, reaction conditions and chemical structure of divinyl monomers. As example, the molecular bridge length between double bonds may have significant effects. Much work remains to be done before Ge is understood in vinyl-divinyl systems. 36 3.0 MATERIALS AND METHODS Methods and some monomers used in this study were described in detail earlier (67,69,79). Only general monomer characteristics, brief definitions of polymerization para meters, as well as thermomechanical and physical-mechanical tests for polymer products are repeated below. 3.1 Monomers • Two kinds of monomers were used in this study. The vinyl monomer was methyl methacrylate (MMA), while a commercially available series of glycol dimethacrylates were used as divinyl monomers. 3.1.1 Methyl methacrylate Methyl methacrylate was the basic monomer used in all experiments. It contained a commercial Inhibitor (50 p.p.m. hydroquinone) as supplied by Eastman Co. No monomer purifica tion was attempted for these experiments. 3.1.2 Divinyl monomers Four different divinyl monomers (DVM) of the common glycol dimethacrylate structure, with various molecular chain 37 lengths between terminal vinyl double bonds, were selected. These comonomers served as crosslinking agents and accelerators for MMA polymerization. All DVM are characterized by the general formula: The index "n" varied from 1 to 4. The four DVM used in this study were: Properties of the MMA and DVM used are given in Table 3-1. All DVM were purchased from Borden Chemical Co., Philadelphia, Pa. Higher homologs of the series were not available at the time. 3.1.3 Calculation of structural parameters To transfer from monomer into polymer, each carbon atom in the polymer chain or in the three-dimensional network must be connected to at least two other atoms by covalent bonds. Linear one-dimensional (thermoplastic) macromolecules, such as poly(MMA) for example, only contain 2-way connected carbon atoms and thus have a connection number (CN) equal to iii. iv. ii. i. Ethylene glycol dimethacrylate (EGDMA), Diethylene glycol dimethacrylate (DEGDMA), Triethylene glycol dimethacrylate (TrEGDMA),and Tetraethylene glycol dimethacrylate (TEGDMA). 38 2,000. Thermosettings crosslinked polymers or copolymers contain both 2-vvay and 3-way connected carbon atoms. Their CN is between 2.000 and 3.000. Recently, Holliday and coworker (45,46) proposed and demonstrated the usefulness of CN for simple topological analysis of random polymer networks. CM describes an average structural feature of polymers and can be extended further to predict physical properties of polymer products. An average CN can be calculated from the chemical structure of monomer repeating units as: 2a + 3b + 4c a + b + c where: a, b and c are, respectively, 2-way, 3-way and 4-way connected atoms in the repeating monomer units. Calculated values for members of the present series are given in Table 3 X o The average CN can be extended further to copolymers as copolymer connection number (CN )«. CNco provides an average number of network bonds, i.e., crosslinking density. The numerical value of CNC0 depends on molar composition of the comonomer mixture. It is calculated as: CN co (CN^^AX nif^^) + (C^DVN * m^DVM^ ••••••• «/3-2/ where: CN,V1MA and CNDVM are connection numbers for MMA and DVM. 39 m^MMA anc* m^DVM are rn°le fractions of MMA and DVM in the comonomer system, respectively. In calculating an average CN only those connections are considered which form part of polymer network. Thus, side substituents such as CH^- or CH^OOC- in poly(MMA), for example, were excluded. 3.1,4 Preparation of comonomer mixtures Mixtures of MMA and respective DVM were prepared on a volume/volume basis in lots of 50 ml to minimize experimental error due to mixing. These were stored at -10 °C prior to polymerization. Volume concentrations, as well as mole ratios are given in Table 3-2. Relative viscosities (£xei) of the pure monomer and comonomer mixtures were measured with a Ubbelohde l/a viscosi-meter (K = 0.05394) at 25 °C and calculated as: t tMMA mixture . where: ^mixture anci ^MMA are efflux times for the comonomer mixture and MMA, respectively, Relative viscosities for pure monomers are given in Table 3-1 and for the comonomer mixtures in Table 3-2. 40 3,2 Radiation Polymerization Technique Although radiation induced polymerization is now a well established technique, only scant attention has been given to polymerization kinetics as related to Ge and production of WPC. One reason has been lack of proper methods for following the transformation of monomers to polymers, especially within the radiation field. Difficulties in studying polymerization kinetics to high degree of conversion are well documented. Davies et al.. (31) studied the kinetics of MMA radiation polymerization in yellow birch (Betula alleghaniensis Britt.) and red pine (P,i,nu,$, resinpsa Ait.) by a method previously described for heat-catalyst bulk polymerization of vinyl monomers (5,88). In his study the exothermic heat released during polymerization was recorded automatically. From the shape of time-temperature exotherms, kinetically important stages of polymerization were derived and these were related to inhibition, Ge phenomena and complete conversion at peak temperature. The same technique was adopted for this study. Detailed descriptions and determination of polymeriza tion parameters have been given previously (67,69,70). 3.2.1 Definition and determination of polymerization parameters The temperature (T), °C versus time (t),.min records obtained, such as shown in Fig, 3-1, were analysed to provide the following polymerization characteristics: 41 i. Initial condition of the system (T35, t0); ii. "Gel-Effect Point" (GEP) by geometric solution (Fig. 3-1) as the exotherm curve intersection by the perpendicular through the common point obtained by extrapolating early and late curve stages, and with components (TGEp, tGEp); iii. "Cure" at the exotherm maximum (MAX) with components (T^^x, ^^/J^) I iv. "Activation" (i) period as time interval to reach GEP and calculated as (tG£p - t ), and v. "Acceleration" (II) period as time interval between GEP and the exotherm maximum, and calculated (t^^ ~ "^GEP^ * As shown also in Fig. 3-1, dose (D) may be substituted for time (t), thereby describing the irradiation requirements at the single dose rate examined in the present study. To compare relative rates of polymerization in "Activation" (I) and "Acceleration" (II) periods, the following polymerization coefficients (PRC) were calculated: i. Polymerization rate coefficient for the "Activation" (PRCj) period as: TGEP - T: 36 /3-4/ PRCT « - 0000000 «i£Oo«*o00««.0 0O0«o«a ~ to 42 ii. Polymerization rate coefficient for the "Acceleration" (PRGn) period as: T T MAX - GEP . , PRCII ~ tMAX - ^EP The ratio of these coefficients, PRCjj/PRCj, numerically expresses the increase in polymerization rate due to the Ge phenomena. Reciprocal of time needed to attain exotherm maximum (l/tjY^) is used as a measure for characterizing the overall curing rate (OCR): 1 OCR. — —— 0400O00000O390O9 ^* 6 / u MAX By analogy, reciprocal of the time to reach GEP (l/t^pp), refers to the overall gelation rate (OGR) and characterizes the efficiency of the crosslinking agent to onset Ge phenomena. 3.2.2 Polymerization procedure For determination of polymerization parameters 5 ml of monomer or comonomer mixture (volume/volume) were placed in a small glass vial, which was then flushed with nitrogen and 43 sealed. Radiation polymerization was done in a Gammacell 220 with dose rate at 0,82 Mrad/hr, as determined by Fricke dosimetry (27). In two experiments, radiation dose rate attenuators were used to evaluate influence of dose rate on OCR. Comonomer mixtures were first conditioned to the ambient Gammacell chamber temperature (36 °C), then set in a styrofoam seat which provided thermal insulation and reproducible position in the chamber. In each case, exotherm temperatures were followed by insert copper-constantan thermocouples, with signals sent to a time based stripchart recorder calibrated against an ice-water reference junction. A similar technique has been described in detail (67,71). Use of the method involves assumptions that polymerization rate relates to heat evolution and that comparisons may be made between the systems studied, 3.2.3 Reproducibility of experimental results Reproducibility of polymerization parameters, as derived from radiation polymerization exotherms by three independent operators, with the MMA-TEGDIvA comonomer system (ll), was tested on sixteen identical experiments, done as described above. The following standard deviation values were calculated (50): i. "tQEP = 17.5 -: 1.5 rnin, ii. tji^ = 23.2 - 1.7 min, 44 iii. TGEP - 63.0 t 2,5 °C, and iv. Tmx = 143.0 t 7.8 °C. 3.3 Properties of Polymer Products Properties of polymer products were evaluated on the basis of their thermomechanical and mechanical strength behaviours. The individual characteristics, determined from unconventional thermomechanical curves, as well as standard compression stress-strain curves are described below. 3.3,1 Thermomechanical properties Thermomechanical properties of the polymer products y^ere obtained by a simple device constructed for recording deformation of loaded and heated specimens (67,69,80). Polymer samples (3 mm high) were rested on a tube support and were loaded via a rod 3.2 x 10"*2 cm2 in cross-section. The rod extension was coupled with a probe leading into the core of a linear variable differential transducer. High-temperature silicone oil was used as heating medium, The oil temperature was regulated to increase the sample temperature at constant rate (12 to 15 °C/min), followed by an insert copper-constantan thermocouple. Signals generated by changes in temperature and position of the transducer probe were fed to a recorder in the X-Y mode. 45 Glass transition temperature (Tg) and thermal distortion temperature (TDT) were determined as demonstrated in Fig, 3-2, In addition, the magnitude of relatively constant deformation across the broad rubbery state temperature range, characteristic of crosslinked polymers, was used to calculate thermomechanical deformation degree (TDD), As calculated here, TDD varies from 0 to 1 for thermoplastic to fully crosslinked polymer products. Numerical values of TDD were calculated as: h - dp TDD = ... »•..!• j i i ., ., • . I.,. . . i « 4 O * O • .1 • • « » 9 O • 9 O 9 fl O O « »/3*'7/ where: h = sample height, mm, and dp = depth of probe penetration, mm. The linear thermomechanical deformation coefficient (LTDC) was calculated according to Holsworth (47) as: k x s h where: k = the sensitivity (mils/inch of recorder chart paper), s = slope of thermal deformation curve in the transition region (Fig, 3-2), and h = sample height. 46 3.3.2 Mechanical strength properties Stress-strain characteristics in compression were determined on a 5S000 kg capacity INSTRON Model TM-L Universal Testing Instrument. It was equipped with a CCM load cell and standard potentiometric-type graph recorder (5l). The following testing conditions were used for all samples: i. cross-head speed at 0.1 cm/min, ii. recorder chart speed at 1*0 cm/min, and iii. full scale load at 5,000 kg. Standard compression test specimens were manufactured as cylinders from cured polymers. Polymerizations were done in a separate experiment with 10 ml of monomer or comonomer mixture. The sample length to diameter ratio ivas 2:1, according to ASTM Standard D 695-68T for determination of compressive properties of rigid plastics (2). Test specimen dimensions with uniform circular cross-sectional area, as machined on a metal lathe, were as follows: i, diameter ~- 1.0 cm, ii. height =2,0 cm, iii, radius of gyration = 0.25, and iv. slenderness ratio = 8.0 Various types of stress-strain curves, obtained with different polymers, and standard nomenclature are shown in Fig. 3-3 (20,72). 47 4,0 RESULTS Radiation polymerization of the MMA-TEGDMA comonomer system was investigated over the concentration range 100:0 to 0:100, Results for individual polymerization parameters of these mixtures, as derived from polymerization exotherm curves, are summarized in Tables 4-1 and 4-2, Graphical interpretations for some of these results are given in Fig, 4-1 and 4-2, The relation between OCR (l/t^v,) and TEG DMA. volume concentration in MMA-TEGDMA comonomer mixtures is plotted in Fig. 4-3. Results with the MMA-TEGDMA comonomer system demonstrated that most acceleration was obtained within a narrow concentration range, especially between 2.5 to 10% DVM concentration. At higher TEG DMA concentrations OCR. wa.s not proportional to volume concentration of the crosslinking agent. For this reason emphasis in further experiments was placed only on studying DVM concentrations up to 30% in comonomer mixtures. Accordingly, polymerization characteristics for MMA with the other three crosslinking agents are summarized in Tables 4-3 and 4-4. Graphical interpretation of tMAX anc* t(3£p, as functions of DVM concentration in these systems, is given Fig. 4-4 and 4-5, Polymerization rate coefficients in "Activation" (PRCj) and "Acceleration" (PRCjj) periods as a function of DVM concentration are plotted in Fig, 4-6. 48 Illustrations in Fig. 4-7 show the relationship between tjV^ and time required to onset Ge (t^pp) for the four, systems studied, including results with the S-TEGDMA system as taken from earlier work (70). The OCR (l/tMAV) increased proportionally with DVM MAX concentration. Linear relationships between OCR and DVM concentration for the four systems are given in Fig. 4-8. For comparison, OCR values as calculated from results of Duran and Meyer (33) are included. The (l/t^Ax /^'\onc^ proportionality constants calculated from slopes in Fig. 4-8 represent the overall acceleration constant (K) for individual DVM. These are inversely related to DVM connection number (CNj^y^) as seen in Fig. 4-9. The linear relationship between OCR and DVM concentration allows calculation and prediction of curing times (t^x) f°r MMA-DVM mixtures. Differences between measured and predicted curing times for the four systems at low DVM concentrations are summarized in Table 4-5. Similar calculations for the 5-TEGDMA comonomer system are given in Table 4-6 as taken from earlier work (70). The rather good agreement between predicted and experimentally measured curing times for different comonomer systems of the present and previous (70) studies suggested 49 further application of this new technique to published heat-catalyst results. Such data from quite dissimilar experiments (53) are examined in Table 4-7. Further, OCR as a function of crosslinking agent concentration for these data is demonstrated in Fig. 4-10. Differences between heat-catalyst curing times published by Duran and Meyer (33) and calculated by the new method are given in Table 4-8. The overall acceleration constant and predicted curing times were calculated only from two randomly chosen experiments (the "two-point method"). One problem encountered with the heat-catalyst curing process is that reaction temperatures are virtually uncontrollable and peak temperature increases very rapidly up to 180-190 °C (53). Table 4-9 demonstrates that, using a controlled radiation curing method, polymerization rate can be altered over wide range and the associated peak exotherm temperature can be considerably reduced. The OCR varied linearly with the square root of radiation dose rate, as demonstrated in Fig. 4-11. Shapes of thermomechanical curves* obtained by a simple device used are reproduced for MMA-EGDMA and MMA-TEGDMA systems in Fig. 4-12 and 4-13, respectively. Thermomechanical parameters such as Tg, TDD and TDT, as well as crosslinking density as represented by copolymer connection numbers (CNC0), 50 axe given in Table 4-10 for the four systems studied. T , TDT and TDD relate mobility of heated polymer segments. Variation of these parameters with crosslinking density, calculated as CNC0, is represented in Fig. 4-14 and 4-15. LTDC characterizes deformation rate in the transition region. The exponential relationship between LTDC- and DVM concentration for the two extreme systems is illustrated in Fig. 4-16. The relationship between LTDC and CN for the four systems is given in Fig. 4-17. Compression stress-strain curves for products from the MMA-EGDMA comonomer system are simulated in Fig. 4-18, For comparison similar curves for the MMA-TEGDMA system are shown in Fig, 4-19. Numerical values for some physical-mechanical parameters of the polymer products, as derived from compression stress-strain tests for the four systems examined, are summarized in Table 4-11. Relationships between compression stress at rupture, compression strain at rupture and area under the stress-strain curve as an estimate of toughness, and DVM concentraion, are shown for the various systems in Fig. 4-20 to 4-23, Compression stress at rupture, as a function of CNco for the four systems examined, is given in Fig, 4-24. The slope of the initial straight line portion of stress-strain curves represents the elastic modulus (E), Numerical values of E, plastic deformation and area under stress-strain curve (F) for the different polymer products are summarized in Table 4-12. Correlation between plastic deformation and toughness as estimated by area under the stress-strain curve is demonstrated in Fig. 4-25. 52 5.0 DISCUSSION Some early results on accelerated radiation polymerization of MMA-TEGDMA comonomer mixtures (79) showed improved curing times and strength properties of the resulting polymer products. These preliminary experiments encouraged further systematic studies on radiation polymerization of vinyl-divinyl comonomer systems. Subsequently, the MMA-TEGDMA and S-TEGDMA comonomer systems were studied in detail over full concentration ranges of the mixtures (67,69,70), These results, briefly summarized as follows, served as the initial observa tions on which the present study was developed. 5.1 Radiation Polymerization of the MMA-TEGDMA Comonomer System Radiation polymerization parameters for the MMA-TEGDMA system were derived at different comonomer compositions (vol/ vol mixtures) from polymerization exotherm curves. These values obtained from bulk polymerizations are summarized in Tables 4-1 and 4-2. The accelerating ability of TEGDMA is illustrated over a wide concentration range by a hyperbolic decrease in t^^ as shown in Fig. 4-1, Pronounced acceleration accompanying TEGDMA addition as measured by t^^ 1S primarily restricted to a narrow concentration interval , Additions of TEGDMA up to 10% are of 53 particular interest; amounts in excess of 10% are less effective. For example, addition of 10% TEGDMA to MMA decreased t^^ ^rom H7 min» f°x pure MMA, to 31 min. Further TEGDMA additions influenced tjV1AX only moderately. The 50:50 comonomer composition, however, represented the most efficient mixture over the whole concentration range with tj^x a"t only 15 min. Comonomer mixtures with higher concentration of crosslinking agent were less radiation sensitive. It is assumed that at high concentrations the crosslinking agent functions as a diffusion barrier limiting translocation of monomer to active radical sites. The accelerating ability of TEGDMA as related to Ge may be expressed quantitatively by PRC as determined in "Activation" (PRCj) and "Acceleration" (PRCTJ) periods, i'.e., before and after the onset of GEP, respectively. Both coefficients vary with composition of the comonomer mixture as shown in Fig. 4-2. Up to 20% TEGDMA addition both coefficients increased very rapidly due to reduced termination in viscous and partly crosslinked media (43). Further increase in TEGDMA concentra tion affected not only the rate of termination, but also influenced the propagation rate. Both PRCj and PRCJ-J- became stabilized within the intermediate range of TEGDMA concentration (20-50%). In highly crosslinked systems, i.e., over 50% TEGDMA, chain growth propagation becomes fully diffusion-controlled; the reaction system was immobilized and consequently less 54 radiation sensitive. The dose required to obtain a solid copolymer with the 50:50 mixture was 0.2 Mrad (Table 4-2). Such a comonomer composition is 7.7 times more radiation sensitive than pure MMA. The reciprocal of t^^ ^^MAX^ characterizes OCR /3-6/. From the relationship between OCR and TEGDMA concentration (Fig. 4-3), it is evident that for lower TEGDMA concentrations (up to 10%) OCR increased linearly. At higher TEGDMA concentrations OCR deviated from proportionality as accelerating efficiency decreased, possibly due to a diffusion barrier set in the more highly crosslinked networks. For concentrations falling within the proportionality range it was possible to predict the curing times of other mixtures according to the following empirical equation: l/t^Ax (mixture) = l/tMAX(MMA) + K /DVM/ ........,/5-l/ where: /DVM/ = vol - concentration of TEGDMA, and K = overall acceleration constant (OAC), slope as in Fig. 4-3. Using this equation it is possible to predict required curing times within the most important concentration region. The proportionality constant (K) characterizes overall accelerating ability of a particular DVM or crosslinking agent. Its value for the MMA-TEGDMA system (0 to 10% TEGDMA) as 55 calculated from the linear portion of Fig. 4-3 is 1.1 x 10~J . -1 -1 rain .cone . Deviation of OCR from the proportionality line within 10 to 20% TEGDMA concentration interval (Fig. 4-3) is in good agreement with results, derived from ESR studies by Szocz and Lazar (100). They studied decay and segmental mobility of polymeric chains, as well as monomer molecules within crosslinked polyglycol methacrylate network. For comonomer mixtures having higher densities of crosslinking, i.e., at higher TEGDMA concentrations, acceleration according to Ge has to be considered as the overall effect of two concurrent factors: i. DVM acceleration resulting from decreased termination in the partly crosslinked network, and ii. DVM retardation resulting from diffusion barriers and consequent diffusion-controlled propagation in highly crosslinked networks. Gradual increases of TEGDMA up to 10% creates reaction conditions in which i predominates over ii. Additional increase in DVM concentration increasingly enlarges 11 causing deviation of OCR from the proportionality line (Fig. 4-3). 56 5.2 Influence of Molecular Bridge Length in Divinyl Monomers Crosslinking density of gelled MMA-DVM network depends on: i. frequency of crosslinks on the polymer backbone i.e., poly(MMA), and ii. molecular bridge length between DVM double bonds. It seemed reasonable to assume that variation in DVM molecular bridge length would influence the DVM accelerating ability and affect the delay or premature onset of GEP. This hypothesis was tested with a series of dimethacrylate esters selected to act as crosslinking agents. Accelerating abilities of EGDMA, DEGDMA and TrEGDMA are given in Tables 4-3 and 4-4, while graphical interpretations of these results are illustrated in Fig. 4-4 and 4-5. Changes in the accelerating ability of the different MMA-DVM systems studied, as shown by t^AX ^n FI9» 4~4» indicate that accelerating ability changed according to DVM molecular bridge length. With increasing bridge length .mono- (EGDMA), di (DEGDMA), tri- (TrEGDMA) to tetraethylene glycol dimethacrylate (TEGDMA) \ tj^ decreased over the whole concentration range studied. Acceleration by DVM in MMA-DVM mixtures is thus shown to be directly related to DVM molecular bridge length. 57 For examples at 2*5% DVM concentration tiVlAX decreased from 83 min'for MMA-EGDMA to 60 rain for the MMA-TEGDMA comonomer system. Numerical values for MMA-DEGDMA and MMA-TrEGDMA systems, at the same concentration, were 77 and 72 min, respectively. Similar results were obtained by evaluation of half-time concentration values, i.e., DVM concentrations required to reduce the curing time to one-half of that for pure MMA. Extrapolated values for half-time concentrations increased with decreasing DVM molecular bridge length. Such values for the four system studies were (Fig. 4-4): i. 'MMA-EGDMA 1%} ii. MMA-DEGDMA 5%, iii. MMA-TrEDGMA A%, and iv. MMA-TEGDMA 3%. Comparison of half-time concentrations for the two extreme systems of this study (MMA-EGDMA and MMA-TEGDMA) shows that when EGDMA replaced TEGDMA, twice as much DVM was required to reduce t^AY to one-half that for pure MMA. Higher EGDMA concentrations in the MMA-EGDMA system increased crosslinking. density of the gelled network, creating diffusion barriers in the system. The propagation reaction is assumed to become diffusion-controlled at an earlier reaction stage for MMA-EGDMA than in the MMA-TEGDMA system. Consequently, t^AX increases progressively. Differences In crosslinking densities in these two systems can be demonstrated by the average segment molecular 58 weight between two crosslinks on the poly(MMA) backbone. For example, mixtures of 93:7 MMA-EGDMA and 97:3 MMA-TEGDMA represent comonomers of identical curing times, equalling one-half of that needed to cure MMA. However, the crosslink frequency is considerably higher in 93:7 MMA-EGDMA system in proportion to differences in DVM- concentration and respective CNj3YM» The estimated average segment molecular weights between two crosslinks, assuming random distribution of DVM in the system, is nearly 10,000 for the 97:3 MMA-TEGDMA system, but in the 93:7 MMA-EGDMA system only. 1,600-3,400 (based on MMA/DVM mole ratios given in Table 3-2). In addition the length of the molecular bridge between double bonds, which is four times longer in TEGDMA, assures higher segmental mobility and flexibility in the MMA-TEGDMA mixtures due to the numerous flexible C - 0 - C linkages (lO). Additional substituents or branching of the molecular bridge increases the effective diffusion barrier and, consequently, t^x» This is also evident from lower accelerating ability of the trifunctional crosslink ing agent used by Duran and Meyer (33), as demonstrated in Fig. 4-4. Formation of ring structures arising from internal cyclization may also influence curing times. Considering EGDMA as an example, formation of the following ring structure is theoretically possible: 59 CH2 (CHq)C CO CO 0 - CH. l2 - CH, 2 - 0 V (CH0)C CH2 -CO CO 0 - CH - CH0 - 0 2 2 An additional ethylene glycol unit in the DVM molecular bridge results in enlargement of the ring size by three members. Thus, the 8-membered ring of EGDMA enlarges to 11-, 14-, and 17-membered rings for DEGDMA, TrEGDMA and TEGDMA, respectively. function as additional diffusion barriers. In addition, the internal linkage constitutes a loss of intermolecular bonding which would otherwise participate in crosslinking and gel formation. The overall result of both effects is delayed GEP and increased curing time. Formation of 6-membered rings is most favourable (59,78) and possibility of ring formation decreases with increasing ring size. This would explain the delay in onset of GEP for DVM studied in the sequence from TEGDMA to EGDMA, i.e., 23 to 41 min at 10% DVM concentration (Fig. 4-5 and Tables 4-1 and 4-3). Once GEP has been passed, formation of such internal links becomes progressively less The ring structures, surrounding active radical sites 60 important as the distinction between internal and external links fades. Consequently, PRCJJ is independent of the structure of DVM (Fig, 4-6) and t-,,^ is directly proportional to tQgp regardless of DVM molecular bridge length (Fig, 4-7), Similar conclusions were drawn from results on accelerated radiation polymerization of the S-TEGDMA comonomer system (70), The formation of ring structures in DVM polymerizations has been proposed as a reason for poor correlation between predicted and actual gelation (38,40,48,91). Subsequently, proposed alternating inter-intra molecular propagation for these polymerization systems has been verified for a number of DVM (17,18,40). However, there is not enough direct evidence at this time supporting internal ring structures in studied crosslinked polymer products. Further structural analyses of copolymers may provide the necessary evidence to back up these contentions. The relationship between PRCj and PRCJJ at various DVM concentrations is indicated in Fig. 4-6, Both, PRCj and PRCJJ increased with increasing amount of DVM in the comonomer mixture over the concentration range studied (up to 30% DVM). Absolute PRCJJ_ values at the same concentration level differed considerably from PRCj values, as expected from two separate accelerating effects in the system studied: i. acceleration by increased viscosity as represented by PRCj, and 61 ii. acceleration by Ge as represented by PRCjr. Numerical values of PRCJJ are at least one order of magnitude higher than those of PRCj (Tables 4-2 and 4-4). This is in a good agreement with rate constants observed before and after onset of GEP reported by Barthalemy (4). PRCJJ was found to be independent of DVM structure, while PRCj increased with initial viscosity of the comonomer mixtures, given in Table 3-2. 5.3 Prediction and Calculation of Curing Times In previous studies (67,69) an empirical method was suggested for predicting curing times (t^^) f°r "the MMA-TEGDMA comonomer system. The empirical equation /5-l/ was found to be valid for TEGDMA concentration up to '\Q% in the MMA-TEGDMA comonomer mixture. Application of /5-l/ to the present data derived for the MMA-DVM series, allows integration and comparison of previous data with results of the present study. Mathematical treatment of data in Tables 4-1 and 4-3 gives the following OAC, as calculated from linear relationships between OAC and DVM concentration in Fig. 4-8: . -1 -1 mm • cone ia ^MMA-EGDMA * 1"L X 10 _ r- '-3 11• ^MMA-DEGDMA ~ lo5 X 10 iii. ^MMA-TrEGDMA = 1,8 x 10 3 lv* KMMA-TEGDMA = 2,4 x 10"3 62 Numerical values of OAC for the different MMA-DVM systems demonstrate that accelerating ability increases with DVM molecular bridge length. As illustrated in Fig. 4-9 OAC values are inversely related to DVM connection number (CNQY^K After calculation of CN , using /3-l/, one can estimate OAC from the following equation: 1//KMMA~DVM = 5,2 X CNDVM - 10.55 ....... ./5-2/ where: CNnw,,, is connection number of respective DVM. The linear relationship given by /5-2/ is illustrated in Fig, 4-9. Relative accelerating ability of the DVM studied, expressed as OAC ratios with respect to the least effective in the series (EGDMA), increased as: EGDMA : DEGDMA : TrEGDMA : TEGDMA = 1.0 : 1.36 : 1.64 : 2.18 Correlation of OAC with the DVM molecular bridge length is in good agreement with recent data on polymerization of dimethacrylate esters having variable bridge distances (8). Increase in absolute values of propagation constants (k ) with P molecular bridge length is demonstrated in Table 2-2. 63 From calculated OAC of individual comonomer systems it is possible to predict occurrence of maxima on polymerization exotherm curves. Differences in curing times (tjy^) calculated from /5-l/g and those measured experimentally, are given in Table 4-5 for the four systems studied. These results demonstrate the usefulness of /5-l/, first derived for the MMA-TEGDMA system (67,69), later applied to the S-TEGDMA system (70) as recorded in Table 4-6. The equation can be applied to a variety of vinyl-divinyl comonomer systems. The average error for predicting curing times of the four systems studied was t 5.7% (Table 4-r5). 5,3.1 Application of the derived equation to published results Kenaga (53) and recently Duran and Meyer (33) used the polymerization exotherm technique to evaluate the accelerating ability of various di- and trifunctional crosslinking agents polymerized by heat-catalyst systems. Both MMA (33) and styrene-type monomers (53) were polymerized in wood. Due to similarities between the conclusions of these authors and the implications of results from the present study, it was of interest to test applicability of Eq. /5-l/ to prediction of curing times from the data published. Numerical values of OAC, calculated from Kenaga1s data (53); were plotted against concentration of crosslinking agents. The expected linear relationships for these comonomer systems are given in Fig. 4-10. The following OAC values were 64 calculated for these systems: min"""*" cone, i. KTBS-TMPTMA 2.6 x 10~4 ii. KTBS-Tr EGDMA = 3,6 x 10-4 iii. KTBS-EGDMA 4.0 x 10~4 iv. KTBS-TEGDMA 4,8 x lO"4 -1 Only small differences were found between OAC of individual systems used by Kenaga (53), The reason for this may be the limited number of experiments carried out over the rather wide concentration range (only four experiments within the 0-30% concentration interval). However, OAC for all three di-functional crosslinking agents were higher than those calculated for the tri-functional TMPTMA, This suggests that substitution on the molecular bridge functions as a diffusion barrier for the propagation reaction. Calculated OAC from data of Kenaga (53) were used to predict curing times for individual comonomer mixtures according to /5-l/. Differences in curing times (t^^) between calculated and published values are summarized in Table 4-7. Good agreement was found between actual and predicted values, regardless of differences in polymerization conditions and initiating system used. The average error of t^^- was less than t 5%. 65 Only two experiments have to be run in order to predict OAC. Expected curing times for different comonomer mixtures within concentration range covered by the two experiments can be calculated with the aid of /5~lA This "two-point method" was tested by using experimental data published by Duran and Meyer (33), The following tv/o experi ments were randomly chosen: 93:2; 91:9; Based on these two experiments, the calculated OAC value (K„,„ T,.nT,,, = 1.03 x 10"""3 min" cone." ) was used for MMA-TMPTMA predicting curing times of various MMA-TMPTMA compositions. Differences between calculated and published values (33.) are summarized in Table 4-8. Agreement again, was quite good. By integrating experimental results from this work with data already published, it is demonstrated that acceleration ability and curing times for different comonomer systems, regardless of the polymerization conditions, can be estimated within the most desirable practical concentration region by /5-l/ with a high level of confidence. From direct comparison of the respective OAC values it is apparent that all DVM studied were more effective accelerators than the trifunctional TMPTMA. This i.s graphically illustrated in Fig. 4-4 and 4-8, i. comonomer composition, MMA:TMPTMA = curing time, t,,.., = 108.3 min; and 3 MAX ii. comonomer composition, MMA:TMPTMA = curing time, tjvy^ = 60.8 min. 66 A further disadvantage of trifunctional crosslinking agents is that they evolve more heat during the polymerization process. Peak temperature (T^AX) increased very rapidly to 180-190 °C (33) which may be injurious to WPC. This could be avoided by lowering OCR if radiation is used as the energy source for polymerization. Data in Table 4-9 and Fig. 4-11 demonstrate that OCR varies linearly with the square root of radiation dose rate. At lower dose rates the temperature rises more gradually and T^^ is considerably lower. Another disadvantage of trifunctional crosslinking agents is their high tendency to develop diffusion barriers. Polymerization may cease due to lack of monomer diffusion in the highly crosslinked network. This problem is readily demonstrated with the MvlA-TMPTMA system. For example, "tjvsAX at 15 and 20% TMPTiMA in the system is essentially the same at 55 and 49.4 min, respectively. Conversion degree at these concentrations, however, decreased from 85.6% to 82.3% (33). In addition, trifunctional crosslinking agents form brittle polymer products with lower abrasion resistance (63). This was reported for WPC by Kenaga (53). 5.4 Analysis of Crosslinked Polymer Product Thermomechanical Curves Thermomechanical properties of crosslinked polymer products depend primarily upon the tightness of the network 67 structure, i.e., crosslinking density caused by a given concentration of crosslinking agent. All DVM studied here functioned as efficient crosslinking agents and transformed linear and thermoplastic poly(MMA) to fully or partly cross-linked products. Linear, fully and partly crosslinked polymer products exhibit different thermomechanical curves as demonstrated in Fig. 3-2. Crosslinking efficiency of individual DVM studied was not identical but varied with molecular bridge length. It increased according to the sequence: TEGDMA <^ TrEGDMA <f DEGDMA <^ EGDMA This is demonstrated by shape of thermomechanical curves for copolymer products formed from the two DVM having extreme CN values, i.e., EGDMA with CN 2.200 (Fig. 4-12) and TEGDMA.with CN 2.105 (Fig. 4-13). Comparison of Fig. 4-12 and 4-13 shows that small additions of either DVM to MMA rapidly changed the linear poly(MMA) to a crosslinked thermoset plastic with increased network strength at higher temperatures, Transformation efficiency of EGDMA was, however, significantly higher. Differences in crosslinking efficiency for these two DVM can be demonstrated by comparison of respective thermo mechanical parameters as obtained at the same DVM concentration 68 level, as shown in Table 4-10, At 10% EGDMA in the MMA-EGDMA system, for example, T , TDD and TDT were 127 °C, 77% and 202 °C. The same parameters for 10% TEGDMA in the MMA-TEGDMA system were considerably lower; T^ 113 °C,.TDD 52% and TDT 165 °C„ To obtain the same parameter values with TEGDMA, its concentration has to be increased to approximately 30% (Table 4-10 and Fig. 4-12 and 4-13). Analysis of thermomechanical data for the four systems studied, Table 4-10, leads to the overall observation that increased DVM concentration influenced thermomechanical parameters in two ways: i. increased TQ, TDT and TDD, and ii. • decreased LTDC. Tg is an important parameter which is related to mobility of macromolecular segments (72,73). As expected, replacement of van der Waal's forces between polymer chains by carbon-carbon bonds reduced mobility cf polymer segments • and increased T . As illustrated in Fig. 4-14, it is possible to assess the contribution of DVM molecular bridge length to overall mobility of the crosslinked network in the four MMA-DVM systems studied. At the same crosslinking density (as expressed by copolymer CN) the shorter DVM bridge length gave lower segmental mobility and higher T (Fiq. 4-14). Stabilization of Tg at higher crosslinking densities (Fig. 4-14) can be interpreted by overlapping of two independent effects as related to T_ as: 69 i. crosslinking effect, and ii. copolymerization effect. The crosslinking effect always increases T^,whereas the copolymerization effect decreases T . Both effects are additive (61). The crosslinking effect prevails at lower CNC0, At higher DVM concentration the contribution of the crosslinking effect is balanced by the copolymerization effect. The overall result is T stabilization (rig. 4-14). Resistance of individual polymer products to high temperature deformation can be expressed by TDD, while strength of the crosslinked network is proportional to TDT values. As demonstrated for the four stystems studied (Fig, 4-15), both parameters (TDD and TDT) are dependent..on copolymer connection number (CNC0K regardless of the size of the molecular bridge of the crosslinking agent used. Both parameters Increased rapidly within the narrow DVM concentra tion interval. Further addition of DVM to induce higher crosslinking densities changed TDD and TDT only moderately. This is an important observation and suggestively the effect coincides with both optimal acceleration and thermomechanical properties of polymer products at low DVM concentrations (compare Tables 4-3 and 4-10). The linear thermomechanical deformation coefficient (LTDC) characterizes behaviour of heated polymer products within the transition region. LTDC represents the rate of polymer 70 deformation associated with the transition from plastic to rubbery state. Deformation of crosslinked polymer products in the rubbery region is constant across a broad temperature interval until the polymer loses coherence at temperatures equalling TDT (Fig. 3-2, 4-12 and 4-13). It is to the advantage of crosslinked polymer products of the present study that LTDC decreased exponentially with DVM concentration in the system. This is demonstrated for the two system extremes (MMA-EGDMA and MMA-TEGDMA) using the semi-logarithmic plot in Fig. 4-16, Further, the relationship between LTDC and polymer crosslinking density as represented by copolymer connection number (CNC0) can be used to great advantage in predicting thermomechanical behaviour of complex crosslinked polymer products derived from comonomer mixtures. 5.5 Analysis of Polymer Product Compression Stress-Strain Curves Compression stress-strain curves were found to follow patterns represented by curves illustrated in Fig. 3-3. These show a wide variation in properties ranging from elastic, semi-rigid, hard, tough to brittle materials (20,72). In general, soft and weak polymers (Fig. 3-3a) exhibit low modulus of elasticity (E), low yield point and moderate deformation at rupture. Hard and brittle materials show high E, no well-defined yield point and low deformation at rupture (Fig. 3-3b). Soft and tough plastics (Fig. 3-3c) show 71 low E and yield point but high deformation and rupture stress. Hard and strong plastics (Fig. 3-3d), on the other hand, exhibit high E and yield point but only moderate deformation* Finally, hard and tough materials (Fig. 3-3e) show E, yield point, deformation and rupture stress all to be high. Typical compression stress-strain curves for the two extreme DVM systems studied over the full concentration range (MMA-EGDMA and MMA-TEGDMA), are reproduced in Fig. 4-18 and 4-19. Linear poly(MMA) exhibited compression stress-strain properties similar to those of poly(S) (20,70); i.e., it was hard and moderately tough (Fig. 3-3d). Highly crosslinked homopolyrners of pure EGDMA (Fig. 4-18) and TEGDMA (Fig. 4-19) exhibited behaviour characteristic of hard and brittle polymers (Fig. 3-3b). It was of particular interest to study shapes of compression stress-strain curves as obtained for the wide range of MMA-DVM comonomer mixtures. Experiments were concentrated within the most attractive concentration interval, i.e., up to 10% DVM in the respective c.omonomer systems. As shown in Tables 4-1 and 4-3 and Fig. 4-4, this region was of particular interest because of significantly accelerated curing. OCR within this concentration interval was proportional to DVM volume concentration (Fig. 4-8). As demonstrated in Fig. 4-18 and 4-19, addition of EGDMA or TEGDMA to MMA caused change in shape of polymer compression stress-strain curves according to amount of DVM added. 72 They changed from hard and brittle-types (Fig. 3-3b) to hard and tough-types (Fig. 3-3e). These changes in stress-strain response indicate improvement in mechanical properties as follows: i. rupture stress, plastic deformation and area under the stress-strain curve were much increased with 2.5 to 10% DVM addition to MMA. f, ii. development of well-defined yield points at higher MMA concentration, and iii. no significant change in slope of the initial Hookean portion occurred. Numerical data of individual mechanical parameters, derived from compression stress-strain curves for the four MMA-DVM systems studied are summarized in Tables 4-11 and 4-12. Graphical interpretation of compression stress and strain at rupture and area under the stress-strain curve, as a function of comonomer composition for the four systems studied, are given in Fig. 4-20 through 4-23. By comparison of the results compiled in Tables 4-11 and 4-12 the following observations can be made: i. compression stress-strain properties of poly(MMA) with respect to rupture, yield and toughness parameters were higher than those of any DVM homopolymers studied; ii. properties of products from comonomer mixtures are not additives i.e., the components do not contribute strength in proportion to their presence; iiia compression stress and strain, as well as area under stress-strain curves, for all systems studied, exhibited well-defined maxima (Fig. 4-20 through 4-23); iv. superior strength properties for the system* studied were restricted to the narrow . concentration region, within 5 to 10% DVM in the system; and v. the concentration interval showing superior strength properties broadened with increasing DVM molecular bridge length, i.e., in the sequence from EGDMA to TEGDMA. Individual MMA-DVM systems differed only in specific details. Consider, as an example, location of the maxima on properties/composition curves (Fig. 4-20 through 4-23). They appeared at approximately 5% EGDMA concentration in the 'MMA-EGDMA system (Fig. 4-20). However, in the MMA-TEGDMA system the maxima were located near 10% TEGDMA concentration. It can. be estimated from the respective MMA/DVM mole ratios, i.e., 34.3 for the MMA-EGDMA and 24,4 for the MMA-TEGDMA.system (Table 3-2), that copolymers with superior strength properties possess approximately one crosslink for every 25 to 35 monomer units on the poly(MMA) backbone. Considering the MW of MMA to 74 be equal to 100, a number average molecular weight of 2,500 to 3,500 is obtained for poly(MMA) segments between two successive junctions. These values are in very good agreement with averages derived for crosslinked rubbers and thermoset copolymers (73), as calculated from swelling equilibria measurements. From the limited differences in segmental MvV between crosslinks, estimated for the two extreme comonomer systems studied, it was suggested that compression strength parameters can be related to comonomer connection number (CN ). CMC0 of individual copolymers, as calculated from /3-2/,are included in Table 4-11. Compression stress at rupture, as demonstrated in Fig. 4-24 for all four systems studied, is strongly related to CNC0, irrespective of the bridge length of crosslinking agent used. The crosslinking density of polymer networks as expressed by CN is a useful structural parameter. Although CN tells nothing about the configurational aspects of the crosslinked networks, it does quantitatively characterize resistance to both mechanical and thermomechanical deformations. Physical and thermomechanical properties of polymer products are assumed to be functions of crosslinking density as described by CM co Observation of maxima at low DVM'concentrations (Fig. 4-20 through 4-23) demonstrates an important discovery; that strength properties of solid crosslinked polymer products vary with concentration of crosslinking agent in the same manner as strength properties of crosslinked rubbers and elstomers (28,29,32,35,3?,63,94,102). For practical applications, a narrow DVM concentration interval (up to. 10%) is the most attractive. Within this concentration range both maximum acceleration and superior mechanical and thermo mechanical properties were obtained. Introduction of DVM with MMA within this range also rapidly increased the area under the compression stress-strain curve. The resulting copolymers are capable of considerable energy storage before failure. It was also observed that failure of these copolymers occurred with tremendous sound effects due to release of the energy stored. In spite of the significance and importance of polymer toughness, standardized procedures for its evaluation are still lacking (72). From the observation that small stresses in the plastic range produced considerable deformation in tough polymer products (Fig. 4-18 and 4-19), it was assumed that plastic deformation is indicative of toughness. This is demonstrated by linear relationship between the area, under the compression stress-strain curve and plastic deformation for' the four systems studied in Fig. 4-25. Toughness of these copolymers seems to be independent of DVM molecular bridge length. A similar conclusion was reported for the S-TEGDMA comonomer system (70). 76 6.0 CONCLUSIONS lo Acceleration in radiation polymerization of vinyl-divinyl comonomer systems via. gel-effect (Ge) in cross-linked networks was related to the chemical structure of the crosslinking agents, in particular to their molecular bridge length. The overall curing rate (OCR) was found to be proportional to volume concentration of divinyl monomer (DVM). The overall acceleration constant (K) is inversely related to DVM connection number (CNgy^) as: 1/K = 5,2 x CNDVM - 10,55 2. The relative acceleration ability of DVM studied increases with DVM molecular bridge length in the order: EGDMA : DEGDMA : TrEGDMA : TEGDMA = 1.00: 1036 : 1,64 : 2.18. The half-time concentration values for EGDMA, DEGDMA, TrEGDMA and TEGDMA were approximately 7, 5, 4, and 3% (vol/vol), respectively. 3. Substantial decrease in curing time (t^^) was obtained with up to 10% DVM in the respective comonomer mixtures. Within this concentration interval superior mechanical and thermomechanical properties of copolymers were also observed. 4. Tfie empirical equation for calculating the overall 77 acceleration constant and prediction of curing times was derived and applied to the four systems studied. Its extension to published results on acceleration in heat-catalyst systems was found to be fully applicable. Agreement between predicted and published results was withini5/o error for all copolymer systems observed. b. Copolymer connection number (CN ) was introduced and found to be a useful structural parameter for crosslinked copolymers. It characterizes and correlates quantitatively the mechanical and thermomechanical properties with copolymer crosslinking densities. 6. The MMA-TEGDMA comonomer system was found to be the most suitable and economically attractive. It represents a well balanced compromise of improved polymerization parameters and copolymer properties, suitable for wood-polymer composite products. 78 7.0 RECOMMENDATIONS FOR FURTHER STUDY Based on theoretical considerations and experimental results of the present study the following are recommended as deserving of further research: i. extend accelerated polymerization to the MMA-methyl acrylate system to examine influence of -CH3 groups on Ge acceleration; ii. extend the present MMA-DVM systems to higher homologous members (hexa-, deca-, etc., polyethylene glycol dimethacrylate) to examine effects of Ge onset and delayed diffusion-controlled propagation; iii. examine structure of polymer products to collect evidence for possible internal ring formation; iv. move from bulk copolymerization to accelerated polymerization within wood structures; v. study the effect of a third component in the MMA-DVM system, for example to increase OCR in the presence of oxygen and/or to impart fire resistance properties (68); vi. further extend utilization of exothermic heat as presently proposed for one-step production of veneer polymer overlaid plywoods (52,81). 79 8.0 LITERATURE CITED 1. 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Conversion, FL lP' /o • /O/ %/hz kp kt x 10~5 (kp/ktI^2)xl02 0 3.5 384 442 5.78 10 2.7 234 273 4.58 20 6.0 267 72.6 8.81 30 15.4 303 14.2 25*60 40 23.4 368 8.93 33.90 50 24.5 258 4.03 40o60 60 20.0 74 0.498 33.20 70 13.1 16 0.0564 21.30 80 2.8 1 0.0076 3.95 Table 2-2. Some data on polymerization of dimethacrylatic esters (photoinitiator-benzoin 0*2%) (.8). N The compound Symbol M. Viscosity The degree of The tempera W _ 105 M (sec-1) K, c.p. transformation (%) ture of poly merization 1. mole" 'sec-1 1. mole"' sec I Methylmcthacrylale MMA 100 50 50 25 0-2 _ 2 Dimctlmcryiaic of butyk'iicKlycoi 226 40 0 25 ' 3-8 600 8.10s 3 Dinielhaciyiate of biaylciicsjlyci.il MU 226 — 30 25 40 112 2-3.104 4 Dinictliitcrylalc of butylcneglycol MB 226 — 5 25 . 33-0 17 83.10* 5 Diriicthacrylafehe.xa-mcihylciu'ijlycol MO 244 4-9 0 25 13-0 1200 6-2.105 r> Diiv.eiliacrylatelicxa-nicihylcncglycol MG 244 — ' 5 25 7-0 245 3-7.104 7 Dimelliacrylalehexa-mclliylcncylycol MG 244 — 30 25 4-0 26 1 -3.10J 8 Diir.ctlucrylatedeea-mciliylcncglycol MD 300 7-7 0 25 160 1880 • 4-2.10s 9 Dimethacrylalcdoca-inclhylciicglycol MD 300 — 5 25 24-0 1400 1 -5.10s 10. Dimcthacrylatcdcca-mcthylcncglycol MD 300 — 30 25 29-0 S40 2-5.104 11 D i m c 111 a c r y 1 a 1 c (bis-dicthylencglycol) plithalolc MGPh 566 51-0 0 30-6 20-0 2470 4-8.105 12 Dimethacrylate (bis-diclliylcncylycol) plithalolc) MGI'h 566 — 5 30-6 24-0 2300 2-7.105 13 DiiiK-lbaciylatc (/;;> diclhylcncglycol) plithalote MGPh 566 — 30 30-6 54-0 1750 3-2.10* CO vO Notes: (I) lor MMA at a 0 per cent Kn 300 I. mole"' sec"1 (T 25°). (2) The kinetics of polymerization of MB, MG, MD, MGF were studied by methods of precision dilatomctry and thermometry. 90 Table 3-1. Some properties of methyl methacrylate (MM) and divinyl monomers (DVM) used In this study* Name, (abr„) n Mw d, CM grel formula g/cm 25°C Methyl methacrylate, (MMAJ CsH 0 — 100 0.940 2.000 1,0 5 9 2 Ethylene glycol dimethacrylate, (EGDMA) 1 198 1,045 2.200 4,2 C10H14°4 Diethylene glycol dimethacrylate, (DEGDMA) 2 242 1.062 2,150 6.9 C12H18°5 Trmethylene glycol dimethacrylate,(TrEGDMA) 3 286 1,090 2.125 10.5 C14H22°6 Tetraethylene glycol dimethacrylate, (TEGDMA) 4 330 1.140 2.105 23.4 C16H26°7 91 Table 3-2. Concentrations and relative viscosities of different methyl methacrylate (MMA)-divinyl monomer (DVM) mixtures. DVM DVM fraction in Mole ratio s comonomer mixture volume mole DVM/MMAxlO MMA/DVM 25° C 0.025 0.013 0.14 70.5 1.04 0.050 0.028 0.29 34.3 1.08, 0,100 0.059 0.63 15.9 1,14 EGDMA 0.150 0.087 1.00 10.0 1.24 0.200 0.123 1.40 7,1 1.33 0,300 0.194 2.40 4.2 .1.41 0.025 0.012 0.13 83.5 1,05 0,050 0.024 0,25 40,5 1.11 DEGDMA 0.100 0.049 0.52 19.2 1,18 0.150 0.077 0.83 12,0 1,27 ,0.200 0.104 1,16 8.6 1,34 0.300 0.167 2.00 5.0 1.55 0.025 0.011 0.12 85.4 1.08 0.050 0.020 0.21 47.0 1.20 Tr EGDMA 0.100 0.043 0.45 22.2 1.28 0.150 0.065 0,69 14.4 1,42 0.200 0.092 1.01 9.9 1 o 53 0.300 0.144 1,69 5.9 1.83 0.025 0.009 0.09 102.0 1.14 0.050 0.019 0.19 57.8 1,29 TEGDMA 0.100 0.039 0.41 24.4 1.48 0.800 0.138 1.88 5.3 ' 2.54 92 Table 4-1. Polymerization exotherm characteristics for the MMA-TEGDMA comonomer system (67,69). Comonomer Gel-Effect Point composition, (GEP) MAX vol. % MMA TEGDMA ^GEP, TGEP, H'AX, TMAX, min °C min °C 100 0 106 62 117 120 97.5 2.5 52 69 60 159 95 5 30 60 45 160 90 10 23 57 31 167 70 30 14 54 20 165 50 50 10 53 15 157 30 70 13 57 18 149 0 100 16 61 22 130 93 Table 4-2. Calculated polymerization parameters for the MMA-TEGDMA comonomer system (67,69). Comonomer Exotherm peak Polymerization PRCTT Rate XV Composition, parameters Coefficient (PRC)., v ol % °C/min MMA TEGDMA Dose, Mrad £T, °c PRCI PRCXI 100 0 1.50 84 0.24 5.2 21.6 95,5 2.5 0.81 123 0.64 5.0 ' 7.9 95 5 0.61 124 0.80 6.7 8.4 90 10 0.42 131 0.91 13.8 15.2 70 30 0.27 129 1.28 18.3 14.3 50 50 0.20 121 lo64 20.0 12.7 30 70 0.24 111 1.60 16.7 9.8 0 100 0.30 94 1.56 11.5 7.3 94 Table 4-3. Polymerization exotherm characteristics for MMA-EGDMA, -MMA-DEGDMA and MMA-TrEGDMA comonomer systems. Comonomer Gel-Effect Point composition, (GEP) MAX DVM vol % MMA t „ T t T DVM GEP, GEP, MAX, MAX, min OC min °C 97.5 2.5 69 68 83 149 95 5 55 62 66 156 90 10 41 57 50 171 EGDMA 85 15 34 57 41 174 80 20 30 56 37 176 70 30 25 59 31 . 176 0 100 21 52 37 114 97.5 2.5 64 66 77 156 95 5 50 64 61 164 90 10 28 59 39 176 DEGDMA 85 15 25 58 33 178 80 20 23 56 29 176 70 3D 21 60 27 179 0 100 18 56 30 • 128 97.5 2.5 59 68 72 154 95 5 44 64 54 160 90 10 27 57 36 174 TrEGDMA 85 15 22 56 29 174 30 20 20 56 27 134 70 30 18 56 24 175 0 100 18 57 28 127 95 Table 4-4. Calculated polymerization parameters for MMA-EGDMA, MMA-DEGDMA and MMA-TrEGDMA comonomer systems. DVM Comonomer Exotherm peak Polymerization PRC composition, Rate / vol % parameters Coeff Icient(PRC), pRC 0C/rr nm MMA DVM Dose, AT, PRCj PRC Mrad °C II 97.5 2.5 0.91 113 0,46 5.8 1 o 9 95 5 0.73 120 0.47 8,5 18,1 90 10 0.55 .135 0.51 12.6 24.8 EGDMA 85 15 0.45 138 0.62 16.7 26,9 80 20 0,39 140 0o66 17.1 25.8 70 30 0.34 140 0.92 19.5 2JL Q 2 0 100 0.39 78 0.76 3.9 5.1 97.5 2.5 0.85 120 0,53' 6.9 13.0 95 5 0,67 128 0,56 9.1 16.2 90 10 0,43 140 0.80 11.7 14.7 DEGDMA 85 15 0.36 142 0,88 17,2 X 9 <> !D 80 • 20 0,32 140 0,90 15,0 16.6 70 30 0.30 143 1.10 19.8 18.0 0 100 0.33 92 1.11 6,0 5.4 97.5 2.5 0.79 118 0.54 6.6 12.2 95 5 0.59 124 0.64 9.6 J. 3«5 TrEGDMA 90 10 0,39 133 0.77 13.0 16.9 85 15 0.32 138 0,91 16.9 18*5 80 20 0.30 146 1,00 18.0 18.0 70.. 30 0,26 139 1.20 19,0 15.8 0 100 0.3.1 91 1.16 7,0 6.0 96 Table 4-5. Differences between measured and calculated curing times for lower concentrations of divinyl monomer (DVM) in MMA-DVM systems* DVM Comonomer composition, vol 0/ t MAX, mm Difference MMA DVM' calculated measured min 0/ EGDMA ,97.5 95 90 85 2.5 5 15 88 70 49 38 83 66 50 41 +5 +4 -I -3 +6.0 + 6.1 -2.0 -7.3 97.5 2,5 81 77 +4 +4.9 DEGDMA 95 5 62 61 + 1 + 1,6 90 10 42 39 +3 +7.1 85 15 31 33 -2 -6,5 97.5 2.5 76 72 +4 + 5.5 TrEGDMA 95 5 56 54 +2 +3.7 90 10 37 36 + 1 + 2,8 85 15 27 29 -2 -6.9 97.5 2.5 68 60 +8 • 13 o 5 TEGDMA 95 5 48 45 + 3 +6,7 90 10 30 31 -1 -3.3 'An average error for predicting curing time for the four systems studied. 97 Table 4-6, Differences between measured and calculated curing times for lower concentrations of TEGDMA in the styrene (S)-TEGDMA system (70), Comonomer composition, vol % min Difference S TEGDMA calculated measured min % 95 5 887 822 ,+ 55 +6.5 90 10 445 462 -17 -3.8 80 20 222 228 -6 -2.6 80 20 222 222 0 0.0 70 30 148 135 +13 +9.6 60 40 110 97 + 13 +13.2 50 50 69 87 -18 -20.6 98 Table 4-7, Differences in calculated and published curing times for TBS - di- and tri-vinyl comonomer systems (53). Crosslinking• monomer • tMAX,• min .Difference type 0/ '° measured calcu lated min /° 5 52 53 +1 +1.9 EGDMA 10 46 48 + 2 +4.3 20 40 40 0 0 30 34 35 + 1 +3,1 5 36 36 0 0 TrEGDMA 10 34 34 0 0 20 30 30 0 0 30 27 27 0 0 5 40 41 +1 . +2.5 TEGDMA 10 35 37 + 2 + 5.7 • 20 34 32 -2 -5,9 30 27 28 +1 + 3.7 5 50 49 -1 -2.1 TMPTMA 10 48 46 -2 -4.2 20 40 42 + 2 +5,0 30 37 37 0 0 99 Table 4-8. Differences in calculated and published.curing times for heat-catalyst cured MMA - trirnethylol ' propane-trimethacrylate (TMPTMA) polymerization system (33). TMPTMA, t MAX, min Differences /o calculated •mea sured • min ,°/ yo 1 123,0 123.4 -0.4 -0o3 2* 108.3 108.3 0.0 0.0 5 81 o 5 81.3 + 0.2 + 0.3 7 69.8 72.5 -2.7 -3,7 9* 60.8 60.8 0.0 0.0 12 51.3 55«5 -4.2 -7,6 * Values used for calculation of overall accelera tion constant by "two-point method," 100 Table 4-9. Radiation polymerization of TEGDMA at different dose rates. Dose rate MAX l/2 t T r ad/sec (r ad/sec) MAX, "MAX, l/t xlO MAX mm °C 220 14.8 202 14.1 156 12.5 22 130 4.55 31 107 3.22 89 88 1.12 101 Table 4-10. Thermomechanical properties of radiation cured poly (MMA) and crosslinked MMA-DVM polymer products. Comonomer Composition, LTDCxiO4, T TDD, TDT, Monomer vol % CM CO 0 C MMA DVM 1/°C °c 0/ /o MMA 100 0 2.000 551 108 0 125 97.5 2.5 2.003 388 115 49 175 95 5 2.006 302 123 60 198 EGDMA 90 70 10 30 2.012 2,039 125 15 127 130 77 92 202 214 50 50 2.072 4 130 94 250* 97.5 2.5 2.002 437 114 41 158 95 5 2.004 350 115 46 164 DEGDMA 90 70 10 30 2.007 2.025 263 82 119 122 61 82 175 200 50 50 2.048 21 125 87 198 97.5 2.5 2.001 476 111 25 155 95 5 2.003 375 113 50 165 TrEGDMA 90 10 2.005 275 116 63 180 70 30 2,018 102 119 83 • 195 50 50 2.036 57 122 92 207 95 5 2.002 425 110 37 . 160 90 10 2.004 326 113 52 165 TEGDMA 85 15 2.007 275 115. 61 185 70 30 2.014 126 117 81 203 50 50 2.029 63 117 88 197 Over 250 °C, maximum for equipment 102 Table 4-11. Mechanical properties of radiation cured poly (MMA) and crosslinked MMA-DVM polymer product s. Comonomer YIELD RUPTURE composition, vol. % CN Monomer 00 MMA DVM STRESS, STRAIN, STRESS, STRAIN, •kg/cm2 % kg/cm2 % MMA 100 0 2.000 1,080 6,0 2,100 50.5 97,5 2.5 2,003 1,080 7,0 4,450 62.2 95 5 2.006 1,060 6.7 4,770 67.5 90 • 10 2.012 19080 7.0 3,950 55.0 EGDMA 80 20 2.024 1,020 6.0 2,550 38.5 50 50 2,072 955 5.0 1,530 20.0 40 60 2.092 — — 1,330 17.5 20 80 2.138 — — 1,210 12,5 0 100 2.200 895 5.5 97,5 2.5 2.002 1,150 7.5 3,915 60,5 95 5 2.004 1,050 7,0 4,680 65.5 DEGDMA 90 10 2.007 1,050 7.0 3,950 54.0 70 30 2.025 1,050 6.5 2,770 42.5 50 50 . 2.048 1,020 6.0 1,910 27.0 20 80 2,099 895 5.5 1,400 15.0 0 100 2,150 — —- 825 5.5 97,5 2.5 2.001 1,020. 7,0 3,630 63.0 95 5 2,003 1,050 7.5 4,650 66.0 TrEGDMA 90 10 2.005 1,020 7.6 4,580 62,5 70 30 2.018 1,000 7.0 3,120 48.0 60 40 2.026 960 6,5 2,510 44.5 50 50 2.036 950 6.0 2,230 36.0 30 70 2.061 950 5.5 1,520 20,0 0 100 2.125 — —- 1,250 11.5 95.5 2.5 2.001 925 6.0 4,710 67.0 95- 5 2., 002 955 6.5 5,100 68.5 TEGDMA 90 10 2,004 1,080 7.0 5,030 67.0 70 30 2,014 1,050 7.0 3,890 59.5 50 50 2.029 955 7.0 2,450 47,0 40 60 2,037 860 6,0 2,250 41.0 20 80 2.062 765 5.0 1,520 2.7.0 • .0 100 2,105 510 2.5 .1,660 26.5 103 Table 4-12. Calculated parameters from compression stress-strain curves for radiation cured poly (MMA) and MMA-DVM polymer products. Comonomer composition, E, Plastic F vol, % Deforma-Monorner , _3 tion, kg/cm^xlO MMA • DVM % cm' MMA 100 0 19.0 44.5 32.3 97.5 2.5 20.0 55.0 49.5 95 5 19.0 61.0 55.7 90 10 19.0 48.0 45.8 EGDMA so 20 19,0 32.5 27.8 '50 50 18.5 15.0 11.1 40 60 18.0 6.8 20 SO 18.0 —— 6.1 0 100 16.5 —— 1.0 97.5 2.5 19.0 53.0 50.9 95 5 19.5 58.5 56.6 90 10 19.0 44.0 48.1 DEGDMA 70 30 18.0 36.0 30.4 50 50 18.0 21.0 17.1 20 80 17,0 9.5 7.3 0 100 17.0 —— 1.5 97.5 2,5 18.0 56.0 47.5 95 5 19.5 58.5 56,5 90 10 20.0 55,0 54.1 TrEGDMA 70 30 17.0 41.0 34.8 60 40 16.5 38,0 26,6 50 50 17.0 30.0 23.3 30 70 17.0 14,5 10.9 0 100 17.0 7.7 97.5 2,5 18.5 61.0 55.6 95 5 18.5 62.0 59.5 90 10 20,0 60,0 57.5 TEGDMA 70 30 19.5 52.5 49.4 50 50 17,0 40.0 34.8 40 60 16.0 35,0 25.3 20 80 15.0 22.0 1.4,5 0 100 15.0 24.0 13,9 104 Figure 3-1. Solution of a typical polymerization exotherm curve including derivation of "Gel-Effect Point" (GEP), "Cure" (MAX), and showing "Activation" (I) and "Acceleration" (II) periods (67,69,71). t t t 0 GEP MAX Time (t)» min D D D 0 GEP MAX Dose (D), Mrad 105 Figure 3-2. Typical thermomechanical curves for thermoplastic (I), partly crosslinked (2) and fully crosslinked (3) polymer products; and showing for (2} solutions for glass transition temperature (Tg), thermal dis tortion temperature (TDT) and slope (s) in the transition region (67969). c o Temperature (T), °C 106 Figure 3-3. Polymer stress-strain curve nomenclature and typical curves for different types of plastics (20,72). S_train at rupture_ stress at rupture Plastic Deformation strain y soft and weak hard and brittle soft and tough r 1 hard and / strong / hard and tough 107 Figure 4-1. Relationship between "^MAX and volume concentra tion of TEGDMA in the MMA-TEGDMA comonomer mixture (67,69). 108 Figure 4-2. Polymerization rate coefficients in "Activation" (PRCj) and "Acceleration" (PRCJJ) periods as functions of TEGDMA volume concentration in the MMA-TEGDMA comonomer mixture (67,69). 0 20 40 60 80 100 TEGDMA, vol. % 109 Figure 4-3. Relationship between overall curing rate (l/tj^) and TEGDMA volume concentration in the MMA-TEGDMA comonomer mixture (67,69), 60 c •H e o < 50 40 30 20 10 0 0 10 20 30 40 50 TEGDMA, vol. % 110 Figure 4-4. Relationship between tMAX and divinyl monomer (DVM) volume concentration in MMA-DVM comonomer mixtures. 0 10 20 30 DVM, vol. % Ill 112 Figure 4-6. Polymerization rate coefficients in "Activation" (PRCj) and "Acceleration" (PRG__) periods as functions of divinyl monomer (DVM) volume concentration in MMA-DVM comonomer mixtures. O MMA - EGDMA X MMA - TrEGDMA A MMA - DEGDMA . Q MMA - TEGDMA DVM, vol. % 113 Figure 4-7. Relationship between WMX and ''GEP for different MMA-DVM comonomer systems and the S- TEGDMA system. 70. 60 50 40 30 20 10 0 0 10 20 30 40 50 ^GEP, min 114 Figure 4-8. Relationship between overall curing rate -(l/twA^) and DVM concentration in MMA-DVM mixtures. 1 O MMA - EGDMA H MMA - TEGDMA A MMA - DEGDMA . © MMA - TMPTMA (33) * MMA - TrEGDMA A MMA 0 5 10 15 DVM, vol. % 115 Figure 4-9. Overall acceleration constant (K) and its reciprocal (l/K) as functions of divinyl monomer connection number (CNr,.,,,, Table 3-l). UVM O MMA-EGDMA X MMA-TrEGDMA A MMA-DEGDMA IS MMA-TEGDMA 2.100 2.150 2.200 CNDVM 116 Figure 4-10. Relationship between overall curing rate (l/t^y) and DVM concentration in t-butyl styrene (TBS/-DVM mixtures. Evaluation of original heat-catalyst data from (53). B A X 0 TBS-EGDMA TBS-TrEGDMA TBS-TEGDMA TBS-TMPTMA 40 c •H E CO O 30 20 10 0 20 30 Crosslinking agent, % 117 Figure 4-11, Overall curing rate (l/t^) of TEGDMA as a function of radiation dose'rate. Figure 4-12. Shape of thermomechanical curves for MMA-EGDMA polymer products. Numbers indicate per cent of EGDMA in comonomer mixture and copolymer connection number (CN). 100 c o •H +> 3 m o M-i cu Q 75 50 25 50 100 RO• 0070 ^0: | 2.POO, 150 200 Temperature, °C co Figure 4-13. Shape of thermomechanical curves for MMA-TEGDMA polymer products. Numbers indicate per cent of TEGDMA in comonomer mixture and copolymer connection number (CNC0) 0 50 100 150 200 Temperature °C Figure 4-14. Glass transition temperature (T ) as a function of copolymer connection number (CNC0) for different Mf'M-DVM polymer products. Figure 4-15. Thermal deformation degree (TDD) and thermal distortion temperature (TDT) as functions of copolymer connection number (CNco) for different MMA-DVM polymer products* 122 Figure 4-16, Linear thermomechanical deformation coefficient (LTDC). as a function of divinyl monomer (DVM) concentration in MMA-DVM polymer products. 0 10 20 30 40 50 DVM, vol, % Figure 4-17. Linear thermomechanical deformation coefficient tLJ/DC) as a function of copolymer connection number (CN ) for. different MMA-DVM polymer products. 2.000 2.010 2.020 2.030 2.040 CN co 124 Figure 4-18. Shape of compression stress-strain curves for MMA-EGDMA polymer products. Rate of strain 0.1 cm/min. 125 Figure 4-19. Shape of compression stress-strain curves for MMA-TEGDMA polymer products. Rate of strain 0.1 cm/min. 126 Figure 4-20. Compression stress-strain parameters as functions of comonomer composition. The MMA-EGDMA comonomer system. (Rate of strain 0.1 cm/min.) 0 Compression stress at rupture, kg/cm2xl0~2 •Jf Compression strain at rupture, % A Area under stress-strain curve, F, cm2. EGDMA MMA concentration, vol. % 127 Figure 4-21. Compression stress-strain parameters as functions of comonomer composition. The MMA-DEGDMA comonomer system. (Rate of strain 0.1 cm/min.) 0 Compression stress at rupture, kg/cm^xl0~2 •X* Compression strain at rupture, % A Area under the stress-strain curve F, cm^. T x DEGDMA 0 20 40 60 80 100 MMA 100 80 60 40 20 0 concentration, vol. % 128 Figure 4-22. Compression stress-strain parameters as functions of comonomer composition. The MMA-TrEGDMA comon omer system. (Rate of strain 0.1 cm/min). © Compression stress at rupture, kg/cm2xl0~ •ft Compression strain at rupture, % A Area under the stress-strain curve F, cm^ TrEGDMA 0 20 40 60 80 100 MMA 100 80 60 40 20 0 concentration, vol. % 129 Figure 4-23. Compression stress-strain parameters as functions of comonomer composition. The MMA-TEGDMA comonomer system. (Rate of strain 0.1 cm/min.) © Compression stress at rupture, kg/cm2xl0""2 •ft Compression strain at rupture, % A Area under the stress-strain curve Ff cm2 TEGDMA 0 20 40 60 80 100 MMA 100 80 60 40 20 0 concentration, vol. % oer 131 Figure 4-25, Relationship between area under the compression stress-strain curve (F) and plastic deformation for different MMA-DVM polymer products, 0 15 30 45 60 Plastic deformation, % 

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