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Enthalpy relaxation in pure and filled copolymers

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Enthalpy relaxation in pure and filled copolymers

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Content ENTHALPY RELAXATION IN PURE AND FILLED COPOLYMERS by Sharad Kumar A Thesis Presented to the FACULTY OF THE SCHOOL OF ENGINEERING UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the degree MASTER OF SCIENCE IN CHEMICAL ENGINEERING July 1984 UMI Number: EP41814 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Dissertation Publishing UMI EP41814 Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106- 1346 Ch Xfb Ja33j- & 9 T h is thesis, w ritten by SHARAV KUMAR under the guidance of h i 5 F a c u lty C om m ittee and ap p ro ved by a ll its members, has been presented to and accepted by the School of E n g in e e rin g in p a rtia l fu lfillm e n t of the re quirem ents fo r the degree of MASTER OF SCIENCE IN CHEMICAL ENGINEERING Dot, Ju* y u - m 4 F a c u lty C om m ittee ■airmt ACKNOWLEDGEMENTS I am deeply grateful to my advisor Dr. Salovey for his guidance and generous help provided all through this study. I take this opportunity to express my gratitude to Dr. J. D. Goddard and Dr. W. V. Chang for their helpful suggestions and encouragements. Finally , I am extremely thankful to Parker Seal Company for allowing me access to their DSC. TABLE OF CONTENTS Page No. ACKNOWLEDGEMENT -------------------------------------- '• LIST OF FIGURES------------------------------------- »V LIST OF TABLES----------------------------------- V ABSTRACT y j CHAPTER 1. INTRODUCTION ------------------------- 1 2. AGING PHENOMENA ---------------------- 4 3. ENTHALPY RELAXATION ------------------ 15 4. MEASUREMENT OF EXCESS ENTHALPY ------ 21 5. EXPERIMENTAL DETAILS ----------------- 28 6. RESULTS------------------------------- 35 7. DISCUSSION--------------------------- 38 8. CONCLUSION — ----------------------- 47 REFERENCES-------------------------------------------- 49 APPENDIX---------------------------------------------- 53 LIST OF FIGURES FIGURE Page No. 2.1. Enthalpy / Volume plot for a glassy polymer ---------------------------------- 5 2.2. The qualitative free volume concept ----------- 8 2.3* Origin of aging and free volume concept ------- 9 3.1. Typical endotherms for an annealed polymer ---- 17 4.1. Enthalpy versus temperature plot for a glassy polymer--------------------------- 22 4.2. Specific heat versus temperature plot for a glassy polymer--------------------------- 24 7.1. Excess enthalpy versus annealing time for pure and filled PT-1200 -------------------- 42 7.2. Excess enthalpy versus annealing time for pure and filled SP2------------------------ 43 A.1. PT-1200 Tg measurement------------------------- 54 A.2. PT-1200 annealed for 15 Min. at 58 C ----------- 55 A.3. PT-1200 annealed for 30 Min. at 58 C ----------- 56 A.4. PT-1200 annealed for 60 Min. at 58 C ----------- 57 A.5. PT-1200 annealed for 100 Min. at 58 C ---- ----- 58 A.6. PT-1200 annealed for 250 Min. at 58 C -------— 59 A.7. PT-1200 annealed for 160 Hrs. at 58 C --------— 60 A.8. PT-1200 annealed for one month at 58 C -------- 61 LIST OF TABLES TABLE 6.1. Enthalpy Relaxation after annealing at Tg-10 C --------- 7.1. Excess Enthalpy -------------- 7.2. Enthalpy Relaxation half times ABSTRACT Excess enthalpy following annealing for various periods of time at (Tg-10)°C was measured by differential scanning calorimetry of electrophotographic toners, copolymers of styrene and butylmethacrylate containing carbon black. An approximate equilibrium enthalpy relaxation after annealing the pure copolymers for one month was 3*30 kJ/kg for a copolymer with 66.5% styrene and 2.72 kJ/kg for a copolymer containing *19.8$ styrene. The rate of enthalpy relaxation was reduced by increasing the styrene content of the pure copolymer. The incorporation of carbon black with high surface area reduces the rate of enthalpy relaxation and also the effect of corban black becomes more prominent with increasing butylmethacrylate concentration. CHAPTER 1 INTRODUCTION Random copolymers of styrene and n-butylmethacrylate containing carbon black filler are used as commercial toners in the electrophotographic printing process (1). The quality of printing depends on the adhesion of a toner to a latent image and subsequent fixing of the toner by fusion on to paper (2). These are affected by the molecular mobility and rheological behaviour of the polymer (3**0 • An attempt was made to investigate the effect of carbon black filler on the mobility of copolymer chains in the vicinity of glass transition temperature (Tg). Random copolymers of styrene and butylmethacrylate at room temperature are polymeric glasses in non-equilibrium states that depend on thermal history and have excess thermodynamic properties such as excess enthalpy and volume. If such glasses are annealed below their glass transition temperatures, these properties relax toward values characterstic of an equilibrium amorphous state. Volume relaxation was experimentally examined by Kovacs et al (5,6) and Uchidoi and was also analyzed by Kovacs et al (8,9) using a phenomenological theory involving a single relaxation time. Enthalpy relaxation has been studied by a number of investigators including Petrie et al (10-12), Straff et al (1 3 ) j Adachi et al (14), Chen et al (15) and Yoshida et al (16,17). On the other hand it has been reported that mechanical properties of a glassy polymer change from ductile to brittle when annealed at a temperature few degrees lower than Tg (20-22). Struik (20) has measured a significant change in mechanical properties during isothermal annealing of polymer glasses and other glasses. The variation of mechanical properties of glassy polymer with annealing at a temperature below Tg is thought to be correlated to the molecular mobility in the glassy state (17). However the relationship between the relaxation process of thermodynamic properties and the variation of mechanical properties has not been fully understood. In order to discuss this relationship, information as follows is necessary. First a suitable mechanism of volume and enthalpy relaxation is needed. Second, the magnitude of molecular motion should be considered in order to assess the molecular mobility in the glassy state. In this study the effect of a filler viz carbon black on the enthalpy relaxation process is evaluated based on relaxation times which were obtained assuming a single time for analysis of relaxation process. CHAPTER 2 AGING PHENOMENA It is well known that amorphous solids are not in thermodynamic equilibrium at temperatures below their glass transition. Such materials should be regarded as solidified supercooled liquid whose volume and enthalpy are greater than they would be in their equilibrium state (see figure 2.1). The non-equilibrium state appears to be unstable. Volume and enthalpy relaxation studies (5-19) of glassy materials have indeed revealed that they undergo slow process which attempt to establish equilibrium, indicating that even below Tg, molecular mobility is not quite zero. Liquid Initial state of glass C L Anticipated equilibrium state of glass L D Temperature Figure 2.1 Enthalpy/volume plot for a glassy polymer. 5 This gradual approach to equilibrium affects many properties of the material (5,20). These properties change with time, and the material is said to undergo aging. Aging is a gradual continuation of the glass formation that sets in around Tg (see figure 2.1). Therefore it affects all those temperature dependent properties which change drastically and abruptly at Tg. During aging these properties change in the same direction as during cooling through the Tg range; the material becomes stiff and more brittle, its damping decreases, and so does its creep and stress relaxation rates, dielectric constant, dielectric loss, etc (20). ORIGIN OF AGING The free volume concept states that the transport mobility, M, of particles in a closely packed system primarily depends on the degree of packing, or in other terms on the free volume, Vf. With increasing degree of packing, this mobility decreases, at first slowly, but 6 later on at an ever increasing rate. At a critical degree of packing, the mobility steeply falls to zero (see figure 2.2). Figure 2.3 shows the changes that happen when an amorphous polymer is cooled from a temperature Tf above Tg to a temperature Ta below Tg, after which it is kept at Ta. In polymers, the transport mobility, M, must be attributed to the segmental mobility, i.e. the rate factor for changes in chain configuration. Since a polymer behaves as a rubber or a fluid above Tg, even at very small strains, its segmental mobility must be large, and so its free volume, Vf must also be large. When the polymer is cooled, Vf and M decrease simultaneously. Since free volume is made up of holes and molecules attract one another, the existence of free volume represents an increase in internal energy of U with respect to the zero free volume state. Free volume actually exists because it is also accompnied with an increase,AS, in entropy. In fact, Vf has precisely that value for which AU balances TAS, and Vf and the mobility, M, will increase simultaneously (20,23). -O o 2; Degree of packing Free volume Figure 2.2 The qualitative free volume concept segments 1 mobi1i ty M 1sothe rmaI decrease in n— free volume V x T T 1, a g f Temperature — Figure 2.3 Origin of aging and free volume concept The changes in Vf are brought about by a redistribution of the holes (20,23,24). The rate of this process is determined by the segmental mobility, M, rendering the following closed-loop scheme :Vf determines M, while M detrmines the rate dVf/dt, at which Vf changes; symbolically, > Vf ===> M ====> dVf/dt This closed-loop scheme, which implies that volume-relaxation is basically non-linear (20,23,24) is essential for an understanding of glass transition and aging. In the first place, it shows that during cooling, Vf cannot decrease indefintely. Below a certain temperature, M becomes so small that Vf almost stops decreasing with temperature. The material then passes through its glass transition. Upon further cooling Vf can only change slightly and slowly. Likewise, M no longer changes rapidly with T, though it continues to decrease slightly because of the attendant decrease in thermal activation (see figure 2.3). 10. A second consequence of above scheme is that below Tg the mobility cannot become zero. A decrease in M requires a decrease in Vf, which implies that there must be some mobility. Therefore, M cannot vanish in a finite time; the state of zero mobility can only be approached asymptotically. Consequently, when the polymer is cooled to some temperature Ta below Tg, the mobility M will be small, but not zero. Since at this temperature Vf is greater than its equilibrium value, the volume will continue to decrease slowly. This contraction will be accompnied by a decrease in the mobility, M, with concomitant changes in all those properties of glassy polymer which depend on it. BASIC ASPECTS OF AGING 1. Aging affects properties primarily via change in relaxation times - The basic property that changes during aging is the segmental mobility, M. Since the relaxation times in the glassy polymer are directly related to M, the mechanical or dielectric properties of the material will be influenced by aging by way of changes in the relaxation times. 2. Aging is thermoreversible - When a glassy polymer is heated above Tg it readily reaches the thermodynamic equilibrium. Since by definition, the sample has then "forgotten" its thermal history, any previous aging it may have undergone below Tg will be erased. Aging is therefore a thermoreversible process that can be reproduced an arbitrary number of times on the same sample. This can be done by restarting every time at the same temperature above Tg. 3. Aging is a general phenomenon - Aging is a basic feautre of glassy state. It is found in all glasses, irrespective of their specific chemical, polymeric or monomeric structure. This has been confirmed by Struik (20) . 4. All the polymers age in a similar way - Struik (20) has shown that aging behavior of all the polymers is very similar. 12 5. Aging does not affect secondary relaxation - Below Tg, Vf shrinks to a value at which segmental motion becomes strongly hindered though it remains possible. In general, secondary relaxation requires much less space than the motion of the segment as a whole. Therefore, Vf will remain sufficiently large to permit these small scale secondary motions to occur. 6. Aging disappears at low temperatures Experiments (20) have shown that aging disappears below T2, the second order glass transition temperature. The disappearance of aging below T2 can be explained in following way. When a polymer is cooled through the T2 range, the polymer segments will (partially) loose their flexibility (e.g. because side group motion becomes frozen). Above T2, however the free volume has already become so small that the motion of the segments is strongly hindered, although they are still internally inflexible. Segmental motion, will therefore be much more hindered, or even impossible, at temperautre below T2. Here, segmental motion, and therefore aging also, will practically disappear. 13 7. Aging persists for very long times - The time t needed for the establishment of equilibrium at T < Tg can be estimated from free volume theory (5,20). It follows that t incrases almost exponentially with Tg-T, roughly by a factor of 10 per 3°C. At a temperature of no more than 20°C below Tg, t reaches a value of 100 years, which implies practically speaking, aging will persist for entire lifetime of a plastic product. CHAPTER 3 ENTHALPY RELAXATION Because of kinetic aspects associated with transformation of a melt to a glass, the glassy states of materials prepared under normal cooling conditions have excess enthalpy and volume relative to those of the corresponding equilibrium glassy states that can be achieved through slow cooling or annealing regimes (12). For glasses with excess thermodynamic properties, there is a thermodynamic potential for the propeties to approach those of the equilibrium state, i.e., to decrease with time, the rate of decrease being detemined by the level of molecular mobility or segmental mobility in the glassy state. Since the magnitude of the change in physical properties is determined by the extent of displacement from the equilibrium state, the maximum change possible in physical properties as a result of in excess thermodynamic properties would increase monotonically with decreasing temperature. The increase in excess thermodynamic properties with decreasing temperature is illustrated in figure 2.1, in which the volume or enthalpy of a supercooled liquid is plotted as a function of temperature over the temperature range extending from temperatures above the glass transition temperature range of glass transformation down to temperature below T2, the anticipated second order glass transition temperature (12). However with decreasing annealing temperature below Tg, the rate of enthalpy relaxation becomes very slow and the time required for enthalpy to decrease by a specific amount becomes exceedingly long (11). The enthalpy relaxation in a polymeric glass due to annealing can be easily measured by differrential scanning calorimeter. The procedure involves monitoring of the absorption of thermal energy that is superimposed on the specific heat changes associated with glass transition observed during programmed heating cycles of aged or annealed glasses. Typical DSC scans are illustrated in figure Annealing o o Anneali ng •s Annea1i ng Temperature Figure 3.1 Typical endotherms for an annealed polymer 17i The rate of enthalpy relaxation in a polymer depends on a number of factors. Petrie et al (11) have done studied the effect of molecular weight on the rate of enthalpy relaxation for atactic polystyrene. They noted that the relaxation rate at comparable temperature intervals below Tg, (Tg-Ta), increases somewhat with decreasing molecular weight below a critical region corresponding to the critical molecular weight range observed in molecular weight dependence of Tg. This result suggests that molecular chain dimension has an effect on the limited segmental mobility occuring in the glassy state. Similar studies were done by Yoshida et al (17). They studied enthalpy relaxation on the bulk polymerized atactic poly(methyl methacrylate), poly(ethyl methacrylate), poly(isopropyl methacrylate), and poly(tert-butyl methacrylate). They found that the rate of enthalpy relaxation was influenced by the ester groups of poly (alkyl methacrylates). With increase in mass of side chains, the relaxation times, obtained based on the assumption of a single relaxation time were shifted to longer times. In their other study (16) they measured enthalpy relaxation in polystyrene, poly(4-hydroxystyrne), and styrene/H-hydroxystyrene copolymers. It was found that the relaxation time strongly depends on the content of hydroxystyrene in the polymer. They ascribed this phenomenon to the formation of hydrogen bonds between hydroxyl groups which act to restrict the segmental motion of the main chain. Recently Hodge et al (19) have developed a simple four parameter model which reproduces following experimental observations on enthalpy relaxation. 1. Sub-Tg endothermal peaks are observed in DSC scans of annealed polymeric glasses. The peaks are assymetric, with low temperature tails and relatively steep high temperature edges. 2. The peaks increase in magnitude (Cpmax) and shift to higher temperatures (Tmax) with increased annealing time, t and annealing temperature, Ta. At long t and/or high Ta, the sub Tg peaks merge with the glass transition and become well known Cp overshoot. 3. The decrease in enthalpy after annealing AH is propotional to Ta if Tg-Ta> 20°K. 19 4. AH and Cpmax are approximately linear function of log t. 5. Tmax is approximately linear function of log Ta. 6. Tmax is approximately linear function of log t. 7. Increased heating rate increases Tmax and Cpmax. CHAPTER 4 MEASUREMENT OF EXCESS ENTHALPY A schematic diagram of the enthalpy relaxation process which occurs during isothermal annealing is presented in figure 4.1. The enthalpy change of a quenched glass is shown as solid line a-e. Above Tg it joins with that of a liquid line e-f. At temperatures above Tg, the thermodynamic properties such as enthalpy, H, or volume, V, are defined only by the pressure P and temperature T. In this temperature region, an amorphous polymer is liquid and may be considered as a substance which reaches thermodynamic equilibrium readily at a given P and T. With annealing at a temperature, Ta, below Tg, the enthalpy of a quenched glass decreases to that of equilibrium state which is shown as dotted line c-d, obtained by extrapolation of enthalpy change of the liquid. The enthalpy change of partially annealed glass * (T ) a T T T f o Figure ^.1 Enthalpy versus temperature plot for a glassy polymer. 22 is shown as the chain line b-e; above Tg, it recovers rapidly to that of the liquid. With longer annealing time, the temperature of rapid change shifts to a higher temperature and enthalpy change increases. In figure 4.2 the corresponding heat capacity changes for a quenched and an annealed glass as observed by DSC are illustrated. For a quenched glass only a step change in heat capacity is observed at Tg. For an annealed glass, however not only a step but a peak in heat capacity is observed at Tg which corresponds to the rapid recovery of enthalpy. With annealing the area of endotherm increases, and Tg of the sample shifts to a higher temperature. Generally it is convenient to express the enthalpy changes that occur during isothermal annealing of a glassy polymer in terms of variations in the enthalpy displacement from equilbrium glassy state eg. Ht (Excess Enthalpy). The excess enthalpy for the glass annealed at Ta for time t is defined as (see figure 4.1) T T T f a Figure b.2 Specific heat versus temperature plot for a glassy polymer. 24 AHt = Ht(Ta)-He(Ta) (1) (1) can also be represented as AHt = ( Ho(Ta)-He(Ta) ) - ( Ho(Ta)-Ht(Ta) ) ---- (2) 1st term in (2) can be expressed as AHo = Ho(Ta)-He(Ta) = ( He(Tf)-He(Ta) ) - ( He(Tf)-Ho(Ta) ) fTf |fTg fTf “ | = \ Cpl dT - |\ Cpg dT + \ Cpl dT I J Ta [jTa jTg i where Cpl and Cpg are heat capacities of the liquid and glassy state, respectively. Cpl dT Ta Tg Cpg dT 25 Now if Cpl and Cpg are not strong function of temperature then Ho(Ta)-He(Ta) can be represented as m o = Ho(Ta)-He(Ta) = (Cpl-Cpg) (Tg-Ta) ---- (3) Above equation has been frequently used by many authors (10-12,16,17). 2nd term in equation (2) can be expressed as Ho(Ta)-Ht(Ta) = ( He(Tf)-Ht(Ta) ) - ( He(Tf) Ho(Ta) ) where Cpa and Cpo are the heat capacities of the annealed and quenched glass repectively. Therefore, in principle it is possible to obtain Ho(Ta)-Ht(Ta) by integrating two DSC thermograms for the annealed and quenched glasses over the temperature range from Ta to Tf. Now a close look at the first term in equation (2) will show that it can also be calculated by the same method which was used for obtaining the second Cpa dT Cpo dT 26 term, i.e. Ho(Ta)-He(Ta) = ( Ho(Ta)-Ht(Ta) ) Annealing Time t > c*? Tf I \ Cpa dT Ta Tf Ta Cpo dT i t > oo 27 CHAPTER 5 EXPERIMENTAL DETAILS MATERIALS PT-1200 and SP2, copolymers of styrene and butylmethacrylate were obtained from Hercules Inc. and from Scientific Polymer Products respectively. Their composition was determined by elemental analysis (Galbraith laboratories, Inc., Knoxville, TN.) following purification by reprecipitation from tetrahydrofuran solutions. From the amounts of carbon and hydrogen in the copolymer, the styrene composition was found to be 66.57. for PT-1200 and 49-87 for SP2. The glass transition temperatures of the pure copolymers were measured by differential scanning calorimeter (Perkin-Elmer Co. model DSC-2C) at a heating rate of 10 °C/min and found to be 68*0 for PT-1200 and 54.5 °C for SP2. From the glass transition temperatures of the homopolymers (25,26), the corresponding styrene concentration is calculated to be 66.3% for PT-1200 and 49-1% for SP2. The molecular weight distribution of PT-1200 was estimated by intrinsic viscosity measurements in tetrahydrofuran solution (Canon-Ubbelhode) and by gel permeation chromotagraphy (GPC, Water Associates, model R-400, five mierostyragel columns). A "universal caliberation" of GPC was determined by measuring the intrinsic viscosity and elution volume in GPC of fractions of PT-1200 (27). The weight average molecular weight was calculated to be 63,000 for PT-1200 with a heterogeneity index approximating 2.0. For SP2, the GPC molecular weight was analyzed using a polystyrene caliberation and found to be 46% higher and exhibited a heterogeneity index of 1.8. The carbon black sample was obtained from Columbian Chemicals Co. and is designated as Raven 7000. As reported by the manufacturer, this furnace black has a surface area of 625 square metre per gram by BET, a particle diameter of 15 mu and a structure characterization by DBP absorption of 105 cc/100 gram. Thus, the material is of relatively fine particle size and exhibits high surface area and a complex structure. SAMPLE PREPARATION Carbon black and the copolymer in powder form were dry mixed and then melt blended at ISO^C in an internal mixer (Brabender Plasticorder). Thin films of pure copolymer and of copolymer containing carbon black were prepared by heating the powder in an oven prior to calorimetric measurements. Similar results were also found for the copolymers by heating the compacted powder directly in the calorimeter. CALORIMETRIC MEASUREMENTS A differential scanning calorimeter (Perkin-Elmer DSC-2C) was used to anneal and measure the heat capacity of all samples as a function of temperature at a heating rate of 10°C/min. The amount of sample was adjusted to include exactly 10 mgm. of pure copolymer. The calorimeter was repeatedly caliberated with indium and lead standards. Annealing and DSC measurements were done in a nitrogen atmosphere. Annealing for 160 Hrs. and one month were done in an oven. For measurements of enthalpy relaxation the following method was adopted. O 1. Heat the sample at 10 C/min to approximately 40 °C above Tg to remove the old thermal history. 2. Quench cool the sample at maximum possible rate on the instrument viz 320°C/min to 40°C below Tg. 3- Reheat the quenched sample at 10 C/min to approximately 40 °C above Tg and identify the glass transition temperature. 4. Quench the sample to 10°C below Tg at 320°C/min. 5. Anneal the sample at the temperature (Tg-10) °C for desired amount of time. 6. After annealing quench it at 320°C/min to about 40 ° C below Tg to restrict any further enthalpy relaxation. 7. Heat the sample at 10°C/min to 40°C above Tg to get the endotherm of the annealed sample. 8. Quench cool at 320°C/min to 40°C below Tg and reheat at 10 °C/min to get the endotherm of quenched sample. 9. The area between the endotherms of annealed and quenched sample gives the amount of enthalpy relaxation. However when experiments were carried out a baseline drift was observed repeatedly which resulted in endotherms of quenched and annealed samples that were neither superimposable in the glassy state nor in the melt state. Unable to use the above method the following method was adopted as an alternative to successfully overcome this difficulty. 1. Put identical samples in the sample holder as well as reference holder. 2. Heat at 10"C/min to 40 °C above Tg to remove the old thermal history. 3- Quench the sample at 320°C/min to 40°C below Tg. 4. Take out the sample from reference holder and store it at a low temperature (Tg-40)°C. 5. Heat the sample which is in sample holder to 40 °C above Tg. 6. Quench the sample at 320°C/min to 10°C below Tg. 7. Anneal the sample at 10*C below Tg for desired amount of time. 8. After annealing quench the sample to 40°C below Tg. 9- Put back the quenched sample in reference holder from where it was taken out. 33 10. Heat at 10 0C/rain to get the difference endotherm of annealed and quenched sample. 34 CHAPTER 6 RESULTS Calorimetric measurements of the heat capacity of quenched copolymer samples on heating at 10eC/min from well below Tg, yield a characterstic displacement in the endothermic direction. Linear extrapolation of the resulting heat capacity curve above and below this displacement permits the identification of the midpoint in temperature as Tg. The plot for. glass transition temperature measurement of pure PT-1200 is shown in figure A.I. Using the experimental technique described in chapter 5 for measuring difference endotherms on DSC between annealed and quenched samples, a small endothermic peak is observed in the vicinity of Tg. Simple extrapolation of the linear base line on the either side of the peak allowes determination of the enthalpy relaxation from area under the curves. Enthalpy relaxation measurements for pure PT-1200 at various intervals of time are shown in figure A.2 to figure A.8. The enthalpy relaxation in kJ/kg is tabulated for pure copolymers and for copolymers containing carbon black in Table 6.1. Since annealing was done at (Tg-10)°C, values of Tg are also given. Table 6.1 Enthalpy Relaxation in kJ/kg after annealing at (Tg-10)*C j COPOLYMER Tg°C Annealing Time I 15 Min 130 I Min 60 Min 100 Min 250 Min 1160 I iHrs I I a I Pure PT1200 68 0.89 11.00 1.13 1.46 1.80 I I 12.38 1 1 1 I PT 1200 with I 10 % I carbon black 68.5 0.75 10.96 1.13 1.42 1.76 1 1 12.22 | 1 1 I PT 1200 with I 20 % I carbon black 68.5 0.67 10.96 1.09 1.38 1.72 1 1 12.13 I I I I PT 1200 with I 30 % I carbon black 69.5 0.63 10.84 1.00 1.34 1.59 I I 12.01 | I I I b I Pure SP2 54.5 0.92 11.21 1.38 1.55 2.05 I I 12.51 I I I I SP2 with I 20 % I carbon black 55.5 0.71 11.00 1.21 1.38 1.88 I I 12.34 I 1 1 I SP2 with I 30 % I carbon black 56 0.63 10.84 1.09 1.26 1.76 I 1 12.26 | 1 1 a-3.30 kJ/kg ( Enthalpy relaxation after annealing at (Tg-10)°C for one month ) b-2.71 kJ/kg ( Enthalpy relaxation after annealing at (Tg-10)°C for one month ) CHAPTER 7 DISCUSSION The specific temperature selected for annealing was a result of a compromise between the thermodynamic driving force for enthalpy relaxation, which is very small close to Tg, and the rate of relaxation which becomes increasingly slow as one goes below Tg. By trial and error, (Tg-10)°C was found to give the maximum heat absorption for reasonable changes in time. An attempt was made to calculate "equilbrium" enthalpy relaxation or excess enthalpy in the quenched state (AHo) by using equation (3). However, it was found that enthalpy relaxation for one month has a higher value than those obtained by equation (3)* For example, using equation (3) AHo for PT-1200 would approximate to 2.13 O kJ/kg but annealing at (Tg-10) C for one month gives a value of 3-305 kJ/kg for enthalpy relaxation. o Assuming that annealing at (Tg-10) C for one month yields an approximate "equilibrium" enthalpy relaxation (AHo) and that this "equilibrium" enthalpy relaxation does not change on the addition of carbon black, excess enthalpy can be expressed as being equal to equilibrium enthalpy relaxation minus the observed enthalpy change. The excess enthalpy in kJ/kg is tabulated for pure copolymers and for copolymers containing carbon black in table 7.1. It is suggested that the poor agreement between values of AHo, calculated by equation (3) with those of measured is due to dependence of heat capacities on temperature and Tg on annealing. The excess enthalpy of an annealed polymeric glass can be described as (17, 23) : AHt/AHo = EXP ( (-t/tau)**beta ) where AHt is the excess enthalpy at time t AHo is the excess enthalpy of the quenched sample beta is a measure of nonexponentiality and 0<beta<1.0 and tau is a characterstic relaxation time 39 Table 7.1 Excess Enthalpy in kJ/kg I I I COPOLYMER I I I I_____ _ _ Annealing Time I I I I i 1 15 Min 30 Min 60 Min 1 1 1 1 1 100 I j Min | -I - I 250 Min 1 1 160 I Hrs j - - - I I Pure I PT-1200 I I_____________ 2.41 2.30 2.17 I I I 1.84 I I I _ i_ ____i 1.50 I 0 .92 I I _______I I PT-1200 I with 10 % I carbon black |_ _ _ _ 2.55 2.34 2.17 I I I 1.88 I I I -1 I 1.54 I 1.08 I I I PT-1200 I with 20 % I carbon black I 2.60 2.34 2.21 I I I 1.88 I I I -I- I 1.58 I •1.17 I I 1 I PT-1200 I with 30 % I carbon black j 2.67 2.46 2-30 I I I 1.96 I I I -I- I 1.71 I 1.29 I I - I I Pure SP2 I I 1.80 1.51 1.34 I I I 1.17 I -1 I 0.67 I 0.21 | I - -1 I SP2 with I 20 % I carbon black I 2.01 1.72 1.51 I I I 1.34 I 1 1 1 1 0.84 I 0.38 I I I I SP2 with 1 1 I I 30 % 2.09 1.88 1.63 1 1.46 I 0.96 0.461 I carbon black _ ------------- 1 1 I If beta = 1, then the process may be characterized by a single relaxation time. Although beta is generally not equal to one and AHt/AHo also depends on the departure from equilibrium, it is instructive to examine the time at which AHt/AHo = 0.5 (15,16). Accordingly, the excess enthalpy was plotted against log annealing time during isothermal annealing at (Tg-10)°C yielding a series of almost parallel curves which are shown in figure 7-1 and 7.2. The half times in seconds are listed in table 7.2. The rate of enthalpy relaxation is four times faster for SP2 copolymer as compared to PT-1200. This is surprising, since the molecular weight of PT-1200 was approximately 60,000, while that of SP2 was about 90,000 (11). Apparently, a far more important factor seems to be the styrene content of copolymer which is 66$ for PT-1200 and 50$ for SP2. It seems that by increasing the amount of styrene, one increases the half-time for enthalpy relaxation. This is consistent with the styrene units imparting greater rigidity to the copolymer molecules and raising the observed glass transition temperature. 4 - 1 f cn >- CL t o JZ 4J c w t / l < u u X 2 - 1 _ 0 a x 0 & o 0 a s o 0 o X 0 - PT1200 with 30% C-black - PT1200 with 20% C-black _ PT1200 with 10% C-black - Pure PT1200 □ x o a x 10 100 1000 Annealing time in mi . ' n — 1 Q0.00. Figure 7.1 Excess enthalpy versus annealing time for pure and f i l l e d PT-1200. -F ro Excess Enthalpy KJ/Kg <> a 0 o 0 Q O — SP2 with 30% C-black □ _ SP2 with 20% C-b.lack O - Pure SP2. 0 a d _L 10 100 1000 Annealing time in min 10000 Figure 7.2 Excess enthalpy versus annealing time for pure and f i l l e d SP2 -F CO Table 7.2 Enthalpy Relaxation half time in seconds 1 I COPOLYMER 1 | I I I Amount of carbon I black I I I 1 1 1 I I 0 % I I I 10 % I 20 % I I I 30 % I I I i i PT-1200 I I I 9600 I I I 10800 I 12600 I I I 18000 I I I I I SP2 I I I 2400 I I I I 4700 I I I 6900 I I I The incorporation of carbon black filler reduces the rate of enthalpy relaxation. Thus a loading of 30% carbon black increased the corresponding half time by a factor of 1.9 for PT-1200 and a factor of 2.9 for SP2. It is clear that the inclusion of carbon black is more effective in impeding the molecular mobility in the SP2 copolymer. This is because the SP2 copolymer contains 50% butylmethacrylate as compared to 3^/^ in PT-1200. Butyl methacrylate is the polar monomer and interacts more strongly with carbon black providing molecular attachments to the carbon black particles. These data are completely in consistent with rheological measurements, in which the effect of shear rate, carbon black surface area and concentration, and copolymer molecular weight and composition were studied (3). Some comments are necessary on the major assumptions in this work at this point. Regarding the selection of equilibrium enthalpy relaxation (AHo) for the copolymers, with increasing annealing times these values may increase further. However, for analyzing enthalpy relaxation for short interval of times, enthalpy relaxation occuring in one month may be regarded as good approximation of AHo. © Furthermore both copolymers were annealed at (Tg-10) C for the same period of time and the comparisons are probably valid. The second assumption that carbon black does not affect AHo may be a well justified assumption since AHo corresponds to the maximum segmental motion possible in glassy polymer and one does expect it to change with the addition of a filler. CHAPTER 8 CONCLUSION Random copolymers of styrene and butylmethacrylate were quenched through glass transition range at 320°C/min and isothermally annealed at (Tg-10) °C for various interval of times. The amount of enthalpy relaxation occuring during annealing was measured by differential scanning calorimetry using a direct comparison between annealed and quenched samples. The rate of enthalpy relaxation was analyzed by plotting excess enthalpy versus log of annealing time. It was found that the rate of enthalpy relaxation was reduced with increasing styrene content in the copolymer. This is probably because of phenyl ring present in styrene which imparts greater restriction to the segmental motion in the polymer. Enthalpy relaxation meaurements were also done on copolymers containing carbon black. It was found the incorporation of carbon black with high surface area reduced the rate of enthalpy relaxation, increasingly so with butyl methacrylate content. This is probably due to a specific interaction between the more polar butyl methacrylate and the carbon black surface resulting in more effective attachment and immoblization, of polymer chains. REFERENCES 1. U. Vahtra and R.F. Wolter, IBM J. Res. Develop., 22, 34 (1978). 2. K.D. Brooms, IBM J. Res. Develop., 22, 26 (1978). 3. K. Lakdawala and R. Salovey, submitted for publication. 4. S.K. Ahuja, page 469 in "Rheology, volume 2, Fluids", edited by G. Astarita, G. Marruci and L. Nicolais, Plenum press, New York (1980). 5. A.J. Kovacs, J. Polym. Sci., 30, 131 (1958). 6. A.J. Kovacs, Fortschr. Hochpolym. Forsch., 3> 394 (1963). 7. M. Uchidoi, K. Adachi and Y. Ishida, Polymer Journal, 10, 161 (1978). 8. J.M. Hutchinson and A.J. Kovacs, J. Polym. Sci., Polym. Phys. Ed., 14, 1575 (1976). 9. A.J. Kovacs, J.J. Aklonis, J.M. Hutchinson and A.R. Ramos, J. Polym. Sci., Polym. Phys. Ed., 17, 1097 (1979). 10. S.E.B. Petrie, J. Polym. Sci., A-2, 10, 1255 (1972). 11. A.S. Marshall and S.E.B. Petrie, J. Appl. Phys., 46, 4223 (1975). 12. S.E.B. Petrie, J. Macromol. Sci., Physics Ed., B12, 225 (1976). 13* R. Straff and D.R. Uhlmann, J. Polym. Sci, Polym. Physics Ed., 14, 1087, (1976). 14. K. Adachi and T. Kotaka, Polymer Journal, 14, 959 (1982). 50 15. H.S. Chen and T.T. Wang, J. Appl. Phys., 52 (10), 5898 (1981). 16. H. Yoshida and Y. Kobayashi, Polymer Journal, Vol no 14, 855 (1982). 17. H. Yoshida and Y. Kobayashi, J. Macromol. Sci., Physics Ed., B21 (4), 565 (1982). 18. J.M.O. Reilly, J. Appl. Phys., 50 (10), 6083 (1979). 19. I.M. Hodge and A.R. Berens, Macromolecules, 15, 762 (1982). 20. L.C.E. Struik, Physical Aging in Amorphous Polymers and other Materials, Elsvier, Amsterdam, 1978. 21. K. Neki and P.H. Geil, J. Macromol. Sci., Physics Ed., B8, 295 (1973). 22. R.M. Mininni, R.S. Moore, J.R. Flick and S.E.B. Petrie, J. Macromol. Sci., Physics Ed., B8, 3^3 (1973). 51 23. D. Turnbull and M.H. Cohen, J. Chem. Phys., 34, 120 (1961). 24. D. Turnbell and M.H. Cohen, J. Chem. Phys., 31, 1164 (1959). 25. W.A. Lee and R.A. Rutherford in "Polymer Handbook, Second Edition", edited by J. Brandrup and E.H. Immergut, pages 147 and 154, John Wiley and Sons, New York (1975),. 26. A. Rudin, "The Elements of Polymer Science and Engineering", Ch. 11, page 402, Academic Press, New York (1982) . 27. W.W. Yau, J.J. Kirkland and D.D. Bly, "Modern Size - Exclusion Liquid Chrmotography", Ch. 9, page 291, John Wiley and Sons, New York (1979). 52 APPENDIX 53 MIDPOINT = 68.13°C o 100 110 Temperature ( ° C ) Figure A.1 PT-1200 Tg measurement. UJ LO < o z: CAL/GRAM = .21 50 60 70 80 Temperature ( * C ) 90 100 cn Cn Figure A.2 PT-1200 annealed for 15 Min. at 58 C 2 < _ > L u l ( / ) CAL/GRAH = ,2k 100 Temperature fC) Figure A .3 PT-1200 annealed for 30 Min. at 58 C. MCAL/S EC 2 CAL/GRAM = .27 80 60 90 100 70 50 Temperature ft) Figure A.^ PT-1200 annealed for 60 Min. at 58 °C. 2 CAL/GRAM = .35 80 60 50 70 90 100 Temperature fC) Figure A .5 PT-1200 annealed for 100 Min. at 58 C. MCAL/SEC 2 CAL/GRAM = .^3 60 50 80 70 90 Temperature (*C) Figure A .6 PT-1200 annealed for 250 Min. at 5 8 °C. cn CD MCAL/SEC 2 CAL/GRAM = .57 100 Temperature ( a C) CD o Figure A .7 PT-1200 annealed for 160 Hrs. at 58°C.

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Creator Kumar, Sharad (author)

Core Title Enthalpy relaxation in pure and filled copolymers

Degree Master of Science

Degree Program Chemical Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag chemistry, polymer,engineering, chemical,OAI-PMH Harvest

Language English

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Advisor Salovey, Ronald (committee chair), Chang, Wenji Victor (committee member), Shing, Katherine S. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c20-313931

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