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Thermodynamics of high-elastic deformation of filled polyvinylchloride
Polymer Science U.S.S.R. Vol. 23, lqo. 1, pp. 181-191, 1 9 8 1 Yrhtted in Poland
0032-8950/811010181-11807.5010 O 1982 Pergamon Press Ltd.
THERMODYNAMICS OF HIGH-ELASTIC DEFORMATION OF FILLED POLYVINYLCHLORIDE* V. V. GUZEYEV, ZH. I. SHKALENKO a n d ¥ u . M. M_AnrNsKn V. A. Kargin Scientific Research Institute of Chemistry and Polymer Technology L. Ya. Karpov Scientific Research Institute of Physico-Chemistry
(Received 20 November 1979) A study was made of the effect of a n u m b e r of fillers of different types and surface on thermodynamics of high-elastic deformation of PVC. I n their effect on thermodynamic stress components the fillers studied form two groups: 1--polar active filler influencing both energy and entropy stress components; 2--nonpolar filler which cause basically conformation changes in the polymer. I n small amounts with slight deformation fillers of group 1 contribute to structure formation of PVC, with high concentrations the filler "inhibits" structure formation. Fillers of group 2 do not influence process of structure formation during deformation of PVC. T ~ process of polymer elongation, particularly in the high-elastic state considerably changes t h e initial isotropic structure as a consequence of orientation capable of altering the thermo-
dynamic state of the polymer. As a result of adsorption interaction of its surface with the polymer the addition of a filler changes the mobility of polymers segments, which also influences the thermodynamic state of the polymer and the complex of physico-chemical and mechanical properties of t h e composition. Interaction of the polymer with the filler surface or adhesion between them is one of the major factors accounting for the reinforcement of polymers by fillers [1]. I t follows logically from the foregoing that it is advisable to examine thermodynamics of high-elastic deformation of filled polymers which together with studies of structure, mechanical and other properties contributes to a better understanding of processes of interaction of polymers with various fillers and of the effect of fillers on physico-mechanical properties of polymer compositions. Numerous studies have shown that the thermodynamic method of investigating polymer elongation provides extensive information in spite of the fact that giving an accurate quantitative description of structural changes during deformation in terms of entropy and internal energy does not always answer the problem of actual deformation mechanism. This is in no way a shortcoming of the method, merely a limitation typical of any experiment, b a s e d on thermodynamics. As noted by Flory, "the final aim of thermodynamic analysis is the compilation of quantitative characteristics, which may be interpreted physically, particularly in structural terms" [2]. The effect of filling on thermodynamics of deformation of polymers has been examined in comparatively few studies [3-7]; these are valuable, however, in so much as they try to link the mechanism of reinforcing rubber with fillers with their effect on the energy a n d entropy components of stress. * Vysokemol. soyed. A23: ~No. 1, 161-170, 1981. 181
1'82
V . V . GUZEYEV'et al.
The effect of filling and plasticization on thermodynamics of deformation of PVC has been studied by the authors of previous papers [8-10], who indicated that high-elastic deformation of PVC is of mixed entropy--energy type and that the addition of fillers and plasticization have a marked effect on ~he ratio of entropy and energy cor~aponents of stress. G'
5
8
(~, ~,~),I05, ~/m z
t.~ ~
I0
.
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¢3
20~t y),
.+t+
3 ° ~~ - - . - -
,
I
~Ao._. •
-.
zo - 1 -
e,~
I
350
400 T, K
-/0
FIG. 1
FIG. 2
FIe. 1. Typical thermoelastic curves of plasticized compositions (PVC: D D P = 2 : 1), containing 25 50 (9) and 150 parts by wt. filler Form of filler and extent of elongation: /--without filler 17%; 2--whiting 16.5%; 3--quartz 15.2%; 4--BS-30; 16.8% ; 5~-AMP 15.1%; 6--AM-2, 15-3°/o; 7--kaolin 22%; 8--Aerosil A-175, 14.7%; 9--aerosil A-1759"9~o; 10--kaolin 10.7~/o.
(2-8),
(10).
(1',
2")
FIG. 2. Variation of equilibrium stress (1, 2), entropy 2') and energy (1", components in elongation of plasticized compositions (PVC : D D P = 2 : l) with T = 8 0 ° without filler (1, 1"); with 7.4 vol. °/o Aerosil A-175 (2, 2',
1',
2").
I t was interesting to examine the effect on t h e r m o d y n a m i c s o f high-elastic d e f o r m a t i o n o f P V C o f fillers v a r y i n g in the t y p e a n d size of surface; this enabled some general relations to be derived governing the effect of phase i n t e r a c t i o n o n t h e r m o d y n a m i c s of d e f o r m a t i o n a n d m e c h a n i c a l properties of compositions b a s e d on PVC.
Thermodynamics of high-elastic deformation of filled PVC
183
Samples for investigating the effect of filling on thermo-elastic properties of compositions contained for 100 parts by wt. PVC 50 parts by wt. didecylphthalate (DDP), heat-stabilizers-7 parts by wt. dibasic lead phthalate and 1 part by wt. lead stearate, 0.3 part by wt. antioxidant (diphenylolpropane) and a varying amount of fillers. A list of fillers examined and some of their properties are shown in Table 1. In contrast with methods of deriving the dependence of equilibrium stress of PVC f on temperature described by us [8], the sensitivity of the angle of force measurement of the device was increased in this study, which revealed a curvature in the dependence o f f on T for unfilled and most filled samples (Fig. 1). Samples containing high concentrations of Aerosil A-175 and kaolin were exceptions. With an increase in filler concentration and elongation, thermo-elastic curves are displaced upwards along the stress axis and acquire a considerable gradient. The curvature of thermoelastic curves observed may mean that if elongation is carried out at high temperature, on cooling the elongated sample ordering takes place causing a further drop in internal energy and entropy, which is expressed in an increase in the gradient of thermo-elastic curves during cooling. It should be noted that all structural processes observed in these experiments are reversible. According to a former study [2], the gradient of tangents to thermo-elastic curves at certain temperatures gives a reduction of entropy in elongation, while intercepts by tangents on the stress axis when T : 0 ° K , give the variation of internal energy or enthalpy during elongation. As before [5, 6, 8], to calculate entropyfs and energy fu components of stress, thb following equations were used
f , : --T
fu= ~
\aLlv,~, v,~
\aT/p,a - -
~T p.x
(l)
,
(2)
where S, U, V, T, L, P, f are the entropy, internal energy, volume, temperature, length, external pressure and equilibrium stress of the elongated sample, respectively; ~:L/Lo, where L0 is the length of the lion-elongated sample at temperature T. The relative error in determining f was + 3% and in determining f, and f~+ 5%. Figure 2 shows a t y p i c a l p a t t e r n of the v a r i a t i o n of equilibrium stress a n d t h e r m o d y n a m i c c o m p o n e n t s in elongation of filled and unfilled PVC. A reduct i o n can be seen in b o t h cases in internal e n e r g y a n d e n t r o p y d u r i n g elongation; as s h o w n for unfilled PVC [10], this is due to processes o f orientation, s t r u c t u r e f o r m a t i o n a n d i n t r a m o l e c u l a r t r a n s i t i o n of gauche-trans-conformations of PVC macromolecules. L e t us examine the effect of filling on f, fs and fu. Dependences of f, f8 a n d fu on the degree of filling in d e f o r m a t i o n of samples b y 10% are shown in Fig. 3. True elongation of the p o l y m e r m a t r i x with these filling a n d d e f o r m a t i o n processes differs o n l y slightly from the elongation of the sample, which does n o t affect the results in question. Figure 3 shows t h a t equilibrium stress increases in filling using a n y of t h e fillers. Curve for f of samples with the whiting passes s o m e w h a t lower t h a n t h e
184
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Thermodynamics of high-elastic deformation of filled PVC
18~
relationship calculated from the Guth and Smallwood formula [11]
f=fo(1 ~- 2.5vu-~ 14. lv~)
(3)
(v~ being the volume fraction of the filler) up to a concentration of 15°/o and! with higher concentration f becomes higher than prescribed by formula (3). Curve for f for samples with quartz powder passes below the curve calculated using the Guth-Smallwood formula, while curves of f for samples with other fillers passes above the calculation curve, which is evidence of the distinct rSle of surface effects in increasing f during filling. Furthermore, Fig. 3 shows that fs and fu change during filling; in their effect on thermodynamic components of stress fillers may be divided into two groups: fillers influencing both the energy and entropy components of stress belong to the first group; fillers increasing entropy components and not affecting or slightly affecting the energy component are in the second group. Fillers of group 1--Aerosil and kaolin--are characterized by the existence of strong polar (silanol) groups on the surface and high or average specific surface. Fillers of group 2--whiting, AM-2, AMP, BS-30, quartz powder--are characterized either by the absence of polar groups on the surface, or in the presence of polar groups (quartz)--by low specific surface. BS-30 is an exception. The considerable effect of Aerosil and kaolin on fu and f8 proves that in the presence of these fillers PVC undergoes marked structure formation in elongation. Figure 3 also shows that changes in fu for Aerosil and kaolin and in fs for Aerosil are the greatest. It is obvious that with an Aerosil concentration o f 6-7% and a kaolin concentration of 20-25% some changes take place in elongation of filled samples. Deformation of PVC containing less than ~ 5% Aerosil or ~ 20°/o kaolin may, apparently, be regarded as elongation of the polymer. matrix containing separate filler particles with a boundary polymer layer immobilized b y the surface or separate agglomerates and short chains of these particles. With higher concentrations particles of these fillers, apparently, form either a three-dimensional chain structure (Aerosil), or a carcass (kaolin), in which boundary layers of the polymer around each particle combine into a sole polymer system immobilized by the surface of the filler. This pattern does not conflict with the electron-microscope structure of these compositions [12]. With an Aerosil or kaolin concentration higher than "critical" elongation of the sample results in deformation of boundary PVC layers which in turn produces disorder in macro-chains in the boundary layer, as confirmed by a change in the shape of internal energy curves, while for Acrosil, a change also in entropy curves. Thermodynamic data therefore suggest that PVC in boundary layers near the surface of Aerosil and kaolin particles is more ordered than thal far from the surface. Comparatively slight deformations of PVC studied in this experiment contribute to establishing dipole-dipole contacts between the polymer and filler with moderate concentration of the latter, which in turn contributes to
186
V.V. GUZEYEVet al.
:structure formation of the system shown in a sudden reduction of internal energy and entropy. This mechanism which explains the experimental dependence of internal energy and entropy variation in elongation on Aerosil and kaolin content, was briefly described by the authors previously [9]. Studying thermodynamics of deformation of polyurethanes filled with Aerosil A-175 Lipatov at al. [7] detected a similar course in the variation offu and f8 with Aerosil content; while analysing the results obtained the authors quoted the interpretation given by us [9] noting t h a t it is suitable for explaining the behaviour of filled polyurethanes. This agreement is important as it not only emphasizes the rSle of deformation in structure formation of the polymer on the surface of the polar filler, but also reveals the general nature of properties of boundary layers of two different classes of polymer near the surface with the same filler. In spite of an average degree of dispersion (Ssp----10 mS/g), kaolin has a very active influence on thermodynamics of elongation which, in addition to the high concentration of polar surface groups, m a y be due to the anisotropic planar structure of particles; this, apparently, contributes during the elongation of the sample to "adjoining" of macro-chains to the particle surface and their ordering in the boundary layer. Furthermore, orientation Of lamellar particles of kaolin along the axis of elongation produces an entropy orientation force [1], which has a further effect on increasing tensile stress in filling. This, is apparently, one of the causes of the high thermodynamic activity of kaolin. The mechanism proposed is confirmed by the variation in thermodynamic values for samples containing fillers of group 2. Depletion of silanol polar groups of the surface of Aerosfl or a marked reduction in their proportion during chemisorption of modifying agents (AMP and AM-2), or a reduction in the dispersion of the filler h a s the result t h a t filling has little effect on the variation of internal energy in elongation, and stress increase (or increase in the modulus of elasticity) when adding these fillers is basically due to processes related to conformation effect--geometrical limitation of space [1, 14]. The formation of boundary layers of "isoenergetic" fillers is evidently mainly of conformation entropy type. Regarding the effect of BS:30 on fu the following m a y be stated. It appears t h a t the addition of BS-30 of considerable specific surface results in a reduction of fu although to a lesser extent than the addition of A-175, but to a greater e x t e n t than the addition o f kaolin. However, as was shown previously [15], BS-30 particles being commensurate with inter-structural regions o f PVC, are wedged in them, weakening structural interaction. For this reason no further drop is observed in fu when filling using BS-30. Let us examine the change of f, fs and fu of elongated samples, with the content of AM-2. Figure 3 indicates t h a t at low concentrations ( ~ 2 %) small maximum (values are observed in the variation of f, f8 and fu, which are qualitatively similar to those observed for samples containing BS-30. Small amounts of AM-2 pene-
Thermodynamics of high-elastic deformation of filled PVC
187
trating the interglobular space, the same w a y as BS-30, apparently, have a dual function. On the one hand, AM-2 particles reduce structural interaction, screening purely geometrically polar groups of PVC, which lowers structure formation, i.e. reduces changes in fu and fs in elongation; on the other hand, AM-2 particles immobilize t h e boundary layer (which is, apparently, smaller than in the case of Aerosil); this, in the end, results in a greater increase in f than specified b y the Guth-Smallwood equation.
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II
'//7
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e'
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0
-'2
,
~ 7"
3
"
~
~
1.0 ! 0.5 /q 80
FIG. 3
I00
120 7""
Fro. 4
FIG. 3. Effect of filler o n f (1-7), f, (1"-7') andfu (1"'-7") in elongation of plasticized compositions (PVC : DDP=2 : 1) with T=80 ° and 2=1.10; calculation curve according to the equation f=fo(l+2.Sv2+14.1 v~) (8). Fillers: Aerosil A-175 (1, 1', •"); AM-2 (2, 2', 2"); BS-30 (3, 3', 3"); kaolin (4, 4", 4"); AMP (5, 5', 5"); whiting (6, 6', 6"); quartz (7, 7', 7"). FIG. 4. Dependence on temperature of gradients (Of/OT)p,x of thermoelastic curves when 2= 1.10:1 (broken lme)--without filler; 2, 5, 6--kaolin; 3, 4--A-175; 7, 9--BS-30; 8--AM-2; 10, 12--quartz; 11, 13--whiting; 14--AMP. Filler content, parts by w~.: 4, 8, 9, •4--35; 3, 6, 7, 12, •3--50; 5, 10, 11--100; 2--150. As noted previously, the gradient of thermoelastic curves increases for most samples examined with reduction a of temperature, which points to an increase in processes of structure formation of elongated samples during cooling. Figure 4 shows gradients (~f/~T)p,~ of thermoelastie curves, according to temperature with a degree of elongation )~=1.01, while curves for filler concentrations < 10 vol. % are not given since in gradient they are similar to until-
188
V.V. GUZ~.YEVeta/.
led samples. It can be seen t h a t no increase in gradient typical of most thermoelastic curves occurs with a reduction in temperature for samples containing comparatively large amounts--9.9 (curve 4) and 13.6 vol. ~ (curve 3) Aerosil and 31.6 vol ~ (curve 2) kaolin. I n other words, in compositions containing active fillers (group 1) in quantities, when particles form a continuous three-dimensional structure and when a considerable part of polymer is in boundary layers, the polymer phase is unable to undergo structure formation on cooling the elongated sample (Fig. 4). Furthermore, studying Fig. 3 we noted t h a t structure formation decreases even during elongation when the composition contains considerable amounts of fillers and a large part of the polymer is immobilized by the surface of particles and structure formation in PVC, both during elongation and cooling is hindered~ i.e. the filler is in high concentrations an inhibitor of structure formation. /.1
/.2
it
f ~'--0
--[
0
0-'--"
--
9 , 1 0 ~ 12 . ~
~
~
~ +.,~
FIG. 5. Dependence of f,,/f on ghe degree of elongation at 80°: 1 (broken line)--withouV filler; 2, 8--aerosil A-175; 3, 12, 13--kaolin; 4--AMP; 5, 10--BS-30; 6, 7--whiting; 9--AM-2; 11, 14--quartz. Filler content, parts by we.: 4, 8, 9, 10-- 35; 2, 5, 7, 12, 14-- 50; 6, 11, 13-- 100; 3-- 150. Fillers of group 2, which are characterized by a low effect on the variation of internal energy in filling (Fig. 3) do not show either structure-forming, or inhibiting properties in elongation. This is confirmed by data of Fig. 4 (curves d, 8), from which it follows t h a t if Aerosil inhibits structure formation in a proportion of 9.9 vol. % (35 parts by wt.) (the gradient remains unchanged during cooling), AM-2 of high specific surface does not inhibit structure formation in a proportion of 12 vol % (35 parts by wt.) (the gradient increases from 0.7 × 10 -5 N/m~.deg at 120 ° to 1.5× 105 N/m2.deg at 80°). The gradient of thermo-elastic curves of samples containing lower proportions of fillers (Fig. 4, curves 5-14) is negative and practically agrees with the curve
Thermodynamics of high-elastic deformation of filled PVC
189
gradient for an unfilled sample, i.e. these fillers do not have an appreciable effect, at the concentrations studied, on structure formation of PVC during cooling. Let us try and answer the question concerning the type of structure formed during deformation, temperature variation and filling PVC. Figures 5 and 6 show values of f u l l for the compositions studied according to the degree of elongation for temperatures of 80 and 120 °. It can be seen that in the elongation range studied f u l l shows slight dependence on 2, but depends on the extent and form of the filler and temperature. f 1-
2
I'2
)t
O--
12 ~ ~ 13..~ ~
~ "
~-, .
.
Fio. 6. Dependence of f u l l on the degree of elongation at 120°: 1 (broken line)--without filler; 2--AMP; 3, 8--BS-30; 4--whiting; 5--AM-2; 6, //--quartz; 7, 13 -- aerosil A-175; 9, 10, 12--kaolin. Filler content, parts by wt.: 2, 5, 8, •3--35; 3, 7, 10, ••--50; 4, 6, 12--100; 9--150. It is of interest to determine temperature To, at which no change occurs in internal energy during the elongation of compositions. T o is found from dependences o f f u l l on 1 / T , which are straight lines. Table 2 shows T o values for the samples studied with 2 = 1.10, determined b y extrapolation of experimental straight lines to the axis of abscissae. Tabulated data only concern samples, for which the dependence of f in T is characterized b y a curvature; as noted previously, this points to structural changes in the temperature range examined. It can be seen from Table 2 that for an unfilled sample To----130°; for samples filled with Aerosil ~nd kaolin, it is higher than 130 ° and for samples filled with AM-2, AMP, BS-30, whiting and quartz powder, it is lower than 130 °, or close to it. Therefore, if we assume that on cooling samples below T o an ordered PVC phase is formed, it m a y be concluded that active polar fillers (Aerosil, kaolin)
190
V . V . GUZEYEV e$ al.
c o n t r i b u t e to t h e s t a r t o f s t r u c t u r e f o r m a t i o n , since T o for Aerosil a n d k a o l i n is h i g h e r t h a n T o for unfilled P V C a n d n o n - p o l a r fillers (AM-2, AMP, whiting) inhibit t h e s t a r t of s t r u c t u r e f o r m a t i o n since T o for t h e m is lower t h a n T o for a n unfilled sample. I t can be seen from Fig. 4 (curves 2-4) t h a t w i t h large a m o u n t s o f Aerosil a n d kaolin t e m p e r a t u r e v a r i a t i o n has a slight influence over s t r u c t u r a l changes in PVC.
As indicated previously [16], crystallinity of PVC on heating to 160 ° is practically unchanged. It is therefore logical to assume that in the temperature relationship shown in Fig. 4 a mesomorphous PVC phase exists [17]. TABLE 2. To VALUES OALCVI,A~ED FOR 2=1-10 Filler Without filler Aerosil A-175
Dehydrated kaolin
Silica filler BS-30
Modified Aerosil AMP
Modified Aerosil AM-2
Quartz powder
Chemically precipitated
Filler conteI~ parts b y wt. vol. %
0'5 3 25 3 25 5O 100 5 25 35 5O 5 25 35 5 25 35 3 25 100 3 25 5O 100
0.2 1-0
0'2 7.0 13.2 23.1 1.9 8'7 11.9 16.0 2.1 9.0 12-1 2-0 9-1 12'3 1-0 8"1 25"9 0"9 6'7 12"5 22'3
To° 130 137 149 142 161 166 148 175 126 126 129 123 114 ll4 107 118 118 121 123 138 123 132 121 130 121
I t follows from Fig. 4 t h a t the m e s o m o r p h o u s phase does n o t h a v e a specific melting p o i n t t y p i c a l o f the crystalline phase, however, there is a t e m p e r a t u r e (To) , above which it, a p p a r e n t l y , b e c o m e s disordered. This i n t e r p r e t a t i o n provides f u r t h e r i n f o r m a t i o n a b o u t PVC as a p o l y m e r with different levels of heterogeneity. T r a n s l a t e d by E. SE~P.E
Computer simulation of motion of macromolecules with crosslinks
191
REFERENCES 1. Yu. S. LIPATOV, Fizicheskaya khimiya napolnennyldl polimerov (Physical Chemistry of Filled Polymers). Izd. "Khimiya". 1977 2. P. J. FLORY, Principles of Polymer Chemistry, New York, 1953 3. R. L. ZAPP and E. GUTH, Industr. and Engng. Chem. 43: 430, 1951 4. E. L. WARRICK, J. Polymer Sci. 27: 19, 1958 5. A. V. GALANTI and L. H. SPERLINGZ, J. Polymer Sci. B8; 115, 1970 6. A. V. GALANTI and L. H. SPERLING, Polymer Engng. Sei. 10; 117, 1970 7. Yu. S. IAPATOV, V. V. GORICHKO and L. M. SERGEYEVA, Sintez i fizikokhimiya polimerov (poliuretany), Resp. mezhved, sb., 1977 8. V.V. GUZEYEV, ZHLI. SHKALENKO, Yu. M. M~LINSKII and V. A. KARGIN, Vysoko. mol. soyed. A13; 958, 1971. (Not translated in Polymer Sci. U.S.S.R.) 9. V. V. GUZEYEV, Zh. I. SKKALENKO and Yu. M. M~LINSKII, Sb. Struktura i svoistva poverldmostnykh sloyev polimerov (Structure and Properties of Polymer Surface Layers). Izd. "Naukova dumka", 1972 10. V. V. GUZEYEV, Zh. I. SHKALENKO, Yu. M. MALINSKII, Vysokomol. soyed. A17; 1843. 1975 (T-anslated in Polymer Sci. U.S.S.R. 17: 8, 2124, 1975) l l . E. GUTH, J. Appl. Phys. 16: 20, 1945 12. V. Y. GUZEYEV, D. N. BeRT and S. I. PEREDEREYEVA, Kolloidn. zh. 33; 349, 1971 13. M. V. VOL'KENSHTEIN, Yu. Ya. GOTLIR, Vysokomol. soyed. 1: 1063, 1959 (Translated in Polymer Sci. U.S.S.R. 1: 3, 385, 1970) 14. Yu. M. MALINSKII, Uspekhi khimii 39; 1511, 1970 15. V. V. GUZEYEV, M. N. RAFIKOV and Yu. M. MALINSKII, Vysokomol. soyed. A17: 804, 1975 (Translated in Polymer Sci. U.S.S.R. 17: 4, 923, 1975) 16. S. OTHA, T. KAgYOMA and M. TAKAYANAGI, Polymer Engng. Sci. 16: 465, 1976 17. E. V. GOUINLOCK, Polymer Prepints 15: 494, 1974
Polymer Science U.S.S.R. Vol. 23, ,N~o.1, pp. 191-203, 1981 Printed in Poland
0032-3950/81/010191-13507.50/0 © 1982 Pergamon Press Ltd.
COMPUTER SIMULATION OF THE MOTION OF MACROMOLECULES WITH CROSSLINKS* I. I, ROMANTSOVA
and Yr. A. T~_aAN
Institute of Mineral Fuels Institute of Volcanology DVNTs, U.S.S.R. Academy of Sciences
(Received 20 November 1979) An algorithm was proposed and formulated in this study for tile simulation of Brownian movement of macromolecules ~4th crosslinks using a simple lattice model of a polymer chain. The movement of crosslinks was effected by the transition of kinetic units containing from four to six combined units the transition being compati* Vysokomol. soyed. A23: No. 1, 171-180, 1981.
0032-8950/811010181-11807.5010 O 1982 Pergamon Press Ltd.
THERMODYNAMICS OF HIGH-ELASTIC DEFORMATION OF FILLED POLYVINYLCHLORIDE* V. V. GUZEYEV, ZH. I. SHKALENKO a n d ¥ u . M. M_AnrNsKn V. A. Kargin Scientific Research Institute of Chemistry and Polymer Technology L. Ya. Karpov Scientific Research Institute of Physico-Chemistry
(Received 20 November 1979) A study was made of the effect of a n u m b e r of fillers of different types and surface on thermodynamics of high-elastic deformation of PVC. I n their effect on thermodynamic stress components the fillers studied form two groups: 1--polar active filler influencing both energy and entropy stress components; 2--nonpolar filler which cause basically conformation changes in the polymer. I n small amounts with slight deformation fillers of group 1 contribute to structure formation of PVC, with high concentrations the filler "inhibits" structure formation. Fillers of group 2 do not influence process of structure formation during deformation of PVC. T ~ process of polymer elongation, particularly in the high-elastic state considerably changes t h e initial isotropic structure as a consequence of orientation capable of altering the thermo-
dynamic state of the polymer. As a result of adsorption interaction of its surface with the polymer the addition of a filler changes the mobility of polymers segments, which also influences the thermodynamic state of the polymer and the complex of physico-chemical and mechanical properties of t h e composition. Interaction of the polymer with the filler surface or adhesion between them is one of the major factors accounting for the reinforcement of polymers by fillers [1]. I t follows logically from the foregoing that it is advisable to examine thermodynamics of high-elastic deformation of filled polymers which together with studies of structure, mechanical and other properties contributes to a better understanding of processes of interaction of polymers with various fillers and of the effect of fillers on physico-mechanical properties of polymer compositions. Numerous studies have shown that the thermodynamic method of investigating polymer elongation provides extensive information in spite of the fact that giving an accurate quantitative description of structural changes during deformation in terms of entropy and internal energy does not always answer the problem of actual deformation mechanism. This is in no way a shortcoming of the method, merely a limitation typical of any experiment, b a s e d on thermodynamics. As noted by Flory, "the final aim of thermodynamic analysis is the compilation of quantitative characteristics, which may be interpreted physically, particularly in structural terms" [2]. The effect of filling on thermodynamics of deformation of polymers has been examined in comparatively few studies [3-7]; these are valuable, however, in so much as they try to link the mechanism of reinforcing rubber with fillers with their effect on the energy a n d entropy components of stress. * Vysokemol. soyed. A23: ~No. 1, 161-170, 1981. 181
1'82
V . V . GUZEYEV'et al.
The effect of filling and plasticization on thermodynamics of deformation of PVC has been studied by the authors of previous papers [8-10], who indicated that high-elastic deformation of PVC is of mixed entropy--energy type and that the addition of fillers and plasticization have a marked effect on ~he ratio of entropy and energy cor~aponents of stress. G'
5
8
(~, ~,~),I05, ~/m z
t.~ ~
I0
.
O
<>
¢3
20~t y),
.+t+
3 ° ~~ - - . - -
,
I
~Ao._. •
-.
zo - 1 -
e,~
I
350
400 T, K
-/0
FIG. 1
FIG. 2
FIe. 1. Typical thermoelastic curves of plasticized compositions (PVC: D D P = 2 : 1), containing 25 50 (9) and 150 parts by wt. filler Form of filler and extent of elongation: /--without filler 17%; 2--whiting 16.5%; 3--quartz 15.2%; 4--BS-30; 16.8% ; 5~-AMP 15.1%; 6--AM-2, 15-3°/o; 7--kaolin 22%; 8--Aerosil A-175, 14.7%; 9--aerosil A-1759"9~o; 10--kaolin 10.7~/o.
(2-8),
(10).
(1',
2")
FIG. 2. Variation of equilibrium stress (1, 2), entropy 2') and energy (1", components in elongation of plasticized compositions (PVC : D D P = 2 : l) with T = 8 0 ° without filler (1, 1"); with 7.4 vol. °/o Aerosil A-175 (2, 2',
1',
2").
I t was interesting to examine the effect on t h e r m o d y n a m i c s o f high-elastic d e f o r m a t i o n o f P V C o f fillers v a r y i n g in the t y p e a n d size of surface; this enabled some general relations to be derived governing the effect of phase i n t e r a c t i o n o n t h e r m o d y n a m i c s of d e f o r m a t i o n a n d m e c h a n i c a l properties of compositions b a s e d on PVC.
Thermodynamics of high-elastic deformation of filled PVC
183
Samples for investigating the effect of filling on thermo-elastic properties of compositions contained for 100 parts by wt. PVC 50 parts by wt. didecylphthalate (DDP), heat-stabilizers-7 parts by wt. dibasic lead phthalate and 1 part by wt. lead stearate, 0.3 part by wt. antioxidant (diphenylolpropane) and a varying amount of fillers. A list of fillers examined and some of their properties are shown in Table 1. In contrast with methods of deriving the dependence of equilibrium stress of PVC f on temperature described by us [8], the sensitivity of the angle of force measurement of the device was increased in this study, which revealed a curvature in the dependence o f f on T for unfilled and most filled samples (Fig. 1). Samples containing high concentrations of Aerosil A-175 and kaolin were exceptions. With an increase in filler concentration and elongation, thermo-elastic curves are displaced upwards along the stress axis and acquire a considerable gradient. The curvature of thermoelastic curves observed may mean that if elongation is carried out at high temperature, on cooling the elongated sample ordering takes place causing a further drop in internal energy and entropy, which is expressed in an increase in the gradient of thermo-elastic curves during cooling. It should be noted that all structural processes observed in these experiments are reversible. According to a former study [2], the gradient of tangents to thermo-elastic curves at certain temperatures gives a reduction of entropy in elongation, while intercepts by tangents on the stress axis when T : 0 ° K , give the variation of internal energy or enthalpy during elongation. As before [5, 6, 8], to calculate entropyfs and energy fu components of stress, thb following equations were used
f , : --T
fu= ~
\aLlv,~, v,~
\aT/p,a - -
~T p.x
(l)
,
(2)
where S, U, V, T, L, P, f are the entropy, internal energy, volume, temperature, length, external pressure and equilibrium stress of the elongated sample, respectively; ~:L/Lo, where L0 is the length of the lion-elongated sample at temperature T. The relative error in determining f was + 3% and in determining f, and f~+ 5%. Figure 2 shows a t y p i c a l p a t t e r n of the v a r i a t i o n of equilibrium stress a n d t h e r m o d y n a m i c c o m p o n e n t s in elongation of filled and unfilled PVC. A reduct i o n can be seen in b o t h cases in internal e n e r g y a n d e n t r o p y d u r i n g elongation; as s h o w n for unfilled PVC [10], this is due to processes o f orientation, s t r u c t u r e f o r m a t i o n a n d i n t r a m o l e c u l a r t r a n s i t i o n of gauche-trans-conformations of PVC macromolecules. L e t us examine the effect of filling on f, fs and fu. Dependences of f, f8 a n d fu on the degree of filling in d e f o r m a t i o n of samples b y 10% are shown in Fig. 3. True elongation of the p o l y m e r m a t r i x with these filling a n d d e f o r m a t i o n processes differs o n l y slightly from the elongation of the sample, which does n o t affect the results in question. Figure 3 shows t h a t equilibrium stress increases in filling using a n y of t h e fillers. Curve for f of samples with the whiting passes s o m e w h a t lower t h a n t h e
184
V. V. G u z ~ v
~.
~
D !
r~
©
oo
~,I ~"~1 @~I
o
~I
D
@,I
o
(D
,m
i
~.~ +~
~0 ~0
r~ o
o
o
r~
0
m
4~
k)I i o
q
ff.1 =. ~D
!
~D
~z ©
i
..~iil®-
Thermodynamics of high-elastic deformation of filled PVC
18~
relationship calculated from the Guth and Smallwood formula [11]
f=fo(1 ~- 2.5vu-~ 14. lv~)
(3)
(v~ being the volume fraction of the filler) up to a concentration of 15°/o and! with higher concentration f becomes higher than prescribed by formula (3). Curve for f for samples with quartz powder passes below the curve calculated using the Guth-Smallwood formula, while curves of f for samples with other fillers passes above the calculation curve, which is evidence of the distinct rSle of surface effects in increasing f during filling. Furthermore, Fig. 3 shows that fs and fu change during filling; in their effect on thermodynamic components of stress fillers may be divided into two groups: fillers influencing both the energy and entropy components of stress belong to the first group; fillers increasing entropy components and not affecting or slightly affecting the energy component are in the second group. Fillers of group 1--Aerosil and kaolin--are characterized by the existence of strong polar (silanol) groups on the surface and high or average specific surface. Fillers of group 2--whiting, AM-2, AMP, BS-30, quartz powder--are characterized either by the absence of polar groups on the surface, or in the presence of polar groups (quartz)--by low specific surface. BS-30 is an exception. The considerable effect of Aerosil and kaolin on fu and f8 proves that in the presence of these fillers PVC undergoes marked structure formation in elongation. Figure 3 also shows that changes in fu for Aerosil and kaolin and in fs for Aerosil are the greatest. It is obvious that with an Aerosil concentration o f 6-7% and a kaolin concentration of 20-25% some changes take place in elongation of filled samples. Deformation of PVC containing less than ~ 5% Aerosil or ~ 20°/o kaolin may, apparently, be regarded as elongation of the polymer. matrix containing separate filler particles with a boundary polymer layer immobilized b y the surface or separate agglomerates and short chains of these particles. With higher concentrations particles of these fillers, apparently, form either a three-dimensional chain structure (Aerosil), or a carcass (kaolin), in which boundary layers of the polymer around each particle combine into a sole polymer system immobilized by the surface of the filler. This pattern does not conflict with the electron-microscope structure of these compositions [12]. With an Aerosil or kaolin concentration higher than "critical" elongation of the sample results in deformation of boundary PVC layers which in turn produces disorder in macro-chains in the boundary layer, as confirmed by a change in the shape of internal energy curves, while for Acrosil, a change also in entropy curves. Thermodynamic data therefore suggest that PVC in boundary layers near the surface of Aerosil and kaolin particles is more ordered than thal far from the surface. Comparatively slight deformations of PVC studied in this experiment contribute to establishing dipole-dipole contacts between the polymer and filler with moderate concentration of the latter, which in turn contributes to
186
V.V. GUZEYEVet al.
:structure formation of the system shown in a sudden reduction of internal energy and entropy. This mechanism which explains the experimental dependence of internal energy and entropy variation in elongation on Aerosil and kaolin content, was briefly described by the authors previously [9]. Studying thermodynamics of deformation of polyurethanes filled with Aerosil A-175 Lipatov at al. [7] detected a similar course in the variation offu and f8 with Aerosil content; while analysing the results obtained the authors quoted the interpretation given by us [9] noting t h a t it is suitable for explaining the behaviour of filled polyurethanes. This agreement is important as it not only emphasizes the rSle of deformation in structure formation of the polymer on the surface of the polar filler, but also reveals the general nature of properties of boundary layers of two different classes of polymer near the surface with the same filler. In spite of an average degree of dispersion (Ssp----10 mS/g), kaolin has a very active influence on thermodynamics of elongation which, in addition to the high concentration of polar surface groups, m a y be due to the anisotropic planar structure of particles; this, apparently, contributes during the elongation of the sample to "adjoining" of macro-chains to the particle surface and their ordering in the boundary layer. Furthermore, orientation Of lamellar particles of kaolin along the axis of elongation produces an entropy orientation force [1], which has a further effect on increasing tensile stress in filling. This, is apparently, one of the causes of the high thermodynamic activity of kaolin. The mechanism proposed is confirmed by the variation in thermodynamic values for samples containing fillers of group 2. Depletion of silanol polar groups of the surface of Aerosfl or a marked reduction in their proportion during chemisorption of modifying agents (AMP and AM-2), or a reduction in the dispersion of the filler h a s the result t h a t filling has little effect on the variation of internal energy in elongation, and stress increase (or increase in the modulus of elasticity) when adding these fillers is basically due to processes related to conformation effect--geometrical limitation of space [1, 14]. The formation of boundary layers of "isoenergetic" fillers is evidently mainly of conformation entropy type. Regarding the effect of BS:30 on fu the following m a y be stated. It appears t h a t the addition of BS-30 of considerable specific surface results in a reduction of fu although to a lesser extent than the addition of A-175, but to a greater e x t e n t than the addition o f kaolin. However, as was shown previously [15], BS-30 particles being commensurate with inter-structural regions o f PVC, are wedged in them, weakening structural interaction. For this reason no further drop is observed in fu when filling using BS-30. Let us examine the change of f, fs and fu of elongated samples, with the content of AM-2. Figure 3 indicates t h a t at low concentrations ( ~ 2 %) small maximum (values are observed in the variation of f, f8 and fu, which are qualitatively similar to those observed for samples containing BS-30. Small amounts of AM-2 pene-
Thermodynamics of high-elastic deformation of filled PVC
187
trating the interglobular space, the same w a y as BS-30, apparently, have a dual function. On the one hand, AM-2 particles reduce structural interaction, screening purely geometrically polar groups of PVC, which lowers structure formation, i.e. reduces changes in fu and fs in elongation; on the other hand, AM-2 particles immobilize t h e boundary layer (which is, apparently, smaller than in the case of Aerosil); this, in the end, results in a greater increase in f than specified b y the Guth-Smallwood equation.
rs ,r.). loS, ~/,. z
G "
II
'//7
s'
e'
N/m~'d~s 2 (•-f)P"•1oS y
v
2.0-
1.5
2 0 i l l e G vol.% 30
0
-'2
,
~ 7"
3
"
~
~
1.0 ! 0.5 /q 80
FIG. 3
I00
120 7""
Fro. 4
FIG. 3. Effect of filler o n f (1-7), f, (1"-7') andfu (1"'-7") in elongation of plasticized compositions (PVC : DDP=2 : 1) with T=80 ° and 2=1.10; calculation curve according to the equation f=fo(l+2.Sv2+14.1 v~) (8). Fillers: Aerosil A-175 (1, 1', •"); AM-2 (2, 2', 2"); BS-30 (3, 3', 3"); kaolin (4, 4", 4"); AMP (5, 5', 5"); whiting (6, 6', 6"); quartz (7, 7', 7"). FIG. 4. Dependence on temperature of gradients (Of/OT)p,x of thermoelastic curves when 2= 1.10:1 (broken lme)--without filler; 2, 5, 6--kaolin; 3, 4--A-175; 7, 9--BS-30; 8--AM-2; 10, 12--quartz; 11, 13--whiting; 14--AMP. Filler content, parts by w~.: 4, 8, 9, •4--35; 3, 6, 7, 12, •3--50; 5, 10, 11--100; 2--150. As noted previously, the gradient of thermoelastic curves increases for most samples examined with reduction a of temperature, which points to an increase in processes of structure formation of elongated samples during cooling. Figure 4 shows gradients (~f/~T)p,~ of thermoelastie curves, according to temperature with a degree of elongation )~=1.01, while curves for filler concentrations < 10 vol. % are not given since in gradient they are similar to until-
188
V.V. GUZ~.YEVeta/.
led samples. It can be seen t h a t no increase in gradient typical of most thermoelastic curves occurs with a reduction in temperature for samples containing comparatively large amounts--9.9 (curve 4) and 13.6 vol. ~ (curve 3) Aerosil and 31.6 vol ~ (curve 2) kaolin. I n other words, in compositions containing active fillers (group 1) in quantities, when particles form a continuous three-dimensional structure and when a considerable part of polymer is in boundary layers, the polymer phase is unable to undergo structure formation on cooling the elongated sample (Fig. 4). Furthermore, studying Fig. 3 we noted t h a t structure formation decreases even during elongation when the composition contains considerable amounts of fillers and a large part of the polymer is immobilized by the surface of particles and structure formation in PVC, both during elongation and cooling is hindered~ i.e. the filler is in high concentrations an inhibitor of structure formation. /.1
/.2
it
f ~'--0
--[
0
0-'--"
--
9 , 1 0 ~ 12 . ~
~
~
~ +.,~
FIG. 5. Dependence of f,,/f on ghe degree of elongation at 80°: 1 (broken line)--withouV filler; 2, 8--aerosil A-175; 3, 12, 13--kaolin; 4--AMP; 5, 10--BS-30; 6, 7--whiting; 9--AM-2; 11, 14--quartz. Filler content, parts by we.: 4, 8, 9, 10-- 35; 2, 5, 7, 12, 14-- 50; 6, 11, 13-- 100; 3-- 150. Fillers of group 2, which are characterized by a low effect on the variation of internal energy in filling (Fig. 3) do not show either structure-forming, or inhibiting properties in elongation. This is confirmed by data of Fig. 4 (curves d, 8), from which it follows t h a t if Aerosil inhibits structure formation in a proportion of 9.9 vol. % (35 parts by wt.) (the gradient remains unchanged during cooling), AM-2 of high specific surface does not inhibit structure formation in a proportion of 12 vol % (35 parts by wt.) (the gradient increases from 0.7 × 10 -5 N/m~.deg at 120 ° to 1.5× 105 N/m2.deg at 80°). The gradient of thermo-elastic curves of samples containing lower proportions of fillers (Fig. 4, curves 5-14) is negative and practically agrees with the curve
Thermodynamics of high-elastic deformation of filled PVC
189
gradient for an unfilled sample, i.e. these fillers do not have an appreciable effect, at the concentrations studied, on structure formation of PVC during cooling. Let us try and answer the question concerning the type of structure formed during deformation, temperature variation and filling PVC. Figures 5 and 6 show values of f u l l for the compositions studied according to the degree of elongation for temperatures of 80 and 120 °. It can be seen that in the elongation range studied f u l l shows slight dependence on 2, but depends on the extent and form of the filler and temperature. f 1-
2
I'2
)t
O--
12 ~ ~ 13..~ ~
~ "
~-, .
.
Fio. 6. Dependence of f u l l on the degree of elongation at 120°: 1 (broken line)--without filler; 2--AMP; 3, 8--BS-30; 4--whiting; 5--AM-2; 6, //--quartz; 7, 13 -- aerosil A-175; 9, 10, 12--kaolin. Filler content, parts by wt.: 2, 5, 8, •3--35; 3, 7, 10, ••--50; 4, 6, 12--100; 9--150. It is of interest to determine temperature To, at which no change occurs in internal energy during the elongation of compositions. T o is found from dependences o f f u l l on 1 / T , which are straight lines. Table 2 shows T o values for the samples studied with 2 = 1.10, determined b y extrapolation of experimental straight lines to the axis of abscissae. Tabulated data only concern samples, for which the dependence of f in T is characterized b y a curvature; as noted previously, this points to structural changes in the temperature range examined. It can be seen from Table 2 that for an unfilled sample To----130°; for samples filled with Aerosil ~nd kaolin, it is higher than 130 ° and for samples filled with AM-2, AMP, BS-30, whiting and quartz powder, it is lower than 130 °, or close to it. Therefore, if we assume that on cooling samples below T o an ordered PVC phase is formed, it m a y be concluded that active polar fillers (Aerosil, kaolin)
190
V . V . GUZEYEV e$ al.
c o n t r i b u t e to t h e s t a r t o f s t r u c t u r e f o r m a t i o n , since T o for Aerosil a n d k a o l i n is h i g h e r t h a n T o for unfilled P V C a n d n o n - p o l a r fillers (AM-2, AMP, whiting) inhibit t h e s t a r t of s t r u c t u r e f o r m a t i o n since T o for t h e m is lower t h a n T o for a n unfilled sample. I t can be seen from Fig. 4 (curves 2-4) t h a t w i t h large a m o u n t s o f Aerosil a n d kaolin t e m p e r a t u r e v a r i a t i o n has a slight influence over s t r u c t u r a l changes in PVC.
As indicated previously [16], crystallinity of PVC on heating to 160 ° is practically unchanged. It is therefore logical to assume that in the temperature relationship shown in Fig. 4 a mesomorphous PVC phase exists [17]. TABLE 2. To VALUES OALCVI,A~ED FOR 2=1-10 Filler Without filler Aerosil A-175
Dehydrated kaolin
Silica filler BS-30
Modified Aerosil AMP
Modified Aerosil AM-2
Quartz powder
Chemically precipitated
Filler conteI~ parts b y wt. vol. %
0'5 3 25 3 25 5O 100 5 25 35 5O 5 25 35 5 25 35 3 25 100 3 25 5O 100
0.2 1-0
0'2 7.0 13.2 23.1 1.9 8'7 11.9 16.0 2.1 9.0 12-1 2-0 9-1 12'3 1-0 8"1 25"9 0"9 6'7 12"5 22'3
To° 130 137 149 142 161 166 148 175 126 126 129 123 114 ll4 107 118 118 121 123 138 123 132 121 130 121
I t follows from Fig. 4 t h a t the m e s o m o r p h o u s phase does n o t h a v e a specific melting p o i n t t y p i c a l o f the crystalline phase, however, there is a t e m p e r a t u r e (To) , above which it, a p p a r e n t l y , b e c o m e s disordered. This i n t e r p r e t a t i o n provides f u r t h e r i n f o r m a t i o n a b o u t PVC as a p o l y m e r with different levels of heterogeneity. T r a n s l a t e d by E. SE~P.E
Computer simulation of motion of macromolecules with crosslinks
191
REFERENCES 1. Yu. S. LIPATOV, Fizicheskaya khimiya napolnennyldl polimerov (Physical Chemistry of Filled Polymers). Izd. "Khimiya". 1977 2. P. J. FLORY, Principles of Polymer Chemistry, New York, 1953 3. R. L. ZAPP and E. GUTH, Industr. and Engng. Chem. 43: 430, 1951 4. E. L. WARRICK, J. Polymer Sci. 27: 19, 1958 5. A. V. GALANTI and L. H. SPERLINGZ, J. Polymer Sci. B8; 115, 1970 6. A. V. GALANTI and L. H. SPERLING, Polymer Engng. Sei. 10; 117, 1970 7. Yu. S. IAPATOV, V. V. GORICHKO and L. M. SERGEYEVA, Sintez i fizikokhimiya polimerov (poliuretany), Resp. mezhved, sb., 1977 8. V.V. GUZEYEV, ZHLI. SHKALENKO, Yu. M. M~LINSKII and V. A. KARGIN, Vysoko. mol. soyed. A13; 958, 1971. (Not translated in Polymer Sci. U.S.S.R.) 9. V. V. GUZEYEV, Zh. I. SKKALENKO and Yu. M. M~LINSKII, Sb. Struktura i svoistva poverldmostnykh sloyev polimerov (Structure and Properties of Polymer Surface Layers). Izd. "Naukova dumka", 1972 10. V. V. GUZEYEV, Zh. I. SHKALENKO, Yu. M. MALINSKII, Vysokomol. soyed. A17; 1843. 1975 (T-anslated in Polymer Sci. U.S.S.R. 17: 8, 2124, 1975) l l . E. GUTH, J. Appl. Phys. 16: 20, 1945 12. V. Y. GUZEYEV, D. N. BeRT and S. I. PEREDEREYEVA, Kolloidn. zh. 33; 349, 1971 13. M. V. VOL'KENSHTEIN, Yu. Ya. GOTLIR, Vysokomol. soyed. 1: 1063, 1959 (Translated in Polymer Sci. U.S.S.R. 1: 3, 385, 1970) 14. Yu. M. MALINSKII, Uspekhi khimii 39; 1511, 1970 15. V. V. GUZEYEV, M. N. RAFIKOV and Yu. M. MALINSKII, Vysokomol. soyed. A17: 804, 1975 (Translated in Polymer Sci. U.S.S.R. 17: 4, 923, 1975) 16. S. OTHA, T. KAgYOMA and M. TAKAYANAGI, Polymer Engng. Sci. 16: 465, 1976 17. E. V. GOUINLOCK, Polymer Prepints 15: 494, 1974
Polymer Science U.S.S.R. Vol. 23, ,N~o.1, pp. 191-203, 1981 Printed in Poland
0032-3950/81/010191-13507.50/0 © 1982 Pergamon Press Ltd.
COMPUTER SIMULATION OF THE MOTION OF MACROMOLECULES WITH CROSSLINKS* I. I, ROMANTSOVA
and Yr. A. T~_aAN
Institute of Mineral Fuels Institute of Volcanology DVNTs, U.S.S.R. Academy of Sciences
(Received 20 November 1979) An algorithm was proposed and formulated in this study for tile simulation of Brownian movement of macromolecules ~4th crosslinks using a simple lattice model of a polymer chain. The movement of crosslinks was effected by the transition of kinetic units containing from four to six combined units the transition being compati* Vysokomol. soyed. A23: No. 1, 171-180, 1981.