Volume relaxation in filled polystyrene

VOLUME RELAXATION IN FILLED POLYSTYRENE* V . P . PRIVAT,~O, S. S. I)EMCHENKO, Y u . D. BESKLUBEI~KO a n d Y u . S. LIPATOV High Polymer Chemistry Institute, Ukr.S.S.R. Academy of Sciences

(Received 29 November 1976) The restoration of the volume after sudden removal of pressure from bulk polystyrene (PS) samples containing 0, 5, 20, or 50 wt.% glass powder as filler was studied. The vohune relaxation could not be quantitatively described within the limitations of the existing phenomenological theories. Addition of filler has been found to lead to a noticeable inhibition of the relaxation processes in the polymer at fairly high temperatures, b u t reduction of temperature to Tg greatly reduced the difference owing to the smaller temperature dependence of the activation energy of relaxation in filled samples when compared with that of the unfilled; the latter is assumed to be explainable b y the decrease of the characteristic parameter To in the ¥ o g e l - T a i n m a n equation, which is defined as the temperature at which the residual free volume disappears on adding the filler. The result is t h a t the bulk viscosity of the unfilled PS is similar to t h a t of the filled at the Tg, i.e. about (2-5) × 1014 poise.

TB-E observations of the volume relaxation of a polymer is known to provid~ information [1] about the type of structural rearrangement which is accompanied b y the change of the substance from the non-equilibrium to the equilibrium state after a sudden change of one of the thermodynamic parameters (temperature T or pressure P) while the other remains constant. Kinetic studies of t h e cubic relaxation on amorphous polymers in the Tg range, after the temperature jump AT had taken place, showed t h a t the filler addition results in a slowing down of the relaxation processes [2]. The effect of fillers on relaxation after a zip jump has not been examined so far, although it is known that the type o f the relaxation processes in unfilled polymers differs from t h a t to be found after

LiT [3-5]. EXPERIMENTAL The samples used were the type D atactic bulk polystyrene (GOST 9440-60) batch containing 0, 5, 20 or 50 w t . % of glass powder as filler (consequently called PS-0, PS-5 etc.). The average particle size of the filler was 2 pm the preparation method of the samples was described before [6]. The measurements were made on the apparatus working on the principle described in the paper b y Martinyuk and Semenchenko [7], which is illustrated in Fig. 1. The 12-16 m m high polymer sample I is placed into the pressure chamber consisting of sleeve 2 of 8.53 m m int.dia., piston 3 and test tube 4, and the whole assembly is * Vysokomol. soyed. A19: No. 8, 1763-1769, 1977. 2016

Volume relaxation in filled polystyrene

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seated in the opening of oil thermostat 12, connected to au ultra-thermostat 1-10 by moans of screw 11. The stress is applied by piston 3 through an annealed and polished shoot 6, which is fitted on support 5, on which rests a small sphere 7. The force of compression is regulated by the use of weight 8. The sample volumes wore determined at various pressures a n d temperatures from the height indicated by arrow 10 (on a 10 -a m m scale of divisions) which rests on the support surface 9, which is rigidly attached to piston h e m 3. T h e normal working of the indicating arrow is ensured by a water-cooling system 14. Th e sample temperature is measured by a thermocouplo (chromel-Kopol) 15, situated at halfheight of the sample and the determination accuracy w~s -t-0.5°C (16--axis, 17--bearing, 1 8 - - stand, 19 -- thormocouplo).

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FIG. 1. Sketch of the experimental apparatus (see text).

I n order to eliminate any effects of the thermal or mechanical history of sample on t h e relaxation properties, we made use of the following experimental scheme: the test sample was heated to 160-165°0 at which it was kept under nominal pressure P o x 162 kg/om 2 for 15 min, followed by applying the required pressure P1 for the next 15 min, and then cooling a t a 1-2°C/rain rate at P l = c o n s t until the measurement temperature was attained. I n addition the sample was kept under isobaric-isothermal conditions for 15 rain and the pressure was then rapidly reduced to P0 while following the height changes as a function of time. Overflow losses of the polymer from the pressure chamber were checked by measuring t h e sample height after a second heating to 160°C, but also by weighing after the completion o f the experiment.

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V . P . P~AT,I~O S~ ~ . RESULTS

Typical curves of the volume reduction of sample PS-0 at various temperatures a f t e r A p = 140 a n d 280 kg]cm =are shown as examples in l~ig. 2; they are plotted in (v--voo)]v®-log coordinates [1] (v, v=--specific volumes of the sample at time + a n d at + ~ o0 respectively). Similar diagrams were drawn for all the other samples. The cubic relaxation curves of t h e :PS can be seen to have a typically sigmoid shape with a more or less long linear part at t h e

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l+zo. 2. Volume reduction curves for sample PS-0 at ziP: a--140; b--280 kg]cm = a n d tem* peratures of: a: 1--109.5; 2--112.5; 3--114.5; 4--116; 5-- 119.5°C. b: 1--109; 2--114; 3--117; 4--119; ~--124°C. The full lines were calculated from eqn. (1) and the results given in t h e text for temperatures of (°C): 1'--109.5; 2'--112.5; 3'--114.5.

inflexion point. The t a n g e n t angle at inflexion point X is shown on the temperature depend+ ence diagram reproduced in Fig. 3. One can see t h a t a zip increase results in a steady increase of X which is typical for the non-linear viscosity range [1, 4, 5, 8]. The X-values increase linearily at the start as a function of temperature until limit T ' is reached, after which there is a rapid drop of the T-Z dependence (Fig. 3). Kovacs [9] had shown the latter to be usually linear in the region of the glass-like state. On this basis one can assume t h e temperature T ' a t which the X-T "flattens" to be the T= of the polymer at pressure P0This conclusion was qualitatively confirmed by the following observations.

Volume relaxation in filled polystyrene

2019

1. The relaxation curves got at T < T ' do not reach the equilibrium of specific volume vm during the experimentation time (Fig. 2). 2. A pressure reduction from P1 to P0 is accompanied b y a sudden decrease of the sample height h at T > T ' and an h-increase at T < T ' , while there is no change of h at T ~- T' (Fig. 4). Special experiments with a thermocouple immediXxl/? s

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FIG. 3. Diagram of the parameter ;¢ as a function of temperature for samples of: 1, I'--PS-0; 2, 2'--PS-5; 3'--PS-20; 4, d'--PS-50, at ziP, kg/cm2: 1, 2, 4--140; 1'-4'--280. Fro. 4. The temperature dependence of the height difference for: a--PS-0; b--PS-50 a~ LIP, kg/cm2: 1-- 140; 2--280.

ately inside the sample showed that a sudden pressure reduction results in an instantaneous temperature drop of the sample b y several °C, after which it rises again to its original value. The detected negative jump of h at T < T ' is explained b y a rapid rate of advance of the adiabatic cooling front in the rigid, glass-like matrix after a sudden pressure removal. 3. The relaxation curves can be made to coincide in the T > T ' region b y shifting along the log t axis (Fig. 2), and this is characteristic of the polymer in the highly elastic state [5]. (Our results were unfortunately not numerous enough to verify the temperature-time superimposition in greater detail). The enumerated findings allowed the estimation of T ' ~ T g of the studied samples with a :t:2°C error; they are given in Table 1. Please note that the values

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V . P . PRIVAI.,KOet al.

d o not agree as expected with those of Tg found at P = 1 6 2 kg]cm ~ determined under isochorous cooling conditions [6]. This result is the natural consequence of the glass-like polymer structure depending on the mechanical and thermal history of the sample. An analysis of the shape of the produced relaxation curves showed the volume reduction kinetics after the zip jump not to be an exponential function (v-roe)] /(Vo-Voo)=exp(--t/z), which would predict a linear dependence of log (v-v~o)/ /(%-v oo)on t [1] (v0 is spec. volume of sample at t = 0 ; z, relaxation time). Generally :speaking, this result is not unexpected because the ratio (v-voo)/voo as a function of log t being linear in the region of the inflexion point. Such a shape of the cubic relaxation curve is normally associated with the presence of a relaxation time spectrum [5, 9], or a spectrum of activation energies [10], but Kovacs [1] stated t h a t it could also be the result of non-linearity. The kinetics of the volume reduction must be described in this case by [1]:

/~i ( - r e ) - Ei ( - v ) = (t-to)/~,

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i n which Ei(--Vo) and Ei(--v) are integral functions [11], vo=KJ/l,t(vo--V~o)/Voo , and r=K2Mcc(v--voo)/Voo; A~ is the difference between the thermal expansion coefficients above and below the Tg; K2, parameter linked with the free volume. The values of the parameters in eqn. (1), determined from the experimental results for PS-0 at A P = 1 4 0 kg/cm ~ in accordance with the Kovacs [1] recommendations, are contained in Table 2. The theoretical relaxation curves for PS-0 calculated from eqn. (1) for some *emperatures, using the data given above, and z values corresponding to the irdtexion point of the experimental isotherms, are reproduced in Fig. 2. I t is easy to see t h a t the "autocatalysed" volume increase predicted by eqn. (1) is far superior to t h a t detected by experiment. A better agreement of the experimental and theoretical isotherms can be obtained by calculating the latter when t h e z values used were more t h a n a factor of ten larger t h a n the experimental. A similar conclusion can be reached also as regards the correlations of the relaxation isotherms for other samples. The results of the analysis made here thus show t h a t the experimentally found cubic relaxation curves for PS without and with filler cannot be quantitatively described within the framework of the phenomenological theories existing at present. The available findings however permit a qualitative assessment of the effect of the filler on the temperature dependence of the relaxation rate in the studied system. The temperature dependence of the most probable relaxation period Zo determined by the standard method [12] as the period in which the deformation dropped by a factor e when compared with the initial is illustrated in Fig. 6. The found dependences for all the samples, with the exception of the unfilled PS at A P = 2 8 0 kg/cmL are well approximated by straight lines, although t h e y a r e known to be non-linear [5, 13] for other visco-elastic properties of polymers

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Volume relaxation in filled polystyrene

near the Tg. This state of affairs appears to-be due in our case to the determinations having been made in a relatively narrow temperature range. The activation energies of the cubic relaxation, AE, determined from the slope of the plotted lines (Fig. 5), are listed in Table 1, which also gives the 30 values and the cubic Io~ "~ [sec 7 lZ

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Fifi. 5. The temperature dependence of log v for: a - - P S - 0 ; b--PS-5; c--PS-20; d - - P S - 5 0 a t AP, kg/cm2: 1--140; 2--280. The vertical lines in the diagram show the width of t h e linear parts on the relaxation curves.

viscosity coefficient at Tg (30, g and ~/v,g respectively), which were calculated from ~/v, g----30, g/Aft [1]. The numerical values of the isothermal compressibility factor Aft below and above the Tg as the difference (Table 1) were taken from earlier work [6]. Our results show that the values of ~/v g fall into the range (1.5-4-7) × 1014 poise for all the systems and are thus at least one power of ten above the "universal" shear viscosity of liquids at the Tg [5, 13]. One also notices that the 30, g (and correspondingly the ~]v g) tend to increase as AP increases. The calculated ~v, g also drop at the start on changing from the pure to the filled polymer samples, a n d then increase again (Table 1). These differences must be regarded as small however, when one remembers the uncertainty of the used T~ values (see above). Our results appear to permit the assumption that the cubic viscosity of all the studied systems is approximately of the same order at the T~, i.e. (2-5)× 1014 poise. This conclusion appears at first glance to contradict a fairly large number of data [14-18], according to which filler addition results in a large increase in shear viscosity (i.e. of the structural relaxation p e r i o d s ) o f polymer melts. The detected reduction of the activation energy of volume relaxation after addition

V.P. P~rVATXOeta/.

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of filler (Table 1) also disagrees with the activation energy of shear viscosity usually found in pure and filled polymers [17]. One can show however t h a t these contradictions are easily eliminated b y the following arguments. The activation ~nergy of the relaxation process is known to be generally described b y the equation [13, 18]:

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dE=lOB [T/(T-- To)]z,

in which B and To are parameters of the Vogel-Tamman equation [5, 13, 18]; R, gas constant. As eqn. (2) shows, d E can drop as a result of either B or T~ decreasing when Tg values are similar (which is the case here). As the energy TABLE 1. T H ~ VALUE RELAXATION PARAMETERS OF lrILLED P S

Sample PS-0 PS-5 PS-20 PS-50

105, cm/kg

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°C

113 112 -114

160 (170) 75 (100) - (200) 250 (300)

(117) (115) (113) (114)

1.51 2.02 3.15 4.00

t/K × 10 t~,

poise 4.45 (4.70) 1.55 (2.05)

JE, kcal/molo 132 (--) 105 (89)

- - (2.65)

- - (83)

2.62 (3.15)

105 (95)

.Vote. The brackets contain the results at ~P=280 kg/cm'.

parameter B tends to increase as the filler content increases [18], it can be assumed t h a t the detected decrease in AE is due in filled systems to a decrease in To. This assumption was confirmed b y the results of analysing the thermodynamio properties of the studied systems [6], according to which an increase of the glass TABLE 2. EQUATION (I)PARAMETERS

T, °C

--(vo--v~o)/vo~

Z--re

Ks/A~× 10-I

109"5 112"5 114.5 116"0 119"5

2"40 1"84 1"51 1"39 1"22

3.45 1.96 0.99 0-70 0.13

10.25 5-35 3.09 1.86 0.40

Kl× l0 s, dog-1. 32-30 16.85 9-75 5.86 1.28

* Calculated for A~=8.15 × 10-' deg-* [6].

powder content in PS leads to a steady (regular) decrease of the Gibbs-DiMarzio theoretical parameter T2 [19], which in its physical meaning is equivalent t o T O [13]. A T O reduction with increasing filler content was also observed b y u s during the viscosity study of filled oligo-ethcr melts [18], so that one can say t h a t this t y p e of T O change is common to filled amorphous polymers. I f one considers that the viscosity of pure and filled polymers is approximately the same at the Tg (see above), a temperature increase to T>>Tg must produce larger viscosities of the filled polymers owing to the lower temperature dependence

Vohune relaxation in filled polystyrene

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of AE, as is clearly illustrated by Fig. 6. Furthermore, the "current" activation energy of viscous flow (or of the relaxation process) must be the same at fairly high temperatures (Fig. 6). The presented thoughts are in complete qualitative accord with the experimental findings of our work and with those given in t h e literature [14-18].

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Fro. 6. Theoretical temperature-viscosity curves for: /--unfilled; 2--filled polymers. The volume relaxation in unfilled and filled PS thus cannot be quantitatively described within the existing framework of phenomenological theories at the T~. The filler addition results in a noticeable inhibition of the relaxation processes at sufficiently high temperatures, but a reduction to the Tg minimizes these differences owing to the smaller temperature dependence of the activation energy of relaxation of the filled samples, which is assumedly explainable b y a decrease of the T O in the Vogel-Tamman equation when the filler is added. The viscosity of pure and filled PS is therefore much the same at the Tg, namely about (2-5) × 1014 poise. Translated by K . A. ALI~I~

REFERENCES

'~. A. J. KOVACS, Fortsch. Hochpol. Forsch. 3: 394, 1964 2. Yu. S. LIPATOV, Fiziko-khimiya napolnermykh polimerov (The Physical Chemistry of Filled Polymers). Izd. "Naukova dumka", 1967 3. T. E. •ELLER, Dissertation, 1968 4. G. REHAGE and W. BORCHARD, Physics of Glassy Polymers, edited by R. N. Haward, 54, London, 1972 5. J. D. FERRY, Viscoleastic Properties of Polymers, 2nd e4., 574, Wiley, 1970 6. V. P. P~RIVALKO, Yu. D. BESKLUBENKO, Yu. S. LIPATOV, S. S. DEMCHENKO,

and G. I. ~ L E N K O , Vysokomol. soyed. AI9: 1744, 1977 (Translated in Polymer Sci. U.S.S.r. 19: 8, 1977) 7. M. M. MARTINYLrK and V. K. SEMENCHENKO, Kolloid. Zhur. 26: 83, 1964 8. V. P. PRIVALKO, Yu. D. BESKLUBENKO, Yu. S. LIPATOV and S. S. DEMCHENKO~

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9. 10. 11.

12. 13. 14. 15. 16. 17. 18. 19.

A. A. RAKHNYAMSKAYAe$ al.

Sb.: Fizicheskie i fiziko-khimicheskie svoistva polimerov (In: The Physical and P h y sico-ehemlcal Properties of Polymers). Izd. " N a u k o v a d u m k a " , 1977 A. J. KOVACS, J. P o l y m e r Sei. 30: 131, 1958 R. M. KIMiWEL and D. R. U H ~ , J. Appl. Phys. 40: 4254, 1969 G. KORN and T. KORN, Spravochnik po m a t e m a t i k e d l y a n a u c h n y k h rabotnikov i inzhenerov (Mathematical H a n d b o o k for Scientists and Engineers). 21, Izd. "l~auka", 1968 L V. RADCHENKO, Molekulyarr~aya fizika (Molecular Physics). ch. 15, " N a u k a " , 1965 G. C. BERRY and T. G. FOX, Adv. Polymer Sci. 5: 261, 1968 G. KRAUS, Editor, Usilenie elastomerov (The Reinforcement of Elastomers). Izd. " K h i m i y a " , 1968 G. M. BARTNEV and N. V. ZAKHARENKO, Kolloid. Zhur. 24: 121, 1962 P. P. A. SMIT, Theol. A c t a 8: 277, 1969 G. KRAUS, ~ u b b e r Chem. and Teetmol. 38: 1070, 1965 Yu. S. LIPATOV, V. P. PRIVALKO and V. F. SHUMSKII, Vysokomol. soyed. A15: 2106, 1973 (Translated in P o l y m e r Sei. U.S.S.I~. 15: 9, 2386, 1973) J. H. GIBBS and E. A. DiMARZIO, J. Chem. Phys. 28: 373, 1958

'THE REACTIVITIES OF THE OXIME GROUPS IN 4-VINYL- AND 2 - M E T H Y L - 5 - V I N Y L P Y R I D I N E C O P O L Y M E R S WITH THEIR N-PHENACYLOXIME DERIVATIVES* A. A. I~AKHIWYAI~SKAYA,Yu. E. Kn~s~ and V. A. KABANOV M. V. Lomonosov State University, Moscow

(Received 30 November 1976) The acylation kinetics of the oxime group present in pply-4-vinylpyridine a n d ~poly-2-methyl-5-vinylpyridine p a r t l y quaternized with bromophenacyloximo have been studied. A considerable increase in the nueleophilicity of the oxime groups p r e s e n t in the copolymers has been detected when t h e y were compared with the res p e c t i v e low molecular weight analogues; it was accompanied b y an anomalous p K a reduction. We also show t h a t the rate constant for acylation decreases in t h e copolymers with the quaternization efficiency of the polymer; in contrast with the low molecular weight analogues it also strongly a n d exclusively depends on the concentrat i o n of various low molecular weight salts present in the reaction mixture. All these effects are due to a large extent to t h e influence of the micro-environment a n d t h e electrostatic reaction of the pyridine, having a positive charge with the oximo with its negative charge. * Vysokomol. soyed. A19: No. 8, 1770-1779, 197 7.