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Volume Relaxation in Amorphous Polymers Around Glass-Transition Temperature

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Volume Relaxation in Amorphous Polymers Around Glass-Transition Temperature Polymer Journal, Vol. 10, No. 2, pp 161-167 (1978) Volume Relaxation in Amorphous Polymers around Glass-Transition Temperature Masataka Ucmnor, Keiichiro ADACHI, and Yoichi IsHIDA Department of Polymer Science, Faculty of Science, Osaka University, Toyonaka, Osaka, 560 Japan. (Received June 15, 1977) ABSTRACT: Relaxation of volume, enthalpy, and dielectric polarization have been studied for poly(vinyl acetate) and polystyrene around a glass-transition point. It has been concluded that the correlation time of micro brownian motion in glassy polymers shifts with time during the period of volume relaxation. The time dependence of dielectric relaxation time rn has been represented approximately by log rn=a log t-b where a and b denote constants. By application of this equation to the volume and enthalpy relaxation processes, the time dependence of the specific volume V(t) or enthalpy H(t) can be represented in the form V(t)- V(oo)=ct-B where Band c are constants. The values of B for the volume relaxation agree well with those for the enthalpy. KEY WORDS: Volume Relaxation I Dielectric Relaxation I Enthalpy Relaxation I Poly( vinyl acetate) I Polystyrene I Glassy State I The glass-transition temperature Tg of amor­ styrene6 and analyzed the results in terms of phous polymer is the temperature at which the cor­ Bueche's theory. 7 However these authors could relation time ofmicrobrownian motion is measured not satisfactorily explain the difference among in experimental scale. Below Tg, the internal state relaxation curves measured after being subjected is usually not in equilibrium on account of the to different thermal histories. prolonged relaxation time. 1 ' 2 If a polymer is The correlation time for microbrownian motion allowed to stand long enough even at a temperature has been generally related to free volume as pro­ below Tg, its internal state will approach equili­ posed by Doolittle.8 On the other hand, Adam brium gradually accompanied by variation of ther­ and Gibbs expressed the correlation time as a modynamic quantities such as volume, enthalpy, function of configurational entropy and tempera­ etc. Study of volume relaxation is essential for ture. 9 From these theories, we can infer that understanding the glass transition and the glassy the correlation time depends not only on tempera­ state of amorphous polymer. ture but also on the internal state. The relaxa­ Volume relaxations of polystyrene and poly­ tion time in the volume relaxation process would (vinyl acetate) were studied by Kovacs, who vary with specific volume due to feedback effect as showed the volume relaxation curves measured at indicated by Kovacs. 4 different temperatures are superposable. 3 He The purpose of the present study is to clarify explained the shape of the curves assuming that the how the relaxation time depends on time and also relaxation time depends not only on temperature to formulate the volume relaxation curve as a but also on free volume fraction. 4 Goldstein and function of time. Also the relaxations of different Nakonecznyj studied volume relaxation on zinc thermodynamic quantities are compared. Thus chloride and tried to explain the data in terms of the the volume and enthalpy relaxations have been wide distribution of relaxation time. 5 Hozumi measured on poly(vinyl acetate) and polystyrene. et al., also measured volume relaxation of poly- In order to investigate the time dependence of 161 M. UCHIDOI, K. ADACHI, andY. ISHIDA correlation time of microbrownian motion, we were 43° and 103°C, respectively, determined by a measured the shift of dielectric relaxation time in differential scanning calorimetry at the heating the course of the volume relaxation. rate of 10°Cjmin. Films for dilatometric measure­ A similar dielectric study just below glass ments with a thickness of about 0.5 mm were transition point has already been made by Kastner obtained by pressing the bulk PVAC and PS who showed that the dielectric loss factor cor­ samples, respectively, at 140° and 200°C under a responding the tail of the loss peak decreased vacuum of 10-2 torr. Bubble-free portions of the gradually with volume relaxation. 10 However, films were cut into pieces of 0.5-cm square and he could not observe a shift in the loss peak since used for the measurement. he measured at a relatively high-frequency range. Dilatometry We cannot judge from his data whether the loss Dilatometer is schematically shown in Figure 1. peak actually shifted to a lower frequency or the The area of the cross section of capillary was magnitude of dispersion decreased with the volume 2.70±0.05 x 10-3 cm2 • The amount of the PVAC relaxation as claimed by Williams11 and Saito and and the PS sealed in dilatometers were 2.779 and 12 Nakajima. In this study, we have carried out 6.070 g, respectively. After the specimens were dielectric measurements in a low-frequency range sealed in a dilatometer, they were degassed under a where we can observe the loss peak. A study of vacuum of 10-5 torr for ten hours at l20°C for the the mechanical relaxation in the course of volume PV AC and 220°C for the PS. The fluctuation of relaxation was reported by Kovacs, et al. 13 They temperature in a bath was regulated within showed that tan o for shear deformation varied ±0.1 oc. The specific volume was measured with time below the glass-transition point. How­ pycnometrically at 27°C. ever, they did not explicitly show the time de­ pendence of the relaxation time. Dielectric Measurement Dielectric measurements in the ultra low­ EXPERIMENTAL frequency region were performed by means of the transient current method using an electrometer Samples model 640 (Keithley, Ohio). Transient currents Poly(vinyl acetate) (PV AC) waspr epared by measured from 2 to 3 x 105 sec have been trans­ radical polymerization in methanol at 60°C using formed into the cmplex dielectric constant c:* by azobisisobutylonitrile as the initiator. The polymer was recovered from the reaction mixture c:*-c:oo=--1 t ) e iwtdt (1) by precipitating in an excess of petroleum ether CoE o under vigorous stirring and was dried under a where w, C0 , E, and J(t) denote angular frequency, vacuum of 10-2 torr for several days. Polystyrene the capacitance of the empty condenser, applied (PS) was a commercial sample (Dow Chemical voltage, and transient current respectively. In Co.) purified by precipitating in methanol from this transformation, I(t) in the region of less than benzene solution. The viscosity-average molec­ 2 sec and that longer than 3 x 105 sec have been ular weights of the PVAC and the PS samples were estimated by exponential extrapolation. The 2.5 x 105 and 1.0 x 10\ respectively. The glass­ calculation was performed with an electronic transition temperatures of the PVAC and the PS computer. Since a time scale of t sec corresponds mm-------i' ! <X: n;) 2,.. Figure 1. Cross sectional view of a dilatometer. 162 Polymer J., Vol. 10, No.2, 1978 Volume Relaxation in Amorphous Polymers around Glass-Transition Temperature to the frequency scale of (2rrt)- 1, s" thus calculated CURVE I I00°C ___,. 37.2"C is reliable at least in the range of log f from -1.1 2 33.3 _, 37.2 31.0 37.2 to -6.3. 4 100 33.3 Enthalpy Jl.,feasurement 100 31.0 The enthalpy relaxations were measured on the PVAC by means of a Calvet microcalorimeter (Setram, Lyon). A glass ampule containing 1.987 g of the PV AC was used for the measure­ ment. Procedure of Temperature Jump In order to observe the volume or enthalpy relaxations around Tg, we employed a tempera­ ture jump technique, in which the sample tempera­ 2 3 4 5 6 ture was changed rapidly from an initial tempera­ log( !/sec) ture T1 to an annealing temperature T,. The Figure 2. Volume relaxations of the PVAC at various temperature jump should be accomplished in­ temperatures, T, after being subjected to various stantaneously. In volume measurements, a modes of temperature jumps as indicated. dilatometer was initially immersed in a bath of temperature T1, and subsequently transferred to another bath of temperature T,. The tempera­ ture jump was also performed by changing the temperature of the bath rapidly. In either case the temperature equilibrium was attained in three minutes. Enthalpy measurements were carried out as follows. An ampule containing the PVAC 4o.2-c was heated up to 100°C, and then immersed for -I five minutes in a water bath of temperature T., log (//sec) and then set in the calorimeter. It took 30 min to attain an equilibrium temperature. In diele­ Figure 3. Time dependence of the slopes of volume relaxation curves of the PVAC. ctric measurements, it also took 30 min to attain equilibrium. curves log ( -dV/d log t) varies in an approxi­ RESULTS AND DISCUSSION mately linear manner with log t as shown in Figure 3. The dependence of log ( -dV/d log t) on Volume Relaxation temperature becomes smaller with a decrease in Figure 2 shows examples of the volume relaxa­ the annealing temperatures. This means that the tion curves for the PVAC after respective tempera­ volume varies in proportion to log t in a region ture jumps described in the figure. V and log t relatively far below Tg. This linearity was already denote the specific volume and the common pointed out by Fox and Flory for polystyrene.14 logarithm of the elapsed time subsequent to the It should be noted that in the period in which the temperature jump. The shapes of volume relaxa­ relaxation terminates, log ( -d V/d log t) decreases tion curves subsequent to the temperature jump rapidly, as can be seen in Figure 3.
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