Isothermal contraction

In reality, the data on isothermal contraction for many polymers6 treated according to the free-volume theory show that quantitatively the kinetics of the process does not correspond to the simplified model of a polymer with one average relaxation time. It is therefore necessary to consider the relaxation spectra and relaxation time distribution. Kastner72 made an attempt to link this distribution with the distribution of free-volume. Covacs6 concluded in this connection that, when considering the macroscopic properties of polymers (complex moduli, volume, etc.), the free-volume concept has to be coordinated with changes in molecular mobility and the different types of molecular motion. These processes include the broad distribution of the retardation times, which may be associated with the local distribution of the holes. 

The activation energy of isothermal contraction in polymer blends calculated in 9 is considerably lower than for pure components, this pointing to the appearance of the free-volume as well, which facilitates the relaxation processes and diminishes the activation energy. 

Calculate the work done by a gas which is compressed adiabatically from a state represented by the point A (Fig. 121) along the path AB until a state B is reached. It is then allowed to expand isothermally along the path BG until a state C is reached. This is followed by an adiabatic expansion along CD and by an isothermal contraction along DA until the original state A is reached. 

FIGURE 9.3 (a) Isothermal contraction of poly(vinyl acetate) at various temperatures as indicated, following quenching from 40°C (b) contraction and expansion isotherms of poly(vinyl acetate) at 7 =35°C for two different initial temperatures. (From Kovacs [1963], with permission. Copyright 1963, Springer.)... 

Since the thickness of the PEO lamellae L is essentially constant (see Section 6.2.2), the isothermal contraction (v — Vp) is always proportional to the surface area of the crystals S (neglecting the lateral faces and assuming the crystals are two dimensional). Thus... 

Three groups of isothermal contraction curves are plotted in Figure 6.19. Experiments were performed by dissolving the block copolymer in ethylbenzene at the value of 7 indicated, quenching to the crystallization temperature 7, and measuring the contraction (r, - as a function of t — r ), where t is the time after quenching, and 1, the time needed for thermal equilibration. 

Recognizing that Tg has a kinetic component because it is associated with cooperative motion of the elements of the lattice structure moving to create free volume for the molecules or polymer chains to move, leads to the idea that Tg can change with storage time. Figure 7.13 indicates the isothermal contraction of glucose after quenching from Tq = 40 °C to different temperatures. 

Changes in Relaxation Times during Isothermal Contraction near the Glass Transition... 

Perhaps the most direct observation of the relation between relaxation times and free volume, as expressed in its most general form by equation 49, is obtained from viscoelastic" " (or viscosity or dielectric ) measurements repeated over a period of time during the spontaneous contraction of a glassy sample that occurs after quenching it to a temperature near or below Tg, as portrayed in Fig. 11 -7. As the volume decreases, the relaxation times increase. Since the contraction takes place at constant temperature and pressure, the change in ar can be entirely attributed to collapse of free volume as a function of elapsed time. Moreover, since the occupied volume should remain constant at constant T and P, experimental measurements of the decrease in v provide the decrease in ly directly. Thus, during such an isothermal contraction at temperature T, the fractional free volume at time t is... 

The inclusion of values in Table 1 l-III derived from dynamic bulk viscoelastic measurements implies the concept that the relaxation times describing time-de-pendent volume changes also depend on the fractional free volume—consistent with the picture of the glass transition outlined in Section C. In fact, the measurements of dynamic storage and loss bulk compliance of poly(vinyl acetate) shown in Fig. 2-9 are reduced from data at different temperatures and pressures using shift factors calculated from free volume parameters obtained from shear measurements, so it may be concluded that the local molecular motions needed to accomplish volume collapse depend on the magnitude of the free volume in the same manner as the motions which accomplish shear displacements. Moreover, it was pointed out in connection with Fig. 11 -7 that the isothermal contraction following a quench to a temperature near or below Tg has a temperature dependence which can be described by reduced variables with shift factors ay identical with those for shear viscoelastic behavior. These features will be discussed more fully in Chapter 18. 

FIG. 18-9. Storage shear modulus plotted against logarithm of radian frequency for poly(vinyl acetate) after sudden quench from 45° to 20° or 30°, at different elapsed times in minutes as indicated by numbers at left. Heavy curves refer to measurements at voluminal equilibrium (after completion of isothermal contraction) at the temperatures indicated at right. ... 

Figure 3 Isothermal contraction of glucose after quenching from Tq — C to different temperatures T, as indicated (after...

Obvioudy, tte presence of a loose temperature glass transition interval can be explained by tte fact that various mechanisms participate in the process of glass transition. Of interest from this point of vfew is the examination of the effect of fillers on such relaxation processes in which sufficiently large structural elements take part. Those phenomena were studied (33. 45-47) by calculating the average relaxatirai time proceeding from the data on the isothermic contraction of the volume of various filled systems by the method proposed in (48). 

The analyas of the data obtained for a number of sterns, containing both inorganic and polymeric fillers, shows that the average time of relaxation of the process of isothermic contraction t v increases in the presence of hard particles. However, from the point of view of understanding the mechanism of the processes which occur in the interface, it is mote cmrect to compare tte relaxation time at corresponding temperatures equidistant from the glass transient t nperature, rather than at equal temperatures. 

Fig. S. Dependence of the avoage lelaxation time of isothermical contraction on the diffemice be-tween measurement and glass ten pmatuies for different systems. 1 low molecubt nilMA,...

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