Relaxation volume

The decrease in volume that accompanies physical aging is known as volume recovery or volume relaxation. Dilatometry (Dil) can be used to follow the volume relaxation in glasses by monitoring the time-dependence of the volume change on aging. The material is either cooled from above Tg to the aging temperature 7], (down-jump) and the isothermal volume contraction is measured or the sample is heated in the glassy state (up-jump), in which case an expansion follows. 

The simplest volume recovery experiment is the down-jump. Volumetric data collected at a series of aging temperatures are normalized to examine the relative departure from equilibrium (6), which is defined as  

Work by Kovacs [75] on the volume relaxation of poly(vinyl acetate) highlighted the nonlinearity in the kinetics of isothermal recovery processes, and that the distribution of relaxation times, t, was necessary if the memory effects in glasses were to be explained. These ideas are incorporated in some of the phenomenological models developed to describe the aging of a glass and met in earlier sections. 

As pointed out earlier, most aging studies of blends have employed enthalpy relaxation and very few measurements have been made using volume relaxation. Notably, the volume changes during isothermal volume recovery are small, typically of the order of 1% or less and require high-precision measurements. 

Isothermal, isobaric volume relaxation can be described in terms of the volume relaxation rate (by) [1]  

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There are a number of important concepts which emerge in our discussion of viscosity. Most of these will come up again in subsequent chapters as we discuss other mechanical states of polymers. The important concepts include free volume, relaxation time, spectrum of relaxation times, entanglement, the friction factor, and reptation. Special attention should be paid to these terms as they are introduced. 

However, it is expected the reaction rates below Tg may be affected also by volume relaxation (physical aging) which was not taken into account and which will result in the dependence of k-p not only on T and a but also on time t. If we take the positive deviations of experiments in Figure 14 as a measure of the volume relaxation effect then the physical aging increases the apparent mobility although it leads also to a denser (and less mobile) state. 

Irradiation was performed with a similar lamp as used with DSC. Prior to irradiation the samples were flushed with nitrogen for 15 minutes. After the irradiation the samples were kept in the vessel overnight to allow for volume relaxation and decay of trapped radicals. Next a similar layer was prepared on the back of the substrate in order to obtain a symmetrical sample. 

An experimental and theoretical study of the degassing of an LDPE high-density foam is presented. Measurements of the mass, dimensions, and density as a function of storage time are reported. A geometrical model is described to represent the basic mass transport and volume relaxation processes in a cellular system. Model predictions were compared with experimental results. 12 refs. 

Because of the strong dependence of composite properties on this final conversion, it is imperative that models of polymerizing systems be used to predict the dependence of the rate of polymerization and, hence, conversion on reaction conditions. The complexities of modeling such systems with autoacceleration, autodeceleration, and reaction diffusion all coupled with volume relaxation are enormous. However, several preliminary models for these systems have been developed [177,125,126,134-138]. These models are nearly all based on the coupled cycles illustrated in Fig. 5. 

The lower cycle represents the chemical changes occurring during polymerization and relates them to the free volume of the system. In general, free volume of a polymer system is the total volume minus the volume occupied by the atoms and molecules. The occupied volume might be a calculated van der Waals excluded volume [139] or the fluctuation volume swept by the center of gravity of the molecules as a result of thermal motion [140,141]. Despite the obscurity in an exact definition for the occupied volume, many of the molecular motions in polymer systems, such as diffusion and volume relaxation, can be related to the free volume in the polymer, and therefore many free volume based models are used in predicting polymerization behavior [117,126,138]. 

Fig. 5. Coupled polymerization (lower) and volume relaxation (upper) cycles that describe the changes occurring during polymerization...

Frequency-Dependent Specific Heat. We mention measurements of volume relaxation through the frequency-dependent specific heat Cn(co) as in fluids near the glass transition [52]. This is feasible when the experimental frequency co is of the order fi0 in small gels. The deviations of the entropy, temperature, and volume are related by SS = CV5T + (dH/dT)v8Vand the relaxation equation reads... 

The idea that the fractional free-volume at glass temperature as found experimentally depends on the mode of molecular motions was put forward in 196746 47 as a result of calculating/g from data obtained from isothermal volume relaxation for some polymer systems. By estimating average relaxation time at different temperatures it was possible to find the fractional free-volume/g at Te according to WLF theory. If we accept the validity of the theory as regards the universal dependence of the reduction factor aT on (T - Tg), then on the basis of data on Aa and theoretical values aT calculated from universal values of the coefficients C and C, it is possible to make an estimate of/g. In this case the value found corresponds to the universal one. If, however, we use the experimental values aT, the fractional free-... 

As the average relaxation time becomes even longer than 104 s long times must be allowed before the sample itself achieves equilibrium. Eventually this becomes impractical and the sample becomes a glass. The longest volume relaxation times exceed the patience of the experimenter and the sample is allowed to remain in the nonequilibrium state. However, the sample does not remain in the same state as time increases because it will still relax toward the equilibrium state. The fundamental assumption of stationarity of the fluctuations is then violated and interpretation of the PCS becomes a problem. Such considerations have not stopped people from collecting data in this regime45, but they do preclude a clean interpretation. 

There is a region of thin films with thicknesses between the two previously described extreme limits, ranging from 100nm to several micrometers, where volume relaxation processes - and, hence, the change in gas-permeability properties with time - are much more rapid than that expected based on observations of bulk specimens as shown below. 

The authors explained the observed temporary cessation of heat release by the difference between the rate of polymer formation and that of volume relaxation. According to their observations, the difference between the two phenomena leads to a situation in which the free radicals are spatially separated from the unreacted VA molecules. The subsequent spatial relaxation brings them into contact and the reaction starts again. 

In order to study the molecular aggregation during the volume relaxation of network epoxies, CP/MAS carbon-13 (natural abundance) NMR was utilized. The Hartman-Hahn cross-polarization technique 129) was used with a cross contact time of 1 mi llisecond for transfer of proton polarization to carbon nuclei. The protondecoupling was achieved at the radio frequency of 56.4 MHz. Carbon-13 14.2 MHz spectra were measured in a 1.4 Tesla magnetic field. Room temperature (23 °C) experiments were performed at 54.7° MAS at 1 KHz. The spinner was constructed using an Andrew-type rotor driven by compressed air. 

The main consequence of this reduced mobility is an extension of the glass transition region towards the high temperature side it will show a lower and an upper value, viz. Tg(L) and Tg(U), the values of the undisturbed amorphous region and that of regions with reduced mobility. By means of this model, Struik could interpret his measurements on volume relaxation (physical ageing) and creep in semicrystalline materials. 

We intend to come back on the phenomenon of volume relaxation in Chap. 13, where it will be discussed and also in context of physical ageing and creep. 

These relaxation time equations together with Eqs. (2), (15), and (19) can be utilized in analyzing the experimental measurements of volume relaxation and recovery, of linear and nonlinear viscoelastic relaxations, and of yield behavior and stress-strain relationships. 

By including the effect of volume relaxation below Tg, calculations of the PVT properties of amorphous polymer have been extended from the equilibrium liquid to nonequilibrium glassy states. The study reveals the effects of kinetic, pressure, and stresses on Tg, which depends on relaxation time. 

Recently Moore and Petrie (5) have demonstrated that control of sample thermal history can result in transition from ductile to brittle behavior for polyethylene terephthalate. This transition in behavior was related to volume relaxation of the glassy state. 

The effects of morphology (i.e., crystallization rate) (6,7, 8) on the mechanical properties of semicrystalline polymers has been studied without observation of a transition from ductile to brittle failure behavior in unoriented samples of similar crystallinity. Often variations in ductlity are observed as spherulite size is varied, but this is normally confounded with sizable changes in percent crystallinity. This report demonstrates that a semicrystalline polymer, poly(hexamethylene sebacate) (HMS) may exhibit either ductile or brittle behavior dependent upon thermal history in a manner not directly related to volume relaxation or percent crystallinity. 

If the step in temperature is larger than a couple of degrees Celsius, then the aging process is not governed by a linear spectrum. Figure 4-15 shows the volume relaxation of poly(vinyl acetate) at a temperature of after the sample had been equilibrated at initial temperatures Ti of 30°C and 40°C and then suddenly heated or cooled to Tf = 35°C. Note that for AT = 5°C, the volume relaxation is asymmetric the relaxation following a jump up in temperature is very slow, and it eventually accelerates. The opposite occurs for a downward jump in temperature. 

The evolution of the thermodynamic properties with time governs the viscoelastic response of materials in the glassy state. The volume relaxation... 

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