Volume relaxation spectrum

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. 

In a good solvent, where there are excluded-volume effects, G and G" can be fit to the Zimm theory simply by adjusting h downward, for finite Ns (Ferry 1980). Thus, as the solvent quality improves, the relaxation spectrum becomes more Rouse-like (since... 

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. 

Ac Is a measure of the Intensity of the dielectric relaxation spectrum (the relaxation strength) and it Is in turn related to the number of relaxing dipoles (N) per unit volume by the equatlon(2ZjJi, ... 

Since there is a shift in the viscoelastic relaxation spectrum to longer times with aging time, aging can be followed using stress relaxation, creep or volume relaxation measurements. It has been shown that for aging experiments [Struik, 1978], momentary creep curves have a universal shape and a master curve can be constructed using either time-aging (t - y or time-temperature (t - T) superposition. 

Since the volume fractions of free, cpf, and bound, cp, water are both unknown, it is convenient to measure the dielectric permittivity in a frequency range where the dielectric loss of bound water may be safely neglected. The relaxation spectrum of free and bound water for our systems will safely satisfy this requirement at the measurement frequency of 75 GHz. In this case, die complex permittivity of the bound water is equal to its real part, i.e., = s -i-... 

Two types of rheological phenomena can be used for the detection of blend s miscibility (1) influence of polydispersity on the rheological functions and (2) the inherent nature of the two-phase flow. The first type draws conclusions about miscibility from, e.g., coordinates of the relaxation spectrum maximum cross-point coordinates (Gx, ( x) (Zeichner and Patel 1981) free-volume gradient of viscosity, a = d(lnri)/df the initial slope of the stress growth function, S = d(lnriE)/dln t the power-law exponentn = d(lnCTi2)/dlny = S, etc. The second type involves evaluation of the extrudate swell parameter, B = = D/Dq, strain (or form) recovery, apparent yield stress, etc. 

The second dependence in Eq. (2.32) is valid when all fractions are either entangled or not. In consequence, the relaxation spectrum of a miscible polymer blend is a linear combination of the component relaxation spectra and their weight fractions, W(. A strong deviation from linearity in plots of log Hq versus Mw/Afn and log Wmax versus log r]o indicates immiscibility [87, 88]. The principle that in miscible blends polydispersity can be calculated and used to test for system miscibility was extended to other rheological functions sensitive to polydispersity, namely, the power-law exponent (n), the cross-point coordinates (G, o) ), the free volume gradient of viscosity, the initial slope of stress growth function, and so on [3]. 

It seems difficult, in view of these observations, to escape the conclusion that the observed solute relaxation is due to the presence of dipole ion-pairs and to dismiss alternate interpretation of the solute relaxation as due to the relaxation of the transport of ionic charges. In fact, should this be the case, it is not apparent why one cannot observe the solute dielectric relaxation when the electrolyte is completely dissociated, therefore having the largest possible number of electrical carriers per unit volume. The interpretation becomes more challenging for electrolytes in media of permittivity lower than 15 other complex ionic species possessing permanent dipole moments may cause the appearance of additional contributions to the relaxation spectrum of the solute. 

As the compatibility of the two IPN components is increased the glass transition behavior changes from two distinct transitions to one broad transition in a systematic manner. It is concluded that a broadened transition can result even in thermodynamically compatible mixes if the minimum volume required for independent contribution to the relaxation spectrum is subject to wide composition variation. 

While borrowing from the classical models, these phenomenological approaches have also helped to clarify and refine the concepts of free-volume and configurational entropy and have focused attention on the nature of the relaxation spectrum (7-10,109,110). When a hquid in equiUbrium at a temperature Ti is suddenly cooled to a temperature, T2, its structure has no time to adjust and its properties (such as volume V, enthalpy H, or index of refraction n) exhibit instantaneous, solidlike changes characteristic of the glassy state as illustrated in Figure 9. For example, the instantaneous change in the enthalpy H may be written as follows ... 

Fig. 4. Comparison of the two dielectric relaxation modes (upper spectrum) and the two volume relaxation modes at lOO C (lower spectrum from Kovacs et al., ref. 69).

In order to obtain information about molecular dynamics from a dielectric relaxation spectrum, the complex dielectric permittivity is related to the correlation function of the electric dipole moment m, of the ith species and the dipole moment Mj of a small (in comparison with the whole sample) macroscopic volume V surrounding m,. Mj is the sum of permanent dipole moments in this volume Mi N being the number of dipole moments in the volume. The... 

The a- and ajS-processes are characterized by a broad asymmetric dielectric relaxation spectrum, which can be well represented by the Kohlrausch Williams-Watts (KWW) decay function (cf. eqn. (4.17)). The major factor leading to the broad DR spectra for a- and ajS-relaxations is that chain segments relax in cooperation with their environment. In order to explain the mechanism of this relaxation, the concepts of defect diffusion and free-volume fluctuation are used. For example, Bendler has proposed a model in which the KWW function is interpreted as the survival probability of a frozen segment in a swarm of hopping defects with a stable waiting-time distribution At for defect motion. 

In a solution where a nonzero volume change between the electronic isomers, HS and LS, is encountered, the position of the spin equilibrium will depend on pressure. The volume change, usually denoted here AF°, may be obtained from the study of the pressure dependence of equilibrium properties such as the magnetic susceptibility or the electronic spectrum. In favorable cases, A F° values may be derived from the amplitude of sound absorption observed in ultrasonic relaxation measurements of a spin equilibrium as will be shown in the... 

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