Thermal Density Fluctuation

These circumstances may explain why it took ten years for the phenomenon to be experimentally observed after the prediction. In 1973, prior to this finding, Lon Hocker, George Benedek, and Tanaka realized that a gel scattered light, and the light intensity fluctuated with time [5]. They established that the scattering is due to the thermal density fluctuations of the polymer network and derived a theory that explained the fluctuation. These fluctuations are similar to... 

MCT considers interacting Brownian particles, predicts a purely kinetic glass transition, and describes it using only equilibrium structural input, namely the equilibrium structure factor Sq [3,46] measuring thermal density fluctuations. MCT-ITT extends this statistical mechanics, particle based many-body approach to dispersions in steady flow assuming a linear solvent velocity profile, but neglecting the solvent otlrerwlse. 

In this chapter the dilute particulate system, the nonparticulate two-phase system, and the periodic system are discussed in Sections 5.2, 5.3, and 5.5, respectively. Section 5.4 deals with scattering from a fractal object, which may be regarded as a special kind of nonparticulate two-phase system. The soluble blend system is dealt with in Chapter 6. The method discussed in Section 4.2 for determining, for a single component amorphous polymer, the thermal density fluctuation from the intensity I(q) extrapolated to q -> 0 can also be regarded as a small-angle technique. 

The S-S theory has also been used for computation of the thermal density fluctuation in the molten and glassy states [Balik et al 1982] ... 

Balik, C. M., Jamieson, A. M., and Simha, R., On the theory of thermal density fluctuations in the glassy state application to poly(vinyl acetate). Colloid Polym. Sci., 260,477-486 (1982). 

Jain, S. C., Simha, R., Relaxation in the glassy state Volume, enthalpy, and thermal density fluctuations, MflcromoZecMto, 15(6), pp. 1522-1525 (1982). 

In order to describe the static structure of the amorphous state as well as its temporal fluctuations, correlation functions are introdnced, which specify the manner in which atoms are distributed or the manner in which fluctuations in physical properties are correlated. The correlation fimctions are related to various macroscopic mechanical and thermodynamic properties. The pair correlation function g r) contains information on the thermal density fluctuations, which in turn are governed by the isothermal compressibility k T) and the absolute temperature for an amorphous system in thermodynamic equilibrium. Thus the correlation function g r) relates to the static properties of the density fluctuations. The fluctuations can be separated into an isobaric and an adiabatic component, with respect to a thermodynamic as well as a dynamic point of view. The adiabatic part is due to propagating fluctuations (hypersonic soimd waves) and the isobaric part consists of nonpropagating fluctuations (entropy fluctuations). By using inelastic light scattering it is possible to separate the total fluctuations into these components. 

The dynamics of slowly varying thermal density fluctuations has been studied by means of pcs (28,29) in the frequency range between 10 and 10 Hz for several polymeric systems in the molten state as well as in the glassy state. The measured intensity autocorrelation function C q, t) is related to the normalized time correlation function t) by... 

In equation 18, rcorr(s) is the intensity afte correction fix thermal density fluctuation, and t is the thickness cf the interphase (a region possessing an intermediate electron density between pc and Pa). Plotting ln(I corr(s) s ) vs. s, the scattering at large s is used to find the slope, rc t, from which fte interphase thickness is found (15). 

The quantity/], arises from density fluctuations and Kp is the Porod constant Note the strong positive deviation in the Porod plot (f(q)q versus q ) illustrated as an inset to Figure 2. Positive deviations from Porod s law are caused by thermal density fluctuations [6]. A regression analysis of tiie linear part of the curve gives values of = 0.0S and = 356. A most be subtracted from the raw intensity data before both dj and the invariant are calculated. 

It is well known that transport phenomena in condensed matter are strongly dependent on cooperative phenomena and that transport coefficients display anomaleous behavior near phase transitions. The general physical reason for this behavior is that transport coefficients can be expressed in terms of correlations of fluctuations in appropriate fields. Since these correlations decay slowly in time and get long ranged close to phase transitions it is expected that the the transport capacity will be strongly affected as the transition point is approached and the thermal density fluctuations blow up. 

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