Kinetics of Volume Changes

Volume changes of polystyrene following sudden temperature changes to final temperature T2 — 90.70 C at 1 atm with different positive and negative values of AT = T2 Ti as indicated, plotted as (c — 02)/(0 — 02)- (Data of Goldbach and Rehage. ) 

Asymmetric isothermal volume changes of poly(vinyl acetate) at 35 following sudden AT of -5 and +5 respectively, plotted as (o — 02)/02 against t — 0.01 in hours with logarithmic scale. (Kovacs. ) 

With this concept, equation 5 can be applied to isothermal volume contraction following At 0, if ap is replaced by Op = exp — 1 //]), where f and fi 

Other discrepancies which may be attributed to a distribution of retardation times and fluctuations in free volume these cannot be described without more parameters. Recently, more extended theoretical treatments by Narayanaswamy. a Moyni-han. and Kovacs and collaborators have introduced additional parameters. Use of a spectrum of retardation times with a time scale which depends not only on temperature and pressure but also on the instantaneous state of the system 

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Fig. 25a, b. a. Collective diffusion coefficient D of a NIPA gel as determined by the kinetics of volume change, as a function of temperature. It diminishes at the critical point, b. collective diffusion coefficient as determined from the density fluctuations by use of photon correlation spectroscopy. The agreement between the results obtained from dynamics of microscopic fluctuations and from kinetics of macroscopic volume change is excellent considering the difficulty in the dynamic experiments... 

It has been shown both theoretically and experimentally that the kinetics of volume change and the dynamics of concentration fluctuations of a gel are controlled by a diffusive process in which many chains of the network move cooperatively (9-i3). The first part of this chapter describes how the... 

In this chapter, we describe how time-resolved photoacoustic calorimetry (PAC) can be used to obtain both the energetics and kinetics of carbenes in solution.7-9 PAC measures the magnitude and temporal profile of volume changes in solution following deposition of energy. These time-resolved volume changes can be directly related to carbene reaction enthalpies. We will first discuss the principles of this photoacoustic technique and then how it has been... 

Both sets of volume changes (77) and (79) can be found experimentally if all kinetic constants are evaluated at each of a series of pressures (Morild, 1977a,b Morild and Tvedt, 1978). 

U. Gosele. Thin-film compound formation Kinetics and effects of volume changes / In Alloying (Eds. J.L. Walter, M.R. Jackson, Ch.T. Sims). - Metals Park (Ohio) ASM International, 1988.-P.489-519. 

Figure 12-6 Effectiveness factor ratios for first-order kinetics on spherical catalyst pellets for various values of the Thiele modulus of a sphere, (h.,. as a function of volume change. [From V. W, Weekman and R. L. Goring. J. Caial.. 4,...

Robertson et al. [1984] developed a stochastic model for predicting the kinetics of physical aging of polymer glasses. The equilibrium volume at a given temperature, the hole fraction, and the fluctuations in free volume were derived from the S-S cell-hole theory. The rate of volume changes was assumed to be related to the local free volume content thus, it varied from one region to the next according to a probability function. The model predictions compared favorably with the results from Kovacs laboratory. Its evolution and recent advances are discussed by Simha and Robertson in Chapter 4. 

Then, assuming first-order kinetics, no volume change, that is, e,4 = 0, and with Arrhenius dependence of k on T, Equation 1.59 can be written as... 

Many electron reactions are diffusion controlled, but here we are concerned with those reactions which do not fall into this category. Considerable progress has been made on the experimental side in identifying factors which influence electron kinetics. One key factor is the energy level of the electron at the bottom of the conduction band of the liquid, denoted V. Other important factors are entropy and volume changes. How influences electron reactions is reviewed, and the significance of volume changes as revealed by recent pressure studies is discussed. 

A. Letton (Dow Chemical Company, Freeport, Texas) You said that the percent densification may be used as a measure of physical aging. It seems to me, based on the model of Kovacs et al. [A.J. Kovacs, J.J. Aklonis, J.M. Hutchinson, and A.R. Ramos, J. Polym. Sci., Polym. Phys. Ed., 17,1097-1162 (1979)] and some of the other models U.S. Chow, Macromolecules, 17, 2336-2340 (1984) R.R. Lagasse and J.G. Curro, Macromolecules, 15,1559-1561 (1982)], that you shouldn t be looking at percent densification as a direct correlation, but rather at the kinetics of the change in the relative volume parameter, the delta parameter that they use. I m wondering if you looked at that test to correlate it with physical aging ... 

Particularly for the direct observation of volume changes, dilatometry has been used in the past with great success. The method is useful for the determination of volume changes, AV, that occur, for example, upon mixing of proteins with particular reactants in solution, and for the observation of kinetic processes. In this context, titration experiments and the study of hydrolysis, denaturafion, and crystallization reactions may be mentioned. Voliune changes of a few hundredths il can be followed, provided the temperature is accurate to 0.001 °C. Since, however, the changes in volume found by dilatometry cannot be interpreted simply in terms of specific volumes, we will focus primarily on the volume quantities obtainable from the densimetric techniques. 

Melting, a major physical event, has small, subtle effects on shock-compression wave profiles. The relatively small volume changes and limited mixed-phase regions result in modest, localized changes in loading wave speed. Consequently, shock-induced melting and freezing remains an area with little data and virtually no information on the influence of solid properties and defects on its kinetics. 

The concentrations of reactants are of little significance in the theoretical treatment of the kinetics of solid phase reactions, since this parameter does not usually vary in a manner which is readily related to changes in the quantity of undecomposed reactant remaining. The inhomogeneity inherent in solid state rate processes makes it necessary to consider always both numbers and local spatial distributions of the participants in a chemical change, rather than the total numbers present in the volume of reactant studied. This is in sharp contrast with methods used to analyse rate data for homogeneous reactions in the liquid or gas phases. 

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