Relaxation times enthalpy

The data shown in Fig. 5 makes it possible to estimate the enthalpy relaxation time in the case of the ASW/Acetic acid mixture at 175 K (i.e. at the onset temperature of heat capacity rise). Taking into account the value of the heating rate in our experiments (10 K-s" ), we arrive at the conclusion that the relaxation time is on the order s at 175 K... 

Analysis of the enthalpy relaxation the enthalpy relaxation time and the activation energy were calculated by KWW in accordance with the previous work (Kawai et al., 2004). The KWW theory was originally proposed in dielectric relaxation study by Williams and Watts (1970), then applied in the form of nonexponential function such as the enthalpy relaxation. In KWW theory, the enthalpy relaxation, AH eiax/ which corresponds to the peak area given from the enthalpy relaxation is expressed by the equation... 

Figure 6. Arrhenius temperature plots for enthalpy-relaxation times at a constant excess enthalpy of 0.5 cal g for PC...

Enthalpy relaxation time, determined by differential scanning calorimetry,608 and mechanical relaxation, determined by dynamic mechanical analysis,609 can also be used as measures of molecular mobility of amorphous pharmaceutical solids. 

For the tyrosine-derived polycarbonates tested, the enthalpy relaxation process was not sensitive to the length of the pendent chain. This obser ation suggests that structural relaxation in these polymers is limited by backbone flexibility, and that the fraction of free volume in these polymers is not the limiting factor for polymer mobility. Furthermore, since the enthalpy relaxation time is short at aging temperatures of Tg-15°C, a few hours of storage at that temperature will be sufficient to bring the physical aging process to completion. The results obtained by dynamic... 

For small enough temperature steps (< lOK) during small step annealing the vacancy concentration practically remains constant and corresponds to the instantaneous aimealing temperature. This allows for an easy analysis of SRO-kinetics yielding SRO-relaxation times and SRO-activation enthalpies, which by usual interpretation correspond to H +Hf. 

SRO SRO-relaxation kineties yielding SRO-relaxation times and aetivation enthalpies ... 

Time resolution of the enthalpy changes is often possible and depends on a number of experimental parameters, such as the characteristics of the transducer (oscillation frequency and relaxation time) and the acoustic transit time of the system, za, which can be defined by ra = r0/ua where r0 is the radius of the irradiated sample, and va is the speed of sound in the liquid. The observed voltage response of the transducer, V (t) is given by the convolution of the time-dependent heat source, H (t) and the instrument response function,... 

The ultimate goal of kinetics studies is the identification of a (unique) chemical kinetic mechanism, which consists of a reaction scheme such as the one shown in Figure 1.3 and the corresponding numerical values of the rate coefficients, k, which incorporate entropy and enthalpy differences. This is an inverse problem, since only the concentration profile or, in less favorable conditions, only the relaxation times can be observed, and the reaction mechanism must be deduced from this information. Any experimental method that establishes a connection between the signal and the concentration of molecules can be used to investigate kinetics. However, it is necessary that the method has sufficient time resolution since time is the crucial parameter in kinetic experiments. 

From the amplitude of the low-frequency excess sound absorption, A, the volume difference between the two isomers can be evaluated. This again requires knowledge of the equilibrium constant, in order to evaluate f, of the relaxation time t, and of the standard enthalpy... 

The available evidence thus suggests that relaxation times for planar-tetrahedral equilibria in nickel(II) complexes in solution at room temperature fall in the range 0.1-10 /isec, corresponding to rate constants of the order 105-107 sec-1. These relaxation times are several orders of magnitude longer than those observed for octahedral spin equilibria. The reaction coordinate for the planar-tetrahedral equilibria is characterized by large enthalpies of activation for the reaction in both directions, in contrast with a relatively low enthalpy of activation for the high-spin to low-spin process in octahedral iron complexes. 

The measurement of relaxation times 7j and T2 and the subsequent application of the theory formulated by Bloembergen et al. (236), and extended by Kubo and Tomita (272) and Torrey (288), leads to the determination of motional and thermodynamic parameters such as mean times between molecular jumps, diffusion coefficients, and activation enthalpies for translation. For example, Resing and Thompson (289, 290) used this... 

One theory that describes the temperature dependence of relaxation time and structural recovery is the Tool-Narayanaswamy-Moynihan (TNM) model developed to describe the often nonlinear relationship between heating rate and Tg. In this model, the structural relaxation time, x, is referenced as a function of temperature (T), activation enthalpy (Ah ), universal gas constant (R), hctive temperature (7)), and nonlinearity factor (x) (Tool, 1946 Narayanaswamy, 1971 Moynihan et al., 1976) ... 

The long time limit was chosen to be the time where the transient absorption reaches a maximum.) We observe three relaxation processes (i.e., N — 3). The kinetic phases are well separated in time, spanning hundreds of nanoseconds to hunderds of microseconds. The amplitudes contribute more or less equally to the total decay, the slowest phase contributing the least. What is particularly interesting, however, is that the relaxation times for the 1620 cm-1 data are faster than those at 1661 cm-1. This is easily seen in Fig. 17.7 where the observed rate constants (1/t = kohs — kF + ku) for each phase are plotted in Arrhenius coordinates (i.e., In feobs vs. 1/T). The activation enthalpy ATP can then be determined from the slope according to... 

The structural relaxation time defines the activation enthalpy Ah for small deviation from equilibrium... 

As mentioned earlier, the relaxation enthalpy was measured by superimposing the first and the second DSC scans for each specimen. Figure 23 shows the relaxation-enthalpy loss versus logarithmic sub-Tg annealing time at 80°, 110°, and 140 °C. There is clearly a linear relationship between the enthalpy relaxation process and the logarithmic aging time, Ta. 

Very important phenomena in polymer behaviour, such as viscoelasticity, stress, strain, volume and enthalpy relaxation, ageing, etc., are characterised by time-dependence of the polymer properties. 

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