Entropy parameters

Intrinsic viscosity measurements revealed a conformational transition upon heating from 26 to 40 °C, while the UV absorbance of the solution was insensitive to the change. The entropy parameters for PA were also discussed in light of the Flory-Krigbaum correlation between the second virial coefficient and theta temper-... 

Pure component experimental data for sorption of methane and krypton on 5A zeolite at 238, 255. and 271K, and in the pressure range of 0 to 97.36 kPa were also obtained during this work (shown in Figures 3 and U). Further sorption data for methane on 5A zeolite (10, 13, 1 0, and for krypton on 5A zeolite (10. 15) are also plotted for other temperatures, all of which appear to be consistent. These experimental data were used to derive the energy and entropy parameters in equation U for the isotherm model of Schirmer et al. by a minimization of a sum of squares optimization procedure. 

Table 8. Concentration dependent parameters p, and p2 in the y parameter, Flory s theta temperature 9, and the entropy parameter J/ of cellulose diacetate, determined by different methods611... 

This expression is known as the van t Hoff eqnation. It is useful because the thermodynamic enthalpy and entropy parameters for the analyte transfer from the mobile to the stationary phase may be evalnated via the effect of temperature on the thermodynamic eqnilibrinm constant. Under simple reversed phase conditions for an analyte E, Kle is snfficient to describe the system and since... 

The entropy parameter, needed but is generally used as an adjustable... 

Fig. 26. Hypothetical simulated spinodal curves for the phase separation of two polymers on heating illustrating the effect of the interaction parameter (Xjj) the non-combinatorial entropy parameter (Qjj) and die ratio of surface areas per unit volume Sj/Sj. The curves are all simulated using values of y, = Yz = 1 (Jcm" K" ) tj/r, - 1 VJ = 100,000 cm" mole" a, = 5x10", 04 = 4x I0" K" . If X,j = —0.6 J cm", Qjj = 0, and Sj/S, = 1, the curve is much flatter than those in the previous f ure. If there is a larger (favourable) X,j, say —1.2 and this is balanced by an unfavourable —0.0023 J cm K., then...

It is possible to simulate the spinodal curves of the phase diagram of polymer pairs using the Equation-of-state theory developed by Flory and co-workers. It is only, however, possible to do this using the adjustable non-combinatorial entropy parameter, Qjj. Another problem arises in the choice of a value for the interaction parameter Xjj. This is introduced into the theory as a temperature independent constant whereas we know that in many cases the heat of mixing, and hence is strongly temperature dependent. The problem arises because Xj was never intended to describe the interaction between two polymers which are dominated by a temperature dependent specific interaction. 

Outliers in QSAR 1.92 included the 4-t-butyl and 4-OH analogs, whereas the 4-CONH, analog was an outlier in QSAR 1.93. These results were recently reanalyzed by Kim (217,218) with respect to the role of enthal-pic and entropic contributions to ligand binding with a-chymotrypsin. Use of the Fu-jiwara hydrophobic enthalpy parameter n and the hydrophobic entropy parameter irg led to the development of QSAR 1.94 and 1.95(219). 

The function [(1/2) x] can also be expressed in terms of two mixing parameters, an enthalpy parameter xtj and an entropy parameter i/rp that is... 

Thermodynamic Roughening. A crystal in a solution that is precisely saturated may have faces that are not flat and smooth on a microscopic scale. This means that there is a transition zone of some molecules thick between the solid and the liquid phase. This roughness persists at increasing supersaturation. Whether roughening occurs depends on the surface entropy parameter... 

To reiterate, systems at stable equilibrium must be described in general in terms of two fixed state variables. If two different equilibrium states having the same values of two state variables exist, then either both are metastable, or one is stable and one is metastable, and the metastable states in fact should be described in terms of three or more constraint variables. Usually, however, the third constraint is an activation energy barrier and is not thought of as a third variable (though in principle it is). For each choice of the two state variables that the two states have in common, there exists a function (another state variable) that is minimized or maximized at stable equilibrium therefore, by comparing values of this variable one can tell which of the two states is more stable. Note finally that although we have many potentials, the existence of the entropy parameter is the fundamental fact that allows us to define them all. It appears in one way or another in all thermodynamic potentials. 

In the other case the vapour mass fiaction at the relief device entrance must be estimated taking into account the flushing flow hypothesis. This allows the calculation of the so-called entropy parameter ro, which is required for the determination of the critical mass flow density G. ... 

Precipitation data for several systems have proved the validity of Equation 8.47. Linear plots are obtained with a positive slope from which the entropy parameter /i can be calculated, as shown in Figure 8.4. Typical values are shown in Table 8.1, but /i values measured for systems such as polystyrene-cyclohexane have been found to be almost ten times larger than those derived from other methods of measurement. This appears to arise from the assumption in the Flory-Huggins theory that is concentration independent and improved values of /i are obtained when this is rectified. 

Theta Temperatures and Entropy Parameters for Some Polymer-Solvent Systems... 

Values of 0 and Xj/i, in Table 8.1, show that for systems 1 to 4 the entropy parameter is positive, as expected, but for poly(acrylic acid) in dioxan and polymethacrylonitrile in butanone, f is negative at the theta temperature. As /i = when T= 0, the enthalpy is also negative for these systems. This means that systems 5 and 6 exhibit an unusual decrease in solubility as temperature rises, and the cloud-point curve is now inverted as in area B. The corresponding critical temperature is located at the minimum of the miscibility curve and is known as the lower critical solution temperature (LCST). 

Equation (6-45) contains the excess chemical potential instead of the chemical potential itself because the ideal term X X 2 has been omitted. This omission was necessary because the considerations have to be restricted to a small volume of solution where the segment distribution is uniform enough so that the lattice theory can be applied. Although in this equation the quantity (xo 0 ) is derived from the enthalpy of mixing and the factor 0.5 from the entropy of mixing, it is convenient to replace this combination of terms by another with a new enthalpy parameter k and a new entropy parameter... 

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