Intrinsic entropy

Note first that even in the absence of a temperature gradient a flux of entropy and matter can occur. For, when Xq = 0, /i = L/i Zi -b L/2X2, where ( = 0, 1, 2. For purposes of identification we first consider the constant temperature case, where we define (5 ) and (5 )2 as the entropy intrinsic to (i.e., exclusive of entropy transport) one mole of species 1 and 2. Then at constant T the entropy flux is given by the postulated form... 

FIGURE 16.2 The intrinsic binding energy of the enzyme-snbstrate (ES) complex (AGi ) is compensated to some extent by entropy loss dne to the binding of E and S (TAS) and by destabilization of ES (AGt) by strain, distortion, desolvation, and similar effects. If AGi, were not compensated by TAS and AG, the formation of ES would follow the dashed line. 

Due to the smallness of the entropy of mixing, most polymer mixtures are at least partially incompatible, and blends contain A-rich and B-rich domains, separated by interfaces. The intrinsic width of these interfaces is rather broad (it varies from w = aJin... 

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-... 

Just as the intrinsic energy of a body is defined only up to an arbitrary constant, so also the entropy of the body cannot, from the considerations of pure thermodynamics, be specified in absolute amount. We therefore select any convenient arbitrary standard state a, in which the entropy is taken as zero, and estimate the entropy in another state /3 as follows The change of entropy being the same along all reversible paths linking the states a and /3, and equal to the difference of the entropies of the two states, we may imagine the process conducted in the following two steps ... 

Both conditions must be satisfied simultaneously, for the condition that both phases become identical at the critical point certainly requires that their intrinsic energies and entropies per unit mass are equal ... 

The entropy and intrinsic energy of steam (or other vapours) may be determined by the following method, due to Clausius. 

All of these point defects are intrinsic to the heterogeneous solid, and cirise due to the presence of both cation and anion sub-lattices. The factors responsible for their formation are entropy effects (stacking faults) and impurity effects. At the present time, the highest-purity materials available stiU contain about 0.1 part per billion of various impurities, yet are 99.9999999 % pure. Such a solid will still contain about IQi impurity atoms per mole. So it is safe to say that all solids contain impurity atoms, and that it is unlikely that we shall ever be able to obtain a solid which is completdy pure and does not contain defects. 

Equation 3.6.10. given above shows that intrinsic defect concentrations will increase with increasing temperature and that they will be low for high Enthalpy of defect formation. This arises because the entropy effect is a positive exponential while the enthalpy effect is a negative exponential. Consider the following examples of various types of compounds and the natural defects which may occur (depending upon how the compounds were originally formed) ... 

An alternative method, which uses the concept of maximum entropy (MaxEnt), appeared to be a formidable improvement in the treatment of diffraction data. This method is based on a Bayesian approach among all the maps compatible with the experimental data, it selects that one which has the highest prior (intrinsic) probability. Considering that all the points of the map are equally probable, this probability (flat prior) is expressed via the Boltzman entropy of the distribution, with the entropy defined as... 

In some instances, distinct polymorphic forms can be isolated that do not interconvert when suspended in a solvent system, but that also do not exhibit differences in intrinsic dissolution rates. One such example is enalapril maleate, which exists in two bioequivalent polymorphic forms of equal dissolution rate [139], and therefore of equal free energy. When solution calorimetry was used to study the system, it was found that the enthalpy difference between the two forms was very small. The difference in heats of solution of the two polymorphic forms obtained in methanol was found to be 0.51 kcal/mol, while the analogous difference obtained in acetone was 0.69 kcal/mol. These results obtained in two different solvent systems are probably equal to within experimental error. It may be concluded that the small difference in lattice enthalpies (AH) between the two forms is compensated by an almost equal and opposite small difference in the entropy term (-T AS), so that the difference in free energy (AG) is not sufficient to lead to observable differences in either dissolution rate or equilibrium solubility. The bioequivalence of the two polymorphs of enalapril maleate is therefore easily explained thermodynamically. 

The estimation of the number of Frenkel defects in a crystal can proceed along lines parallel to those for Schottky defects by estimating the configurational entropy (Supplementary Material S4). This approach confirms that Frenkel defects are thermodynamically stable intrinsic defects that cannot be removed by thermal treatment. Because of this, the defect population can be treated as a chemical equilibrium. For a crystal of composition MX, the appropriate chemical equilibrium for Frenkel defects on the cation sublattice is... 

Twice the intrinsic ("real ) electrochemical entropy of activation, obtained from 2TAS =... 

Intrinsic entropy of activation for homogeneous self-exchange. Values for V and... 

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