Entropic contribution interaction parameter

It is important for the theoretical understanding of the formation of various topologies that these aggregates have entropic contributions on the scale of the objects, i.e. on a much larger scale than set by the molecules. These cooperative entropic effects should be included in the overall Helmholtz energy, and they are essential to describe the full phase behaviour. It is believed that the mechanical parameters discussed above kc,k and J0, control the phase behaviour, where it is understood that these quantities may, in principle, depend on the overall surfactant (lipid) concentration, i.e. when the membranes are packed to such a density that they strongly interact. 

The Flory-Huggins interaction parameter, x Is the sum of enthalpic (xH) and entropic (x ) contributions to the polymer-solute interactions (28). xs is an emPitical constant related to the coordination of the polymer subunits (29). Chiou et al. (20) have selected a value of 0.25 for xs of humlc matter. From regular solution theory, xq is given by... 

Flory-Huggins interaction parameter (-) enthalpic contribution to x ( ) entropic contribution to x ( ) efficiency factor for sorption (-)... 

Since the Flory interaction parameter, x> was derived by considering only interaction energies between the molecules, it should not contain any entropic contributions and Equation (2D-9) should yield the correct value for the Flory-/ parameter. Unfortunately, x contains not only enthalpic contributions from interaction energies, but also entropic contributions. The solubility parameter includes only interaction energies and by the definition of regular solutions does not include any excess entropy contributions. Blanks and Prausnitz (1964) point out that the Flory / parameter is best calculated from... 

Originally x was stated to be independent of polymer concentration. The X-parameters determined by many investigators using one or another of the methods for measuring colligative properties of polymer-liquid solutions (mentioned below) show that this is not the case (see Tables 3-22 of Reference 43) nor does x vary linearly with 1/T as stated in Eq. 7. Later [44] a quantity Aws representing an entropic contribution from contact interaction was added to the Flory-Huggins definition of x to produce a relationship linear in 1/T. 

Other unfavourable entropic contributions to the free energy exist which make the entropy of mixing negative. The TAS term in Eq. (1) is thus more unfavourable at higher temperatures. Such terms could possibly arise out of the specific interactions which themselves infer an ordering of the system. Such terms involving an empirical parameter have been included in modified versions of the Equation-of-state theory... 

The retention times of analytes are controlled by the concentration(s) of the organic solvent(s) in the mobile phase. If a relatively small entropic contribution to the retention is neglected, theoretical considerations based either on the model of interaction indices [58], on the solubility parameter theory [51,52] or on the molecular statistical theory [57], lead to the derivation of a quadratic equation for the dependence of the logarithm of the retention factor of a solute. A, on the concentration of organic solvent. aqueous-organic mobile phase ... 

Here, L is the number of cells in each lattice layer k Indicates all molecules and vacancies in the system a and p refer to the segment types (CH2(3) or vacancy) u (z)/kT is an - essentially entropic - contribution following from the self consistency of the method which takes care that all sites are occupied by segments (or molecules or vacancies) a or P is the Flory-Huggins parameter for interactions... 

The interpretation of the Flory-Huggins interaction parameter as a residual free energy function [14] rather than the original enthalpy parameter allows separation into enthalpic and entropic contributions... 

Guillet and coworkers (8-10) have determined the solubility parameter of polymers from the probe-polymer interaction coefficients. They separated the interaction parameter into entropic and enthalpic contributions, such that Xi2=X h+Xs to yield, in combination with Hildebrand s solution theory, the following expression ... 

Each blend pair xx/x2 has a characteristic entropic contribution %ss hardly sensitive to the isotope swapping. Within each such pair the larger bulk interaction parameter % corresponds to a bigger difference between solubility parameters 8a and SB and, hence, to an increase in both the enthalpic contribution %sH>mn an(j thg surface parameter %s itself. This explains qualitatively the remarks made for Fig. 27a. 

A fundamental limitation for fhe apphcation of geometric fitting procedures is that fhe complexation free energies are fhe sum of enthalpic and entropic contributions, with the consequence that selectivity can be inversed at different temperatures. Positive cooperativity between different interactions in a complex will usually lead to tighter association at fhe expense of motional freedom and fhus of entropy [51]. The interplay and often observed compensation of enthalpic and entropic contributions have been discussed in several reviews [10, 52, 53], particularly with emphasis on biological systems, and cannot be dealt with in detail here. Unfortunately, many published enthalpy-entropy compensations are blurred by possible artifacts, as the two underlying parameters do not represent independent variables [54]. 

Table 2.6. Enthalpic and entropic contributions to the H-F binary interaction parameter, %i2 Eq 2.43)...

The lattice theories are the oldest and most frequently used to interpret and to predict the thermodynamic properties of multicomponent systems containing polymers. The Huggins-Flory lattice theory is the best known. To use the theory one must know the temperature, pressure and concentration dependence of the enthalpic and entropic contributions to the binary interaction parameter, P, ) + P, , ) / T. 

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