Volume effective, for

Expansion of Thickness of the Adsorbed Layer. In the low salt concentration the large thickness compared with the case of the Theta solvent (4.17 M NaCl) is considered to be due to the electrostatic repulsion, i.e., the excluded volume effect of the adsorbed NaPSS chains. Usually, the expansion factor at, defined by the ratio of the thickness in good solvent and that in the Theta solvent, is used to quantitatively evaluate the excluded volume effect for the adsorbed polymers. 

In benzene, the distribution constant depends on specific interactions between the solute and the benzene pi-electrons. Table 4.4 shows the importance of the volume effect for the mercury halide benzene system (Cl[Pg.132]

Zimmerman, S.B., and S.O. Trach (1991). Estimation of macromolecular concentrations and excluded volume effects for the cytoplasm of Escherichia coli. J. Mol. Biol. 222 599-620. 

Krishnan and Friedman, 1974), the main contribution to the salting out stems from the COR term [eqn (21)], i.e. an excluded volume effect. For alkane — R4N+ co-sphere interactions, hydrophobic association is important. 

The mixing of surfactant and polymer in the porous medium occurs due to both dispersion and the excluded volume effect for the flow of polymer molecules in porous media, which in turn could lead to the phase separation. Figure 16 illustrates the schematic explanation of the surfactant-polymer incompatibility and concomittant phase separation. We propose that around each micelle there is a region of solvent that is excluded to polymer molecules. However, when these micelles approach each other, there is overlapping of this excluded region. Therefore, if all micelles separate out then the excluded region diminishes due to the overlap of the shell and more solvent becomes available for the polymer molecules. This effect is very similar to the polymer depletion stabilization (55). Therefore, this is similar to osmotic effect where the polymer molecule tends to maximize the solvent for all possible configurations. ... 

The same workers found significantly smaller volume effects for reversible electron transfer between xanthene dyes and transition metal cyanides, Eq. 

As mentioned in Section III.B, it is essential to consider the volume effect for a quantitative analysis of the thermal effect. This volume effect should be particularly important for the dissociation (or combination) reaction because one molecule breaks into two or more species (or vise versa for combination), and this process creates (or decreases) an additional void volume around each species. In order to measure the volume effect experimentally, either the temperature or solvent dependence method was used, but it contains some difficulties (Section III.B). Another method was proposed to overcome the limitations of the traditional method [119,120]. This method was based on a time-resolved measurement in a longer time scale that is, separation of the thermal effect and the other contributions due to the chemical species (species grating) is achieved based on the difference of the diffusion constants of the thermal energy and chemical species. Next, the volume effect is considered in more detail. 

Thus, the dimension is also characteristic of volume effects for mac-romolecular coil in solution in virtue of its unequivocal dependence on . 

Let us consider now the examples, demonstrating, how the fractal dimension Dy can characterize volume effects for biopolymers (and polymers at all) [39, 41]. With this purpose the available in literature values for two polysaccharides (polymaltotrioze (pullulan), for which a =0.66 [18], and rodexman, for which a 0.75 [17]) and also dimethyldiallylam-monium chloride (DMDAAC), for which a 0.82 in water solutions [42] were used. According to the Eq. (4) estimation the values 7) are equal to... 

The two quantifies are related, in the absence of excluded volume effects, for simple chains by... 

Wonlocalized interactions play a unique role in the assembly of SPs. particularly in their hierarchical evolution from nano to mesoscopic dimensions. One type of smoothed-out interaction is described by thermodynamic parameters of compatibility between solute and solvent species (i.e., the x parameter), and another type is related to thermodynamic parameters describing excluded volume effects for unimers and growing... 

This first part of this article deals only with treatment of bonded interactions of polymer chains, appropriate only for modeling chains under -point conditions. Problems connected with effects of excluded volume are presented at the end of this chapter. The excluded volume effect for chains in good solvents are also presented in Chaps. IIB [10] and HID [11] of this handbook and in books by Freed [12], de Gennes [13], des Cloizeaux and Jannink [14], and... 

Thus the real, dimensionless, expansion parameter is When i is small, the chain is ideal. When is large, the chain shows strong excluded volume effects. (For intermediate values a precise interpolation formula I r the most simplified models R/Ro is a function of only. This point will be discussed mote in Chapter XI. 

Fig. 49. The calculated magneto-volume effect for Y(Fei Coj2 (marked theory) compared with the same effect estimated from experiments (see text). (After Eriksson et al. 1989b.)...

The computer simulation studies of Frenkel et al. [45] indicate that the excluded volume effects for molecular hard cores must play an important role in the stabilization of the smectic phase. In particular, it has been shown that hard spherocylinders, interacting only via hard-core repulsion, can form nematic, smectic A, and columnar phases. 

The effective surface area a is the suffice area of the packing per 1 m of its volume, effective for the mass transfer processes. Because it is related wife fee wetted area of fee packing eh, both values are usually considered together. Their dimension is mVm or m ... 

Polymer-polymer interactions also act to suppress excluded volume effects for chains in good solvents. Mean coil dimensions shrink, and the minimum at low r disappears in the distribution function W(r), figure 1. These circumstances lead to an increase in as well as in W(0). 

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