Exclusion volume effective

It should be noted that the concentration effect, though intuitively clear-cut and understandable, has a limit in its validity. It is due to the plain fact that molecules or ions occupy definite exclusion volumes. Because of this exclusion volume effect, the reactants can be concentrated only up to a certain upper limit. According to Kosh-land [61], the intramomolecular reaction rate is only 4.6 times larger than the inter-molecular one when the reactants have the same exclusion volumes as the solvent... 

This was precisely the point where a was defined to equal unity, so it is entirely appropriate that inter- and intramolecular exclusion volumes are effectively zero under the same conditions. 

A similar effect may exist for hydrophobic interaction between solute and stationary phase, as one solute may adsorb more strongly to the stationary phase than another. It has also been remarked that a flexible polymer confined to a pore should be at a lower entropy than one in bulk solution, leading to exclusion in excess of that expected for a simple geometric solid.23 Even in the absence of interactions, a high concentration of a small component can lead to an excluded volume effect, since the effective volume inside the pore is reduced. 

Surprisingly enongh, the above processes are very fast and separation of macromolecnles on this principle can be considered an equilibrium process. The precise measurements of retention volumes of polymers under conditions of their partial pore permeation in absence of enthalpic interaction did not reveal practically any effect of the eluent flow rate [55]. On the contrary, in a review, Aubert and Tirrell [66] have demonstrated that the SEC exclusion volumes can be flow rate dependent due to both anomalous and physical effects. The former are caused by... 

The effect of limited penetration of the pores by the largest molecules may also be applied beneficially for the separation of very large molecules. Depending on the size of the molecules (in solution), they will be more ore less excluded from the pores, and hence the retention times will be affected. This effect is used in size exclusion chromatography (SEC) or gel permeation chromatography (GPC). In this technique, any interactions between the solute molecules and the stationary phase are purposefully avoided. The solute molecules remain exclusively in the mobile phase, but the accessible mobile phase volume, and hence the retention volume, may vary between the total volume of the mobile phase and the so-called exclusion volume, which is the total volume of mobile phase outside the pores. The latter elution volume applies to very large solute molecules (excluded solutes),... 

It can be proved that these unperturbed dimensions approximate to the statistically determined dimensions of the isolated chain under 0 conditions the excluded volume effect is compensated by a positive, i. e. unfavorable, polymer-solvent interaction enogy. The rmperturbed dimensions of polymer chains are, therefore, subject in general to direct experimental determination in dilute solution in appropriate solvents in which the volume exclusion effect upon coil dimensions is nullified. 

Exclusion effects are commonly called excluded volume effects . 

Two diverse views of non-specific adhesion processes form the bases for contemporary theories introduced to rationalize observations of colloidal stability and flocculation in solutions of macromolecules (see 16-18 for general reviews). The first view is based on adsorption and cross-bridging of the macromolecules between surfaces. Theories derived from this concept indicate a strong initial dependence on concentration of macromolecules there is a rapid rise in surface adsorption for infinitesimal volume fractions (32) followed by a plateau with gradual attenuation of surface-surface attraction because of excluded volume effects in the gap at larger volume fractions (19-20). The interaction of the macroinolecule with the surface is assumed to be a snort range attraction proportional to area of direct contact. The second - completely disparate - view of non-specific adhesion is based on the concept that there is an exclusion or depletion of macromolecules in the vicinity of the surface, i.e. no adsorption to the surfaces. Here, theory shows that attraction is caused by interaction of tne (depleted) concentration profiles associated with each surface which leads to a depreciated macrornolecular concentration at the center of the gap. The concentration... 

The emission parameter, is calculated, taking into account contribution of matrix frustration to the free energy of cluster distributions in binary alloys (Lepinoux 2006,2009). This effect is typical for concentrated alloys, when Frenkel s model of ideal cluster gas (Frenkel 1955) is not valid and it is necessary to consider the interaction between the clusters by means of so-called exclusion volume, i.e., the number of forbidden atomic sites (or volume normalized by the atomic volume) to a -mer by an n-mer. In our paper it is suggested to take into account the frustration effect empirically by the use of the thermodynamic free energy expression from CALPHAD (Andersson and Sundman 1987) with the correction suggested by Bonny et al. (2010). 

The OP correlation functional (Tsuneda et al. 1999) determines the exclusion volume of the correlation hole, by assuming that it is proportional to the exclusion volume of the exchange hole coming from the combined exchange functional, in order to enhance the physical validity of the CS-type correlation functional. In this functional, only electron correlations of opposite-spin pairs are explicitly incorporated, while electron correlations of parallel-spin pairs are secondary effects from the combined exchange functional. It has only one semiempirical parameter, which is the minimum required for adapting to the exchange functional. As a result, a simple correlation functional was derived ... 

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