Molar volume of solvent

Vr = Volume fraction of polymer in swollen gel f.1 = Huggins solvent/polymer interaction parameter V0 = Molar volume of solvent (cm3)... 

Fluctuation theory gives Eq. (32), which is converted to Eq. (33) via thermodynamic transpositions and approximation of partial molar volume of solvent to its molar volume Vj ... 

In Fiery s theory of the excluded volume (27), the chains in undiluted polymer systems assume their unperturbed dimensions. The expansion factor in solutions is governed by the parameter (J — x)/v, v being the molar volume of solvent and x the segment-solvent interaction (regular solution) parameter. In undiluted polymers, the solvent for any molecule is simply other polymer molecules. If it is assumed that the excluded volume term in the thermodynamic theory of concentrated systems can be applied directly to the determination of coil dimensions, then x is automatically zero but v is very large, reducing the expansion to zero. 

In the above equations, % is the polymer-solvent interaction parameter, kB the Boltzmann constant, T the absolute temperature, NA Avogadro s number, v, the molar volume of solvent. If the network is made up only of neutral monomers, 7im and 7te sum up to generate the total osmotic pressure it . On the other hand, when ionizable species are contained in the network, the osmotic pressure due to ions must be considered. The contribution from counter ions [5,10,11] is... 

Kg is the experimental distribution coefficient and K g the corrected value. This correction is required, because any measure for the interactions that occur in certain solvents should be more related to the ratio of mole fractions than to the ratio of concentrations of the solute in the liquid phase and in the gas phase. We may assume the molar volume of the gas phase to be constant and hence irrelevant if our purpose is a classification of solvents. However, the molar volumes of solvents vary a great deal. The Kg values for n-octane in various hydrocarbon solvents vary up to a factor of 3.9 between cyclohexane and squalane [216]. The Kg values vary by a more realistic factor of 1.5 [214]. 

Molar volume, m /mol Molar volume of solute, m /mol Molar volume of solvent, m /mol Partial molar volume of the /th component, m /mol Pressure, Pa... 

This nr1 dependence of the second virial coefficient has been already predicted in the Flory excluded volume theory [6] let a be the expansion factor of a chain molecule and Vs the molar volume of solvents. Following Flory, one has... 

Subsequently another new criterion has been introduced (47) in terms of the relative partial molar volume reduction (RPMVR) of solvent. This is based on the fact that the partial molar volume of solvent, V2 slowly decreases with increasing CO2 mole fraction and drastically reduces at high values of... 

The variation in the molar volume of the solution at a high CO2 dissolution is relatively less sensitive than the partial molar volume of the solvent. The plots in Figure 22 compare the molar volume v and the partial molar volumes of solvent and CO2 for hexane-C02 and ethyl acetate-C02 systems. It can be observed that the plots of vi, v, and vi intersect at a high value of 1, at which v tends to pass through a minimum, though not prominently, since all three values are equal at this value of Xi. In other words, the value of Xi corresponding to the minimum molar volume can be obtained graphically only from the point of intersection of these three plots. 

If the molar volume of solvent is V, with the same volume unit as is used to express the concentration Ci and C (e.g., liters), then for dilute solution Cl = 1/Fi and... 

SOLUBILITY PARAMETERS AND MOLAR VOLUMES OF SOLVENTS AND SOLVENT UPTAKE BY NAFION (3). 

V = partial specific volume of solute Na = Avogadro s number V = molar volume of solvent... 

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