Ideality, deviation from virial function

Virial Function. A useful form of expression for deviations from the ideal gas law is the virial equation,... 

The most general of the equations of state is the virial equation, which is also the most fundamental since it has a direct theoretical connection to the intermolecular potential function. The virial equation of state expresses the deviation from ideality as a series expansion in density and, in terms of molar volume, can be written... 

Such equations (sometimes the expansion is written in powers of P) are called virial equations of state, and the coefficients P, C, D,... are the second, third, fourth,... virial coefficients. The thermodynamic functions Cp, H and S of the real gas deviate from the expressions already presented by correction factors that are functions of the virial coefficients. For example, the deviation of Cp from the ideal gas heat capacity, C°, is given by ... 

At even quite moderate pressures of a few atmospheres the static permittivites of gases show significant deviations from simple linear proportionality to density expected for ideal gases without significant effects of molecular interactions. As with the equation of state for pressure as a function of density these deviations can be described by a virial series in powers of density with second and higher order dielectric virial coefficients. To introduce these in convenient form for theoretical analysis a macroscopic spherical sample in vacuum is assumed with a uniform field (before insertion of the sample) from external chargee. As the macroscopic in the sample is then given by =... 

As well as controlling chain dimensions, solvent quality affects the thermodynamics of dilute polymer solutions. This is because interactions between polymer chains are modified by the presence of solvent molecules. In particular, solvent molecules will change the excluded volume for a polymer coil, i.e. how much volume it takes up and prevents neighbouring chains from occupying. In a theta solvent, the excluded volume is zero (this holds for the excluded volume for a polymer segment or the whole coil). The solution is said to he ideal if the excluded volume vanishes. Deviations from ideality for polymer solutions are described in terms of a virial equation, just as deviations from ideal gas behaviour are. The virial equation for a polymer solution in terms of polymer concentration is given by Eq. (2.9). The second virial coefficient depends on interactions between pairs of molecules in particular it is proportional to the excluded volume. Therefore, in a theta solvent, = 0. If the solvent is good then Ai > 0, but if it is poor Ai < 0. If the solvent quality varies as a function of temperature and theta (0) conditions are attained, this occurs at the theta temperature. 

We have used the results of the general theory discussed in the earlier part of this paper in the calculation of the second virial coefficient of solutions of compact and flexible macromolecules. Our results express the large deviation of the macromolecular solutions from an ideal solution as functions of the large dimensions or on the large internal degrees of... 

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