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Virial coefficients appear as coefficients in the virial expansion of the pressure of a many-particle system in powers of the density, providing systematic corrections to the ideal gas law. They are characteristic of the interaction potential between the particles and in general depend on the temperature. The second virial coefficient depends ...
The second, B, and third, C, virial coefficients have been studied extensively and tabulated for many fluids for more than a century.Two of the most extensive compilations are in the books by Dymond [2] [3] and the National Institute of Standards and Technology's Thermo Data Engine Database [4] and its Web Thermo Tables. [5]
An advantage of the Debye plot is the possibility to determine the second virial coefficient. This parameter describes the interaction between particles and the solvent. In macromolecule solutions, for instance, it can assume negative (particle-particle interactions are favored), zero, or positive values (particle-solvent interactions are favored).
This binary interaction parameter or second virial coefficient depends on ionic strength, on the particular species i and j and the temperature and pressure. The quantities μ ijk represent the interactions between three particles. Higher terms may also be included in the virial expansion.
A is the first virial coefficient, which has a constant value of 1 and makes the statement that when volume is large, all fluids behave like ideal gases. The second virial coefficient B corresponds to interactions between pairs of molecules, C to triplets, and so on. Accuracy can be increased indefinitely by considering higher order terms.
The Boyle temperature is formally defined as the temperature for which the second virial coefficient, , becomes zero. It is at this temperature that the attractive forces and the repulsive forces acting on the gas particles balance out. This is the virial equation of state and describes a real gas. Since higher order virial coefficients are ...
Both phase equilibrium properties and homogeneous state properties at arbitrary density can in general only be obtained from molecular simulations, whereas virial coefficients can be computed directly from the Lennard-Jones potential. [36] Numerical data for the second and third virial coefficient is available in a wide temperature range.
B reflects the energy of binary interactions between solvent molecules and segments of polymer chain. When B > 0, the solvent is "good," and when B < 0, the solvent is "poor". For a theta solvent, the second virial coefficient is zero because the excess chemical potential is zero; otherwise it would fall outside the definition of a theta solvent.