Second Virial Coefficient Calculations for Square-Well Chain Molecules

Abstract

The second virial coefficient, Bz, has been calculated for square-well chain molecules of lengths n = 2-50 and well widths of X = 0.25-1.0 by Monte Carlo integration. The theta temperature, at which Bz = 0, is independent of chain length around X = 0.5, increases with chain length for X > 0.5, and decreases with chain length for X < 0.5. A scaling relation, Te*(n) -To*(-) a n", accurately describes the departure of the theta temperature from the infinite chain length value for X 1 0.6. A closed-form expression for the second virial coefficient of square-well chains is presented which accurately fits the Monte Carlo data for n = 2-50 and X = 0.25-0.75. When compared to the Monte Carlo results, the second virial coefficient predicted by the generalized Flory-dimer theory for square-well chains is found to be increasingly inaccurate as chain length increases. If we correct the generalized Flory-dimer equation of state by forcing it to have the correct second virial coefficient, the compressibility factor is accurately predicted at densities below 7 = 0.04.

Critical temperature of infinitely long chains from Wertheim's perturbation theory

“…In [56,57]. Y is the critical temperature of the in® nitely long chain, obtained either from Wertheim's theory or from Monte Carlo (MC) results of [54,55] One ® nal comment concerning the Y temperature. Wertheim's theory assumes that the Y temperature of chains made of¯exible tangent monomers is independent of the bonding angle and the torsional potential.…”

Square-well chain molecules: a semi-empirical equation of state and Monte Carlo simulation data

“…To gain insight into the microscopic and macroscopic behavior of chain molecules, many investigators have performed molecular simulations for various model chain fluids, such as hard-sphere chains [1][2][3][4][5][6][7], square-well chains [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], Lennard-Jones chains [14], and Yukawa chains [23][24][25]. Among these chain fluids, the square-well chain fluid is the simplest one having both repulsive and attractive parts.…”

“…For pure square-well chain fluids PVT properties [9][10][11]13,14], vapor-liquid equilibrium (VLE) phase envelopes [8,14,17], second virial coefficients [12], configurational internal energy [15], and constant-volume heat capacity [19] data are available. For square-well chain mixtures, Gulati and Hall [16] and Paredes et al [19] calculated PVT properties and configurational internal energy, Davies et al [17] computed the VLE properties for mixtures of square-well monomers and dimers, while McCabe et al [45] studied non-conformal monomer-dimer mixtures.…”

The SW-MSA Calculation of Self-Diffusion Coefficients in Liquid Lithium and Rubidium

“…This model in different modifications is widely studied by means of both theoretical and computer-simulation methods [4][5][6] and applied to investigate different-kind real substances, such as non-polar molecular fluids [7,8], colloids [9][10][11][12], aqueous electrolyte solutions [13,14], polymers [15,16], polar and associating compounds [17], quasi-crystals [18]. To liquid metals the SW model is applied beginning with the work [19] up to now [20][21][22][23][24].…”