Evaluating virial coefficients for multicomponent mixtures: hard sphere mixtures and flexible chains

Virial coefficients of Lennard-Jones mixtures

We report results of calculations of the second through sixth virial coefficients for four prototype Lennard-Jones (LJ) mixtures that have been the subject of previous studies in the literature. Values are reported for temperatures ranging from T=0.6 to T=10.0, where here the temperature is given units of the LJ energy parameter of one of the components. Thermodynamic stability of the mixtures is studied using the virial equation of state (VEOS) with the calculated coefficients, with particular focus on characterizing the vapor-liquid critical behavior of the mixtures. For three of the mixtures, vapor-liquid coexistence and critical data are available for comparison at only one temperature, while for the fourth we can compare to a critical line. We find that the VEOS provides a useful indication of the presence and location of critical behavior, although in some situations we find need to consider "near-miss" critical behavior, where the classical conditions of criticality are nearly but not exactly satisfied.

Osmotic pressure and virial coefficients of star and comb polymer solutions: dissipative particle dynamics

The effects of macromolecular architecture on the osmotic pressure pi and virial coefficients (B(2) and B(3)) of star and comb polymers in good solvents are studied by dissipative particle dynamics simulations for both dilute and semiconcentrated regimes. The dependence of the osmotic pressure on polymer concentration is directly calculated by considering two reservoirs separated by a semipermeable, fictitious membrane. Our simulation results show that the ratios A(n+1) identical with B(n+1)/R(g)(3n) are essentially constant and A(2) and A(3) are arm number (f) dependent, where R(g) is zero-density radius of gyration. The value of dimensionless virial ratio g = A(3)/A(2)(2) increases with arm number of stars whereas it is essentially arm number independent for comb polymers. In semiconcentrated regime the scaling relation between osmotic pressure and volume fraction, pi proportional to phi(lambda), still holds for both star and comb polymers. For comb polymers, the exponent lambda is close to lambda(*) (approximately = 2.73 for linear chains) and is independent of the arm number. However, for star polymers, the exponent lambda deviates from lambda(*) and actually grows with increasing the arm number. This may be attributed to the significant ternary interactions near the star core in the many-arm systems.

Isotropic-nematic phase transition in athermal solutions of rod-coil diblock copolymers

We present a hybrid method to investigate the isotropic-nematic (I-N) transition in athermal solutions of rod-coil copolymers. This method incorporates the scaled-particle theory for semiflexible chains with two-chain Monte Carlo simulation for the osmotic second virial coefficient and for the angle-dependent excluded volume. We compare the theoretical prediction with Monte Carlo simulations for fused rod-coil copolymers and find good agreement for both the equation of state and the orientational order parameter. The theory is also used to examine the effects of the bond length, the chain length, and the chain composition on orientational ordering in athermal solutions of rod-coil block copolymers. It predicts I-N transition in rod-coil copolymers with fixed rod length but a variable flexible tail in good agreement with experiments.

Isotropic-nematic phase transition: Influence of intramolecular flexibility using a fused hard sphere model

The role of flexibility on the liquid crystal isotropic-nematic phase transition has been studied by means of Monte Carlo simulation. We present equations of state for the isotropic-nematic branches and, in the isotropic phase, numerically calculated values for the virial coefficients B2, B3, and B4. We have studied two models: 11 hard sphere monomers fused in a linear configuration with a reduced bond length of 0.6 and a 15-monomer version of this model in which monomers at one end of the chain become flexible. We have observed spontaneous nematic liquid crystal formation for both of the fully rigid models, and also for models with up to six flexible monomers in the tail. We conclude that molecular flexibility has a strongly destabilizing effect on the nematic phase. This is probably due to the decrease in shape anisotropy that flexible tails allow.