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Register a new userThe vanishing limit of the square-well fluid: the adhesive hard sphere model as a reference system
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We report a simulation study of the gas-liquid critical point for the square-well potential, for values of well width delta as small as 0.005 times the particle diameter sigma. For small delta, the reduced second virial coefficient at the critical point B_2*c is found to depend linearly on delta. The observed weak linear dependence is not sufficient to produce any significant observable effect if the critical temperature T_c is estimated via a constant B_2*c assumption, due to the highly non linear transformation between B_2*c and T_c. This explains the previously observed validity of the law of corresponding states. The critical density rho_c is also found to be constant when measured in units of the cubed average distance between two bonded particles (1+0.5 delta)/sigma. The possibility of describing the delta -> 0 dependence with precise functional forms provides improved acccurate estimates of the critical parameters of the adhesive hard-sphere AHS model.
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The solid-solid coexistence of a polydisperse hard sphere system is studied by using the Monte Carlo simulation. The results show that for large enough polydispersity the solid-solid coexistence state is more stable than the single-phase solid. The two coexisting solids have different composition distributions but the same crystal structure. Moreover, there is evidence that the solid-solid transition terminates in a critical point as in the case of the fluid-fluid transition.
In a companion paper, we derived analytical expressions for the structure factor of the square-shoulder potential in a perturbative way around the high- and low-temperature regimes. Here, various physical properties of these solutions are derived. In particular, we investigate the large wave number sector, and relate it to the contact values of the pair-correlation function. Then, thermoelastic properties of the square-shoulder fluids are discussed.
By extending the nonequilibrium potential refinement algorithm and lattice switch method to the semigrand ensemble, the semigrand potentials of the fcc and hcp structures of polydisperse hard-sphere crystals are calculated with the bias sampling scheme. The result shows that the fcc structure is more stable than the hcp structure for polydisperse hard-sphere crystals below the terminal polydispersity.
Colloidal systems observed in video microscopy are often analysed using the displacements correlation matrix of particle positions. In non-thermal systems, the inverse of this matrix can be interpreted as a pair-interaction potential between particles. If the system is thermally agitated, however, only an effective interaction is accessible from the correlation matrix. We show how this effective interaction differs from the non-thermal case by comparing with high-statistics numerical data from hard-sphere crystals.
The coupling-parameter method, whereby an extra particle is progressively coupled to the rest of the particles, is applied to the sticky-hard-sphere fluid to obtain its equation of state in the so-called chemical-potential route ($mu$ route). As a consistency test, the results for one-dimensional sticky particles are shown to be exact. Results corresponding to the three-dimensional case (Baxters model) are derived within the Percus-Yevick approximation by using different prescriptions for the dependence of the interaction potential of the extra particle on the coupling parameter. The critical point and the coexistence curve of the gas-liquid phase transition are obtained in the $mu$ route and compared with predictions from other thermodynamics routes and from computer simulations. The results show that the $mu$ route yields a general better description than the virial, energy, compressibility, and zero-separation routes.
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