Virial coefficients and demixing in the Asakura-Oosawa model.

The problem of demixing in the Asakura-Oosawa colloid-polymer model is considered. The critical constants are computed using truncated virial expansions up to fifth order. While the exact analytical results for the second and third virial coefficients are known for any size ratio, analytical results for the fourth virial coefficient are provided here, and fifth virial coefficients are obtained numerically for particular size ratios using standard Monte Carlo techniques. We have computed the critical constants by successively considering the truncated virial series up to the second, third, fourth, and fifth virial coefficients. The results for the critical colloid and (reservoir) polymer packing fractions are compared with those that follow from available Monte Carlo simulations in the grand canonical ensemble. Limitations and perspectives of this approach are pointed out.

[1]  S. Wereley,et al.  Soft Matter , 2014 .

[2]  K. Binder,et al.  Perspective: The Asakura Oosawa model: a colloid prototype for bulk and interfacial phase behavior. , 2014, The Journal of chemical physics.

[3]  A. Parola,et al.  How soft repulsion enhances the depletion mechanism. , 2014, Soft matter.

[4]  Douglas J. Ashton,et al.  Three-body interactions in complex fluids: virial coefficients from simulation finite-size effects. , 2014, The Journal of chemical physics.

[5]  Andrés Santos,et al.  Communication: Virial coefficients and demixing in highly asymmetric binary additive hard-sphere mixtures. , 2013, The Journal of chemical physics.

[6]  I. Urrutia.  Analytical behavior of the fourth and fifth virial coefficients of a hard-sphere mixture. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  A. Pelissetto,et al.  Fluid–fluid demixing curves for colloid–polymer mixtures in a random colloidal matrix , 2011, 1109.1405.

[8]  Douglas J. Ashton,et al.  Depletion potentials in highly size-asymmetric binary hard-sphere mixtures: comparison of simulation results with theory. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  M. Schmidt,et al.  Binary non-additive hard sphere mixtures: fluid demixing, asymptotic decay of correlations and free fluid interfaces , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[10]  M. L. Haro,et al.  Critical consolute point in hard-sphere binary mixtures: Effect of the value of the eighth and higher virial coefficients on its location , 2010 .

[11]  S. B. Yuste,et al.  Virial coefficients, thermodynamic properties, and fluid-fluid transition of nonadditive hard-sphere mixtures. , 2009, The Journal of chemical physics.

[12]  J. Kolafa,et al.  Analytical expressions for the fourth virial coefficient of a hard-sphere mixture. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  J. Errington,et al.  Fluid phase behavior of a model colloid-polymer mixture: Influence of polymer size and interaction strength. , 2008, The Journal of chemical physics.

[14]  Jochen Zausch,et al.  Statics and dynamics of colloid-polymer mixtures near their critical point of phase separation: A computer simulation study of a continuous Asakura-Oosawa model. , 2008, The Journal of chemical physics.

[15]  E. Sanz,et al.  Crystallization and gelation in colloidal systems with short-ranged attractive interactions. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  L. Reatto,et al.  Critical behavior in colloid-polymer mixtures: theory and simulation. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  L. Reatto,et al.  Fluid–fluid and fluid–solid phase separation in nonadditive asymmetric binary hard-sphere mixtures , 2005 .

[18]  Peter Sollich,et al.  Effects of polymer polydispersity on the phase behaviour of colloid–polymer mixtures , 2004, cond-mat/0411701.

[19]  Peter Sollich,et al.  Effects of colloid polydispersity on the phase behavior of colloid-polymer mixtures. , 2004, The Journal of chemical physics.

[20]  S. B. Yuste,et al.  Equation of state of nonadditive d-dimensional hard-sphere mixtures. , 2004, The Journal of chemical physics.

[21]  J. Horbach,et al.  Critical behaviour and interfacial fluctuations in a phase-separating model colloid–polymer mixture: grand canonical Monte Carlo simulations , 2004 .

[22]  K. Binder,et al.  Critical phenomena in colloid-polymer mixtures: interfacial tension, order parameter, susceptibility, and coexistence diameter. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  M. López de Haro,et al.  Rescaled density expansions and demixing in hard-sphere binary mixtures. , 2004, The Journal of chemical physics.

[24]  R. Evans,et al.  Statistical mechanics of inhomogeneous model colloid—polymer mixtures , 2003 .

[25]  R. Vink,et al.  Grand canonical Monte Carlo simulation of a model colloid-polymer mixture: coexistence line, critical behavior, and interfacial tension. , 2003, The Journal of chemical physics.

[26]  M. Fisher,et al.  Fluid Critical Points from Simulations: the Bruce-Wilding method and Yang-Yang anomalies , 2003, cond-mat/0310247.

[27]  A. Vlasov,et al.  Binary mixtures of hard spheres: how far can one go with the virial equation of state? , 2003 .

[28]  H. Löwen,et al.  Density functional theory for a model colloid-polymer mixture: bulk fluid phases , 2002 .

[29]  J. Hansen,et al.  Influence of polymer-excluded volume on the phase-behavior of colloid-polymer mixtures. , 2002, Physical review letters.

[30]  H. Löwen,et al.  Phase behavior and structure of star-polymer-colloid mixtures , 2002 .

[31]  M. Dijkstra,et al.  Effective Interactions, Structure, and Isothermal Compressibility of Colloidal Suspensions , 2000 .

[32]  Evans,et al.  Density functional for a model colloid-polymer mixture , 2000, Physical review letters.

[33]  Joseph M. Brader,et al.  Phase behaviour and structure of model colloid-polymer mixtures , 1999 .

[34]  J. Hansen,et al.  Crystallization and phase separation in nonadditive binary hard-sphere mixtures , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[35]  R. Blaak.  Exact analytic expression for a subset of fourth virial coefficients of polydisperse hard sphere mixtures , 1998, cond-mat/9812097.

[36]  F. Saija,et al.  Virial expansion of a non-additive hard-sphere mixture , 1998 .

[37]  J. Hansen,et al.  Osmotic depletion, non-additivity and phase separation , 1997 .

[38]  D. Frenkel,et al.  Depletion effects in binary hard-sphere fluids , 1996 .

[39]  E. Hamad.  Contact pair correlation functions and equation of state for nonadditive hard‐sphere mixtures , 1996 .

[40]  Poon,et al.  Phase behavior of a model colloid-polymer mixture. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[41]  D. Frenkel.  The simulation of entropic phase transitions , 1994 .

[42]  D. Frenkel,et al.  Colloids dispersed in polymer solutions. A computer simulation study , 1994 .

[43]  P. B. Warren,et al.  Phase Behaviour of Colloid + Polymer Mixtures , 1992 .

[44]  Meijer,et al.  Computer simulation of polymer-induced clustering of colloids. , 1991, Physical review letters.

[45]  C. Hall,et al.  Polymer-induced phase separations in nonaqueous colloidal suspensions , 1983 .

[46]  Fumio Oosawa,et al.  Interaction between particles suspended in solutions of macromolecules , 1958 .

[47]  Fumio Oosawa,et al.  Surface Tension of High‐Polymer Solutions , 1954 .

[48]  Takuji Nishimura,et al.  Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator , 1998, TOMC.

[49]  A. Vrij,et al.  Polymers at Interfaces and the Interactions in Colloidal Dispersions , 1976 .