When depletion goes critical

Depletion interactions in correlated fluids are investigated both theoretically and experimentally. A formally exact derivation of a general expression for depletion interactions is presented and then specialized to the case of critical correlations in the depletant by employing a long wavelength approximate analysis. A scaling expression is obtained in the critical region, suggesting a close connection to the critical Casimir effect. As a result we are able to compute the full scaling function of the critical Casimir effect in terms of the known scaling form of the depletant equation of state. These predictions are experimentally tested in a colloidal suspension with a micellar solution as depletion agent. Colloids are seen to aggregate reversibly when the micellar concentration exceeds a temperature dependent value which becomes remarkably small as the temperature approaches the lower consolution point of the micellar suspension. Continuity between the standard depletion picture at low temperature and the Casimir effect in the critical region is demonstrated by identifying several approximate scaling laws which compare favorably with the theoretical analysis. The transition line is seen to lie close to the curve of maximum susceptibility of the depletant. A model, analyzed within mean field approximation, is shown to reproduce the main qualitative features of the phenomenon.

[1]  Beysens,et al.  Adsorption phenomena at the surface of silica spheres in a binary liquid mixture. , 1985, Physical review letters.

[2]  M. Corti,et al.  Critical Behavior of a Micellar Solution , 1980 .

[3]  N. Ashcroft,et al.  Weighted-density-functional theory of inhomogeneous liquids and the freezing transition. , 1985, Physical review. A, General physics.

[4]  Chen,et al.  Reexamination of the static and dynamic critical phenomena in water-amphiphile micellar solutions. , 1989, Physical review. A, General physics.

[5]  R. Kjellander.  Phase separation of non-ionic surfactant solutions. A treatment of the micellar interaction and form , 1982 .

[6]  R. Piazza,et al.  Phase Separation and Gel-like Structures in Mixtures of Colloids and Surfactant , 1994 .

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

[8]  Jingtao Wang,et al.  Nature of vapor-liquid asymmetry in fluid criticality. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Manohar,et al.  Application of Baxter's model to the theory of cloud points of nonionic surfactant solutions. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[10]  Fumio Oosawa,et al.  On Interaction between Two Bodies Immersed in a Solution of Macromolecules , 1954 .

[11]  R. Goldstein.  Model for phase equilibria in micellar solutions of nonionic surfactants , 1986 .

[12]  J. Bibette,et al.  Creaming of emulsions: the role of depletion forces induced by surfactant , 1992 .

[13]  S. Egelhaaf,et al.  Nonionic Micelles near the Critical Point: Micellar Growth and Attractive Interaction† , 2000 .

[14]  R. Evans.  The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform, classical fluids , 1979 .

[15]  R. Piazza,et al.  Depletion interaction and phase separation in mixtures of colloidal particles and nonionic micelles , 1996 .

[16]  D. Frenkel,et al.  Extended corresponding-states behavior for particles with variable range attractions , 2000, cond-mat/0004033.

[17]  J. Rieger,et al.  Depletion-induced phase separation in colloid-polymer mixtures. , 2003, Advances in colloid and interface science.

[18]  A. Parola,et al.  Enhancement of depletion forces by electrostatic depletant repulsion. , 2010, The Journal of chemical physics.

[19]  D. Cannell,et al.  Observation of 3D-Ising exponents in micellar solutions. , 1988, Physical review letters.

[20]  S. Dietrich,et al.  Direct measurement of critical Casimir forces , 2008, Nature.

[21]  C. Minero,et al.  Cloud point transition in nonionic micellar solutions , 1984 .

[22]  R. Rusconi,et al.  "Sticky" hard spheres: equation of state, phase diagram, and metastable gels. , 2007, Physical review letters.

[23]  Andrea Pelissetto,et al.  Critical phenomena and renormalization-group theory , 2002 .

[24]  D. Weitz,et al.  Gelation of particles with short-range attraction , 2008, Nature.

[25]  L. Reatto,et al.  A statistical model for non-ionic micellar solutions and their phase diagrams , 1984 .

[26]  K. Gubbins,et al.  Anomalous temperature dependence of surfactant self-assembly from aqueous solution. , 2004, Physical review letters.

[27]  Francesco Sciortino,et al.  Theoretical and numerical study of the phase diagram of patchy colloids: ordered and disordered patch arrangements. , 2008, The Journal of chemical physics.

[28]  D. Frenkel,et al.  Phase diagram of the adhesive hard sphere fluid. , 2004, The Journal of chemical physics.

[29]  J. Hayter,et al.  Neutron scattering study of micelle structure in isotropic aqueous solutions of poly(oxyethylene) amphiphiles , 1985 .

[30]  L. Rupert,et al.  A thermodynamic model of clouding in ethoxylate mixtures , 1992 .

[31]  Asymmetric fluid criticality. I. Scaling with pressure mixing. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  M. Dijkstra,et al.  Phase diagram of highly asymmetric binary hard-sphere mixtures. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[33]  T. Bellini,et al.  Static and dynamic light scattering study of fluorinated polymer colloids with a crystalline internal structure , 1994 .

[34]  L. Reatto,et al.  Three-Body Forces and Phase Separation in Micellar Solutions , 1987 .

[35]  K. E. Starling,et al.  Equation of State for Nonattracting Rigid Spheres , 1969 .

[36]  Kyozi Kawasaki,et al.  Kinetic equations and time correlation functions of critical fluctuations , 1970 .

[37]  C. Minero,et al.  Critical properties of nonionic micellar solutions , 1985 .

[38]  O. Vasilyev,et al.  Universal scaling functions of critical Casimir forces obtained by Monte Carlo simulations. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.