Structure of colloid-polymer suspensions

We discuss structural correlations in mixtures of free polymer and colloidal particles on the basis of a microscopic, two-component liquid-state integral equation theory. Whereas in the case of polymers much smaller than the spherical particles the relevant polymer degree of freedom is the centre of mass, for polymers larger than the (nano-) particles, conformational rearrangements need to be considered. They have the important consequence that the polymer depletion layer exhibits two widely different length scales, one of the order of the particle radius, the other of the order of the polymer radius or the polymer-density screening length in dilute or semidilute concentrations, respectively. Because we find a spinodal instability (mostly) below the overlap concentration, the latter length is (mostly) set by the radius of gyration. As a consequence of the structure of the depletion layer, the particle-particle correlations depend on both length scales for large polymers. Because of the high local compressibility of large polymers, the local depletion layer is a strong function of particle density, but a weak function of polymer concentration. The amplitude of the long-ranged tail of the depletion layer also depends asymptotically only on the colloid concentration, while the range increases upon approaching the (mean-field) spinodal. The colloid correlations may be understood as characteristic for particles with a short-ranged potential when small polymers are added, and as characteristic for particles with a long-ranged, van der Waals-like attraction when the added free polymer coils are much larger. Small polymers fill the voids between the particles rather homogeneously, exhibiting correlations inside the mesh (which gets squeezed by the colloids) and Porod-like correlations for larger distances. The structure factor of large polymers, however, exhibits no ramified mesh and becomes a Lorentzian characterized by the mixture correlation length, which diverges at the spinodal.

[1]  Peter A. Williams,et al.  Phase Behavior of Polymers with Concentrated Dispersions of Surfactants , 1994 .

[2]  T. Odijk.  Protein−Macromolecule Interactions , 1996 .

[3]  P. Pusey,et al.  Structure of marginal and fully developed colloidal liquids , 1999 .

[4]  Intermolecular structure factors of macromolecules in solution: integral equation results. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  ENTROPIC FORCES IN BINARY HARD SPHERE MIXTURES: THEORY AND SIMULATION , 1997, cond-mat/9701086.

[6]  T. Odijk.  Remarks on the depletion interaction between nanoparticles and flexible polymers , 2000 .

[7]  C. Zukoski,et al.  Effects of polyethylene glycol on protein interactions , 2000 .

[8]  K. Schweizer,et al.  Integral equation theory of polymer melts: intramolecular structure, local order, and the correlation hole , 1988 .

[9]  J. Banys,et al.  Glass behaviour in the solid solution of deuterated betaine phosphate0.15 betaine phosphite0.85 , 2000 .

[10]  G. Uhlenbeck,et al.  Studies in statistical mechanics , 1962 .

[11]  E. Glandt,et al.  Monte Carlo simulation of adhesive spheres , 1987 .

[12]  A. Khokhlov,et al.  AGGREGATION OF COLLOIDAL PARTICLES INDUCED BY POLYMER CHAINS : THE RISM INTEGRAL EQUATION THEORY , 1997 .

[13]  A. A. Louis,et al.  Accurate effective pair potentials for polymer solutions , 2000 .

[14]  Daan Frenkel,et al.  Simulation of the adhesive-hard-sphere model , 1988 .

[15]  K. Schweizer,et al.  Microscopic theory of polymer-mediated interactions between spherical particles , 1998 .

[16]  John S. Rowlinson,et al.  New Model for the Study of Liquid–Vapor Phase Transitions , 1970 .

[17]  M. Fuchs.  Analytic solutions of the PRISM equations for Gaussian polymers , 1997 .

[18]  Wilson C. K. Poon,et al.  Delayed sedimentation of transient gels in colloid–polymer mixtures: dark-field observation, rheology and dynamic light scattering studies , 1999 .

[19]  R. Sear.  Scattering from small colloidal particles in a semidilute polymer solution , 1997, cond-mat/9711044.

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

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

[22]  P. Schoot.  Protein-induced collapse of polymer chains. , 1998 .

[23]  The structure of colloid-polymer mixtures , 1999, cond-mat/9904223.

[24]  P. Gennes.  Scaling Concepts in Polymer Physics , 1979 .

[25]  C. Tanford.  Macromolecules , 1994, Nature.

[26]  J. Lewis.  Colloidal Processing of Ceramics , 2004 .

[27]  Schmidt.  Density functional for additive mixtures , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  Shaw,et al.  Free polymer in a colloidal solution. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[29]  Faraday Discuss , 1985 .

[30]  Jun Chen,et al.  Ã 2Πu state-intermediated two-photon dissociation of CS2+ via the first channel , 2001 .

[31]  Warren,et al.  Effect of polymer nonideality in a colloid-polymer mixture. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  A. Khokhlov,et al.  Interaction of Colloidal Particles with Macromolecules: The RISM Integral Equation Theory , 1997 .

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

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

[35]  H. Lekkerkerker,et al.  Fluid-fluid phase separation in colloid-polymer mixtures studied with small angle light scattering and light microscopy , 1996 .

[36]  D. H. Napper.  Polymeric stabilization of colloidal dispersions , 1983 .

[37]  C. Zukoski,et al.  Entropy driven phase transitions in colloid-polymer suspensions: Tests of depletion theories , 2002 .

[38]  Mean-field fluid behavior of the gaussian core model , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[39]  J. D. Cloizeaux,et al.  Polymers in Solution: Their Modelling and Structure , 2010 .

[40]  Luc Belloni,et al.  REVIEW ARTICLE: Colloidal interactions , 2000 .

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

[42]  A. Yethiraj.  Theory for chain conformations and static structure of dilute and semidilute polyelectrolyte solutions , 1998 .

[43]  K. Schweizer,et al.  Solvation potentials for macromolecules , 1994 .

[44]  K. Schweizer,et al.  Structure and thermodynamics of anisotropic polymer fluids , 2000 .

[45]  D. Frenkel,et al.  Computer simulation of colloid-polymer mixtures , 1995 .

[46]  Zamora,et al.  Phase behavior of small attractive colloidal particles. , 1996, Physical review letters.

[47]  E. Eisenriegler.  UNIVERSAL DENSITY-FORCE RELATIONS FOR POLYMERS NEAR A REPULSIVE WALL , 1997 .

[48]  E. Eisenriegler.  Small mesoscopic particles in dilute and semidilute solutions of nonadsorbing polymers , 2000 .

[49]  V. Popov,et al.  Filled polymers: Mechanical properties and processability , 1990 .

[50]  Structure and thermodynamics of colloid-polymer mixtures: A macromolecular approach , 2000, cond-mat/0007273.

[51]  J. Lebowitz,et al.  Thermodynamic Properties of Mixtures of Hard Spheres , 1964 .

[52]  Daan Frenkel,et al.  Determination of phase diagrams for the hard-core attractive Yukawa system , 1994 .

[53]  B. Widom.  Intermolecular Forces and the Nature of the Liquid State: Liquids reflect in their bulk properties the attractions and repulsions of their constituent molecules. , 1967, Science.

[54]  V. Prasad,et al.  Glasslike kinetic arrest at the colloidal-gelation transition. , 2001, Physical review letters.

[55]  R. J. Baxter.  Percus-Yevick Equation for Hard Spheres with Surface Adhesion , 1968 .

[56]  H. M. Schaink,et al.  Mean field calculation of polymer segment depletion and depletion induced demixing in ternary systems of globular proteins and flexible polymers in a common solvent , 1997 .

[57]  I. R. Mcdonald,et al.  Theory of simple liquids , 1998 .

[58]  B. Vincent.  The effect of adsorbed polymers on dispersion stability , 1974 .

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

[60]  Robert Evans,et al.  Fundamentals of Inhomogeneous Fluids , 1992 .

[61]  Tong,et al.  Depletion interactions in colloid-polymer mixtures. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[63]  K. Schweizer,et al.  PRISM theory of the structure, thermodynamics, and phase transitions of polymer liquids and alloys , 1994 .

[64]  Hanke,et al.  Polymers interacting with spherical and rodlike particles. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[65]  K. Schweizer,et al.  A Liquid-State Theory of Dense Star Polymer Fluids , 1995 .

[66]  Schweizer,et al.  Integral-equation theory of the structure of polymer melts. , 1987, Physical review letters.

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

[68]  D. Chandler,et al.  Hydrophobicity at Small and Large Length Scales , 1999 .

[69]  Macromolecular theory of solvation and structure in mixtures of colloids and polymers. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[70]  K. Schweizer,et al.  Liquid‐state theory of the density dependent conformation of nonpolar linear polymers , 1994 .

[71]  D. Frenkel,et al.  Numerical study of the phase diagram of a mixture of spherical and rodlike colloids , 1994 .

[72]  L. Belloni,et al.  Mixtures of charged colloids and nonadsorbing flexible polyelectrolytes: An integral equation study , 2000 .

[73]  L. Schäfer.  Excluded Volume Effects in Polymer Solutions , 1999 .

[74]  Chandler.  Gaussian field model of fluids with an application to polymeric fluids. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[75]  K. Schweizer,et al.  Integral equation theory of polymer melts: density fluctuations, static structure factor, and comparison with incompressible and continuum limit models , 1988 .

[76]  C. Zukoski,et al.  Concentration Fluctuations in a Model Colloid-Polymer Suspension : experimental Tests of Depletion Theories , 2002 .

[77]  D. Heyes,et al.  Square-well and square-shoulder fluids: Simulation and equations of state , 1992 .

[78]  Klein,et al.  Depletion forces in colloidal mixtures , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[79]  Polymer depletion effects near mesoscopic particles. , 1998, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[80]  K. Schweizer,et al.  Liquid crystallinity in flexible and rigid rod polymers , 2000 .

[81]  C. Kruif,et al.  Depletion-Induced Phase Separation of Aggregated Whey Protein Colloids by an Exocellular Polysaccharide , 2000 .

[82]  Benedek,et al.  Phase Diagram of Colloidal Solutions. , 1996, Physical review letters.

[83]  David Chandler,et al.  Optimized Cluster Expansions for Classical Fluids. II. Theory of Molecular Liquids , 1972 .

[84]  Phase separation in mixtures of colloids and long ideal polymer coils. , 2000, Physical review letters.

[85]  W. Gotze,et al.  Relaxation processes in supercooled liquids , 1992 .

[86]  A. Khokhlov,et al.  Phase behavior of polymer containing colloidal dispersions: The integral equation theory , 2000 .

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

[88]  T. Vilgis,et al.  On the conformation of non-adsorbing polymers in colloidal suspensions , 1997 .

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

[90]  J. Hansen,et al.  Effective interactions between electric double layers. , 2000, Annual review of physical chemistry.

[91]  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.

[92]  K. Schweizer,et al.  Correlation effects in dilute particle-polymer mixtures , 1998 .

[93]  M. Muthukumar.  Localization of a polymeric manifold in quenched random media , 1989 .

[94]  G. Patey,et al.  Hypernetted‐chain closure with bridge diagrams. Asymmetric hard sphere mixtures , 1990 .

[95]  D Chandler,et al.  Van der Waals Picture of Liquids, Solids, and Phase Transformations , 1983, Science.

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

[97]  Matthias Fuchs,et al.  Mode-coupling theory of the slow dynamics of polymeric liquids: Fractal macromolecular architectures , 1997 .

[98]  K. Schweizer,et al.  Variational approach to the conformation of flexible polymers in solution , 1993 .

[99]  C. Zukoski,et al.  DEPLETION INTERACTIONS IN THE PROTEIN LIMIT : EFFECTS OF POLYMER DENSITY FLUCTUATIONS , 1999 .

[100]  R. Sear.  Phase behavior of a simple model of globular proteins , 1999, cond-mat/9904426.

[101]  P. B. Warren,et al.  Phase separation in concentrated mixtures of polymers and surfactants , 1995 .

[102]  R. Dickman,et al.  Polymer‐induced forces between colloidal particles. A Monte Carlo simulation , 1994 .

[103]  R. Verberg,et al.  Viscosity and diffusion in hard-sphere-like colloidal suspensions , 1998 .