Effects of colloid polydispersity on the phase behavior of colloid-polymer mixtures

Multiphase Coexistence in Binary Hard Colloidal Mixtures: Predictions from a Simple Algebraic Theory

A general theoretical framework is proposed to quantify the thermodynamic properties of multicomponent hard colloidal mixtures. This framework is used to predict the phase behavior of mixtures of rods with spheres and rods with plates taking into account (liquid) crystal phases of both components. We demonstrate a rich and complex range of phase behaviors featuring a large variety of different multiphase coexistence regions, including two five-phase coexistence regions for hard rod/sphere mixtures, and even a six-phase equilibrium for hard rod/plate dispersions. The various multiphase coexistences featured in a particular mixture are in line with a recently proposed generalized phase rule and can be tuned through subtle variations of the particle shape and size ratio. Our approach qualitatively accounts for certain multiphase equilibria observed in rod/plate mixtures of clay colloids and will be a useful guide in tuning the phase behavior of shape-disperse mixtures in general.

Multiphase Coexistences in Rod-Polymer Mixtures

Using recently derived analytical equations of state for hard rod dispersions, we predict the phase behavior of athermal rod-polymer mixtures with free volume theory. The rods are modeled as hard spherocylinders, while the nonadsorbing polymer chains are described as penetrable hard spheres. It is demonstrated that all of the different types of phase states that are stable for pure colloidal rod dispersions can coexist with any combination of these phases if polymers are added, depending on the concentrations, rod aspect ratio, and polymer-rod size ratio. This includes novel two-, three-, and four-phase coexistences and isostructural coexistences between dilute and concentrated phases of the same kind, even for the more ordered (liquid) crystal phases. This work provides insight into the conditions at which particular multiphase coexistences are expected for well-defined model colloidal rod-polymer mixtures. We provide a quantitative map detailing the various types of isostructural coexistences, which confirms an early qualitative hypothesis by Bolhuis et al. ( J. Chem. Phys. 107, 1997 1551).

Effects of Polydispersity on the Phase Behavior of Additive Hard Spheres in Solution

The ability to separate enzymes, nucleic acids, cells, and viruses is an important asset in life sciences. This can be realised by using their spontaneous asymmetric partitioning over two macromolecular aqueous phases in equilibrium with one another. Such phases can already form while mixing two different types of macromolecules in water. We investigate the effect of polydispersity of the macromolecules on the two-phase formation. We study theoretically the phase behavior of a model polydisperse system: an asymmetric binary mixture of hard spheres, of which the smaller component is monodisperse and the larger component is polydisperse. The interactions are modelled in terms of the second virial coefficient and are assumed to be additive hard sphere interactions. The polydisperse component is subdivided into sub-components and has an average size ten times the size of the monodisperse component. We calculate the theoretical liquid-liquid phase separation boundary (the binodal), the critical point, and the spinodal. We vary the distribution of the polydisperse component in terms of skewness, modality, polydispersity, and number of sub-components. We compare the phase behavior of the polydisperse mixtures with their concomittant monodisperse mixtures. We find that the largest species in the larger (polydisperse) component causes the largest shift in the position of the phase boundary, critical point, and spinodal compared to the binary monodisperse binary mixtures. The polydisperse component also shows fractionation. The smaller species of the polydisperse component favor the phase enriched in the smaller component. This phase also has a higher-volume fraction compared to the monodisperse mixture.

Phase diagram of mixtures of colloids and polymers in the thermal crossover from good to θ solvent

We determine the phase diagram of mixtures of spherical colloids and neutral nonadsorbing polymers in the thermal crossover region between the θ point and the good-solvent regime. We use the generalized free-volume theory, which takes into account the polymer-concentration dependence of the depletion thickness and of the polymer compressibility. This approach turns out to be quite accurate as long as q = Rg/Rc ≲ 1 (Rg is the radius of gyration of the polymer and Rc is the colloid radius). We find that, close to the θ point, the phase diagram is not very sensitive to solvent quality, while, close to the good-solvent region, changes of the solvent quality modify significantly the position of the critical point and of the binodals. We also analyze the phase behavior of aqueous solutions of charged colloids and polymers, using the approach proposed by Fortini et al. [J. Phys.: Condens. Matter 17, 7783 (2005)].

Crowding of polymer coils and demixing in nanoparticle-polymer mixtures

The Asakura-Oosawa-Vrij (AOV) model of colloid-polymer mixtures idealises nonadsorbing polymers as effective spheres that are fixed in size and impenetrable to hard particles. Real polymer coils, however, are intrinsically polydisperse in size (radius of gyration) and may be penetrated by smaller particles. Crowding by nanoparticles can affect the size distribution of polymer coils, thereby modifying effective depletion interactions and thermodynamic stability. To analyse the influence of crowding on polymer conformations and demixing phase behaviour, we adapt the AOV model to mixtures of nanoparticles and ideal, penetrable polymer coils that can vary in size. We perform Gibbs ensemble Monte Carlo simulations, including trial nanoparticle-polymer overlaps and variations in the radius of gyration. Results are compared with predictions of free-volume theory. Simulation and theory consistently predict that ideal polymers are compressed by nanoparticles, and that compressibility and penetrability stabilise nanoparticle-polymer mixtures.

Phase equilibria in polydisperse nonadditive hard-sphere systems

Colloidal particles naturally exhibit a size polydispersity that can greatly influence their phase behavior in solution. Nonadditive hard-sphere (NAHS) mixtures are simple and well-suited model systems to represent phase transitions in colloid systems. Here, we propose an analytical equation of state (EOS) for NAHS fluid mixtures, which can be straightforwardly applied to polydisperse systems. For positive values of the nonadditivity parameter Delta the model gives accurate predictions of the simulated fluid-fluid coexistence curves and compressibility factors. NPT Monte Carlo simulations of the mixing properties of the NAHS symmetric binary mixture with Delta>0 are reported. It is shown that the enthalpy of mixing is largely positive and overcomes the positive entropy of mixing when the pressure is increased, leading to a fluid-fluid phase transition with a lower critical solution pressure. Phase equilibria in polydisperse systems are predicted with the model by using the density moment formalism [P. Sollich, Adv. Chem. Phys. 116, 265 (2001)]. We present predictions of the cloud and shadow curves for polydisperse NAHS systems composed of monodisperse spheres and polydisperse colloid particles. A fixed nonadditivity parameter Delta > 0 is assumed between the monodisperse and polydisperse spheres, and a Schulz distribution is used to represent the size polydispersity. Polydispersity is found to increase the extent of the immiscibility region. The predicted cloud and shadow curves depend dramatically on the upper cutoff diameter sigmac of the Schulz distribution, and three-phase equilibria can occur for large values of sigmac.

Multiphase coexistence in polydisperse colloidal mixtures

The authors study the phase behavior of mixtures of monodisperse colloidal spheres with a depletion agent which can have arbitrary shape and can possess a polydisperse size or shape distribution. In the low concentration limit considered here, the authors can employ the free-volume theory and take the geometry of particles of the depletion agent into account within the framework of fundamental measure theory. The authors apply their approach to study the phase diagram of a mixture of (monodisperse) colloidal spheres and two polydisperse polymer components. By fine tuning the distribution of the polymer, it is possible to construct a complex phase diagram which exhibits two stable critical points.

Influence of polydispersity on the critical parameters of an effective-potential model for asymmetric hard-sphere mixtures

We report a Monte Carlo simulation study of the properties of highly asymmetric binary hard-sphere mixtures. This system is treated within an effective fluid approximation in which the large particles interact through a depletion potential [R. Roth, Phys. Rev. E 62 5360 (2000)] designed to capture the effects of a virtual sea of small particles. We generalize this depletion potential to include the effects of explicit size dispersity in the large particles and consider the case in which the particle diameters are distributed according to a Schulz form having a degree of polydispersity 14%. The resulting alteration (with respect to the monodisperse limit) of the metastable fluid-fluid critical point parameters is determined for two values of the ratio of the diameters of the small and large particles: q(triple bond)sigma(s)/(-)sigma(b)=0.1 and q=0.05. We find that the inclusion of polydispersity moves the critical point to lower reservoir volume fractions of the small particles and high volume fractions of the large ones. The estimated critical point parameters are found to be in good agreement with those predicted by a generalized corresponding states argument which provides a link to the known critical adhesion parameter of the adhesive hard-sphere model. Finite-size scaling estimates of the cluster percolation line in the one phase fluid region indicate that inclusion of polydispersity moves the critical point deeper into the percolating regime. This suggests that phase separation is more likely to be preempted by dynamical arrest in polydisperse systems.

Experimental phase diagram of a model colloid-polymer mixture in the protein limit

Sterically stabilized silica nanoparticles were synthesized, and turbidity measurements confirmed that they behaved as hard spheres in cyclohexane. Poly(isoprene) was added to give mixtures in the protein limit with a polymer coil/colloid radius ratio of 4.8. Their phase behavior under good solvent conditions was studied experimentally. The critical colloid volume fraction was phi = 0.13, whereas recent simulations (Bolhuis, P. G.; Meijer, E. J.; Louis, A. A. Phys. Rev. Lett. 2003, 90, 068304) predicted phi = 0.24. This difference is ascribed to the fact that many systems showing good solvent scaling behavior of the polymer still have a Flory-Huggins parameter close to 0.5, for instance, chi = 0.45 in this work.

Mixtures of charged colloid and neutral polymer: Influence of electrostatic interactions on demixing and interfacial tension

The equilibrium phase behavior of a binary mixture of charged colloids and neutral, nonadsorbing polymers is studied within free-volume theory. A model mixture of charged hard-sphere macroions and ideal, coarse-grained, effective-sphere polymers is mapped first onto a binary hard-sphere mixture with nonadditive diameters and then onto an effective Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)]. The effective model is defined by a single dimensionless parameter-the ratio of the polymer diameter to the effective colloid diameter. For high salt-to-counterion concentration ratios, a free-volume approximation for the free energy is used to compute the fluid phase diagram, which describes demixing into colloid-rich (liquid) and colloid-poor (vapor) phases. Increasing the range of electrostatic interactions shifts the demixing binodal toward higher polymer concentration, stabilizing the mixture. The enhanced stability is attributed to a weakening of polymer depletion-induced attraction between electrostatically repelling macroions. Comparison with predictions of density-functional theory reveals a corresponding increase in the liquid-vapor interfacial tension. The predicted trends in phase stability are consistent with observed behavior of protein-polysaccharide mixtures in food colloids.

Capillary Length in a Fluid−Fluid Demixed Colloid−Polymer Mixture

We report measurements of the interfacial profile close to a vertical wall in a fluid-fluid demixed colloid-polymer mixture. The profile is measured by means of laser scanning confocal microscopy. It is accurately described by the interplay between the Laplace and hydrostatic pressure and from this description the capillary length is obtained. For different statepoints approaching the critical point the capillary length varies from 50 to 5 microm. These results are compared to theory. The mass density difference Deltarho is calculated from the bulk phase behavior, which is described within free volume theory with polymers modeled as penetrable hard spheres. The interfacial tension gamma is calculated within a squared gradient approximation. The capillary length is then given through with g equal to the Earth's acceleration. Predictions from theory are in overall qualitative agreement with experiment without the use of any adjustable parameter.