Phase separation in mixtures of colloids and long ideal polymer coils

Colloidal suspensions with free polymer coils which are larger than the colloidal particles are considered. The polymer-colloid interaction is modeled by an extension of the Asakura-Oosawa model. Phase separation occurs into dilute and dense fluid phases of colloidal particles when polymer is added. The critical density of this transition tends to zero as the size of the polymer coils diverges.Comment: 5 pages, 3 figure

Demixing in a single-peak distributed polydisperse mixture of hard spheres

An analytic derivation of the spinodal of a polydisperse mixture is presented. It holds for fluids whose excess free energy can be accurately described by a function of a few moments of the size distribution. It is shown that one such mixture of hard spheres in the Percus-Yevick approximation never demixes, despite its size distribution. In the Boublik-Mansoori-Carnahan-Starling-Leland approximation, though, it demixes for a sufficiently wide log-normal size distribution. The importance of this result is twofold: first, this distribution is unimodal, and yet it phase separates; and second, log-normal size distributions appear in many experimental contexts. The same phenomenon is shown to occur for the fluid of parallel hard cubes.Comment: 4 pages, 2 figures, needs revtex, multicol, epsfig and amstex style file

Flory-Huggins theory for athermal mixtures of hard spheres and larger flexible polymers

A simple analytic theory for mixtures of hard spheres and larger polymers with excluded volume interactions is developed. The mixture is shown to exhibit extensive immiscibility. For large polymers with strong excluded volume interactions, the density of monomers at the critical point for demixing decreases as one over the square root of the length of the polymer, while the density of spheres tends to a constant. This is very different to the behaviour of mixtures of hard spheres and ideal polymers, these mixtures although even less miscible than those with polymers with excluded volume interactions, have a much higher polymer density at the critical point of demixing. The theory applies to the complete range of mixtures of spheres with flexible polymers, from those with strong excluded volume interactions to ideal polymers.Comment: 9 pages, 4 figure

What do emulsification failure and Bose-Einstein condensation have in common?

Ideal bosons and classical ring polymers formed via self-assembly, are known to have the same partition function, and so analogous phase transitions. In ring polymers, the analogue of Bose-Einstein condensation occurs when a ring polymer of macroscopic size appears. We show that a transition of the same general form occurs within a whole class of systems with self-assembly, and illustrate it with the emulsification failure of a microemulsion phase of water, oil and surfactant. As with Bose-Einstein condensation, the transition occurs even in the absence of interactions.Comment: 7 pages, 1 figure, typeset with EUROTeX, uses epsfi

A coil-globule transition of a semiflexible polymer driven by the addition of spherical particles

The phase behaviour of a single large semiflexible polymer immersed in a suspension of spherical particles is studied. All interactions are simple excluded volume interactions and the diameter of the spherical particles is an order of magnitude larger than the diameter of the polymer. The spherical particles induce a quite long ranged depletion attraction between the segments of the polymer and this induces a continuous coil-globule transition in the polymer. This behaviour gives an indication of the condensing effect of macromolecular crowding on DNA.Comment: 12 pages, 4 figure

Interfacial tension and nucleation in mixtures of colloids and long ideal polymer coils

Mixtures of ideal polymers with hard spheres whose diameters are smaller than the radius of gyration of the polymer, exhibit extensive immiscibility. The interfacial tension between demixed phases of these mixtures is estimated, as is the barrier to nucleation. The barrier is found to scale linearly with the radius of the polymer, causing it to become large for large polymers. Thus for large polymers nucleation is suppressed and phase separation proceeds via spinodal decomposition, as it does in polymer blends.Comment: 4 pages (v2 includes discussion of the scaling of the interfacial tension along the coexistence curve and its relation to the Ginzburg criterion

Phase behaviour of a model of colloidal particles with a fluctuating internal state

Colloidal particles are not simple rigid particles, in general an isolated particle is a system with many degrees of freedom in its own right, e.g., the counterions around a charged colloidal particle.The behaviour of model colloidal particles, with a simple phenomenological model to account for these degrees of freedom, is studied. It is found that the interaction between the particles is not pairwise additive. It is even possible that the interaction between a triplet of particles is attractive while the pair interaction is repulsive. When this is so the liquid phase is either stable only in a small region of the phase diagram or absent altogether.Comment: 12 pages including 4 figure

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

We study the equilibrium behaviour of a mixture of monodisperse hard sphere colloids and polydisperse non-adsorbing polymers at their $\theta$-point, using the Asakura-Oosawa model treated within the free-volume approximation. Our focus is the experimentally relevant scenario where the distribution of polymer chain lengths across the system is fixed. Phase diagrams are calculated using the moment free energy method, and we show that the mean polymer size $\xi_{\rm c}$ at which gas-liquid phase separation first occurs decreases with increasing polymer polydispersity $\delta$. Correspondingly, at fixed mean polymer size, polydispersity favours gas-liquid coexistence but delays the onset of fluid-solid separation. On the other hand, we find that systems with different $\delta$ but the same {\em mass-averaged} polymer chain length have nearly polydispersity-independent phase diagrams. We conclude with a comparison to previous calculations for a semi-grandcanonical scenario, where the polymer chemical potentials are imposed, which predicted that fluid-solid coexistence was over gas-liquid in some areas of the phase diagram. Our results show that this somewhat counter-intuitive result arose because the actual polymer size distribution in the system is shifted to smaller sizes relative to the polymer reservoir distribution.Comment: Changes in v2: sketch in Figure 1 corrected, other figures improved; added references to experimental work and discussion of mapping from polymer chain length to effective radiu

Theory for polymer coils with necklaces of micelles

If many micelles adsorb onto the same polymer molecule then they are said to form a necklace. A minimal model of such a necklace is proposed and shown to be almost equivalent to a 1-dimensional fluid with nearest-neighbour interactions. The thermodynamic functions of this fluid are obtained and then used to predict the change in the critical micellar concentration of the surfactant in the presence of the polymer. If the amount of polymer is not too large there are two critical micellar concentrations, one for micelles in necklaces and one for free micelles.Comment: 12 pages, 5 figure

The cytoplasm of living cells: A functional mixture of thousands of components

Inside every living cell is the cytoplasm: a fluid mixture of thousands of different macromolecules, predominantly proteins. This mixture is where most of the biochemistry occurs that enables living cells to function, and it is perhaps the most complex liquid on earth. Here we take an inventory of what is actually in this mixture. Recent genome-sequencing work has given us for the first time at least some information on all of these thousands of components. Having done so we consider two physical phenomena in the cytoplasm: diffusion and possible phase separation. Diffusion is slower in the highly crowded cytoplasm than in dilute solution. Reasonable estimates of this slowdown can be obtained and their consequences explored, for example, monomer-dimer equilibria are established approximately twenty times slower than in a dilute solution. Phase separation in all except exceptional cells appears not to be a problem, despite the high density and so strong protein-protein interactions present. We suggest that this may be partially a byproduct of the evolution of other properties, and partially a result of the huge number of components present.Comment: 11 pages, 1 figure, 1 tabl