Phase behaviour of colloids

Lekkerkerker FI N W, Peon W C K, Pusey P N, Stroobants A and Warren P B 1992 Phase behaviour of colloid + polymer mixtures Europhys. Lett. 20 559-64... 

Agatonovic-Kustrin S, Alany RG. Role of genetic algorithms and artificial neural networks in predicting phase behaviour of colloidal delivery systems. Pharm Res 2001 18 1049-55. 

A semi-grand canonical treatment for the phase behaviour of colloidal spheres plus non-adsorbing polymers was proposed by Lekkerkerker [141], who developed free volume theory (also called osmotic equilibrium theory ), see Chap. 3. The main difference with TPT [115] is that free volume theory (FVT) accounts for polymer partitioning between the phases and corrects for multiple overlap of depletion layers, hence avoids the assumption of pair-wise additivity which becomes inaccurate for relatively thick depletion layers. These effects are incorporated through scaled particle theory (see for instance [136] and references therein). The resulting free volume theory (FVT) phase diagrams calculated by Lekkerkerker et al. [142] revealed that for <0.3 coexisting fluid-solid phases are predicted, whereas at low colloid volume fractions a gas-hquid coexistence is found for q > 0.3, as was predicted by TPT. 

In this overview on the history of depletion in colloidal dispersions we have focused on nuxtures of colloidal spheres and non-adsorbing polymers, which have received most attention. Since the 1990s depletion phenomena have also been studied systematically in dispersions of colloidal rods [227, 228], platelets [229], rocks [230] (colloidal particles with an irregular surface) or cubes [231] plus nonadsorbing polymers or in mixtures of different colloids with large size asymmetry [232-235]. In Chap. 5 we concentrate on mixtures of colloidal large spheres plus added small spheres or added colloidal rods. Finally, in Chap. 6 we concentrate on the phase behaviour of colloidal rod plus polymer dispersions. 

In this chapter we discuss the basics of the phase behaviour of hard spheres plus depletants. Phase transitions are the result of physical properties of a collection of particles depending on many-body interactions. In Chap. 2 we focused on two-body interactions. As we shall see, depletion elfects are commonly not pair-wise additive. Therefore, the prediction of phase transitions of particles with depletion interaction is not straightforward. As a starting point a description is required for the thermodynamic properties of the pure colloidal dispersion. Here the colloid-atom analogy, recognized by Einstein and exploited by Perrin in his classical experiments, is very useful. Subsequently, we explain the basics of the free volume theory for the phase behaviour of colloids -I- depletants. In this chapter we treat only simplest type of depletant, the penetrable hard sphere. 

In Chap. 3 we introduced the phase behaviour of hard spheres mixed with penetrable hard spheres (phs). This provides a starting point for describing the phase behaviour of colloid-polymer mixtures. In Sect. 4.1 we show that the phs-description using penetrable hard spheres is adequate for mixtures in the colloid-limit small q with polymer chains smaller than the particle radius. In Sect. 4.2 we treat the modifications for the case that the polymers are treated as ideal chains. More advanced treatments accounting for non-ideal behaviour of depletion thickness and osmotic pressure for interacting polymer chains enable to also describe intermediate and large q situations. This is the topic of Sect. 4.3. In Sect. 4.4 we qualitatively consider work available on the effects of polydispersity on... 

Phase Behaviour of Colloid -i- Ideal Polymer Mixtures... 

Analytical approximations for the phase behaviour of colloid-polymer mixtures can be found in [39] for those who need simple, approximate yet reasonably accurate descriptions of equilibrium phase diagrams. Using Y instead of p turns all phase diagrams to more universal ones with a polymer coneentration variable that is always of order unity for the relevant characteristie parts of the phase behaviour. 

Phase Behaviour of Colloidal Sphere-Rod Mixtures Experiment... 

So far we have considered the phase behaviour of colloidal spheres plus deple-tants. In Chap. 3 we considered the simplest type of depletant, the penetrable hard sphere. We then extended this treatment in Chap. 4 to ideal and excluded volume polymers and in Chap. 5 we considered small colloidal spheres (ineluding mieelles) and colloidal rods as depletants. In this chapter we consider the phase behaviour of mixtures of colloidal rods plus polymeric depletants. For an overview of several types of colloidal rods encountered in practice we refer to [1]. 

Lekkerkerker H, Poon W, Pusey P, Stroobants A, Warren P (1992) Phase behaviour of colloid + polymer mixtures. Europhys Lett 20 559... 

The remainder of this contribution is organized as follows. In section C2.6.2, some well studied colloidal model systems are introduced. Methods for characterizing colloidal suspensions are presented in section C2.6.3. An essential starting point for understanding the behaviour of colloids is a description of the interactions between particles. Various factors contributing to these are discussed in section C2.6.4. Following on from this, theories of colloid stability and of the kinetics of aggregation are presented in section C2.6.5. Finally, section C2.6.6 is devoted to the phase behaviour of concentrated suspensions. 

Altliough tire behaviour of colloidal suspensions does in general depend on temperature, a more important control parameter in practice tends to be tire particle concentration, often expressed as tire volume fraction ((). In fact, for hard- sphere suspensions tire phase behaviour is detennined by ( ) only. For spherical particles... 

Pusey P N and van Megen W 1986 Phase behaviour of concentrated suspensions of nearly hard colloidal spheres Nature 320 340-2... 

Rosenbaum D, Zamora P C and Zukoski C F 1996 Phase behaviour of small attractive colloidal particles Phys. Rev. Lett. 76 150-3... 

P.N. Pusey and W. van Megen Phase Behaviour of Concentrated Suspensions of Nearly Hard Colloidal Spheres. Nature (Lond.) 320, 340 (1986). 

In Part Four (Chapter eight) we focus on the interactions of mixed systems of surface-active biopolymers (proteins and polysaccharides) and surface-active lipids (surfactants/emulsifiers) at oil-water and air-water interfaces. We describe how these interactions affect mechanisms controlling the behaviour of colloidal systems containing mixed ingredients. We show how the properties of biopolymer-based adsorption layers are affected by an interplay of phenomena which include selfassociation, complexation, phase separation, and competitive displacement. 

Finkelmann, H., Lehmann, B. and Rehage, G. Phase behaviour of lyotropic liquid crystalline side chain polymers in aqueous solutions. Colloid Polymer Sci. 260, 56 (1982)... 

I.V. Rao and E. Ruckenstein Phase behaviour of mixtures of sterically stabilized colloidal dispersions and free polymer, JOURNAL OF COLLOID AND INTERFACE SCIENCE 108 (1985) 389-402. 

Kuineda, H.,Hasegawa,Y., John, A. C.,Naito, M.,and Muto, M. (1996), Phase behaviour of polyoxyethylene hydrogenated caster oil in oil / water systems, Colloid Surfaces, 209-216. 

Schurtenberger, P., Peng, Q., Leser, M. E., and Luisi, P. L. (1993), Structure and phase behaviour of lecithin-based microemulsions A study of chanin length dependence, J. Colloid Interface Sci, 156,43-51. 

Yaghmur, A., Aserin, A. and Garti, N. (2002) Phase behaviour of microemulsions based on food-grade non-ionic surfactants Effect of polyols and short-chain alcohols. Colloid Surf. A, 209,71-81. 

Kahlweit, M. (1982) The phase behaviour of the type H20-oil-nonionic surfactant-electrolyte. /. Colloid Interface Sci., 90,197-202. 

We may draw a close analogy here between the behaviour of colloidal dispersions and molecular systems. Thus the first case discussed above is analogous to the presence of clusters of molecules in a vapour approaching its condensation point, or in a solution close to saturation. The limiting concentration at which flocculation occurs corresponds to the saturation vapour pressure, or to the solubility of a solid in solution. More complex colloidal systems often exhibit phase behaviour which is paralleled by various phase separation phenomena in molecular systems. Detailed discussion ofthese matters is outside the scope of this book. However, pursuit of these analogies and their interpretation is a currently active area of research. 

ZHA Zhang, K.-W., Karlstrbm, G., and Lindman, B., Phase behaviour of systems of a non-ionic surfactant and a non-ionic polymer in aqueous solution. Colloids Surfaces, 61, 147, 1992. 

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The physical behaviour of colloidal particles is largely affected by the properties of the interface between the particle and the continuous phase. The term interface does not describe a conceptual 2-dimensional boundary, but refers to a strucmred region around the geometric surface of the particle where neither the bulk properties of the particulate phase nor those of the continuous phase prevail. It thus includes the surface atoms of the particle as well as layers of adsorbed ions or molecules or even the ion cloud that surrounds a charged suspended particle. 

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