Colloid-polymer mixtures

Figure C2.6.10. Phase diagram of colloid-polymer mixtures polymer coil volume fraction vs particle...

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... 

Peon W C K, Pirie A D and Pusey P N 1995 Gelation in colloid-polymer mixtures Faraday Discuss. 101 65-76... 

Verhaegh NAM, Asnaghi D, Lekkerkerker FI N W, Giglio M and Cipelletti L 1997 Transient gelation by spinodal decomposition in colloid-polymer mixtures Phys/ca A 242 104-18... 

Tuinier, R., Rieger, J., and de Kmif, C.G. (2003). Depletion-induced phase separation in colloid-polymer mixtures. <7v. ColloidInterf. Sci. 103, 1-31. 

R. L. C. Vink and J. Horbach (2004) Grand canonical Monte Carlo simulation of a model colloid-polymer mixture Coexistence line, critical behavior, and interfacial tension. J. Chem. Phys. 121, pp. 3253-3258... 

Figure C2.6.10. Phase diagram of colloid-polymer mixtures polymer coil volume fraction jiri n vs particle volume fraction ( ). (a) Narrow attractions, 5/a = 0.1. Only a fluid-crystal transition is present. Tie lines indicate coexisting phases, (b) Longer range attractions, 5/a = 0.4. Gas, liquid and crystal phases (G, L and C) are present, as well as a critical point (CP). The three-phase triangle is shaded (reproduced with permission from [99]. Copyright 1992 EDP Sciences).

Monte Carlo simulations provide a rewarding and invaluable approach to solving these systems, and computer simulations and theory can isolate the molecular factors that control polyelectrolyte conformations in solution. Therefore, they are exU cmely useful to address the optimization of colloid-polymer mixtures and guide the design of new experiments. A simple model involving one chain interacting with one particle has been described, but the same model can be extended to more concentrated systems, e.g. involving several chains (and/or colloidal particles) with explicit counter ions, co-ions and solvent molecules. 

The two independent variables used in Eq. (1), which determine the total scattering intensity of the colloid-polymer mixture, are the concentrations... 

In the above, — 33(0)/2 is the second virial coefficient for the colloid-polymer micelles, and the scattering amplitude of the colloid-polymer micelle is assumed to be /i -f u /2, with fi and /z being the scattering amplitudes for the colloidal particle and the polymer molecule, respectively. One can immediately see that the intercept Y lo) in Eq. (6) decays much faster than that in Eq. (4) (/2//1 — 0.1 for our colloid-polymer mixture). This difference in Y uj) reflects the fact that the scattering from the colloid-polymer micelles is coherent, and it is incoherent if colloidal particles and polymer molecules axe independent with each other. The slope P(cc ) is a measure of the interaction volume of the mixture. When there is no adsorption in the colloid-polymer mixture, the total interaction volume of the mixture is a intensity normalized sum of the individual excluded volumes (i.e. the second virial coefficients) of a colloidal particle and a polymer molecule as well as the excluded volume between the two species. For the complete adsorption, on the other hand, the interaction volume is just the excluded volume of the colloid-polymer micelle. 

At a finite colloid concentration p = pj, the scattering intensity in the colloid-polymer mixture can be written as... 

W.C.K. Poon, A.D. Pirie, P.N. Pusey, Gelation in colloid-polymer mixtures. Faraday Discuss. 101, 65-76 (1995). doi 10.1039/fd9950100065... 

In a mixture of hard spheres and depletants a phase transition occurs upon exceeding a certain concentration of colloidal spheres and/or depletants. This is the subject of Chaps. 3-6 in this book. A key parameter in describing the phase stability of colloid-polymer mixtures is the size ratio q,... 

Explain why the osmotic pressure of the polymer solution in a colloid-polymer mixture plays a similar role as air pressure in Von Guericke s experiment. 

Inspired by the work of De Gennes [102, 103], fundamental work commenced on colloid-polymer mixtures in which the polymers are relatively large compared to the colloids. This regime is relevant for mixtures of polymer or polysaccharides mixed with proteins and is often denoted as the protein limit q> 1). The opposite case (small q) is known as the colloid limit. We distinguish three regimes, see Fig. 1.20, in colloid-polymer mixtures small q (also termed the colloid limit ) of... 

Fig. 1.20 Sketch of the diffeient regimes size ratio in colloid-polymer mixtures. Left the colloid limit of relatively small polymer chains. Middle the equal size regime. Right the protein limit regime of relatively large polymer chains...

When a colloid-polymer mixture phase separates into a coUoid-rich and polymer-rich phase an interface appears in between. For a colloidal gas-liquid... 

Until the end of the 1990s most theoretical approaches were based on describing polymer chains as ideal or as penetrable hard spheres. Especially at the turn of the last century a wealth of different approaches were proposed to describe colloid-polymer mixtures in which interactions between polymer segments were accounted for. Essential was the progress made in Monte Carlo computer simulation studies on depletion effects [172-179] to test such theories. 

For a dilute colloidal dispersion, g(r) = exp[—lT(r)/kr], where W r) is the pair interaction. The quantity g r) can be measured using confocal laser scanning microscopy. This method allows to perform quantitative three-dimensional real space measmements of the positions of the (fluorescently labeled) colloidal particles. Analysis of the positions of the particles yields g(r). This means that confocal microscopy enables to indirectly measure both the potential of mean force and (using a dilute dispersion) the pair interaction in a mixture of colloids and depletants. Royall et al. [91] have performed such a study in a colloid-polymer mixture with free polymers as depletants. 

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