Macromolecular theory of solvation and structure in mixtures of colloids and polymers

Fuchs, Matthias; Schweizer, Kenneth S.

doi:10.1103/physreve.64.021514

Cited by 96 publications

(159 citation statements)

References 72 publications

(168 reference statements)

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“…This observation agrees with prior PRISM studies that attribute this to the local nature of the PY closure, 45 which cannot account for nonlocal correlations between the particle and monomer sites not in contact with the particle. A modified PY closure has been developed recently for polymer coil-particle systems to correct for this nonlocal effect, 45,46 but the development of this new closure is beyond the scope of this study.…”

Section: A Local Structurementioning

confidence: 99%

Polymer–particle mixtures: Depletion and packing effects

Doxastakis

Chen

Guzmán

et al. 2004

The Journal of Chemical Physics

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The structure of polymers in the vicinity of spherical colloids is investigated by Monte Carlo simulations and integral equation theory. Polymers are represented by a simple bead-spring model; only repulsive Lennard-Jones interactions are taken into account. Using advanced trial moves that alter chain connectivity, depletion and packing effects are analyzed as a function of chain length and density, both at the bond and the chain level. Chain ends segregate to the colloidal surface and polymer bonds orient parallel to it. In the dilute regime, the polymer chain length governs the range of depletion and has a negligible influence on monomer packing in dense polymer melts. Polymers adopt an ellipsoidal shape, with the larger axis parallel to the surface of the particle, as they approach larger colloids. The dimensions are perturbed within the range of the depletion layer.

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Section: A Local Structurementioning

confidence: 99%

Polymer–particle mixtures: Depletion and packing effects

Doxastakis

Chen

Guzmán

et al. 2004

The Journal of Chemical Physics

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“…In recent years, there have been significant theoretical developments which take into account the polymeric excluded-volume interactions [30][31][32][33][34][35][36][37][38][39][40][41]. As examples of methods that enable the prediction of the phase behavior of colloid-polymer mixtures we mention polymer-colloid liquid state theory [31][32][33][34], thermodynamic perturbation theories [12,35], density functional theory [36,37], a Gaussian-core model [14,38,39], and computer simulations of HS plus self-avoiding polymer chains [40,41].…”

Section: General Backgroundmentioning

confidence: 99%

“…As examples of methods that enable the prediction of the phase behavior of colloid-polymer mixtures we mention polymer-colloid liquid state theory [31][32][33][34], thermodynamic perturbation theories [12,35], density functional theory [36,37], a Gaussian-core model [14,38,39], and computer simulations of HS plus self-avoiding polymer chains [40,41]. To obtain phase lines these methods require a significant amount of numerical work.…”

Section: General Backgroundmentioning

confidence: 99%

Analytical phase diagrams for colloids and non-adsorbing polymer

Fleer

Tuinier

2008

Advances in Colloid and Interface Science

116

201

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We review the free-volume theory (FVT) of Lekkerkerker et al. [Europhys. Lett. 20 (1992) 559] for the phase behavior of colloids in the presence of non-adsorbing polymer and we extend this theory in several aspects:(i) We take the solvent into account as a separate component and show that the natural thermodynamic parameter for the polymer properties is the insertion work Πv, where Π is the osmotic pressure of the (external) polymer solution and v the volume of a colloid particle. (ii) Curvature effects are included along the lines of Aarts et al. [J. Phys.: Condens. Matt. 14 (2002) 7551] but we find accurate simple power laws which simplify the mathematical procedure considerably. (iii) We find analytical forms for the first, second, and third derivatives of the grand potential, needed for the calculation of the colloid chemical potential, the pressure, gas-liquid critical points and the critical endpoint (cep), where the (stable) critical line ends and then coincides with the triple point. This cep determines the boundary condition for a stable liquid.We first apply these modifications to the so-called colloid limit, where the size ratio q R = R/a between the radius of gyration R of the polymer and the particle radius a is small. In this limit the binodal polymer concentrations are below overlap: the depletion thickness δ is nearly equal to R, and Π can be approximated by the ideal (van 't Hoff) law Π = Π 0 = φ/N, where φ is the polymer volume fraction and N the number of segments per chain. The results are close to those of the original Lekkerkerker theory. However, our analysis enables very simple analytical expressions for the polymer and colloid concentrations in the critical and triple points and along the binodals as a function of q R . Also the position of the cep is found analytically. In order to make the model applicable to higher size ratio's q R (including the so-called protein limit where q R N 1) further extensions are needed. We introduce the size ratio q = δ/a, where the depletion thickness δ is no longer of order R. In the protein limit the binodal concentrations are above overlap. In such semidilute solutions δ ≈ ξ, where the De Gennes blob size (correlation length) ξ scales as ξ ∼ φ − γ , with γ = 0.77 for good solvents and γ = 1 for a theta solvent. In this limit Π = Π sd ∼ φ 3γ . We now apply the following additional modifications:(iv) Π = Π 0 + Π sd , where Π sd =Aφ 3γ ; the prefactor A is known from renormalization group theory. This simple additivity describes the crossover for the osmotic pressure from the dilute limit to the semidilute limit excellently. (v) δ − 2 = δ 0 − 2 + ξ − 2 , where δ 0 ≈ R is the dilute limit for the depletion thickness δ. This equation describes the crossover in length scales from δ 0 (dilute) to ξ (semidilute).With these latter two modifications we obtain again a fully analytical model with simple equations for critical and triple points as a function of q R . In the protein limit the binodal polymer concentrations scale as q R 1/γ , and phase diagrams φq ...

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“…The influence of the polymer-polymer interactions has been studied first by Warren et al [20] who used the perturbation theory around the AOV reference model. Fuchs and Schweizer [21,22,23] have noted that the polymer-polymer interactions lead to an upward shift of the spinodal. These findings have been confirmed by the results of the modified free volume theory [24], the geometry-based density functional approach [25] and sophisticated computer simulation techniques [26].…”

Section: Introductionmentioning

confidence: 99%

Demixing in athermal mixtures of colloids and excluded-volume polymers from density functional theory

Bryk

2005

The Journal of Chemical Physics

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We study the structure and interfacial properties of model athermal mixtures of colloids and excluded volume polymers. The colloid particles are modeled as hard spheres whereas the polymer coils are modeled as chains formed from tangentially bonded hard spheres. Within the framework of the nonlocal density functional theory we study the influence of the chain length on the surface tension and the interfacial width. We find that the interfacial tension of the colloid-interacting polymer mixtures increases with the chain length and is significantly smaller than that of the ideal polymers. For certain parameters we find oscillations on the colloid-rich parts of the density profiles of both colloids and polymers with the oscillation period of the order of the colloid diameter. The interfacial width is few colloid diameters wide and also increases with the chain length. We find the interfacial width for the end segments to be larger than that for the middle segments and this effect is more pronounced for longer chains.

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Macromolecular theory of solvation and structure in mixtures of colloids and polymers

Cited by 96 publications

References 72 publications

Polymer–particle mixtures: Depletion and packing effects

Polymer–particle mixtures: Depletion and packing effects

Analytical phase diagrams for colloids and non-adsorbing polymer

Demixing in athermal mixtures of colloids and excluded-volume polymers from density functional theory

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