The physics of a model colloid polymer mixture

Poon, Wilson

doi:10.1088/0953-8984/14/33/201

Cited by 530 publications

(778 citation statements)

References 97 publications

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“…The depth of the attractive potential is controlled by the polymer concentration, and since the attraction is shortranged, colloidal gels are formed at some threshold polymer concentrations 3,[28][29][30] .…”

Section: Model and Theorymentioning

confidence: 99%

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Theoretical predictions of structures in dispersions containing charged colloidal particles and non-adsorbing polymers

Xie

Turesson

Woodward

et al. 2016

Phys. Chem. Chem. Phys.

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We develop a theoretical model to describe structural effects on a specific system of charged colloidal polystyrene particles, upon the addition of non-adsorbing PEG polymers. This system has previously been investigated experimentally, by scattering methods, so we are able to quantitatively compare predicted structure factors with corresponding experimental data. Our aim is to construct a model that is coarse-grained enough to be computationally manageable, yet detailed enough to capture the important physics. To this end, we utilize classical polymer density functional theory, wherein all possible polymer configurations are accounted for, subject to a mean-field Boltzmann weight. We make efforts to counteract drawbacks with this mean-field approach, resulting in structural predictions that agree very well with computationally more demanding simulations. Electrostatic interactions are handled at the fully non-linear Poisson-Boltzmann level, and we demonstrate that a linearization leads to less accurate predictions. The particle charge is an experimentally unknown parameter. We define the surface charge such that the experimental and theoretical gel point at equal polymer concentration coincide. Assuming a fixed surface charge for a certain salt concentration, we find very good agreement between measured and predicted structure factors across a wide range of polymer concentrations. We also present predictions for other structural quantities, such as radial distribution functions, and cluster size distributions. Finally, we demonstrate that our model predicts the occurrence of

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Section: Model and Theorymentioning

confidence: 99%

“…Colloidal particles usually interact with each other via shortranged van der Waals (vdW) attractions, and when this attraction is strong, the system may form a gel 2,3 . Colloidal gels find a variety of applications as well 4 .…”

Section: Introductionmentioning

confidence: 99%

Theoretical predictions of structures in dispersions containing charged colloidal particles and non-adsorbing polymers

Xie

Turesson

Woodward

et al. 2016

Phys. Chem. Chem. Phys.

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“…An osmotic equilibrium or free volume theory (FVT) [25], in which polymer partitioning over the coexisting phases is taken into account, was later developed by Lekkerkerker et al [26]. This theory gives a fair description of the phase behavior of model systems of colloidal dispersions of (pseudo)hard spheres mixed with well-defined synthetic polymer chains, as long as the polymer chains are small compared to the colloids (the so-called colloid limit, where the binodal polymer concentrations are below overlap) [27]. The theory compares well with computer simulations of HS's plus ideal chains [10] or HS's plus FOS's [11,28,29].…”

Section: General Backgroundmentioning

confidence: 99%

Analytical phase diagrams for colloids and non-adsorbing polymer

Fleer

Tuinier

2008

Advances in Colloid and Interface Science

115

195

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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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“…For monodisperse colloids, this attraction is given by the Asakura-Oosawa interaction [1], which is slightly modified to include polydispersity [42]. The attraction strength is set by the concentration of polymers, φ p , and the range by the polymer size, ξ (see below).…”

Section: Simulation Setupmentioning

confidence: 99%

Bond formation and slow heterogeneous dynamics in adhesive spheres with long-ranged repulsion: Quantitative test of mode coupling theory

et al. 2007

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A colloidal system of spheres interacting with both a deep and narrow attractive potential and a shallow long-ranged barrier exhibits a prepeak in the static structure factor. This peak can be related to an additional mesoscopic length scale of clusters and/or voids in the system. Simulation studies of this system have revealed that it vitrifies upon increasing the attraction into a gel-like solid at intermediate densities. The dynamics at the mesoscopic length scale corresponding to the prepeak represents the slowest mode in the system. Using mode coupling theory with all input directly taken from simulations, we reveal the mechanism for glassy arrest in the system at 40% packing fraction. The effects of the low-q peak and of polydispersity are considered in detail. We demonstrate that the local formation of physical bonds is the process whose slowing down causes arrest. It remains largely unaffected by the large-scale heterogeneities, and sets the clock for the slow cluster mode. Results from mode-coupling theory without adjustable parameters agree semi-quantitatively with the local density correlators but overestimate the lifetime of the mesoscopic structure (voids).

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The physics of a model colloid polymer mixture

Cited by 530 publications

References 97 publications

Theoretical predictions of structures in dispersions containing charged colloidal particles and non-adsorbing polymers

Theoretical predictions of structures in dispersions containing charged colloidal particles and non-adsorbing polymers

Analytical phase diagrams for colloids and non-adsorbing polymer

Bond formation and slow heterogeneous dynamics in adhesive spheres with long-ranged repulsion: Quantitative test of mode coupling theory

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