Computer simulations of phase transitions of bulk and confined colloid–polymer systems

Chou, Cheng‐Ying; Vo, Trinh; Panagiotopoulos, Athanassios Z.; Robert, M.

doi:10.1016/j.physa.2006.01.079

Cited by 27 publications

(34 citation statements)

References 53 publications

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“…16 were in near quantitative agreement with experimental binodals, demonstrating the influence of another characteristic length scale in the protein limit, d = σ s /σ c , where σ s is the diameter of a monomer segment [16,21]. These clearly showed that for athermal systems with monomer-monomer excluded volumes, critical densities for d < 0.25 collapse to a uniform master curve under rescaling arguments; however, for d ≥ 0.25 at identical q r , the solutions start demixing at much lower concentrations.…”

supporting

confidence: 67%

Structure of phase-separated athermal colloid-polymer systems in the protein limit

2013

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Structural features of phase separated athermal colloid-polymer mixtures in the so-called "protein limit," where polymer chain dimensions exceed those of the colloid, are investigated using grand canonical Monte Carlo simulations on a fine lattice. Previous work [N. A. Mahynski, et al. Phys. Rev. E 85, 051402 (2012)] has shown that this model accurately captures the phase behavior of experimental systems, and that colloids with sufficiently small diameters, σc, relative to that of the monomeric segments, σs, phase separate more readily than their large-diameter counterparts. In the present study, we directly connect colloid and polymer structure with their phase behavior by investigating these solutions along their binodal curves; we also explore the role of colloid surface curvature in destabilizing such solutions. Our findings suggest that simple consideration of an additional depletion radius, on the order of the σs, leads to a quantitatively accurate prediction of the division between stable and unstable ranges of d = σs/σc. We compare these results to continuum models with different bonding potentials between monomer segments in order to elucidate the significance of the lattice model's bond fluctuations and inherently coarse colloid surface. In a number of cases, the continuum models deviate both qualitatively and quantitatively from the lattice results, but the binodals of the continuum models are presently not known, making a strong conclusion about these differences impossible.

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confidence: 67%

Structure of phase-separated athermal colloid-polymer systems in the protein limit

2013

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“…However, the predicted values in the theory of Pelisetto and Hansen [12] are consistently very low. Also the simulations by Chou et al [41] give rather low y i c values. Despite the more or less systematic variations between the various models, they all follow the q R 1.3 scaling in the protein limit, although for the simulations of Chou et al [41] this applies only for q R above 4.…”

Section: Critical Points In Simulations and Other Theoriesmentioning

confidence: 94%

“…Also the simulations by Chou et al [41] give rather low y i c values. Despite the more or less systematic variations between the various models, they all follow the q R 1.3 scaling in the protein limit, although for the simulations of Chou et al [41] this applies only for q R above 4. The last four columns in Table 8.2 give the value of y i c q R − 1.3 in the protein limit:…”

Section: Critical Points In Simulations and Other Theoriesmentioning

confidence: 94%

“…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%

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Analytical phase diagrams for colloids and non-adsorbing polymer

Fleer

Tuinier

2008

Advances in Colloid and Interface Science

115

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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Phase Behavior of Polymer‐Containing Systems: Recent Advances Through Computer Simulation

Binder

Müller

Vink

2011

Macro Theory & Simulations

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Computer simulations dealing with the phase transitions and phase diagrams of polymer solutions, polymer mixtures, and polymers in heterogeneous environments are still a methodological challenge, since nontrivial structure occurs from the Angstrom‐scale of covalent chemical bonds to the micrometer scale in the resulting multiphase materials. A brief review of strategies that were developed to deal with these problems will be given, and a few highlights of recent results from the research groups of the authors will be described.magnified image

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Computer simulations of phase transitions of bulk and confined colloid–polymer systems

Cited by 27 publications

References 53 publications

Structure of phase-separated athermal colloid-polymer systems in the protein limit

Structure of phase-separated athermal colloid-polymer systems in the protein limit

Analytical phase diagrams for colloids and non-adsorbing polymer

Phase Behavior of Polymer‐Containing Systems: Recent Advances Through Computer Simulation

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