Strong, weak and metastable liquids

Lekkerkerker, H. N. W.

doi:10.1016/s0378-4371(97)00302-6

Cited by 49 publications

(35 citation statements)

References 38 publications

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“…Experiments on model colloid-polymer mixtures [4][5][6] and simulations [7] have confirmed this picture, which in fact is quite general [8]. These developments have renewed interest in the nature of the liquid state [8].…”

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confidence: 63%

Structure of Marginal and Fully Developed Colloidal Liquids

et al. 1999

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The structures of three colloidal liquids at their triple points are studied. The interparticle attraction in these liquids, induced by the depletion effect of free polymer, has variable range. In one case, the liquid state is "marginal" -in the phase diagram the critical point lies nearly on the line of triple coexistence. Structure factors of the liquids, measured by a new application of two-color dynamic light scattering, show that their local structures are similar, while long-range fluctuations increase as the liquids become more marginal. [S0031-9007(98)

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confidence: 63%

Structure of Marginal and Fully Developed Colloidal Liquids

et al. 1999

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“…The phase behavior of colloids and atomic fluids is often described in terms of two parameters determining the pair potential between two colloids or atoms: the range and the strength of the interaction [24,[62][63][64][65][66]. For example, a very popular system in which the range and strength are easily varied is a Yukawa fluid, consisting of hard spheres with an exponential attraction [64,[67][68][69].…”

Section: The Contact Potentialmentioning

confidence: 99%

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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“…[1][2][3][4] For qϾ0.3 a colloidal system can exist in solid, liquid, and vapor states as illustrated in Fig. 1͑a͒.…”

Section: Introductionmentioning

confidence: 99%

Atomic-force-microscopy studies of phase separations in macromolecular systems

1998

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Atomic force microscopy ͑AFM͒ has been used to visualize events arising from the formation of intervening metastable phases at the surfaces of macromolecular crystals growing from solution. Crystals investigated were of the proteins canavalin, thaumatin, lipase, xylanase, and catalase, crystals of transfer RNA, and crystals of satellite tobacco mosaic virus. Two types of aggregates were observed. The first were small, linear and branched aggregates, perhaps fractile in structure. These were incorporated into growing crystals as impurities, and they produced defects of various kinds. The second aggregate form we infer to be liquid-protein droplets which were particularly evident in freshly mixed protein-precipitant solutions. Droplets, upon sedimentation, have two possible fates. In some cases they immediately restructured as crystalline multilayer stacks whose development was guided by and contiguous with the underlying lattice. These contributed to the ordered growth of the crystal by serving as sources of growth steps. In other cases, liquid-protein droplets formed distinct microcrystals, somehow discontinuous with the underlying lattice, and these were subsequently incorporated into the growing substrate crystal with the formation of defects. Scarring experiments with the AFM tip indicated that liquid-protein droplets with the potential to rapidly crystallize were a consequence of concentration instabilities near the crystal's surfaces. The AFM study suggests that phase separation and the appearance of aggregates having limited order is a common occurrence in supersaturated macromolecular solutions such as the protein-precipitant solutions used for crystallization.

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Strong, weak and metastable liquids

Abstract: A discussion is given on the effect of the ratio (range of attractive interaction)/(range of repulsive interaction) on the phase behaviour of colloidal systems, simple fluids and protein solutions.

Cited by 49 publications

References 38 publications

Structure of Marginal and Fully Developed Colloidal Liquids

Structure of Marginal and Fully Developed Colloidal Liquids

Analytical phase diagrams for colloids and non-adsorbing polymer

Atomic-force-microscopy studies of phase separations in macromolecular systems

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