Predicting the gas–liquid critical point from the second virial coefficient

127

148

The depletion interaction between two spheres due to nonadsorbing ideal polymers is calculated from the polymer concentration profile using the excess ͑negative͒ adsorption. Computer simulations show that the polymer concentration profiles around two spheres are well described by the product function of the concentration profile around a single sphere. From the interaction potential between two spheres the second osmotic virial coefficient, B 2 , is calculated for various polymer-colloid size ratios. We find that when the polymers become smaller than the spheres, B 2 remains positive in the dilute regime. This shows that the depletion interaction is ineffective for relatively small spheres.

Section: Fig 8 Interaction Potential Between Two Spheres Immersed Imentioning

confidence: 99%

Depletion interaction between spheres immersed in a solution of ideal polymer chains

Tuinier

Vliegenthart

Lekkerkerker

2000

127

148

“…Such virial coefficients are very sensitive to the strength and nature of the depletion interaction 28 . A recent study 67 has shown that for many simple systems consisting of a HS like repulsion with an additional attractive potential, the location of the liquid-gas or fluid-fluid critical point can be correlated with the point where the reduced virial coefficient…”

Section: Second Virial Coefficients Phase-diagramsmentioning

confidence: 99%

Polymer induced depletion potentials in polymer-colloid mixtures

Louis

Bolhuis

Meijer

et al. 2002

138

151

The depletion interactions between two colloidal plates or between two colloidal spheres, induced by interacting polymers in a good solvent, are calculated theoretically and by computer simulations. A simple analytical theory is shown to be quantitatively accurate for case of two plates. A related depletion potential is derived for two spheres; it also agrees very well with direct computer simulations. Theories based on ideal polymers show important deviations with increasing polymer concentration: They overestimate the range of the depletion potential between two plates or two spheres at all densities, with the largest relative change occurring in the dilute regime. They underestimate the well depth at contact for the case of two plates, but overestimate it for two spheres. Depletion potentials are also calculated using a coarse graining approach which represents the polymers as "soft colloids": good agreement is found in the dilute regime. Finally, the effect of the polymers on colloid-colloid osmotic virial coefficients is related to phase behavior of polymer-colloid mixtures.

“…To estimate whether this deviation has a significant effect on the computed phase behavior, we calculate the normalized second virial coefficients B * 2 for both fitted and measured potentials for system 2. According to Noro and Frenkel's extended principle of corresponding states, the second virial coefficient is a rough estimator of the phase behavior that should arise from a given potential: 34,35 a B * 2 that is positive correlates with net repulsion between the particles, indicating that a phase transition should not occur; a B * 2 that is close to zero indicates little net attraction or repulsion between the particles, so a phase transition is not expected. Phase transitions are expected to occur when B * 2 becomes smaller than −1.5.…”

Section: B Potential Modelmentioning

confidence: 99%

Temperature-sensitive colloidal phase behavior induced by critical Casimir forces

Dang

Verde

Nguyen

et al. 2013

We report Monte Carlo simulations of phase behavior of colloidal suspensions with near-critical binary solvents using effective pair potentials from experiments. At off-critical solvent composition, the calculated phase diagram agrees well with measurements of the experimental system, indicating that many-body effects are limited. Close to the critical composition, however, agreement between experiment and simulation becomes poorer, signaling the increased importance of many-body effects. Both at and off the critical solvent concentration, the colloidal phase diagram is qualitatively similar to those of molecular systems and obeys the principle of corresponding states with one striking difference: it occurs in a narrow temperature interval of <1 • C below the solvent phase separation temperature.