When depletion goes critical

Abstract

Depletion interactions in correlated fluids are investigated both theoretically andexperimentally. A formally exact derivation of a general expression for depletioninteractions is presented and then specialized to the case of critical correlations in thedepletant by employing a long wavelength approximate analysis. A scaling expression isobtained in the critical region, suggesting a close connection to the critical Casimir effect.As a result we are able to compute the full scaling function of the critical Casimir effectin terms of the known scaling form of the depletant equation of state. Thesepredictions are experimentally tested in a colloidal suspension with a micellarsolution as depletion agent. Colloids are seen to aggregate reversibly when themicellar concentration exceeds a temperature dependent value which becomesremarkably small as the temperature approaches the lower consolution point ofthe micellar suspension. Continuity between the standard depletion picture atlow temperature and the Casimir effect in the critical region is demonstratedby identifying several approximate scaling laws which compare favorably withthe theoretical analysis. The transition line is seen to lie close to the curve ofmaximum susceptibility of the depletant. A model, analyzed within mean fieldapproximation, is shown to reproduce the main qualitative features of the phenomenon.