Critical Casimir effect in classical binary liquid mixtures

Abstract

If a fluctuating medium is confined, the ensuing perturbation of its fluctuation spectrum generates Casimirlike effective forces acting on its confining surfaces. Near a continuous phase transition of such a medium the corresponding order parameter fluctuations occur on all length scales and therefore close to the critical point this effect acquires a universal character, i.e., to a large extent it is independent of the microscopic details of the actual system. Accordingly it can be calculated theoretically by studying suitable representative model systems. We report on the direct measurement of critical Casimir forces by total internal reflection microscopy with femtonewton resolution. The corresponding potentials are determined for individual colloidal particles floating above a substrate under the action of the critical thermal noise in the solvent medium, constituted by a binary liquid mixture of water and 2,6-lutidine near its lower consolute point. Depending on the relative adsorption preferences of the colloid and substrate surfaces with respect to the two components of the binary liquid mixture, we observe that, upon approaching the critical point of the solvent, attractive or repulsive forces emerge and supersede those prevailing away from it. Based on the knowledge of the critical Casimir forces acting in film geometries within the Ising universality class and with equal or opposing boundary conditions, we provide the corresponding theoretical predictions for the sphere-planar wall geometry of the experiment. The experimental data for the effective potential can be interpreted consistently in terms of these predictions and a remarkable quantitative agreement is observed.

Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques

“…From our analysis above we conclude that the DA provides a rather reliable approximation for the scaling functions K (±,−) (Θ, ∆, L ) for both (±, −) BCs for a wide range of parameters, which happen to be the relevant ones for experiments involving colloids in binary liquid mixtures [32,44]. In particular, the DA agrees rather well with the actual, full MFT data in the mixed state of the binary liquid at t > 0, for distance-to-radius ratios ∆ 1/3, as well as for elongated cylinders L 4.…”

“…The overlap of the particle projection with the chemical step varies linearly with the position X, which leads as a function of Ξ to a linear interpolation between +1 and −1 of the scaling function ω (a < |a > ,b) [Eq. (32)]. Due to the DA, for α = π/2 there is a non-analyticity at |X| = L/2.…”

Many-body effects for critical Casimir forces

“…In (e) the two pairwise normal forces have opposite directions with the repulsive one being the stronger one [32,47,48]. The corresponding dashed arrows have the same meaning as in (a) and (b).…”

Bonn, Wegdam, and Schall Reply:

“…Both issues-the actual form of the potential and the possible absence of critical scaling-could in principle be resolved by a complete calculation of the Casimir interaction without any approximations, which appears to be feasible [4,5]. Until this is done, it seems difficult to assess, e.g., the reason for the deviation of the last data point from our simple arguments in [1] …”