Critical Casimir Force

It was already predicted by Fisher and de Gennes [147] that suppression of the critical fluctuations by confinement between two closely separated walls should lead to a force between the plates. Unlike the classical Casimir force, this so-called critical Casimir force strongly depends on temperature and should be largest when approaching the critical temperature (for an introduction, see Ref [148]). The length scale of the fluctuations is described by means of the so alled bulk order parameter It changes with temperature according to 

coo is an amplitude that corresponds to a typical length scale of the intermo-lecular pair potential. The critical exponent b 0.65 is an universal quantity its precise value depends on the internal symmetry of the system. The free energy per unit area of a system confined by two parallel walls at distance x at temperature T can 

First indirect experimental observations of the critical Casimir force were made by Chan and Garcia [152]. They measured the thickness of He films on a copper substrate and detected a thinning of the films close to the critical point of transition to superfluidity, indicating an attractive critical Casimir force. For a He/ He mixture close to the tricritical point, the same authors found a repulsive critical Casimir force, which caused film thickening on the copper substrate [153] (for a later, refined theoretical analysis, see Ref [154]). The tricritical point is the point in the phase diagram where the superfluidity transition line terminates at the top coexistence line of He/He. 

Whether the critical Casimir force is attractive or repulsive depends on the boundary conditions. If the order parameter vanishes at both surfaces (symmetric boundary conditions), the resulting critical Casimir forces is attractive. For nonsym-metric boundary conditions (i.e., if the order parameter remains finite at one of the interfaces while it vanishes at the other), the critical Casimir force is repulsive. The critical Casimir force for a binary liquid mixture of methylcyclohexane and per-fluoromethylcyclohexane was studied by Fukuto et al. [155]. The increase in thickness of such a liquid film on a silicon wafer close to critical point was measured using X-ray reflectivity and agreed with theoretical models. 

Critical Casimir forces are rather weak and therefore hard to detect. What might stiH make them interesting for future applications is the fact that they are based on a very universal concept, can be controlled by temperature, and can be either attractive or repulsive depending on surface treatment 

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Machta BB, Veatch SL, Sethna IP (2012) Critical Casimir forces in cellular membranes. Phys Rev Lett 109 138101... 

Long-range fluctuations in matter close to a critical point (phase transition) can lead to long-range forces, which are called critical Casimir forces. 

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