# Difference between revisions of "Critical Casimir effect in three-dimensional Ising systems: Measurements on binary wetting films"

Original entry: Nefeli Georgoulia, APPHY 226, Spring 2009

## Overview

Authors: Masafumi Fukuto, Yohko F. Yano & Peter S. Pershan

Source: Physical Review Letters, Vol.94, 135702, (2005)

Soft Matter key words: Thermodynamic Casimir force, Correlation length, Thin films, Wetting

## Abstract

Fig.1 : M.i Fukuto, Y. F. Yano & P.S. Pershan

In analogy to the quantum electrodynamics Casimir force, arising between conducting plates due to confinement of zero-point fluctuations of vacuum fields, a thermodynamic Casimir force has been introduced. The latter arises by confining a fluid with diverging bulk correlation lenght $\xi$ to a finite dimension L. Authors of this paper set out to experimentally confirm theoretical predictions for this force, in binary thin wetting films close to liquid/vapor coexistence. They extract a Casimir amplitude $\Delta_{+-}$ as well as a Casimir scaling function $\theta_{+-}$ which, they find, depends monotonically on dimensionality.

## Soft Matter Snippet

Fig.2 : M. Fukuto, Y. F. Yano & P. S. Pershan
Fig.3 : M.i Fukuto, Y. F. Yano & P.S. Pershan

The experimental setup consists of a $SiO_2/Si$ substrate on which methylcyclohexane and perfluoromethylcyclohexane form a 3D Ising film by complete wetting. The two solvents de-mix at a bulk critical point (BPC) of $T = 46.2^{\circ} C.$ The authors measure film thickness while varying temperature t, mole fraction $\phi$ or chemical potential $\Delta \mu$. They illustrate this schematically on the phase diagram of fig.1. They chose to measure film thickness employing x-ray reflectivity, for which they use a fixed anode tube. The radiation is reflected off of a vertically oriented substrate in the horizontal scattering plane, at an incident angle $\alpha$, corresponding to a wave vector $q_z = \frac{4 \pi}{\lambda} sin(\alpha)$ normal to the surface. The film thickness $L = <\frac{n \pi}{q_{z,n}}>$ is obtained via the interference fringes arising from the substrate/film and film/vapor interfaces.

Figure 2 contains some of the results. On fig 2a, the variation of film thickness is plotted as a function of temperature. Open symbols and closed correspond to data on cooling and heating of the film respectively. Film thickening, which signifies the presence of Casimir force, is observed at a critical $T_c$ regardless of the direction of temperature variation. However, for $T< T_c$, a hysteresis is observed between cooling and heating. No hysteresis is present when $T>T_c$.

The same film thickening at $x_c$ is observed when plotting volume fraction $x$ as a function of film thickness. In this case no hysteresis is present. These data are deemed robust and are subsequently used to extract the Casimir amplitude $\Delta_{+-}$ and the Casimir scaling function $\theta_{+-}$. The scaling function is plotted on figure 3, as a function of rising temperature and rising molar fraction.