Critical Casimir force in ${}^4$He films: confirmation of finite-size scaling

Abstract

We present new capacitance measurements of critical Casimir force-induced thinning of ${}^4$He films near the superfluid/normal transition, focused on the region below $T_{\lambda }$ where the effect is the greatest. ${}^4$He films of 238, 285, and 340 Åthickness are adsorbed on N-doped silicon substrates with roughness $\approx 8\mathring{A}$. The Casimir force scaling function $\vartheta$, deduced from the thinning of these three films, collapses onto a single universal curve, attaining a minimum $\vartheta =-1.30\pm 0.03$ at $x=t{d}^{1/\nu }=-9.7\pm 0.8{\mathring{A}}^{1/\nu }$. The collapse confirms the finite-size scaling origin of the dip in the film thickness. Separately, we also confirm the presence down to $2.13K$ of the Goldstone/surface fluctuation force, which makes the superfluid film $\sim 2\mathring{A}$ thinner than the normal film.

4 pages, 3 figures, submitted to PRL

Cited by in corpus (40)

• The Casimir effect: from quantum to critical fluctuations
• Universal scaling functions of critical Casimir forces obtained by Monte Carlo simulations
• Critical Casimir forces in colloidal suspensions on chemically patterned surfaces
• Monte Carlo simulation results for critical Casimir forces
• Tunability of Critical Casimir Interactions by Boundary Conditions
• Critical Casimir Effect in superfluid wetting films
• Thinning of superfluid films below the critical point
• Critical Casimir effect for colloids close to chemically patterned substrates
• Thermodynamic Casimir effects involving interacting field theories with zero modes
• Aspect-ratio dependence of thermodynamic Casimir forces
• Thermodynamic Casimir Forces between a Sphere and a Plate: Monte Carlo Simulation of a Spin Model
• Interplay of critical Casimir and dispersion forces
• Trapping colloids near chemical stripes via critical Casimir forces
• Critical Casimir Effect: Exact Results
• Critical Casimir forces steered by patterned substrates
• Critical Casimir forces and adsorption profiles in the presence of a chemically structured substrate
• Critical adsorption and critical Casimir forces for geometrically structured confinements
• Transient Casimir forces from quenches in thermal and active matter
• Fluctuation-induced forces in strongly anisotropic critical systems
• Exact thermodynamic Casimir forces for an interacting three-dimensional model system in film geometry with free surfaces
• Casimir force in O(n) lattice models with a diffuse interface
• Critical Casimir force in slab geometry with finite aspect ratio: analytic calculation above and below $T_c$
• Crossover from Goldstone to critical fluctuations: Casimir forces in confined O$(\mathbf{n})$ symmetric systems
• Thermodynamic Casimir Effect in Films: the Exchange Cluster Algorithm
• Critical Casimir forces in the presence of random surface fields
• Liquid bridging of cylindrical colloids in near-critical solvents
• Exact results for the behavior of the thermodynamic Casimir force in a model with a strong adsorption
• Bulk and boundary effects on the decay of the thermodynamic Casimir force
• Critical and near critical phase behaviour and interplay between the thermodynamic Casimir and van der Waals forces in confined non-polar fluid medium with competing surface and substrate potentials
• Effective Pair Interaction of Patchy Particles in Critical Fluids
• Fluctuation-induced forces between rings threaded around a polymer chain under tension
• Effective interaction between a colloid and a soft interface near criticality
• Casimir effect in a dilute Bose gas in canonical ensemble within improved Hartree-Fock approximation
• Phase diagram of fluid phases in ${}^3$He -${}^4$He mixtures
• Finite-size Nagle-Kardar model: Casimir force
• Critical Casimir forces between planar and crenellated surfaces
• Fluctuations of the critical Casimir force
• The square lattice Ising model on the rectangle III: Hankel and Toeplitz determinants
• Exact solution for the order parameter profiles and the Casimir force in ${}^4$He superfluid films in an effective field theory
• Proposed fitting function for the critical Casimir force on ${}^4$He film below the $\lambda$ point