Critical Casimir forces and adsorption profiles in the presence of a chemically structured substrate

Abstract

Motivated by recent experiments with confined binary liquid mixtures near demixing, we study the universal critical properties of a system, which belongs to the Ising universality class, in the film geometry. We employ periodic boundary conditions in the two lateral directions and fixed boundary conditions on the two confining surfaces, such that one of them has a spatially homogeneous adsorption preference while the other one exhibits a laterally alternating adsorption preference, resembling locally a single chemical step. By means of Monte Carlo simulations of an improved Hamiltonian, so that the leading scaling corrections are suppressed, numerical integration, and finite-size scaling analysis we determine the critical Casimir force and its universal scaling function for various values of the aspect ratio of the film. In the limit of a vanishing aspect ratio the critical Casimir force of this system reduces to the mean value of the critical Casimir force for laterally homogeneous ++ and +- boundary conditions, corresponding to the surface spins on the two surfaces being fixed to equal and opposite values, respectively. We show that the universal scaling function of the critical Casimir force for small but finite aspect ratios displays a linear dependence on the aspect ratio which is solely due to the presence of the lateral inhomogeneity. We also analyze the order-parameter profiles at criticality and their universal scaling function which allows us to probe theoretical predictions and to compare with experimental data.

revised version, section 5.2 expanded; 53 pages, 12 figures, iopart class

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Cited by in corpus (19)

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• Boundary Criticality of the 3D O($N$) Model: From Normal to Extraordinary
• Aspect-ratio dependence of thermodynamic Casimir forces
• Thermodynamic Casimir Forces between a Sphere and a Plate: Monte Carlo Simulation of a Spin Model
• Trapping colloids near chemical stripes via critical Casimir forces
• Critical Casimir Effect: Exact Results
• Critical Casimir forces steered by patterned substrates
• Critical behavior in the presence of an order-parameter pinning field
• Thermodynamic Casimir Effect in Films: the Exchange Cluster Algorithm
• 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
• The ordinary surface universality class of the three-dimensional O($N$) model
• Critical Casimir forces between planar and crenellated surfaces
• Finite-Size Scaling at fixed Renormalization-Group invariant
• Two-dimensional critical systems with mixed boundary conditions: Exact Ising results from conformal invariance and boundary-operator expansions
• Bound of Casimir Effect by Holography
• Surface critical behavior of the three-dimensional O(3) model
• Boundary operator product expansion coefficients of the three-dimensional Ising universality class
• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class
• Casimir effect in critical $\mathrm{O}(N)$ models from non-equilibrium Monte Carlo simulations