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Register a new userCritical Casimir interaction between colloidal Janus-type particles in two spatial dimensions
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We study colloidal particles with chemically inhomogeneous surfaces suspended in a critical binary liquid mixture. The inhomogeneous particle surface is composed of patches with alternating adsorption preferences for the two components of the binary solvent. By describing the binary liquid mixture emph{at} its consolute point in terms of the critical Ising model we exploit its conformal invariance in two spatial dimension. This allows us to determine exactly the universal profiles of the order parameter, the energy density, and the stress tensor as well as some of their correlation functions around a single particle for various shapes and configurations of the surface patches. The formalism encompasses several interesting configurations, including Janus particles of circular and needle shapes with dipolar symmetry and a circular particle with quadrupolar symmetry. From these single-particle properties we construct the so-called small particle operator expansion (SPOE), which enables us to obtain asymptotically exact expressions for the position- and orientation-dependent critical Casimir interactions of the particles with distant objects, such as another particle or the confining walls of a half plane, strip, or wedge, with various boundary conditions for the order parameter. In several cases we compare the interactions at large distances with the ones at close distance (but still large on the molecular scale). We also compare our analytical results for two Janus particles with recent simulation data.
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Langevin equations for the self-thermophoretic dynamics of Janus motors partially coated with an absorbing layer that is heated by a radiation field are presented. The derivation of these equations is based on fluctuating hydrodynamics and radiative heat transfer theory involving stochastic equations for bulk phases and surface processes that are consistent with microscopic reversibility. Expressions for the self-thermophoretic force and torque for arbitrary slip boundary conditions are obtained. The overdamped Langevin equations for the colloid displacement and radiative heat transfer provide expressions for the self-thermophoretic velocity and its reciprocal contribution where an external force can influence the radiative heat transfer. A nonequilibrium fluctuation formula is also derived and shows how the probability density of the Janus particle displacement and radiation energy transfer during the time interval [0,t] are related to the mechanical and thermal affinities that characterize the nonequilibrium system state.
The critical Casimir force (CCF) arises from confining fluctuations in a critical fluid and thus it is a fluctuating quantity itself. While the mean CCF is universal, its (static) variance has previously been found to depend on the microscopic details of the system which effectively set a large-momentum cutoff in the underlying field theory, rendering it potentially large. This raises the question how the properties of the force variance are reflected in experimentally observable quantities, such as the thickness of a wetting film or the position of a suspended colloidal particle. Here, based on a rigorous definition of the instantaneous force, we analyze static and dynamic correlations of the CCF for a conserved fluid in film geometry for various boundary conditions within the Gaussian approximation. We find that the dynamic correlation function of the CCF is independent of the momentum cutoff and decays algebraically in time. Within the Gaussian approximation, the associated exponent depends only on the dynamic universality class but not on the boundary conditions. We furthermore consider a fluid film, the thickness of which can fluctuate under the influence of the time-dependent CCF. The latter gives rise to an effective non-Markovian noise in the equation of motion of the film boundary and induces a distinct contribution to the position variance. Within the approximations used here, at short times, this contribution grows algebraically in time whereas, at long times, it saturates and contributes to the steady-state variance of the film thickness.
Using general scaling arguments combined with mean-field theory we investigate the critical ($T simeq T_c$) and off-critical ($T e T_c$) behavior of the Casimir forces in fluid films of thickness $L$ governed by dispersion forces and exposed to long-ranged substrate potentials which are taken to be equal on both sides of the film. We study the resulting effective force acting on the confining substrates as a function of $T$ and of the chemical potential $mu$. We find that the total force is attractive both below and above $T_c$. If, however, the direct substrate-substrate contribution is subtracted, the force is repulsive everywhere except near the bulk critical point $(T_c,mu_c)$, where critical density fluctuations arise, or except at low temperatures and $(L/a) (betaDelta mu) =O(1)$, with $Delta mu=mu-mu_c <0$ and $a$ the characteristic distance between the molecules of the fluid, i.e., in the capillary condensation regime. While near the critical point the maximal amplitude of the attractive force if of order of $L^{-d}$ in the capillary condensation regime the force is much stronger with maximal amplitude decaying as $L^{-1}$. Essential deviations from the standard finite-size scaling behavior are observed within the finite-size critical region $L/xi=O(1)$ for films with thicknesses $L lesssim L_{rm crit}$, where $L_{rm crit}=xi_0^pm (16 |s|)^{ u/beta}$, with $ u$ and $beta$ as the standard bulk critical exponents and with $s=O(1)$ as the dimensionless parameter that characterizes the relative strength of the long-ranged tail of the substrate-fluid over the fluid-fluid interaction. We present the modified finite-size scaling pertinent for such a case and analyze in detail the finite-size behavior in this region.
The Casimir effect in quantum electrodynamics (QED) is perhaps the best-known example of fluctuation-induced long-ranged force acting on objects (conducting plates) immersed in a fluctuating medium (quantum electromagnetic field in vacuum). A similar effect emerges in statistical physics, where the force acting, e.g., on colloidal particles immersed in a binary liquid mixture is affected by the classical thermal fluctuations occurring in the surrounding medium. The resulting Casimir-like force acquires universal features upon approaching a critical point of the medium and becomes long-ranged at criticality. In turn, this universality allows one to investigate theoretically the temperature dependence of the force via representative models and to stringently test the corresponding predictions in experiments. In contrast to QED, the Casimir force resulting from critical fluctuations can be easily tuned with respect to strength and sign by surface treatments and temperature control. We present some recent advances in the theoretical study of the universal properties of the critical Casimir force arising in thin films. The corresponding predictions compare very well with the experimental results obtained for wetting layers of various fluids. We discuss how the Casimir force between a colloidal particle and a planar wall immersed in a binary liquid mixture has been measured with femto-Newton accuracy, comparing these experimental results with the corresponding theoretical predictions.
We study crystal melting in two-dimensional antiferromagnets, by analyzing the statistical mechanics of the six-state clock model on a lattice in which defects (dislocations and disclinations) are allowed to appear. We show that the elementary dislocations bind to fractional magnetic vortices. We compute the phase diagram by mapping the system into a Coulomb gas model. Surprisingly, we find that in the limit of dominant magnetic interactions, antiferromagnetism can survive even in the hexatic and liquid phases. The ensuing molten antiferromagnets are topologically ordered and are characterized by spontaneous symmetry breaking of a non-local order parameter.
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