Bulk Correlation Length Research Articles

Emergent long-range couplings in arrays of fluid cells.

We present a system exhibiting extraordinarily long-range cooperative effects, on a length scale far exceeding the bulk correlation length. We give a theoretical explanation of these phenomena based on the mesoscopic picture of phase coexistence in finite systems, which is confirmed by MonteCarlo simulation studies. Our work demonstrates that such action at a distance can occur in classical systems involving simple or complex fluids, such as colloid-polymer mixtures or ferromagnets.

On the Relation Between Casimir Forces and Bulk Correlations

Within a microscopic approach we show that in the case of an ideal quantum gas enclosed in a slit the Casimir force can be simply expressed in terms of the bulk one-particle density matrix. The corresponding formula, which holds both for bosons and fermions, allows to relate the range of the Casimir force to the bulk correlation length. The low-temperature behavior of the Casimir forces is derived.

Order of wetting transitions in electrolyte solutions.

For wetting films in dilute electrolyte solutions close to charged walls we present analytic expressions for their effective interface potentials. The analysis of these expressions renders the conditions under which corresponding wetting transitions can be first- or second-order. Within mean field theory we consider two models, one with short- and one with long-ranged solvent-solvent and solvent-wall interactions. The analytic results reveal in a transparent way that wetting transitions in electrolyte solutions, which occur far away from their critical point (i.e., the bulk correlation length is less than half of the Debye length) are always first-order if the solvent-solvent and solvent-wall interactions are short-ranged. In contrast, wetting transitions close to the bulk critical point of the solvent (i.e., the bulk correlation length is larger than the Debye length) exhibit the same wetting behavior as the pure, i.e., salt-free, solvent. If the salt-free solvent is governed by long-ranged solvent-solvent as well as long-ranged solvent-wall interactions and exhibits critical wetting, adding salt can cause the occurrence of an ion-induced first-order thin-thick transition which precedes the subsequent continuous wetting as for the salt-free solvent.

Drag Coefficient of a Spherical Droplet Immersed in a Near-Critical Binary Fluid Mixture

We consider a spherical liquid droplet immersed in a near-critical binary fluid mixture. A weak preferential attraction is assumed between the droplet and one of the two mixture components, and the difference in the viscosity is neglected between the mixture components. Using the Gaussian free-energy functional, we calculate the drag coefficient of a droplet. Whether it is increased or decreased by the preferential attraction turns out to depend on the bulk correlation length and the ratio of the viscosity of the surrounding mixture to that of the droplet.

Drag Coefficient of a Rigid Spherical Particle in a Near-Critical Binary Fluid Mixture

We calculate the drag coefficient of a rigid spherical particle in an incompressible binary fluid mixture. A weak preferential attraction is assumed between the particle surface and one of the fluid components, and the difference in the viscosity between the two components is neglected. Using the Gaussian free-energy functional and solving the hydrodynamic equation explicitly, we can show that the preferential attraction makes the drag coefficient larger as the bulk correlation length becomes longer. The dependence of the deviation from the Stokes law on the correlation length, when it is short, turns out to be much steeper than the previous estimates.

Wetting Reversal at Gelation Transition Freezes Thermodynamically Unstable States

The contact angle of a drop of gelling solution on a flat, solid surface was monitored as the hot solution was allowed to cool. When a solvent with a high cohesive energy and a wettable solid surface was used, a wetting solution turned into a dewetting solid at the gelation transition. The density profiles in gel as probed by confocal Raman microscopy reveal that the adsorption of both gelator and solvent shifts at the transition and the solvent is severely depleted from the interfacial region. Thus, the wetting reversal is accompanied by the interfacial desolvation. As a result of the adsorption shift during the gelation process in progress, a locally concentrated region of the gelator is frozen in space far away from the surface. This is a thermodynamically unstable state but can be realized reproducibly. The profile analysis also shows that the effect of the surface extends out to a few hundred micrometers, 2 orders of magnitude larger than the bulk correlation length.

The imperfect Bose gas in d dimensions: critical behavior and Casimir forces

We consider the d-dimensional imperfect (mean-field) Bose gas confined in a slit-like geometry and subject to periodic boundary conditions. Within an exact analytical treatment we first extract the bulk critical properties of the system at Bose–Einstein condensation and identify the bulk universality class to be the one of the classical d-dimensional spherical model. Subsequently we consider finite slit width D and analyze the excess surface free energy and the related Casimir force acting between the slit boundaries. Above the bulk condensation temperature (T > Tc) the Casimir force decays exponentially as a function of D, with the bulk correlation length determining the relevant length scale. For T = Tc and for T < Tc its decay is algebraic. The magnitude of the Casimir forces at Tc and for T < Tc is governed by the universal Casimir amplitudes. We extract the relevant values for different d and compute the scaling functions describing the crossover between the critical and low-temperature asymptotics of the Casimir force. The scaling function is monotonic at any d∈(2,4) and becomes constant for d > 4 and T ≤ Tc.

Giant Proximity Effect in Superfluid Helium

Recently, it was shown that two confined regions of liquid 4He exhibit a proximity effect over distances much larger than the correlation length ξ[1; 2]. Here we report measurements of the superfluid fraction ρs/ρ and specific heat cp of a 33.6 nm film. Comparison with previous data from a 31.7 nm film in contact with an array of 34 × 106 (2 μm)3 boxes of 4He allows us to show quantitatively the enhancement in ρs/ρ and cp due to the presence of the boxes in the temperature region where the film orders. The enhancement in ρs/ρ is observed up to distances 650 times the bulk correlation length. This anomalously large length scale is analogous to a giant proximity effect observed in High-Tc superconductors (HTSC)[3].

Universal anisotropic finite-size critical behavior of the two-dimensional Ising model on a strip and ofd-dimensional models on films

Anisotropy effects on the finite-size critical behavior of a two-dimensional Ising model on a general triangular lattice in an infinite-strip geometry with periodic, antiperiodic, and free boundary conditions (bc) in the finite direction are investigated. Exact results are obtained for the scaling functions of the finite-size contributions to the free energy density. With ξ(>) the largest and ξ(<) the smallest bulk correlation length at a given temperature near criticality, we find that the dependence of these functions on the ratio ξ(<)/ξ(>) and on the angle parametrizing the orientation of the correlation volume is of geometric nature. Since the scaling functions are independent of the particular microscopic realization of the anisotropy within the two-dimensional Ising model, our results provide a limited verification of universality. We explain our observations by considering finite-size scaling of free energy densities of general weakly anisotropic models on a d-dimensional film (i.e., in an L×∞(d-1) geometry) with bc in the finite direction that are invariant under a shear transformation relating the anisotropic and isotropic cases. This allows us to relate free energy scaling functions in the presence of an anisotropy to those of the corresponding isotropic system. We interpret our results as a simple and transparent case of anisotropic universality, where, compared to the isotropic case, scaling functions depend additionally on the shape and orientation of the correlation volume. We conjecture that this universality extends to cases where the geometry and/or the bc are not invariant under the shear transformation and argue in favor of validity of two-scale factor universality for weakly anisotropic systems.

The Bulk Correlation Length and the Range of Thermodynamic Casimir Forces at Bose-Einstein Condensation

The relation between the bulk correlation length and the decay length of thermodynamic Casimir forces is investigated microscopically in two three-dimensional systems undergoing Bose-Einstein condensation: the perfect Bose gas and the imperfect mean-field Bose gas. For each of these systems, both lengths diverge upon approaching the corresponding condensation point from the one-phase side, and are proportional to each other. We determine the proportionality factors and discuss their dependence on the boundary conditions. The values of the corresponding critical exponents for the decay length and the correlation length are the same, equal to 1/2 for the perfect gas, and 1 for the imperfect gas.

Capillary Emptying and Short-Range Wetting

We consider a liquid trapped in a narrow horizontal capillary, under the influence of gravity. As the slit is widened, the meniscus, separating the capillary liquid from gas, deforms and develops a long tongue extending along the bottom wall. As a critical slit width is approached, the length of the tongue diverges continuously, leading to the emptying of the capillary. We show that the critical singularities characterizing emptying are the same as those at short-ranged wetting transitions, but at a scale set by the capillary length rather than the bulk correlation length. These meso- or macroscopic versions of both complete and critical wetting are observable in the laboratory and are studied here using a colloid-polymer mixture.

Simulated flow around a rectangular 5:1 cylinder: Spanwise discretisation effects and emerging flow features

In the present contribution, a systematic parametrical study on the spanwise length of the computational domain and on the spanwise grid density is proposed in the framework of the Benchmark on the Aerodynamics of a Rectangular 5:1 Cylinder (BARC). The study aims at evaluating the effects of these computational features on the simulated flow field in terms of bulk parameters, spanwise-averaged distributions, correlation coefficient and correlation length. The effectiveness of the adopted computational approach to provide the correlation measures is discussed. In particular, dense spanwise grids seem to be a key element to simulate some emerging and unexpected features of the cylinder aerodynamic behaviour, such as the asymmetry of the time-averaged flow field.

Scaling properties of fluid adsorption near the base of a cylinder

We consider the adsorption of fluid at the foot of a cylinder that protrudes from a flat substrate made of the same material. Provided the contact angle θ is small enough, a drop of liquid condenses near the base, the size of which can be determined using simple macroscopic arguments. The adsorption in this geometry shows scaling behavior related to a number of different interfacial phase transitions and, for systems with short-ranged forces, shows a remarkable property; for small θ, the height of the drop (measured from the base) and the width (measured from the cylinder axis) are near identical to expressions for the thickness and parallel correlation length for microscopic wetting films (at planar walls). The only difference is that the bulk correlation length is replaced by the radius of the cylinder. By taking into account the correct singular behavior of the line tension we show that this geometrical amplification of the microscopic lengths occurs for second-order, first-order, and complete wetting transitions, and is specific to three dimensions. Similar phenomena occurs for long-ranged forces, and shows crossover scaling behavior.

Effect of ions on confined near-critical binary aqueous mixture

Near-critical binary mixtures containing ions and confined between two charged and selective surfaces are studied within a Ginzburg–Landau theory extended to include electrostatic interactions. Charge density profiles and the effective interactions between the confining surfaces are calculated in the case of chemical preference of the ions for one of the solvent components. Close to the consolute point of the binary solvent, the preferential solubility of ions leads to the modification of the charge density profiles with respect to the ones obtained from Debye–Huckel theory. As a result, the electrostatic contribution to the effective potential between the charged surfaces can exhibit an attractive well. Our calculations are based on the approximation scheme that is valid if the bulk correlation length of a solvent is much larger than the Debye screening length; in this critical regime, the effect of charge on the concentration profiles of the solvent is subdominant. Such conditions are met in the recent measurements of the effective forces acting between a substrate and a spherical colloidal particle immersed in the near-critical water–lutidine mixture [Nature, 2008, 451, 172]. Our analytical results are in quantitative agreement with the experimental ones.

Magnetic phase transition in Heisenberg antiferromagnetic films with easy-axis single-ion anisotropy

The staggered susceptibility of spin-1 and spin-3/2 Heisenberg antiferromagnet with easy-axis single-ion anisotropy on the cubic lattice films consisting of n=2, 3, 4, 5 and 6 interacting square lattice layers is studied by high-temperature series expansions. Sixth order series in J/kBT have been obtained for free-surface boundary conditions. The dependence of the Néel temperature on film thickness n and easy-axis anisotropy D has been investigated. The shifts of the Néel temperature from the bulk value can be described by a power law n−λ with a shift exponent λ, where λ is the inverse of the bulk correlation length exponent. The effect of easy-axis single-ion anisotropy on shift exponent of antiferromagnetic films has been studied. A comparison is made with related works. The results obtained are qualitatively consistent with the predictions of finite-size scaling theory.

Fluid Adsorption at the Base of a Cylinder

We consider the adsorption of fluid at a cylinder protruding from a flat substrate. For small contact angles θ, a liquid drop condenses at the base, the size of which is determined by macroscopic arguments. The adsorption exhibits scaling behavior related to a number of phase transitions and, for systems with short-ranged forces, shows a remarkable property: for small θ, the height and width of the drop are near identical to expressions for the thickness and parallel correlation length for microscopic wetting films. The only difference is that the bulk correlation length is replaced by the cylinder radius. This geometrical amplification of the microscopic lengths occurs for second-order, first-order, and complete wetting transitions, and is specific to three dimensions. Similar phenomena occurs for long-ranged forces, and shows crossover scaling behavior.

Surface melting of electronic order in La0.5Sr1.5MnO4

We report temperature-dependent surface x-ray scattering studies of the orbital ordered surface in La$_{0.5}$Sr$_{1.5}$MnO$_4$. We find that the interfacial width of the electronic order grows as the bulk ordering temperature is approached from below, though the bulk correlation length remains unchanged. Close to the transition, the surface is so rough that there is no well-defined electronic surface, despite the presence of bulk electronic order, that is the electronic surface has melted. Above the bulk transition, finite-sized isotropic fluctuations of orbital order are observed, with a correlation length equal to that of the electronic surfaces' in-plane correlation length at the transition temperature.

Exact results for the bipartite entanglement entropy of the AKLT spin-1 chain

We study the bipartite entanglement between a subsystem of size l and the rest of the system of total size L as it occurs in a spin-1 Affleck–Kennedy–Lieb–Tasaki (AKLT) chain subject to open boundary conditions. In this case, the ground-state manifold is four-fold degenerate and there is strong dependence on the parity of the number of spins, L. We present exact analytical results for the von Neumann entanglement entropy, as a function of both the size of the subsystem, l, and the total system size, L, for all four degenerate ground states for both odd and even L. In the large l, L limits the entanglement entropy approaches ln (2) for the SzT = ±1 while it approaches twice that value, 2ln (2), for the SzT = 0 states. In all cases, it is found that this constant is approached exponentially fast defining a length scale ξ = 1/ln (3) equal to the known bulk correlation length.

Molecular modeling of intermolecular and intramolecular excluded volume interactions for polymers at interfaces

A hybrid modeling approach is proposed for inhomogeneous polymer solutions. The method is illustrated for the depletion problem with polymer chains up to N=10(3) segments in semidilute solutions and good solvent conditions. In a three-dimensional volume, a set of freely jointed chains is considered for which the translational degrees of freedom are sampled using a coarse grained Monte Carlo simulation and the conformational degrees of freedom of the chains are computed using a modified self-consistent field theory. As a result, both intramolecular and intermolecular excluded volume effects are accounted for, not only for chains near the surface, but in the bulk as well. Results are consistent with computer simulations and scaling considerations. More specifically, the depletion thickness, which is a measure for the bulk correlation length, scales as delta proportional to phi(-0.75) and converges to the mean field result in the concentrated regime.

Thermally excited capillary waves at vapor/liquid interfaces of water–alcoholmixtures

The density profiles of liquid/vapor interfaces of water–alcohol (methanol, ethanol andpropanol) mixtures were studied by surface-sensitive synchrotron x-ray scatteringtechniques. X-ray reflectivity and diffuse scattering measurements, from the pure andmixed liquids, were analyzed in the framework of capillary wave theory to address thecharacteristic length scales of the intrinsic roughness and the shortest capillarywavelength (alternatively, the upper wavevector cutoff in capillary wave theory). Ourresults establish that the intrinsic roughness is dominated by average interatomicdistances. The extracted effective upper wavevector cutoff indicates capillarywave theory breaks down at distances of the order of bulk correlation lengths.