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Measurements of local density fluctuations are crucial to characterizing the interfacial properties of equilibrium fluids. A specific case that has been well-explored involves the heightened compressibility of water near hydrophobic entities. Commonly, a spatial profile of local fluctuation strength is constructed from the measurements of the mean and variance of solvent particle number fluctuations in a set of contiguous subvolumes of the system adjacent to the solvo-/hydrophobe. An alternative measure proposed by Evans and Stewart [J. Phys.: Condens. Matter 27, 194111 (2015)] defines a local compressibility profile in terms of the chemical potential derivative of the spatial number density profile. Using Grand canonical Monte Carlo simulation, we compare and contrast the efficacy of these two approaches for a Lennard-Jones solvent at spherical and planar solvophobic interfaces and SPC/E water at a hydrophobic spherical solute. Our principal findings are as follows: (i) the local compressibility profile χ(r) of Evans and Stewart is considerably more sensitive to variations in the strength of local density fluctuations than the spatial fluctuation profile F (r) and can resolve much more detailed structure; and (ii) while the local compressibility profile is essentially independent of the choice of spatial discretization used to construct the profile, the spatial fluctuation profile exhibits a strong systematic dependence on the size of the subvolumes on which the profile is defined. We clarify the origin and nature of this finite-size effect. [ABSTRACT FROM AUTHOR]

Simulations of water near extended hydrophobic spherical solutes have revealed the presence of a region of depleted density and accompanying enhanced density fluctuations. The physical origin of both phenomena has remained somewhat obscure. We investigate these effects employing a mesoscopic binding potential analysis, classical density functional theory (DFT) calculations for a simple Lennard-Jones solvent, and Grand Canonical Monte Carlo (GCMC) simulations of a monatomic water (mw) model. We argue that the density depletion and enhanced fluctuations are near-critical phenomena. Specifically, we show that they can be viewed as remnants of the critical drying surface phase transition that occurs at bulk liquid–vapor coexistence in the macroscopic planar limit, i.e., as the solute radius Rs → ∞. Focusing on the radial density profile ρ(r) and a sensitive spatial measure of fluctuations, the local compressibility profile χ(r), our binding potential analysis provides explicit predictions for the manner in which the key features of ρ(r) and χ(r) scale with Rs, the strength of solute–water attraction ɛsf, and the deviation from liquid–vapor coexistence of the chemical potential, δμ. These scaling predictions are confirmed by our DFT calculations and GCMC simulations. As such, our theory provides a firm basis for understanding the physics of hydrophobic solvation. [ABSTRACT FROM AUTHOR]

We study the monatomic water model of Molinero and Moore the grand canonical ensemble Monte Carlo simulation. Measurements of the probability distribution of the number density obtained via multicanonical sampling and histogram reweighting provide accurate estimates of the temperature dependence of both the liquid–vapor coexistence densities and the surface tension. Using finite-size scaling methods, we locate the liquid–vapor critical point at Tc = 917.6 K, ρc = 0.311 g cm−3. When plotted in scaled variables, in order to test the law of corresponding states, the coexistence curve of monatomic water is close to that of real water. In this respect, it performs better than extended simple point charge (SPC/E), TIP4P, and TIP4P/2005 water. [ABSTRACT FROM AUTHOR]

For a standard model of patchy colloidal fluids with patch number M = 2, where chain formation (polymerization) occurs, we show that Wertheim theory predicts critical behavior at vanishing density and temperature. The analysis is based on determining lines in the phase diagram of maximal correlation length and compressibility. Simulation studies identify the latter line and confirm our prediction of Fisher–Widom crossover, i.e., the asymptotic decay of the pair correlation function changes from monotonic to damped oscillatory as the density is increased. For M > 2, it is known that phase separation occurs with a true critical point. Our results support the notion that a "disappearing" critical point occurs in the limit M = 2 and we uncover its remnants. [ABSTRACT FROM AUTHOR]

We revisit the competition between attractive and repulsive interparticle forces in simple fluids and how this governs and connects the macroscopic phase behavior and structural properties, as manifested in pair correlation functions. We focus on the asymptotic decay of the total correlation function h(r) which is, in turn, controlled by the form of the pair direct correlation function c(r). The decay of rh(r) to zero can be exponential (monotonic) if attraction dominates repulsion and exponentially damped oscillatory otherwise. The Fisher-Widom (FW) line separates the phase diagram into two regions characterized by the two different types of asymptotic decays. We show that there is a new and physically intuitive thermodynamic criterion which approximates well the actual FW line. This new criterion defines a line where the isothermal compressibility takes its ideal gas value χ T = χ T id . We test our hypothesis by considering four commonly used models for simple fluids. In all cases, the new criterion yields a line in the phase diagram that is close to the actual FW line for the thermodynamic state points that are most relevant. We also investigate (Widom) lines of maximal correlation length, emphasizing the importance of distinguishing between the true and Ornstein-Zernike correlation lengths. [ABSTRACT FROM AUTHOR]

Understanding the phase behaviour of mixtures continues to pose challenges, even for systems that might be considered “simple.” Here, we consider a very simple mixture of two colloidal and one non-adsorbing polymer species, which can be simplified even further to a size-asymmetrical binary mixture, in which the effective colloid-colloid interactions depend on the polymer concentration. We show that this basic system exhibits surprisingly rich phase behaviour. In particular, we enquire whether such a system features only a liquid-vapor phase separation (as in one-component colloid-polymer mixtures) or whether, additionally, liquid-liquid demixing of two colloidal phases can occur. Particle-resolved experiments show demixing-like behaviour, but when combined with bespoke Monte Carlo simulations, this proves illusory, and we reveal that only a single liquid-vapor transition occurs. Progressive migration of the small particles to the liquid phase as the polymer concentration increases gives rise to composition inversion—a maximum in the large particle concentration in the liquid phase. Close to criticality, the density fluctuations are found to be dominated by the larger colloids. [ABSTRACT FROM AUTHOR]

We report a theoretical and simulation study of the drying and wetting phase transitions of a truncated Lennard-Jones fluid at a flat structureless wall. Binding potential calculations predict that the nature of these transitions depends on whether the wall-fluid attraction has a long ranged (LR) power law decay or is instead truncated, rendering it short ranged (SR). Using grand canonical Monte Carlo simulation and classical density functional theory, we examine both cases in detail. We find that for the LR case wetting is first order, while drying is continuous (critical) and occurs exactly at zero attractive wall strength, i.e., in the limit of a hardwall. In the SR case, drying is also critical but the order of the wetting transition depends on the truncation range of the wall-fluid potential. We characterize the approach to critical drying and wetting in terms of the density and local compressibility profiles and via the finitesize scaling properties of the probability distribution of the overall density. For the LR case, where the drying point is known exactly, this analysis allows us to estimate the exponent ν║, which controls the parallel correlation length, i.e., the extent of vapor bubbles at the wall. Surprisingly, the value we obtain is over twice that predicted by mean field and renormalization group calculations, despite the fact that our three dimensional system is at the upper critical dimension where mean field theory for critical exponents is expected to hold. Possible reasons for this discrepancy are discussed in the light of fresh insights into the nature of near critical finite-size effects. [ABSTRACT FROM AUTHOR]

In classical density functional theory (DFT), the part of the Helmholtz free energy functional arising from attractive inter-particle interactions is often treated in a mean-field or van der Waals approximation. On the face of it, this is a somewhat crude treatment as the resulting functional generates the simple random phase approximation (RPA) for the bulk fluid pair direct correlation function. We explain why using standard mean-field DFT to describe inhomogeneous fluid structure and thermodynamics is more accurate than one might expect based on this observation. By considering the pair correlation function g(x) and structure factor S(k) of a one-dimensional model fluid, for which exact results are available, we showthat the mean-field DFT, employed within the test-particle procedure, yields results much superior to those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that one should not judge the quality of a DFT based solely on the approximation it generates for the bulk pair direct correlation function. [ABSTRACT FROM AUTHOR]

Using classical density functional theory (DFT), we calculate the density profile (r) and local compressibility X(r) of a simple liquid solvent in which a pair of blocks with (microscopic) rectangular cross section are immersed. We consider blocks that are solvophobic, solvophilic and also ones that have both solvophobic and solvophilic patches. Large values of X(r) correspond to regions in space where the liquid density is fluctuating most strongly. We seek to elucidate how enhanced density fluctuations correlate with the solvent mediated force between the blocks, as the distance between the blocks and the chemical potential of the liquid reservoir vary. For sufficiently solvophobic blocks, at small block separations and small deviations from bulk gas-liquid coexistence, we observe a strongly attractive (near constant) force, stemming from capillary evaporation to form a low density gas-like intrusion between the blocks. The accompanying X(r) exhibits a structure which reflects the incipient gas-liquid interfaces that develop. We argue that our model system provides a means to understanding the basic physics of solvent mediated interactions between nanostructures, and between objects such as proteins in water that possess hydrophobic and hydrophilic patches. [ABSTRACT FROM AUTHOR]

A binary solvent mixture close to critical demixing experiences fluctuations whose correlation length, ξ, diverges as the critical point is approached. The solvent-mediated (SM) interaction that arises between a pair of colloids immersed in such a near-critical solvent can be long-ranged and this so-called critical Casimir interaction is well-studied. How a (dense) suspension of colloids will self-assemble under these conditions is poorly understood. Using a two-dimensional lattice model for the solvent and hard disks to represent the colloids, we perform extensive Monte Carlo simulations to investigate the phase behaviour of this model colloidal suspension as a function of colloid size and wettability under conditions where the solvent reservoir is supercritical. Unlike most other approaches, where the solvent is modelled as an implicit background, our model employs an explicit solvent and treats the suspension as a ternary mixture. This enables us to capture important features, including the pronounced fractionation of the solvent in the coexisting colloidal phases, of this complex system. We also present results for the partial structure factors; these shed light on the critical behaviour in the ternary mixture. The degree to which an effective two-body pair potential description can describe the phase behaviour and structure of the colloidal suspension is discussed briefly. [ABSTRACT FROM AUTHOR]

For binary fluid mixtures of spherical particles in which the two species are sufficiently different in size, the dominant wavelength of oscillations of the pair correlation functions is predicted to change from roughly the diameter of the large species to that of the small species along a sharp crossover line in the phase diagram [C. Grodon et al., J. Chem. Phys. 121, 7869 (2004)]. Using particle-resolved colloid experiments in 3d we demonstrate that crossover exists and that its location in the phase diagram is in quantitative agreement with the results of both theory and our Monte-Carlo simulations. In contrast with previous work [J. Baumgartl et al., Phys. Rev. Lett. 98, 198303 (2007)], where a correspondence was drawn between crossover and percolation of both species, in our 3d study we find that structural crossover is unrelated to percolation. [ABSTRACT FROM AUTHOR]

We determine the solvent mediated contribution to the effective potentials for model colloidal or nanoparticles dispersed in a binary solvent that exhibits fluid-fluid phase separation. The interactions between the solvent particles are taken to be purely repulsive point Yukawa pair potentials. Using a simple density functional theory we calculate the density profiles of both solvent species in the presence of the “colloids,” which are treated as external potentials, and determine the solvent mediated (SM) potentials. Specifically, we calculate SM potentials between (i) two colloids, (ii) a colloid and a planar fluid-fluid interface, and (iii) a colloid and a planar wall with an adsorbed wetting film. We consider three different types of colloidal particles: Colloid A that prefers the bulk solvent phase rich in species 2, colloid C that prefers the solvent phase rich in species 1, and “neutral” colloid B that has no strong preference for either phase, i.e., the free energies to insert the colloid into either of the coexisting bulk phases are almost equal. When a colloid that has a preference for one of the two solvent phases is inserted into the disfavored phase at state points close to coexistence a thick adsorbed “wetting” film of the preferred phase may form around the colloids. The presence of the adsorbed film has a profound influence on the form of the SM potentials. In case (i) reducing the separation between the two colloids of type A leads to a bridging transition whereby the two adsorbed films connect abruptly and form a single fluid bridge. The SM potential is strongly attractive in the bridged configuration. A similar phenomenon occurs in case (iii) whereby the thick adsorbed film on colloid A and that at the planar wall, which prefers the same phase as colloid A, connect as the separation between the colloid and the wall is reduced. In both cases the bridging transition is accompanied, in this mean-field treatment, by a discontinuity of the SM force. On the other hand, for the same wall, and a colloid of type C, the SM potential is strongly repulsive at small separations. For case (ii), inserting a single colloidal particle near the planar fluid-fluid interface of the solvent, the density profiles of the solvent show that the interface distortion depends strongly on the nature of the colloid-solvent interactions. When the interface disconnects from the colloid there is, once again, a discontinuity in the SM force. [ABSTRACT FROM AUTHOR]

We investigate the interfacial phase behavior of a binary fluid mixture composed of repulsive point Yukawa particles. Using a simple approximation for the Helmholtz free energy functional, which yields the random phase approximation for the pair direct correlation functions, we calculate the equilibrium fluid density profiles of the two species of particles adsorbed at a planar wall. We show that for a particular choice (repulsive exponential) of the wall potentials and the fluid pair-potential parameters, the Euler–Lagrange equations for the equilibrium fluid density profiles may be transformed into a single ordinary differential equation and the profiles obtained by a simple quadrature. For certain other choices of the fluid pair-potential parameters fluid-fluid phase separation of the bulk fluid is observed. We find that when such a mixture is exposed to a planar hard wall, the fluid exhibits complete wetting on the species 2 poor side of the binodal, i.e., we observe a thick film of fluid rich in species 2 adsorbed at the hard wall. The thickness of the wetting film grows logarithmically with the concentration difference between the fluid state point and the binodal and is proportional to the bulk correlation length of the intruding (wetting) fluid phase. However, for state points on the binodal that are further from the critical point, we find there is no thick wetting film. We determine the accompanying line of first-order (prewetting) surface phase transitions which separate a thin and thick adsorbed film. We show that for some other choices of repulsive wall potentials the prewetting line is still present, but its location and extent in the phase diagram is strongly dependent on the wall-fluid interaction parameters. [ABSTRACT FROM AUTHOR]

The NaK 1 [sup 3]Δ state has been studied by the perturbation-facilitated optical-optical double resonance technique. Mixed singlet-triplet levels, A(2)[sup 1]Σ[sup +](v[sub A],J)∼b(1)[sup 3]Π(v[sub b],J), were pumped from thermally populated rovibrational levels of the ground state, X(1)[sup 1]Σ[sup +](v[sub X],J±1), using a single-mode cw dye laser. A single-mode cw Ti:Sapphire laser was then used to further excite the NaK molecules to various 1 [sup 3]Δ(v[sub Δ],N[sub Δ],J[sub Δ]) rovibrational levels which were detected by observing collision-induced [sup 3]Λ→a(1)[sup 3]Σ[sup +] fluorescence in the green part of the spectrum. The measured energies of the 1 [sup 3]Δ(v[sub Δ],N[sub Δ]) levels were fit to a Dunham expansion, and the Dunham coefficients were used to construct the RKR potential curve. Absolute numbering of the 1 [sup 3]Δ state vibrational levels was established by a comparison of experimental and calculated 1 [sup 3]Δ(v[sub Δ],N[sub Δ],J[sub Δ])←b(1)[sup 3]Π(v[sub b],J[sub b]) absorption line strengths. A deperturbation program was used to determine the vibration-dependent 1 [sup 3]Δ state spin-orbit interaction parameter. Hyperfine structure of the 1 [sup 3]Δ state was studied, and the Fermi-contact interaction term for this state was determined to be ∼0.0111 cm[sup -1]. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We investigate interfacial and capillary phenomena in a simple model for a fluid of hard rods, viz. the Zwanzig model, in which the orientations of rectangular blocks are restricted to three orthogonal directions. The theory, which is based on an Onsager-like free energy functional, predicts local biaxial ordering at the "free" interface between the coexisting isotropic and nematic phases. For an isotropic bulk fluid in contact with a single planar hard wall, we find a continuous surface phase transition from uniaxial to biaxial local symmetry, followed by complete wetting of the wall-isotropic fluid interface by a nematic film with director parallel to the wall, as the reservoir density approaches its value at bulk coexistence. For a fluid confined by two parallel hard walls we determine a first-order capillary nematization transition at large wall separation, which terminates in a capillary critical point when the wall separation is about twice the length of the rods. This transition is the analog of the capillary condensation observed for simple fluids confined by attractive walls but is purely entropy driven here. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We study the effective interactions, structure, and the isothermal compressibility of a binary mixture interacting with pairwise additive pair potentials. By integrating out the degrees of freedom of species 2 in the partition sum we first show that a binary mixture can be mapped formally onto an effective one-component system with an effective Hamiltonian consisting of a structure-independent term, which contributes to the total pressure and chemical potential of the system, but does not affect the phase behavior, and a structure-dependent potential of mean force, which contains pair-, triplet-, and higher-body interactions. We then show that the 1-1 structure factor and pair correlation function, and the total isothermal compressibility of the mixture are equal to those of the effective one-component system, provided the mapping is exact. We illustrate and confirm these results by calculating the structure factors and pair correlation functions of the binary Asakura-Oosawa model, which is a simple model for colloid-polymer mixtures, and those of the corresponding one-component system for a size ratio such that the mapping onto an effective one-component Hamiltonian with a strictly pairwise potential of mean force is exact. The distinction between the osmotic and total compressibility of the mixture is emphasized. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations are used to investigate the asymptotic decay of the total pairwise correlation function h(r) for some model fluids. We determine the poles of the Fourier transform h(q) from the direct correlation function c(r). The leading poles determine the ultimate, r→∞, decay of h(r). For the truncated and shifted Lennard-Jones fluid we calculate the Fisher-Widom (disorder) line in the temperature-density (T,ρ) plane where the ultimate decay of rh(r) crosses over from monotonic (exponential) to exponentially damped oscillatory decay. This line lies close to that obtained in an earlier integral-equation [hypernetted chain-soft core mean spherical approximation (HMSA)] study. For states on the monotonic side of the disorder line, h(r) has a finite number of oscillations and we determine the boundaries which mark regions in the (T,ρ) plane where h(r) has a given number of zeros using a random-phase approximation for c(r). In the case of the hard-sphere fluid, the ultimate decay of h(r) is oscillatory for all densities and we find that simulation results for the period and (exponential) decay length of the oscillations are in good overall agreement with those of Percus-Yevick theory, although there is some indication that systematic differences develop for high-density states ρ[sup *]>=0.85. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]