Direct Determination of Fluid Phase Equilibria by Simulation in the Gibbs Ensemble: A Review

Atomic-Scale Insights into the Phase Behavior of Carbon Dioxide and Water from 313 to 573 K and 8 to 30 MPa

We performed molecular dynamics (MD) simulations of CO2 + H2O systems by employing widely used force fields (EPM2, TraPPE, and PPL models for CO2; SPC/E and TIP4P/2005 models for H2O). The phase behavior observed in our MD simulations is consistent with the coexistence lines obtained from previous experiments and SAFT-based theoretical models for the equations of state. Our structural analysis reveals a pronounced correlation between phase transitions and the structural orderliness. Specifically, the coordination number of Ow (oxygen in H2O) around other Ow significantly correlates with phase changes. In contrast, coordination numbers pertaining to the CO2 molecules show less sensitivity to the thermodynamic state of the system. Furthermore, our data indicate that a predominant number of H2O molecules exist as monomers without forming hydrogen bonds, particularly in a CO2-rich mixture, signaling a breakdown in the hydrogen bond network's orderliness, as evidenced by a marked decrease in tetrahedrality. These insights are crucial for a deeper atomic-level understanding of phase behaviors, contributing to the well-grounded design of CO2 injection under high-pressure and high-temperature conditions, where an atomic-scale perspective of the phase behavior is still lacking.

Controlling the coarsening dynamics of ferrogranular networks by means of a vertical magnetic field

We are exploring in experiments the aggregation process in a shaken granular mixture of glass and magnetized steel beads, filled in a horizontal vessel, after the shaking amplitude is suddenly decreased. Then the magnetized beads form a transient network that coarsens in time into compact clusters, resembling a viscoelastic phase separation [Tanaka, J. Phys.: Condens. Matter 12, R207 (2000)0953-898410.1088/0953-8984/12/15/201], where attached beads represent the slow phase. Here we investigate how a homogeneous magnetic field oriented in vertical direction impedes the emergence and growth of the networks. With increasing field amplitude this phase is replaced by a fluctuating arrangement of repelling, isolated steel beads. The experimental results are compared with those of computer simulations. Coarse-grained molecular dynamics confirms the impact of an applied magnetic field on the structural transitions and allows us to investigate long-time regimes and magnetic response not yet accessible in the experiment. It turns out that an applied magnetic field has different impacts, depending on it strength. It can be used either to slow down the dynamics of the structural transitions without changing the type of the resulting phases and only affecting the amount and sizes of clusters, or to fully impede the formation of network-like and compact aggregates of steel beads.

Relating the length of a magnetic filament with solvophobic, superparamagnetic colloids to its properties in applied magnetic fields

The idea of creating polymer-like structures by crosslinking magnetic nanoparticles (MNPs) opened an alternative perspective on controlling the rheological properties of magnetoresponsive systems, because unlike suspensions of self-assembled MNPs, whose cluster sizes are sensitive to temperature, magnetic filaments (MFs) preserve their initial topology. Considering the length scales characteristic of single-domain nanoparticles used to create MFs, the MNPs can be both ferro- and superparamagnetic. Moreover, steric or electrostatic stabilization might not fully screen van der Waals interactions. In this paper, using coarse-grained molecular dynamics simulations, we investigate the influence of susceptibility of superparamagnetic MNPs-their number and central attraction forces between them-on the polymeric, structural, and magnetic properties of MFs with varied backbone rigidity. We find that, due to the general tendency of MFs with superparamagnetic monomers to bend, reinforced for colloids with a high susceptibility, properties of MFs vary greatly with chain length.

Thermodynamics of liquid and fluid mixtures from the kinetic Monte Carlo viewpoint

In this study a binary mixture is modelled in a uniform simulation cell at various temperatures using an extended version of the grand canonical kinetic Monte Carlo (GC-kMC) method. The main goal of this study is to consider the thermodynamic properties of binary liquids, gases, and gas-liquid mixtures from a more general point of view than that applied to the particular case of vapour-liquid equilibrium when the pressure and partial chemical potentials in coexisting phases are the same. Particular attention is paid to thermodynamic functions such as chemical potentials, Gibbs free energy and entropy. For the pair potential of unlike molecules a more universal scheme is proposed in comparison with the Lorentz-Berthelot combining rule. The approach is tested on an Ar-Kr mixture in a wide range of temperatures. In all cases, the obtained values of chemical potentials, pressure and internal energy for the entire set of component densities and temperature fully satisfy the Gibbs-Duhem equation with a high degree of accuracy. For the case of vapour-liquid equilibrium, the developed approach made it possible to reproduce the experimental pressure-composition diagrams with the highest accuracy ever achieved in the literature. Despite the fact that the Ar-Kr mixture, according to Raoult's law, is close to an ideal system, it was found that the partial pressures in the liquid phase or in a dense supercritical gas mixture are non-linear functions of the composition, and the partial pressure of the heavier component (Kr) can even be negative.

Numerical Techniques for Applications of Analytical Theories to Sequence-Dependent Phase Separations of Intrinsically Disordered Proteins

Biomolecular condensates, physically underpinned to a significant extent by liquid-liquid phase separation (LLPS), are now widely recognized by numerous experimental studies to be of fundamental biological, biomedical, and biophysical importance. In the face of experimental discoveries, analytical formulations emerged as a powerful yet tractable tool in recent theoretical investigations of the role of LLPS in the assembly and dissociation of these condensates. The pertinent LLPS often involves, though not exclusively, intrinsically disordered proteins engaging in multivalent interactions that are governed by their amino acid sequences. For researchers interested in applying these theoretical methods, here we provide a practical guide to a set of computational techniques devised for extracting sequence-dependent LLPS properties from analytical formulations. The numerical procedures covered include those for the determination of spinodal and binodal phase boundaries from a general free energy function with examples based on the random phase approximation in polymer theory, construction of tie lines for multiple-component LLPS, and field-theoretic simulation of multiple-chain heteropolymeric systems using complex Langevin dynamics. Since a more accurate physical picture often requires comparing analytical theory against explicit-chain model predictions, a commonly utilized methodology for coarse-grained molecular dynamics simulations of sequence-specific LLPS is also briefly outlined.

Insights into Sorption and Molecular Transport of Aqueous Glucose into Zeolite Nanopores

Liquid-phase heterogeneous catalysis using zeolites is important for biomass conversion to fuels and chemicals. There is a substantial body of work on gas-phase sorption in zeolites with different topologies; however, studies investigating the diffusion of complex molecules in liquid medium into zeolitic nanopores are scarce. Here, we present a molecular dynamics study to understand the sorption and diffusion of aqueous β-d-glucose into β-zeolite silicate at T = 395 K and P = 1 bar. Through 2-μs-long molecular dynamics trajectories, we reveal the role of the solvent, the kinetics of the pore filling, and the effect of the water model on these properties. We find that the glucose and water loading is a function of the initial glucose concentration. Although the glucose concentration increases monotonically with the initial glucose concentration, the water loading exhibits a nonmonotonic behavior. At the highest initial concentration (∼20 wt %), we find that the equilibrium loading of glucose is approximately five molecules per unit cell and displays a weak dependence on the water model. Glucose molecules follow a single-file diffusion in the nanopores due to confinement. The dynamics of glucose and water molecules slows significantly at the interface. The average residence time for glucose molecules is an order of magnitude larger than that in the bulk solution, while it is about twice as large for the water molecules. Our simulations reveal critical molecular details of the glucose molecule's local environment inside the zeolite pore relevant to catalytic conversion of biomass to valuable chemicals.

Gibbs-ensemble Monte Carlo simulation of H2-H2O mixtures

The miscibility gap in hydrogen-water mixtures is investigated by conducting Gibbs-ensemble Monte Carlo simulations with analytical two-body interaction potentials between the molecular species. We calculate several demixing curves at pressures below 150 kbar and temperatures of 1000 K ≤T≤ 2000 K. Despite the approximations introduced by the two-body interaction potentials, our results predict a large miscibility gap in hydrogen-water mixtures at similar conditions as found in experiments. Our findings are in contrast to those from ab initio simulations and provide a renewed indication that hydrogen-water immiscibility regions may have a significant impact on the structure and evolution of ice giant planets like Uranus and Neptune.

Generalized equation of state for fluids: From molecular liquids to colloidal dispersions

In this work, a new parameterization for the Statistical Association Fluid Theory for potentials of Variable Range (SAFT-VR) is coupled to the discrete potential theory to represent the thermodynamic properties of several fluids, ranging from molecular liquids to colloidal-like dispersions. In this way, this version of the SAFT-VR approach can be straightforwardly applied to any kind of either simple or complex fluid. In particular, two interaction potentials, namely, the Lennard-Jones and the hard-core attractive Yukawa potentials, are discretized to study the vapor-liquid equilibrium properties of both molecular and complex liquids, respectively. Our results are assessed with Monte Carlo computer simulations and available and accurate theoretical results based on the self-consistent Ornstein-Zernike approximation.

Gibbs-ensemble Monte Carlo simulation of H_{2}-He mixtures

We explore the performance of the Gibbs-ensemble Monte Carlo simulation technique by calculating the miscibility gap of H_{2}-He mixtures with analytical exponential-six potentials. We calculate several demixing curves for pressures up to 500 kbar and for temperatures up to 1800K and predict a H_{2}-He miscibility diagram for the solar He abundance for temperatures up to 1500K and determine the demixing region. Our results are in good agreement with ab initio simulations in the nondissociated region of the phase diagram. However, the particle number necessary to converge the Gibbs-ensemble Monte Carlo method is yet too large to offer a feasible combination with ab initio electronic structure calculation techniques, which would be necessary at conditions where dissociation or ionization occurs.

Ab initio Gibbs ensemble Monte Carlo simulations of the liquid-vapor equilibrium and the critical point of sodium

The ab initio (ai) Gibbs ensemble (GE) Monte Carlo (MC) method coupled with Kohn-Sham density functional theory is successful in predicting the liquid-vapour equilibrium of insulating systems. Here we show that the aiGEMC method can be used to study also metallic systems, where the excited electronic states play an important role and cannot be neglected. For this we include the electronic free energy in the formulation of the effective energy of the system to be used in the acceptance criteria for the MC moves. The application of this aiGEMC method to sodium yields a good agreement with available experimental data on the liquid-vapour equilibrium densities. We predict a critical point for sodium at 2338 ± 108 K and 0.24 ± 0.03 g cm-3. The liquid structure stemming from aiGEMC simulations is very similar to the one from ab initio molecular dynamics. Since this method can determine phase transition without computing the Gibbs free energy, it may offer a new possibility to study other materials with a reasonable computational cost.

Direct Simulations of Phase Behavior of Mixtures of Oppositely Charged Proteins/Nanoparticles and Polyelectrolytes

We use direct simulations of particle-polyelectrolyte mixtures using the single chain in mean field framework to extract the phase diagram for such systems. At high charges of the particles and low concentration of polymers, we observe the formation of a coacervate phase involving the particles and polyelectrolytes. At low particle charges and/or high concentration of polymers, the mixture undergoes a segregative phase separation into particle-rich and polymer-rich phases, respectively. We also present results for the influence of particle charge heterogeneity on the phase diagram.

Molecular Mechanism of Gas Solubility in Liquid: Constant Chemical Potential Molecular Dynamics Simulations

Accurate prediction of gas solubility in a liquid is crucial in many areas of chemistry, and a detailed understanding of the molecular mechanism of the gas solvation continues to be an active area of research. Here, we extend the idea of the constant chemical potential molecular dynamics (CμMD) approach to the calculation of the gas solubility in the liquid under constant gas chemical potential conditions. As a representative example, we utilize this method to calculate the isothermal solubility of carbon dioxide in water. Additionally, we provide microscopic insight into the mechanism of solvation that preferentially occurs in areas of the surface where the hydrogen network is broken.

Efficient determination of solid-state phase equilibrium with the multicell Monte Carlo method

Building on our previously introduced multicell Monte Carlo (MC)^{2} method for modeling phase coexistence, this paper provides important improvements for efficient determination of phase equilibria in solids. The (MC)^{2} method uses multiple cells, representing possible phases. Mass transfer between cells is modeled virtually by solving the mass balance equation after the composition of each cell is changed arbitrarily. However, searching for the minimum free energy during this process poses a practical problem. The solution to the mass balance equation is not unique away from equilibrium, and consequently the algorithm is in risk of getting trapped in nonequilibrium solutions. Therefore, a proper stopping condition for (MC)^{2} is currently lacking. In this work, we introduce a consistency check via a predictor-corrector algorithm to penalize solutions that do not satisfy a necessary condition for equivalence of chemical potentials and steer the system toward finding equilibrium. The most general acceptance criteria for (MC)^{2} is derived starting from the isothermal-isobaric Gibbs ensemble for mixtures. Using this ensemble, translational MC moves are added to include vibrational excitations as well as volume MC moves to ensure the condition of constant pressure and temperature entirely with a MC approach, without relying on any other method for relaxation of these degrees of freedom. As a proof of concept the method is applied to two binary alloys with miscibility gaps and a model quaternary alloy, using classical interatomic potentials.

The effect of surface roughness on the phase behavior of colloidal particles

Shape anisotropy of colloidal particles can give rise to complex intermolecular interactions that determine particle packing and phase behavior. The vapor-liquid coexistence curves of attractive rough particles display a shift when compared to attractive smooth spherical particles. We use Integral Equation Theory (IET) to determine the vapor-liquid spinodal phase diagram of smooth and rough colloidal particles interacting through square-well attraction. Additionally, we use Gibbs Ensemble Monte Carlo (GEMC) simulations to locate their vapor-liquid coexistence curves. We model a rough colloidal particle as a spherical core with small beads embedded on its surface. The critical point of smooth spherical particle systems predicted by theory and simulations is in quantitative agreement. An increase in surface roughness due to an increase in either the number of beads or the diameter of the beads has a modest effect on the local structure of the system in the supercritical region. In contrast, increasing surface roughness consistently shifts the vapor-liquid coexistence curves to higher temperatures. The critical temperature is found to be a quadratic function of the number of beads. At a fixed bead size and number of beads, the critical temperature does not vary with the arrangement of beads on the core. Both IET and GEMC simulations predict that unlike critical temperatures, critical packing fractions vary non-monotonically with surface roughness. We find that the feasibility and accuracy of the integral equation theory depend sensitively on the chosen closure combination.

Tuning Water Networks via Ionic Liquid/Water Mixtures

Water in nanoconfinement is ubiquitous in biological systems and membrane materials, with altered properties that significantly influence the surrounding system. In this work, we show how ionic liquid (IL)/water mixtures can be tuned to create water environments that resemble nanoconfined systems. We utilize molecular dynamics simulations employing ab initio force fields to extensively characterize the water structure within five different IL/water mixtures: [BMIM + ][BF 4 - ], [BMIM + ][PF 6 - ], [BMIM + ][OTf - ], [BMIM + ][NO 3 - ]and [BMIM + ][TFSI - ] ILs at varying water fraction. We characterize water clustering, hydrogen bonding, water orientation, pairwise correlation functions and percolation networks as a function of water content and IL type. The nature of the water nanostructure is significantly tuned by changing the hydrophobicity of the IL and sensitively depends on water content. In hydrophobic ILs such as [BMIM + ][PF 6 - ], significant water clustering leads to dynamic formation of water pockets that can appear similar to those formed within reverse micelles. Furthermore, rotational relaxation times of water molecules in supersaturated hydrophobic IL/water mixtures indicate the close-connection with nanoconfined systems, as they are quantitatively similar to water relaxation in previously characterized lyotropic liquid crystals. We expect that this physical insight will lead to better design principles for incorporation of ILs into membrane materials to tune water nanostructure.

The structure of clusters formed by Stockmayer supracolloidal magnetic polymers

Unlike Stockmayer fluids, that prove to undergo gas-liquid transition on cooling, the system of dipolar hard or soft spheres without any additional central attraction so far has not been shown to have a critical point. Instead, in the latter, one observes diverse self-assembly scenarios. Crosslinking dipolar soft spheres into supracolloidal magnetic polymer-like structures (SMPs) changes the self-assembly behaviour. Moreover, aggregation in systems of SMPs strongly depends on the constituent topology. For Y- and X-shaped SMPs, under the same conditions in which dipolar hard spheres would form chains, the formation of very large loose gel-like clusters was observed (E. Novak et al., J. Mol. Liq. 271, 631 (2018)). In this work, using molecular dynamics simulations, we investigate the self-assembly in suspensions of four topologically different SMPs --chains, rings, X and Y-- whose monomers interact via Stockmayer potential. As expected, compact drop-like clusters are formed by SMPs in all cases if the central isotropic attraction is introduced, however, their shape and internal structure turn out to depend on the SMPs topology.

Small ion effects on self-coacervation phenomena in block polyampholytes

Self-coacervation is a phenomenon in which a solution of polyampholytes spontaneously phase separates into a dense liquid coacervate phase, rich in the polyampholyte, coexisting with a dilute supernatant phase. Such coacervation results in the formation of membraneless organelles in vivo and has further been applied industrially as synthetic encapsulants and coatings. It has been suggested that coacervation is primarily driven by the entropy gain from releasing counter-ions upon complexation. Using fully fluctuating field-theoretic simulations employing complex Langevin sampling and complementary molecular dynamics simulations, we have determined that the small ions contribute only weakly to the self-coacervation behavior of charge-symmetric block polyampholytes in solution. Salt partitioning between the supernatant and coacervate is also found to be negligible in the weak-binding regime at low electrostatic strengths. Asymmetries in charge distribution along the polyampholytes can cause net-charges that lead to "tadpole" configurations in dilute solution and the suppression of phase separation at low salt content. The field and particle-based simulation results are compared with analytical predictions from the random phase approximation (RPA) and postulated scaling relationships. The qualitative trends are mostly captured by the RPA, but the approximation fails at low concentration.

Theoretical equations of state for a charged fluid

In this article, we present a molecular thermodynamic study of a system of N particles contained within a volume V and interacting via a hard-core pair potential with an attractive interaction according to the Wolf model for charged systems. This variable-range potential is characterized by three parameters: the repulsive hard-core diameter σ, the energy-well depth ϵ, and the inverse range α; a fourth parameter of the model is a cut-off distance x_c that depends on α according to the relation x_c = 2/α. Two equations of state (EOSs) are presented and derived from thermodynamic perturbation theory and Monte Carlo (MC) simulation data. The first EOS is given by the standard Zwanzig's high-temperature expansion of the Helmholtz free energy, where the first three perturbation terms a₁, a₂, and a₃ were obtained from MC simulations in the canonical ensemble (NVT) and parameterized as functions of α and the reduced density of particles ρ^* = Nσ³/V. The second EOS was obtained from the discrete perturbation theory applied to a discrete representation of the Wolf potential. Results for pressures, internal energies, and isochoric heat capacities are compared to the MC computer simulation data of the Wolf system, including vapor-liquid coexistence curves, for different values of α. Overall, both EOSs give a very good representation of the thermodynamic properties of the Wolf fluid when 0.3 ≤ α ≤ 1.0 and 0.05 ≤ ρ^* ≤ 0.8. Since the Yukawa fluid can reproduce information of screened ionic interactions, we discuss the equivalence between the Wolf and Yukawa fluids in the context of equivalent systems in liquid theory.

Introducing User-Prescribed Constraints in Markov Chains for Nonlinear Dimensionality Reduction

Stochastic kernel-based dimensionality-reduction approaches have become popular in the past decade. The central component of many of these methods is a symmetric kernel that quantifies the vicinity between pairs of data points and a kernel-induced Markov chain on the data. Typically, the Markov chain is fully specified by the kernel through row normalization. However, in many cases, it is desirable to impose user-specified stationary-state and dynamical constraints on the Markov chain. Unfortunately, no systematic framework exists to impose such user-defined constraints. Here, based on our previous work on inference of Markov models, we introduce a path entropy maximization based approach to derive the transition probabilities of Markov chains using a kernel and additional user-specified constraints. We illustrate the usefulness of these Markov chains with examples.

Deep neural network learning of complex binary sorption equilibria from molecular simulation data

We employed deep neural networks (NNs) as an efficient and intelligent surrogate of molecular simulations for complex sorption equilibria using probabilistic modeling. Canonical (N ₁ N ₂ VT) Gibbs ensemble Monte Carlo simulations were performed to model a single-stage equilibrium desorptive drying process for (1,4-butanediol or 1,5-pentanediol)/water and 1,5-pentanediol/ethanol from all-silica MFI zeolite and 1,5-pentanediol/water from all-silica LTA zeolite. A multi-task deep NN was trained on the simulation data to predict equilibrium loadings as a function of thermodynamic state variables. The NN accurately reproduces simulation results and is able to obtain a continuous isotherm function. Its predictions can be therefore utilized to facilitate optimization of desorption conditions, which requires a laborious iterative search if undertaken by simulation alone. Furthermore, it learns information about the binary sorption equilibria as hidden layer representations. This allows for application of transfer learning with limited data by fine-tuning a pretrained NN for a different alkanediol/solvent/zeolite system.

A simulation method for the phase diagram of complex fluid mixtures

The phase behavior of complex fluid mixtures is of continuing interest, but obtaining the phase diagram from computer simulations can be challenging. In the Gibbs ensemble method, for example, each of the coexisting phases is simulated in a different cell, and ensuring the equality of chemical potentials of all components requires the transfer of molecules from one cell to the other. For complex fluids such as polymers, successful insertions are rare. An alternative method is to simulate both coexisting phases in a single simulation cell, with an interface between them. The challenge here is that the interface position moves during the simulation, making it difficult to determine the concentration profile and coexisting concentrations. In this work, we propose a new method for single cell simulations that uses a spatial concentration autocorrelation function to (spatially) align instantaneous concentration profiles from different snapshots. This allows one to obtain average concentration profiles and hence the coexisting concentrations. We test the method by calculating the phase diagrams of two systems: the Widom-Rowlinson model and the symmetric blends of freely jointed polymer molecules for which phase diagrams from conventional methods are available. Excellent agreement is found, except in the neighborhood of the critical point where the interface is broad and finite size effects are important. The method is easy to implement and readily applied to any mixture of complex fluids.

Virial coefficients, equation of state, and demixing of binary asymmetric nonadditive hard-disk mixtures

Values of the fifth virial coefficient, compressibility factors, and fluid-fluid coexistence curves of binary asymmetric nonadditive mixtures of hard disks are reported. The former correspond to a wide range of size ratios and positive nonadditivities and have been obtained through a standard Monte Carlo method for the computation of the corresponding cluster integrals. The compressibility factors as functions of density, derived from canonical Monte Carlo simulations, have been obtained for two values of the size ratio (q = 0.4 and q = 0.5), a value of the nonadditivity parameter (Δ = 0.3), and five values of the mole fraction of the species with the biggest diameter (x₁ = 0.1, 0.3, 0.5, 0.7, and 0.9). Some points of the coexistence line relative to the fluid-fluid phase transition for the same values of the size ratios and nonadditivity parameter have been obtained from Gibbs ensemble Monte Carlo simulations. A comparison is made between the numerical results and those that follow from some theoretical equations of state.

Single-site Lennard-Jones models via polynomial chaos surrogates of Monte Carlo molecular simulation

In this work, two Polynomial Chaos (PC) surrogates were generated to reproduce Monte Carlo (MC) molecular simulation results of the canonical (single-phase) and the NVT-Gibbs (two-phase) ensembles for a system of normalized structureless Lennard-Jones (LJ) particles. The main advantage of such surrogates, once generated, is the capability of accurately computing the needed thermodynamic quantities in a few seconds, thus efficiently replacing the computationally expensive MC molecular simulations. Benefiting from the tremendous computational time reduction, the PC surrogates were used to conduct large-scale optimization in order to propose single-site LJ models for several simple molecules. Experimental data, a set of supercritical isotherms, and part of the two-phase envelope, of several pure components were used for tuning the LJ parameters (ε, σ). Based on the conducted optimization, excellent fit was obtained for different noble gases (Ar, Kr, and Xe) and other small molecules (CH4, N2, and CO). On the other hand, due to the simplicity of the LJ model used, dramatic deviations between simulation and experimental data were observed, especially in the two-phase region, for more complex molecules such as CO2 and C2 H6.

Characterisation of the thermodynamics, structure and dynamics of a water-like model in 2- and 3-dimensions

The physical properties of colloidal particles suspended in an aqueous environment are well-understood when the latter is considered to be a continuum and a structureless medium. However, this approach fails to explain complex phenomena, for example, the critical Casimir forces among colloids and the colloidal self-assembly near critical solvents, and the inertial contribution of the solvent molecules on the diffusion of non-spherical Brownian particles. Therefore, the role played by the solvent on the physical properties of colloidal dispersions is of paramount relevance. Recently, there has been an interest in the (non-trivial) diffusion mechanisms of a nano-colloidal particle in a solvent that undergoes a vapour-liquid transition. Nonetheless, the models typically used to incorporate the solvent details do not capture quantitatively the thermodynamic properties of real substances. It is then important to study the Brownian motion of colloids in more realistic models. To reach such goal, one first has to characterise the thermodynamic states and the microscopic features of the solvent. Hence, in this contribution, we have investigated the coexistence densities of a core-softened potential in two- and three-dimensions, whose potential parameters are able to capture some anomalies of water. We show that in the two-dimensional case, the potential model exhibits, besides the normal vapour-liquid coexistence region, additional liquid-liquid coexistence densities. We particularly focus our attention to the structural properties and the dynamical behaviour of the solvent around the liquid-liquid critical point and assess the differences with the three-dimensional case.

Prediction of Surface and Bulk Partition of Nonionic Surfactants Using Free Energy Calculations

The surface-bulk partition of nonionic surfactants was predicted by calculating chemical potential differences using two simulation boxes representing the surface and the bulk phases separately. A published coarse grained force field was modified and validated for this application. Thermodynamic integration (TI) was applied to compute excess chemical potentials. The high concentration surface was stabilized by applying an external harmonic potential, and the bulk was treated as ideal solution, which was confirmed by simulation using a lattice model at conditions near the critical micelle concentration (∼10(-5) mol/L). Based on the calculated chemical potential differences with precision of ca. 1 kJ/mol, the equilibria of surface-bulk concentration was predicted well in comparison with the experimental data.

Brownian motion of a nano-colloidal particle: the role of the solvent

Brownian motion of a single nano-colloid is drastically affected by the microscopic details and the thermodynamic state of the solvent.