Connecting density fluctuations and Kirkwood-Buff integrals for finite-size systems

Kirkwood-Buff integrals (KBI) connect the microscopic structure and thermodynamic properties of liquid solutions. KBI are defined in the grand canonical ensemble and evaluated assuming the thermodynamic limit (TL). In order to reconcile analytical and numerical approaches, finite-size KBI have been proposed in the literature, resulting in two strategies to obtain their TL values from computer simulations. (i) The spatial block-analysis method in which the simulation box is divided into subdomains of volume $V$ to compute fluctuations of the number of particles. (ii) A direct integration method where a corrected radial distribution function and a kernel that accounts for the geometry of the integration subvolumes are combined to obtain KBI as a function of $V$. In this work, we propose a method that connects both strategies into a single framework. We start from the definition of finite-size KBI, including the integration subdomain and an asymptotic correction to the radial distribution function, and solve them in Fourier space where periodic boundary conditions are trivially introduced. The limit $q\to 0$, equivalent to the value of the KBI in the TL, is obtained via the spatial block-analysis method. When compared to the latter, our approach gives nearly identical results for all values of $V$. Moreover, all finite-size effect contributions (ensemble, finite-integration domains and periodic boundary conditions) are easily identifiable in the calculation. This feature allows us to analyse finite-size effects independently and extrapolate the results of a single simulation to different box sizes. To validate our approach, we investigate prototypical systems, including SPC/E water and aqueous urea mixtures

Role of the environment in the stability of anisotropic gold particles

International audienceDespite the long-lasting interest in the synthesis control of nanoparticles (NPs) in both fundamental and applied nanosciences, the driving mechanisms responsible for their size and shape selectivity in an environment (solution) are not completely understood, and a clear assessment of the respective roles of equilibrium thermodynamics and growth kinetics is still missing. In this study, relying on an efficient atomistic computational approach, we decipher the dependence of energetics, shapes and morphologies of gold NPs on the strength and nature of the metal–environment interaction. We highlight the conditions under which the energy difference between isotropic and elongated gold NPs is reduced, thus prompting their thermodynamic coexistence. The study encompasses both monocrystalline and multi-twinned particles and extends over size ranges particularly representative of the nucleation and early growth stages. Computational results are further rationalized with arguments involving the dependence of facet and edge energies on the metal–environment interactions. We argue that by determining the abundance and diversity of particles nucleated in solution, thermodynamics may constitute an important bias influencing their final shape. The present results provide firm grounds for kinetic simulations of particle growth

Fluctuations, Finite-Size Effects and the Thermodynamic Limit in Computer Simulations: Revisiting the Spatial Block Analysis Method

The spatial block analysis (SBA) method has been introduced to efficiently extrapolate thermodynamic quantities from finite-size computer simulations of a large variety of physical systems. In the particular case of simple liquids and liquid mixtures, by subdividing the simulation box into blocks of increasing size and calculating volume-dependent fluctuations of the number of particles, it is possible to extrapolate the bulk isothermal compressibility and Kirkwood–Buff integrals in the thermodynamic limit. Only by explicitly including finite-size effects, ubiquitous in computer simulations, into the SBA method, the extrapolation to the thermodynamic limit can be achieved. In this review, we discuss two of these finite-size effects in the context of the SBA method due to (i) the statistical ensemble and (ii) the finite integration domains used in computer simulations. To illustrate the method, we consider prototypical liquids and liquid mixtures described by truncated and shifted Lennard–Jones (TSLJ) potentials. Furthermore, we show some of the most recent developments of the SBA method, in particular its use to calculate chemical potentials of liquids in a wide range of density/concentration conditions

Thermoresponsive Ionic Liquid/Water Mixtures: From Nanostructuring to Phase Separation

The thermodynamics, structures, and applications of thermoresponsive systems, consisting primarily of water solutions of organic salts, are reviewed. The focus is on organic salts of low melting temperatures, belonging to the ionic liquid (IL) family. The thermo-responsiveness is represented by a temperature driven transition between a homogeneous liquid state and a biphasic state, comprising an IL-rich phase and a solvent-rich phase, divided by a relatively sharp interface. Demixing occurs either with decreasing temperatures, developing from an upper critical solution temperature (UCST), or, less often, with increasing temperatures, arising from a lower critical solution temperature (LCST). In the former case, the enthalpy and entropy of mixing are both positive, and enthalpy prevails at low T. In the latter case, the enthalpy and entropy of mixing are both negative, and entropy drives the demixing with increasing T. Experiments and computer simulations highlight the contiguity of these phase separations with the nanoscale inhomogeneity (nanostructuring), displayed by several ILs and IL solutions. Current applications in extraction, separation, and catalysis are briefly reviewed. Moreover, future applications in forward osmosis desalination, low-enthalpy thermal storage, and water harvesting from the atmosphere are discussed in more detail