Hysteresis And Nucleation Of Liquid-vapor Phase Transition In Confined Spaces: A Study Of Lattice Density Functional Theory

Phase transition between liquid and vapor is one of the most ubiquitous phenomena in nature, with extensive applications in chemical technologies and other process industries. It is a main research field of science and technology, which spans more than a century of history since discoveries of the critical point and the state equation. Recently, with the advancement of science and technology, researches of liquid phase behaviors have been extended to a nano/micro scale from the macro system. In the nano/micro scale, the liquid phase behavior strongly depends on the surface of a confined space. It has been observed that confined fluids in micro-to nanometer pores, regardless of the geometry, exhibit minimal up to significant deviations from the bulk thermodynamic and structural properties. These differences have generated great interest, as the features of confined fluids are encountered in both technology and nature.In this work, the mean-field density functional theory is applied to study liquid-vapor phase transition in several confined spaces. The main contents are as following.1. The adsorption isotherms have been calculated with lattice density functional theory in grand canonical ensemble and in canonical ensemble respectively. The calculation results show that the isotherms for the two ensembles do not in conecide completely. In the hysteresis loop, the isotherm of the canonical ensemble is with phenomena of "oscillation" and "receding", which correspond to the nucleation and lamellar growth of the new phase. With the calculations in the canonical ensemble, more metastable states can be observed than those in the grand canonical ensemble.2. A method to stabilize a nucleus in the framework of the lattice density-functional theory (LDFT) is proposed by imposing a suitable constraint. Using this method, the morphology of critical nucleus and height of the nucleation barrier can be determined without using a predefined nucleus as the input. We apply the method to study the nucleation behavior of vapor-liquid transition in nano-square pores with infinite length and relate the observed hysteresis loop with an adsorption isotherm to the nucleation mechanism. According to the dependence of hysteresis and the nucleation mechanism on the fluid-wall interaction, w, in this work, we have classified w into three regions w≥0.9,0<w≤0.1,0.1<w<0.9, which are denoted as strongly, moderately, and weakly attractive fluid-wall interaction, respectively. The dependence of hysteresis on the fluid-wall interaction is interpreted by the different nucleation mechanisms mentioned. Our constrained LDFT calculations also show that the different transition paths may induce different nucleation behaviors. The transition path dependence should be taken into account if the morphological transition of nuclei exists during a nucleation process. 3. The capillary bridges forming between the tip of atomic force microscopy and the substrate have been studied. In this work, the liquid bridges are assumed to be in thermodynamic equilibrium with the surrounding vapor medium. To study theoretically the stability of the liquid bridge, a constraint is added into the lattice density functional theory to stabilize a series of bridges with different radii at a given tip-substrate distance. With the help of the constraint, we can identify not only stable and metastable states but also transition states for the formation and rupture of the liquid bridges. Using this constrained method we calculate the energy barriers involved in the formation and rupture of the liquid bridges, respectively, and then discuss their stability as well as the origin of the hysteresis behavior observed with atomic force microscope measurements. On the whole, the calculated force-distance curves are found to be qualitatively in agreement with experimental observations. The energy barriers for the formation and rupture of liquid bridges are also analyzed as a function of tip-sample distance, humidity, and tip-fluid interaction.4. The constrained lattice density functional theory has been discussed and extended. Based on Lagrange multiplier method, a constrained term about volume or surface of the nucleus is introduced to the grand potential functional of lattice density functional theory. With the help of the constrained term, the density profile of the transition state between stable and metastable state can be obtained. The calculation results show that the two forms of the constrained term are equivalent. By compared with classical nucleation theory, the physical meaning of the Lagrange multiplier can be obtained, and the constrained method can be extended to universal nucleation study.5. The rupture kinetics and transition pathways of the being stretched liquid bridges connecting an AFM tip and a flat substrate have been studied with kinetic lattice density functional theory. Depending on thermodynamic conditions and the tip velocity, two regimes corresponding to different transition pathways are identified. In the single-bridge regime, the initial equilibrium bridge persists as a single one during the pulling process until the liquid bridge breaks. On the other hand, in the multi-bridge regime the stretched liquid bridge transforms into an intermediate state with a collection of slender liquid bridges, which then break gradually during the pulling process. Moreover, the critical rupture distance at which the bridges break changes with the tip velocity and thermodynamic conditions, and its maximum value occurs near the boundary between the single-bridge regime and the multi-bridge regime, where the longest range capillary force is produced. In this work, the effects of tip velocity, tip size, tip-fluid interaction, and humidity on rupture kinetics and transition pathway are also systematically studied.