Equilibrium and Nonequilibrium Thermodynamics of Planar and Curved Interfaces
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- Institutt for kjemi 
Interfaces can be found everywhere and their properties are of major importance to a wide variety of processes, ranging from DNA replication to weather forecasts. This work is a fundamental study of systems with planar and curved interfaces at equilibrium and nonequilibrium. First, we studied the thermodynamic stability of bubbles and droplets in systems with both finite volume and number of particles. We showed that the macroscopic capillary approach predicted thermodynamic stability limits nearly identical to those from square gradient theory, a more rigorous mesoscopic theory. Both approaches gave a stable and unstable branch of solutions, representing bubbles and droplets in the canonical ensemble. They also predicted a minimum threshold size for stability. This minimum threshold size was used to explain how fluids can be superstabilized in nanocontainers and to derive formulas to estimate the container volume below which no droplet or bubble can form. Finite-size effects also influence nucleation processes. A comprehensive theoretical analysis of cavitation and droplet formation in finite systems was presented. Using general thermodynamic arguments, we derived simple, yet accurate formulas to calculate the finite-size corrections for the critical size, the nucleation barrier, and the nucleation rates in the canonical ensemble. These formulas can be used to select the appropriate system size for simulations or to obtain a precise evaluation of nucleation rates of complex substances at atmospheric conditions by using a small number of molecules and correcting for finite-size effects. Next, the curvature dependence of the surface tension was examined by evaluating the leading terms of an expansion in the total and Gaussian curvatures. The first-order curvature correction is the Tolman length and the second-order corrections are the rigidity constants. By combining the square gradient theory with an accurate equation of state, we reproduced the surface tension and Tolman length for the shifted and truncated Lennard-Jones fluid from molecular simulations. The curvature expansion accurately described the change in surface tension, until the radius of the bubbles and droplets became similar to the interfacial width of the planar interface at coexistence. For metastablities even closer to the spinodal limits, the curvature remained nearly constant, but the surface tension decreased due to a decreasing difference between the densities of the bubble/droplet interior and exterior. The size of droplets and bubbles in the region of constant curvature was found to be proportional to the correlation length of fluctuations in the liquid phase. The discovery of a region with constant curvature offers a new perspective on how nucleation should be described at high metastabilities. We next estimated the Tolman length and rigidity constants of water. The Tolman length of water was negative and weakly temperature dependent, having the relatively small value of about −0.05 nm, which is in agreement with previous estimates in the literature. Using the leading terms of the curvature expansion, we incorporated the curvature dependence of the surface tension into the framework of classical nucleation theory. The modification corrected the temperature dependence of the nucleation rates given by the classical theory, thereby improving the agreement between theoretical and experimental results. Thus, the procedure offered a promising way to alleviate the problems of classical nucleation theory and obtain quantitatively accurate predictions, which hopefully is possible also for other substances. We next examined the inherent properties of the temperature across interfaces. Several microscopic expressions to calculate temperature in molecular simulations were evaluated, where some included configurational contributions. We investigated their accuracy and usefulness in high- and low-density bulk systems and across vapor-liquid interfaces both at equilibrium and with a temperature gradient. We showed that the configurational temperature was equivalent to the kinetic temperature in steady-state molecular dynamics simulations. This agreement however, was obtained only if the discontinuity in the derivatives of the interaction potential was handled properly by using a sufficiently long truncation distance or tail-corrections. If the entropy density is included as a variable in the square gradient theory framework, the theory suggests that the temperature has different contributions from directions parallel and perpendicular to the interface at equilibrium. We found a similar anisotropy in simulations by examining the configurational temperature in molecular dynamics. The results from the simulations agreed qualitatively with the theory. According to the theory, the temperature anisotropy provides evidence for new entropic contributions to the tension tensor, responsible for ∼20% of the surface tension of argon. Eventually, we studied transport of heat and mass across planar and curved interfaces. The transport equations were formulated with the framework of nonequilibrium thermodynamics by using a set of interface transfer coefficients. We started by investigating the interface transfer coefficients of bubbles and droplets in both single- and two-component systems. We verified that the coefficients obtained by combining the integral relations with results from the equilibrium square gradient model were the same as those obtained by using the nonequilibrium square gradient model, in which gradients in temperature, pressure and composition were imposed across the interface. The local heat transfer characteristics of the interfacial region (local resistivity) were found to have a large influence on the predicted curvature dependence of the interface transfer coefficients. We obtained the general curvature dependence of the interface transfer coefficients by expanding the coefficients in the total and Gaussian curvatures. This provided an accurate description of heat and mass transfer across interfaces of complex nanogeometries. A method to obtain the leading terms in the curvature expansion was presented. The method was demonstrated for an oblate spheroidal droplet (Mentos candy), a prolate spheroidal bubble (rugby ball), and a toroidal bubble (donut). Depending on the sign and magnitude of the total and Gaussian curvatures, the interface transfer could increase or decrease significantly. We next derived analytical expressions for the terms in the curvature expansion of the interface transfer coefficients, allowing us to calculate them with higher accuracy. The magnitude and temperature-dependence of the interface transfer coefficients and the terms in the curvature expansion were discussed in detail for the truncated and shifted Lennard-Jones fluid. The tools developed were next used to describe transfer across planar and curved water interfaces. For the complicated case of water, it was necessary to use a temperature-dependent influence parameter in the square gradient model. We showed how this extension modified the nonequilibrium square gradient model, and lead to thermodynamic quantities that depended on temperature gradients. The modified formulation was found to be thermodynamically consistent and to give an interface at local equilibrium, in agreement with previous work. We then calculated the interface transfer coefficients and the corresponding curvature corrections for the vapor-liquid interface of water from 260 K to 550 K. A novel approach was used; this approach took advantage of low-temperature water evaporation experiments, nonequilibrium molecular dynamics with the TIP4P/2005 model at high temperatures and square gradient theory. We used the framework to obtain new understanding of transport across the interface of coalescing nanosized water droplets, in which the resistance to heat and mass transfer was found to be significantly increased in the junction between the droplets. This work has provided new insight into topics heavily debated in the literature, such as the sign and relevance of the Tolman length and the rigidity constants, and investigated previously unaddressed topics, such as the inherent properties of the temperature across interfaces and the curvature dependence of the interface transfer coefficients. Several tools and techniques developed in this work can be taken advantage of to study the properties of highly metastable fluids, the magnitude and curvature dependence of interface transfer coefficients, improve the predictions from nucleation theory and design future nano devices with enhanced properties.