Atomic force microscopy (AFM) can work in a variety of environment with different humidities. When the tip of AFM approaches a sample, the measured adhesion force would be significantly affected by the presence of nanometer-sized liquid bridge. The formation and rupture of liquid bridges can occur either through equilibrium or nonequilibrium process. In this work, the liquid bridges are assumed to be in thermodynamic equilibrium with the surrounding vapor medium. To study theoretically the stability of 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 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.

To study nucleation phenomena in an open system, a constrained lattice density functional theory (LDFT) method has been developed before to identify the unstable directions of grand potential functional and to stabilize nuclei by imposing a suitable constraint. In this work, we answer several questions about the method on a fundamental level, and give a firmer basis for the constrained LDFT method. First, we demonstrate that the nucleus structure and free energy barrier from a volume constraint method are equivalent to those from a surface constraint method. Then, we show that for the critical nucleus, the constrained LDFT method in fact produces a bias-free solution for both the nucleus structure and nucleation barrier. Finally, we give a physical interpretation of the Lagrange multiplier in the constraint method, which provides the generalized force to stabilize a nucleus in an open system. The Lagrange multiplier is found to consist of two parts: part I of the constraint produces an effective pressure, and part II imposes a constraint to counteract the supersaturation.

In this work, we propose a method to stabilize a nucleus in the framework of lattice density-functional theory (LDFT) by imposing a suitable constraint. Using this method, the shape of critical nucleus and height of the nucleation barrier can be determined without using a predefined nucleus as input. As an application of this method, we study the nucleation behavior of vapor-liquid transition in nanosquare pores with infinite length and relate the observed hysteresis loop on 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 , 0.1< or =w< or =0.9 , and w<0.1 ), 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. Our constrained LDFT calculations also show that the different transition paths may induce different nucleation behaviors. The transition path dependence should be considered if morphological transition of nuclei exists during a nucleation process.

In this work, we study the nucleation mechanism of vapor-to-liquid phase transition from rough substrates, which are modeled as flat substrates decorated with square nanopores with one open end. Our calculations in a constrained lattice density functional theory shows that the presence of nanopores results in an intermediate state, either metastable or unstable, which divides the whole nucleation process into two sequential sub-processes, i.e., pore filling and phase transition outside the pores. Therefore, the nucleation mechanism was found to be one-step (with unstable intermediate states) or two-step (with metastable intermediate states), depending on the fluid-solid interaction, chemical potential, and pore size. The constructed phase diagram of nucleation mechanism shows that there exist six different nucleation mechanisms. In addition, our calculations show that the presence of nanopores on a rough substrate may change the morphology of critical nuclei from their counterpart on a smooth substrate.

In this work, we used constrained lattice density functional theory to investigate how nanoscale seed particles affect heterogeneous vapor-liquid nucleation. The effects of the physical properties of nanoscale seed particles, including the seed size, the strength of seed-fluid attraction, and the shape of the seeds, on the structure of critical nuclei and nucleation barrier were systemically investigated.