Can Continuum Thermodynamics Characterize Wenzel Wetting States of Water at the Nanometer Scale?

Evaporation Dynamics of Macro- and Nanodroplets on Heated Hydrophilic Rough Substrates: The Effect of Roughness and Scale

Droplet evaporation on rough substrates plays an essential role in cooling and micro/nanoparticle assembly. Currently, there are numerous macroscopic experiments and theoretical models to investigate the droplet evaporation behavior on rough substrates. However, due to the complexity of this phenomenon, understanding its mechanisms solely through macroscale studies is difficult. To this end, molecular dynamics simulations of the models with distinct roughness factors are performed, and the obtained results are compared with those of relevant experiments of droplet evaporation on three hydrophilic substrates with different roughness average of 0.1, 0.15, and 0.2 μm, respectively. In this way, we assess the evaporation on these rough systems and the effect of scale on macro- and nanodroplets, which allows us to explore deeper the mechanism of droplet evaporation on rough hydrophilic substrates. In particular, we find that in the case of macroscale droplets, the evaporation mode remains the same with increasing roughness, pointing to a combined mixed and constant-contact-radius (CCR) mode. In the case of nanoscale droplets, the evaporation model is the constant-contact-angle mode when the roughness factor r = 1, while the mixed and CCR modes are found for r = 1.5 and 2, respectively. The scale effect has significant influence on the evaporation pattern of droplets on rough hydrophilic substrates. Moreover, it is also found that increasing the roughness of substrates expands the substrate-droplet contact area on both the macro- and nanoscale, which in turn enhances the heat transfer from the substrate toward the droplet. We anticipate that this first systematic analysis of scale effects provides further insights into the evaporation dynamics of droplets on rough hydrophilic substrates and has significant implications for the advancement of nanotechnology.

Pinning-Depinning Mechanism of the Contact Line during Evaporation of Nanodroplets on Heated Heterogeneous Surfaces: A Molecular Dynamics Simulation

Droplet evaporation on heterogeneous or patterned surfaces has numerous potential applications, for example, inkjet printing. The effect of surface heterogeneities on the evaporation of a nanometer-sized cylindrical droplet on a solid surface is studied using molecular dynamics simulations of Lennard-Jones particles. Different heterogeneities of the surface were achieved through alternating stripes of equal width but two chemical types, which lead to different contact angles. The evaporation induced by the heated substrate instead of the isothermal evaporation is investigated. It is found that the whole evaporation process is generally dominated by the nonuniform evaporation effect. However, at the initial moment, the volume expansion and local evaporation effects play important roles. From the nanoscale point of view, the slow movement of the contact line during the pinning process is observed, which is different from the macroscopic stationary pinning. Particularly, we found that the speed of the contact line may be not only affected by the intrinsic energy barrier between the two adjacent stripes ( ũ) but also relevant to the evaporation rate. Generally speaking, the larger the intrinsic energy barrier, the slower the movement of the contact line. At the specified temperature, when ũ is less than a critical energy barrier ( ũ*), the speed of the contact line would increase with the evaporate rate. When ũ > ũ*, the speed of the contact line is determined only by ũ and no longer affected by the evaporation rate at different stages (the first stick and the second stick).

Characterizing surface wetting and interfacial properties using enhanced sampling (SWIPES)

We introduce an accurate and efficient method for characterizing surface wetting and interfacial properties, such as the contact angle made by a liquid droplet on a solid surface, and the vapor-liquid surface tension of a fluid. The method makes use of molecular simulations in conjunction with the indirect umbrella sampling technique to systematically wet the surface and estimate the corresponding free energy. To illustrate the method, we study the wetting of a family of Lennard-Jones surfaces by water. For surfaces with a wide range of attractions for water, we estimate contact angles using our method, and compare them with contact angles obtained using droplet shapes. Notably, our method is able to capture the transition from partial to complete wetting as surface-water attractions are increased. Moreover, the method is straightforward to implement and is computationally efficient, providing accurate contact angle estimates in roughly 5 nanoseconds of simulation time.

Thermodynamic formulation of the barrier for heterogeneous pinned nucleation: Implication to the crossover scenarios associated with barrierless and homogeneous nucleation

The effect of contact line pinning on nucleation is reported using continuum thermodynamics. Based on the principle of the free-energy maximization, closed-form expressions in the dimensionless form for the free-energy of the three-phase metastable system and the thermodynamic barrier are formulated with respect to the system geometry and the substrate wettability. The condition of maximality limits the dynamic contact angle within the cluster-phase-phobic regime. The dimensionless nucleation barrier or the potency factor can be divided into two components related to the system geometry and the pinning effect. Depending on the relative value of the equilibrium and the critical dynamic contact angle, the contact line pinning can either have favorable or adverse effects. Associated pinning-depinning transition can also lead to the crossovers related to barrierless and homogeneous nucleation. Contact line tension is found to have a considerable effect during these transitional scenarios. Complete wetting transition associated with barrierless nucleation can take place due to the presence of tensile (negative) line tension. On the other hand, complete drying transition related to homogeneous nucleation can occur when line tension is compressive (positive) in nature. The pinning has a favorable effect only when the substrate wettability is within the cluster-phase-philic regime. There can be favorable, adverse, or no pinning effects when the substrate wettability is within the cluster-phase-phobic regime. Although the contact line is pinned, the minimum value of the potency factor is obtained when equilibrium and dynamic contact angles are equal.

Thermostability analysis of line-tension-associated nucleation at a gas-liquid interface

The influence of line tension on the thermostability of a droplet nucleated from an oversaturated vapor at the interface of the vapor and another immiscible liquid is investigated. Along with the condition of mechanical equilibrium, the notion of extremization of the reversible work of formation is considered to obtain the critical parameters related to heterogeneous nucleation. From the energetic formulation, the critical reversible work of formation is found to be greater than that of homogeneous nucleation for high value of the positive line tension. On the other hand, for high value of the negative line tension, the critical reversible work of formation becomes negative. Therefore, these thermodynamic instabilities under certain substrate wettability situations necessitate a free-energetics-based stability of the nucleated droplet, because the system energy is not minimized under these conditions. This thermostability is analogous to the transition-based stability proposed by Widom [B. Widom, J. Phys. Chem. 99, 2803 (1995)]10.1021/j100009a041 in the case of partial wetting phenomena along with the positive line tension. The thermostability analysis limits the domain of the solution space of the present critical-value problem as the thermodynamic transformation in connection with homogeneous and workless nucleation is considered. Within the stability range of the geometry-based wetting parameters, three limiting modes of nucleation, i.e., total-dewetting-related homogeneous nucleation, and total-wetting-associated and total-submergence-associated workless nucleation scenarios, are identified. Either of the two related limiting wetting scenarios of workless nucleation, namely, total wetting and total submergence, is found to be favorable depending on the geometry-based wetting conditions. The line-tension-associated nucleation on a liquid surface can be differentiated from that on a rigid substrate, as in the former, the stability based on mechanical equilibrium and a typical case of workless nucleation with complete submergence are observed.

Understanding Controls on Wetting at Fluorinated Polyhedral Oligomeric Silsesquioxane/Polymer Surfaces

Fluorinated polyhedral oligomeric silsesquioxane (F-POSS) nanoparticles have been widely used to enhance the hydrophobicity or oleophobicity of polymer films via constructing the specific micro/nanoscale roughness. In this work, we study the oleophobicity of pure and F-POSS-decorated poly(vinylidene fluoride) (PVDF) and poly(methyl methacrylate) (PMMA) films using a dynamic density functional theory approach. The role of nanoparticle size and coverage and the chemical features of F-POSS and the polymer film in the wetting behavior of diiodomethane droplets has been integrated to the remaining ratio of surface potential to quantitatively characterize the corner effect. It is shown that, on the basis of universal force field parameters, the theoretically predicted contact angles are in general agreement with the available experimental data.

Dry-Surface Simulation Method for the Determination of the Work of Adhesion of Solid-Liquid Interfaces

We introduce a methodology, referred to as the dry-surface method, to calculate the work of adhesion of heterogeneous solid-liquid interfaces by molecular simulation. This method employs a straightforward thermodynamic integration approach to calculate the work of adhesion as the reversible work to turn off the attractive part of the actual solid-liquid interaction potential. It is formulated in such a way that it may be used either to evaluate the ability of force fields to reproduce reference values of the work of adhesion or to optimize force-field parameters with reference values of the work of adhesion as target quantities. The methodology is tested in the case of water on a generic model of nonpolar substrates with the structure of gold. It is validated through a quantitative comparison to phantom-wall calculations and against a previous characterization of the thermodynamics of the gold-water interface. It is found that the work of adhesion of water on nonpolar substrates is a nonlinear function of the microscopic solid-liquid interaction energy parameter. We also comment on the ability of mean-field approaches to predict the work of adhesion of water on nonpolar substrates. In addition, we discuss in detail the information on the solid-liquid interfacial thermodynamics delivered by the phantom-wall approach. We show that phantom-wall calculations yield the solid-liquid interfacial tension relative to the solid surface tension rather than the absolute solid-liquid interfacial tension as previously believed.

Pinning of the Contact Line during Evaporation on Heterogeneous Surfaces: Slowdown or Temporary Immobilization? Insights from a Nanoscale Study

The question of the effect of surface heterogeneities on the evaporation of liquid droplets from solid surfaces is addressed through nonequilibrium molecular dynamics simulations. The mechanism behind contact line pinning which is still unclear is discussed in detail on the nanoscale. Model systems with the Lennard-Jones interaction potential were employed to study the evaporation of nanometer-sized cylindrical droplets from a flat surface. The heterogeneity of the surface was modeled through alternating stripes of equal width but two chemical types. The first type leads to a contact angle of 67°, and the other leads to a contact angle of 115°. The stripe width was varied between 2 and 20 liquid-particle diameters. On the surface with the narrowest stripes, evaporation occurred at constant contact angle as if the surface was homogeneous, with a value of the contact angle as predicted by the regular Cassie-Baxter equation. When the width was increased, the contact angle oscillated during evaporation between two boundaries whose values depend on the stripe width. The evaporation behavior was thus found to be a direct signature of the typical size of the surface heterogeneity domains. The contact angle both at equilibrium and during evaporation could be predicted from a local Cassie-Baxter equation in which the surface composition within a distance of seven fluid-particle diameters around the contact line was considered, confirming the local nature of the interactions that drive the wetting behavior of droplets. More importantly, we propose a nanoscale explanation of pinning during evaporation. Pinning should be interpreted as a drastic slowdown of the contact line dynamics rather than a complete immobilization of it during a transition between two contact angle boundaries.

Evaluation of macroscale wetting equations on a microrough surface

The wettability of critical droplets on microscale geometric rough surfaces has been investigated using a density functional theory approach. In order to analyze the effect of roughness on nucleation free-energy barriers, the local density fluctuations at liquid-solid interfaces induced by the multi-interactions of a corner substrate are presented to interpret the interfacial free-energy variations, and the vapor-liquid-solid contact line tensions are derived from the contact angles of nuclei to account for the three-phase contact energies. The corresponding wetting diagrams have been constructed in Cassie, Wenzel, and impregnation regions. It is shown that, under the same condition, modest deviations between the microscale and the macroscale models can be observed within the Cassie region, whereas these deviations have been enlarged in the Wenzel and impregnation regions as well as the Cassie-Wenzel transition region. These deviations are also correlated to the roughness of the surface. The reason can be attributed to the cooperative effect of the liquid-solid interfacial free energy and line tension. This study offers a fundamental understanding of wettability of ultrasmall droplets on a microscale geometric rough surface.

Nanotopographic substrates of poly (methyl methacrylate) do not strongly influence the osteogenic phenotype of mesenchymal stem cells in vitro

The chemical, mechanical, and topographical features of the extracellular matrix (ECM) have all been documented to influence cell adhesion, gene expression, migration, proliferation, and differentiation. Topography plays a key role in the architecture and functionality of various tissues in vivo, thus raising the possibility that topographic cues can be instructive when incorporated into biomaterials for regenerative applications. In the literature, there are discrepancies regarding the potential roles of nanotopography to enhance the osteogenic phenotype of mesenchymal stem cells (MSC). In this study, we used thin film substrates of poly(methyl methacrylate) (PMMA) with nanoscale gratings to investigate the influence of nanotopography on the osteogenic phenotype of MSCs, focusing in particular on their ability to produce mineral similar to native bone. Topography influenced focal adhesion size and MSC alignment, and enhanced MSC proliferation after 14 days of culture. However, the osteogenic phenotype was minimally influenced by surface topography. Specifically, alkaline phosphatase (ALP) expression was not increased on nanotopographic films, nor was calcium deposition improved after 21 days in culture. Ca: P ratios were similar to native mouse bone on films with gratings of 415 nm width and 200 nm depth (G415) and 303 nm width and 190 nm depth (G303). Notably, all surfaces had Ca∶P ratios significantly lower than G415 films. Collectively, these data suggest that, PMMA films with nanogratings are poor drivers of an osteogenic phenotype.

Model atomistic protrusions favouring the ordering and retention of water

The ordering of water molecules near model linear atomistic protrusions is studied using classical molecular dynamics simulations.

Impact of small-scale geometric roughness on wetting behavior

We examine the extent to which small-scale geometric substrate roughness influences the wetting behavior of fluids at solid surfaces. Molecular simulation is used to construct roughness wetting diagrams wherein the progression of the contact angle is traced from the Cassie to Wenzel to impregnation regime with increasing substrate strength for a collection of systems with rectangularly shaped grooves. We focus on the evolution of these diagrams as the length scale of the substrate features approaches the size of a fluid molecule. When considering a series of wetting diagrams for substrates with fixed shape and variable feature periodicity, we find that the diagrams progressively shift away from a common curve as the substrate features become smaller than approximately 10 fluid diameters. It is at this length scale that the macroscopic models of Cassie and Wenzel become unreliable. Deviations from the macroscopic models are attributed to the manner in which the effective substrate-fluid interaction strength evolves with periodicity and the important role that confinement effects play for substrates with small periodicities.

Wetting on physically patterned solid surfaces: the relevance of molecular dynamics simulations to macroscopic systems

We used molecular dynamics (MD) simulations to study the wetting of Lennard-Jones cylindrical droplets on surfaces patterned with grooves. By scaling the surface topography parameters with the droplet size, we find that the preferred wetting modes and contact angles become independent of the droplet size. This result is in agreement with a mathematical model for the droplet free energy at small Bond numbers for which the effects of gravity are negligible. The MD contact angles for various wetting modes are in good agreement with those predicted by the mathematical model. We construct phase diagrams of the dependence of the wetting modes observed in the MD simulations on the topography of the surface. Depending on the topographical parameters characterizing the surface, multiple wetting modes can be observed, as is also seen experimentally. Thus, our studies indicate that MD simulations can yield insight into the large-length-scale behavior of droplets on patterned surfaces.