Wetting Transition on Patterned Surfaces: Transition States and Energy Barriers

Wetting transitions are studied in the two-dimensional Ising ferromagnet confined between walls where competitive surface fields act. In our finite samples of size L×M, the walls are separated by a distance L, M being the length of the sample. The surface fields are taken to be short-range and nonuniform, i.e., of the form H(1),δH(1),H(1),δH(1),..., where the parameter -1≤δ≤1 allows us to control the nonuniformity of the fields. By performing Monte Carlo simulations we found that those competitive surface fields lead to the occurrence of an interface between magnetic domains of different orientation that runs parallel to the walls. In finite samples, such an interface undergoes a localization-delocalization transition, which is the precursor of a true wetting transition that takes place in the thermodynamic limit. By exactly working out the ground state (T=0), we found that besides the standard nonwet and wet phases, a surface antiferromagnetic-like state emerges for δ<-1/3 and large fields (H(1)>3), H(1)(tr)/J=3, δ(tr)=-1/3,T=0, being a triple point where three phases coexist. By means of Monte Carlo simulations it is shown that these features of the phase diagram remain at higher temperatures; e.g., we examined in detail the case T=0.7×T(cb). Furthermore, we also recorded phase diagrams for fixed values of δ, i.e., plots of the critical field at the wetting transition (H(1w)) versus T showing, on the one hand, that the exact results of Abraham [Abraham, Phys. Rev. Lett. 44, 1165 (1980)] for δ=1 are recovered, and on the other hand, that extrapolations to T→0 are consistent with our exact results. Based on our numerical results we conjectured that the exact result for the phase diagram worked out by Abraham can be extended for the case of nonuniform fields. In fact, by considering a nonuniform surface field of some period λ, with λ<<M, e.g., [H(1)(x,λ)>0], one can obtain the effective field H(eff) at a λ coarse-grained level given by H(eff)=1/λ∑(x=1)(λ)H(1)(x,λ). Then we conjectured that the exact solution for the phase diagram is now given by H(eff)/J=F(T), where F(T) is a function of the temperature T that straightforwardly follows from Abraham's solution. The conjecture was exhaustively tested by means of computer simulations. Furthermore, it is found that for δ≠1 the nonwet phase becomes enlarged, at the expense of the wet one, i.e., a phenomenon that we call "surface nonuniformity-induced nonwetting," similar to the already known case of "roughness-induced nonwetting."

Bouncing and non-bouncing impact dynamics of a droplet on a solid surface are studied experimentally and numerically. High-speed visualization and an in-house dual-grid level-set method based solver are employed. Two established contact angle models, namely, Kistler and Fukai models, are implemented in the solver. While the Kistler model employs a time-varying dynamic contact angle, the Fukai model accounts for a quasi-dynamic contact angle based on contact line velocity. Better agreement between the present numerical result and present as well as published experimental results of a dynamic contact angle is found for the Kistler model, specifically for more transient contact angle variations cases that correspond to the less viscous droplets on the hydrophilic surfaces (Ca = 0.005–0.037 and θeq = 22°–90°). This is because the Kistler model can replicate more dynamic variations of the contact angles during spreading and receding as compared to the Fukai model, while both the Fukai and Kistler models numerical results are found in good agreement with the measurements for less transient contact angle variations cases that correspond to the high viscous droplets on the hydrophilic/hydrophobic surfaces (Ca = 7.596 and θeq = 86°–125°). Finally, the coupled effects of liquid surface tension, liquid viscosity, substrate wettability, and impact velocity during droplet bouncing and non-bouncing are presented through an energy budget analysis. At a given impact velocity, for less-viscous and less-surface tension liquids, the viscous dissipation is substantial irrespective of the surface wettability, whereas for less-viscous and high-surface tension liquids, the viscous dissipation is smaller on hydrophobic surfaces as compared to that on hydrophilic surfaces.

Droplet evaporation is widespread in natural and industrial application, and the rapid and efficient evaporation can significantly improve energy efficiency. However, the fundamental mechanism of contact line dynamics and the microscopic characteristics of evaporating nanodroplets are not well understood. Moreover, how to design a nanostructure surface to enhance nanodroplet evaporation remains unclear. Here, through molecular dynamics simulation, we investigated the evaporation dynamics of nanodroplets on various nanoring surfaces with different geometric parameters and wettability. By measuring the changes of contact radius and contact angle, the results showed that nanodroplets successively exhibit constant contact angle (CCA), constant contact radius (CCR), and mix mode during evaporation, and the evaporation-induced CCA-CCR transition, in essence, is a Cassie-Wenzel wetting transition, whose onset time is remarkably dependent on the surface roughness and wettability. We found that this evaporation-induced wetting transition is postponed on the surface with small nanostructure spacing and weak hydrophilicity, and the evaporation rate of nanodroplets improves accordingly. The dense and hydrophobic nanostructures can not only restrain the Cassie-Wenzel transition, but also enhance the evaporation rate of nanodroplets. Last, through the potential energy field analysis of nanoring substrates, we revealed that the Cassie-Wenzel wetting transition of nanodroplets is a process of molecule migration to low potential energy regions. Our work provides guidance for designing nanostructure surfaces to effectively control the droplet wetting state and enhance its mass transfer performance of phase change.

Initiation mechanisms of enhanced pyrolysis and oxidation of JP-10 (exo-tetrahydrodicyclopentadiene) on functionalized graphene sheets: Insights from ReaxFF molecular dynamics simulations

We present an efficient algorithm for calculating the minimum energy path (MEP) and energy barriers between local minima on a multidimensional potential energy surface (PES). Such paths play a central role in the understanding of transition pathways between metastable states. Our method relies on the original formulation of the string method [Phys. Rev. B, 66,052301 (2002)], i.e. to evolve a smooth curve along a direction normal to the curve. The algorithm works by performing minimization steps on hyperplanes normal to the curve. Therefore the problem of finding MEP on the PES is remodeled as a set of constrained minimization problems. This provides the flexibility of using minimization algorithms faster than the steepest descent method used in the simplified string method [J. Chem. Phys., 126(16), 164103 (2007)]. At the same time, it provides a more direct analog of the finite temperature string method. The applicability of the algorithm is demonstrated using various examples.

The 1,3-dipolar cycloaddition reactions of diazomethane with ethylene and formaldehyde as well as the nitrogen elimination reactions from the cycloadducts have been studied using density functional and conventional ab initio methods. The exothermicity of the reactions is underestimated by DFT methods with respect to CCSD(T) due to an overestimation of the C−N dissociation energy of diazomethane. For the cycloaddition reactions all methods lead to similar transition state geometries, and the potential energy barriers computed using DFT methods are similar to the CCSD(T) ones. On the other hand, for the nitrogen elimination reactions transition state geometries and energy barriers are more dependent on the level of calculation. The results obtained show that for the reaction between diazomethane and ethylene the pyrazoline intermediate is more stable than the reactants and that the Gibbs energy barrier for nitrogen elimination is larger than the barrier corresponding to its formation. On the contrary, for formaldehyde the kinetically most favorable cycloadduct, 1,2,3-oxadiazoline, is less stable than the reactants and has a lower barrier for nitrogen elimination.

Calculating Transition Energy Barriers and Characterizing Activation States for Steps of Fusion

The interaction between water and organic substances is of extreme importance in physical, biological, and geological chemistries. Understanding the interactions between water and organic interfaces is one of the earliest chemical quandaries. In this research, self-assembled monolayers (SAMs) were used as a tool to investigate the interaction between water molecules and hydrophobic surfaces. Real-time adsorption and desorption kinetics of water on hydrophobic SAM surfaces was monitored using a new type of field effect transistor (FET)-like device called MOCSER (molecular controlled semiconductor resistor) coated with SAMs. A quartz crystal microbalance (QCM) was used as a complementary technique to give an estimate of total water mass adsorbed. It is shown that water adsorption depends on relative humidity and is reversible. The amount of adsorbed water increased with surface corrugation. The measurements suggest that adsorption takes place as small water clusters, originating on irregularities on the surface organic layer. Molecular dynamics simulations were carried out to study the interactions of water and hydrophobic surfaces as well. These simulations also suggest the formation of water microdroplets on hydrophobic surfaces, and indicate a strong correlation between increased surface corrugation and adsorption. This paper examines the possible consequences of these interactions on the properties of organic aerosols in the troposphere.

Vapor condensation on solid surfaces plays a crucial role across a wide range of industrial applications. Recent advances of nanotechnology have made possible the manipulation of the condensation process through the control of surface structures. In this work, we study vapor condensation on hydrophobic surfaces patterned with microscale pillars. The critical nuclei, the activation barriers, and the minimum energy paths are computed using the climbing string method. The effects of pillar height, interpillar spacing, the level of supersaturation, and the intrinsic wettability of the solid surface on the nucleation process are investigated. Two nucleation scenarios are obtained from the computation. In the case of high pillar, narrow interpillar spacing, low supersaturation, and/or low surface wettability, the critical nucleus prefers the suspended Cassie state; otherwise, it prefers the impaled Wenzel state. A comparison of the nucleation barrier with that on a flat surface of the same material reveals that vapor condensation is inhibited by the microstructures in the former case, while enhanced in the latter case. The critical values of the pillar height, the interpillar spacing, and the supersaturation at which the critical nucleus changes from the Cassie state to the Wenzel state are identified from the phase diagram of the critical nucleus. It is found that the dependence of the critical interpillar spacing on the supersaturation follows closely the curve of the critical radii in a homogeneous nucleation. The relaxation dynamics of the condensate after the critical nucleus is formed is computed by solving the steepest descent equation. It is observed that when the pillar is low and/or the interpillar spacing is wide, a condensate initially in the Cassie state may evolve into the Wenzel state during the relaxation.

The rate of thermally activated transitions can generally be described by the Arrhenius law, as k=f0 exp(-ΔE/kBT). In the previous expression, ΔE is the internal energy barrier, and f0 is a prefactor that encompasses both dynamical and entropic contributions. In this work, we show how the activation entropy can play a crucial role in thermally activated magnetic transitions. To that end, we study two types of transitions involving solitons either as the stable state or the transition state, namely, skyrmion annihilation, and domain-wall mediated magnetization reversal in nanodisks.The aforementioned transitions pertain to the class of rare events, i.e., they are unlikely to arise in the course of a Langevin simulation, because the mean waiting time between events is much larger than the integration timestep. In this case, one possible approach is to use a form of reaction rate theory to calculate the energy barrier and the Arrhenius prefactor. To this end, we apply Langer’s theory [1], which is an extension of the Kramers method to many dimensions. Alternatively, one may use a path sampling method such as forward flux sampling [2] in order to sample the transition path ensemble from the system’s dynamics and extract a transition rate. In this work, we employ both methods in conjunction to study the thermal stability of magnetic skyrmions and nanodisks, for which the two methods show a good agreement.Magnetic skyrmions are particle-like, two-dimensional, non-collinear solitonic spin textures with a nontrivial topology. In ultrathin films and multilayers, small skyrmions are stabilized by an interfacial form of the Dzyaloshinskii-Moriya interaction (DMI). Skyrmion-based designs currently appear very promising for novel spintronics devices, e.g., for racetrack memories and logic gates, reservoir computing, or probabilistic computing [3]. Isolated skyrmions exist as metastable excitations of the collinear magnetic ground state and can be longed-lived. For applications, a stability of up to 10 years at room temperature is a technological requirement, and the ability to accurately predict that stability is therefore crucial. We find that skyrmions can be stabilized not only by an internal energy barrier, but also by a large activation entropy. This stems from the fact that the metastable skyrmion state possesses a large entropy compared to the transition state, because skyrmions exhibit stable internal modes of deformation [4]. When applying a destabilizing magnetic field perpendicular to the skyrmion core, the skyrmion lifetime decreases quickly with the field amplitude. This results from a shrinking of the skyrmion, which simultaneously reduces the the energy barrier, as well as the activation entropy through the suppression of the stable internal modes (Fig. 1) [5].Next, we compute the mean waiting times between thermally activated domain-wall mediated magnetization reversals in a perpendicularly magnetized nanodisk. We use parameters that resemble that of a free CoFeB layer, as typically used in magnetoresistive random access memories [6]. By varying the perpendicular anisotropy and the interfacial DMI, we find that the Arrhenius prefactor can take extreme, seemingly non-physical values up to 1021 Hz, which is orders of magnitude beyond the typically assumed value of 109 Hz, and vary drastically as a function of material parameters. We show that the prefactor behaves like an exponential of the energy barrier, which stems from a linear variation of the activation entropy with the energy barrier (Fig. 2) [7]. This phenomenon, known as the Meyer-Neldel rule, or entropy-enthalpy compensation, has been reported across diverse fields of the natural sciences for over a century—in semiconductors, chemical reactions, biological death rates, etc [8]. In magnetism, it was only recently observed in the decay of the skyrmion lattice [9]. This result implies that the transition state, which, in the case of the magnetization reversal, is a domain wall found in the center of the disk, tend to possess a very large entropy compared to the collinear ground state. This is verified by the existence of gapless, low energy modes propagating along domain walls [10].These findings suggest that the Arrhenius prefactor, which is typically taken as an attempt frequency within the characteristic timescale of a magnetic system's dynamics, may in some cases contain a very large entropic contribution which should not be neglected. This seems to be particularly true in magnetic transitions involving solitons. **

The kinetics of phase transitions in the two dimensional Ising model under different conditions is studied using the string method. The key idea is to work in collective variables, consisting of block of spins, which allow for a continuous approximation of the collective variable state-space. The string method computes the minimum free energy path (MFEP) in this collective variable space, which is shown to explain the mechanism of the phase transformation (in particular, an approximation of its committor function, its free energy and its transition state). In this paper the theoretical background of the technique as well as its computational aspects are discussed in details. The string method is then used to analyze phase transition in the Ising model with imposed boundary conditions and in a periodic system under an external field of increasing magnitude. In each case, the mechanism of the phase transformation is elucidated.

Engineering the geometry of stripe-patterned surfaces toward efficient wettability switching

The pattern design of superhydrophobic surfaces can be significantly aided by computations that predict the Cassie-Baxter (CB) to Wenzel (W) transition, which is responsible for the break-down of superhydrophobic behavior. We present a computational framework for the optimization of patterned surfaces based on the energy barriers of the CB-W transitions which comprises the following elements: (a) design of structured surface patterns, for example, arrays of pillars, with parameterized geometric features such as size, pitch, slope, and roundness. (b) Computation of the wetting states with a modified Young-Laplace equation that facilitates the introduction of solid/liquid interactions for complex surface patterns and has significantly lower computational cost than other commonly used methods, such as the volume-of-fluid, phase-field, and so forth. (c) Incorporation of the modified Young-Laplace in the simplified string method, allowing the calculation of the minimum energy paths of wetting transitions which, apart from the energy barriers, also reveal the transition mechanisms (CB failure modes). (d) Accommodation of large-scale problems with good parallel performance and scalability on multicore-distributed memory systems using fast iterative solvers and the Message Passing Interface communication protocol. We demonstrate the computational framework with a shape optimization study of inverted conical frustum pillars. The optimization objective function is the resistance to the CB-W transition, which is quantified by the energy barrier-a relatively large energy barrier suggests improved superhydrophobicity. We also report the parallel performance, in terms of parallel speedup for problems ranging from three hundred thousands to 12 million degrees of freedom, solved using up to 40 processing cores.

The concerted and the stepwise mechanisms of the Diels−Alder reaction between butadiene and ethylene were studied by ab initio MO methods. For the stepwise mechanism, three process are included: the first process is the formation of biradical intermediate with a transition state, the second is the rotation for the new bond axis with a transition state, and the third is the other bond formation without an energy barrier. The transition state for the first process has a higher energy barrier of 4 kcal/mol than that for the second process at the CAS-MP2/6-311+G(d,p) calculation level. For the concerted mechanism, the energy barrier height of the transition state is 2.7 kcal/mol lower than that of the first process of the stepwise mechanism by the CAS-MP2/6-311+G(d,p) level. Both reaction mechanisms were analyzed by a CiLC−IRC method. The CiLC−IRC analysis shows the nature of the aromaticity for the transition state of the concerted mechanism. The CiLC−IRC analysis also shows that the transition state of the second process of the stepwise mechanism causes from the static energy as the rotational barrier of methyl group.

Bouncing and non-bouncing impact dynamics of a droplet on a solid surface are studied experimentally and numerically. High-speed visualization and an in-house dual-grid level-set method based solver are employed. Two established contact angle models, namely, Kistler and Fukai models, are implemented in the solver. While the Kistler model employs a time-varying dynamic contact angle, the Fukai model accounts for a quasi-dynamic contact angle based on contact line velocity. Better agreement between the present numerical result and present as well as published experimental results of a dynamic contact angle is found for the Kistler model, specifically for more transient contact angle variations cases that correspond to the less viscous droplets on the hydrophilic surfaces (Ca = 0.005–0.037 and θeq = 22°–90°). This is because the Kistler model can replicate more dynamic variations of the contact angles during spreading and receding as compared to the Fukai model, while both the Fukai and Kistler models numerical results are found in good agreement with the measurements for less transient contact angle variations cases that correspond to the high viscous droplets on the hydrophilic/hydrophobic surfaces (Ca = 7.596 and θeq = 86°–125°). Finally, the coupled effects of liquid surface tension, liquid viscosity, substrate wettability, and impact velocity during droplet bouncing and non-bouncing are presented through an energy budget analysis. At a given impact velocity, for less-viscous and less-surface tension liquids, the viscous dissipation is substantial irrespective of the surface wettability, whereas for less-viscous and high-surface tension liquids, the viscous dissipation is smaller on hydrophobic surfaces as compared to that on hydrophilic surfaces.