Spreading dynamics of polymer nanodroplets

Influence of Temperature-Guided SAM Growth on Wetting and Its Mass Transfer Models

The formation and growth of self-assembled monolayers (SAMs) composed of amphiphiles have garnered significant attention due to their diverse technical applications. This article reports the findings of molecular dynamics simulations aimed at elucidating the intricate relationship between the wetting behavior of amphiphiles, specifically n-alkanols, and the growth of their SAMs on a mica surface under varying temperature conditions. The investigation quantifies the structural characteristics of the formed SAMs, including density profiles, in-plane radial distribution functions, order parameters, and end-to-end length distributions of n-alkanol molecules within the SAM. Thermodynamic properties, such as the second virial coefficient and excess entropy, are examined in relation to temperature and time. The growth of the SAM is assessed by analyzing characteristic time scales at different temperatures and in-plane diffusion of n-alkanol molecules and utilizing classical theories of mass transfer to quantify the growth rate as a function of temperature. These results are then correlated with changes in the contact angle and spreading coefficient of n-alkanol droplets on the mica surface over time, providing insights into the impact of SAM growth on the wetting behavior and the mass transfer model of such systems.

Thermally assisted mobility of nanodroplets on surfaces with weak defects

HYPOTHESIS

Thermal activation plays an essential role in contact line dynamics on nanorough surfaces. However, the relation between the aforementioned concept and the sliding motion of nanodroplets remains unclear. As a result, thermally assisted motion of nanodroplets on nanorough surfaces is investigated in this work.

EXPERIMENTS

Steady slide and random motion of nanodroplets on surfaces with weak defects are investigated by Many-body Dissipative Particle Dynamics. The surface roughness is characterized by the slip length acquired from the velocity profile associated with the flowing film.

FINDINGS

The slip length is found to decline with increasing the defect density. The linear relationship between the sliding velocity and driving force gives the mobility and reveals the absence of contact line pinning. On the basis of the Navier condition, a simple relation is derived and states that the mobility is proportional to the slip length and the reciprocal of the product of viscosity and contact area. Our simulation results agree excellently with the theoretical prediction. In the absence of external forces, a two-dimensional Brownian motion of nanodroplets is observed and its mean square displacement decreases with increasing the defect density. The diffusivity is proportional to the mobility, consistent with the Einstein relation. This consequence suggests that thermal fluctuations are able to overcome contact line pinning caused by weak defects.

Roles of energy dissipation and asymmetric wettability in spontaneous imbibition dynamics in a nanochannel

HYPOTHESIS

The imbibition dynamics is controlled by energy dissipation mechanisms and influenced by asymmetric wettability in a nanochannel. We hypothesize that the imbibition dynamics can be described by a combined model of the Lucas-Washburn equation and the Cox-Voinov law considering velocity-dependent contact angles.

METHODS

Molecular dynamics simulations are utilized to investigate the imbibition dynamics. A wide range of wetting conditions is achieved via adjusting the liquid-solid interaction parameters, and the spontaneous imbibition processes are quantified and compared.

FINDINGS

The critical condition for the occurrence of spontaneous imbibition is analyzed from a surface energy perspective. The analyses of energy conversion and dissipation indicate that the viscous dissipation is dominant during spontaneous imbibition. The classical Lucas-Washburn equation is modified with the Cox-Voinov law considering the effect of the dynamic contact angle and an effective equilibrium contact angle. We show that the proposed theory well captures the imbibition dynamics embodied in the growth of imbibition length as well as the transient interface shape and velocity for both the symmetric and asymmetric wetting conditions. In nanochannels with asymmetric wettability, the imbibition length difference between the sidewalls and interface oscillations increases with wetting disparity. Our findings deepen the understanding of imbibition dynamics on the nanoscale, and provide a theoretical reference for relevant applications.

Wetting characteristics of polymer adhesives with different chain bending stiffness

Polymer adhesives are widely used in daily applications and in industry owing to their flexibility and overall non-toxicity, particularly in interfacial adhesion. The spreading of polymer adhesives on adherend is one of the essential considerations for the interfacial adhesion of polymer adhesives, which is strongly related to their wetting behaviors. While relationships between polymer microstructure and adhesion have been investigated in previous studies, it remains challenging to unveil the effect of polymer microstructure on wettability. To address this issue, here we utilize coarse-grained molecular dynamics (CGMD) simulations to systematically elucidate how the wettability of a polymer adhesive droplet on a surface depends on bending stiffness. The wetting dynamics and the contact angle are studied to show the evolution of morphology of droplets during the wetting process. The results indicate the wettability is weakened by the increase of bending stiffness of polymer chain. Detailed thermodynamic property analysis is further conducted, revealing that the adhesion between the polymer droplet and substrate deteriorates due to the decline of wettability. Interestingly, we observe such deterioration becomes more significant by both increasing the temperature and decreasing the bending stiffness. Our study sheds light on the dependence of chain bending stiffness and temperature on the wetting behavior of polymer adhesive droplets, and offers insights, which, upon experimental validation can then be used for the design of adhesives or hydrogels.

Wetting Simulations of High-Performance Polymer Resins on Carbon Surfaces as a Function of Temperature Using Molecular Dynamics

Resin/reinforcement wetting is a key parameter in the manufacturing of carbon nanotube (CNT)-based composite materials. Determining the contact angle between combinations of liquid resin and reinforcement surfaces is a common method for quantifying wettability. As experimental measurement of contact angle can be difficult when screening multiple high-performance resins with CNT materials such as CNT bundles or yarns, computational approaches are necessary to facilitate CNT composite material design. A molecular dynamics simulation method is developed to predict the contact angle of high-performance polymer resins on CNT surfaces dominated by aromatic carbon, aliphatic carbon, or a mixture thereof (amorphous carbon). Several resin systems are simulated and compared. The results indicate that the monomer chain length, chemical groups on the monomer, and simulation temperature have a significant impact on the predicted contact angle values on the CNT surface. Difunctional epoxy and cyanate ester resins show the overall highest levels of wettability, regardless of the aromatic/aliphatic nature of the CNT material surface. Tetrafunctional epoxy demonstrates excellent wettability on aliphatic-dominated surfaces at elevated temperatures. Bismaleimide and benzoxazine resins show intermediate levels of wetting, while typical molecular weights of polyether ether ketone demonstrate poor wetting on the CNT surfaces.

Spreading Time of Impacting Nanodroplets

The kinematic time and maximum spreading time for the impact of nanodroplets of different types of fluids on solid surfaces with different wettability are investigated. It shows that the capillary regime still exits for the nanodroplet impact, even if viscous dissipation increases significantly when the droplet size reduces to the nanoscale. By taking into account the influence of liquid types and surface wettability, we first obtain scaling laws of the maximum spreading time for the capillary and viscous regimes. We further propose a universal scaling law by interpolating the scaling laws in the two asymptotic regimes. The universal scaling law is in excellent agreement with molecular dynamics simulations for various liquids and surface wettability.

Taking a closer look: A molecular-dynamics investigation of microscopic and apparent dynamic contact angles

HYPOTHESIS

Molecular dynamics (MD) may be used to investigate the velocity dependence of both the microscopic and apparent dynamic contact angles (θ_m and θ_app).

METHODS

We use large-scale MD to explore the steady displacement of a water-like liquid bridge between two molecularly-smooth solid plates under the influence of an external force F⁰. A coarse-grained model of water reduces the computational demand and the solid-liquid affinity is varied to adjust the equilibrium contact angle θ⁰. Protocols are devised to measure θ_m and θ_app as a function of contact-line velocity U_cl.

FINDINGS

For all θ⁰, θ_m is velocity-dependent and consistent with the molecular-kinetic theory of dynamic wetting (MKT). However, θ_app diverges from θ_m as F⁰ is increased, especially at the receding meniscus. The behavior of θ_app follows that predicted by Voinov: (θ_app)³ = (θ_m)³ + 9Ca·ln(L/L_m), where Ca is the capillary number and L and L_m are suitably-chosen macroscopic and microscopic length scales. For each θ⁰, there is a critical velocity U_crit and contact angle θ_crit at which θ_app→0 and the receding meniscus deposits a liquid film. Setting θ_app=0, θ_m=θ_crit and U_cl=U_crit in the Voinov equation yields the value of L/L_m. The predicted values of θ_app then agree well with those measured from the simulations. Since θ_m obeys the MKT, we have, therefore, demonstrated the utility of the combined model of dynamic wetting proposed by Petrov and Petrov.

Atomistic Investigation on the Wetting Behavior and Interfacial Joining of Polymer-Metal Interface

Polymer-metal hybrid structures can reduce the weight of components while ensuring the structural strength, which in turn save cost and subsequently fuel consumption. The interface strength of polymer-metal hybrid structure is mainly determined by the synergistic effects of interfacial interaction and mechanical interlocking. In this study, the wetting behavior of polypropylene (PP) melt on metal surface was studied by molecular dynamics simulation. Atomistic models with smooth surface and nano-column arrays on Al substrate were constructed. Influences of melt temperature, surface roughness and metal material on the wetting behavior and interfacial joining were analyzed. Afterwards the separation process of injection-molded PP-metal hybrid structure was simulated to analyze joining strength. Results show that the initially sphere-like PP model gradually collapses in the wetting simulation. With a higher temperature, it is easier for molecule chains to spread along the surface. For substrate with rough surface, high density is observed at the bottom or on the upper surface of the column. The contact state is transitioning from Wenzel state to Cassie–Baxter state with the decrease of void fraction. The inner force of injection-molded PP-Fe hybrid structure during the separation process is obviously higher, demonstrating a greater joining strength.

Unraveling the Mechanism of a Rising Three-Phase Contact Line along a Vertical Surface Using Many-Body Dissipative Particle Dynamics

We present coarse-grained molecular (many-body dissipative particle) dynamics simulations to unravel the wetting mechanism of spontaneous rise of a liquid thin film along vertical flat and rough surfaces. We show that the displacement of the rising contact line, in single- and double-wall geometry, exhibits a ballistic motion (∼t) followed by a diffusive dynamics (∼[Formula: see text]) during the rise of the liquid thin film against gravity. Dynamic contact angle decreases as the contact line transitions from ballistic to diffusive regime. Explicit analysis of the velocity and vorticity profile in the bulk and in the proximity of the contact line suggests an unsteady flow field behind the rising three-phase contact line. Furthermore, our simulation results indicate that contact line dynamics and the flow field behind the contact line are independent of the surface roughness.

Molecular Dynamics Simulation of the Superspreading of Surfactant-Laden Droplets. A Review

Superspreading is the rapid and complete spreading of surfactant-laden droplets on hydrophobic substrates. This phenomenon has been studied for many decades by experiment, theory, and simulation, but it has been only recently that molecular-level simulation has provided significant insights into the underlying mechanisms of superspreading thanks to the development of accurate force-fields and the increase of computational capabilities. Here, we review the main advances in this area that have surfaced from Molecular Dynamics simulation of all-atom and coarse-grained models highlighting and contrasting the main results and discussing various elements of the proposed mechanisms for superspreading. We anticipate that this review will stimulate further research on the interpretation of experimental results and the design of surfactants for applications requiring efficient spreading, such as coating technology.

Atomistic Study of Dynamic Contact Angles in CO2-Water-Silica System

The dynamic wetting for the CO₂-water-silica system occurring in deep reservoirs is complex because of the interactions among multiple phases. This work aims to quantify the contact angle of CO₂-water flow in the silica channel at six different flow velocities using molecular dynamics. The dynamic contact angle values at different contact line velocities are obtained for the CO₂-water-silica system. By calculating the rates of the adsorption-desorption process of CO₂ and water molecules on the silica surface using molecular dynamics simulations, it has been found that the results of the dynamic contact angle can be explained by the molecular kinetic theory and predicted from the equilibrium molecular simulations. Moreover, the capillary pressure at different contact line velocities is predicted according to the Young-Laplace equation. The change in contact angles at different velocities is compared with empirical equations in terms of capillary number. The results of this study can help us better understand the dynamic process of the multiphase flow at the nanoscale under realistic reservoir conditions.

Predictive Model to Probe the Impact of Gravity and Surface Tension on Rising Wetting Thin Films

Utilizing kinetic Monte Carlo simulations, we developed a three-dimensional Ising lattice gas model to reveal the wetting mechanism of a liquid film rising along a vertical substrate. The model takes into account the impact of surface tension, gravity, and interaction energy between liquid particles and between liquid and substrate on the rise of the liquid film. We verify that in low gravitational acceleration regime, the growth of the liquid film follows the universal law of [Formula: see text]. As gravitational acceleration and surface tension vary, the simulation results show the detailed dynamics of the solid-liquid interface. Explicit analysis of the interface displacement and roughness under different gravitational accelerations and surface tensions is also presented.

Spreading of a granular droplet under horizontal vibrations

By means of three-dimensional discrete element simulations, we study the spreading of a granular droplet on a horizontally vibrated plate. Apart from a short transient with a parabolic shape, the droplet adopts a triangular profile during the spreading. The dynamics of the spreading is governed by two distinct regimes: a superdiffusive regime in the early stages driven by surface flow followed by a second one which is subdiffusive and governed by bulk flow. The plate bumpiness is found to alter only the spreading rate but plays a minor role on the shape of the granular droplet and on the scaling laws of the spreading. Importantly, we show that in the subdiffusive regime, the effective friction between the plate and the granular droplet can be interpreted in the framework of the μ(I)-rheology.

Measurement of nanoscale molten polymer droplet spreading using atomic force microscopy

We present a technique for measuring molten polymer spreading dynamics with nanometer scale spatial resolution at elevated temperatures using atomic force microscopy (AFM). The experimental setup is used to measure the spreading dynamics of polystyrene droplets with 2 μm diameters at 115-175 °C on sapphire, silicon oxide, and mica. Custom image processing algorithms determine the droplet height, radius, volume, and contact angle of each AFM image over time to calculate the droplet spreading dynamics. The contact angle evolution follows a power law with time with experimentally determined values of -0.29 ± 0.01, -0.08 ± 0.02, and -0.21 ± 0.01 for sapphire, silicon oxide, and mica, respectively. The non-zero steady state contact angles result in a slower evolution of contact angle with time consistent with theories combining molecular kinetic and hydrodynamic models. Monitoring the cantilever phase provides additional information about the local mechanics of the droplet surface. We observe local crystallinity on the molten droplet surface, where crystalline structures appear to nucleate at the contact line and migrate toward the top of the droplet. Increasing the temperature from 115 °C to 175 °C reduced surface crystallinity from 35% to 12%, consistent with increasingly energetically favorable amorphous phase as the temperature approaches the melting temperature. This platform provides a way to measure spreading dynamics of extremely small volumes of heterogeneously complex fluids not possible through other means.

On the cohesion of fluids and their adhesion to solids: Young's equation at the atomic scale

Using large-scale molecular dynamics simulations, we model a 9.2nm liquid bridge between two solid plates having a regular hexagonal lattice and analyse the forces acting at the various interfaces for a range of liquid-solid interactions. Our objective is to study the mechanical equilibrium of the system, especially that at the three-phase contact line. We confirm previous MD studies that have shown that the internal pressure inside the liquid is given precisely by the Laplace contribution and that the solid exerts a global force at the contact line in agreement with Young's equation, validating it down to the nanometre scale, which we quantify. In addition, we confirm that the force exerted by the liquid on the solid has the expected normal component equal to γ_lvsinθ⁰, where γ_lv is the surface tension of the liquid and θ⁰ is the equilibrium contact angle measured on the scale of the meniscus. Recent thermodynamic arguments predict that the tangential force exerted by the liquid on the solid should be equal to the work of adhesion expressed as Wa⁰=γ_lv(1+cosθ⁰). However, we find that this is true only when any layering of the liquid molecules close to liquid-solid interface is negligible. The force significantly exceeds this value when strong layering is present.

Size dependence of static polymer droplet behavior from many-body dissipative particle dynamics simulation

We used molecular simulation to study the static behavior of polymer droplets in vacuum and on solid surfaces, namely the size of the droplet and the contact angle, respectively. The effects of the polymer chain length and the total number of particles were calculated by the many-body dissipative particle dynamics method. For the spherical droplet containing the same number of particles, we show that its radius depends on the polymer chain length. The radius of the droplet is also proportional to one-third power of the total number of particles for all given chain lengths. For the hemispherical droplet, the contact angle increases with the number of particles in the droplet, and this effect is relatively strong, especially for longer polymer chains. The effect of wettability of the solid surface was also investigated by using polymerphobic (low-affinity) and polymerphilic (high-affinity) surfaces. As the chain length increases, the contact angle on the low-affinity surface decreases, while that on the hydrophilic surface increases. The simulation reveals that there is a critical affinity for the monomer on the solid surface; above and below which the wettability increases and decreases as the molecular length increases, respectively.

Effect of a Single Nanoparticle on the Contact Line Motion

In this paper, we use a single nanoparticle (NP) to achieve active control of the droplet contact line. When the droplet is out of equilibrium, the resulting excess free energy provides the driving force for the depinning of the contact line and the NP. There are three ways to increase the energy barriers to be surmounted and to realize the pinning of the contact line, namely, the enhancement of the interactions between the NP and the substrate, the increase in substrate hydrophilicity, and the reduction in the NP hydrophilicity. On this basis, we obtained three styles of contact line motion including complete slipping, alternate pinning-depinning, and complete pinning and theoretically interpreted them. The basic theory presented in this paper can be applied to explain and regulate the dynamics of the contact line involved in many physical processes such as evaporation and spreading.

Classification of precursors in nanoscale droplets

Molecular precursors, ultrathin films that precede spreading droplets, are still far from being understood, despite intensive study. The inherent microscopic length scales make small-scale experimental techniques and molecular simulation ideal methods to study this phenomenon. Previous work on molecular precursors using nanoscale droplets, however, consistently suffers from incorrect measurement of the dimensions of the precursor film. An alternative method to accurately characterize the precursor film is presented here. In contrast to previous measures, this method (i) allows for easy detection and characterization of precursors and (ii) yields wetting dynamics that agree with experimental observations. Finally, we briefly comment on previous studies whose conclusions may merit reconsideration in light of the present work.

Requirements for the Formation and Shape of Microscopic Precursors in Droplet Spreading

While the mass transport mechanisms and dynamics of molecular precursors, ultrathin films that precede spreading droplets, are well understood, the requirements for their formation and the reasons for the occurrence of different precursor shapes remain unclear. In this work, we study these requirements using molecular dynamics simulations of spreading droplets and extensive free energy computations. For a simple simulation model, we demonstrate that with growing droplet-substrate attraction, spreading passes succesively through regimes with no precursor, a monolayer precursor, and a continuously growing precursor. We show that the onset of layer formation and the changes in the precursor shape correlate with the free energy of layer formation. On the basis of these findings, we show that a positive spreading coefficient is sufficient but not necessary for precursor formation.

Modelling the superspreading of surfactant-laden droplets with computer simulation

The surfactant-driven superspreading of droplets on hydrophobic substrates is considered. A key element of the superspreading mechanism is the adsorption of surfactant molecules from the liquid-vapour interface onto the substrate through the contact line, which must be coordinated with the replenishment of interfaces with surfactant from the interior of the droplet. We use molecular dynamics simulations with coarse-grained force fields to provide a detailed structural description of the droplet shape and surfactant dynamics during the superspreading process. We also provide a simple method for accurate estimation of the contact angle subtended by the droplets at the contact line.

Smoothing of contact lines in spreading droplets by trisiloxane surfactants and its relevance for superspreading

Superspreading, the greatly enhanced spreading of aqueous solutions of trisiloxane surfactants on hydrophobic substrates, is of great interest in fundamental physics and technical applications. Despite numerous studies in the last 20 years, the superspreading mechanism is still not well understood, largely because the molecular scale cannot be resolved appropriately either experimentally or using continuum simulations. The absence of molecular-scale knowledge has led to a series of conflicting hypotheses based on different assumptions of surfactant behavior. We report a series of large-scale molecular dynamics simulations of aqueous solutions of superspreading and non-superspreading surfactants on different substrates. We find that the transition from the liquid-vapor to the solid-liquid interface is smooth for superspreading conditions, allowing direct adsorption through the contact line. This finding complements a study [Karapetsas et al., J. Fluid Mech., 2011, 670, 5-37], which predicts that superspreading can occur if this adsorption path is possible. Based on the observed mechanism, we provide plausible explanations for the influence of the substrate hydrophobicity, the surfactant chain length, and the surfactant concentration on the superspreading phenomenon. We also briefly address that the observed droplet shape is a mechanism to overcome the Huh-Scriven paradox of infinite viscous dissipation at the contact line.

Self-assembly of collagen on flat surfaces: the interplay of collagen-collagen and collagen-substrate interactions

Fibrillar collagens, common tissue scaffolds in live organisms, can also self-assemble in vitro from solution. While previous in vitro studies showed that the pH and the electrolyte concentration in solution largely control the collagen assembly, the physical reasons why such control could be exerted are still elusive. To address this issue and to be able to simulate self-assembly over large spatial and temporal scales, we have developed a microscopic model of collagen with explicit interactions between the units that make up the collagen molecules, as well as between these units and the substrate. We have used this model to investigate assemblies obtained via molecular dynamics deposition of collagen on a substrate at room temperature using an implicit solvent. By comparing the morphologies from our molecular dynamics simulations with those from our atomic-force microscopy experiments, we have found that the assembly is governed by the competition between the collagen-collagen interactions and those between collagen and the substrate. The microscopic model developed here can serve for guiding future experiments that would explore new regions of the parameter space.

Beyond Tanner's law: crossover between spreading regimes of a viscous droplet on an identical film

We present results on the leveling of polymer microdroplets on thin films prepared from the same material. In particular, we explore the crossover from a droplet spreading on an infinitesimally thin film (Tanner's law regime) to that of a droplet leveling on a film thicker than the droplet itself. In both regimes, the droplet's excess surface area decreases towards the equilibrium configuration of a flat liquid film, but with a different power law in time. Additionally, the characteristic leveling time depends on molecular properties, the size of the droplet, and the thickness of the underlying film. Flow within the film makes this system fundamentally different from a droplet spreading on a solid surface. We thus develop a theoretical model based on thin film hydrodynamics that quantitatively describes the observed crossover between the two leveling regimes.

Effect of molecular weight on the capillary absorption of polymer droplets

We study capillary absorption of small polymer droplets into nonwettable capillaries using coarse-grained molecular dynamics simulations and a simple analytical model. Studies of droplets of simple fluids have revealed that the capillary process depends on the ratio of tube-to-droplet radii [Willmott Faraday Discuss., 2010, 146, 233; Marmur J. Colloid Interface Sci. 1988, 122, 209]. Here we consider the absorption of droplets of polymers and study the effect of polymer chain length on the capillary absorption process. Our simulations reveal that for droplets of the same size (radius), the critical tube radius, below which there is no absorption, increases with the length of the polymer chains that constitute the droplets. We propose a model to explain this effect, which incorporates an entropic penalty for polymer confinement and find that this model agrees quantitatively with the simulations. We also find that the absorption dynamics is sensitive to the polymer chain length. In some cases during the capillary uptake transient partial absorption states, where the droplet is partially in and partially out of the tube, were observed. Such dynamics cannot be explained by a generalized Lucas-Washburn approach.

Predicting the wetting dynamics of a two-liquid system

We propose a new theoretical model of dynamic wetting for systems comprising two immiscible liquids, in which one liquid displaces another from the surface of a solid. Such systems are important in many industrial processes and the natural world. The new model is an extension of the molecular-kinetic theory of wetting and offers a way to predict the dynamics of a two-liquid system from the individual wetting dynamics of its parent liquids. We also present the results of large-scale molecular dynamics simulations for one- and two-liquid systems and show them to be in good agreement with the new model. Finally, we show that the new model is consistent with the limited data currently available from experiment.

Molecular transport and flow past hard and soft surfaces: computer simulation of model systems

The equilibrium and flow of polymer films and drops past a surface are characterized by the interface and surface tensions, viscosity, slip length and hydrodynamic boundary position. These parameters of the continuum description are extracted from molecular simulations of coarse-grained models. Hard, corrugated substrates are modelled by a Lennard-Jones solid while polymer brushes are studied as prototypes of soft, deformable surfaces. Four observations are discussed. (i) If the surface becomes strongly attractive or is coated with a brush, the Navier boundary condition fails to describe the effect of the surface independently of the strength and type of the flow. This failure stems from the formation of a boundary layer with an effective, higher viscosity. (ii) In the case of brush-coated surfaces, flow induces a cyclic, tumbling motion of the tethered chain molecules. Their collective motion gives rise to an inversion of the flow in the vicinity of the grafting surfaces and leads to strong, non-Gaussian fluctuations of the molecular orientations. The flow past a polymer brush cannot be described by Brinkman's equation. (iii) The hydrodynamic boundary condition is an important parameter for predicting the motion of polymer droplets on a surface under the influence of an external force. Their steady-state velocity is dictated by a balance between the power that is provided by the external force and the dissipation. If there is slippage at the liquid-solid interface, the friction at the solid-liquid interface and the viscous dissipation of the flow inside the drop will be the dominant dissipation mechanisms; dissipation at the three-phase contact line appears to be less important on a hard surface. (iv) On a soft, deformable substrate like a polymer brush, we observe a lifting-up of the three-phase contact line. Controlling the grafting density and the incompatibility between the brush and the polymer liquid we can independently tune the softness of the surface and the contact angle and thereby identify the parameters for maximizing the deformation at the three-phase contact.

Viscoelastic behaviors in polymeric nanodroplet collisions

Viscoelastic behaviors in the head-on collisions of polymeric nanodroplets are reported. We propose a new model for normal forces between two colliding droplets. By decomposing the force into an elastic component and a dissipative component and carefully analyzing the equation of motion, we obtain some conditions on the model parameters imposed by the thermodynamic arguments. By employing molecular dynamics simulations, we can explicitly determine the corresponding model parameters by fitting. We compare the model predictions with the simulation results.

Spreading and retraction as a function of drop size

We simulate the spreading and retraction of a two-dimensional drop over a thin film in the small slope limit for drop heights ranging from a few nanometers to hundreds of nanometers. Drop motion is initiated by an impulsive change in surface wettability expressed in terms of disjoining pressure. Owing to the presence of the film, these simulations require no closure condition at the 'apparent' contact line. Rather, we study the relationships that emerge between the apparent contact line velocity and dynamic contact angles. The disjoining pressure that we study includes stabilizing van der Waals interactions and destabilizing acid-base interactions. Changes in wetting conditions that promote spreading place the thin film surrounding the drop out of equilibrium; the drop spreads as the film thickens to its new equilibrium value. Changes in wetting conditions that promote retraction can either place the thin film out of equilibrium in a stable regime, or they can place the thin film in a spinodally unstable regime. We study drop rearrangement as a function of drop scale for these three cases. Small drops, with heights on the same order as the film thickness, are strongly influenced by disjoining pressure gradients everywhere beneath them. Larger drops, with heights at least an order of magnitude greater than the film thickness, have disjoining pressure gradients isolated near the apparent contact line at all times. For these larger drops, after initial dynamics, macroscopic behavior is recovered; drops move in agreement with Tanner's law. However, dynamics associated with the thin film can play a leading role in the ensuing drop response even after Tanner's law emerges. In particular, when drops retract over spinodally unstable films, retraction occurs in three regimes. Rims form near the apparent contact line over time scales comparable to the time scale for the instability. The rim geometry can be characterized in terms of spinodal film thicknesses. The rims then propagate toward the bulk drop. Finally, the rim disappears and the drop assumes a cap-like shape. Tanner's law is obeyed during the latter two regimes. Attempts to simulate drop rearrangements disregarding the thin film dynamics before Tanner's law manifests can lead to erroneous outcomes, as shown in simulations of drop retraction on a solid surface with an imposed Navier slip length.

Droplet spreading driven by van der Waals force: a molecular dynamics study

The dynamics of droplet spreading is investigated by molecular dynamics simulations for two immiscible fluids of equal density and viscosity. All the molecular interactions are modeled by truncated Lennard-Jones potentials and a long-range van der Waals force is introduced to act on the wetting fluid. By gradually increasing the coupling constant in the attractive van der Waals interaction between the wetting fluid and the substrate, we observe a transition in the initial stage of spreading. There exists a critical value of the coupling constant, above which the spreading is pioneered by a precursor film. In particular, the dynamically determined critical value quantitatively agrees with that determined by the energy criterion that the spreading coefficient equals zero. The latter separates partial wetting from complete wetting. In the regime of complete wetting, the radius of the spreading droplet varies with time as [Formula: see text], a behavior also found in molecular dynamics simulations where the wetting dynamics is driven by the short-range Lennard-Jones interaction between liquid and solid.

Influence of solid-liquid interactions on dynamic wetting: a molecular dynamics study

Large-scale molecular dynamics (MD) simulations of liquid drops spreading on a solid substrate have been carried out for a very wide range of solid-liquid interactions and equilibrium contact angles. The results for these systems are shown to be consistent with the molecular-kinetic theory (MKT) of dynamic wetting, which emphasizes the role of contact-line friction as the principal channel of energy dissipation. Several predictions have been confirmed. These include a quantitative link between the dynamics of wetting and the work of adhesion and the existence of an optimum equilibrium contact angle that maximizes the speed of wetting. A feature of the new work is that key parameters (κ(0) and λ), normally accessible only by fitting the MKT to dynamic contact angle data, are also obtained directly from the simulations, with good agreement between the two sources. This validates the MKT at some fundamental level. Further verification is provided by contact angle relaxation studies, which also lend support to the interfacial tension relaxation process invoked in Shikhmurzaev's hydrodynamic model of dynamic wetting.

Enhanced droplet spreading due to thermal fluctuations

The lubrication equation that governs the dynamics of thin liquid films can be augmented to account for stochastic stresses associated with the thermal fluctuations of the fluid. It has been suggested that under certain conditions the spreading rate of a liquid drop on a surface will be increased by these stochastic stresses. Here, an atomistic simulation of a spreading drop is designed to examine such a regime and provide a quantitative assessment of the stochastic lubrication equation for spreading. It is found that the atomistic drop does indeed spread faster than the standard lubrication equations would suggest and that the stochastic lubrication equation of Grün et al (2006 J. Stat. Phys. 122 1261-91) predicts the spread rate.

Spreading of diblock copolymer droplets: a probe of polymer micro-rheology

We present an experimental study of the spreading dynamics of symmetric diblock copolymer droplets above and below the order-disorder transition. Disordered diblock droplets are found to spread as a homopolymer and follow Tanner's law (the radius grows as R approximately t(m), where t is time and m = 1/10). However, droplets that are in the ordered phase are found to be frustrated by the imposed lamellar microstructure. This frustration is likely at the root of the observed deviation from Tanner's law: droplet spreading has a much slower power law (m approximately 0.05+/-0.01). We show that the different spreading dynamics can be reconciled with conventional theory if a strain-rate-dependent viscosity is taken into account.

Tension amplification in molecular brushes in solutions and on substrates

Molecular bottle-brushes are highly branched macromolecules with side chains densely grafted to a long polymer backbone. The brush-like architecture allows focusing of the side-chain tension to the backbone and its amplification from the pico-Newton to nano-Newton range. The backbone tension depends on the overall molecular conformation and the surrounding environment. Here we study the relation between the tension and conformation of the molecular brushes in solutions, melts, and on substrates. In solutions, we find that the backbone tension in dense brushes with side chains attached to every backbone monomer is on the order of f(0)N(3/8) in athermal solvents, f(0)N(1/3) in theta solvents, and f(0) in poor solvents and melts, where N is the degree of polymerization of side chains, f(0) approximately equal k(B)T/b is the maximum tension in side chains, b is the Kuhn length, k(B) is Boltzmann's constant, and T is the absolute temperature. Depending on the side chain length and solvent quality, molecular brushes develop tension on the order of 10-100 pN, which is sufficient to break hydrogen bonds. Significant amplification of tension occurs upon adsorption of brushes onto a substrate. On a strongly attractive substrate, maximum tension in the brush backbone is approximately f(0)N, reaching values on the order of several nano-Newtons, which exceeds the strength of a typical covalent bond. At low grafting density and high spreading parameter, the cross-sectional profile of an adsorbed molecular brush is approximately rectangular with a thickness approximately b (A/S)1/2, where A is the Hamaker constant, and S is the spreading parameter. At a very high spreading parameter (S > A), the brush thickness saturates at monolayer approximately b. At a low spreading parameter, the cross-sectional profile of adsorbed molecular brush has a triangular tent-like shape. In the cross-over between these two opposite cases, covering a wide range of parameter space, the adsorbed molecular brush consists of two layers. Side chains in the lower layer gain surface energy due to the direct interaction with the substrate, while the second layer spreads on the top of the first layer. Scaling theory predicts that this second layer has a triangular cross-section with width R approximately N(3/5) and height h approximately N(2/5). Using self-consistent field theory we calculate the cap profile y(x) = h(1 - x2/R2)2, where x is the transverse distance from the backbone. The predicted cap shape is in excellent agreement with both computer simulation and experiment.

Simulations of liquid nanocylinder breakup with dissipative particle dynamics

In this work, we use a dissipative-particle-dynamics-based model for two-phase flows to simulate the breakup of liquid nanocylinders. Rayleigh's criterion for capillary breakup of inviscid liquid cylinders is shown to apply for the cases considered, in agreement with prior molecular dynamics (MD) simulations. Also, as shown previously through MD simulations, satellite drops are not observed, because of the dominant role played by thermal fluctuations which lead to a symmetric breakup of the neck joining the two main drops. The parameters varied in this study are the domain size, cylinder radius, thermal length scale, viscosity, and surface tension. The breakup time does not show the same scaling dependence as in capillary breakup of liquid cylinders at the macroscale. The time variation of the radius at the point of breakup agrees with prior theoretical predictions from expressions derived with the assumption that thermal fluctuations lead to breakup.