{\it Surface-directed spinodal decomposition} (SDSD) is the kinetic interplay of phase separation and wetting at a surface. This process is of great scientific and technological importance. In this paper, we report results from a numerical study of SDSD on a chemically patterned substrate. We consider simple surface patterns for our simulations, but most of the results apply for arbitrary patterns. In layers near the surface, we observe a dynamical crossover from a {\it surface-registry regime} to a {\it phase-separation regime}. We study this crossover using layer-wise correlation functions and structure factors, and domain length scales.
This paper is the second in a two-part exposition on {\it surface-directed spinodal decomposition} (SDSD), i.e., the interplay of kinetics of wetting and phase separation at a surface which is wetted by one of the components of a binary mixture. In our first paper [P. Das, P.K. Jaiswal and S. Puri, Phys. Rev. E {\bf 102}, 012803 (2020)], we studied SDSD on chemically heterogeneous and physically flat substrates. In this paper, we study SDSD on a chemically homogeneous but morphologically patterned substrate. Such substrates arise in a vast variety of technological applications. Our goal is to …
Simulations show that when a phase-separated binary AB fluid is driven to flow past chemically patterned substrates in a microchannel, the fluid exhibits unique morphological instabilities. For the pattern studied, these instabilities give rise to the simultaneous, periodic formation of monodisperse droplets of A-in-B and B-in-A. The system bifurcates between time-independent behavior and different types of regular, non-decaying oscillations in the structural characteristics. The surprisingly complex behavior is observed even in the absence of hydrodynamic interactions and arises from the inte…
We investigate the slip boundary condition for single-phase flow past a chemically patterned surface. Molecular dynamics (MD) simulations show that modulation of fluid-solid interaction along a chemically patterned surface induces a lateral structure in the fluid molecular organization near the surface. Consequently, various forces and stresses in the fluid vary along the patterned surface. Given the presence of these lateral variations, a general scheme is developed to extract hydrodynamic information from MD data. With the help of this scheme, the validity of the Navier slip boundary conditi…
We investigate the behavior of colloidal particles immersed in a binary liquid mixture of water and 2,6-lutidine in the presence of a chemically patterned substrate. Close to the critical point of the mixture, the particles are subjected to critical Casimir interactions with force components normal and parallel to the surface. Because the strength and sign of these interactions can be tuned by variations in the surface properties and the mixtures temperature, critical Casimir forces allow the formation of highly ordered monolayers but also extend the use of colloids as model systems.
Nematic liquid crystals confined to geometrically as well as chemically patterned substrate on one end and a flat substrate with strong anchoring on the other is studied using non-Boltzmann Monte Carlo methods. We observe significant deviations from the continuum-based predictions of the phase diagram which was studied as a function of tilt angle at the top substrate and thickness of the cell. Onset of biaxiality at larger tilt angles at the top substrate is observed. A phase shift introduced between the geometrical and chemical pattern has significant effect on the director structures in the …
Recent experiments have demonstrated a fluctuation-induced lateral trapping of spherical colloidal particles immersed in a binary liquid mixture near its critical demixing point and exposed to chemically patterned substrates. Inspired by these experiments, we study this kind of effective interaction, known as the critical Casimir effect, for elongated colloids of cylindrical shape. This adds orientational degrees of freedom. When the colloidal particles are close to a chemically structured substrate, a critical Casimir torque acting on the colloids emerges. We calculate this torque on the basi…
Molecular dynamics simulations of dense and rarefied fluids comprising small chain molecules in chemically patterned nano-channels predict a novel switching from Poiseuille to plug flow along the channel. We also demonstrate behavior akin to the lotus effect for a nanodrop on a chemically patterned substrate. Our results show that one can control and exploit the behavior of fluids at the nanoscale using chemical patterning.
We explore numerically the feasibility of using chemical patterning to control the size and polydispersity of micron-scale drops. The simulations suggest that it is possible to sort drops by size or wetting properties by using an array of hydrophilic stripes of different widths. We also demonstrate that monodisperse drops can be generated by exploiting the pinning of a drop on a hydrophilic stripe. Our results follow from using a lattice Boltzmann algorithm to solve the hydrodynamic equations of motion of the drops and demonstrate the applicability of this approach as a design tool for micoflu…
In this paper, the pinning and depinning mechanism of the contact line during droplet evaporation on chemically stripe-patterned surfaces is numerically investigated using a thermal multiphase lattice Boltzmann (LB) model with liquid-vapor phase change. A local force balance in the context of diffuse interfaces is introduced to explain the equilibrium states of droplets on chemically patterned surfaces. It is shown that, when the contact line is pinned on a hydrophobic-hydrophilic boundary, different contact angles can be interpreted as the variation of the length of the contact line occupied …
Colloids immersed in a critical or near-critical binary liquid mixture and close to a chemically patterned substrate are subject to normal and lateral critical Casimir forces of dominating strength. For a single colloid we calculate these attractive or repulsive forces and the corresponding critical Casimir potentials within mean-field theory. Within this approach we also discuss the quality of the Derjaguin approximation and apply it to Monte Carlo simulation data available for the system under study. We find that the range of validity of the Derjaguin approximation is rather large and that i…
We compare numerical and experimental results exploring the behaviour of liquid drops moving across a surface patterned with hydrophobic and hydrophilic stripes. A lattice Boltzmann algorithm is used to solve the hydrodynamic equations of motion of the drops allowing us to investigate their behaviour as the stripe widths and the wettability contrast are altered. We explain how the motion of the drop is determined by the interplay between the driving force and the variation in surface force as the drop moves between regions of different contact angle and we find that the shape of the drops can …
We investigate contact angle hysteresis on chemically patterned and superhydrophobic surfaces, as the drop volume is quasi-statically increased and decreased. We consider both two, and three, dimensions using analytical and numerical approaches to minimise the free energy of the drop. In two dimensions we find, in agreement with other authors, a slip, jump, stick motion of the contact line. In three dimensions this behaviour persists, but the position and magnitude of the contact line jumps are sensitive to the details of the surface patterning. In two dimensions we identify analytically the a…
Catalytically active Janus particles suspended in solution create gradients in the chemical composition of the solution along their surfaces, as well as along any nearby container walls. The former leads to self-phoresis, while the latter gives rise to chemi-osmosis, providing an additional contribution to self-motility. Chemi-osmosis strongly depends on the molecular interactions between the diffusing chemical species and the wall. We show analytically, using an approximate "point-particle" approach, that by chemically patterning a planar substrate one can direct the motion of Janus particles…
Controlling the spatial distribution of liquid droplets on surfaces via surface energy patterning can be used to control material delivery to specified regions via selective liquid/solid wetting. While studies of the equilibrium shape of liquid droplets on heterogenous substrates exist, much less is known about the corresponding wetting kinetics. We make significant progress towards elucidating details of this topic by studying, via large-scale atomistic simulations, liquid nanodroplets spreading on chemically patterned surfaces. A model is presented for lines of polymer liquid (droplets) on s…
We investigate theoretically the morphology of a thin nematic film adsorbed at flat substrate patterned by stripes with alternating aligning properties, normal and tangential respectively. We construct a simple "exactly-solvable" effective interfacial model where the liquid crystal distortions are accounted for via an effective interface potential. We find that chemically patterned substrates can strongly deform the nematic-air interface. The amplitude of this substrate-induced undulations increases with decreasing average film thickness and with increasing surface pattern pitch. We find a reg…
We study spinodal phase separation in unstable thin liquid films on chemically disordered substrates via simulations of the thin-film equation. The disorder is characterized by immobile patches of varying size and Hamaker constant. The effect of disorder is pronounced in the early stages (amplification of fluctuations), remains during the intermediate stages and vanishes in the late stages (domain growth). These findings are in contrast to the well-known effects of quenched disorder in usual phase-separation processes, viz., the early stages remain undisturbed and domain growth is slowed down …
Chemically patterned surfaces are of significant interest in the context of microfluidic applications. Miniaturization of such devices will eventually lead to structures on the nano-scale. Whereas on the micron scale purely macroscopic descriptions of liquid flow are valid, on the nanometer scale long-ranged inter-molecular interactions, thermal fluctuations such as capillary waves, and finally the molecular structure of the liquid become important. We discuss the most important conceptual differences between flow on chemically patterned substrates on the micron scale and on the nanometer scal…
A mesoscopic continuum model is employed to analyse the transport mechanisms and structure formation during the redistribution stage of deposition experiments where organic molecules are deposited on a solid substrate with periodic stripe-like wettability patterns. Transversally invariant ridges located on the more wettable stripes are identified as very important transient states and their linear stability is analysed. It is found that there exist two different instability modes that result (i) at large ridge volume in the formation of bulges that spill from the more wettable stripes onto the…
Self-phoretic Janus particles move by inducing -- via non-equilibrium chemical reactions occurring on their surfaces -- changes in the chemical composition of the solution in which they are immersed. This process leads to gradients in chemical composition along the surface of the particle, as well as along any nearby boundaries, including solid walls. Chemical gradients along a wall can give rise to chemi-osmosis, i.e., the gradients drive surface flows which, in turn, drive flow in the volume of the solution. This bulk flow couples back to the particle, and thus contributes to its self-motili…
We consider a nematic liquid crystal confined by two parallel flat substrates whose anchoring conditions vary periodically in one lateral direction. Within the Gaussian approximation, we study the effective forces between the patterned substrates induced by the thermal fluctuations of the nematic director. The shear force oscillates as function of the lateral shift between the patterns on the lower and the upper substrates. We compare the strength of this fluctuation-induced lateral force with the lateral van der Waals force arising from chemically structured adsorbed monolayers. The fluctuati…
The instability, dynamics and morphological transitions of patterns in thin liquid films on periodic striped surfaces (consisting of alternating less and more wettable stripes) are investigated based on 3-D nonlinear simulations that account for the inter-site hydrodynamic and surface-energetic interactions. The film breakup is suppressed on some potentially destabilizing nonwettable sites when their spacing is below a characteristic lengthscale of the instability, the upper bound for which is close to the spinodal lengthscale. The thin film pattern replicates the substrate surface energy patt…
We use a Ginzburg-Landau free energy functional to investigate diblock copolymer morphologies when the copolymer melt interacts with one surface or is confined between two chemically patterned surfaces. For temperatures above the order-disorder transition a complete linear response description of the copolymer melt is given, in terms of an arbitrary two-dimensional surface pattern. The appearance of order in the direction parallel to the surface is found as a result of the order in the perpendicular direction. Below the order-disorder point and in a thin-film geometry, our procedure enables th…
We study the normal and lateral effective critical Casimir forces acting on a spherical colloid immersed in a critical binary solvent and close to a chemically structured substrate with alternating adsorption preference. We calculate the universal scaling function for the corresponding potential and compare our results with recent experimental data [Soyka F., Zvyagolskaya O., Hertlein C., Helden L., and Bechinger C., Phys. Rev. Lett., 101, 208301 (2008)]. The experimental potentials are properly captured by our predictions only by accounting for geometrical details of the substrate pattern for…
Recent experiments have measured the critical Casimir force acting on a colloid immersed in a binary liquid mixture near its continuous demixing phase transition and exposed to a chemically structured substrate. Motivated by these experiments, we study the critical behavior of a system, which belongs to the Ising universality class, for the film geometry with one planar wall chemically striped, such that there is a laterally alternating adsorption preference for the two species of the binary liquid mixture, which is implemented by surface fields. For the opposite wall we employ alternatively a…
We investigate the morphology of diblock copolymers in the vicinity of flat, chemically patterned surfaces. Using a Ginzburg-Landau free energy, spatial variations of the order parameter are given in terms of a general two-dimensional surface pattern above the order-disorder transition. The propagation of several surface patterns into the bulk is investigated. The oscillation period and decay length of the surface $q$-modes are calculated in terms of system parameters. We observe lateral order parallel to the surface as a result of order perpendicular to the surface. Surfaces which has a finit…
A nematic liquid crystal in contact with a grating surface possessing an alternating stripe pattern of locally homeotropic and planar anchoring is studied within the Frank--Oseen model. The combination of both chemical and geometrical surface pattern leads to rich phase diagrams, involving a homeotropic, a planar, and a tilted nematic texture. The effect of the groove depth and the anchoring strengths on the location and the order of phase transitions between different nematic textures is studied. A zenithally bistable nematic device is investigated by confining a nematic liquid crystal betwee…
Mixtures of several macromolecular species can lead to the formation of higher-order structures that often display non-ideal mixing behavior. In this work, we propose a minimal model of a quaternary system which considers the formation of a complex via a chemical reaction involving two macromolecular species; the complex may then phase separate from the buffer and undergo a further transition into a gel-like state over time. First, a ternary phase diagram that captures the volume fraction of each species and phases at equilibrium is constructed. Specifically, we investigate how physical parame…
We report experiments investigating the behaviour of micron-scale fluid droplets jetted onto surfaces patterned with lyophobic and lyophilic stripes. The final droplet shape depends on the droplet size relative to that of the stripes. In particular when the droplet radius is of the same order as the stripe width, the final shape is determined by the dynamic evolution of the drop and shows a sensitive dependence on the initial droplet position and velocity. Numerical solutions of the dynamical equations of motion of the drop provide a close quantitative match to the experimental results. This p…
Among the various kinds of effective forces in soft matter, the spatial range and the direction of the so-called critical Casimir force - which is generated by the enhanced thermal fluctuations close to a continuous phase transition - can be controlled and reversibly modified to an uncommonly large extent. In particular, minute temperature changes of the fluid solvent, which provides the near-critical thermal fluctuations, lead to a significant change of the range and strength of the effective interaction among the solute particles. This feature allows one to control, e.g., the aggregation of …
Patterned Substrates Unlock Self-Electrophoretic Phenomenon in Active Janus Microswimmers
Istituto di BioRobotica-Scuola Superiore Sant’Anna（机器人研究所圣安娜高等学院）；Wageningen University & Research（瓦赫宁根大学与研究）；Center for Materials Interfaces, Electron Crystallography, Italian Institute of Technology（意大利理工学院材料界面与电子晶体学中心）
We investigate the effect of chemically patterned surfaces on the morphology of diblock copolymers below the order-disorder transition. Profiles for lamellar phases in contact with one surface, or confined between two surfaces are obtained in the weak segregation limit using a Ginzburg-Landau expansion of the free energy, and treating it with mean-field theory. The periodically patterned surface induces a tilt of the lamellae in order to match the surface periodicity. The lamellae relax from the constrained periodicity close to the surface to the bulk periodicity far from it. The phases we inv…
We model an infinitely long liquid bridge confined between two plates chemically patterned by stripes of same width and different contact angle, where the three-phase contact line runs, on average, perpendicular to the stripes. This allows us to study the corrugation of a contact line in the absence of pinning. We find that, if the spacing between the plates is large compared to the length scale of the surface patterning, the cosine of the macroscopic contact angle corresponds to an average of cosines of the intrinsic angles of the stripes, as predicted by the Cassie equation. If, however, the…
We have discovered an optically uniform type of domain that occurs in Twisted Nematic (TN) cells that are constructed from substrates chemically patterned with stripes via microcontact printing of Self-Assembled Monolayers (SAM); such domains do not occur in TN cells constructed from uniform substrates. In such a cell, the azimuthal anchoring at the substrates is due to the elastic anisotropy of the liquid crystal rather than the conventional rubbing mechanism. A model is presented that predicts the relative stability of the twisted and anomalous states as a function of the material and design…
We show both numerically and analytically that a chemically patterned active pore can act as a micro/nano-pump for fluids, even if it is fore-aft symmetric. This is possible due to a spontaneous symmetry breaking which occurs when advection rather than diffusion is the dominant mechanism of solute transport. We further demonstrate that, for pumping and tuning the flow rate, a combination of geometrical and chemical inhomogeneities is required. For certain parameter values, the flow is unsteady, and persistent oscillations with a tunable frequency appear. Finally, we find that the flow may lose…
A phenomenological mean-field theory is used to investigate the properties of solvent-diluted di-block copolymers (BCP), in which the two BCP components (A and B) form a variety of phases that are diluted by a solvent (S). Using this approach, we model mixtures of di-block copolymers and a solvent and obtained the corresponding critical behavior. In the low solvent limit, we find how the critical point depends on the solvent density. Due to the non-linear nature of the coupling between the A/B and BCP/solvent concentrations, the A/B modulation induces modulations in the polymer-solvent relativ…
The dissipative particle dynamics (DPD) simulation method has been shown to be a promising tool to study self-assembly of soft matter systems. In particular, it has been used to study block copolymer (BCP) self-assembly. However, previous parametrizations of this model are not able to capture most of the rich phase behaviors of block copolymers in thin films nor in directed self-assembly (chemoepitaxy or graphoepitaxy). Here we extend the applicability of the DPD method for BCPs to make it applicable to thin films and directed self-assembly. Our new reparametrization is able to reproduce the b…
In this paper we revisit the problem of a nematic liquid crystal in contact with patterned substrates. The substrate is modelled as a periodic array of parallel infinite grooves of well-defined cross section sculpted on a chemically homogeneous substrate which favors local homeotropic anchoring of the nematic. We consider three cases: a sawtooth, a crenellated and a sinusoidal substrate. We analyse this problem within the modified Frank-Oseen formalism. We argue that, for substrate periodicities much larger than the extrapolation length, the existence of different nematic textures with distinc…
The complicated dynamics of the contact line of a moving droplet on a solid substrate often hamper the efficient modeling of microfluidic systems. In particular, the selection of the effective boundary conditions, specifying the contact line motion, is a controversial issue since the microscopic physics that gives rise to this displacement is still unknown. Here, a sharp interface, continuum-level, novel modeling approach, accounting for liquid/solid micro-scale interactions assembled in a disjoining pressure term, is presented. By following a unified conception (the model applies both to the …
We present several ordering mechanisms in diblock copolymers. For temperatures above the order-disorder temperature and in the weak segregation regime, a linear response theory is presented which gives the polymer density in the vicinity of confining flat surfaces. The surfaces are chemically patterned where different regions attract different parts of the copolymer chain. The surface pattern or template is decomposed into its Fourier modes, and the decay of these modes is analyzed. The persistence of the surface pattern into the disordered bulk is given for several types of patterns (e.g. uni…
