Viscoelastic theory for nematic polymer interfaces

A macroscopic theory for the dynamics of compressible nematic polymer‐viscous fluid interfaces is developed from first principles. The theory is used to define and characterize the basic interfacial viscoelastic material properties of the ordered interfaces. The theory is based on a decomposition of the kinematic fields and nematic tensor order parameter that takes into account the symmetry breaking of the interface. The interfacial rate of entropy production used to identify the interfacial viscoelastic modes is given in terms of surface rate of deformation tensor and the surface Jaumann derivative of the tangential component nematic tensor order parameter. The derived surface viscous stress tensor is asymmetric and thus describes surface flow‐induced changes in the tensor order parameter. Consistency with the Boussinesq surface fluid appropriate for Newtonian interfaces is established. The interfacial material functions are identified as the dynamic surface tension, the interfacial dilational viscosities, and the interfacial shear viscosities. The interfacial material functions depend on the surface tensor order parameter and as a consequence anisotropy is their characteristic feature. Two characteristic interfacial tensions and two dilational viscosities are predicted depending on the director orientation. In addition six interfacial shear viscosities arise as the directors sample the velocity, velocity gradient, and vorticity directions. Finally the theory provides for the necessary theoretical tools needed to describe the interfacial dynamics of nematic polymer interfaces, such as capillary instabilities, Marangoni flows, and wetting phenomena.     

Fluctuating Interfaces in Liquid Crystals

Summary: We review and compare recent work on the properties of fluctuating interfaces between isotropic and nematic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard rods with aspect ratio 15:1, and the fluctuation spectrum of interface positions (the capillary wave spectrum) has been analyzed. In addition, the capillary wave spectrum has been calculated analytically within the Landau-de Gennes theory. The theory predicts that the interfacial fluctuations can be described in terms of a wave vector dependent interfacial tension, which is anisotropic at small wavelengths (stiff director regime) and becomes isotropic at large wavelengths (flexible director regime). After determining the elastic constants in the nematic phase, theory and simulation can be compared quantitatively. We obtain good agreement for the stiff director regime. The crossover to the flexible director regime is expected at wavelengths of the order of several thousand particle diameters, which was not accessible to our simulations.     

Nematic-isotropic interfacial tension anisotropy of a calamitic lyotropic liquid crystal

In a planar oriented sample of a calamitic nematic lyotropic system (mixture of sodium lauryl sulphate/water/decanol), isotropic pretransitional domains appear at the nematic to isotropic transition. The domains are oblong in shape with the long axis along the orientational direction. We show experimental evidence that this oblong shape is determined by the nematic-isotropic interfacial tension anisotropy. Two uniparametric models of simple angular dependences for the interfacial tension are tested. Using the differential system obtained from the Young-Laplace condition at the nematic-isotropic interface, the domain shape can be numerically calculated for each value of the interfacial tension anisotropy. By processing the values of the transmitted light through both an isolated isotropic domain and its surrounding nematic zone, we obtain the anisotropy of the interfacial tension as the main fitting parameter. An estimation of the ratio of the extreme values for the interfacial tension is given.     

Capillary waves in a colloid-polymer interface

The structure and the statistical fluctuations of interfaces between coexisting phases in the Asakura-Oosawa model [J. Chem. Phys. 22, 1255 (1954)] for a colloid-polymer mixture are analyzed by extensive Monte Carlo simulations. We make use of a recently developed grand canonical cluster move with an additional constraint stabilizing the existence of two interfaces in the (rectangular) box that is simulated. Choosing very large systems, of size L x L x D with L=60 and D=120, measured in units of the colloid radius, the spectrum of capillary wave-type interfacial excitations is analyzed in detail. The local position of the interface is defined in terms of a (local) Gibbs surface concept. For small wave vectors capillary wave theory is verified quantitatively, while for larger wave vectors pronounced deviations show up. When one analyzes the data in terms of the concept of a wave vector-dependent interfacial tension, a monotonous decrease of this quantity with increasing wave vector is found. Limitations of our analysis are critically discussed.     

Molecular dynamics study of the n-hexane-water interface: towards a better understanding of the liquid-liquid interfacial broadening

By molecular dynamics simulations, we have studied the hydrophilic-hydrophobic interface between water and n-hexane liquid phases. For all temperatures studied our computed interfacial tension agrees very well with the experimental value. However, the interfacial width calculated from capillary wave theory systematically overestimates the width obtained from fitting either the total density or composition profile. We rationalize the applicability of capillary wave theory for our system by reconsidering the usual value taken for the correlation length. This is motivated by the presence of order at the interface. Possible implications for recent experimental studies on the structure of model alkane-water interfaces are discussed, including the significance of the intrinsic width parameter.     

Diamagnetic orientation of a fluid of hard thin disks and anisotropy of the water diffusivity in the nematic phase of a suspension of clay platelets

Monte Carlo simulations of the diamagnetic orientation of a fluid of hard thin disks in a magnetic field are presented. The particle density and magnetic field dependences of the eigenvalues of the order parameter tensor are calculated in the presence of a wall which promotes nematic order in a definite direction. The existence of a paranematic region is confirmed, and the approach to the Langevin regime at low densities in the paranematic regime is examined. A relationship between the eigenvalues of the tensor and the anisotropy of water diffusivity in the nematic phase of a colloidal suspension is proposed. This permits a comparison between the Monte Carlo simulations and diffusion-weighted magnetic resonance imaging, which shows consistency with the experimental data.     

Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Nematic-isotropic interfaces exhibit novel dynamics due to anchoring of the liquid crystal molecules on the interface. The objective of this study is to demonstrate the consequences of such dynamics in the flow field created by an elongated nematic drop retracting in an isotropic matrix. This is accomplished by two-dimensional flow simulations using a diffuse-interface model. By exploring the coupling among bulk liquid crystal orientation, surface anchoring and the flow field, we show that the anchoring energy plays a fundamental role in the interfacial dynamics of nematic liquids. In particular, it gives rise to a dynamic interfacial tension that depends on the bulk orientation. Tangential gradient of the interfacial tension drives a Marangoni flow near the nematic-isotropic interface. Besides, the anchoring energy produces an additional normal force on the interface that, together with the interfacial tension, determines the movement of the interface. Consequently, a nematic drop with planar anchoring retracts more slowly than a Newtonian drop, while one with homeotropic anchoring retracts faster than a Newtonian drop. The numerical results are consistent with prior theories for interfacial rheology and experimental observations.     

Phenomenological theory of textured mesophase polymers in weak flows

A macroscopic viscoelastic model for incompressible, isothermal, homogeneous lyotropic mesophases exhibiting the nematic polydomain texture is presented. Under equilibrium static conditions the model describes a three dimensional tessellation, where each region or nematic domain has a characteristic size and orientation, and where the polydomain texture has a random orientation. Close form expressions that define the characteristic texture size and the number of randomly oriented domains are given. When subjecting the model lyotropic liquid crystalline polymer displaying the polydomain texture to a steady rectilinear shear flow, the predicted characteristic texture size decreases with increasing shear rates. The power law scaling relations of texture size with shear rate are in excellent agreement with the experimental measurements. The steady shear flow orientation predictions, characterized by a positive shear dependent alignment angle and a low orientation, are in agreement with experimental data.     

Interfaces in polymer blends

We investigate the structure and thermodynamics of interfaces in dense polymer blends using Monte Carlo (MC) simulations and self‐consistent field (SCF) calculations. For structurally symmetric blends we find quantitative agreement between the MC simulations and the SCF calculations for excess quantities of the interface (e.g., interfacial tension or enrichment of copolymers at the interface). However, a quantitative comparison between profiles across the interface in the MC simulations and the SCF calculations has to take due account of capillary waves. While the profiles in the SCF calculations correspond to intrinsic profiles of a perfectly flat interface the local interfacial position fluctuates in the MC simulations. We test this concept by extensive Monte Carlo simulations and study the cross‐over between “intrinsic” fluctuations which build up the local profile and capillary waves on long (lateral) length scales. Properties of structurally asymmetric blends are exemplified by investigating polymers of different stiffness. At high incompatibilities the interfacial width is not much larger than the persistence length of the stiffer component. In this limit we find deviations from the predictions of the Gaussian chain model: while the Gaussian chain model yields an increase of the interfacial width upon increasing the persistence length, no such increase is found in the MC simulations. Using a partial enumeration technique, however, we can account for the details of the chain architecture on all length scales in the SCF calculations and achieve good agreement with the MC simulations. In blends containing diblock copolymers we investigate the enrichment of copolymers at the interface and the concomitant reduction of the interfacial tension. At weak segregation the addition of copolymers leads to compatibilization. At high incompatibilities, the homopolymer‐rich phase can accommodate only a small fraction of copolymer before the copolymer forms a lamellar phase. The analysis of interfacial fluctuations yields an estimate for the bending rigidity of the interface. The latter quantity is important for the formation of a polymeric microemulsion at intermediate segregation and the consequences for the phase diagram are discussed.     

Computational modelling of nematic phase ordering by film and droplet growth over heterogeneous substrates

This paper presents a computational study of defect nucleation associated with the kinetics of the isotropic‐to‐nematic phase ordering transition over heterogeneous substrates, as it occurs in new liquid crystal biosensor devices, based on the Landau–de Gennes model for rod‐like thermotropic nematic liquid crystals. Two regimes are identified due to interfacial tension inequalities: (i) nematic surface film nucleation and growth normal to the heterogeneous substrate, and (ii) nematic surface droplet nucleation and growth. The former, known as wetting regime, leads to interfacial defect shedding at the moving nematic‐isotropic interface. The latter droplet regime, involves a moving contact line, and exhibits two texturing mechanisms that also lead to interfacial defect shedding: (a) small and large contact angles of drops spreading over a heterogeneous substrate, and (b) small drops with large curvature growing over homogeneous patches of the substrate. The numerical results are consistent with qualitative defect nucleation models based on the kinematics of the isotropic–nematic interface and the substrate–nematic–isotropic contact line. The results extend current understanding of phase ordering over heterogeneous substrates by elucidating generic defect nucleation processes at moving interfaces and moving contact lines.     

Nematic-amorphous polymer interfaces in the presence of a compatibilizer

We introduce and apply a variant of a dynamic self-consistent field simulation in two dimensions to predict the structure of interfaces between a nematic and an amorphous polymer compatibilized by a diblock copolymer. First, we investigate the effect of the nematic order on the polymer polymer interface without compatibilizer. Then we include the compatibilizer and consider two interfacial setups previously used in experiments, i.e., the bilayer setup and the trilayer setup. In the bilayer setup the diblock copolymer is mixed into the amorphous homopolymer and migrates to the interface in the course of the simulation forming a layered structure. We compare the amount of copolymer at the interface for initial concentrations of the copolymer below and above the critical micelle concentration. In the trilayer setup the initial thickness of the diblock copolymer is varied. The resulting interfacial morphology evolves in the competition between the lamellar structure induced by the interface and a micellar structure, which is intrinsic to the copolymer.     

Preparation of microscopic and planar oil-water interfaces that are decorated with prescribed densities of insoluble amphiphiles

Langmuir monolayers (monolayers of insoluble molecules formed at the surface of water), and associated Langmuir-Blodgett/Schaefer monolayers prepared by transfer of Langmuir films to the surfaces of solids, are widely used in studies aimed at understanding the physicochemical properties of biological and synthetic molecules at interfaces. In this article, we report a general and facile procedure that permits transfer of Langmuir monolayers from the surface of water onto microscopic and planar interfaces between oil and aqueous phases. In these experiments, a metallic grid supported on a hydrophobic solid is used to form oil films with thicknesses of 20 mum and interfacial areas of 280 mum x 280 mum. Passage of the supported oil films through a Langmuir monolayer is shown to lead to quantitative transfer of insoluble amphiphiles onto the oil-water interfaces. The amphiphile-decorated oil-water interfaces hosted within the metallic grids (i) are approximately planar, (ii) are sufficiently robust mechanically so as to permit further characterization of the interfaces outside of the Langmuir trough, (iii) can be prepared with prescribed and well-defined densities of amphiphiles, and (iv) require only approximately 200 nL of oil to prepare. The utility of this method is illustrated for the case of the liquid crystalline oil 4-pentyl-4'-cyanobiphenyl (5CB). Transfer of monolayers of either dilauroyl- or dipalmitoylphosphatidylcholine (DLPC and DPPC, respectively) to the nematic 5CB-aqueous interface is demonstrated by epifluorescence imaging of fluorescently labeled lipid and polarized light imaging of the orientational order within the thin film of nematic 5CB. Interfaces prepared in this manner are used to reveal key differences between the density-dependent phase properties of DLPC and DPPC monolayers formed at air-water as compared to that of nematic 5CB-aqueous interfaces. The methodology described in this article should be broadly useful in advancing studies of the interfacial behavior of synthetic and biological molecules at liquid-liquid interfaces.     

Dynamics of liquid interfaces under various types of external perturbations

Dynamic interfacial parameters are the key properties of interfaces in many modern technologies and can be studied in various ways. For applications like foams and emulsions, the dynamics of adsorption and the dilational and shear rheology of liquid–fluid interfaces are investigated most frequently. This work gives an insight into recently developed new experimental approaches, such as fast capillary pressure tensiometry for growing and oscillating drops. These experiments are presented in comparison to more classical techniques like drop profile tensiometry and capillary wave damping. Progress in these experiments based on generated interfacial perturbations can be expected only by a close link to respective CFD simulations. We also present the state of the art of CFD simulations, which have reached a high level during the last decade and provide a substantial basis for dynamic interfacial experiments.     

Molecular dynamics simulation of phase separating binary liquids in cylindrical Couette flow

We use molecular dynamics simulations to study phase separation of a 50:50 (by volume) fluid mixture in a confined and curved (Taylor-Couette) geometry, consisting of two concentric cylinders. The inner cylinder may be rotated to achieve a shear flow. In nonsheared systems we observe that, for all cases under consideration, the final equilibrium state has a stacked structure. Depending on the lowest free energy in the geometry the stack may be either flat, with its normal in the z direction, or curved, with its normal in the r or theta direction. In sheared systems we make several observations. First, when starting from a prearranged stacked structure, we find that sheared gradient and vorticity stacks retain their character for the durations of the simulation, even when another configuration is preferred (as found when starting from a randomly mixed configuration). This slow transition to another configuration is attributed to a large free energy barrier between the two states. In case of stacks with a normal in the gradient direction, we find interesting interfacial waves moving with a prescribed angular velocity in the flow direction. Because such a wave is not observed in simulations with a flat geometry at similar shear rates, the curvature of the wall is an essential ingredient of this phenomenon. Second, when starting from a randomly mixed configuration, stacks are also observed, with an orientation that depends on the applied shear rate. Such transitions to other orientations are similar to observations in microphase separated diblock copolymer melts. At higher shear rates complex patterns emerge, accompanied by deviations from a homogeneous flow profile. The transition from steady stacks to complex patterns takes place around a shear rate 1/tau(dv), where tau(dv) is the crossover time from diffusive to viscous dominated growth of phase-separated domains, as measured in equilibrium simulations.     

Anisotropic interfacial free energies of the hard-sphere crystal-melt interfaces

We present a reliable method to define the interfacial particles for determining the crystal-melt interface position, which is the key step for the crystal-melt interfacial free energy calculations using capillary wave approach. Using this method, we have calculated the free energies gamma of the fcc crystal-melt interfaces for the hard-sphere system as a function of crystal orientations by examining the height fluctuations of the interface using Monte Carlo simulations. We find that the average interfacial free energy gamma(0) = 0.62 +/- 0.02k(B)T/sigma(2) and the anisotropy of the interfacial free energies are weak, gamma(100) = 0.64 +/- 0.02, gamma(110) = 0.62 +/- 0.02, gamma(111) = 0.61 +/- 0.02k(B)T/sigma(2). The results are in good agreement with previous simulation results based on the calculations of the reversible work required to create the interfaces (Davidchack and Laird, Phys. Rev. Lett. 2000, 85, 4571). In addition, our results indicate gamma(100) > gamma(110) > gamma(111) for the hard-sphere system, similar to the results of the Lennard-Jones system.     

Computational modelling of nematic phase ordering by film and droplet growth over heterogeneous substrates

This paper presents a computational study of defect nucleation associated with the kinetics of the isotropic-to-nematic phase ordering transition over heterogeneous substrates, as it occurs in new liquid crystal biosensor devices, based on the Landau-de Gennes model for rod-like thermotropic nematic liquid crystals. Two regimes are identified due to interfacial tension inequalities: (i) nematic surface film nucleation and growth normal to the heterogeneous substrate, and (ii) nematic surface droplet nucleation and growth. The former, known as wetting regime, leads to interfacial defect shedding at the moving nematic-isotropic interface. The latter droplet regime, involves a moving contact line, and exhibits two texturing mechanisms that also lead to interfacial defect shedding: (a) small and large contact angles of drops spreading over a heterogeneous substrate, and (b) small drops with large curvature growing over homogeneous patches of the substrate. The numerical results are consistent with qualitative defect nucleation models based on the kinematics of the isotropic-nematic interface and the substrate-nematic-isotropic contact line. The results extend current understanding of phase ordering over heterogeneous substrates by elucidating generic defect nucleation processes at moving interfaces and moving contact lines.     

Monte Carlo simulation of equilibrium reactions at modified vapor-liquid interfaces

The equilibrium conversion of a chemical reaction is known to be affected by its local environment. Various factors may alter reaction equilibria, including shifts in pressure or temperature, solvation, adsorption within porous materials, or the presence of an interface. Previously, reactive Monte Carlo simulations have been used to predict the equilibrium behavior of chemical reactions at vapor-liquid interfaces. Here, a route is tested for tuning the interfacial conversion of a Lennard-Jones dimerization reaction by adding surfactants to the vapor-liquid interface. Several temperatures are explored as well as several different surfactant models. Even with the addition of a small concentration of surfactants, the simulations predict significant shifts in the conversion at the interface. In general, the shifts in the conversion tend to be related to the values of the interfacial tension.     

Surface-active particles with microstructured surfaces

Interfaces adsorbing solid particles have recently attracted great attentions in the field of materials science, because they are useful as templates of well-ordered particle arrays or of microstructured hollow spheres. The solid particles are adsorbed at the interfaces and form self-assembled structures when the particles have suitable wettability to both fluids. Here, we show theoretically how the microstructure on the particle surface affects their adsorption properties. The physical properties of the interface adsorbing a particle will be described with consideration for surface area magnification due to the microstructure. The microstructure on the surface changes drastically the wettability and the equilibrium position of the adsorbed particle and prevents the particle from adsorption at the interface. The range of the interfacial tensions at which the particle is adsorbed becomes narrower with the increase of the magnification. On the other hand, the particle which is partially covered with the microstructured surface is adsorbed firmly at the interface in an oriented state. We should consider not only the interfacial tensions but also the surface structure to control the adsorption behavior of the particle.