Mechanical model for anisotropic curved interfaces with applications to surfactant-laden liquid-liquid crystal interfaces

A mechanical model for anisotropic curved interfaces, applicable to thermodynamically closed surfactant-laden liquid-liquid crystal interfaces is developed. The model takes into account the mechanical effects due to surface bending and surface tilting (anchoring) and incorporates liquid crystal anisotropy into classical fluid membrane mechanics. In the absence of the aligned liquid crystal, the model converges to the fluid membrane mechanical model, and in the absence of surfactant, it converges to the nematic interface mechanical model. Use of the well-known Helfrich-Rapini-Papoular surface energies leads to the Laplace equation for anisotropic curved interfaces, whose material limits are the vesicle shape equation and the liquid crystal Herring equation. Applications of the model to shape selection in liquid drops embedded in aligned nematic liquid crystals illustrates the competition between anchoring and bending and shows how anisotropic surface tension distorts the droplet and how bending tends to restore the spherical shape. This theory presented in this article shows that the interaction of interfacial anchoring and bending creates new regimes in classical fluid membrane mechanics.     

Shear and dilatational relaxation mechanisms of globular and flexible proteins at the hexadecane/water interface

Proteins adsorbed at fluid/fluid interfaces influence many phenomena: food emulsion and foam stability (Murray et al. Langmuir 2002, 18, 9476 and Borbas et al. Colloids Surf., A 2003, 213, 93), two-phase enzyme catalysis (Cascao-Pereira et al. Biotechnol. Bioeng. 2003, 83, 498; 2002, 78, 595), human lung function (Lunkenheimer et al. Colloids Surf., A 1996, 114, 199; Wustneck et al.; and Banerjee et al. 2000, 15, 14), and cell membrane mechanical properties (Mohandas et al. 1994, 23, 787). Time scales important to these phenomena are broad, necessitating an understanding of the dynamics of biological macromolecules at interfaces. We utilize interfacial shear and dilatational deformations to study the rheology of a globular protein, lysozyme, and a disordered protein, beta-casein, at the hexadecane/water interface. Linear viscoelastic properties are measured using small amplitude oscillatory flow, stress relaxation after a sudden dilatational displacement, and shear creep response to probe the rheological response over broad experimental time scales. Our studies of lysozyme and beta-casein reveal that the interfacial dissipation mechanisms are strongly coupled to changes in the protein structure upon and after adsorption. For beta-casein, the interfacial response is fluidlike in shear deformation and is dominated by interfacial viscous dissipation, particularly at low frequencies. Conversely, the dilatational response of beta-casein is dominated by diffusion dissipation at low frequencies and viscous dissipation at higher frequencies (i.e., when the experimental time scale is faster than the characteristic time for diffusion). For lysozyme in shear deformation, the adsorbed protein layer is primarily elastic with only a weak frequency dependence. Similarly, the interfacial dilatational moduli change very little with frequency. In comparison to beta-casein, the frequency response of lysozyme does not change substantially after washing the protein from the bulk solution. Apparently, it is the irreversibly adsorbed fraction that dominates the dynamic rheological response for lysozyme. Using stress relaxation after a sudden dilatational displacement and shear creep response, the characteristic time of relaxation was found to be 1000 s in both modes of deformation. The very long relaxation time for lysozyme likely results from the formation of a glassy interfacial network. This network develops at high interfacial concentrations where the molecules are highly constrained because of conformation changes that prevent desorption.     

Dynamic rheological characterization of polyamide/modified polyolefin laminates

 In this work dynamic rheological and peel strength measurements on laminates of polyamide and several modified polyolefins were made to evaluate the interfacial compatibilization phenomena. The polyolefins used were a low-density polyethylene, without any treatment and γ-ray irradiated in air, and two copolymers, an ethylene–tert-butyl acrylate–acrylic acid terpolymer and a partially neutralized ethylene–methacrylic acid copolymer containing sodium cations. Multilayer structures containing different amounts of both interfacial surface and volume fraction were studied. Relationships between viscoelastic functions and composition were used to analyze the effect of bulk and surface modification in the polyolefins at the interface with the polyamide. The results show that dynamic rheological measurements of stratified polymers can be used as a tool to investigate interfacial activity in multiphase systems. Received: 2 January 1998/Accepted: 21 March 1998     

Generalized nematostatics

The generalized equations of bulk and interfacial nematostatics in terms of the tensor order parameter are derived using calculus of variations, taking into account long and short range nematic bulk free energies as well as anchoring and saddle-splay surface free energies. A general expression for the surface stress tensor order parameter for a nematic liquid crystal/isotropic fluid (NLC/I) interface has been derived, and found to represent normal, shear, and bending stresses. It is shown that the surface stress tensor is asymmetric. It is also found that anchoring energy contributes to bending and normal stresses, while saddle-splay energy contributes to normal and shear stresses. The rotational identifies governing the bulk and surface stress tensors are derived and used to show that the equations of nematostatics are fully consistent with the general balance equations of polar fluids. The equations presented provide a theoretical framework for solving interfacial problems involving NLCs that is applicable to cases where variations in liquid crystalline order and saddle-splay energy play significant roles.     

Generalized nematostatics

The generalized equations of bulk and interfacial nematostatics in terms of the tensor order parameter are derived using calculus of variations, taking into account long and short range nematic bulk free energies as well as anchoring and saddle-splay surface free energies. A general expression for the surface stress tensor order parameter for a nematic liquid crystal/isotropic fluid (NLC/I) interface has been derived, and found to represent normal, shear, and bending stresses. It is shown that the surface stress tensor is asymmetric. It is also found that anchoring energy contributes to bending and normal stresses, while saddle-splay energy contributes to normal and shear stresses. The rotational identifies governing the bulk and surface stress tensors are derived and used to show that the equations of nematostatics are fully consistent with the general balance equations of polar fluids. The equations presented provide a theoretical framework for solving interfacial problems involving NLCs that is applicable to cases where variations in liquid crystalline order and saddle-splay energy play significant roles.     

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.     

Theoretical model for the wetting of a rough surface

Many applications would benefit from an understanding of the physical mechanism behind fluid movement on rough surfaces, including the movement of water or contaminants within an unsaturated rock fracture. Presented is a theoretical investigation of the effect of surface roughness on fluid spreading. It is known that surface roughness enhances the effects of hydrophobic or hydrophilic behavior, as well as allowing for faster spreading of a hydrophilic fluid. A model is presented based on the classification of the regimes of spreading that occur when fluid encounters a rough surface: microscopic precursor film, mesoscopic invasion of roughness and macroscopic reaction to external forces. A theoretical relationship is developed for the physical mechanisms that drive mesoscopic invasion, which is used to guide a discussion of the implications of the theory on spreading conditions. Development of the analytical equation is based on a balance between capillary forces and frictional resistive forces. Chemical heterogeneity is ignored. The effect of various methods for estimating viscous dissipation is compared to available data from fluid rise on roughness experiments. Methods that account more accurately for roughness shape better explain the data as they account for more surface friction; the best fit was found for a hydraulic diameter approximation. The analytical solution implies the existence of a critical contact angle that is a function of roughness geometry, below which fluid will spread and above which fluid will resist spreading. The resulting equation predicts movement of a liquid invasion front with a square root of time dependence, mathematically resembling a diffusive process.     

The surface tension of a solid at the solid-vacuum interface, an evaluation from adsorption and wall potential calculations

A method for the evaluation of quantities that are experimentally inaccessible such as the surface tension at the solid-vacuum interface and the superficial tension of the fluid in contact with the solid is presented. The approach is based on consideration of an equilibrium of a fluid in solid capillary wherein a balance between surface and capillary forces has been replaced by conceptual alternative interfacial and centrifugal forces. This approach involves the simultaneous numerical solution one the special forms of the Gibbs equation for solid-fluid interface and a generalized Kelvin equation derived earlier. The latter equation takes into account interactions between the solid thick cylindrical wall and confined fluid, this body-body interaction potential has been primarily calculated using the Lennard-Jones (6-12) expression for the atom-atom pair potentials and expressed by hypergeometrical functions having good convergences. All numerical calculations shown here have been performed for the model graphite-argon system at 90 K. Finally, an analysis of the accuracy of the proposed method is considered.     

Nemato-capillarity theory and the orientation-induced Marangoni flow

The macroscopic equations of nemato-capillarity, including the interfacial linear momentum balance equation and the interfacial director torque balance equation, are presented. The interfacial linear momentum balance equation for isotropic fluid-nematic liquid crystals involves the surface divergence of the surface stress tensor. It is shown that the surface stress tensor for isotropic fluid-nematic interfaces is, in most cases of interest, dominated by elastic modes. It is found that the anisotropic elastic contribution to the surface stress tensor gives rise to bending stresses, not observed in interfaces between isotropic fluids. In addition it is found that the anisotropic contribution to the surface elasticity also gives rise to tangential forces. Thus when the director orientation deviates from the easy axis of an isotropic fluidnematic interface and the deviation has surface gradients, an orientation-driven Marangoni flow can exist. The strength of this novel effect is proportional to the anchoring energy of the interface, and the direction of flow is from low energy regions towards high energy regions, that is, from regions where the director is aligned along the easy axis towards regions where the director deviates from the easy axis.     

Thermodynamics of soft anisotropic interfaces

The Gibbs-Duhem equation for interfaces between nematic liquid crystals and isotropic fluids is formulated and shown to be a generic equation for soft anisotropic surfaces. The one-to-one correspondence between the nematic and crystalline surface Gibbs-Duhem equations is established. Consistency between the surface Gibbs-Duhem equation and the classical equations of interfacial nematostatics is shown. Using a phase space that takes into account thermodynamics, liquid crystalline order, and geometric variables, the generalized nematic surface Gibbs-Duhem equation reveals the presence of couplings between shape, adsorption, temperature, and average molecular orientation. Merging the thermodynamic analysis with nematostatics results in a model for morphactancy, that is, adsorption-induced interfacial shape selection. The specific roles of gradient bulk Frank elasticity, interfacial tension, and anchoring energy are elucidated by analyzing particular paths in the thermodynamic-geometric phase space.     

Model filled rubber. II. Particle composition dependence of suspension rheology

Monodisperse size colloidal particles varying in chemical composition were synthesized by emulsifier‐free emulsion polymerization. Using a stress‐controlled rheometer, the rheological behavior of colloidal suspensions in a low molecular weight liquid polysulfide was investigated. All suspensions exhibited shear thinning behavior. The shear viscosity, dynamic moduli, and yield stress increased as interactions between particles and matrix increased. The rheological properties associated with network buildup in the suspensions were sensitively monitored by a kinetic recovery experiment. We propose that interfacial interactions by polar and hydrogen bonding between particles and matrix strongly promote affinity of matrix polymer to the filler particles, resulting in adsorption or entanglement of polymer chains on the filler surface. A network structure was formed consisting of particles with an immobilized polymer layer on the particle surface with each particle floc acting as a temporary physical crosslinking site. As the interfacial interaction increases, the adsorbed layer thickness on the filler particles, hence, the effective particle volume fraction, increases. As a result, the rheological properties were enhanced in the order PS < PMMA < PSVP. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 815–824, 1999     

Dynamics of droplet motion under electrowetting actuation

The static shape of droplets under electrowetting actuation is well understood. The steady-state shape of the droplet is obtained on the basis of the balance of surface tension and electrowetting forces, and the change in the apparent contact angle is well characterized by the Young-Lippmann equation. However, the transient droplet shape behavior when a voltage is suddenly applied across a droplet has received less attention. Additional dynamic frictional forces are at play during this transient process. We present a model to predict this transient behavior of the droplet shape under electrowetting actuation. The droplet shape is modeled using the volume of fluid method. The electrowetting and dynamic frictional forces are included as an effective dynamic contact angle through a force balance at the contact line. The model is used to predict the transient behavior of water droplets on smooth hydrophobic surfaces under electrowetting actuation. The predictions of the transient behavior of droplet shape and contact radius are in excellent agreement with our experimental measurements. The internal fluid motion is explained, and the droplet motion is shown to initiate from the contact line. An approximate mathematical model is also developed to understand the physics of the droplet motion and to describe the overall droplet motion and the contact line velocities.     

Surface tension and capillary waves at the nematic-isotropic interface in ternary mixtures of liquid crystal, colloids, and impurities

In mixtures of thermotropic liquid crystals with spherical poly(methyl methacrylate) particles, self-supporting networklike structures are formed during slow cooling past the isotropic-to-nematic phase transition. Experimental results support the hypothesis that a third component, alkane remnants slowly liberated from the particles, plays a crucial role. A theoretical model, based on the phenomenological Landau-de Gennes, Carnahan-Starling, and hard-sphere crystal theories, is developed to describe the continuous phase separation in a ternary nematic-impurity-colloid mixture. The interfacial tension and the dispersion relation of the surface modes of the nematic-isotropic interface are determined. The colloids decrease the interfacial tension and the damping rate of surface waves, whereas impurities act in an opposite way. This should strongly influence the formation of abovementioned networklike structures and could help explain some of their rheological properties.     

气相二氧化硅填充极性低聚物的界面与流变

气相二氧化硅(FS)/低聚物纳米复合材料应用广泛于涂料、胶黏剂、锂离子电池、液体防弹衣等诸多领域.然而,极性低聚物与FS表面相互作用复杂,FS/低聚物复合材料(ONCs)的流变响应多种多样.如何实现ONCs流变行为调控,是长期困扰工业界的难题.本文详细总结了FS在ONCs领域的应用,将FS粒子间相互作用与ONCs流变性质相关联,综述ONCs界面层结构的表征、调控手段及界面层与流变行为的关系.结合本课题组对FS/极性低聚物体系界面及流变行为的研究成果,提出未来ONCs领域的2个重要方向,即研究界面结构与粒子-极性低聚物相互作用间的关系,并通过界面设计实现对纳米粒子/极性低聚物复合材料的流变行为的精确调控.     

Dynamics of encapsulation and controlled release systems based on water-in-water emulsions: negligible surface rheology

A nonequilibrium thermodynamic model based on the interfacial transport phenomena (ITP) formalism was used to study deformation-relaxation behavior of water-in-water emulsions. The ITP formalism allows us to describe all water-in-water emulsions with one single theory. Phase-separated biopolymer solutions, hydrogel beads, liposomes, polymersomes, colloidosomes, and aqueous polymer microcapsules are all limiting cases of this general theory with respect to rheological behavior of the bulk phases and interfaces. Here we have studied two limiting cases of the general theory, with negligible surface rheology: phase-separated biopolymer solutions and hydrogel beads. We have determined the longest relaxation time for a small perturbation of the interfaces in these systems. Parameter maps were calculated which can be used to determine when surface tension, bending rigidity, permeability, and bulk viscoelasticity dominate the response of a droplet or gel bead. In phase-separated biopolymer solutions and dispersions of hydrogel beads six different scaling regimes can be identified for the relaxation time of a deformation. Hydrogel beads may also have a damped oscillatory response to a deformation. The results presented here provide new insight into the complex dynamics of water-in-water emulsions and also suggest new experiments that can be used to characterize the interfacial properties of these systems.     

Ultra-sensitive imaging and interfacial analysis of patterned hydrophilic SAM surfaces using energy dissipation chemical force microscopy

Energy dissipation chemical force microscopy has been used to analyze the dissipative properties of chemically similar regions of hydroxyl- and carboxyl-terminated SAMs on gold with a hydroxyl-terminated tip. Energy dissipation imaging quantitatively isolates dissipative interfacial interactions from topography, producing a significantly more informative image than phase imaging. Also, energy dissipation force curves probed the rheological properties of the tip-sample interaction. Viscosity of the confined water increased slightly over that of the bulk, and SAM deformation was found to have a longer retardation time than restructuring of interfacial ions and solvent during tip-sample contact.     

Sorbitan tristearate layers at the air/water interface studied by shear and dilatational interfacial rheology

The shear and dilatational rheology of condensed interfacial layers of the water-insoluble surfactant sorbitan tristearate at the air/water interface is investigated. A new interfacial shear rheometer allows measurements in both stress- and strain-controlled modes, providing comprehensive interfacial rheological information such as the interfacial dynamic shear moduli, the creep response to a stress pulse, the stress relaxation response to a strain step, or steady shear curves. Our experiments show that the interfacial films are both viscoelastic and brittle in nature and subject to fracture at small deformations, as was supported by in-situ Brewster angle microscopy performed during the rheological experiments. Although any large-deformation test is destructive to the sample, it is still possible to study the linear viscoelastic regime if the deformations involved are controlled carefully. Complementary results for the dilatational rheology in area step compression/expansion experiments are reported. The dilatational behavior is predominantly elastic throughout the frequency spectrum measured, whereas the layers exhibit generalized Maxwell behavior in shear mode within a deformation frequency regime as narrow as two decades, indicating the presence of additional relaxation mechanisms in shear as opposed to expansion/compression. If the transient rheological response from stress relaxation experiments is considered, then the data can be described well with a stretched exponential model both in the shear and dilatational deformations.     

The ring puckering potential function of trimethylene sulfide and trimethylene selenide

The rotational constants A,B and C are functions of the vibrational quantum numbers for the out-of-plane bending modes of trimethylene sulfide and trimethylene selenide. Infrared and microwave spectroscopy have been used to determine the dependence between these parameters. The height and shape of the barrier arising from combination of the ring bending modes is also determined. CNDO/2 calculations are used to predict the position of the hydrogen atoms of the methylene groups in trimethylene sulfide and trimethylene selenide. The four-membered rings are non-planar for several vibrational states of the ring bending modes.     

Surface tension correlation for pure polar fluids by a new molecular model and SRK equation of state

In this work, a new model based on molecular thermodynamic was presented to correlate the surface tension of pure polar liquids. This model was developed based on the Davis theory. According to this theory, the surface tension is defined as a function of radial distribution function (RDF) and potential function (PF) as well. The proposed model includes three additive terms; hard sphere, dispersion and polar interactions. The RDF of Kolafa equation of state and Dirac delta function as a PF were used for hard sphere interaction. The RDF expression of Xu and Hu was considered for both dispersion and polar interactions. The presented model has two adjustable parameters, size and energy, which were obtained by optimization of an objective function for each pure fluid. This proposed approach was used for 19 pure polar fluids divided into 6 groups; organic acids, alcohols, ketones, ethers, aldehydes, and water. The average absolute deviation percent (AAD%) obtained for 19 fluids are 0.74. Also the surface tension of these 19 fluids was calculated by the use of SRK EOS and Sugden empirical formula in two cases. In case 1, Sugden's Parachor was calculated from Hugill and van Welsenes correlation and in case 2, it was obtained by optimization of an objective function for each component. The values of AAD% are 43.544 and 2.281 for cases 1 and 2, respectively. These results show the new model, which includes two adjustable parameters, can correlate the surface tension of the pure polar liquids with a high accuracy.