Analysis of tear film rupture: effect of non-Newtonian rheology

We investigate the rupture mechanism of a precorneal thin mucus coating sandwiched between the aqueous tear film and the corneal epithelial surface with a monolayer of surfactant overlying the aqueous layer. The Ostwald constitutive relation is employed to model mucus and a linear equation of state describing the relationship between surface tension and surfactant concentration is adopted. Three nonlinear coupled evolution equations governing the transport of surfactant, mucus, and total liquid layer thicknesses, based on lubrication theory and a perturbation expansion technique, have been derived. The resulting equations are solved numerically in order to explore the influence of the rheological properties of mucus, aqueous-mucus thickness ratio, aqueous-mucus interfacial tension, Marangoni number, and surfactant concentration on both the onset of instability and tear film evolution in the presence of van der Waals interactions, which could rupture the tear film. Our results reveal that the influence of rheological properties, aqueous-mucus thickness ratio, and interfacial tension on the time required for film rupture can be significant and varies considerably, depending on the magnitude of the Hamaker constants governing the strength of the van der Waals forces.     

A metastable van der waals gel: transitioning from weak to strong attractions

Here we describe a method to create gels where the gel point is decoupled from gel elastic properties. Working with charge stabilized polystyrene latex particles with diameters, D, of 508-625 nm at ionic strengths of 0.1-1 M, the gel volume fraction is varied from 0.10-0.35 through the addition of less than monolayer coverage of hexaethylene glycol monododecyl ether (C6E12). At each surfactant concentration, the gel volume fraction depends on the background ionic strength. The changes in gel point with surfactant concentration suggest the strength of interparticle attraction decreases with increasing surfactant concentration. These changes are not reflected in the gel moduli, which are independent of surfactant concentration and ionic strength. We propose a model to describe this behavior based on gelation due to localization in a shallow truncated van der Waals minimum produced by the surfactant acting as a steric stabilizing layer. The surfactant remains mobile on the surface. Below the gel volume fraction, the time particles spend in the truncated well are not sufficient for the surfactant to be displaced such that the particles can only sample the shallow well. Above the gel volume fraction, particles are localized in the truncated van der Waals minima for sufficient periods of time to displace the surfactant layers with the result being that the particles fall into a primary van der Waals minimum. The result is gel points sensitive to surfactant concentration but moduli that are independent of the gel volume fraction.     

The standard free energy of surfactant adsorption at air/water and oil/water interfaces: Theoretical vs. empirical approaches

The standard free energy of surfactant adsorption represents the work of transfer of a surfactant molecule from the bulk of solution to an infinitely diluted adsorption layer. This quantity can be determined by non-linear fits of surface-tension isotherms with the help of a theoretical model of adsorption. Here, the models of Frumkin, van der Waals and Helfand-Frisch-Lebowitz are applied, and the results are compared. Irrespective of the differences between these models, they give close values for the standard free energy. The results from the theoretical approach are compared with those from the most popular empirical approach. The latter gives values of the standard free energy, which are considerably different from the respective true values, with c.a. 10 kJ/mol for nonionic surfactants, and with c.a. 20 kJ/mol for ionic surfactants. These differences are due to contributions from interactions between the molecules in dense adsorption layers. It is concluded that the true values of the standard free energy can be determined with the help of an appropriate theoretical model. For the processed sets of data, the van der Waals model gives the best results, especially for the determination of the standard adsorption enthalpy and entropy from the temperature dependence of surface tension. The results can be useful for the development of a unified approach to the thermodynamic characterization of surfactants.     

Analysis of dynamic surface tension of tetraethyleneglycol monooctyl ether at air/water interface

The dynamic surface tension of the aqueous solutions of tetraethyleneglycol monooctyl ether (C₈E₄), a nonionic surfactant, was measured at different concentrations and temperatures. Present data at 298.15 K clearly indicate that the mechanism of adsorption is purely diffusion controlled at low concentrations (0.1~0.4 mmol/kg), and there is a switchover in adsorption mechanism to the mixed diffusion-kinetic control at higher concentrations. The calculated activation energies increase with concentration, and thus, with surface density, but decrease with temperature. The magnitude of activation energy and its increase with surface density suggest that the barrier is due to the free surface site formation by overcoming mainly the attractive van der Waals forces between the chain of adsorbed C₈E₄ molecules.     

用DVR方法研究Ar-HF和Ar-DF的振转光谱

本文用离散变量表示(DVR)方法研究了Ar-HF和Ar-DF体系的振转光谱。对这两个体系的已观测到的振转能级, 用DVR方法得到的计算值与实验结果十分吻合, 误差一般小于0.1cm^-^1, 最大偏差为0.24cm^-^1对Ar-HF的(1113)态。该研究结果与Hutson等用耦合孔道法得到的计算结果基本一致, 但对(3210)振动能级和对(3002)-(3110)态的能级分裂值, 本文计算结果更接近观测值。     

Anisotropic adsorption of molecular assemblies on crystalline surfaces

Orientational order of surfactant micelles and proteins on crystalline templates has been observed but, given that the template unit cell is significantly smaller than the characteristic size of the adsorbate, this order cannot be attributed to lattice epitaxy. We interpret the template-directed orientation of rodlike molecular assemblies as arising from anisotropic van der Waals interactions between the assembly and crystalline surfaces where the anisotropic van der Waals interaction is calculated using the Lifshitz methodology. Provided the assembly is sufficiently large, substrate anisotropy provides a torque that overcomes rotational Brownian motion near the surface. The probability of a particular orientation is computed by solving a Smoluchowski equation that describes the balance between van der Waals and Brownian torques. Torque aligns both micelles and protein fibrils; the interaction energy is minimized when the assembly lies perpendicular to a symmetry axis of a crystalline substrate. Theoretical predictions agree with experiments for both hemi-cylindrical micelles and protein fibrils adsorbed on graphite.     

Van der Waals surface graphs and molecular shape

A van der Waals surface graph is the graph defined on a van der Waals surface by the intersections of the atomic van der Waals spheres. A van der Waals shape graph has a vertex for each atom with a visible face on the van der Waals surface, and edges between vertices representing atoms with adjacent faces on the van der Waals surface. These are discrete invariants of three‐dimensional molecular shape. Some basic properties of van der Waals surface graphs are studied, including their relationship with the Voronoi diagram of the atom centres, and a class of molecular embeddings is identified for which the dual of the van der Waals surface graph coincides with the van der Waals shape graph. This revised version was published online in July 2006 with corrections to the Cover Date.     

Film drainage between two surfactant-coated drops colliding at constant approach velocity

The drainage of the intervening continuous phase film between two drops approaching each other at constant velocity under the influence of insoluble surfactant is investigated. The mathematical model to be solved is a coupled pair of fourth-order nonlinear partial differential equations which arise from the relationships governing the evolution of the film thickness and the surfactant interfacial concentration in the lubrication approximation. We adopt a simplified approach which uses lubrication theory to describe the flow within the drop, marking a departure from the conventional framework in which Stokes flow is assumed. When the model is solved numerically together with the relevant initial and boundary conditions, the results obtained are compared with those found in the literature using the "boundary integral" method to solve for the flow in the drop phase. The close agreement between the results inspires confidence in the predictions of the simplified approach adopted. The analysis on the effect of insoluble surfactant indicates that its presence retards the drainage of the film: The fully immobile interface limit is recovered even in the presence of a small amount of surfactant above a critical concentration; film rupture is either prolonged or prevented. The retardation of the film was attributed to gradients of interfacial tension which gave rise to the Marangoni effect. A study of the influence of various system parameters on the drainage dynamics was conducted and three regimes of drainage and possible rupture were identified depending on the relative magnitudes of the drop approach velocity and the van der Waals interaction force: Nose rupture, rim rupture, and film immobilization and flattening. Finally, the possibility of forming secondary droplets by encapsulating the continuous phase film into the coalesced drop at rupture was examined and quantified in light of these regimes.     

Generalized van der Waals Theory of Interfaces in Simple Fluid Mixtures

An efficient implementation of the generalized van der Waals theory of fluids is presented for the calculation of surface tension in simple fluid mixtures. While detailed correlation analysis is avoided the dominant binding energy contribution and the negative contribution due to the nonlocal entropy are accounted for in the free energy density functional by simple physical approximations of the type originally introduced by van der Waals. Efficient computation is achieved by the use of a single-parameter optimization of a tanh-shaped profile representing the total density as well as the composition variation across the interface. This simple profile nevertheless incorporates the expected adsorption to the interface of the volatile component. Application is made to argon/krypton mixtures represented by Lennard-Jones potentials and Lorentz-Berthelot combining rules. Surface tension predictions compare well with both experimental observations and computer simulation results which also indicated close agreement in particle density profiles, especially if the Berthelot rule is amended with a binary interaction parameter slightly (3%) less than unity. Copyright 2001 Academic Press.     

The Dynamics of Marangoni-Driven Local Film Drainage between Two Drops

A study of Marangoni-driven local continuous film drainage between two drops induced by an initially nonuniform interfacial distribution of insoluble surfactant is reported. Using the lubrication approximation, a coupled system of fourth-order nonlinear partial differential equations was derived to describe the spatio-temporal evolution of the continuous film thickness and surfactant interfacial concentration. Numerical solutions of these governing equations were obtained using the Numerical Method of Lines with appropriate initial and boundary conditions. A full parametric study was undertaken to explore the effect of the viscosity ratio, background surfactant concentration, the surface Péclet number, and van der Waals interaction forces on the dynamics of the draining film for the case where surfactant is present in trace amounts. Marangoni stresses were found to cause large deformations in the liquid film: Thickening of the film at the surfactant leading edge was accompanied by rapid and severe thinning far upstream. Under certain conditions, this severe thinning leads directly to film rupture due to the influence of van der Waals forces. Time scales for rupture, promoted by Marangoni-driven local film drainage were compared with those associated with the dimpling effect, which accompanies the approach of two drops, and implications of the results of this study on drop coalescence are discussed. Copyright 2001 Academic Press.     

Two-step evaluation of binding energy and potential energy surface of van der Waals complexes

Evaluation of intermolecular distance and binding energy (BE) of van der Waals complex/cluster at ab initio level of theory is computationally demanding when many monomers are involved. Starting from MP2 energy, we reached a two-step evaluation method of BE of van der Waals complex/cluster through reasonable approximations; BE = BE(HF) + sum Mi> Mj{BE (Mi- Mj)(MP2 or MP2.5) - BE(Mi-Mj)(HF)} where HF represents the Hartree-Fock calculation, Mi, Mj, etc. are interacting monomers, and MP2.5 represents the arithmetic mean of MP2 and MP3. The first term is the usual BE of the complex/cluster evaluated at the HF level. The second term is the sum of the difference in two-body BE between the correlated and HF levels of theory. This equation was applied to various van der Waals complexes consisting of up-to-four monomers at MP2 and MP2.5 levels of theory. We found that this method is capable of providing precise estimate of the BE and reproducing well the potential energy surface of van der Waals complexes/clusters; the maximum error of the BE is less than 1 kcal/mol and 1% in most cases except for several limited cases. The origins of error in these cases are discussed in detail.     

p-Difluorobenzene-argon ground state intermolecular potential energy surface

The ground state intermolecular potential energy surface for the p-difluorobenzene-Ar van der Waals complex is evaluated using the coupled cluster singles and doubles including connected triple excitations [CCSD(T)] model and the augmented correlation consistent polarized valence double-zeta basis set extended with a set of 3s3p2d1f1g midbond functions. The surface minima are characterized by the Ar atom located above and below the difluorobenzene center of mass at a distance of 3.5290 A. The corresponding binding energy is -398.856 cm(-1). The surface is used in the evaluation of the intermolecular level structure of the complex. The results clearly improve previously available data and show the importance of using a good correlation method and basis set when dealing with van der Waals complexes.     

Interpretation of surface-tension isotherms of n-alkanoic (fatty) acids by means of the van der Waals model

Here we apply the two-dimensional van der Waals model to interpret surface-tension isotherms of aqueous solutions of n-alkanoic (fatty) acids. We processed available experimental data for a homologous series of eight acids, from pentanoic to dodecanoic (lauric). Only three adjustable parameters have been varied to fit simultaneously all experimental curves. Excellent agreement between the theoretical model and the experiment has been obtained. The determined parameter values comply well with the molecular properties and allow one to calculate the surfactant adsorption, surface elasticity, and the surface pressure vs area isotherms. For the dodecanoic acid, the van der Waals model indicates the existence of a surface phase transition.     

Adsorption of square and rectangular plate-like molecules on a planar surface

A mean-field statistical thermodynamic analysis of monolayer adsorption of rigid square and rectangular plate-like molecules on a homogeneous planar surface is developed. The analysis is simplified by only considering facewise and edgewise modes of adsorption in restricted orthogonal orientations parallel to the surface. The free energy density, adsorbate population distribution and surface spreading pressure are obtained as a function of adsorbate density and compared for square plate molecules using three different sequences of adsorbate molecule placement on the surface to evaluate the configurational degeneracy. It is found that edgewise adsorbed molecules can be anisotropically ordered if the edge length of square and rectangular plate-like molecules exceeds three length units in the absence of anisotropic dispersion interactions. If intermolecular dispersion interactions are present and of sufficient strength, the spreading pressure-density isotherms can exhibit one or two van der Waals loops for square plate molecules with three van der Waals loops possible for rectangular plate adsorbate molecules. The phase transitions for the adsorbed monolayer corresponding to the appearance of these van der Waals loops are discussed.     

An ab initio investigation of the O(3P)-H2(1sigma(g)+) van der Waals well

We report an ab initio study of the van der Waals region of the O(3P)-H2 potential energy surface based on RCCSD(T) calculations with an aug-cc-pVQZ basis supplemented by bond functions. In addition, an open-shell implementation of symmetry-adapted perturbation theory (SAPT) is used to corroborate the RCCSD(T) calculations and to investigate the relative magnitudes of the various contributions to the van der Waals interaction. We also investigate the effect of the spin-orbit coupling on the position and depth of the van der Waals well. We predict the van der Waals minimum to occur in perpendicular geometry, and located at a closer distance than a secondary well in colinear geometry. The potentials obtained in the present study confirm the previous calculations of Alexander [M. H. Alexander, J. Chem. Phys., 1998, 108, 4467], but disagree with the earlier work of Harding and co-workers [Z. Li, V. A. Apkarian and L. B. Harding, J. Chem. Phys., 1997, 106, 942] as well as with recently refitted surfaces of Brand?o and coworkers [J. Brand?o, C. Mogo and B. C. Silva, J. Chem. Phys., 2004, 121, 8861]. Inclusion of spin-orbit coupling reduces the depth of the van der Waals minimum without causing a change in its position.     

Properties of argon liquid-vapor interface

The short-wave cutoff boundary of the capillary wave spectrum is established. Effective thickness L _b of the “bare” density profile in the interfacial layer is calculated according to experimental data on the ellipticity ratio of reflected light. The free parameters of the extended van der Waals theory of capillarity are determined. The positions of the equimolecular dividing surface and tension surface are calculated, as well as the temperature dependence of the Tolman parameter.     

A rheological investigation of the self-assembly and adsorption behavior of a surfactant salt

The properties of a surfactant salt obtained by neutralizing oleic acid with an ethoxylated stearylamine were determined in blends of water and propylene glycol. The adsorption of this surfactant salt onto the surface of a commercial TiO(2) dispersed in blends of water and propylene glycol was studied using a rheometer. At low propylene glycol content the dispersions exhibited Newtonian behavior, but became shear-thinning fluids with high viscosity at propylene glycol contents above a critical concentration. The observed behavior is consistent with a model involving a surfactant bilayer below the critical point, moving to a monolayer above the critical point. The high viscosity above the critical point is generated by reversible flocculation via hydrophobic forces. The viscosity of the dispersion flocculated by the hydrophobic forces was found to be much higher than that caused by flocculation via van der Waals forces in the absence of surfactant. Changing both the total concentration of the surfactant in the dispersion and the dispersion temperature resulted in a reversible transition between the bilayer and the monolayer. Although the surfactant was always above its critical micelle concentration (CMC) the amount on the particle surface varied appreciably with both propylene glycol and surfactant concentration.     

van der Waals interaction between internal aqueous droplets and the external aqueous phase in double emulsions

A mathematical model for analyzing the van der Waals interaction between the internal aqueous droplets (W(1)) and the external aqueous phase (W(2)) of double emulsions has been established. The effects of Hamaker constants of the materials forming the system, especially those of the two different adsorbed surfactant layers with uniform density (A(1) and A(2)), on the van der Waals interaction were investigated. The overall van der Waals interaction across the oil film is a combined result of four individual parts, that is, W(1)-W(2), A(1)-A(2), W(1)-A(1), and A(2)-W(2) van der Waals interaction, and it may be either attractive or repulsive depending on many factors. It was found that the overall van der Waals interaction is dominated by the W(1)-W(2) interaction at large separation distances between the W(1)/O and O/W(2) interfaces, while it is mostly determined by the A(1)-A(2) interaction when the two interfaces are extremely close. Specifically, in the cases when the value of the Hamaker constant of the oil phase is intermediate between those of W(1) and W(2) and there is a thick oil film separating the two interfaces, a weak repulsive overall van der Waals interaction will prevail. If the Hamaker constant of the oil phase is intermediate between those of A(1) and A(2) and the two interfaces are very close, the overall van der Waals interaction will be dominated by the strong repulsive A(1)-A(2) interaction. The repulsive van der Waals interaction at such cases helps stabilize the double emulsions.