Using an extension of the Debye-Huckel theory for strong electrolytes, the thermodynamics, phase behavior, and effective pair colloidal potentials of deionized charged dispersions have been investigated. With the inclusion of colloid size effects, this model predicts the possibility of the existence of two critical points, one of which is thermodynamically metastable but can exhibit interesting behavior at high colloid charges. This analytic model also serves as a pedagogic demonstration that the phase transition is driven by cohesive Coulomb interactions between all charged species in the system and that this cohesion is not inconsistent with a repulsive effective pair potential between the colloidal particles.

The phase behavior of charged colloidal systems has been studied recently by the density functional theory formalism (DFT) [R. van Roij, M. Dijkstra, and J. P. Hansen, Phys. Rev. E 59, 2010 (1999)]. A key feature of this approach is the appearance of a density and temperature-dependent effective Hamiltonian between the charged colloids. Under certain approximations, the effective Hamiltonian is made up only of a sum of position-independent one-body or volume terms and two-body colloid-separation dependent terms. In the limit of low colloidal densities, the DFT results do not reduce to the familiar Debye-Hu ̈ckel limiting law nor do the results agree with previous work based on an identical approach but were developed using traditional statistical-mechanical methods [B. Beresford-Smith, D. Y. C. Chan, and D. J. Mitchell J. Colloid Interface Sci. 105, 216 (1985)]. This paper provides a reconciliation of these differences and comments on the significance of the one-body volume terms in the effective Hamiltonian of a system of charged colloids in determining thermodynamics and phase behavior.

The effect of disjoining pressure between a rigid spherical probe particle (attached to an AFM cantilever) and a liquid interface (e.g., oil/water or air/water) is treated in an analytic manner to describe the total force F exerted on the probe as a function of the distance X of the probe from the rigid substrate (AFM stage) on which the liquid interface resides. Two cases (i) a flat interface under grav- ity and (ii) a drop whose size is sufficiently small that gravity can be neglected have been examined. A simple numerical algorithm is given for computing F(X) (the AFM observable) from a given form for the disjoining pressure. Numerical results are displayed for electrostatic probe/interface interactions which reveal the linear compliance regime experimentally observed in AFM experiments on these systems. The slope of the linear compliance regime is shown to be a function of the properties of the interface (capillary length, particle radius, drop size, contact angle of drop on rigid substrate etc.).

There has been much speculation about the origin of long-range electrostatic attractions between identical colloidal particles in confined geometries. Recently, we proved that such attractive interactions are not to be found in the well-established Poisson-Boltzmann theory, when the particles are immersed in a 1:1 electrolyte whose average ion concentrations are equal. A subsequent approximate analytical investigation (Europhys. Lett. 1999, 46, 407-413) has suggested that such attractive interactions result from a combination of the effects of confinement, imbalance of the average ionic concentrations, and polarization effects in the confining surface. Consequently, we extend our previous proof to encompass the general case of an electrolyte possessing any number of ionic species, where there is no restriction on their average concentrations. In so doing, we rigorously prove that within the framework of the Poisson-Boltzmann theory the interaction between identical colloidal particles is never attractive, irrespective of whether the particles are isolated or confined. Furthermore, we establish a necessary condition for the existence of attractive interactions, which indicates the possibility that an osmotically driven process is behind the observed attractive interactions.

Small colloids in a uni-univalent aqueous electrolyte are modeled by a four-component solvent primitive model. The symmetric Poisson-Boltzmann theory is used to analyze the system and to calculate the second virial coefficient B2 of very dilute particle suspensions for varying solute and solvent concentrations. The results are compared with some experimental results on B2 of the silicotungstate anion suspension in an alkali halide solution.

The proximity effect of one or two flat surfaces on the double- layer interaction between two identically charged colloidal parti- cles immersed in an electrolyte is examined. Simple analytical formulas are presented for the interaction of (i) two particles in the vicinity of a charged flat surface and (ii) two particles confined between two parallel plates. It is found that the surface(s) can strongly influence the pairwise interaction of the particles, leading to increase, decrease, or even elimination of the electrostatic interaction, in comparison to the corresponding result in an un-bounded electrolyte.

Long-range electrostatic attractions between identical colloidal particles in confined geometries have been observed experimen- tally by many workers. A satisfactory theoretical explanation for this behavior has proven elusive. Recent numerical calculations and reports (Nature 393, 621– 623, 663– 665 (1998)), however, have suggested that this problem is closed by demonstrating that this surprising effect is to be found naturally within the well-established Poisson–Boltzmann (PB) theory. We rigorously prove that these claims are false; within the framework of the PB theory, the interaction between identical colloidal particles is always repulsive, irrespective of whether the particles are isolated or confined. A satisfactory theoretical explanation of this surprising phenomenon thus remains an unresolved problem.

It is shown that bubbling on wine bottle labels is due to absorption of water from the glue withh subsequent hygroscopic expansion. Contrary to popular belief, mosts of the glue's water myst be lost to the atmosphere rather than to the paper. A simple lubrication omde is develiped fo spreading the glue piles in teh pressure chambre of the labelling machine. This model predicts a moximum rate for application of labels. Buckling theory shows that the current arrangement of periodic glus strips can indeed accommodata paper expansion. This peoject provides interesting applicaitons of various areas of undergaduate mathematics such as trigonometry, Maclaurin series, dimensional analysis and fluid mechanics. It illustrates that simple mathematical modelling may provide insight intoa complicated real-world problem.

A simple theory of mixtures (Snider, N. S. and Herrington, T. M. 1967, J. Chem. Phys., 47, 2248) is applied to calculate the excess volumes and excess partial molar volumes of liquid argon-krypton mixtures at T = 134.3K and several pressures. This theory gives a good qualitative description of these quantities. In particular, the theory gives the correct sign and asymmetry for the excess volumes and partial molar volumes and, at high pressures, non-monotonic curves for the excess partial molar volumes. However, the theory predicts that these effects occur at higher pressures than are seen experimentally. As pointed out before (Hamann, S. D. 1992, High Temp. High Press., 24, 489), such classic theories as regular solution theory and ideal associated mixtures fail to give even the correct sign for these quantities.

We describe a new approach to the index reconstruction of three-dimensional optical systems with rotational symmetry, which is based on sampling ray paths that lie in the sagittal plane. Since the observed rays are distorted by the optical system itself, they cannot be used directly for index recon- struction. We present an iterative procedure to compute the true ray paths and then to find the index distribution. The utility of the method is verified on the model problem.

We explore the influence of electrolyte concentration on the adsorption of charged spheres using modeling techniques based on random sequential adsorption (RSA). We present a parametric study of the effects of double layer interactions between the charged particles and between the particle and the substrate on the jamming limit using a two-dimensional RSA simulation similar to that of Z. Adamczyk et al. (1990, J. Colloid Interface Sci. 140, 123) along with a simple method of estimating jamming limit coverages. In addition, we present a more realistic RSA algorithm that includes explicit energetic interaction in three dimensions, that is, particle–particle and particle–surface interactions during the approach of a particle to the substrate. The calculation of interaction energies in the 3-D RSA model is achieved with the aid of a three-body superposition approximation. The 3-D RSA model differs from the 2-D model in that the extent of coverage is controlled by kinetic rather than energetic considerations. Re- sults of both models capture the experimentally observed trend of increased surface coverage with increased electrolyte concentra- tion, and both models require the value of a key model parameter to be specified for a quantitative match to experimental data. However, the 3-D model more effectively captures the governing physics, and the parameter in this case takes on more meaningful values than for the 2-D model.

A theoretical description is presented for the equilibrium capillary height (heq) of a solution between parallel, flat, solid surfaces which contain ionizable groups. The heq is related to the change in gravitational potential energy, the intrinsic wettability of the un-ionized surface, and the free energy of formation of the ionizable surface in aqueous solution. The theoretical approach takes into account both the electrostatic free energy of charging the surface and the change in the free energy associated with the acid-base reactions of the surface sites. It is shown that the dependence of heq on pH depends on the number of ionizable surface sites per unit area, the intrinsic acid-base dissociation constant (Kai) of the surface sites, and the background electrolyte. The negative free energy change which accompanies the acid-base reactions dominates over the positive electrostatic free energy of charging the surface. Consequently, the overall free energy of ionization is negative, and an ionized surface is more wettable than an un-ionized surface. The theoretical description is applied to experimental values of heq as a function of pH, measured between two heptylamine plasma polymer surfaces in the presence of 1mM NaCl. The theoretical fit to the data indicates that the plasma polymer surface contains ca. 1017 amines/m2 and the pKai of the amine groups is ca. 5. The surface site density is in reasonable accord with values obtained by both derivatization techniquesandcontactanglemeasurements. The pKai is consistent with a low effective dielectric constant for the polymer-water interface.

The Lifshitz theory of van der Waals interaction has been employed to calculate the contact angles of diiodomethane, 1-bromonaphthalene, 1-methylnaphthalene, bromobenzene, 1-tert-butylnaphthalene, liquid paraffin, and hexadecane on poly(dimethylsiloxane), poly(4-methyl-1-pentene), polyethylene, natural rubber, and polystyrene surfaces. The theoretical treatment is based on the equation cosθ = [(2APVL/ALVL)- (HoLVL/HoPVL)^2] - 1, where θ is the contact angle and APVL and ALVL are the non-retarded Hamaker constants for the heterointeraction between polymer and liquid across vacuum and the homo interaction of the liquid acrossvacuum,respectively. Nonretarded Hamaker constants have been determined from the dielectric properties of the materials and application of the Lifshitz theory. HoLVL and HoPVL are the equilibrium “contact” surface separations associated with the liquid-liquid homointeraction and polymer-liquid heterointeraction across vacuum, respectively. HoLVL values, and the analogous HoPVP values associated with polymer homointeraction, have been estimated from the surface free energies of the dispersive liquids andpolymers. Four different approaches, each with a different assumption regarding the heterointeraction between polymer and liquid, have been used to obtain HoPVL values: (i) HoPVL = HoLVL, (ii) HoPVL = HoPVP, (iii) a geometric mean relationship, HoPVL = (HoPVP HoLVL)^(1/2), and (iv) an arithmetic mean relationship, HoPVL = (HoPVP + HoLVL)/2. Theoretical contact angles obtained with the four approaches have been compared with experimental contact angles. In general, the approaches which employ the combining rules, whether geometric or arithmetic, provide the best agreement between theory and experiment. Previous work that has dealt with the contact angles of n-alkanes on poly(tetrafluoroethylene) has also been re-examined. For the perfluorocarbon-hydrocarbon system none of the approaches are able to reconcile theory and experiment.

This work describes a rheooptical experiment with the ability to distinguish between orientation and deformation of polymers while quantifying the degree of deformation in shear using a polymeric chromophore. The chromophore used is poly(4-butoxycarbonylmethylurethane)diacetylene, referred to as 4BCMU, which is known to display varying optical properties that are attributed to conformational changes in the polymer backbone. The orientation may be measured by changes in the extinction coefficient both perpendicular and parallel to theshearfield. The results obtained for dilute solutions of 4BCMU under shear are explained by an ellipsoidal random coil polymer in the quiescent state orientating in the shear field. In apparent contradiction to earlier theoretical models, no deformation of the polymer is observed within the range of shear fields used in this work. Extant theories have attributed the rheological behavior of polymer solutions to deformation of the spherical random polymer coils under shear.

The electrophoretic mobilities of two interacting spheres are calculated numerically for arbitrary values of the double-layer thickness. A general formula for the electrophoretic translational and angular velocities of N interacting particles is derived for low zeta-potential conditions. The present calculation complements the well-studied case of thin double layers. The results are com- pared with recent reflection calculations and are used to compute the O(\phi) contribution to the electrophoretic mobility of a suspension. Particle interactions can be significant for values of the scaled particle radius ka < 10. At ka = 1 the O(\phi) contribution can increase by a factor of 2 - 3 over its thin-double-layer value. The precise values depend on the strength of the double-layer repulsions as determined by the particle size. Fluctuations in the electrophoretic velocity are also calculated but would appear to be limited to about 10% of the mean velocity. The reflection results to order 1/R^6, where R is the particle separation, are in good agreement with the numerical results for the suspension mobility and fluctua- tions but higher order reflections produce worse results. Although the effects of pair interactions are noticeable, the major result is that pair interactions even for quite thick double layers are not large.

We describe a novel approach to refractive-index reconstruction in two-dimensional systems with no special symmetry, based on observation of traces of rays that travel through the optical system. The mathematical model of ray-tracing analysis is presented in detail, and both the analytical and numerical solutions are given. Methods of data processing in the presence of experimental errors are developed and applied to model problems.

Using an atomic force microscope, the adsorption of 4-(dimethylamino) pyridine and pyridine, in aqueous solution, onto tri sodium citrate equilibrated gold has been monitored by the decrease in the electrostatic potential of the gold surface with time. Pronounced changes in the force-separation curves as a function of time were observed, with determined potential decreases in the range of 20-30 mV. The time dependent diffuse layer potentials changes have been attributed to the displacement of citrate ions on the gold surface by the more strongly adsorbing aromatic amines.

AFM force measurements were carried out between a silica colloid sphere and an alumina flat crystal over a wide pH range and in both 1×10-4 and 1×10-3 M KNO3 aqueous solutions. Microelectrophoresis and streaming potential experiments were performed on the silica colloid sample and the alumina plate, respectively. The potentials measured by the different techniques were in very good agreement. The results clearly indicate that AFM force measurements can be used to accurately determine diffuse layer potentials of metal oxide materials under these solution conditions.

Surface heterogeneities on colloidal particles may cause nonuniform charge distributions, which result in electrostatic potential profiles differing from those seen when charge is distributed uniformly. This, in turn, can give rise to attractive interactions between pairs of such surfaces which may be of greater magnitude and range than van der Waals attractions. We extend previous work on interactions between pairs of heterogeneous plates to pairs of spheres, with nonuniform constant potential or constant charge boundary conditions. As in the planar case, large attractive free energies can be obtained which are not present in the equivalent uniform surfaces. Additionally, large restraining torques can befound, affecting the rotational motion. These torques are not present in uniform charge models and may go some way toward explaining restraining torques found in some experimental systems.

Many surfaces encountered in colloid science are formed by the adsorption of surfactants or polymers on solid surfaces. Due to the formation of surface aggregates, the charge distributions of such surfaces may be nonuniform. Furthermore, these surfaces are expected to have regions with different electrostatic properties due to the presence of two or more different materials. In this paper, we propose a model consisting of periodically alternating regions of constant potential and constant charge, in order to account for the possibility of different regions on the surface possessing different electrostatic properties. Specifically, we consider the behavior of the far field effective electrostatic potential of this model surface when it is immersed in an electrolyte, i.e., the potential associated with the asymptotic exponential tail of the potential distribution in the electrolyte. In doing so, we find the previously unreported phenomenon that the effective potential is strongly dependent on the surface morphology and its associated length scale. Further- more, we find that there also exists the possibility that the constant charge regions will be "invisible" to the potential distribution. These results have direct implications for general nonuniform charge regulating surfaces.

Drainage displacements in three-phase flow under strongly wetting conditions are completely described by a simple generalisation of well understood two-phase drainage mechanisms. As in two-phase flow, the sequence of throat invasions in three-phase flow is determined by fluid connectivity and threshold capillary pressure for the invading interface. Flow through wetting and intermediate spreading films is important in determining fluid recoveries and the progress of the displacement in three-phase flow. Viscous pressure drops associated with flow through films give rise to multiple filling and emptying of pores. A three-phase, two-dimensional network model based on the pore-scale fluid distributions and displacement mechanisms reported by Oren et al. and which accounts for flow through both wetting and intermediate fluid films is shown to correctly predict all the important characteristics of three-phase flow observed in glass micromodel experiments.

In this note we have present theoretical evidence that surface free energies are a good guide to the relative adhesive behavior of low surface free energy ("nonstick") fluorocarbon, silicone, and hydrocarbon solids toward organic "soils" when the interac- tions are governed by van der Waals (dispersion) forces and comparisons are restricted to similar families of materials. Our theoretical considerations also suggest that fluorocarbons are the best candidates for ultra low-adhesive materials, and no smooth homogeneous organic solid can be strictly "nonstick" toward organic "soils" in water but poly(tetrafluoroethylene) surfaces can be truly "nonstick" toward foodstuffs placed in common cooking oils.

We measure the roughness of fracture surfaces generated in uniaxial tension for model materials in two and three dimensions. We study the effect of disorder, of anisotropy of material properties and of dimensionality on surface roughness. Although the roughness exponent ζ is always found within a narrow range, its value systematically decreases as the extent of disorder is increased. For anisotropic materials the scaling properties are found to be independent of the orientation. These results indicate that the scaling properties of the fracture surface are not universal, but depend, albeit weakly, on material properties. While values of the roughness exponent ζ are independent of dimension, differences in the fracture morphology and in the breakdown characteristics are noted.

Surface free energies have been calculated for solid fluorocarbon materials by employing a method that utilizes dielectric data and theoretical predictions of van der Waals (dispersion) interactions. Excellent agreement between the results of direct force measurements and those of the theory for retarded van der Waals interactions supports the methodology. Two relatively new fluorocarbon polymers have been identified as having the lowest known surface free energies of all bulk homogeneous polymeric solids. This study provides confirmation that estimates of solid surface free energies based on contact angle measurements with dispersive organic liquids depend on the dielectric properties of both the liquids and the solid.

Attempting to use ultrafiltration as a method of preparing colloidal suspensions of known composition for use in verifying electrokinetic theories require care in the determination of the bulk suspending electrolyte concenrtation even at low particle volume fraction. A model of such a system is proposed to calculate the actual bulk concentration. The work is based on the supposition that the application of the pressure difference across the colloidal suspension in the ultrafiltration process creates a volume fraction profile within the system. When removed from the applied pressure, the system returns to a uniform state, but with an equivalent bulk concentration that depends on the total particle concentration and the composition of the filtrate. This model predicts that the bulk concentration varies with volume fraction, which is qualitatively similar to experimental observations. However, the magnitude of the changes calculated were not large enough to fully explain the experimental results; this suggest some other factor may also be contributing to the observed phenomema.

A theoretical description is presented for the macroscopic contact angle (θ) of a solid/vapor/aqueous solution interface when the solid surface is ionizable and relatively hydrophobic. The contact angle is related to the free energy of formation of the ionizable surface in aqueous solution. Therefore, the theoretical approach takes into account the electrostatic free energy of charging the surface and the change in the free energy associated with the acid-base reactions of the surface sites. It is shown that the dependence of e on pH depends on the number of ionizable surface sites per unit area, the intrinsic acid-base dissociation constant (Kal) of the surface sites, and the background electrolyte. The negative 'free energy change which accompanies the acid-base reactions dominates over the positive electrostatic free energy of charging the surface; therefore, the overall free energy of ionization is negative, and the ionized surfaces are more wettable than the uncharged surfaces. The theoretical description is applied to experimental values of θ as a function of pH, measured on heptylamine plasma polymer surfaces in the presence of either 1 or 10 mM NaCl. The theoretical fit to the advancing and sessile contact angles indicates that the plasma polymer surface contains ca. 4±1 x 10^17 amines/m^2and the pKai of the amine groups is, ca.6. The surface site density is in accord with values obtained by derivatization techniques, and the pKalis consistent with a low effective dielectric constant for the polymer-water interfacial microenvironment.

The Forster energy transfer between chromophores in several different types of Langmuir-Blodgett (LB) films exposed to aqueous conditions was examined. The donor and acceptor chromophores were either contained in a monolayer of a preformed copolymer incorporating amphiphilic side chains and hydrophilic spacer groups (dansyldihexa- decylamine as the donor and 1,1'-dioctadecyl-3,3,3',3'-tetra methyl indo carbocyanine perchlorate as the acceptor) or grafted to a monolayer of such a copolymer (anthracene as the donor and 7-nitrobenz-2-oxa-l,3-diazole as the acceptor). The monolayers containing donor or acceptor chromophores were separated by neutral spacer layers of cadmium arachidate or copolymer material. It was found that the unattached chromophores diffused through the LB films during the experimental procedure and for several days afterwards. LB films containing chromophores that were grafted to copolymer and copolymer material spacer layers possessed high translayer structural order. There was evidence, however, that indicated that the structure relaxed with time.