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The line energy associated with the triple phase contact line is a function of local surface defects (chemical and topographical); however, it can still be calculated from the advancing and receding contact angles to which those defects give rise. In this study an expression for the line energy associated with the triple phase contact line is developed. The expression relates the line energy to the drop volume, the interfacial energies, and the actual contact angle (be it advancing, receding, or in between). From the expression we can back calculate the equilibrium Young contact angle, θ0, as a function of the maximal advancing, θA, and minimal receding, θR, contact angles. To keep a certain maximal hysteresis between advancing and receding angles, different line energies are required depending on the three interfacial energies and the drop's volume V. We learn from the obtained expressions that the hysteresis is determined by some dimensionless parameter, K , which is some normalized line energy. The value of K  required to keep a constant hysteresis (θA − θR) rises to infinity as we get closer to θ0 = 90°.

Using a surface forces apparatus, we have measured the normal and shear forces between surfaces containing physisorbed hyaluronic acid (HA), which is a major component of synovial fluid and which is believed to play a role in joint lubrication. The adsorption mechanisms involved the ionic binding of negatively charged HA (i) to positively charged surfactant bilayers supported on mica substrates and (ii) to negatively charged mica surfaces via Ca²⁺ bridges. Our results show that physisorbed HA fails as a lubricant when surfaces are pressed strongly together and/or sheared due to the squeezing out of the HA from between the surfaces. On the basis of these and previous studies, we conjecture that HA might function as an effective boundary biolubricant, exhibiting both low friction and low wear, but only if it is chemically or specifically bound exclusively to each surface, but not to both surfaces.

We have studied the properties of layers of end-functionalized poly(ethylene glycol) (PEG) grafted by one end to mica surfaces, and, using a surface force balance, the interaction between two such layers. PEG of molecular weight 3.4 kg/mol, functionalized at both ends with an N-hydroxysuccinimide carbamate (NHS) group, to form NHS−PEG−NHS, does not adsorb on mica. When a trimethylammonium group ((CH3)3N⁺) replaced one of the NHS groups to form ((CH3)3N⁺)−PEG−NHS, a surface layer formed on the mica from its aqueous solution, showing that the functionalized PEG had been attached by its (CH3)3N⁺ end. The properties of the ((CH3)3N⁺)−PEG−NHS layer were examined primarily by surface force measurements as well as by atomic force microscopy, contact angle measurements, and confocal fluorescence microscopy. The layer was found to be very smooth, and the NHS group was found to retain its reactivity also when attached to the surface, demonstrating that the end-functionalized PEG chains can be used as flexible surface-active spacers for binding amino-containing molecules to the surface. Refractive index measurements yield the adsorbance and hence mean interanchor spacing s of the PEG chains, while force profiles revealed the role of both electrostatic double layers and steric components of the normal interactions at different surface separations D. Shear forces between the sliding surfaces were first observed at compression ratios (2L0/D) ~ 1.2, increasing markedly for (2L0/D) > 3, where L0 is the unperturbed PEG-brush thickness. This may be attributed both to the relatively low (L0/s) ratio, which allows high interpenetration and therefore high segmental density and viscous shear dissipation between opposite layers, and to bridging effects.

Poly(γ-benzyl-l-glutamate) (PBLG) is a synthetic polypeptide with a rigid helical conformation in several solvents. Small-angle X-ray and neutron scattering measurements were used to study the reversible gelation process in semidilute isotropic solutions of PBLG in benzyl alcohol. Time-resolved measurements of the scattering signal due to aggregation of PBLG helices into a network of microfibrils show characteristics of a nucleation and growth process with an incubation period which is extremely sensitive to the gelation temperature. Analysis by the Avrami equation yields an exponent of about 2. A mechanism of homogeneous nucleation and one-dimensional growth of fibrils, which incidentally merge or branch to form the network, is proposed. The thermodynamic transition temperature controlling fibril nucleation seems to be below the gel melting temperature. This transition may be an incongruent melting point of an ordered crystalline phase, which lies within the wide biphasic region of the phase diagram.

We report experimental results and a theoretical analysis of the Debye length in aqueous solutions of nonadsorbing polyelectrolytes. The measurements were done using a surface forces apparatus, in which the normal forces between smooth mica surfaces in aqueous hyaluronic acid (HA) solutions were measured as a function of surface separation (to ±1 Å). HA is negatively charged and does not adsorb to the negatively charged surface of mica, as was established by optical and viscosity measurements and in agreement with the measured force−distance curves. From these measurements it appears that the multivalent polyelectrolyte is “depleted” from the gap between the surfaces. We use the mean-field Poisson−Boltzmann theory to theoretically predict the effective Debye length and double-layer force under such conditions and compare the predictions with the experimental results. The comparison gives excellent agreement and shows that the effective Debye length is determined solely by the monovalent ions in the solution. Specifically, the effective Debye length κeff^-1 for the double-layer interaction is determined by an effective ionic concentration given by %@mt;sys@%%@rl@%%@ital@%n%@rsf@%%@sb@%s%@sbx@%%@ital@%n%@rsf@%%@sb@%c%@sbx@%%@rlx@%%@mx@% , where ns and nc are the bulk negative and positive monovalent ion concentrations, respectively.

We have used a new design of the mica surface force balance (SFB), with extreme sensitivity in measuring normal and particularly shear or frictional forces between two surfaces sliding past each other, to measure the forces between two mica surfaces across a confined 4-cyano-4‘-hexabiphenyl nematogen (6CB). In an earlier study (Langmuir 1997, 13, 4466, paper 1 of the series) we investigated the normal force−distance profiles and the orientation of the confined liquid crystal (LC). Here we extend this to study the shear forces Fs between the sliding mica surfaces across the 6CB nematogen as a function of orientation of the confined LC, the applied normal load Fn, the separation D of the mica surfaces, the shear velocity vs, and the relative shear direction of the confining surfaces (which may be varied using the new SFB design). Our results, where the shear forces are measured down to levels that are some orders of magnitude more sensitive than in earlier studies, show that the highly confined nematogen (D in the range from 16 to ca. 100 Å) behaves under shear in a quasi-solidlike fashion for all three orientations studied:  planar, planar twisted, and homeotropic. There is a linear relation between Fs and Fn for each of the three orientations, with the effective friction coefficient (dFs/dFn) largest for the homeotropic orientation and lowest for the planar twisted one. Intriguingly, for the planar orientation a clear increase in the friction could be observed when the initial shear direction was changed by 90°. We attribute this to the effect of the initial shear in orienting the confined nematogen layer in the initial direction, so that subsequent sliding motion at right angles to this encounters greater resistance. We also find that within a range of some 40-fold in vs, there was little change in the shear force, in line with what is generally observed for solid−solid friction, and consistent with the fact that little relaxation in Fs is observed over macroscopic times on applying a step strain to the confined LC.

The forces between layers of poly(ethylene oxide) (PEO), of molecular weights M = 37 × 10³ (PEO37) and M = 112 × 10³ (PEO112) adsorbed onto smooth, curved solid (mica) surfaces across the good solvent toluene have been determined using a surface force balance (SFB). The SFB used is capable of measuring both normal interactions Fn(D) as a function of surface separation D and, with extreme sensitivity, shear or frictional forces Fs(D,vs) between them as they slide past each other at velocity vs. The Fn(D) profiles are closely similar to those measured in earlier studies between adsorbed PEO layers. The shear or frictional forces between the sliding PEO-bearing surfaces are very low up to moderate compressions of the adsorbed layers (local pressures up to ca. 10⁵ N m^-2), corresponding to effective friction coefficients μeff = (Fs/Fn) of order 0.003 or less. This is attributed to the fluid interfacial layer between the adsorbed layers resulting from their weak mutual interpenetration. At higher loads Fs increases markedly, and two forms of behavior are found depending on the PEO molecular weight. For PEO37, a sharp increase in Fs is followed by removal of polymer from within the intersurface gap during sliding, high friction, and adhesion between the surfaces. For the longer PEO112, the initial increase in Fs and in μeff saturates at the highest loads (for the case of μeff even decreasing), indicating that the slip plane has moved from the polymer/polymer midplane to the polymer/solid interface. The dependence of Fs on the sliding velocity in the high-friction regime is weak, suggesting that at low compressions there is a thinning of the mutual adsorbed-layer-interpenetration region at high vs that offsets the higher viscous dissipation in that region. At the highest loads, when the slip plane has shifted to the mica surface, the weak Fs(vs) dependence is characteristic of sliding friction at solid substrates.

Oleic acid and stearic acid are similar surfactants which, however, lead respectively to stability and to precipitation of ferrofluid suspensions:  to understand this, the forces between layers of oleic-like surfactants and between layers of stearic-like surfactants across a hexadecane (HD) medium were measured using a surface force balance (SFB). Separate measurements reveal that only the oleic layers are solvated by HD, while the SFB results reveal that for both surfactants a marked net attraction is present between the surfaces. Simple considerations based on these observations explain why, despite this attraction, ferrofluid dispersions are stabilized by oleic but not by stearic surfactants.