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Princen and co-workers have treated the more general case where w is too small or y too large to give a cylindrical profile [86] (see also Refs. 87 and 88). In such cases, however, a correction may be needed for buoyancy and Coriolis effects [89] it is best to work under conditions such that Eq. 11-35 applies. The method has been used successfully for the measurement of interfacial tensions of 0.001 dyn/cm or lower [90, 91]. 

A recent design of the maximum bubble pressure instrument for measurement of dynamic surface tension allows resolution in the millisecond time frame [119, 120]. This was accomplished by increasing the system volume relative to that of the bubble and by using electric and acoustic sensors to track the bubble formation frequency. Miller and co-workers also assessed the hydrodynamic effects arising at short bubble formation times with experiments on very viscous liquids [121]. They proposed a correction procedure to improve reliability at short times. This technique is applicable to the study of surfactant and polymer adsorption from solution [101, 120]. 

Studies by Eriksson [28] and King and co-workers [29] have shown that adsorption... 

The theoretical treatments of Section III-2B have been used to calculate interfacial tensions of solutions using suitable interaction potential functions. Thus Gubbins and co-workers [88] report a molecular dynamics calculation of the surface tension of a solution of A and B molecules obeying Eq. III-46 with o,bb/ o,aa = 0.4 and... 

As an example, Tajima and co-workers [108] used labeling to obtain the adsorption of sodium dodecyl sulfate at the solution-air interface. The results, illustrated in Fig. Ill-12, agreed very well with the Gibbs equation in the form... 

The actual structure at a vapor-liquid interface can be probed with x-rays. Rice and co-workers [72,73,117] use x-ray reflection to determine the composition perpendicular to the surface and grazing incidence x-ray diffraction to study the transverse structure of an interface. In a study of bismuth gallium mixtures. 

Both the Monte Carlo and the molecular dynamics methods (see Section III-2B) have been used to obtain theoretical density-versus-depth profiles for a hypothetical liquid-vapor interface. Rice and co-workers (see Refs. 72 and 121) have found that density along the normal to the surface tends to be a... 

Tajima and co-workers [108] determined the surface excess of sodium dode-cyl sulfate by means of the radioactivity method, using tritiated surfactant of specific activity 9.16 Ci/mol. The area of solution exposed to the detector was 37.50 cm. In a particular experiment, it was found that with 1.0 x 10" Af surfactant the surface count rate was 17.0 x 10 counts per minute. Separate calibration showed that of this count was 14.5 X 10 came from underlying solution, the rest being surface excess. It was also determined that the counting efficiency for surface material was 1.1%. Calculate F for this solution. 

Finally, Newmann and co-workers [30] (see also Ref. 31) have argued that while free energy contributions may not be strictly additive as in Eq. IV-11, there should, in principle, be an equation of state relating the work of adhesion to the separate liquid surface tensions such as... 

If the spreading is into a limited surface area, as in a laboratory experiment, the film front rather quickly reaches the boundaries of the trough. The film pressure at this stage is low, and the now essentially uniform film more slowly increases in v to the final equilibrium value. The rate of this second-stage process is mainly determined by the rate of release of material from the source, for example a crystal, and the surface concentration F [46]. Franses and co-workers [47] found that the rate of dissolution of hexadecanol particles sprinkled at the water surface controlled the increase in surface pressure here the slight solubility of hexadecanol in the bulk plays a role. 

Neumann has adapted the pendant drop experiment (see Section II-7) to measure the surface pressure of insoluble monolayers [70]. By varying the droplet volume with a motor-driven syringe, they measure the surface pressure as a function of area in both expansion and compression. In tests with octadecanol monolayers, they found excellent agreement between axisymmetric drop shape analysis and a conventional film balance. Unlike the Wilhelmy plate and film balance, the pendant drop experiment can be readily adapted to studies in a pressure cell [70]. In studies of the rate dependence of the molecular area at collapse, Neumann and co-workers found more consistent and reproducible results with the actual area at collapse rather than that determined by conventional extrapolation to zero surface pressure [71]. The collapse pressure and shape of the pressure-area isotherm change with the compression rate [72]. 

The experimental procedure used by Hansen and co-workers involved the use of a loudspeaker magnet to drive a rod touching the surface (in an up-and-down motion) and... 

In the case of Langmuir monolayers, film thickness and index of refraction have not been given much attention. While several groups have measured A versus a, [143-145], calculations by Knoll and co-workers [146] call into question the ability of ellipsometry to unambiguously determine thickness and refractive index of a Langmuir monolayer. A small error in the chosen index of refraction produces a large error in thickness. A new microscopic imaging technique described in section IV-3E uses ellipsometric contrast but does not require absolute determination of thickness and refractive index. Ellipsometry is routinely used to successfully characterize thin films on solid supports as described in Sections X-7, XI-2, and XV-7. 

Photoexcited fluorescence from spread monolayers may be studied [158,159] if the substance has both a strong absorption band and a high emission yield as in the case for chlorophyll [159]. Gaines and co-workers [160] have reported on the emission from monolayers of Ru(bipyridine)3, one of the pyridine ligands having attached C g aliphatic chains. Ruorescence depolarization provides information about the restriction of rotational diffusion of molecules in a monolayer [161], Combining pressure-area... 

McConnell et al. [196] and Andelman and co-workers have predicted [197,198] an ordered array of liquid domains in the gas-liquid coexistence regime caused by the dipole moment difference between the phases. These superstructures were observed in monolayers of dipalmitoyl phosphatidylcholine monolayers [170]. 

Since the development of grazing incidence x-ray diffraction, much of the convincing evidence for long-range positional order in layers has come from this technique. Structural relaxations from distorted hexagonal structure toward a relaxed array have been seen in heneicosanol [215]. Rice and co-workers combine grazing incidence x-ray diffraction with molecular dynamics simulations to understand several ordering transitions [178,215-219]. 

A plot of G x versus composition is shown in Fig. IV-22 for condensed films of octadecanol with docosyl sulfate. Gaines [241] and Cadenhead and Demchak [242] have extended the above approach, and the subject has been extended and reviewed by Barnes and co-workers (see Ref. 243). 

Some fairly typical results, obtained by LaMer and co-workers [275] are shown in Fig. IV-24. At the higher film pressures, the reduction in evaporation rate may be 60-90%—a very substantial effect. Similar results have been reported for the various fatty acids and their esters [276,277]. Films of biological materials may offer little resistance, as is the case for cholesterol [278] and dimyristoylphosphatidylcholine (except if present as a bilayer) [279]. 

Barnes and co-workers have studied mixed-monolayer systems [278,281,283,284] and found some striking nonidealities. Mixed films of octadecanol and cholesterol, for example, show little evaporation resistance if only 10% cholesterol is present [278] apparently due to an uneven granular microstructure in films with cholesterol [284]. Another study of cellulose decanoate films showed no correlation between holes in the monolayer and permeation rate [285]. Polymerized surfactants make relatively poor water evaporation retarders when compared to octadecanol [286]. There are problems in obtaining reproducible values for r [287] due to impurities in the monolayer material or in the spreading solvent. 

Photopolymerization reactions of monolayers have become of interest (note Chapter XV). Lando and co-workers have studied the UV polymerization of 16-heptadecenoic acid [311] and vinyl stearate [312] monolayers. Particularly interesting is the UV polymerization of long-chain diacetylenes. As illustrated in Fig. IV-30, a zipperlike process can occur if the molecular orientation in the film is just right (e.g., polymerization does not occur readily in the neat liquid) (see Refs. 313-315). 

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

Rowell and co-workers [62-64] have developed an electrophoretic fingerprint to uniquely characterize the properties of charged colloidal particles. They present contour diagrams of the electrophoretic mobility as a function of the suspension pH and specific conductance, pX. These fingerprints illustrate anomalies and specific characteristics of the charged colloidal surface. A more sophisticated electroacoustic measurement provides the particle size distribution and potential in a polydisperse suspension. Not limited to dilute suspensions, in this experiment, one characterizes the sonic waves generated by the motion of particles in an alternating electric field. O Brien and co-workers have an excellent review of this technique [65]. 

Relaxations in the double layers between two interacting particles can retard aggregation rates and cause them to be independent of particle size [101-103]. Discrepancies between theoretical predictions and experimental observations of heterocoagulation between polymer latices, silica particles, and ceria particles [104] have promptetl Mati-jevic and co-workers to propose that the charge on these particles may not be uniformly distributed over the surface [105, 106]. Similar behavior has been seen in the heterocoagulation of cationic and anionic polymer latices [107]. 

Usually one varies the head of mercury or applied gas pressure so as to bring the meniscus to a fixed reference point [118], Grahame and co-workers [119], Hansen and co-workers [120] (see also Ref. 121), and Hills and Payne [122] have given more or less elaborate descriptions of the capillary electrometer apparatus. Nowadays, the capillary electrometer is customarily used in conjunction with capacitance measurements (see below). Vos and Vos [111] describe the use of sessile drop profiles (Section II-7B) for interfacial tension measurements, thus avoiding an assumption as to the solution-Hg-glass contact angle. 

The location and shape of the entire electrocapillary curve are affected if the general nature of the medium is changed. Fawcett and co-workers (see Ref. 126) have used nonaqueous media such as methanol, V-methylformamide, and propylene carbonate. In earlier studies, electrocapillaiy curves were obtained for O.OIA/ hydrochloric acid in mixed water-ethanol media of various compositions [117, 118]. The surface adsorption of methanol, obtained from... 

The equations of electrocapillarity become complicated in the case of the solid metal-electrolyte interface. The problem is that the work spent in a differential stretching of the interface is not equal to that in forming an infinitesimal amount of new surface, if the surface is under elastic strain. Couchman and co-workers [142, 143] and Mobliner and Beck [144] have, among others, discussed the thermodynamics of the situation, including some of the problems of terminology. 

While much early work with dispersed electrochemical systems focused on silver halide sols [16], more recent studies by Rusling and co-workers and others exploited... 

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