Henry model

Overbeek and Booth [284] have extended the Henry model to include the effects of double-layer distortion by the relaxation effect. Since the double-layer charge is opposite to the particle charge, the fluid in the layer tends to move in the direction opposite to the particle. This distorts the symmetry of the flow and concentration profiles around the particle. Diffusion and electrical conductance tend to restore this symmetry however, it takes time for this to occur. This is known as the relaxation effect. The relaxation effect is not significant for zeta-potentials of less than 25 mV i.e., the Overbeek and Booth equations reduce to the Henry equation for zeta-potentials less than 25 mV [284]. For an electrophoretic mobility of approximately 10 X 10 " cm A -sec, the corresponding zeta potential is 20 mV at 25°C. Mobilities of up to 20 X 10 " cmW-s, i.e., zeta-potentials of 40 mV, are not uncommon for proteins at temperatures of 20-30°C, and thus relaxation may be important for some proteins. 

Work carried out in our laboratories over the past three years and in conjunction with the research group of Daktemieks at Deakin University has been directed toward the development of novel enantiomerically pure stannanes for use in free-radical reduction chemistry. To that end Dunn prepared a series of menthyl-substituted stannanes 18 -20 and some others derived from aromatic amines (eg. 21, 22).Perchyonok tested these reagents against a series of substrates while Henry modelled the reactions in question through the use of ab initio molecular orbital theory. 

The MichaeUs-Menten-Henri model is one of the simplest for enzymatic action, and considers the velocity of enzymatic conversion at steady state, where there is a constant concentration of the enzyme-substrate complex, which itself can either dissociate or proceed to final product formation. The measured velocity is related to substrate concentration c, and the Michaelis-Menten rate constant M y ... 

As an illustration, below we give the solution of the mixed (diffusion-barrier) problem employing the Henry model to characterize the barrier (see Table 2). In fact, the Henry model is the only one which allows an exact analytical solution for r(f) ... 

The Freundlich equation is defective as a model because of the physically unrealistic/((2) consequences of this are that Henry s law is not approached at low P, nor is a limiting adsorption reached at high P. These difficulties can be patched by supposing that... 

In glassy polymers tire interactions of tire penetrant molecules witli tire polymer matrix differ from one sorjDtion site to anotlier. A limiting description of tire interaction distribution is known under tire name of tire dual-soriDtion model [, 60]. In tliis model, tire concentration of tire penetrant molecules consists of two parts. One obeys Henry s law and tire otlier a Langmuir isotlienn ... 

Many simple systems that could be expected to form ideal Hquid mixtures are reasonably predicted by extending pure-species adsorption equiUbrium data to a multicomponent equation. The potential theory has been extended to binary mixtures of several hydrocarbons on activated carbon by assuming an ideal mixture (99) and to hydrocarbons on activated carbon and carbon molecular sieves, and to O2 and N2 on 5A and lOX zeoHtes (100). Mixture isotherms predicted by lAST agree with experimental data for methane + ethane and for ethylene + CO2 on activated carbon, and for CO + O2 and for propane + propylene on siUca gel (36). A statistical thermodynamic model has been successfully appHed to equiUbrium isotherms of several nonpolar species on 5A zeoHte, to predict multicomponent sorption equiUbria from the Henry constants for the pure components (26). A set of equations that incorporate surface heterogeneity into the lAST model provides a means for predicting multicomponent equiUbria, but the agreement is only good up to 50% surface saturation (9). 

Many additional consistency tests can be derived from phase equiUbrium constraints. From thermodynamics, the activity coefficient is known to be the fundamental basis of many properties and parameters of engineering interest. Therefore, data for such quantities as Henry s constant, octanol—water partition coefficient, aqueous solubiUty, and solubiUty of water in chemicals are related to solution activity coefficients and other properties through fundamental equiUbrium relationships (10,23,24). Accurate, consistent data should be expected to satisfy these and other thermodynamic requirements. Furthermore, equiUbrium models may permit a missing property value to be calculated from those values that are known (2). 

The solvophobic model of Hquid-phase nonideaHty takes into account solute—solvent interactions on the molecular level. In this view, all dissolved molecules expose microsurface area to the surrounding solvent and are acted on by the so-called solvophobic forces (41). These forces, which involve both enthalpy and entropy effects, are described generally by a branch of solution thermodynamics known as solvophobic theory. This general solution interaction approach takes into account the effect of the solvent on partitioning by considering two hypothetical steps. Eirst, cavities in the solvent must be created to contain the partitioned species. Second, the partitioned species is placed in the cavities, where interactions can occur with the surrounding solvent. The idea of solvophobic forces has been used to estimate such diverse physical properties as absorbabiHty, Henry s constant, and aqueous solubiHty (41—44). A principal drawback is calculational complexity and difficulty of finding values for the model input parameters. 

The solvophobic model has been used to deduce a functional form for a Henry s constant correlation based on molecular coimectivity index and polarizabiHty (42). Accurate predictions are reported over a span of seven log units in Henry s constant. A reHable solvophobic model of aqueous solubiHty has also been reported (45,46). 

Fiend s Constant. Henry s law for dilute concentrations of contaminants ia water is often appropriate for modeling vapor—Hquid equiHbrium (VLE) behavior (47). At very low concentrations, a chemical s Henry s constant is equal to the product of its activity coefficient and vapor pressure (3,10,48). Activity coefficient models can provide estimated values of infinite dilution activity coefficients for calculating Henry s constants as a function of temperature (35—39,49). 

The idea of the activated complex was developed by, among others, Henry Eyring at Princeton in the 1930s. It forms the basis of the transition-state model for reaction rate, which assumes that the activated complex—... 

M. Amon and C. D. Denson [33-34] attempted a theoretical and experimental examination of molding a thin plate from foamed thermoplastic. In the first part of the series [33] the authors examined bubble growth, and in the second [34] — used the obtained data to describe how the thin plate could be molded with reference to the complex situation characterized in our third note. Here, we are primarily interested in the model of bubble growth per se, and, of course, the appropriate simplification proposals [33]. Besides the conditions usual for such situations ideal gets, adherence to Henry s law, negligible mass of gas as compared to mass of liquid, absence of inertia, small Reynolds numbers, incompressibility of liquid, the authors postulated [33] several things that require discussion ... 

It is easily possible to introduce refinements into the dilated van Laar model which would further increase its accuracy for correlating activity coefficient data. However, such refinements unavoidably introduce additional adjustable parameters. Since typical experimental results of high-pressure vapor-liquid equilibria at any one temperature seldom justify more than two adjustable parameters (in addition to Henry s constant), it is probably not useful for engineering purposes to refine Chueh s model further, at least not for nonpolar or slightly polar systems. 

HARRIOTT 25 suggested that, as a result of the effects of interfaeial tension, the layers of fluid in the immediate vicinity of the interface would frequently be unaffected by the mixing process postulated in the penetration theory. There would then be a thin laminar layer unaffected by the mixing process and offering a constant resistance to mass transfer. The overall resistance may be calculated in a manner similar to that used in the previous section where the total resistance to transfer was made up of two components—a Him resistance in one phase and a penetration model resistance in the other. It is necessary in equation 10.132 to put the Henry s law constant equal to unity and the diffusivity Df in the film equal to that in the remainder of the fluid D. The driving force is then CAi — CAo in place of C Ao — JPCAo, and the mass transfer rate at time t is given for a film thickness L by ... 

As most organotins decompose, boiling points of 250 °C were assumed in the absence of a "true boiling point. The values for Henry s law constant and organic carbon/water partition coefficient were all derived from EUSES unless otherwise indicated. The chlorides were chosen as soluble salts in this table toxicity is independent of salt (see section 8), and soluble salts maximize likely environmental exposure, giving worst case in modelling environmental fate. 

This equation can be simplified to give H = P/S, where H is now Henry s law constant, which has dimensions of atm mVmole. Values for H may be calculated or measured (Mackay et al. 1979), and are now widely used infugacity modeling (see Section 3.2). 

Gorin has extended this analysis to include (1) the effects of the finite size of the counterions in the double layer of spherical particles [137], and (2) the effects of geometry, i.e. for cylindrical particles [2]. The former is known as the Debye-Huckel-Henry-Gorin (DHHG) model. Stigter and coworkers [348,369-374] considered the electrophoretic mobility of polyelectrolytes with applications to the determination of the mobility of nucleic acids. 

The Henry s law constant value of 2.Ox 10 atm-m /mol at 20°C suggests that trichloroethylene partitions rapidly to the atmosphere from surface water. The major route of removal of trichloroethylene from water is volatilization (EPA 1985c). Laboratory studies have demonstrated that trichloroethylene volatilizes rapidly from water (Chodola et al. 1989 Dilling 1977 Okouchi 1986 Roberts and Dandliker 1983). Dilling et al. (1975) reported the experimental half-life with respect to volatilization of 1 mg/L trichloroethylene from water to be an average of 21 minutes at approximately 25 °C in an open container. Although volatilization is rapid, actual volatilization rates are dependent upon temperature, water movement and depth, associated air movement, and other factors. A mathematical model based on Pick s diffusion law has been developed to describe trichloroethylene volatilization from quiescent water, and the rate constant was found to be inversely proportional to the square of the water depth (Peng et al. 1994). 

Henry, L.K. et al.. Effects of ozone and oxygen on the degradation of carotenoids in an aqueous model system, J. Agric. Food Chem., 48, 5008, 2000. 

Henry CR. 1998. Surface studies of supported model catalysts. Surf Sci Rep 31 235-325. Henry C. 2003. Adsorption and reaction at supported model catalysts. In Wieckowski A, Savinova ER, Vayenas CG. editors. Catalysis and Electrocatalysis at Nanoparticle Surfaces. New York Marcel Dekker. 

Brian Johnson and Margret Geselbracht are thanked for critically reading this manuscript. On behalf of the Ad Hoc Committee for Solid-State Instructional Materials, it is a pleasure to acknowledge the National Science Foundation (Grant USE—9150484), the Camille and Henry Dreyfus Foundation, the American Chemical Society, the Dow Chemical Company Foundation (Solid-State Model Kit), the University of Wisconsin—Madison Outreach Program (Solid-State Model Kit), and the Institute for Chemical Education for their generous support of this project. 

---