Constant, Benjamin

Among the dynamical properties the ones most frequently studied are the lateral diffusion coefficient for water motion parallel to the interface, re-orientational motion near the interface, and the residence time of water molecules near the interface. Occasionally the single particle dynamics is further analyzed on the basis of the spectral densities of motion. Benjamin studied the dynamics of ion transfer across liquid/liquid interfaces and calculated the parameters of a kinetic model for these processes [10]. Reaction rate constants for electron transfer reactions were also derived for electron transfer reactions [11-19]. More recently, systematic studies were performed concerning water and ion transport through cylindrical pores [20-24] and water mobility in disordered polymers [25,26]. 

Fife and Benjamin, 1973. The reference reaction is attack by alkoxide on ethyl benzoate estimated from the known second order rate constant for attack by hydroxide in water at 25° (Bender, 1951) and allowing a factor of 10 for the higher reactivity of alkoxides (Gilchrist and Jencks, 1960). The pX,-value is taken as that of benzyl alcohol (Takahashi el al., 1971)... 

In their description of metal ion adsorption, Benjamin and Leckie used an apparent adsorption reaction which included a generic relationship between the removal of a metal ion from solution and the release of protons. The macroscopic proton coefficient was given a constant value, suggesting that x was uniform for all site types and all intensities of metal ion/oxide surface site interaction. Because the numerical value of x is a fundamental part of the determination of K, discussions of surface site heterogeneity, which are formulated in terms similar to Equation 4, cannot be decoupled from observations of the response of x to pH and adsorption density. As will be discussed later, It is not the general concept of surface-site heterogeneity which is affected by what is known of x> instead, it is the specific details of the relationship between K, pH and T which is altered. 

The first use of a coupling constant in this manner is attributed to W. Pauli e.g., see Pines, D. The Many-Bo[Pg.180]

Belke et al. (1971) reported general base and general acid catalysis in cyclization of 2-hydroxymethylbenzamide [equation (18)]. However, with 2-hydroxymethyl-6-aminobenzamide strict general base catalysis by buffer bases is observed with a Bronsted coefficient of O 39 (Fife and Benjamin, unpublished data). In contrast with the unsubstituted amide, the Bronsted plot is nicely linear. An amino-group in the 6-position might assist decomposition of a tetrahedral intermediate as in [37a, b] or a kinetic equivalent. The pH-rate constant profile for spontaneous cyclization at zero buffer concentra-... 

Benjamin (B7) has also indicated that, if constant amplification of the most unstable wave per wavelength is assumed, it can be derived from... 

Measurements of 0 and D in rain and river waters have indeed made it possible to confirm (Dall Olio et al., 1979 Salati et al., 1979) the importance of re-evaporated water for the water balance throughout the Basin, and in particular to establish a model indicating the relationship with the new oceanic water. There is a predominant zonal flow from east to west (Newell et al., 1972) and vapour influx from the Atlantic Ocean was estimated from the wind and humidity measurements by radiosonde at Belem. The central east to west region of the Basin between 0° and 5° of the latitude was considered to be subdivided into eight 3° segments between Belem (48° 30 ) and just west of Benjamin Constant (72° 30 ). 

Accurate predictions of the transport of As in groundwater requires site specific data to model adsorption/desorption reactions. In complex mixtures of minerals, it may not be possible to quantify the adsorption properties of individual minerals. Therefore, it has been suggested that adsorption properties of composite materials should be characterized as a whole (Davis and Kent, 1990). Previously published data for adsorption by pure mineral phases such as the surface complexation database for adsorption by ferrihydrite (Dzombak and Morel, 1990) can be a useful starting point for modeling adsorption of solutes in groundwater however, these equilibrium constants may not reflect the adsorption properties of composite oxide coatings on aquifer solids. For example, incorporation of Si, and to a lesser extent, A1 into Fe oxyhydroxides has been shown to decrease adsorption reactivity towards anions (Ainsworth et al., 1989 Anderson and Benjamin, 1990 Anderson et al, 1985). Therefore, equilibrium constants will likely need to be modified for site-specific studies. 

Anderson, P, R., and M. M. Benjamin. 1990a. Constant-capacitance surface complexation model. In Chemical modeling of aqueous systems //, ed D. C. Melchior and R. L. Bassett. Am. Chem. Soc. Symp. Ser. 416, pp. 272-81. Washington DC Am. Chem. Soc. 

The effects of concentration. When metal adsorption at constant pH is plotted against solution concentration using a double logarithmic scale, linear relationships with slope less than unity are commonly obtained (Fig. 3.). This was first noted by Benjamin and Leckie [25]. In their review of a very large data set, Dzombak and Morel [3] reported that this was a common observation for metal reaction with hydrous metal oxides. This behaviour is consistent with a model in which the reacting sites are not uniform that is, there are a few sites of high affinity, rather more of slightly lower affinity and so on. 

Benjamin Thompson), Robert Mayer, Sadi Camot, James Joule, and others (see [2—4] for historical accounts) - that heat is a form of energy. A vast amount of experience and experimentation can be generahzed in the following way (e.g., [5]) in any defined system, although fhe work done on the system (W) or the heat absorbed by fhe system (Q) in going from one state of the system to another varies wifh fhe pafh taken, fhe sum of W and Q is a constant and depends only on the initial and final states of fhe system under consideration. This generalization is formalized as follows ... 

Benjamin PP (1969) A rapid and efficient method of preparing c-human serum albiunin its clinical applications. Int J Appl Radiat Isot 20 187-194 Benjamin PP, Rejali A, Friedell H (1970) Electrolytic complexation of " Tc at constant ciurent its application in nuclear medicine. J Nucl Med 11 147-154 Clarke MJ, Podbielski L (1987) Medical diagnostic imaging with complexes of " Tc. Coord Chem Rev 78 253-331... 

Fig. 32. Adiabatic free energy curves as a function of reaction coordinate for selected overpotential / (in V) and electronic coupling constant F (in eV). Data are taken with permission from the work of Rose and Benjamin [197].

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