Surface concentration, using Gibbs method

The capillary-rise method is used to study the change in surface tension as a function of concentration for aqueous solutions of />butanol and sodium chloride. The data are interpreted in terms of the surface concentration using the Gibbs isotherm. 

The relation between film stability, spreading coefficient on a substrate and surface pressure can be found using the method proposed by Frumkin [20] and Derjaguin [538]. A diagram is drawn of the dependence film tension versus area of a mole of the substance in the film (Ao = I/O, T being the number of moles of the substance in a unit area. At small substance concentrations (pressures) in the gas phase, its adsorption is close to Gibbs adsorption. 

Number of moles of adsorbed gas (surface excess) using the Gibbs method. Surface concentration, n /a, using the Gibbs method. 

Outside of a particular layer of a finite thickness (the physical discontinuity surface), the concentrations of water and hexanol in the corresponding phases are constant. These concentrations are, respectively, c[ and c) in an aqueous solution (liquid) and c i and c i in vapor. Within the discontinuity surface, there is a transition between these concentrations either a smooth one or a positive tongue-like one, as shown in Figure 2.1b. In order to determine the excess (or the difference in the composition to be more precise) of a given component in a surface layer, we need to use Gibbs s method and extrapolate these four constant values to the dividing surface (the geometric discontinuity surface located within the physical discontinuity surface). The excess (adsorption) of... 

This form of the Gibbs fundamental equation demonstrates the importance of surface and interfacial tension measurements of interfacial layers out of the adsorption equilibrium. These methods are the most frequently used techniques to follow the time-dependence of the adsorption process. However, for very slow processes, which occurs in systems with extremely small amounts of surfactants, other methods such as the radio-tracer technique and ellipsometry, or the very recently developed technique of neutron reflectivity, can be used to directly follow the change of surface concentration with time. 

This is the important Gibbs adsorption isotherm. (Note that for concentrated solutions the activity should be used in this equation.) Experimental measurements of y over a range of concentrations allows us to plot y against Inci and hence obtain Ti, the adsorption density at the surface. The validity of this fundamental equation of adsorption has been proven by comparison with direct adsorption measurements. The method is best applied to liquid/vapour and liquid/liquid interfaces, where surface energies can easily be measured. However, care must be taken to allow equilibrium adsorption of the solute (which may be slow) during measurement. 

The proposed approach leads directly to practical results such as the prediction—based upon the chemical potential—of whether or not a reaction runs spontaneously. Moreover, the chemical potential is key in dealing with physicochemical problems. Based upon this central concept, it is possible to explore many other fields. The dependence of the chemical potential upon temperature, pressure, and concentration is the gateway to the deduction of the mass action law, the calculation of equilibrium constants, solubilities, and many other data, the construction of phase diagrams, and so on. It is simple to expand the concept to colligative phenomena, diffusion processes, surface effects, electrochemical processes, etc. Furthermore, the same tools allow us to solve problems even at the atomic and molecular level, which are usually treated by quantum statistical methods. This approach allows us to eliminate many thermodynamic quantities that are traditionally used such as enthalpy H, Gibbs energy G, activity a, etc. The usage of these quantities is not excluded but superfluous in most cases. An optimized calculus results in short calculations, which are intuitively predictable and can be easily verified. 

The preceding discussion of the Gibbs adsorption equation was referenced to a fluid-fluid interface in which the surface excess, T, is calculated based on a measured quantity, a, the interfacial tension. For a sohd-fluid interface, the interfacial tension cannot be measured directly, but the surface excess concentration of the adsorbed species can be, so that the equation is equally useful. In the latter case. Equation (9.16) provides a method for determining the surface tension of the interface based on experimentally accessible data. 

For relatively dilute systems containing surface-active materials (i.e., surfactants see Chapter 3), the concentration of adsorbed material can be calculated from the known amount of material present before adsorption and that present in solution after adsorption equihbrium has been reached. A wide variety of analytical methods for determining the solution concentration are available, and almost all have been used at one time or other. In surfactant systems, the use of the Gibbs equation and measurements of tr are experimentally simple and straightforward (with proper precautions, of course). The utility of a specific method will depend ultimately on the exact nature of the system involved and the resources available to the investigator. 

One of the simplest methods to study adsorption at the oil water interface is to measure the variation of interfacial tension as a function of concentration. If the polymer used for adsorption is monodisperse, then the Gibbs equation (51) may be used to estimate the surface excess. However, if the polymer is polydis-perse, this method will give erroneous values of the surface excess because the larger molecules will tend to adsorb preferentially, and the equation is imable to account for this adsorption behavior. As a result, most of the data available in the literature report the change in the interfacial tension as a function of concentration without attempting to convert it into an adsorbed amoimt. Apart from interfacial tension measurements, other techniques such as total internal reflection fluorescence microscopy (52) and scintillation measurements from radiolabeled polymers (53) have also been used to measure the adsorption at the liquid-liquid interface. 

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