Surface excess concentration experimental measurement

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. 

In this manner, the surface excess of ions can be found from the experimental values of the interfacial tension determined for a number of electrolyte concentrations. These measurements require high precision and are often experimentally difficult. Thus, it is preferable to determine the surface excess from the dependence of the differential capacity on the concentration. By differentiating Eq. (4.2.30) with respect to EA and using Eqs (4.2.24) and (4.2.25) in turn we obtain the Gibbs-Lippmann equation... 

What then is the point of measuring surface excess It will be shown that the surface excess affects many quantities, for example, the interfacial tension at the interlace and the way in which it depends upon concentration. In fact it will be shown (see. Section 6.5.1) that surface excess can be experimentally determined from thermodynamic measurements without recourse to modeling arguments. 

The adsorption isotherm was calculated from the measured concentration change. The number of points and their precision suggests that the adsorption values are good to 5%, except at the very lowest concentrations. The absolute accuracy depends on the cleanliness of the carbon surface, which could contain chemisorbed oxygen, and on the completeness of the dispersion process. These possible errors would lead to low values for the experimental surface excess. Comparison of the area per adsorbed ion at apparent surface saturation with the calculated area in different orientations suggests that the entire B.E.T. area is available for adsorption in the dispersions. 

An adsorption isotherm for a single gaseous adsorptive on a solid is the function which relates at constant temperature the amount of substance adsorbed at equilibrium to the pressure (or concentration) of the adsorptive in the gas phase. The surface excess amount rather than the amount adsorbed is the quantity accessible to experimental measurement, but, at lower pressures, the difference between the two quantities becomes negligible (see Appendix II, Part I, 1.1.11). 

When a solute avoids the interface (T < 0), the surface tension increases by adding the substance. Experimentally Equation (3.52) can be used to determine the surface excess by measuring the surface tension versus the bulk concentration. If a decrease in the surface tension is observed, the solute is enriched in the interface. If the surface tension increases upon addition of solute, then the solute is depleted in the interface. 

The surface activity of these compounds was not studied in detail. As mentioned in the Experimental Section, all were about equivalent in nucleating particles during emulsion polymerization. The resulting latexes when dialyzed to remove excess salt were stable against settling even at 10% solids over many months. Data on samples where both latex particle size and critical micelle concentration were measured is shown in Table II. 

A study of iron, cadmium and lead mobility in remote mountain streams of California by Erel et al. (1990) showed that the excess of atmospheric pollution-derived lead and cadmium is rapidly removed downstream. The comparison of truly dissolved, colloidal, and surface particle concentrations measured in the stream with the results of a model of equilibrium adsorption indicates that the mechanism of removal in this organic-poor environment is essentially by uptake onto hydrous iron oxides. The experimentally determined partition coefficients (Dzomback and Morel, 1990) explain the behavior of lead however, they fail to explain the cadmium removal. It is proposed by the authors that cadmium is taken up by surfaces other than hydrous iron oxides. 

In the field of adsorption from solution, many discussions and reviews were published about the measurement of the adsorbed amount and the presentation of the corresponding data [14, 45—47]. Adsorption isotherms are the first step of any adsorption study. They are generally determined from the variation of macroscopic quantities which are rigorously measurable far away from the surface (e.g., the concentration of one species, the pressure, and the molar fraction). It is then only possible to compare two states with or without adsorption. The adsorption data are derived from the difference between these two states, which means that only excess quantities are measurable. Adsorption results in the formation of a concentration profile near an interface. Simple representations are often used for this profile, but the real profile is an oscillating function of the distance from the surface [15, 16]. Without adsorption, the concentration should be constant up to the soHd surface. Adsorption modifies the concentration profile of each component as well as the total concentration profile. It must be noted also that when the liquid is a pure component its concentration profile, i.e., its density, is also modified. Experimentally, the concentration can be measured at a large distance from the surface. The surface excess of component i is the... 

Surface tensions of the soluble alkali salt of di- and tri-hydroxy bile salts have been widely employed [5,11,12,33,70-74] to measure CMCs of bile salts (see Section VI.l). Employing Gibbs adsorption isotherm equation and the steep slope of the experimental surface tension versus bile salt concentration curve, the surface excess, i.e. concentration of bile salt molecules/cn of interface, can be calculated accurately in high bulk ionic strength [12,70], Using this value and Avogadro s number, the area per molecule at the interface can be calculated [6]. These values (Table 3b),... 

It is important to realise that the Gibbs model does not imply that the surface excess is concentrated at the Gibbs dividing surface this is clearly physically impossible since molecules have a finite size and cannot occupy a mathematical surface. What the Gibbs method docs is to recognise the existence of concentration profiles such as those shown in Figure 5.3, whose exact form cannot yet be measured experimentally, and to provide a method of expressing the observable consequences of their existence. 

The experimental adsorption isotherms of the alkali decyl sulfates are plotted in Fig. 3. The standard error of the data points was found to be 7x10 mol/cm from repeated measurements. As can be expected the isotherms are not simple Langmuir-type ones. The character of the isotherms shows a pronounced change at around 2-2.5x10 mol/cm surface excess. Below this concentration range the slope of the adsorption isotherms increases, which reflects that the driving force of the adsorption increases as the surface coverage, 0, increases. 

In Equation 3.26, T is the equilibrium surface excess, C the bulk concentration, t the time, and D the surfactant monomer diffusion coefficient. Eastoe et al. have measured the time dependence of the DST and the relaxation time %2 for solutions of many surfactants nonionic, dimeric, and zwitterionic. In all instances the fitting of the data to Equation 3.26 with the experimentally determined value of %2 was poor. The authors concluded that the micelle dissociation may have an effect on the measured DST only if the concentration of monomeric surfactant in the subsurface diffusion layer is limiting or when the micelle lifetimes are extremely long. No surfactant for which this last condition is fulfilled was evidenced by the authors. They also concluded that the rapid dissociation of monomers from micelles present in the subsurface was not likely to limit the surfactant adsorption and thus the DST. 

Here, F is the surface excess of the solute and a is its activity. The change in surface tension of the liquid is at constant temperature that is the reason why Eq. (6.65) is called isotherm. Equation (6.65) tells us that when a solute is enriched at the interface (F > 0), the surface tension decreases when the solution concentration is increased. Such solutes are said to be surface active and they are called surfactants or surface-active agents. Often, the term amphiphilic molecule or simply amphi-phUe is used. When a solute avoids the interface (F < 0), the surface tension increases by adding the substance. Experimentally, Eq. (6.65) can be used to determine the surface excess by measuring the surface tension versus the bulk concentration. If a decrease in the surface tension is observed, the solute is enriched in the interface. If the surface tension increases upon addition of solute, then the solute is depleted in the interface. 

The dye-clay composites were prepared by dispersing the clays in each solvent containing the dye at a quantity of 10-200% of the CEC. This experimental procedure led to almost complete intercalation at room temperature for 2-7 days. The composite was recovered by filtration and washing several times with each solvent for eliminating an excess of dye, and then dried in air. Assuming that the loss of dye adsorbed on the surface was fairly small upon washing, the net weight of dye intercalated was estimated from the residual dye concentration in a solvent measured by a colorimetric analysis. 

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