Surface excess, relative

One important advantage of the polarized interface is that one can determine the relative surface excess of an ionic species whose counterions are reversible to a reference electrode. The adsorption properties of an ionic component, e.g., ionic surfactant, can thus be studied independently, i.e., without being disturbed by the presence of counterionic species, unlike the case of ionic surfactant adsorption at nonpolar oil-water and air-water interfaces [25]. The merits of the polarized interface are not available at nonpolarized liquid-liquid interfaces, because of the dependency of the phase-boundary potential on the solution composition. 

The meaning of the surface excess is illustrated in Fig. 1, in which the solid line represents the actual concentration profile of an adsorbate i, when the bulk concentration of i in the phase a (a = O or W) is c . The hatched area corresponds to be the surface excess of i, T,. This quantity depends on the location of the dividing surface. On the other hand, the experimentally accessible quantity should not depend on the location of the artificially introduced dividing surface. The relative surface excess, which is independent of the location of the dividing surface, is defined by relativizing it with respect to those of certain reference components. In oil water interfaces, the mutual solubility of solvents can be significant. The relative surface excess in Eq. (3) is then related to the surface excesses through... 

When a component of interest is considerably surface active, its adsorbed amount is high even when its bulk concentration is low. The second terms on the right-hand side of Eqs. (4)-(6) are then small and the relative surface excesses are simply taken as the surface excesses, which, in turn, may be seen as the surface concentration. For example, dilaur-oylphosphatidylcholine forms a saturated monolayer in the liquid-expanded state at the nitrobenzene-water interface when its concentration in nitrobenzene is 10 moldm [30]. Then the experimentally obtained value, 1.76 x 10 °molcm, can be considered to be the surface concentration. 

Thermodynamics of the ITIES was developed by several authors [2-6] on the basis of the interfacial phase model of Gibbs or Guggenheim. General treatments were outlined by Kakiuchi and Senda [5] and by Girault and Schiffrin [6]. At a constant temperature T and pressure p the change in the surface tension y can be related to the relative surface excess concentrations Tf " of the species i with respect to both solvents [6],... 

Girault and Schiffrin [4] used a similar approach to derive the expression for the relative surface excess of water with respect to the electrolyte RX and the organic solvent,... 

Eqs. (15), (17), and (21) can be used to define other observable quantities, such as relative surface excess concentrations of ions, which also comprise the contributions from the free ionic and ion-pair surface excesses, e.g., for the ideally polarized ITIES,... 

Apparently, the relative surface excess concentrations T" " and r l represent the total amount of the components R and Y (either as free ions or as ion pairs) that should be added to the system to maintain figy and fij x respectively as well as E x constant when the area of the interface is increased by a unit amount. 

Kakiuchi and Senda [36] measured the electrocapillary curves of the ideally polarized water nitrobenzene interface by the drop time method using the electrolyte dropping electrode [37] at various concentrations of the aqueous (LiCl) and the organic solvent (tetrabutylammonium tetraphenylborate) electrolytes. An example of the electrocapillary curve for this system is shown in Fig. 2. The surface excess charge density Q, and the relative surface excess concentrations T " and rppg of the Li cation and the tetraphenylborate anion respectively, were evaluated from the surface tension data by using Eq. (21). The relative surface excess concentrations and of the d anion and the... 

Negative adsorption occurs when a charged solid surface faces an ion in an aqueous suspension and the ion is repelled from the surface by Coulomb forces. The Coulomb repulsion produces a region in the aqueous solution that is depleted of the anion and an equivalent region far from the surface that is relatively enriched. Sposito (1984) characterized this macroscopic phenomenon through the definition of the relative surface excess of an anion in a suspension, by... 

The plastic behavior necessarily follows an elastic regime that could not be probed within the explored 4> range ((/> > 70%). By integrating Eq. (4.20), the relative surface excess (S - So)/So can be calculated ... 

At(p = 70%, the relative surface excess is of the order of 0.1%. At this volume fraction, the surface stress has already reached its asymptotic value. Thus, the plastic strain of the surface is smaller than 0.1%. 

Adsorption (or desorption) is the process by which a net accumulation (or loss) of a substance occurs at an interface between two phases. In a typical experiment, two phases are mixed intimately to provoke a chemical reaction leading to adsorption or desorption, and then a physical separation is made, with one of the separates being a single phase and the other, a mixture of the two reacted phases. For example, a solid-phase adsorbent and an aqueous solution could be mixed, and then separated by centrifugation into an aqueous phase (supernatant solution) and a slurry that contains both the solid adsorbent and some aqueous solution. If is the moles of substance i in the reacted mixture and m is the molality of substance i in the separated aqueous phase, then the relative surface excess, np, of substance i, as compared to another substance j, is defined by1... 

The strict thermodynamic analysis of an interfacial region (also called an -> interphase) [ii] is based on data available from the bulk phases (concentration variables) and the total amount of material involved in the whole system yielding relations expressing the relative surface excess of suitably chosen (charged or not charged) components of the system. In addition, the - Gibbs equation for a polarizable interfacial region contains a factor related to the potential difference between one of the phases (metal) and a suitably chosen - reference electrode immersed in the other phase (solution) and attached to a piece of the same metal that forms one of the phases. 

There are two ways to control the electrical state determination at constant charge, oM, or at constant cell potential. From a thermodynamic point of view, isotherms with respect to relative surface excesses may be determined at constant charge or at any well-defined constant potential. However, the interpretation and physical meaning of the results may be significantly more difficult in the case when constant cell potential (-> cell voltage) is used. 

In general the values of rA and rB depend on the position chosen for the Gibbs dividing surface. However, two quantities, TB(A) and rB(n) (and correspondingly wBa(A) and nB°(n)), may be defined in a way that is invariant to this choice (see [l.e]). TB(A) is called the relative surface excess concentration of B with respect to A, or more simply the relative adsorption of B it is the value of rB when the surface is chosen to make rA = 0. rB(n) is called the reduced surface excess concentration of B, or more simply the reduced adsorption of B it is the value of rB when the surface is chosen to make the total excess r = rt = 0. 

Since the reduced and relative surface excess isotherms convey composite information on the adsorption of the two components, there is a strong incentive to determine the individual (or separate ) isotherms, i.e. the adsorbed amount n (or ) versus concentration, mole fraction or mass fraction. It will be recalled that this implies some assumptions about the thickness, composition and structure of the adsorbed layer, and therefore is not to be recommended for reporting adsorption from solution data in a standard form. Indeed, this second step is already part of the theoretical interpretation of the adsorption mechanisms. 

A possible way to increase the accuracy of this immersion approach is to use the slurry method and to analyse a weighed sample of the slurry in the bottom of the test-tube, instead of analysing the supernatant (Nunn etal., 1981). One then simply makes use of Equation (5.49), the operational expression of the relative surface excess of the solute with respect to the solvent. Here n1 and n2 are the total amounts of solute and solvent in the sample of slurry (either adsorbed or in solution) and c[ and c their concentrations in the solution. If one uses a liquid-solid ratio large enough to avoid any measurable change in concentration on adsorption, then c and c are simply the concentrations in the starting solution. The measurement is accurate provided the quantitative analysis of the slurry, which involves measuring the total amounts of 2 and 1... 

Both surface excess amounts must also remain unchanged this necessarily holds when using reduced surface excess amounts by the application of Equation (5.75), since nfn) = -nf"] (see Equation (5.10)) so that it is enough to maintain a constant nfn). This does not hold, however, when relative surface excess amounts or simple surface excess amounts are used. 

A more direct way of comparing the strength of specific adsorption is shown in Fig. lOH, which displays the relative surface excess for... 

Fig. lOH Relative surface excess of different anions, multiplied by zF, as a function of potential, in O.IN solutions of their respective salts, at 25°C. Reprinted with permission from Grahame and Soderberg, J. Chem. Phys., 22, 449, (1954). Copyright 1954, the American Institute of Physics. 

It should be borne in mind that all the data reported in the literature for mercury are values of the relative surface excess F , not the fractional coverage 0. In dilute solutions the relative surface excess is very nearly equal to the surface excess, in view of its definition, given by Eq. 28H... 

Reference electrodes, 37 Relative surface excess, 236 Relaxation time, 358, 366, 369 Repassivation potential, 514 Resistance overpotential, 107 Reverse-pulse techniques, 397 Reverse-step voltaininetry, 400 Reversibility, 78... 

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