Relative surface excess amount

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. 

That is, the thermodynamically determinable relative surface excess amount is practically the same as the total amount of substance in the monomolecular layer, and on the basis of the aforementioned... 

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. 

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. 

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. 

The meaning of relative and reduced surface excess amounts.145... 

The meaning of relative and reduced surface excess amounts Although the relative and the reduced surface excess amounts (or masses) do not depend on the position of the GDS, there is a special position of the GDS which cancels the last term of the defining equations ((5.48) and (5.55)) and gives a useful idea of the meaning of these two quantities. For Equation (5.48), this special position of the GDS is the one for which the surface excess amount n of component 1 is zero. We then get ... 

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... 

Electrocapillary methods, described in Sections 13.2 and 13.3, are very useful in the determination of relative surface excesses of specifically adsorbed species on mercury. As discussed in Section 13.4, such methods are less straightforward with solid electrodes. For electroactive species and products of electrode reactions, the faradaic response can frequently be used to determine the amount of adsorbed species (Section 14.3). Nonelectro-chemical methods can also be applied to both electroactive and electroinactive species. For example, the change in concentration of an adsorbable solution species after immersion of a large-area electrode and application of different potentials can be monitored by a sensitive analytical technique (e.g., spectrophotometry, fluorimetry, chemiluminescence) that can provide a direct measurement of the amount of substance that has left the bulk solution upon adsorption (7, 44). Radioactive tracers can be employed to determine the change in adsorbate concentration in solution (45). Radioactivity measurements can also be applied to electrodes removed from the solution, with suitable corrections applied for bulk solution still wetting the electrode (45). A general problem with such direct methods is the sensitivity and precision required for accurate determinations, since the bulk concentration changes caused by adsorption are usually rather small (see Problem 13.7). 

The second quantity obtained from the Gibbs-Duhem equation is the relative surface excess which is the difference of the amount of a substance in the interphase and the relative amount of solvent (s) expressed by the ratio of the mole fractions r, and x. ... 

In Figure 2.2 equilibrium adsorption data for carbon dioxide (CO2) on zeolite Na 13X (Linde, UOP) are presented for temperatures 298 K and 303 K. The mol numbers of the Gibbs surface excess amounts per unit mass of sorbent are depicted as function of the sorptive gas pressure and temperature. Relative uncertainties of measurements are about ( ttiGE/ GE)-2%- The subcritical isotherms are in the range of pressure measured of Type I - lUPAC classification [2.20]. 

We present a discussion of the uncertainty contributions to the amount of fluid in the continuous phase or the density of the same from the SU in sample and dosing volumes and associated pressure data, and the manifold and adsorption system temperature. Each of the coefficients in the EoS also has its inherent uncertainty, which also needs to be considered. We use nitrogen adsorption data (relative to helium dead-space measurements) for a microporous activated carbon cloth (ACC) to demonstrate uncertainty in the various EoS evaluation and its propagation to the combined standard uncertainty in the (Gibbs) specific surface excess amount,, equivalent to the traditionally known amount adsorbed (in low pressure measurement), shown in Eq. (2)... 

The information one can derive from measurements of the surface tension as a function of potential is specified in Eqs. (9.9)-(9.14). It includes the dependence of charge and the double-layer capacitance on potential and the relative surface excess of all the species in solution, except the solvent), as a function of potential and of the composition of the solution. It should be noted, however, that all these quantities must be obtained by numerical differentiation of the experimental results. This requires very high accuracy in measurement, since differentiation inherently amplifies experimental errors (while integration tends to smooth them out). The range of values of y in most cases is (0.250—0.426) N m . The best measurements recorded claim an accuracy of 0.1 mN m which amounts to about (0.04-0.02)%. 

Third, a curious and subtle concept was explained, the concept of surface excess, r. This is not to be confused with adsorption, although the surface excess may become nearly identical to the total amount adsorbed under certain limiting conditions. The surface excess of a particular species is the excess of that species present in the surface phase relative to the amount that would have been present had there been no double layer. The surface excess, therefore, represents the accumulation or depletion of the species in the entire interphase region. Further, electrocapillaiy measurements and radiochemical experiments permit a direct experimental description of the surface excess of a species. 

When a polymer simply contains ionic salts that are not bound covalently to the polymer chains themselves, e.g. tetraalkylammonium toluenesulphonate, the situation is more complicated, because ions of both sign are mobile and are available for transfer. The magnitude of the net charge transferred will then depend on the relative transfer aptitude of the two ions in the salt. Both of the ions tend to transfer in excessive amounts, which contaminates the second surface and produces a relatively low net surface charge density. 

A comprehensive study on the sonochemical synthesis of colloidal solutions of noble metals was conducted by Grieser and coworkers [32-34]. The 515 kHz ultrasound-initiated reduction of AuCl4 to Au (0) was examined as a function of the concentration of various surface-active solutes [32]. The amount of AuCU reduced in the presence of ethanol, 1-propanol, and 1-butanol was found to be dependent on the surface excess of the alcohol at the gas/solution interface, i.e., the relative concentration of the alcohol at the gas/solution interface compared to the bulk solution concentration. The efficiency of reduction of AuCl4 in the presence of the surfactants sodium dodecyl sulfate or octaethylene glycol monodecyl ether was found to be related to the monomer concentration of the surfactant in solution. 

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