Surface versus concentration

Equation 9 states that the surface excess of solute, F, is proportional to the concentration of solute, C, multipHed by the rate of change of surface tension, with respect to solute concentration, d /dC. The concentration of a surfactant ia a G—L iaterface can be calculated from the linear segment of a plot of surface tension versus concentration and similarly for the concentration ia an L—L iaterface from a plot of iaterfacial teasioa. la typical appHcatioas, the approximate form of the Gibbs equatioa was employed to calculate the area occupied by a series of sulfosucciaic ester molecules at the air—water iaterface (8) and the energies of adsorption at the air-water iaterface for a series of commercial aonionic surfactants (9). 

In addition to the stepwise mechanism, Dautzenberg and Platteeuw proposed another platinum-catalyzed cyclization mechanism (23). This might correspond simply to a disguised stepwise aromatization where the further reaction of unsaturated intermediates is very rapid compared with their desorption. Thus, hydrogen pressure would govern the probability of desorption versus further reaction. Since the cyclization of triene is irreversible, a very low steady-state surface triene concentration must be sufficient to ensure a measurable reaction rate. 

From the plots of y versus concentration, the slope is related to the surface excess, Fsaikyisuifate- The area/molecule values indicate that the molecules are aligned vertically on the surface, irrespective of the alkyl chain length. If the molecules were oriented flat, then the value of area/molecule would be much larger (approximately 100 A2). Further, the fact that the alkyl chain length has no effect on the area also proves this assumption. These conclusions have been verified from spread monolayer studies. Further, it is also found that the polar group, that is, -SO4-, would occupy something like 50 A2. Later, it will be shown that other studies conhrm that the area per molecule is approximately 50 A2. 

It has been shown (Friberg, 2003 Birdi, 2002, 2008) that there exists a correlation between foam stability and the elasticity [E] of the film (i.e., the monolayer). In order for E to be large, surface excess must be large. Maximum foam stability has been reported in systems with fatty acid and alcohol concentrations well below the minimum in y. Similar conclusions have been observed with -C12H25S04Na [SDS] + -C12H25OH systems that give minimum in y versus concentration with maximum foam at the minimum point (Chattoraj and Birdi, 1984). Because of mixed mono-layer formation it has been found that SDS + C12H25OH (and some other additives) make liquid-crystalline structures at the surface. This leads to a stable foam (and liq-... 

Fig. 3. Schematic diagrams a surface tension versus concentration of a surfactant, b phase diagram of a surfactant near the Krafft temperature, c phase diagram of 3-0-dodecyl-D-glucitol [11]...

Molecular weight of a solute from tt versus A isotherms Use of the van t Hoff equation for monolayers Suppression of evaporation by monolayers Surface excess concentration from surface tension data... 

Fig. 14. The interfacial shear strength versus surface oxygen concentration for the A and HM carbon fibers. The large increase from the untreated (U) case to the surface treated case (S) for both fibers is due to removal of the native defect surface layer plus the addition of surface chemical groups. Removal of the surface groups with various treatments indicates that the surface chemical effect was a minor part of the overall increase. From Drzal et al.751...

The emf of the lithium-aluminium system versus pure lithium in a Lil-KI-LiCl molten eutectic is shown in Fig. 8.2 as a function of temperature and composition. It can be seen that the emf remains constant (at about 300 mV more negative than pure lithium) in the range of stability of the /3-phase (-7-47 atoms per cent of lithium), thus implying a constant lithium activity in the alloy surface. At concentrations greater than 47 atoms per cent, the lithium activity becomes strongly composition-depen-dent. 

Plots of surface tension versus concentration for n-pentanol [49], LiCl (based on Ref. [50]), and SDS in an aqueous medium at room temperature are shown in Fig. 3.7. The three curves are typical for three different types of adsorption. The SDS adsorption isotherm is typical for amphiphilic substances. In many cases, above a certain critical concentration defined aggregates called micelles are formed (see Section 12.1). This concentration is called the critical micellar concentration (CMC). In the case of SDS at 25°C this is at 8.9 mM. Above the CMC the surface tension does not change significantly any further because any added substance goes into micelles not to the liquid-gas interface. 

Figure 3.7 Plots of surface tension versus concentration for n-pentanol [49], LiCl (based on ref. [50]), and SDS in an aqueous medium at room temperature.

A final area of difficulty is in the application of data analysis to specific models of adsorption isotherms. This difficulty results from the fact that different models for adsorption isotherms generate plots of surface versus dissolved concentration that have characteristic shapes. If a plot of observational data results in a curve with a shape similar to that generated by a model, this result is often taken as proof that the particular model applies. Unfortunately, this assumption has been made for situations where many of the basic requirements of the model are violated in the system under study. The Langmuir adsorption isotherm model has suffered considerable abuse by geochemists in this regard. It should be remembered that "shapes" of adsorption isotherms are far from proof that a specific model applies. 

The surface excess concentration (T), which is the surface concentration of surfactant, can be determined by the representative Gibbs adsorption equation. The T can be obtained from the slope of a plot shown in Figure 2.1 (y versus log[C] at constant temperature). 

The dynamic method permits the purification from better soluble impurities as well as continuous solubility measurements at the same time. An adsorption effect of the stationary phase which is used to precipitate the dyestuff on its surface is not found within the experimental accuracy. The measurements of l,4-bis-(n-alkylamino)-9,10-anthraquinone (with n-alkyl = butyl, octyl) show two intersection points in the plot of pressure versus concentration. 

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. 

An early normalizing procedure, proposed by Kiselev (1957) to compare adsorption isotherms of hydrocarbons, water vapour, etc. on a series of different adsorbents, was simply to plot the surface excess concentration F (=n/A), obtained from a knowledge of the BET-nitrogen surface area, A (BET), versus p/p°. It is also possible to plot, instead of f, the reduced adsorption , n/nm, which still relies on the BET method to determine the monolayer capacity nm but does not require knowledge of the molecular cross-sectional area a. 

As envisioned previously, ESI response is concentration-dependent. A linear response versus concentration is up to the maximum concentration of about 10 M. When analyte concentration exceeds this limit, the ESI response levels off. This is because ESI intensity is proportional to the surface concentration of an ion. At about lO M, the droplet surface is completely saturated and higher concentration will not increase the total number of surface charges available for ion formation [25]. This will impact the high concentration end of quantitation using LC/ESl-MS. For the low concentration end, the detection limit depends on the sensitivity of LC/MS system, including efficient ion transfer/detection and removal of chemical noise in the system. 

Figure 13.11. Ligand- and proton-promoted dissolution of AI2O3. (a) The ligand-catalyzed dissolution of a trivalent metal (hydr)oxide. (b) Measurement of Al(UI)(aq) as a function of time at constant pH at various oxalate concentrations. The dissolution Idnetics are given by a reaction of zero order. The dissolution rate, / l, is given by the slope of the (Al(III)(aq)] versus time curve, (c) Dissolution rate as a function of the surface ligand concentration for various ligands. The dissolution is proportional to the surface concentration of the ligand, <=MeL> or C(. (/ l = (d) Proton-promoted...

Figure 3.3 The different types of excess isotherms. Plots of the surface excess concentration, r (mmol/g), with n total number of mole of components 1 and 2, versus the mole fraction (except Figure 3.3-11, plot of (mg/g) versus weight fraction, wi). (I) 1,2-Dichloroethane (1) and benzene (2) on alumina gel at 25°C. (II) Benzene (1) and n-heptane on (a) alumina gel, (b) silica gel at 25°C. (Ill) Ethanol (1) and water (2) on charcoal at 25°C. (IV) Benzene (1) and ethanol (2) on charcoal at 25°C. (V) 1,2-Dichloroethane (1) and benzene (2) on charcoal at 25°C. Reproduced from G. Schay, Surf. Coll. Sci, 2 (1969) 155 (Figs. 1 to 5), with kind permission of Springer Science and Business Media.

Fig. 9. Surface carbon concentration as measured by XPS versus time (O) T = 560 K and ( ) / 506K. From (36).

Adsorption reactions by soil minerals and soils have been described historically using empirical adsorption isotherm equations. As their name implies, it is understood that they are used for experiments at constant temperature, which unless indicated, otherwise is standard temperature, T = 298 K. An adsorption isotherm is a plot of the concentration adsorbed to a solid surface versus the concentration in aqueous solution for different total concentrations of a chemical species. Typically, adsorption isotherm equations are very good at describing experimental data, despite their lack of theoretical basis. Popularity of these equations stems in part from their simplicity and from the ease of estimation of their adjustable parameters. 

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