Concentration dependence of surface

The derivative of the experimentally determined concentration dependency of surface tension, a = f x2), according to X2 we can extend as follows... 

Fig. 3.73. Concentration dependences of surface pressure for C 2S04Na ( ) and C 4 04Na ( ) solutions and their 3 1 (molar fractions) mixture (A) in the presence of 0.03 M NaCI theoretical values for the mixture calculated from Eq. (3.41) data reported in [70].

Figure 5.7 Concentration dependence of surface tension in poly(MPC) and PMB-X aqueous solution. The pictures represent the solubility of paclitaxel (PTX) in an aqueous solution of poly(MPC) and PMB-30W.

Seidel, A., and Carl, P.S., Concentration dependence of surface diffusion for adsorption on energetically heterogeneous adsorbents, Chem. Eng. Sci.. 44(1). 189-194(1989). 

The concentration dependence of surface tension for a surfactant solution is distinctive because it is sensitive to the formation of micelles. Unlike non-amphiphilic molecules, the decrease of surface tension with increasing concentration is non-monotonic. Upon increasing the concentration of a pure amphiphile, the surface tension decreases rapidly from the value y = 72 mN m for pure water until a point at which it levels off and becomes almost independent of concentration (Fig. 4.16). This point is the CMC. Note that the concentration is plotted on a logarithmic scale in Fig. 4.16. The reason for this will become apparent when we consider Eq. (4.27). The limiting value of surface tension above the CMC is typically around 35 mN m. That the surface tension is independent of concentration above the CMC is sometimes ascribed to saturation of the surfactant in the surface monolayer. However, it is actually due to a chemical potential that is almost independent of concentration above the CMC, as discussed in the following section. 

The temperature-concentration dependence of surface tensions o( 7 w) was correlated in Averbukh et al. [80] by... 

The simplest case to be analyzed is the process in which the rate of one of the adsorption or desorption steps is so slow that it becomes itself rate determining in overall transformation. The composition of the reaction mixture in the course of the reaction is then not determined by kinetic, but by thermodynamic factors, i.e. by equilibria of the fast steps, surface chemical reactions, and the other adsorption and desorption processes. Concentration dependencies of several types of consecutive and parallel (branched) catalytic reactions 52, 53) were calculated, corresponding to schemes (Ila) and (lib), assuming that they are controlled by the rate of adsorption of either of the reactants A and X, desorption of any of the products B, C, and Y, or by simultaneous desorption of compounds B and C. 

The concentration dependence of CO oxidation over Pt at (02) (CO) l differs from the concentration dependence of CO oxidation over copper chromite at (02)°-2(C0). This can be explained by the fact that after the departure of a C02 molecule, the reoxidation of platinum surfaces is slow but the reoxidation of base metal oxide surfaces is fast. On the other hand,... 

The measurement of the concentration dependence of the changes in surface potential was also used to find critical concentration for forming a micellar solution. Near this critical concentration, one can observe a very strong fall in A%. ... 

Studies of the adsorption of surface active electrolytes at the oil-water interface provide a convenient method for testing electrical double layer theory and for determining the state of water and ions in the neighborhood of an interface. The change in the surface amount of the large ions modifies the surface charge density. For instance, the surface ionic area of 100 per ion corresponds to 16, /rC/cm. The measurement of the concentration dependence of the changes of surface potential were also applied to find the critical concentration of formation of the micellar solution [18]. 

The degree of coverage, however, seems to influence the adsorbate composition at low methanol concentrations also. In particular, on smooth platinum, the dependence of surface composition on 6 is observed at concentrations as low as 5x 10-3 M (Fig. 2.7). In this case it could be possible that COH can be formed as long as adjacent sites are available. At high coverage (by all species involved in the adsorption process), the formation of COH should be geometerically prevented. 

What characterizes surfactants is their ability to adsorb onto surfaces and to modify the surface properties. At the gas/liquid interface this leads to a reduction in surface tension. Fig. 4.1 shows the dependence of surface tension on the concentration for different surfactant types [39]. It is obvious from this figure that the nonionic surfactants have a lower surface tension for the same alkyl chain length and concentration than the ionic surfactants. The second effect which can be seen from Fig. 4.1 is the discontinuity of the surface tension-concentration curves with a constant value for the surface tension above this point. The breakpoint of the curves can be correlated to the critical micelle concentration (cmc) above which the formation of micellar aggregates can be observed in the bulk phase. These micelles are characteristic for the ability of surfactants to solubilize hydrophobic substances in aqueous solution. So the concentration of surfactant in the washing liquor has at least to be right above the cmc. 

Fig. 8. Concentration dependence of ultrasound backscatter signal by plates coated with a layer of targeted microbubbles. Surface concentrations of microbubbles (as observed by bright-field optical microscopy, bottom) increase from left to right. Imaging performed using a fundamental frequency scheme. Samples placed on top of an ultrasound tissue phantom. Reprinted from Advanced Drug Delivery Reviews v. 37, A.L. Klibanov, Targeted delivery of gas-filled microspheres, contrast agents for ultrasound imaging, p. 145. Copyright, 1999, with permission from Elsevier Science...

Fig. 10 Concentration dependence of the pseudo first-order rate constants in a 100 mM phosphate buffer at pH 7.5 and 37 °C for a niunber of surface active betaine esters with hydrophobic tails of different sizes. For comparison, the rate constant for a non-siuface active compound (ethyl betainate) is included, (o) Oleyl betainate, ( ) tetradecyl be-tainate, ( ) dodecyl betainate, ( ) decyl betainate, (0) ethyl betainate. All compounds have chloride counterions...

Several other empirical relations for diffusion coefficients have been suggested Olson and Walton (01) have devised a means for estimating diffusion coefficients of organic liquids in water solution from surface-tension measurements. Hill (H5) has proposed a method based on Andrade s theory of liquids which allows for the concentration dependence of the diffusion coefficient in a binary liquid mixture. The formula of Arnold (A2, T6, p. 102) does not seem generally useful inasmuch as it contains two constants ( abnormality factors ) characteristic of the solute and of the solvent. 

Fig. 10. Double extrapolation surface of viscosity time-decay and concentration dependence of poly(sec-butyl isocyanide) in dichloroacetic acid at 30° C (20)...

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