Surfactant calculations

FIG. 3 Lime soap dispersing power of some alkyl ether carboxylates compared to other surfactants (DIN 53903). AEC, alkyl ether carboxylate AMEC, amidether carboxylate CAPB, cocamidoproplylbetaine OEC, oleyl ether carboxylate SLES, sodium lauryl ether sulfate. % surfactant soap = % surfactant calculated on the soap needed to disperse the lime soap. (From Refs. 61 and 64.)... 

The time, f,-, for the induction period (region I) to end is an important factor in determining the surface tension as a function of time, since only when that period ends does the surface tension start to fall rapidly. The value of f,- has been shown (Gao, 1995 Rosen, 1996) to be related to the surface coverage of the air-aqueous solution interface and to the apparent diffusion coefficient, Dap, of the surfactant, calculated by use of the short-time approximation of the Ward-Tordai equation (Ward, 1946) for diffusion-controlled adsorption (equation 5.6) ... 

A most noticeable feature is the maximum in both adsorption isotherms. Since the maximum is present even in the isotherm for the pure surfactant it can be explained only by accepting the idea of declining selectivity with increasing surfactant concentration. Selectivity values for TRS 10-80 surfactant, calculated from Equation (10) with monolayer values determined from cross-sectional areas of surfactant (22A ) and water (8.3A ) molecules, are shown in Figure 10. The specific area for Berea sandstone was assumed to be 1 m /g. 

Some of the observed spectral changes which occur on solubilization will be due to change in the dissociation of the chromophoric species. The pK of three dyes in water and 0.025 m NaLS is compared in Table 11.14. An increase in pK is observed in the micellar state. The ionization of p-nitrophenol in the same surfactant calculated from the absorbance of the phenolate ion at 400 nm has been assessed. Fig. 11.33 shows the fractional ionization, a, as a function of pH in a range of surfactant concentrations. Herries et al [218] calculate theoretical ApKa as follows. Let C pH be the concentration of unionized p-nitrophenol in... 

A zero or near-zero contact angle is necessary otherwise results will be low. This was found to be the case with surfactant solutions where adsorption on the ring changed its wetting characteristics, and where liquid-liquid interfacial tensions were measured. In such cases a Teflon or polyethylene ring may be used [47]. When used to study monolayers, it may be necessary to know the increase in area at detachment, and some calculations of this are available [48]. Finally, an alternative method obtains y from the slope of the plot of W versus z, the elevation of the ring above the liquid surface [49]. 

A 1.5% by weight aqueous surfactant solution has a surface tension of 53.8 dyn/cm (or mN/m) at 20°C. (a) Calculate a, the area of surface containing one molecule. State any assumptions that must be made to make the calculation from the preceding data, (b) The additional information is now supplied that a 1.7% solution has a surface tension of 53.6 dyn/cm. If the surface-adsorbed film obeys the equation of state ir(o - 00) = kT, calculate from the combined data a value of 00, the actual area of a molecule. 

Tajima and co-workers [108] determined the surface excess of sodium dode-cyl sulfate by means of the radioactivity method, using tritiated surfactant of specific activity 9.16 Ci/mol. The area of solution exposed to the detector was 37.50 cm. In a particular experiment, it was found that with 1.0 x 10" Af surfactant the surface count rate was 17.0 x 10 counts per minute. Separate calibration showed that of this count was 14.5 X 10 came from underlying solution, the rest being surface excess. It was also determined that the counting efficiency for surface material was 1.1%. Calculate F for this solution. 

A surfactant for evaporation control has an equilibrium film pressure of 15 dyn/cm. Assume a water surface and 25°C and calculate the distance traveled by the spreading film in 8 sec. 

The adsorption of the surfactant Aerosol OT onto Vulcan Rubber obeys the Langmuir equation [237] the plot of C/x versus C is linear. For C = 0.5 mmol/1, C/x is 100 mol/g, and the line goes essentially through the origin. Calculate the saturation adsorption in micromoles per gram. 

Calculate the friction force between the surfactant layers in air in Fig. XII-12 using the relationship in Eq. XII-19. How does this compare with the friction shown in Fig. XII-12 ... 

Consider the case of an emulsion of 1 liter of oil in 1 liter of water having oil droplets of 0.6 /rm diameter. If the oil-water interface contains a close-packed monolayer of surfactant of 18 per molecule, calculate how many moles of surfactant are present. 

Figrue BE 16.20 shows spectra of DQ m a solution of TXlOO, a neutral surfactant, as a function of delay time. The spectra are qualitatively similar to those obtained in ethanol solution. At early delay times, the polarization is largely TM while RPM increases at later delay times. The early TM indicates that the reaction involves ZnTPPS triplets while the A/E RPM at later delay times is produced by triplet excited-state electron transfer. Calculation of relaxation times from spectral data indicates that in this case the ZnTPPS porphyrin molecules are in the micelle, although some may also be in the hydrophobic mantle of the micelle. Furtlier,... 

Tarazona A, Kreisig S, Koglin E and Schwuger M J 1997 Adsorption properties of two cationic surfactant classes on silver surfaces studied by means of SERS spectroscopy and ab initio calculations Prog. Colloid Polym. Sol. 103 181-92... 

Figure 5.4. Plot of the apparent second-order rate constant, kapp (= kotJ[5.2]i) versus the concentration of surfactant for the Diels-Alder reaction of S.lg with 5.2 in CTAB solution at 25 C. The inset shows the treatment of these data using Equation 5.6. From slope and intercut P j can be calculated (see Table 5.2).

Surfactants for Mobility Control. Water, which can have a mobihty up to 10 times that of oil, has been used to decrease the mobihty of gases and supercritical CO2 (mobihty on the order of 50 times that of oil) used in miscible flooding. Gas oil mobihty ratios, Af, can be calculated by the following (22) ... 

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). 

The final factor influencing the stabiHty of these three-phase emulsions is probably the most important one. Small changes in emulsifier concentration lead to drastic changes in the amounts of the three phases. As an example, consider the points A to C in Figure 16. At point A, with 2% emulsifier, 49% water, and 49% aqueous phase, 50% oil and 50% aqueous phase are the only phases present. At point B the emulsifier concentration has been increased to 4%. Now the oil phase constitutes 47% of the total and the aqueous phase is reduced to 29% the remaining 24% is a Hquid crystalline phase. The importance of these numbers is best perceived by a calculation of thickness of the protective layer of the emulsifier (point A) and of the Hquid crystal (point B). The added surfactant, which at 2% would add a protective film of only 0.07 p.m to emulsion droplets of 5 p.m if all of it were adsorbed, has now been transformed to 24% of a viscous phase. This phase would form a very viscous film 0.85 p.m thick. The protective coating is more than 10 times thicker than one from the surfactant alone because the thick viscous film contains only 7% emulsifier the rest is 75% water and 18% oil. At point C, the aqueous phase has now disappeared, and the entire emulsion consists of 42.3% oil and 57.5% Hquid crystalline phase. The stabilizing phase is now the principal part of the emulsion. 

The effective surface viscosity is best found by experiment with the system in question, followed by back calculation through Eq. (22-55). From the precursors to Eq. (22-55), such experiments have yielded values of [L, on the order of (dyn-s)/cm for common surfactants in water at room temperature, which agrees with independent measurements [Lemhch, Chem. Eng. ScL, 23, 932 (1968) and Shih and Lem-lich. Am. Inst. Chem. Eng. J., 13, 751 (1967)]. However, the expected high [L, for aqueous solutions of such sldn-forming substances as saponin and albumin was not attained, perhaps because of their non-newtonian surface behavior [Shih and Lemhch, Ind. Eng. Chem. Fun-dam., 10, 254 (1971) andjashnani and Lemlich, y. Colloid Inteiface ScL, 46, 13(1974)]. 

Based on the calculation of the solvatation free energy of methylene fragment with carboxyl at the aliphatic carboxylic acids extraction, the uniqueness of cloud-point phases was demonstrated, manifested in their ability to energetically profitably extract both hydrophilic and hydrophobic molecules of substrates. The conclusion is made about the universality of this phenomenon and its applicability to other kinds of organized media on the surfactant base. 

The example illustrates how Monte Carlo studies of lattice models can deal with questions which reach far beyond the sheer calculation of phase diagrams. The reason why our particular problem could be studied with such success Hes of course in the fact that it touches a rather fundamental aspect of the physics of amphiphilic systems—the interplay between structure and wetting behavior. In fact, the results should be universal and apply to all systems where structured, disordered phases coexist with non-struc-tured phases. It is this universal character of many issues in surfactant physics which makes these systems so attractive for theoretical physicists. 

FIG. 13 Phase diagram of a vector lattice model for a balanced ternary amphiphilic system in the temperature vs surfactant concentration plane. W -I- O denotes a region of coexistence between oil- and water-rich phases, D a disordered phase, Lj an ordered phase which consists of alternating oil, amphiphile, water, and again amphi-phile sheets, and L/r an incommensurate lamellar phase (not present in mean field calculations). The data points are based on simulations at various system sizes on an fee lattice. (From Matsen and Sullivan [182]. Copyright 1994 APS.)... 

The ratio E/ps, calculated for different phases below the bifurcation, is shown in Fig. 15. In the special case of the C phase the surface intersects itself therefore, in the computation of S/p we have subtracted the volume occupied along the lines of intersection, since it would be counted twice otherwise. The surface area per volume is an increasing function of the surfactant volume fraction and it determines the sequence of phases. Moreover, we have found that the effect of broadening of the interface on the value S/p in different phases is different, and we have a quantitative... 

This section deals with the experimental determination of the rate of oil solubilization in aqueous solutions of AOS and IOS [70]. The experimental method [71] consists of injecting 25 pi of n-hexadecane (containing 5 wt % Dobanol 45-3 as an emulsifier) into 50 ml water this produces a turbid macroemulsion upon vigorous stirring. At the start of the experiment, a concentrated solution of the surfactant under test is injected and the decrease in turbidity is followed with a photometer. The time elapsed to reach 90% of the initial turbidity is recorded (t ) and the pseudo rate constant of oil solubilization is calculated from... 

Active matter (anionic surfactant) in AOS consists of alkene- and hydroxy-alkanemonosulfonates, as well as small amounts of disulfonates. Active matter (AM) content is usually expressed as milliequivalents per 100 grams, or as weight percent. Three methods are available for the determination of AM in AOS calculation by difference, the two-phase titration such as methylene blue-active substances (MBAS) and by potentiometric titration with cationic. The calculation method has a number of inherent error factors. The two-phase titration methods may not be completely quantitative and can yield values differing by several percent from those obtained from the total sulfur content. These methods employ trichloromethane, the effects from which the analyst must be protected. The best method for routine use is probably the potentiometric titration method but this requires the availability of more expensive equipment. 

Similarly, the presence of sulfonate esters also indicates incomplete hydrolysis. Residual saponifiable material in a final AOS product is then a measure of the quality of the surfactant. In practice, such material can be extracted, subjected to drastic conditions of saponification, and the quantity of residual saponifiable material calculated. Methods have been developed which can be used for the determination of 10 or more ppm of saponifiable material in the neutral oil of AOS. Unfortunately, the procedures outlined below are now of historic interest only, since they give unrealistically high values for residual saponifiable material content. Methods listed in the sultones section are now the analyses of choice. 

Fujiwara et al. used the CMC values of sodium and calcium salts to calculate the energetic parameters of the micellization [61]. The cohesive energy change in micelle formation of the a-sulfonated fatty acid methyl esters, calculated from the dependency of the CMC on the numbers of C atoms, is equivalent to that of typical ionic surfactants (Na ester sulfonates, 1.1 kT Ca ester sulfonates, 0.93 kT Na dodecyl sulfate, 1.1 kT). The degree of dissociation for the counterions bound to the micelle can be calculated from the dependency of the CMC on the concentration of the counterions. The values of the ester sulfonates are also in the same range as for other typical ionic surfactants (Na ester sulfonates, 0.61 Ca ester sulfonates, 0.70 Na dodecyl sulfate, 0.66). 

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