Surfactant concentration, minimum

Thus, the dependence of the differential capacity on the potential in this case has a minimum and two maxima. The potential minimum has a value of Ep = Emax. As d2/5/dEl<0 in the vicinity of the minimum, it follows from Eq. (4.3.53) that the differential capacity decreases with increasing concentration c in this region. The potentials of the maxima, given by the relationship Ep = Emax y/3RT/2a, lie symmetrically on either side of max. A qualitatively similar picture would be obtained for a more complex isotherm (see Fig. 4.9), but the peak potentials would depend on the surfactant concentration. 

According to this equation, the plot of l/kw as function of C would show a minimum and the plot beyond Cmin would be linear with a positive slope and positive intercept. However, at the optimum surfactant concentration corresponding to the maximum in the plot of kv against [Surfactant], the following relationship is obtained. 

It is worth noting that if the two surfactants which are mixed do not share the same value of k, as for instance an alkylbenzene sulfonate (k = 0.16) and an alkylsuhate (k = 0.10), then Eqs. 10-12 have to be divided by k to be expressed in ACN units which have the same meaning in all cases, whatever the k s [33]. The value a/k has been called EPACNUS (Extrapolated Preferred Alkane Carbon Number at Unit Sahnity and no-alcohol), since it is the value of ACN when the conditions S = 1 wt % NaCl,/(A) = 0 and T = 25 °C are satisfied. If the optimiun formulation is determined experimentally, not from the occurrence of three-phase behavior but from the minimum of interfacial tension, as is often the case at low surfactant concentration or when the oil phase is not transparent, it is called EACNmin or Umin [17,34,35]. 

Fig. 10 Effect of surfactant concentration on the optimum formulation (minimum tension position) for anionic mixtures (/e/t), pure anionic surfactant center) and ethoxylated nonionic mixtures (right)...

In mixed sur-factant systems, the interactions betMeen sur-factants a-f-fects the tendency -for monolayer formation. At concentrations above the CMC, the surface tension may very slOMly increase or decrease. The surface tension at the CMC is close to the minimum surface tension which a surfactant system can attain. Therefore, in terms of surface tension reduction, the surfactant concentration required to attain a specified surface tension below the CMC and the surface tension at the CMC are indicative of the usefulness of a system. 

The minimum mixed surfactant concentration in the solution phase,... 

The cmc at the point of maximum synergism, i.e., the minimum total mixed surfactant concentration in the solution phase required for mixed micelle formation, C 2 nin given by the relationship ... 

C. ,) and their mixtures above the CMC. Tne d dtrease in flotabi1ity begins at a concentration corresponding to the adsorption density e s i, and reaches a minimum at the surfactant concentration 5 CMC (Fig. 6). Similarly as in Figs. 3 and 4, only arrows for e s 1 and CMC, resp., were used. The minimum flotability of barite in the mixtures of pure surfactants C.q + nd C.q +... 

Above 30 surfactant the MEDD apparently reached a minimum value of 1-2 pm. This third region was a function of the lower detection limit of the apparatus. Table II shows that the proportion of emulsion droplets below 3 and 1 um increased as the surfactant concentration Increased. The data emphasize the marked reduction in emulsion droplet size which occurred above 30 w/w surfactant. 

A plot of the temperatures required for clouding versus surfactant concentration typically exhibits a minimum in the case of nonionic surfactants (or a maximum in the case of zwitterionics) in its coexistence curve, with the temperature and surfactant concentration at which the minimum (or maximum) occurs being referred to as the critical temperature and concentration, respectively. This type of behavior is also exhibited by other nonionic surfactants, that is, nonionic polymers, // - a I k y I s u I Any lalcoh o I s, hydroxymethyl or ethyl celluloses, dimethylalkylphosphine oxides, or, most commonly, alkyl (or aryl) polyoxyethylene ethers. Likewise, certain zwitterionic surfactant solutions can also exhibit critical behavior in which an upper rather than a lower consolute boundary is present. Previously, metal ions (in the form of metal chelate complexes) were extracted and enriched from aqueous media using such a cloud point extraction approach with nonionic surfactants. Extraction efficiencies in excess of 98% for such metal ion extraction techniques were achieved with enrichment factors in the range of 45-200. In addition to metal ion enrichments, this type of micellar cloud point extraction approach has been reported to be useful for the separation of hydrophobic from hydrophilic proteins, both originally present in an aqueous solution, and also for the preconcentration of the former type of proteins. 

The value of Qst can be determined from the slope of the plot (log c)r against T. Measurements in the system N-dodecylammonium acetate-quartz showed that -AG increased with increasing temperature over the whole concentration range whereas the adsorption density against temperature showed a minimum over the greatest part of the concentration range. In the range of equilibrium surfactant concentrations of 1 - 9 x 10"4 mol 1" the values of - AG 12.55 to 17.58 kJ/mol were found for temperatures between 5 and 45 °C. 

The efficiency of surfactant adsorption is determined as a function of minimum bulk surfactant concentration, C that produces saturation adsorption (rmax) at the liquid-gas or liquid-liquid interface. This minimum concentration is defined as p C20 which is (— log C2o) reducing the surface or interfacial tension by 20 dyne cm-1 (n = 20 dyne cm-1). With Qo, r lies between 84 and 99.9% of rmax. The larger the pC2o (smaller the C), the more efficient the surfactant is in adsorbing at the interface and reducing the surface tension at liquid-gas or interfacial tension at liquid-liquid interfaces. The pC20 values for several surfactants can be found in Chapter 2 of [2]. 

It can be summarized that ellipsometric measurements proved the formation of a surfactant adsorption layer on the photoresist surface. At ceg- it is assumed to form a monolayer. To get more information about the adsorption layer and its influence on the surface properties of the photoresist, an electrokinetic characterization of unexposed and processed photoresist in solutions of the cationic surfactant was carried out. The zeta potential of the photoresist layers is given in Fig. 8 as a function of the surfactant concentration. The measurement was performed at pH = 6 in a background electrolyte (KC1) concentration of 10-5 M to ensure the minimum conductivity of the solution necessary for the measurement. 

To estimate the influence of the surfactant adsorption on the capillary forces, the wetting tension yiv cos was calculated from the values given in Fig. 10a. The results drawn in Fig. 10b show for both measurement series a minimum of the capillary forces exactly at the concentration ceff. The capillary forces are reduced by about 20% compared to water. This confirms the hypothesis that the reduction of the pattern collapse is caused by a hydropho-bizing of photoresist processed with the threshold dose by cationic surfactant adsorption. Unfortunately the inverse ADS A method could not be applied at relative surfactant concentrations >0.2 since the bubbles became unstable due to the lower surface tension. Thus it cannot be estimated how the wetting tension evolves at higher concentrations. 

A great advantage of the cationic surfactant rinse is that the minimum of the capillary forces is obtained already at concentrations far below the erne. Low amounts of surfactant are needed and problems as melting of the structures or foaming occurring at high surfactant concentration are avoided. 

Since most drags are insoluble in the propellants, they are usually presented as suspensions. Micronized drag is dispersed with the aid of a surfactant such as oleic acid, sorbitan trioleate or lecithin. At concentrations up to 2% w/w the surfactant stabilizes the suspended particles by adsorption at the drag propellant interface and in addition serves as a valve lubricant. The tendency is to use minimum surfac—tant concentrations to reduce drag solubility within the propellant by solubilization (to reduce Ostwald ripening during the shelf life of the pMDI). Low surfactant concentrations will also avoid substantial reductions in the propellant evaporation rates from aerosolized drops. 

The minimum surfactant concentration (for NP20), ensuring formation of stable aqueous films from a solution containing KC1 (0.5 mol dm3) between drops of liquid hydrocarbons [507] is presented below ... 

The concentration of formation of black spots in emulsion films is close to the emulsifier concentration at which it is possible to disperse a small quantity of the organic phase in certain volume of the aqueous surfactant solution under definite conditions resulting in formation of stable emulsions. Kruglyakov et. al. [510] have compared the concentration of black spot formation in emulsion aqueous films and the minimum surfactant concentration Cmin needed to form stable heptane aqueous emulsion studying the NaDoS emulsifying ability vs. its concentration in the solution. They found that Cmin = 4.110 4 mol dm 3 in a solution containing 51 O 2 mol dm 3 NaCl and Cw = 3.5-4-10 4 mol dm 3, depending on the time of film formation. 

The minimum surfactant concentration at which thin (grey) films were obtained with lifetime longer than 10 min. 

In order to estimate the role of the rate of film thinning being one of the reason for the deviations from Eq. (5.46), the kinetics of pressure change in the upper foam layers (close to the surface) has been studied [2], In these layers the liquid influx from the upper layers has a minimum influence (Fig. 5.21,a). When the foam column is high (5 cm), the foam is of low expansion ratio (n 10) and the surfactant concentrations are low, a monotonous decrease in pressure is observed (Fig. 5.21,a) and Eq. (5.65) describes the microsyneresis quite satisfactorily. 

The parameter Cm can provide important data to be used in estimating the antifoam efficiency, in determining the minimum (threshold) surfactant concentration in the purification of solutions by foam flotation [53], in analysing the causes of foam formation in extraction systems and in establishing the optimum conditions of effective extraction [68]. 

It is known that the three film types are thermodynamically unstable. Long-living films can be obtained when suitable surfactants are employed, creating an energy barrier to film thinning, due either to the repulsion of the diffuse electric layers or the steric interaction of the adsorption surfactant layers. Since the minimum surfactant concentration that provides stable... 

At low surfactant concentrations (for example, the concentrations that are reached at the waste water foam purification from surfactant pollutants) the foaming ability is usually limited by the minimum surfactant concentrations necessary for formation of stable foam films. This concentration is close to the concentration of black spot formation in microscopic films Cbi and black films Cfbu being an important characteristic of the foam stabilising ability of surfactants. The values of Cm for some surfactants are given in Table 3.1 and the dependence of Cm on various factors is considered in Section 3.4. 

Eqs. (10.45) and (10.46) are of little use for determining the limiting values of the purification coefficient, since at low surfactant concentrations foam stability dramatically decreases, and the foam layers containing the adsorbed product have no time to separate from the solution. For this reason determination of the minimum residual surfactant concentration, necessary to obtain a stable foam provides precise information on the purification coefficient. The minimum residual concentration is closed to that for the formation of black spots (cbi) in microscopic foam films, in case they form (cLR = cs,r = cbi) [24]... 

This means that Increased surfactant content was always accompanied by a minimum Increase of water content according to Equation 3. Plotting the solubility of the polymer In the pentanol/styrene solution when pentanol Is gradually replaced by the surfactant/water combination according to Equation 3 shows the reflection between polymer solubility and the amount of surfactant/water aggregate present (21). In fact, a linear reduction of polymer solubility was found with Increase surfactant/water content. Figure 5. A surfactant concentration of 9.5% accompanied by water to 2.46% would result In zero solubility of the polystyrene. This means that a composition of pentanol/styrene 25/75 dissolves 42% polystyrene but that the polystyrene Is completely Insoluble In a composition 75% styrene, 13% pentanol, 9.5% surfactant and 2.5% water. Or, expressed In a different manner 1 molecule of polymer Is removed for 1.3 molecules of surfactant and 3.3 molecules of water added. 

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