Transition critical electrolyte concentration

Other discrepancies between the black film behaviour and DLVO-theory are related to the difference in the critical electrolyte concentration, corresponding to the transition between the two black films types (see Section 3.4.2) the existence of a second minimum in the 11(A) isotherm the sharp rise in the disjoining pressure (after the second minimum). All this is evidenced by the measurements of contact angles between the film and bulk phase. 

The observed change at 2-1 O 2 mol dm 3 CaCl2 is accompanied by the appearance of black spots, leading to the formation of black films that decrease in thickness with the increase in Cei. This shows that CBF are obtained. Thus, a transition from silver to CBF is established. This process is usually observed in films stabilised with ionic surfactants [171]. Here it is possible to interpret the results as additional evidence for the increase in the diffuse electric layer potential as a consequence of Ca2+ ion binding. The next established transition is evidently from CBF to NBF. It occurs at a Cei close to the critical electrolyte concentration of transition to NBF observed for a typical ionic surfactant (NaDoS 1-1 valent electrolyte) [251] (see Section 3.4.1.3). The fact that NBF thickness at high Cei equals that of the NBF obtained... 

The measurement of the parameters reflecting film properties which sharply change at the CBF/NBF transition lays at the basis of all experimental techniques for determination of the black film type. Microscopic black films render vast opportunities in the study of this transition by the dependences of film thickness, lifetime and contact angle on electrolyte concentration in the initial solutions. These dependences allow to estimate the critical electrolyte concentration Cei cr at which the CBF/NBF transition occurs. 

Data about contact angles 0(see Section 2.1.5) are useful in establishing the CBF/NBF transition occurring in films from ionic surfactants. A very sharp jump in the Q(Cei) curve, presented in Fig. 3.63, is observed at this transition [e.g. 96,251,322,323], The critical electrolyte concentration at which the transition occurs from one type of black film to the other can be determined from this jump. For instance, for NaDoS films in the presence of NaCl, Cei.cr = 0.334 mol dm"3 [251,323]. At lower Cei values, CBF with 6 < 1° are stable while at higher Cel values, NBF with 8 of the order of 10° are stable. The data of Huisman and Mysels [252] indicate a bit lower values, i.e. Cei, = 0.2 mol dm"3. 

Critical electrolyte concentrations, corresponding to foam Film transitions (derived from a-parlicle irradiation) [325]... 

The described above principle has served as a basis for the development of a method for foam destruction which is particularly useful for highly stable foams [20]. This method has also been employed for establishing the CBF/NBF transition in a foam. The critical electrolyte concentrations thus obtained proved to be close to those determined with free foam films (see Chapter 3). 

The potential and the charge of the diffuse electric layer is another important surfactant characteristics. Though these parameters are not directly related to the foam stability, they determine the type of foam films which affect foam stability. Another parameter directly connected to (p0 is the critical electrolyte concentration at which a CBF/NBF transition occurs at a given temperature. It allows to distinguish two equilibrium states of black foam films. The role of (p0 in the CBF/NBF transition permitted to find the value of the critical potential surfactant characteristic [71] (see Section 3.4.2). 

Several investigations were carried out to study the above transitions from CF to common black film, and finally to Newton black film. For sodium dodecyl sulphate, the common black films have thicknesses ranging from 200 nm in very dilute systems to about 5.4 nm. The thickness depends heavily on the electrolyte concentration, while the stability may be considered to be caused by the secondary minimum in the energy distance curve. In cases where the film thins further and overcomes the primary energy maximum, it will fall into the primary minimum potential energy sink where very thin Newton black films are produced. The transition from common black films to Newton black films occurs at a critical electrolyte concentration which depends on the type of surfactant... 

Marshall s extensive review (16) concentrates mainly on conductance and solubility studies of simple (non-transition metal) electrolytes and the application of extended Debye-Huckel equations in describing the ionic strength dependence of equilibrium constants. The conductance studies covered conditions to 4 kbar and 800 C while the solubility studies were mostly at SVP up to 350 C. In the latter studies above 300°C deviations from Debye-Huckel behaviour were found. This is not surprising since the Debye-Huckel theory treats the solvent as incompressible and, as seen in Fig. 3, water rapidly becomes more compressible above 300 C. Until a theory which accounts for electrostriction in a compressible fluid becomes available, extrapolation to infinite dilution at temperatures much above 300 C must be considered untrustworthy. Since water becomes infinitely compressible at the critical point, the standard entropy of an ion becomes infinitely negative, so that the concept of a standard ionic free energy becomes meaningless. 

The effect of the concentration of a low-molecular-weight salt on the x vs q>2 dependence for i = 0.012 is shown in Fig. 2. It is clear that electrolyte concentration suppresses the phase transition in the gel both the critical value of and the extent A decrease with increasing concentration of co-ions in the gel c. An analysis of Eq. (6) demonstrates that this is due to a marked decrease in... 

The transition between stability and coagulation, although in principle a gradual one, usually occurs over a reasonably small range of electrolyte concentration, and critical coagulation concentrations can be determined quite sharply. The exact value of the critical... 

An expression for the critical coagulation concentration (c.c.c.) of an indifferent electrolyte can be derived by assuming that a potential energy curve such as V(2) in Figure 8.2 can be taken to represent the transition between stability and coagulation into the primary minimum. For such a curve, the conditions V = 0 and dV/dH = 0 hold for the same value of H. If Vr and VA are expressed as in equations (8.7) and (8.10), respectively,... 

The transition from stable dispersion to aggregation usually occurs over a fairly small range of electrolyte concentration. This makes it possible to determine aggregation concentrations, often referred to as critical coagulation concentrations (CCC). The Schulze-Hardy rule summarizes the general tendency of the CCC to vary inversely with the sixth power of the counter-ion charge number (for indifferent electrolyte). 

Figures 5.37 and 5.38 show the critical thicknesses of rupture, Rp for foam and emulsion films, respectively, plotted vs. the film radius." In both cases the film phase is the aqueous phase, which contains 4.3 x 10 M SDS + added NaCl. The emulsion film is formed between two toluene drops. Curve 1 is the prediction of a simpler theory, which identifies the critical thickness with the transitional one." Curve 2 is the theoretical prediction of Equations 5.270 to 5.272 (no adjustable parameters) in Equation 5.171 for the Hamaker constant the electromagnetic retardation effect has also been taken into account. In addition, Eigure 5.39 shows the experimental dependence of the critical thickness vs. the concentration of surfactant (dodecanol) for aniline films. Figures 5.37 to 5.39 demonstrate that when the film area increases and/or fhe electrolyte concentration decreases the critical film thickness becomes larger.

The onset of pitting corrosion occurs suddenly If one performs electrochemical experiments with stainless steel, e. g. by applying a constant electrical potential to a sample immersed in dilute NaCl solution, the electrical current - which is an indicator for chemical activity (corrosion) on the metal surface - is low over a wide parameter range. But if critical parameters like temperature, potential, or electrolyte concentration exceed a certain critical value, the current rises abruptly and the metal surface is severely affected by pitting corrosion. The transition to high corrosion rates is preceded by the appearance of metastable corrosion pits. 

Figure 9.4 The transition from stability (i) to instability (iii) as the electrolyte concentration is increased. The critical condition for the onset of rapid coagulation (ii) is that at which AG(int) at the maximum of the curve is zero.

In some cases the transition to instability (coagulation) occurs over a relatively narrow and critical range of electrolyte concentration ... 

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