Critical electrolyte concentration

Also of importance for analytical and structural studies are the complexes with alkylammonium salts, widely used under selective conditions of critical electrolyte concentrations (see Section III). 

Some of the pertinent interactions that affect colloid stability are readily apparent from Figs. 7.4 and 7.12. The main effect of electrolytes is a more rapid decay of the repulsion energy with distance and to compact the double layer (reducing k 1). Experimentally it is known that the charge of the counterion plays an important role. The critical electrolyte concentration required just to agglomerate the colloids is proportional to z 6 Aj for high surface potential, and to z 2 A, 2, at low potentials [(4) and (5) in Table 7.3]. This is the theoretical basis for the qualitative valency rule of Schulze and Hardy. 

The last approximate expression shows that, at low electrolyte concentrations (X - °° ), the total adsorption is positive when the potential well is sufficiently deep (A=exp( W, /kT) >2). In this case, the surface tension decreases almost linearly with increasing electrolyte concentration. However, the slope does not remain constant, its magnitude decreasing with increasing electrolyte concentration, because of the surface potential generated by the asymmetric distribution of electrolyte ions. The slope dy/dc becomes positive at concentrations higher than a critical electrolyte concentration, obtained from ... 

Experiments on the stability of water/surfactant films at various pressures were performed by Exerowa et al.2,3 For a dilute aqueous solution of a nonionic surfactant,3 tetraoxyethylene decyl ether (D(EO>4,5 x 10-4 mol/dm3) or eicosaoxyethylene nonylphenol ether (NP(EO)2o, 1 x 10-5 mol/dm3), and electrolyte (KC1), thick films (with thicknesses of the order of 100 A) were observed at low electrolyte concentrations. With an increase of the electrolyte concentration, the film thickness first decreased, which suggests that the repulsion was caused by the double layer. This repulsive force was generated because of the different adsorptions of the two species of ions on the water/ surfactant interface. At a critical electrolyte concentration, a black film was formed, and the further addition of electrolyte did not. modify its thickness, which became almost independent of the external pressure, until a critical pressure was reached, at which it ruptured. While for NP(EO)2o only one metastable equilibrium thickness was found at each electrolyte concentration, in the case of D(EO)4 a hysteresis of the film thickness with increasing and decreasing pressure (i.e., two metastable minima) was observed in the range 5 x 10 4 to 3 x 10 mol/dm3 KC1. The maximum pressure used in these experiments was relatively low, 5 x 104 N/m2, and the Newton black films did not rupture in the range of pressures employed. 

The experimental data reported by Pashley [17] raise two important issues. The first one is why the critical electrolyte concentration at which the hydration force emerges, depends so strongly on the type of electrolyte (6x 10 2 for LiCl, 3x10 / M for KC1). The second issue is why the decay length of the interactions at short separations is about 10 A, about five times largo- than that corresponding to the hydration force between lipid bilayers. 

The equivalent film thickness hw initially decreases and then levels off at a constant value. The plateau starts at a critical electrolyte concentration Cei,cr = 3-1 O 3 mol dm 3 NaCl, similar to low molecular mass surfactants. The increase in bulk copolymer concentration raises the plateau (45 1 nm vs. 39 3 nm), but has no marked influence on the sloped branch. The results for the lower copolymer (P85) are very similar. The equivalent film thickness hw initially decreases and above Ceicr = 3-10 2 mol dm 3 NaCl levels off at a constant value of 17 + 1 nm (Ce , = 7-10 5 mol dm 3 P85). 

The electrostatic interactions may be practically suppressed by increasing the electrolyte concentration (the Debye screening length at 0.1 mol dm 3 NaCl is only 1 nm). Above a critical electrolyte concentration, CeiiCr the equivalent film thickness of such foam films is independent of Cei (Fig. 3.32). At Cei > Cei,cr film thickness is governed by Uvw and n, and the stabilising role of nj( is obvious. 

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]... 

This finding is supported by the results obtained at constant NaDoS concentration and various NaCl concentrations. All points, depicted for NaCl concentration up to 0.32 mol dm 3 lay on curve 1, while for concentrations higher than that, lay on curve 2. Thus, a critical electrolyte concentration Cei,cr is determined which is decisive for the formation of the respective type of foam films. Its value, Cei,cr = 0.33 0.05 mol dm 3, is in a better agreement with the values obtained employing other techniques for foams (see Chapter 6) and foam films (Chapter 3). This result evidences that the foam film type affects the drainage process. However, a quantitative interpretation is not possible. This refers to the jump in the value of the drainage rate (initial slopes) in W(t) dependence for the different types of foam films but does not answer the question why the liquid from a CBF foam drains faster. The solution of these and other problems related to the type of foam films requires its correlating with the... 

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). 

The values of the threshold dilution d, for different temperatures are presented in Fig. 11.7 in Arrhenius co-ordinates for the five samples investigated. As it is seen, linear dependences of similar slope were obtained within the temperature range from 10°C to 30°C. The temperature dependences of d, were determined as concentrations higher than the critical electrolyte concentration Ceixr for formation of foam bilayers from amniotic fluid and it was found that d, is not a function of the electrolyte concentration. 

Note from Eq. (7-13) that when ez sJ ksT > 1, there is a strong dependence of the critical electrolyte concentration on charge valency, namely crit cx z - Thus, multivalent ions are predicted to be very effective at inducing flocculation this is called the Schulze-Hardy rule (Russel 1989 Israelachvili 1991). 

Further evidence to support the above hypothesis on the role of structure in phase separation of aqueous solutions is provided by the effect of additional alcohol. The amount of alcohol was increased from 3.0 to 5.0 gm/dl, the surfactant concentration kept constant, and the salinity varied. The addition of alcohol extended the range of salinity where the aqueous solutions are isotropic to 0.8 gm/dl NaCl. According to the above hypothesis, no phase separation should take place on addition of polymer to the isotropic solutions existing up to 0.8 gm/dl NaCl. Indeed, no phase separation was observed when as much as 1500 ppm Xanthan was added at such compositions. Thus, the addition of alcohol increases the critical electrolyte concentration for phase separation, an effect seen also by others (9). 

It is speculated that the effect of temperature on the critical electrolyte concentration is similarly related to the effect of temperature on the structure of aqueous solutions. An increase in temperature has been shown to extend the range of micellar solutions to a higher salinity in anionic surfactant systems (31). Hence, polymer-aggregate incompatibility would be less when the temperature is increased. However, addition of alcohol or change in temperature... 

Pope et al. (1982) observed that when a polymer was mixed with a surfactant in an oil-free solntion, there was a characteristic phase separation into an aqneons snrfactant-rich phase and an aqueons polymer-rich phase at some sufficiently high salinity (NaCl concentration). They called this the critical electrolyte concentration (CEC). They reported that CEC was independent of the polymer type, polymer concentration, and snrfactant concentration, bnt it was dependent on the nsed snrfactant. This conclnsion cannot be universally valid. Hon (1993) observed that CEC depended on polymer and snrfactant concentrations in a HPAM-petroleum sulfonate solntion. The CEC increased with increasing temperature for the anionic surfactants and decreased with increasing temperature for the nonionic surfactants. It also increased with alcohol concentration. 

Coagulation occurs at a critical electrolyte concentration, the critical coagulation concentration (ccc), which in turn depends on the electrolyte valency. At low surface potentials, ccc oo this referred to as the Schultze-Hardy rule. A rate constant... 

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... 

The electrostatic repulsion between dispersed particles can be diminished by increasing the concentration of background electrolyte (e.g. NaCl, CaCl2)- Polyvalent ions are more effective than monovalent. There is a critical electrolyte concentration for every system at which flocculation or coalescence takes place. These principles must be taken into account when emulsions have to form in very hard water. 

The effect of hydrated radii, valence, and concentration of counterions on oil-external and middle-phase microemulsions was investigated by Chou and Shah [28]. It was observed that I mol of CaCb was equivalent to 16-19 mol of NaCl for solubilization in middle-phase microemulsions, whereas for solubilization in oil-external microemulsions, 1 mol of CaCb was equivalent to only 4 mol of NaCl. For monovalent electrolytes, the values for optimal salinity of solubilization in oil-external and middle-phase microemulsions are in the order LiCl>NaCl>KCl>NH4Cl, which correlates with the Stokes radii of hydrated counterions. The optimal salinity for middle-phase microemulsions and critical electrolyte concentration varied in a similar fashion with Stokes radii of counterions, which was distinctly different for the solubilization in oil-external miroemulsions. Based on these findings, it was concluded that the middle-phase microemulsion behaved like a water-continuous system with respect to the effect of counterions [28]. 

FIGURE 10.15. In an electrostatically stabilized colloid, the concentration of electrolyte will greatly affect the stability of the system (a) with low electrolyte concentration, a relatively high energy barrier will impart stability (b) as electrolyte is added, the stabilizing barrier will be reduced, but reasonable stabihty may be maintained (depending on the valency of the added electrol)de) (c) at a critical electrolyte concentration the energy barrier will effectively disappear and rapid flocculation will occur. 

Partial adhesion on the SdFFF channel wall was achieved by using monodisperse spherical particles of polymethyl methacrylate (PMMA) with nominal diameter 0.358 p.m." " The extent of the PMMA particles adhesion and detachment on and from the channel wall depends on the concentration of the indifferent electrolyte Ba(N03)2 added to the suspending medium to influence the total potential energy of interaction between the PMMA particles and the channel wall. When the concentration of the electrolyte exceeds a given value, which is called critical electrolyte concentration (CEC), total adhesion of the colloidal particles occurs at the beginning of the SdFFF channel wall. 

Successful attempts have been made to modify/minimize preeipitation in polyelectrolyte/oppositely charged surfactant systems. Laurent and Scott (65) reported such an effect with the addition of simple salts and defined a critical electrolyte concentration (c.e.c.) at which precipitation is totally inhibited. (See Chapter 5 and also Section III.E below.) Likewise, Dubin et al. (66,67) have found inhibitory effects on adding nonionic surfactants to these mixed polymer/surfactant systems, presumably a result of mixed micelle formation. 

Reference has already been made to the interesting finding by Laurent and Scott (65) that precipitation of various polyanion/cationic surfactant systems can be totally inhibited by the addition of a sufficient amount of simple salt. This work allowed the definition of a critical electrolyte concentration (c.e.c.), which was found to vary from system to system. Clearly, electrostatic screening effects are again involved. This phenomenon has been confirmed and examined in some detail by Lindman and co-workers (see next section). Less work has been carried out in this respect on polycation/anionic surfactant systems and, at least in some systems involving cationic cellulosic polymer/SDS combinations, resolubilization by salt addition was found not to be facile (59,103). 

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