Antonow s rule

Various means have been developed for prediciting or calculating a yab or a work of adhesion. Two empirical ones are the following. First, an early relationship is that known as Antonow s rule [13],... 

Show what Sb(A)/A(B) should be according to Antonow s rule. 

Equation XII-20 may be combined with various semiempirical equations. Thus if Antonow s rule applies (Eq. IV-8), one obtains... 

The interfacial tension yAB between two liquids with surface tension yA and yB is of interest in such systems as emulsions and wetting (Adamson and Gast, 1997 Chattoraj and Birdi, 1984 Somasundaran, 2006). An empirical relation was suggested (Antonow s rule), by which one can predict the surface tension yAB ... 

Antonow s rule can be understood in terms of a simple physical picture. There should be an adsorbed film or Gibbs monolayer of substance B (the one of lower surface tension) on the surface of liquid A. If we regard this film as having the properties of bulk liquid B, then y A(B) is effectively the interfacial tension of a duplex surface and would be equal to [Y a(b> + Yb[Pg.37]

A very significant observation connecting the interfacial tension between two liquid phases in equilibrium with the surface tension of each separately against the vapour phase was discovered by Antonow. The interfacial tension is equal to the difference between the two surface tensions. It is important to notice that we must deal with phases in equilibrium, since it often happens that the tension of the one pure liquid is greatly reduced by the addition of the second even though the solubility may be exceedingly small In the extreme case, the solubility of one phase in the other is too small to be measured, as in the case of palmitic acid in water, but the surface tension of the solvent may, as we have already seen, nevertheless be reduced very much. The following examples may be quoted in support of Antonow s rule. 

Reynolds excepts from the general validity of Antonow s rule the tension of mercury and amalgams against certain electrolytes and immiscible liquids which react chemically. It is clear that the rule would be difficult to verify satisfactorily in the latter case with mercury in contact with aqueous solutions (or with water) the apparent deviation from the rule is. probably to be accounted for by consideration of the electro-capillary effects (Oh. vn). 

Antonow s rule is tlius only exact when the two mutually saturated liquids possess the same density. The observed values of cti2 should in general be slightly less than those determined from — In the case of oleic acid floating on water Devaux obtained a lens thickness of OT cm. Since p — 0 90 the interfacial surface tension should be O M dyne less than the value obtained with the aid of Antonow s rule. 

The decrease of interfacial tension with rising temperature might normally be ascribed to increase in solubility. We have unfortunately no data with which to compare the interfacial tensions directly with solubility of a pair of partially soluble liquids at different temperatures, but from the results of Whatmough on the surface tensions of such phase pairs we can calculate the interfacial tensions from Antonow s rule. The following values are interpolated from his results. 

Some interesting conclusions may be drawn from a consideration of the magnitude of the interfacial surface tensions of various liquids. The significance of these was first pointed out by Hardy Froc. Roy. Soc. A, Lxxxviii. 303, 1913) and emphasised by Harkins J.A.G.S. XXXVIII. 228,1916 xlil 700,1920). We have noted that Antonow s rule only applies to mutually saturated solutions. If two... 

As a rule the solutes which are positively adsorbed by solid adsorbents are negatively adsorbed at a gas-liquid interface. Such behaviour is in agreement with Antonow s rule that... 

Now Antonow s rule appears to be valid for two liquids provided that saturation be carefully defined and it is true for solid and liquid interfaces provided that the angle of contact be zero. 

A. Winter, Antonow s rule 85 Years Later, in Heterog. Chem. Revs. 2 (1995) 269-308. Lord Rayleigh. PhiL Mag. 151 30 (1890) 456. 

It can be derived from Antonow s rule, 15.7.4], applying it to partial wetting but accounting for the adhesion between solid and liquid, assuming it to be dominated by the Van der Waals, or dispersion, parts of the surface tensions, y and y. Various studies have shown that [5.7.5] is quite effective for materials that mainly interact through dispersion forces and that it remains a reasonable approximation for systems in which other interactions also operate. The root in the r.h.s. of [5.7.5] stems from the assumption that Berthelot s principle may be applied. In sec. 2.11b we argued that this principle may be applied only to the energetic part of the interfacial tensions and that a more correct form is... 

Antonow s rule. The rule states that the interfacial tension of two liquids in equilibrium is equal to the difference between the surface tensions. 

At the interfaces between two liquids an empirical rule, Antonow s rule, is often valid. According to this rule, the interfacial energy a, equals the difference between the surface tensions of more polar (a,) and less polar (a2) liquids, namely... 

TABLE III. 1. The values of the interfacial tension al2 of mutually saturated solutions, as determined experimentally and estimated from Antonow s rule [1],... 

Liquids The surface tension of the less polar phase ct2, mN/m The surface tension of the aqueous phase ct mN/m Interfacial tension, ctI2, mN/m experimental evaluated from Antonow s rule ... 

Fig. III-4. The interfacial composition of condensed phases when Antonow s rule is valid III.2. Adsorption at Interfaces Between Condensed Phases...

A Monte Carlo simulation [102] of a system with short-range forces confirmed these notions. The correlation function clearly exhibited exponentially damped oscillations. From the ratio of the wavelength and correlation length, the value of y characterizing the system could be obtained from Eq. (35), and it was found that 1 > y > 0, indicating that the microemulsion was structured but weakly so. Within the mean-field calculation, however, this is still strong enough that the middle phase should not wet the oil/water interface. However, measurement of all three interfacial tensions within the simulation revealed that Antonow s rule was obeyed, so that the interface was indeed wetted by the middle phase, an effect clearly attributable to the fluctuations included in the simulation. 

Antonow s Rule. An empirical rule for the estimation of interfacial tension between two liquids as the difference between the surface tensions of each liquid. Even for pure liquids this rule is seldom very accurate. 

This work can be calculated if the potential-energy functions for the different phases are known. Equation (7.39) may be combined with various semiempirical equations. If Antonow s rule applies, one obtains = 2yw which agrees well with the benzene-water example [39]. In addition, the surface energies can be related as... 

The situation as depicted in Fig. 3 is only one of two possible configurations. The second situation is the one of complete wetting, and it is characterized by the presence of a macroscopically thick layer of one of the phases between the other two (see Fig. 5). Whereas in the case of partial wetting the three surface tensions involved obey Young s law, in the case of complete wetting the surface tensions are related through Antonow s rule [22,23], which states that the surface tension of the solid-vapor interface, when it is intruded by a macroscopically thick liquid layer, is given by the sum of the surface tensions of the solid-liquid and liquid-vapor interfaces... 

Antonow discovered this rule empirically after measuring the surface tensions of different three-phase systems. At the time, Antonow s rule was the subject of intense scrutiny in the literature partly because Antonow claimed the validity of the rule in any three-phase system with deviations being caused only by supposed nonequilibrium effects [23], We now know that the rule holds exactly, but only in the complete wetting regime. 

Oil and water do not mix this is an everyday observation. Main reason is oil is insoluble in water, and vice versa. At the oil-water interface, one will thus have interfacial surface forces. In this chapter, the methods in which one can indeed disperse oil in water (or vice versa) will be described. The analyses of the IFT, which exists at any oil-water interface, will be described. In the literature, the IFT, 7ab> between two liquids with and Yb has been described in much detail (Adamson and Cast, 1997 Chattoraj and Birdi, 1984 Miqueu et al., 2011 Peng et al., 2011 Somasundaran, 2006). An empirical relation was suggested (Antonow s rule) by which one can predict the surface tension Yab-... 

Antonow s Rule and Interfacial Tension Data (mN/m) (See Text for Details)... 

If we have E >0 and S = 0, then a drop of oil on the surface of a liquid will in principle be spread over that surface to form a duplex flhn at equilibrium (obeying Antonow s rule [20]). In contradiction Harkins [18] has claimed that 5 < 0 always prevails at equilibrium even if the initial spreading coefficient 5 > 0. However, Rowlinson and Widom [19] emphasize convincingly that. S = 0 is allowed so that stable duplex films can often be found between mutually saturated liquids at equilibrium. 

The condition E <0 clearly means that the arrangement shown in Figure 3.5 cannot be realized at equilibrium (or at all). As pointed out by Hirasaki [28], it should not therefore be regarded as in conflict with the requirement, given by Equation 3.11, that the classic equilibrium entry coefficient should have a minimum value of zero. Thus the latter derives from Antonow s rule [20], which deals with equilibrium behavior and is only valid for systems in which the equilibrium disjoining pressure is zero. 

---