Conditions for the Existence of Synergism

2001b Zhou, 2003). Also, it has been observed that bulky head groups in a surfactant are more readily accommodated at the surface of a convex micelle than at the planar air-solution interface (Matsuki, 1997). 

Temperature increase in the 10-40°C range generally causes a decrease in attractive interaction. 

Based upon the same nonideal solution theory used in the evaluation of molecular interaction parameters above, the conditions for the existence of synergism in 

However, it should be understood that, because of the assumptions and approximations used in the nonideal solution theory upon which these relations are based, the calculated values for conditions at the point of maximum synergism may only approximate the values found under experimental conditions and should be used mainly for estimation purposes. This is especially true when commercial surfactants are used that may contain surface-active materials (impurities) of a type different from that of the nominal surfactant. These may cause the molecular interaction parameters to have values somewhat different from those listed in Table 11-1 for the nominal surfactant. When such impurities are suspected, it is advisable to determine experimentally the values of the interaction parameters. 

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The conditions for the existence of synergism of this type are obtaining by starting with the basic equations... 

Analogous expressions have been derived (Rosen, 1986) for the existence of synergism in mixed micelle formation in the presence of a second liquid phase and for the conditions at the point of maximum synergism. 

It is apparent from condition 2 that to increase the probability of synergism existing, the two surfactants selected for the mixture should have Cj and C2 values as close to each other as possible. When the values are equal, any value of (3° (other than 0) will produce synergism or antagonism. 

The first condition means that, for this type of synergism to exist, the two surfactants must have greater attraction for each other in the mixed monolayer at the interface than in the mixed micelle in the solution phase. This is usually obtained when the two surfactants are oppositely charged and have approximately equal hydrophobic chain lengths. From the second condition, it can be shown [6] that when both surfactants have approximately the same surface tension values at their CMCs, then almost any negative value of (P° — P ) will yield synergism of this type. Some data at various interfaces are shown in Table 3. 

When there exists a possibility of the participation of different types of equilibria, it is essential to consider all of them and no species should be excluded unless there is a strong evidence to do so. Thus it becomes a formidable task to find the type of species extracted in these systems. For these systems it may be of more practical utility to report the synergic coefficient values, under different experimental conditions, so that they may be useful in choosing the required extraction conditions. 

From the relations upon which equations 11.1 and 11.2 are based and the definition for synergism or antagonism (negative synergism) of this type, it has been shown mathematically (Hua, 1982b, 1988) that the conditions for synergism or antagonism, in surface tension reduction efficiency to exist are ... 

That is, when dCij/da = 0, the mole fraction of each surfactant in the mixed monolayer equals its mole fraction in the solution phase. Substituting (16) into the relationship (12) and Eq. (14), we obtain the following conditions for synergism of this type to exist ... 

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