34 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS FACTORS INFLUENCING COMPLEX FORMATION SURFACTANT STRUCTURE It has frequently been reported that interaction between uncharged water-soluble polymers and surfactants is much more facile with anionic surfactants than with cationic surfactants and, in turn, very much stronger than with nonionic surfactants. A pro- nounced influence of the particular counterion present in the cationic surfactant on its reactivity with a polymer has been found by Saito (24). This author (25) also reported that modification of the structure of an alkylsulfate by insertion of ethyleneoxide groups considerably weakened its interaction with a polymer (PVP). Branching of a surfactant molecule is also expected to weaken the interaction. CHAIN LENGTH In a homologous series of alkylsulfates, the initial binding concentration, T•, decreases with increasing chain length (8,10,26). A linear relation between log Tx and n, the number of carbons in the alkyl chain, viz. lnT• = n•o/kT + constant exists as has been found between log CMC and n. For PVP/SDS mixtures, Arai et al. (10) found a value for •o of - 1.1 kT. This corresponds to the free energy change per CH 2 group on transferring the surfactant from the unassociated state in water to the complex, and is comparable to the value for the analogous transfer of the surfactant molecule to a micelle. Goddard et al. (27) studied the solubility diagrams of a homologous series of alkyl sodium sulfates in mixture with the cationic cellulosic polymer, PQ-10. In each case it was found that, in the limit, the slope of the points of maximum insolubility in the plot of log polymer versus log surfactant concentration changed from 45 ø to 90 ø (i.e., be- came independent of polymer concentration if the latter were reduced below a certain value). Mathematically, the result could be expressed as Ceexp (mo/kT) = constant where Ce is the polymer concentration-independent surfactant concentration corre- sponding to maximum precipitation. A value of •o of - 1.1 kT was derived, suggesting that the environment of surfactant molecules in the complex resembles that of micelles in this case also. EFFECT OF SALT In the case of unionized polymer/charged surfactant systems, addition of salt depresses the T• values, i.e., promotes the formation of complexes. Murata and Arai, for ex- ample, found the log-log plot of T• against sodium ion concentration for the PVP/SDS association to be linear, with a slope exactly the same as that of the CMC/sodium ion concentration plot for this surfactant (11). Addition of salt also increased the binding ratio of surfactant to polymer, i.e., extended the T•, T 2 range. For example, in the case of PVP/SDS, addition of 0.1 M NaC1 increased the ratio to 0.9 mol SDS per base mol PVP from the 0.3/1 ratio observed in water. A similar effect occurs with PEO/SDS (28).

POLYMER/SURFACTANT INTERACTION 35 A very different effect of salt occurs if the polymer is a polyion and the surfactant bears an opposite charge to it. In this case, while the addition of salt increases the steepness, i.e., the "cooperativity" observed in the binding isotherm, it substantially reduces the affinity of binding, as evidenced by a steady increase in the concentration at which binding commences (29). This result clearly points to the importance of electrostatic attraction between the polyion and the oppositely charged surfactant as being a primary driving force for the association. That electrical screening by the salt is the operating mechanism in weakening attraction is verified inasmuch as the effect is magnified if the salt contains divalent ions, as opposed to monovalent ions, bearing a charge opposite in sign to that of the polyion (30). THE POLYMER A minimum molecular weight of polymer is apparently required to ensure "complete" interaction with the surfactant, and this value is 4000 for PEO and PVP. Below values of ca. 1500, the interaction tendencies with these polymers are restricted. Until quite recently, the list of unionized polymers showing the ability to form com- plexes with ionic surfactant was quite small. The "traditional" list included PEO, PVP, and PVOH. The lack of reactivity in this respect of other polymers, such as HEC, was thought to be due to a lack of macromolecular flexibility, but even the more flexible polysaccharide dextran shows little tendency to interact with SDS or DDBS. Likewise, the relative inactivity of polyacrylamide, PAAm, remained a puzzle. It was recognized that reactivity can be induced in a polymeric structure by introducing hydrophobic sites in the macromolecule. Examples are MeC versus HEC, low-molecular-weight polyal- kyleneoxides in which PO replaces EO, and PVOH specimens prepared from, but still containing residual amounts of, PVAc. In fact, the reactivity of polymers seems to correlate with a kind of "hydrophobicity index": For anionic surfactants, Breuer and Robb (1) listed polymers in the following order of increasing reactivity: PVOH ( PEO ( MeC ( PVAc • PPO -- PVP and for cationic surfactants: PVP ( PEO ( PVOH ( MeC ( PVAc ( PPO Recently, the notion of the importance of hydrophobicity in the polymer in promoting reactivity with surfactants has had strong reinforcement. Lindman and co-workers have shown that hydroxypropyl and ethylhydroxyethyl cellulose (31), and of course MeC (32), all display pronounced association tendencies towards SDS, and "reactivity" can be induced in PAAm by methyl (or other alkyl substitution) of the nitrogen amide group of this polymer (33). These results support the earlier data of Murai et al. on the reaction of SDS with a series of model polypeptides (34). It should be mentioned that very recent work on so-called "associative polymers" (alkyl-substituted water-soluble polymers) is clearly indicating that these structures have pronounced interaction ten- dencies with added surfactant. See below. Turning now to ionized polymers, we point out first the position of PVP in the above two polymer sequence series. This polymer is known to be weakly cationic its slight residual positive charge promotes interaction with anionic surfactants and does the re- verse with cationic surfactants. These effects are magnified when the polymer carries