Klevens equation

Since the well-known Stauff-Klevens equation which relates the number of carbon atoms of a surfactant and the critical micellar concentration was estab-... 

The Stauff-Klevens equation is valid for the critical micelle concentration of homologous surfactants with the same ionic head group ... 

It was also determined that the critical micelle concentration, especially for betaines, but also for surfactants in general, decrease logarithmically as the number of carbon atoms in the alkyl chains increases. This was determined by Klevens (42) and is referred to as the Klevens equation, as follows ... 

The relationship between the hydrocarbon chain length and cmc for ionic surfactants generally fits the Klevens equation... 

In aqueous solutions, the surface tensions of these hybrid surfactants are about equal or slightly lower than that of the corresponding surfactant with a single hydrophobe. The cmc values are relatively low and are governed by the Kleven equation. The increase of the hydrocarbon-chain-length by a CH2 group decreases the cmc by about 35%. The increase of the fluorocarbon chain by each -CF2- group decreases the cmc by about 75%. Quantitative analysis of the F-NMR spectra has revealed that the residence time of the fluorocarbon chain in... 

Alcohol sulfates have lower CMCs than sulfonates, which in turn have lower values than carboxylates. It is known that the CMC decreases logarithmically as the number of carbon atoms of the alkyl chain increases, according to Klevens s equation [86] ... 

Empirical Equations Many investigators have developed empirical equations relating the CMC to the various structural units in surface-active agents. Thus, for homologous straight-chain ionic surfactants (soaps, alkanesulfonates, alkyl sulfates, alkylammonium chlorides, alkyltrimethylammonium bromides) in aqueous medium, a relation between the CMC and the number of carbon atoms N in the hydrophobic chain was found (Klevens, 1953) in the form... 

In these and other papers by Anslow and coworkers the frequency at which absorption is complete, is used to calculate the energy required for the presumed related dissociation process (e.g. of a proton from a carboxyl group, fission of the S—S bond in cystine), using an equation relating the mass of the ion produced to the frequency of complete absorption (see also Anslow, 1932a, b). As the frequency at which complete dissociation commences has been obtained with complete disregard for the well-established selective absorption of saturated carboxylic acids and aminocarboxylic acids in the vacuum ultraviolet below 2000 A. (see Platt and Klevens, 1944, for a review of the available data), and the more easily accessible short wave bands of the aromatic amino acids (see Section III, 1), and as the theoretical basis of the equation concerned is open to serious criticism, this particular aspect of the work will not be considered further. 

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