Modelling of the Critical Micelle Concentration of Cationic Gemini Surfactants Using Molecular Connectivity Indices

Anna Mozrzymas Modelling of the critical micelle concentrations (cmc) using the molecular connectivity indices was performed for a set of 21 cationic gemini surfactants with medium-length spacers. The obtained model contains only the second-order Kier and Hall molecular connectivity index. It is suggested that the index 2v includes some information about flexibility. The obtained model was used to predict log10 cmc of other cationic gemini surfactants. The agreement between calculated and experimental values of log10 cmc for the gemini surfactants that were not used in the correlation is very good. - Critical micelle concentration Gemini surfactants are molecules constructed of two hydrophobic chains and two polar/ ionic headgroups connected by the various spacer groups. Owing to their structure they have unique properties in aqueous solution, such as low critical micelle concentration (cmc) and high surface activity. The cmc values of these surfactants are significantly lower than those of the corresponding monomeric surfactants and in comparison to their monomeric counterparts, gemini surfactants are more efficient at reducing surface tension. Gemini surfactants demonstrate great potential for gene delivery [1]. Cationic gemini surfactants appear to be excellent for binding and compacting DNA. These surfactants bind DNA with higher efficiency and have better transfection efficiencies than their monomeric counterparts. Many conventional surfactants show good anti-microbial properties with respect to a large spectrum of bacteria, fungi and viruses, and simultaneously they are innocuous for living organisms, but the gemini compounds are much more active [2]. Due to these properties, gemini surfactants have been applied in various areas, such as the drug manufacturing especially in gene therapy, the food industry, cosmetics manufacturing especially in the skin care products, anti-bacterial and the anti-fungal preparations. One of the main reasons for the current interest in gemini surfactants is their critical micelle concentration values which are lower, by at least one order of magnitude, than those of the corresponding monomeric surfactants. As is well known, the cmc depends on the molecular structure of the surfactants. In general, the cmc in aqueous solution decreases as the hydrophobic character of the surfactant increases. The first relationship between cmc and structure of a molecule was given by Klevens [3] who empirically found that logarithm of cmc linearly decreases with increase in hydrophobic chain length of the surfactant. Gemini surfactants have two alkyl chains and two headgroups, therefore the influence of the variation of these groups on the cmc can be considerable. The important factor which distinguishes gemini surfactants from conventional monomeric surfactants is the connection of the headgroups by the spacer. The nature of the spacer group (length, flexibility, chemical structure) plays an important role in regulating the aggregation properties in the solution [4]. Not long ago, a quantitative structureproperty relationship (QSPR) was used for predicting the cmc values of conventional non-ionic [58] and ionic [912] surfactants. The values of the cmc of gemini surfactants can be significantly changed by a slight modification of the structure of the molecule; therefore modelling and predicting the critical micelle concentration of gemini surfactants directly from the structure of the molecule by the QSPR analysis can be of great interest. Recently, the QSPR study was performed to relate the structure of cationic gemini surfactants to their critical micelle concentration [13]. In this work, the cmc of gemini surfactants was correlated with 12 descriptors (seven topological among them connectivity indices, three statistical, one geometrical and one functional group descriptors). The previous QSPR models [8, 12] show that critical micelle concentration can be correlated and predicted by using the molecular connectivity indices only. In the present work cationic gemini surfactants are taken into consideration, and just as in the previous papers, in the QSPR study ten indices are used: five connectivity indices and five valence connectivity indices, from zeroth to fourth order in both cases. These indices are calculated from the chemical structure of the molecule and they contain considerable information about the molecule, including the details of electronic structure of each atom and the molecular structure features. The information encoded in molecular connectivity indices has been demonstrated in a variety of examples [14]. As is well known the cmc of the surfactants depends not only on geometrical factors of the molecule but also on other parameters, such as the kind of counterion and electrostatic charge distribution; therefore, just as in the previous paper [12], in order to minimize the influence of factors other than geometrical ones, only cationic gemini surfactants with bromide as counterion were taken into account. Furthermore, among the factors significantly affecting the cmc in aqueous solution are the temperature of the solution and the presence in the solution of added electrolyte and various organic compounds [15]. Therefore all values of cmc taken in the correlation were measured in pure water at room temperature. 2 Data The data set was chosen to contain gemini surfactants with a medium-length spacer. The chemical structures of the surfactants taken into consideration and their abbreviations are shown in Fig. 1. m - s - m m - 6 - n m - 7NH - m (CmN)2(OH)2 Fig. 1 Chemical structures of the surfactants considered and their abbreviations 12 - 4(OH) - 12 R = CmH2m+1 and R1 = CnH2n+1 The cmc of msm gemini surfactants [alkanediyl-a,x-bis(dimethylalkylammonium bromide)] with a given alkyl chain, particularly for the series with m = 12, increases with the spacer length up to a maximum at four or five methylene units and then decrease with further increase in the number of methylene units in the spacer group [16, 17]. The cmc values of dissymmetric surfactants designated as m66 are about one order of magnitude higher than those of the corresponding m6m symmetric surfactants [18] and the cmc decreases as the m/n ratio increases. In the case of the dissymmetric surfactants designated as m6n with m ? n = 24, the cmc values are comparable with those of the symmetric counterparts with m = 12 [19] and the cmc slightly decreases as the m/n ratio increases. The cmc values of m7NHm (1,9-bis(dodecyl)-1,1,9,9-tetramethyl-5-imino-1,9-nonanediammonium dibromide) [20, 21] gemini surfactants are higher than those of the corresponding m7m gemini surfactants [20] whereas the cmc values of (CnN)2(OH)2 (1,4bis(dodecyl-N,N-dimethylammonium bromide)-2,3-butanediol) [22, 23] and 124(OH)12 (1,4-bis(dodecyl-N,N-dimethylammonium bromide)-2-butanol) [23] are lower than those of their hydrophobic spacer homologues. Furthermore, the cmc decreases with increas (...truncated)