Solubilization of solutes in micellar solutions is a process having a wide range of applications starting from the detergency up to the enhancing the aqueous solubility of hydrophobic drugs or separation of products of biosynthesis. The measure of solubilization is a solute partitioning coefficient between the micellar and aqueous phase (Kmw). In pharmaceutical industry, the knowledge of the partitioning of drug candidates in the different media of the human body (n-octanol/water, Kow, or the micelle/water partition coefficient) is of importance at the early stage of the design process and should be known from measurements or calculations. In case of biosynthesis, the separation of products from the reaction media is often made by adding surfactants to the system followed by the separation of the product-containing micellar phase by filtration. In this case, the proper information on Kmw is essential for choosing the surfactant with the highest selectivity. In such applications, the possibility to predict the partitioning of the substance under investigation in solutions containing different surfactants would be especially valuable. Presently, only few models exist allowing the prediction of Kmw. All of them belong to the class of linear correlations between some molecular properties and log(Kmw) values. The partitioning of a drug between the coexisting phases is determined by the thermodynamic equilibrium. Therefore, models based on estimation of chemical potentials or equivalently of activity coefficients can be principally applied to predict the partitioning of organic substances between polar (water) and nonpolar (n-octanol/micelle) phases. The aim of this work is to show that the thermodynamically based models can be effectively utilised to predict the organic substances and drugs partitioning, and the prediction can be achieved quantitatively based solely on the chemical structure of the substances. Furthermore, such models account for the concentration of each ingredient and temperature, so they can be utilised to predict how the solute partitioning changes when these conditions are varied.

Modelling

Two models are examined here: the structure-interpolating UNIFAC model [1] and the a-priori COSMO-RS model [2]. The general applicability of both models for modelling of the partition coefficient has been recently demonstrated for a couple of systems [3]. In the present study, partitioning of a variety of solute classes in aqueous solutions of nonionic and ionic surfactants is investigated.

• UNIFAC

UNIFAC (Universal Quasi-Chemical Functional-Group Activity Coefficient) model is a group-contribution tool, which allows calculations based on functional group parameters giving additive contributions to the properties of the system. The matrix of the model's energy parameters covers more than 50 groups and allows to predict properties of complex multicomponent systems. In order to consider micellar systems in the frame of this model, we have introduced the interfacial contribution to the activity coefficient in terms of the Gibbs-Thompson theory (UNIFAC-IF) [3]. It has to be noted that the corresponding calculations can be carried out rather fast but it is hardly possible to consider steric isomers as well as ionic substances.

• COSMO-RS

COSMO-RS model (Conductor like Screening Model for Real Solvents) is based on quantum mechanics and allows an a priori prediction of thermodynamic properties such as activity coefficients based on the molecular structure only. In the COSMO model [4], the solute molecule is considered to be embedded in a cavity surrounded by a virtual conductor. The transfer from the state of the molecule embedded in a virtual conductor to the real solvent is done by applying the COSMO-RS concept [2] by means of statistical thermodynamics (here different conformers of all components of the mixture are taken into account). Steric isomers as well as ionic substances can be principally modeled.

Results

We illustrate the practical implementation of the theoretical framework by examining a variety of homologous series of organic substances (including drugs) in aqueous solutions of nonionic and ionic surfactants.

• Partition coefficients in the aqueous solutions of nonionic surfactants

Figure 1 shows the predicted micelle/water partition coefficients (COSMO-RS) versus the experimental values taken from literature in the aqueous solutions of the nonionic surfactant, Triton X100. Both models demonstrate a quantitative agreement with the experimental data. The average errors are below 8% and 17% for the COSMO-RS and UNIFAC-IF models, correspondingly.

• Partition coefficients in the aqueous solutions of ionic surfactants

Figure 2 illustrates the potential of the COSMO-RS model to predict Kmw in the aqueous solutions of ionic surfactants. The predicted Kmw of a series of organics in aqueous solution of sodium dodecyl sulphate (SDS) are plotted versus the experimental values. The results are in reasonable consistency with the experimental data [7]. The average error is lower than 15%.

• Partition coefficients of parabens Parabens are used as preservatives in drug formulations, cosmetics, and food. In the present study, the partition coefficients of parabens in aqueous solution of Triton X100 have been measured using ultrafiltration and modelled. The COSMO-RS model shows a good agreement with the experiment while the UNIFAC-IF model overestimates the paraben solubility in water.

Conclusions

The predictive capability of the COSMO-RS and UNIFAC-IF models to describe the micelle/water partition coefficients has been demonstrated. The only information needed for the model prediction is the chemical structure of the substances. Different classes of organic solutes in the aqueous solutions of nonionic and ionic surfactants were tested. The theoretically predicted partition coefficients were found to be in reasonable quantitative agreement with the experimentally measured ones. The theoretical approaches can be extended and applied to multicomponent systems (mixtures of solutes and/or mixtures of surfactants). Effects of temperature and concentration can be examined. The results of the modeling can be used for the prediction of the enhanced drug solubilisation as well as for the optimization of separation and purification processes in biotechnology and pharmaceutical industry.

References

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