Prediction of the Critical Micelle Concentration of Different Classes of Surfactants Using a New Topological Index

Prediction of the critical micelle concentration of different classes of surfactants using a new topological index

Qiang WANG ^a*, Qingzhu JIA ^a, Peisheng MA ^b, Dengfeng Fu ^a, Pengfei Liu ^a, Peng Feng ^a

a. School of Material Science and Chemical Engineering, Tianjin University of Science and Technology, 13St. TEDA, Tianjin, 300457, People's Republic of China

b. School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, People's Republic of China

* To whom correspondence should be addressed. E-mail: wang_q@tust.edu.cn  

 

Abstract    

A quantitative structure-property relationship (QSPR) study was performed on the critical micelle concentration (CMC) of surfactants in this work. Our previous works suggests that it is possible to use a totally same universal framework to predict the critical properties and the thermodynamics properties of organic compounds containing various functionalities. The objective of this work was to determine whether a more general structure-CMC relationship based solely on one topological index, could be developed through the systematic QSPR approach. Based on the chemical graphs, a new topological index calculated from a molecular graph was introduced and named as WQ index. It is evident that the proposed topological index can be used to predict the CMC for surfactants of diverse chemical structure with a significant degree of confidence. The results indicate that our topological index provides very satisfactory results. The AAD for the log₁₀(CMC) prediction of 170 surfactants is 2.61 and the mean absolute relative derivation is 7.5 %, respectively. In addition, the proposed WQ index is very simple to calculate and has strong discriminating power, and it promises to be a useful parameter in QSPR studies.

Keywords: Surfactants; The critical micelle concentration; QSPR; topological index; Prediction;

Introduction

The critical micelle concentration, CMC, of a surfactant is an extremely useful defining property of a surfactant. It was found that, at the CMC, many important properties of the surfactant solution, such as surface tension, interfacial tension, conductivity and osmotic pressure change sharply. As a result, CMC can be regarded as one of the most useful quantities for characterizing surfactants and can be correlated with many industrially important properties¹.

It is well-known that CMC depends on molecular structure. Based on a vast amount of experimental data concerning the CMC of surfactants, many empirical equations relating the CMC to the various structural units in surfactants were obtained^2,3. However, all of these have been limited to a homologous series of surfactants, such as the linear alkyl ethoxylates.

QSAR/QSPR (quantitative structure- activities / properties relationship) models is widely used for the prediction of physicochemical properties and biological activities in chemistry, biochemistry, pharmacology and environmental areas. Nowadays, QSAR/QSPR models using descriptors generated from molecular graphs have been more frequently used to obtain physicochemical and biological properties. Chemical graph theory relies on the observation that the connectivity of a molecule is correlated to many of its intrinsic physical properties, and the special descriptors, topological indices have attracted much recent research interest. With increased computational power and the development of modern QSAR/QSPR approaches, powerful methods for the prediction of CMC have eventually become available^4-11. However, most of the published models focus on homologous series of hydrocarbons. In addition, it is evident that until now no single topological index could be used universally in optimal correlations; thus, more than hundreds of topological indices are in existence.

Authors recently proposed a universal positional distributive group contribution (PDGC) theory for the prediction of various properties (critical temperature, melting point, vaporization enthalpy and so on.) of a diverse set of organics compound^12,13. And it is important to note that our previous works suggests that it is possible to use a totally same universal framework to predict the critical properties and the thermodynamics properties of organic compounds containing various functionalities

In view of the above, the objective of this work was to determine whether a more general structure-CMC relationship based solely on one topological index, could be developed through the systematic QSPR approach, using large databases of molecular descriptors. For this purpose, 170 surfactants from literature were selected as the complete set to develop the QSPR model¹¹.

Method proposed in this work

Based on chemical graphs, a new topological index calculated from a molecular graph was introduced and named as WQ index. This newly proposed topological index is adapted from the distance matrix and the extended distance matrix, from which the extended adjacency matrix, the extended interval matrix and the extended interval jump matrix are deduced. WQ index quantitatively describes the structural information of molecules, taking into account parameters like atom mass,  branching, adjacency pattern, electronegativity, the minimum bond length with adjacent atom, number of hydrogen atom and heteroatom variation etc, which are general but crucial ingredients for modeling thermodynamic properties. Also, the norm(1) and the norm(2) of the above matrixes have be calculated for developing the QSPR model.

Here, using the WQ index, the QSPR model for log₁₀(CMC) prediction is expressed as follows:

  extended distance matrix ;     extended adjacency matrix;

  extended interval matrix;       extended interval jump matrix;

 means the largest column sum of matrix  ;

 means the largest singular value of matrix ;

 is the frobenius-norm of matrix ;

for total number of atoms,  is molecular weight, and M₀ is the constant added.

Results and discussion

Results of this work indicate that the predicted log₁₀(CMC) agree well with the "experimental results", which demonstrates that the new topological index for predicting the log₁₀(CMC) has good overall accuracy. The AAD for the log₁₀(CMC) prediction of 170 surfactants is 2.61 and the mean absolute relative derivation is 7.5 %. And the results show that our new simple model gives lower deviations and can be used with confidence in thermodynamic and engineering calculations.

Conclusion

The objective of this work was to develop and evaluate our new topological index for predicting the CMC of surfactants containing various functional groups. The results indicate that the CMC was successfully predicted. It is evident that the proposed topological index can be used to predict the CMC for surfactants of diverse chemical structure with a significant degree of confidence. The AAD for the log₁₀(CMC) prediction of 170 surfactants is 2.61 and the mean absolute relative derivation is 7.5 %, respectively. In additional, the proposed WQ index is very simple to calculate and has discriminating power. The WQ index with fairly good structural selectivity and correlation ability is a suitable parameter for modeling physicochemical properties as well as physiological activities of diversified and complex compounds. And it promises to be a useful parameter in QSAR/QSPR studies.

Acknowledgements. Research reported in this work was supported by the National Natural Science Foundation of China (No. 20976131). Also, we would give much thanks to Feng Peng, Liu Pengfei and Fu Dengfeng, who have contributed for valuable advice and discussion.

Literature Cited 

[1]      Alan R. Katritzky, Minati Kuanar, Svetoslav Slavov, et al., Chem. Rev. 2010, 110, 5714-5789.

[2]      Becher, P. J. Dispersion Sci. Technol. 1984, 5, 81.

[3]      Ravey, J. C.; Gherbi, A.; Stebe, M. Prog. Colloid Polym. Sci. 1988, 76, 234.

[4]      Huibers, P. D. T.; Lobanov, V. S.; Katritzky, A. R.; Shah, D. O.; Karelson, M. Langmuir 1996, 12, 1462.

[5]      Kuanar, M.; Kuanar, S. K.; Mishra, B. K. Indian J. Chem. 1999, 38A, 113.

[6]      Li, X.; Zhang, G.; Dong, J.; Zhou, X.; Yan, X.; Luo, M. Theochem, 2004, 710, 119.

[7]      Katritzky, A. R.; Pacureanu, L.; Dobchev, D.; Karelson, M. J. Chem. Inf. Model. 2007, 47, 782.

[8]      Anna Mozrzymas, Bo¨Bzenna R¨®zycka-Roszak, J Math Chem. 2011, 49, 276-289.

[9]      Paul D. T. Huibers, Victor S. Lobanov,| Alan R. Katritzky, Dinesh O. Shah, Mati Karelson, Langmuir, 1996, 12, 1462-1470.

[10]  Huibers, P. D. T.; Lobanov, V. S.; Katritzky, A. R.; Shah, D. O.; Karelson, M. J. Colloid Interface Sci. 1997, 187, 113-120.

[11]  David T. Stanton, J Comput Aided Mol Des. 2008, 22, 441-460.

[12]  Wang Qiang, Ma Peisheng, Jia Qingzhu, J Chem Eng Data, 2008, 53, 1103-1109

[13]  Jia Qingzhu, Wang Qiang, Ma Peisheng, J Chem Eng Data, 2010, 55, 5614-5620.