(189g) 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.

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