We propose a "microscopic" model of gemini surfactants in aqueous solution.
Carrying out extensive Monte Carlo simulations, we study the variation of the
critical micellar concentration (CMC) of these model gemini surfactants with
the variation of the (a) length of the spacer connecting the two hydrophilic
heads, (b) length of the hydrophobic tail and (c) the bending rigidity of the
hydrocarbon chains forming the spacer and the tail; some of the trends of
variation are counter-intuitive but are in excellent agreement with the
available experimental results. Our simulations also elucidate the dependence
of the shapes of the micellar aggregates and the magnitude of the CMC on the
geometrical shape and size of the surfactant molecules and the electrical
charge on the hydrophilic heads

D Chowdhury

Deinega Y. F.

Evans D. F.

Gelbert W.

Gompper G.

Liverpool T. B.

Maiti P. K.

P. K Maiti

Rosen M.

Tanford C.

English

arXiv

We propose a “microscopic” model of gemini surfactants in aqueous 
solution. Carrying out Monte Carlo simulations, we study the 
variation of the critical micellar concentration (CMC) of these model 
gemini surfactants with the variation of a) the length of the spacer 
connecting the two hydrophilic heads, b) the length of the hydrophobic tail 
and c) the bending rigidity of the chains forming the spacer 
and the tail; some of the trends of variation are counter-intuitive but 
are in excellent agreement with the available experimental results. 
Our simulations also elucidate the dependence of the shapes of the micellar 
aggregates and the magnitude of the CMC on the geometrical shape and size 
of the surfactant molecules and the electrical charge on the hydrophilic 
heads

P. K. Maiti

D. Chowdhury

EDP Sciences OAI-PMH repository (1.2.0)

Micellar aggregates of gemini surfactants: Monte Carlo 
simulation of a microscopic model

Crossref

Micellar aggregates of gemini surfactants: Monte Carlo simulation of a microscopic model

We propose a "microscopic" model of gemini surfactants in aqueous solution. Carrying out Monte Carlo simulations, we study the variation of the critical micellar concentration (CMC) of these model gemini surfactants with the variation of a) the length of the spacer connecting the two hydrophilic heads, b) the length of the hydrophobic tail and c) the bending rigidity of the chains forming the spacer and the tail; some of the trends of variation are counter-intuitive but are in excellent agreement with the available experimental results. Our simulations also elucidate the dependence of the shapes of the micellar aggregates and the magnitude of the CMC on the geometrical shape and size of the surfactant molecules and the electrical charge on the hydrophilic heads

Maiti, P. K.

Chowdhury, D.

Publications of the IAS Fellows

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Micellar Aggregates of Gemini Surfactants:
Monte Carlo Simulation of a Microscopic Model
Prabal K. Maiti1 and Debashish Chowdhury1,2,∗
1Department of Physics, Indian Institute of Technology,
Kanpur 208016, U.P., India†
2Institute for Theoretical Physics, University of Cologne
D-50937 Ko¨ln, Germany‡
Abstract
We propose a ”microscopic” model of gemini surfactants in aque-
ous solution. Carrying out extensive Monte Carlo simulations, we
study the variation of the critical micellar concentration (CMC) of
these model gemini surfactants with the variation of the (a) length of
the spacer connecting the two hydrophilic heads, (b) length of the hy-
drophobic tail and (c) the bending rigidity of the hydrocarbon chains
forming the spacer and the tail; some of the trends of variation are
counter-intuitive but are in excellent agreement with the available ex-
perimental results. Our simulations also elucidate the dependence of
the shapes of the micellar aggregates and the magnitude of the CMC
on the geometrical shape and size of the surfactant molecules and the
electrical charge on the hydrophilic heads.
Running title: Micellar aggregate of gemini surfactants
PACS Numbers: 68.10.-m, 82.70.-y
————————————————————————–
∗ To whom all correspondence should be addressed;
E-mail: debch@thp.Uni-Koeln.de (till 30th June, 1997).
† (Permanent Address); E-mail: debch@iitk.ernet.in
‡ (Address till 30th June, 1997)
1
Soap molecules are common examples of surfactant molecules; these not
only find wide ranging applications in detergent and pharmaceutical indus-
tries, food technology, petroleum recovery etc. but are also one of the most
important constituents of cells in living systems. Therefore, physics, chem-
istry, biology and technology meet at the frontier area of interdisciplinary
research on association colloids formed by surfactants [1]. The ”head” part
of surfactant molecules consist of a polar or ionic group. The ”tail” of many
surfactants consist of a single hydrocarbon chain whereas that of some other
surfactants, e.g., phospholipids, are made of two hydrocarbon chains both of
which are connected to the same head [2]. In contrast, gemini surfactants
[3, 4, 5, 6], consist of two single-chain surfactants whose heads are connected
by a ”spacer” chain and, hence, these ”double-headed” surfactants are some-
times also referred to as ”dimeric surfactants” [7, 8]. The gemini surfactants
have several unusual properties. Some of these properties, which make these
very attractive for potential industrial use, are crucially influenced by the
aggregation of the surfactants and the morphologies of these supramolecular
aggregates. Therefore, in order to gain insight into the physical origin of
some of the unusual properies of gemini surfactants, in this letter we propose
a simple microscopic model and study the formation and morphologies of
the supramolecular aggregates of these model gemini surfactants by Monte
Carlo (MC) computer simulations.
When put into an aqueous medium, the ”heads” of the surfactants like to
get immersed in water and, hence, called ”hydrophilic” while the tails tend
to minimize contact with water and, hence, called ”hydrophobic” [2]. The
spacer in gemini surfactants is usually hydrophobic but gemini surfactants
2
with hydrophilic spacers have also been synthesized[9]. A multi-component
fluid mixture containing water and surfactants minimizes the free energy by
forming ”self-assemblies” (i.e., supra-molecular aggregates) of surfactants,
such as monolayer and bilayer membranes, micelles, inverted-micelles, vesi-
cles, etc. [10]. Micelles are formed when the concentration of the surfactants
in water exceeds what is known as the critical micellar concentration (CMC)
[2].
On the basis of intuitive physical arguments, it is usually expected that
a longer hydrocarbon chain should lower the CMC. On the contrary, two
unusual features of the CMC of gemini surfactants with ionic heads are: (i)
for a given fixed length of each of the two tails, the CMC increases with the
length of the spacer till it reaches a maximum beyond which CMC decreases
with further increase of the spacer length [7, 11, 12, 13]; (ii) for a given
length of the spacer, the CMC increases with increasing tail length [4, 5].
Moreover, the micellar aggregates formed by the gemini surfactants with
short spacers even at low concentrations just above the CMC are ”long,
thread-like and entangled” [8, 14], in contrast to the spherical shapes of the
micelles formed by single-chain surfactants at such low concentrations. Our
aim is to understand the physical origin of these unusual properties of gemini
surfactants.
A microscopic lattice model of double-chain surfactants (with a single
head) in aqueous solution was developed by Bernardes[15] by modifying the
Larson model of single-chain surfactants [16, 17, 18]. In this letter we propose
a microscopic lattice model of gemini surfactants by extending Bernardes’
model so as to incorporate two hydrophilic heads connected by a hydrophobic
3
spacer.
The Larson model was originally developed for ternary microemulsions
which consist of water, oil and surfactants. In the spirit of lattice gas mod-
els, the fluid under investigation is modelled as a simple cubic lattice of size
Lx × Ly × Lz. Each of the molecules of water (and oil) can occupy a sin-
gle lattice site. A surfactant occupies several lattice sites each successive
pairs of which are connected by rigid nearest-neighbour bond. A single-chain
surfactant can be described by the symbol [18] TmNpHq where T denotes
tail, H denotes head and N denotes the ’liaison’ or neutral part of the sur-
factants. m, p and q are integers denoting the lengths of the tail, neutral
region and head, respectively, in the units of lattice sites. Thus, each surfac-
tant is a self-avoiding chain of length ℓ = (m + p + q). The ”water-loving”
head group is assumed to be ”water-like” and, similarly, the ”oil-loving” tail
group is assumed to be ”oil-like”. Bernardes’ lattice model of double-chain
surfactants with a single hydrophilic head can be described by the symbol
TmNpHqNpTm. In terms of the same symbols, the microscopic lattice model
of a gemini surfactant, which we propose here, can be represented by the
symbol TmNpHqSnHqNpTm where n is the number of lattice sites constitut-
ing the spacer represented by the symbol S. We shall refer to each site on
the surfactants as a monomer.
Jan, Stauffer and collaborators [17] reformulated the Larson model in
terms of Ising-like variables, in the same spirit in which a large number of
simpler lattice models had been formulated earlier [19] for the convenience
of calculations. In this reformulation, a classical Ising spin variable S is as-
signed to each lattice site; Si = 1 (−1) if the i-th lattice site is occupied by
4
a water (oil) molecule. If the j-th site is occupied by a monomer belonging
to a surfactant then Sj = 1,−1, 0 depending on whether the monomer at
the jth site belongs to head, tail or neutral part. The monomer-monomer
interactions are taken into account through the interaction between the cor-
responding pair of Ising spins which is assumed to be non-zero provided the
spins are located on the nearest-neighbour sites on the lattice. Thus, the
Hamiltonian for the system is given by the standard form
H = −J
∑
<ij>
SiSj . (1)
where attractive interaction (analogue of the ferromagnetic interaction in
Ising magnets) corresponds to J > 0 and repulsive interaction (analogue of
antiferromagnetic interaction) corresponds to J < 0 [17]. Temperature T of
the system is measured in the units of J (the Boltzmann constant kB = 1.0).
We have considered three possible Larson-type microscopic lattice models
of ionic gemini surfactants. In the simplest model, which we call model A,
the monomers belonging to heads have Ising spin +2 to mimic the presence
of charge. The repulsive interaction between a pair of ionic heads is taken
into account through an antiferromagnetic interaction J = −1 between pairs
of nearest neighbour sites both of which carry spins +2; however, the in-
teraction between all other pairs of nearest-neighbour spins is assumed to
be J = 1. The short-range of the repulsive (antiferromagnetic) interaction
between the ”charged” heads corresponds to very strong screening of the
Coulomb repulsion between ionic heads by the counterions. Molecular dy-
namics (MD) simulations of a similar molecular model of gemini surfactants
has been carried out by Karaborni et al. [20]. In this letter we summarize
5
only the most important results on the model A with hydrophobic spacer;
the results for the models B and C will be reported, together with the results
for the model A with hydrophilic spacer, in a longer paper elsewhere [21].
In order to investigate the influence of the ionic heads on the results,
we have also considered a model of gemini surfactants with non-ionic polar
heads which is obtained from the model A by replacing all the +2 Ising spin
variables by Ising spin +1 (and, accordingly, the interactions −1 between the
heads on nearest-neighbour sites are replaced by +1). Moreover, in order to
investigate the role of the chain stiffness we have introduced a chain bending
energy; every bend of a tail or a spacer, by a right angle at a lattice site, is
assumed to cost an extra amount of energy K(> 0).
We have carried out MC simulations of the model TmNpHqSnHqNpTm of
gemini surfactants for p = q = 1 and for three differnet values of the tail
length, namely, m = 5, 15 and 25 in water where Lx = Ly = Lz = 100.
The moves allowed for the surfactants in our model are same as described
in ref.[18]. In reality, CMC is not a single concentration (perhaps, it is more
appropriate to call it characteristic micellar concentration [17]). Following
Stauffer et al.[17], we identify CMC as the amphiphile concentration where
half of the surfactants are in the form of isolated chains and the other half
in the form of clusters consisting of more than one neighbouring amphiphile.
For a given m we have computed the CMC for spacer lengths 2 ≤ n ≤ 20.
The non-monotonic variation of CMC of ionic gemini surfactants with the
spacer length, shown in figs. 1 and 2, is in qualitative agreement with the
experimental observations [11, 12, 13, 14]. Moreover, for a given length of the
spacer, the CMC increases when the bending stiffness K of the hydrophobic
6
chains is switched on. Furthermore, we have observed that, for a given length
of the hydrophobic spacer, the CMC of ionic gemini surfactants increase with
the increase of the tail length [21]; this trend of variation is also consistent
with the corresponding experimental observations [4, 5].
For a given tail length, the CMC of model gemini surfactants with non-
ionic polar head groups decreases monotonically with the increase in the
spacer length for both m = 5 and m = 15 (see fig.3). This is in sharp
contrast to the non-monotonic variation observed for ionic gemini surfactants.
However, for a given spacer length, the trend of the variation of CMC of non-
ionic gemini surfactants with the tail length is similar to that observed for
ionic gemini surfactants.
The snapshots of the micellar aggregates formed by the gemini surfactants
with ionic heads are shown for spacer length n = 2 (fig. 4) and for n = 16
(fig.5). The morphology of the aggregates in fig.4 are similar to the ”long,
thread-like and entangled” micelles observed in laboratory experiments [8]
and in MD simulations [20] on gemini surfactants with short spacers. More-
over, our data in fig.5 suggest that rod-like micelles are formed by gemini
surfactants with m = 15 when the spacer length is n = 16. The morpholo-
gies of the aggreagtes in fig.4 and 5 are in sharp contrast with the spherical
shape of the micelles (see fig.6) formed by single-chain ionic surfactants of
comparable tail size even at concentrations somewhat higher than those in
the figures 4 and 5.
We did not observe any significant difference in the shapes of the aggre-
gates of ionic and non-ionic gemini surfactants for given values of m, n and
comparable concentration [21], in spite of qualitatively different trends of
7
variation of CMC with spacer lengths.
Therefore, we conclude that (i) the shapes of aggregates are dominantly
determined by the geometric shape and size of the molecules whereas (ii)
the variation of CMC with spacer length is strongly influenced by the ionic
charge. It would be interesting to investigate the effects of weakening of the
screening (i.e., increasing the range) of the repulsive Coulomb interaction
between the ionic heads on the results reported in this letter; but, such a
MC study will require much larger computational resources.
Acknowledgements: One of us (DC) thanks V.K. Aswal, A.T. Bernardes,
S. Bhattacharya, P.S. Goyal, D. Stauffer and R. Zana for useful discus-
sions/correspondences and the Alexander von Humboldt Foundation for par-
tial financial support.
8
References
[1] Evans D. F. and Wennerstrom H., The colloidal domain where physics,
chemistry, biology and technology meet, VCH, New York (1994).
[2] Tanford C., The Hydrophobic Effect: Formation of Micelles and Biolog-
ical Membranes, (Wiley, New York 1980).
[3] Deinega Y. F., Ulberg Z. R., Marochko L. G., Rudi V. P. and Deisenko
V. P., Kolloidn Zh. 36, 649 (1974).
[4] Menger F. M. and Littau C. A., J. Am. Chem. Soc., 113, 1451 (1991).
[5] Menger F. M. and Littau C. A., J. Am. Chem. Soc., 115, 10083 (1993).
[6] Rosen M., Chemtech 30 (1993).
[7] Zana R., Benrraou M. and Rueff R., Langmuir, 7 ,1072 (1991).
[8] Zana R. and Talmon Y., Nature, 362, 228 (1993).
[9] Song L. D. and Rosen M. J., Langmuir, 12, 1149 (1996).
[10] Gelbert W., Ben Shaul A. and Roux D. (eds.) Micelles, Membranes,
Microemulsions and Monolayers (Springer, Berlin, 1994).
[11] Alami E., Beinert G., Marie P. and Zana R., Langmuir, 9, 1465 (1993).
[12] Frindi M., Michels B., Levy H. and Zana R., Langmuir, 10, 1140 (1994).
[13] De S., Aswal V. K., Goyal P.S. and Bhattacharya S., J. Phys. Chem.
100, 11664 (1996).
9
[14] Hirata H., Hattori N., Ishida M., Okabayashi H., Frusaka M. and Zana
R., J. Phys.Chem. 99, 17778 (1995).
[15] Bernardes A. T., J. Phys. II France 6, 169 (1996); see also Langmuir,
12, 5763 (1996).
[16] Larson R. G., Scriven L. E. and Davis H. T., J. Chem. Phys. 83, 2411
(1985); Larson R. G., J. Chem. Phys. 89, 1642 (1988) and 91, 2479
(1989).
[17] Stauffer D., Jan N., He Y., Pandey R. B., Marangoni D. G. and Smith-
Palmer T., J. Chem. Phys. 100, 6934 (1994); Jan N. and Stauffer D., J.
de Physique I 4, 345 (1994).
[18] Liverpool T. B., in: Annual Reviews of Computational Physics, vol. IV,
ed. D. Stauffer (World Scientific, Singapore 1996).
[19] Gompper G. and Schick M., Phase Transitions and Critical Phenomena,
Vol. 16, ed. C. Domb and J. L. Lebowitz, (Academic Press, London
1994).
[20] Karaboni S., Esselink K., Hilbers P. A. J., Smit B., Karthauser J., van
Os N. M. and Zana R., Science, 266, 254 (1994)
[21] Maiti P. K. and Chowdhury D., to be published
10
Figure Captions:
Fig.1: Variation of CMC of ionic geminis with spacer length; m = 15,
T = 2.2. The symbols 2 and× correspond toK = 0 andK = 2, respectively.
The continuous curves are merely guides to the eye.
Fig.2: Same as fig.1, except that m = 5. The symbols △ and ∗ correspond
to K = 0 and K = 2, respectively.
Fig.3: Variation of CMC of non-ionic geminis with spacer length; m = 15
(2) and m = 5 (△) both with K = 0 and at T = 2.2. The continuous curves
are merely guides to the eye.
Fig.4: Snapshots of the micellar aggregates formed by ionic geminis with
m = 15, n = 2 and K = 0 at T = 2.2 when the surfactant density is 0.007.
The symbols black spheres, dark grey spheres and light grey spheres represent
monomers belonging to head, tail and spacer, respectively.
Fig.5: Same as in fig.5, except that n = 16 and the density is 0.005.
Fig.6: Snapshots of micellar aggregates formed by single-chain ionic surfac-
tants with m = 14 and the density 0.01. The symbols black spheres and grey
spheres represent monomers belonging to head and tail, respectively.
11


Micellar Aggregates of Gemini Surfactants: Monte Carlo Simulation of a
  Microscopic Model

Micellar Aggregates of Gemini Surfactants: Monte Carlo Simulation of a Microscopic Model

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