A molecular dynamics study of structure and dynamics of surfactant molecules in SDS spherical micelle
An analysis of structure and dynamics of surfactant molecules in SDS micelle is presented based on molecular dynamics calculations. Two-dimentional surface correlation function for the hydrophilic sulfur atoms as well as the bond analysis between the hydrophobic alkyl chains shows that the surfact...
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| Опубліковано в: : | Condensed Matter Physics |
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Інститут фізики конденсованих систем НАН України
2007
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| Цитувати: | A molecular dynamics study of structure and dynamics of surfactant molecules in SDS spherical micelle / N. Yoshii, S. Okazaki // Condensed Matter Physics. — 2007. — Т. 10, № 4(52). — С. 573-578. — Бібліогр.: 22 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859479296759824384 |
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| author | Yoshii, N. Okazaki, S. |
| author_facet | Yoshii, N. Okazaki, S. |
| citation_txt | A molecular dynamics study of structure and dynamics of surfactant molecules in SDS spherical micelle / N. Yoshii, S. Okazaki // Condensed Matter Physics. — 2007. — Т. 10, № 4(52). — С. 573-578. — Бібліогр.: 22 назв. — англ. |
| collection | DSpace DC |
| container_title | Condensed Matter Physics |
| description | An analysis of structure and dynamics of surfactant molecules in SDS micelle is presented based on molecular
dynamics calculations. Two-dimentional surface correlation function for the hydrophilic sulfur atoms as well
as the bond analysis between the hydrophobic alkyl chains shows that the surfactant molecules are packed
sparsely in the micelle such that they form a soccer ball-like structure characterized by the coordination number
of three. The hydrophobic bond between the surfactant molecules is produced and annihilated repeatedly
in a time scale of about 100 ps but disappears by their diffusion in a time scale of about 1 ns.
На основi молекулярно-динамiчних розрахункiв представлено аналiз структури i динамiки сурфактних молекул в мiцелi додецилсульфату натрiю. Двомiрна поверхня кореляцiйної функцiї гiдрофiльних атомiв сiрки та аналiз зв’язкiв гiдрофобними вуглецевими ланцюжками показує, що сурфактнi молекули є впакованi хаотично в мiцелi так, що вони утворюють структуру, подiбну до футбольного м’яча, що характеризується координацiйним числом рiвним трьом. Гiдрофобний зв’язок мiж молекулами сурфактанту виникає та анiгелює неодноразово в числовiй школi порядку 100 ps, але зникає завдяки дифузiї у часовiй шкалi порядку 1 ns.
|
| first_indexed | 2025-11-24T11:44:24Z |
| format | Article |
| fulltext |
Condensed Matter Physics 2007, Vol. 10, No 4(52), pp. 573–578
A molecular dynamics study of structure and dynamics
of surfactant molecules in SDS spherical micelle
N.Yoshii1, S.Okazaki2∗
1 Department of Pharmaceutical Sciences, Himeji Dokkyo University, Himeji 670–8524, Japan
2 Institute for Molecular Science, Myodaiji, Okazaki 444–8585, Japan
Received November 5, 2007
An analysis of structure and dynamics of surfactant molecules in SDS micelle is presented based on molecu-
lar dynamics calculations. Two-dimentional surface correlation function for the hydrophilic sulfur atoms as well
as the bond analysis between the hydrophobic alkyl chains shows that the surfactant molecules are packed
sparsely in the micelle such that they form a soccer ball-like structure characterized by the coordination num-
ber of three. The hydrophobic bond between the surfactant molecules is produced and annihilated repeatedly
in a time scale of about 100 ps but disappears by their diffusion in a time scale of about 1 ns.
Key words: molecular dynamics, micelle, surfactant
PACS: 71.15.Pd, 82.70.Uv
1. Introduction
Physical chemistry of micelles has been attracting constant interest of researchers in its long
history because of an abundance of polymorphism in water, i.e. a variety of structure formations
of the surfactant molecules in water [1–4]. Recently, several molecular dynamics (MD) calculations
have been done for spherical micelles formed in water, which leads the researcher’s interest to the
structure and dynamics at a molecular level [5–12].
In a number of our previous studies [13–16], structural stability of the spherical sodium dodecyl
sulfate (SDS) micelle has been analyzed based on the free energy using MD calculations. Firstly,
size distribution of the micelle in water was quantitatively investigated by calculating the free
energy of micelle formation as a function of the micelle size N using thermodynamic integration
method [13]. The distribution showed a sharp peak at N = 57 with the full width at half height of
about 4. Then, the molecular origin of this stability, in other words, the instability of the micelles
that are smaller or larger than the stable one was investigated in detail in terms of hydrophobic
interaction, cavity formation in the micelle core, repulsion between sulfate ions on the surface, and
bridging of the sulfate ions by sodium ions [14–16].
Here, in the present study, we focus our attention on the structure and dynamics of the sur-
factant molecules in the micelle. In particular, coordination of a surfactant molecule by the sur-
rounding surfactant molecules as well as the dissociation dynamics of the bond between them were
investigated from the trajectories of our molecular dynamics calculations.
2. Calculation
Molecular dynamics calculations have been performed for SDS spherical micelles in water. Three
micelle sizes, N = 41, 61, and 81, were tested, among which the second one is the most stable and
mostly found in water. One spherical micelle and 8,488 water molecules are contained in a cubic
cell in the periodic boundary condition. The standard Nosè-Hoover chain as well as the Andersen
isotropic cell fluctuation method was adopted in order to control the system at T = 300 K and
∗E-mail: okazaki@ims.ac.jp
c© N.Yoshii, S.Okazaki 573
N.Yoshii, S.Okazaki
Figure 1. Snapshots of the simulated SDS spherical micelles formed in water. In the figure, water
molecules are not drawn just for clarification.
P = 1 atm. The equations of motion were solved using the method by Martyna et al. [17,18]. The
CHARMM [19,20] and TIP4P [21] potential parameters were used to model the surfactant and
water molecules, respectively. The particle-mesh Ewald method was applied to the evaluation of
the long-ranged coulombic interaction. The SHAKE/ROLL and RATTLE/ROLL algorithms were
also used in order to impose constraints on the bond length with respect to the hydrogen atoms
[17]. Time step ∆t was 1 fs. After the equilibration runs for 1 ns, the trajectories were sampled
from the production runs longer than 1 ns.
3. Results and discussion
A snapshot of the micelles sampled from the trajectories is presented in figure 1 for three sizes
tested in the present study. The micelles of size N = 61 and 81 are all quite spherical, though the
smaller one N = 41 is slightly distorted.
In order to investigate the structure of the spherical micelles, two-dimensional surface correla-
tion function g(Rθ) was defined by
g(Rθ) =
2
N(N − 1)
2
sin θ∆θ
d
(
θ −
∆θ
2
, θ +
∆θ
2
)
, (1)
where N is the micelle size or the number of surfactant molecules in the micelle, R is the averaged
distance from the center of mass of the micelle and the sulfur atom of the surfactant molecule, i.e.
the averaged radius of the spherical micelle, and θ is the angle between two vectors Ri and Rj
from the center of mass of the micelle to the sulfur atoms of the i-th and j-th surfactant molecules,
respectively. The angle θ is calculated by
θ = arccos
(
Ri · Rj
|Ri||Rj|
)
. (2)
d(θ − ∆θ
2
, θ + ∆θ
2
) is the number of pairs of the surfactant molecules whose θ is found between
θ − ∆θ
2
and θ + ∆θ
2
. Thus, Rθ correspond to the distance walking on the surface from one sulfur
atom to the other projected on the surface. The g(Rθ) may be regarded as two-dimensional surface
radial distribution function on the surface of the averaged sphere.
The calculated g(Rθ) is presented in figure 2 for the micelle of size N = 41, 61, and 81. The
figure clearly shows an oscillatory behavior of the function for the large micelles, N = 61 and 81,
implying that the structure is a liquid-like one. On the other hand, noticeable correlation is not
found for the small micelle, N = 41, except for the first peak. The function is not oscillatory but
monotonically approaches unity at long Rθ. The arrangement of the surfactant molecules on the
surface of the small micelle is likely to be a gas-like one, showing unsystematic fluctuation of the
surrounding surfactant molecules.
Integrating the surface correlation function to 9 Å, the first minimum of g(Rθ) for the micelle of
size N = 61, the number of the sulfur atoms nss found in the first coordination shell was calculated
and listed in table 1. Although the coordination number increases slightly with the increasing
micelle size, it turns out to be around 3 for all micelles. This is quite small compared to 6, the
574
Molecular dynamics study of spherical SDS micelle
Figure 2. Two-dimensional correlation function for the hydrophilic sulfur atoms of the SDS
surfactant molecules projected on the surface of the spherical micelle of radius R. For details,
see the text.
Table 1. Calculated coordination number nss of the hydrophilic sulfur atom on the surface of
the SDS micelle, number of the bonds ncnt between hydrophobic alkyl chains in the micelle core,
and relaxation time τ of the bond density correlation function between the hydrophobic alkyl
chains in the core.
N nss ncnt (S > 60 Å2) ncnt (10 Å2 6 S 6 60 Å2) τ /ns
41 2.8 2.8 5.5 0.8
61 3.1 3.0 5.6 1.1
81 3.7 3.1 5.9 1.2
one for the two-dimensional closest packing. Thus, the hydrophilic groups form a sparse surface
structure. The coordination number of 3.0 for the micelle of size N ≈ 60 reminds us of the soccer
ball structure found for the fullerene C60, although the bond found in this system is essentially
different from the sp2 chemical bond. In fact, nss found for the micelle of N = 81 is 3.7, showing
a distorted but still similar to that found for C80 for which the bonding number is absolutely 3.
In the present micelle system, the structure may continuously change to a denser one as the size
becomes greater.
In order to analyze the structure of the micelles more in detail, we defined a bond between the
long hydrophobic groups of the dodecyl sulfate ions inside the micelle core. Here, we define the
bond between two hydrophobic chains by their contact area S of Voronoi polyhedrons relevant to
the hydrophobic groups.
Firstly, Voronoi analysis was performed for the carbon atoms of CH2 and CH3 groups of a SDS
molecule. Then, the area of the polyhedrons relevant to the hydrophobic groups which is in contact
with the hydrophobic groups of the other SDS molecules was obtained. The calculated distribution
of the contact area f(S) is presented in figure 3. From the figure, it is clear that the distribution
may be classified into three. The first one is a major distribution found for S less than 10 Å2. The
second is a peak found around S = 30 Å2 and the last one is a shoulder around S = 100 Å2. These
are commonly found for three micelles. Clearly, the first one may be considered to come from the
non-bonded molecule, the third one represents the entirely bonded pair, and the second is the
partially bonded one. Now, we are able to separately count the number of surrounding surfactant
575
N.Yoshii, S.Okazaki
Figure 3. Distribution of the contact area of the Voronoi polyhedrons between the hydrophobic
alkyl chains of the SDS surfactant molecules in the micelle. For details, see the text.
molecules with S 6 10 Å2, 10 Å2 < S 6 60 Å2, and S > 60 Å2. The averaged bond number ncnt of
the molecules which have large contact S > 60 Å2 with a central molecule is 2.8, 3.0, and 3.1 for
the micelle of N = 41, 61, and 81, respectively, as shown in table 1. These are in good agreement
with the findings for the number of the hydrophilic sulfate groups in the first coordination shell
on the surface. The number of molecules with medium contact, 10 Å2 < S 6 60 Å2, is 5.5, 5.6,
and 5.9 for N = 41, 61, and 81, respectively. The remaining number of molecules may be related
to the ones with small contact area, S 6 10 Å2. All these results clearly show that the skeleton
structure of the surfactant molecules in the micelle is similar to those found for the fullerene where
the number of directly bonded carbon atoms is 3 and the second ones is 6.
In the micelle, the surfactant molecules are bound to each other by hydrophobic interaction.
Since the interaction is not so strong, the molecules associate and dissociate repeatedly inside a
micelle, i.e. a migration takes place. This is a big difference from the rigid fullerenes. Now, it is
interesting to investigate this association and dissociation dynamics from a microscopic viewpoint.
In order to examine the above recombination dynamics of the surfactant molecules as well as
their diffusion in the micelle, we applied an analysis used previously for the clusters formed in
supercritical fluid, where the decrease of the bond density was monitored [22]. A bond matrix
between the surfactant molecules may be described following the definition by the contact area
above
nij =
{
1, if S > 10 Å2 between molecules i and j,
0, otherwise.
(3)
Calculating this matrix element, we may define the bond density correlation function B(t) as
B(t) =
∑
i>j〈{nij(t) − 〈nij〉}{nij(0) − 〈nij〉}〉
∑
i>j〈{nij(0) − 〈nij〉}2〉
, (4)
which describes how the density of the bond found at t = 0 decreases as a function of time. The
function is normalized such that it is unity at t = 0 and zero at t = ∞.
The calculated function is shown in figure 4 for three micelles. In the figure, a two-step relaxation
is found commonly among the three. The fast one at small t is caused by the translational libration
of the surfactant molecules and the slow one after it comes from the diffusion of the molecules.
The relaxation time for the former is roughly of the order of 100 ps. The total relaxation time
τ was evaluated by integrating the function from t = 0 to ∞ after the exponential extrapolation
576
Molecular dynamics study of spherical SDS micelle
Figure 4. Bond density correlation function between the hydrophobic alkyl chains of the SDS
surfactant molecules in the micelle defined by the contact area of the Voronoi polyhedrons. For
details, see the text.
at large t. The calculated relaxation time is listed in table 1. The value ranging from 0.8 ns to
1.2 ns is quite long compared to the fast relaxation of about 100 ps found at small t. This means
that the bond with a neighboring molecule is broken by its diffusion during which production and
annihilation of the bond between them is repeated about 10 times.
4. Conclusion
We presented a molecular dynamics analysis for the structure and dynamics of the SDS micelles
formed by the surfactant molecules in water. The calculated two-dimensional surface distribution
function for the hydrophilic sulfur atoms shows a liquid-like structure for the large micelles while
a gas-like one is found for the small micelle. In particular, the micelle of size N = 61 shows the
coordination number of nss = 3.1 of the sulfur atoms around a central sulfur atom. This implies
that a soccer ball-like structure is formed.
Bond analysis between the hydrophobic alkyl chains in the micelle core also shows the number
of bonds ncnt = 3.0 with the neighboring molecules and ncnt = 5.6 with the second neighboring
molecule. This is in good agreement with the findings in the analysis of the above surface correlation
function.
The bond is produced and annihilated quite frequently compared with the slow diffusion of the
molecule. It disappears by the diffusion, repeating the production and annihilation of the bond by
the translational libration about ten times.
Acknowledgements
This work was supported by the Next Generation Supercomputing Project, Nanoscience Pro-
gram, MEXT, Japan. The work was also supported by Grant-in-Aid for Scientific Research
(Nos. 17105001 and 18066020) from Japan Society for the promotion of Science. The authors thank
Okazaki Research Center for Computational Science, National Institutes of Natural Sciences for
the use of supercomputers.
577
N.Yoshii, S.Okazaki
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Молекулярно-динамiчне вивчення структури i динамiки
сурфактних молекул в сферичнiй мiцелi додецилсульфату
натрiю
Н.Йошi1, С.Оказакi2
1 Факультет фармацевтичних наук, Гiмеї Докiо унiверситет, м. Гiмеї, Японiя
2 Iнститут молекулярних наук, м. Оказакi
Отримано 5 листопада 2007 р.
На основi молекулярно-динамiчних розрахункiв представлено аналiз структури i динамiки сурфа-
ктних молекул в мiцелi додецилсульфату натрiю. Двомiрна поверхня кореляцiйної функцiї гiдрофiль-
них атомiв сiрки та аналiз зв’язкiв гiдрофобними вуглецевими ланцюжками показує, що сурфактнi
молекули є впакованi хаотично в мiцелi так, що вони утворюють структуру, подiбну до футбольного
м’яча, що характеризується координацiйним числом рiвним трьом. Гiдрофобний зв’язок мiж моле-
кулами сурфактанту виникає та анiгелює неодноразово в числовiй школi порядку 100 ps, але зникає
завдяки дифузiї у часовiй шкалi порядку 1 ns.
Ключовi слова: молекулярна динамiка, мiцела, сурфактант
PACS: 71.15.Pd, 82.70.Uv
578
|
| id | nasplib_isofts_kiev_ua-123456789-118949 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-11-24T11:44:24Z |
| publishDate | 2007 |
| publisher | Інститут фізики конденсованих систем НАН України |
| record_format | dspace |
| spelling | Yoshii, N. Okazaki, S. 2017-06-01T15:28:00Z 2017-06-01T15:28:00Z 2007 A molecular dynamics study of structure and dynamics of surfactant molecules in SDS spherical micelle / N. Yoshii, S. Okazaki // Condensed Matter Physics. — 2007. — Т. 10, № 4(52). — С. 573-578. — Бібліогр.: 22 назв. — англ. 1607-324X PACS: 71.15.Pd, 82.70.Uv DOI:10.5488/CMP.10.4.573 https://nasplib.isofts.kiev.ua/handle/123456789/118949 An analysis of structure and dynamics of surfactant molecules in SDS micelle is presented based on molecular dynamics calculations. Two-dimentional surface correlation function for the hydrophilic sulfur atoms as well as the bond analysis between the hydrophobic alkyl chains shows that the surfactant molecules are packed sparsely in the micelle such that they form a soccer ball-like structure characterized by the coordination number of three. The hydrophobic bond between the surfactant molecules is produced and annihilated repeatedly in a time scale of about 100 ps but disappears by their diffusion in a time scale of about 1 ns. На основi молекулярно-динамiчних розрахункiв представлено аналiз структури i динамiки сурфактних молекул в мiцелi додецилсульфату натрiю. Двомiрна поверхня кореляцiйної функцiї гiдрофiльних атомiв сiрки та аналiз зв’язкiв гiдрофобними вуглецевими ланцюжками показує, що сурфактнi молекули є впакованi хаотично в мiцелi так, що вони утворюють структуру, подiбну до футбольного м’яча, що характеризується координацiйним числом рiвним трьом. Гiдрофобний зв’язок мiж молекулами сурфактанту виникає та анiгелює неодноразово в числовiй школi порядку 100 ps, але зникає завдяки дифузiї у часовiй шкалi порядку 1 ns. This work was supported by the Next Generation Supercomputing Project, Nanoscience Pro- gram, MEXT, Japan. The work was also supported by Grant-in-Aid for Scientific Research (Nos. 17105001 and 18066020) from Japan Society for the promotion of Science. The authors thank Okazaki Research Center for Computational Science, National Institutes of Natural Sciences for the use of supercomputers. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics A molecular dynamics study of structure and dynamics of surfactant molecules in SDS spherical micelle Молекулярно-динамiчне вивчення структури i динамiки сурфактних молекул в сферичнiй мiцелi додецилсульфату натрiю Article published earlier |
| spellingShingle | A molecular dynamics study of structure and dynamics of surfactant molecules in SDS spherical micelle Yoshii, N. Okazaki, S. |
| title | A molecular dynamics study of structure and dynamics of surfactant molecules in SDS spherical micelle |
| title_alt | Молекулярно-динамiчне вивчення структури i динамiки сурфактних молекул в сферичнiй мiцелi додецилсульфату натрiю |
| title_full | A molecular dynamics study of structure and dynamics of surfactant molecules in SDS spherical micelle |
| title_fullStr | A molecular dynamics study of structure and dynamics of surfactant molecules in SDS spherical micelle |
| title_full_unstemmed | A molecular dynamics study of structure and dynamics of surfactant molecules in SDS spherical micelle |
| title_short | A molecular dynamics study of structure and dynamics of surfactant molecules in SDS spherical micelle |
| title_sort | molecular dynamics study of structure and dynamics of surfactant molecules in sds spherical micelle |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/118949 |
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