Interaction of the model alkyltrimethylammonium ions with alkali halide salts: an explicit water molecular dynamics study
We present an explicit water molecular dynamics simulation of dilute solutions of model alkyltrimethylammonium surfactant ions (number of methylene groups in the tail is 3, 5, 8, 10, and 12) in mixture with NaF, NaCl, NaBr, and NaI salts, respectively. The SPC/E model is used to describe water molec...
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Інститут фізики конденсованих систем НАН України
2013
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| Цитувати: | Interaction of the model alkyltrimethylammonium ions with alkali halide salts: an explicit water molecular dynamics study / M. Druchok, Č. Podlipnik, V. Vlachy// Condensed Matter Physics. — 2013. — Т. 16, № 4. — С. 43603:1-10. — Бібліогр.: 32 назв. — англ. |
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irk-123456789-1208542017-06-14T03:04:26Z Interaction of the model alkyltrimethylammonium ions with alkali halide salts: an explicit water molecular dynamics study Druchok, M. Podlipnik, Č. Vlachy, V. We present an explicit water molecular dynamics simulation of dilute solutions of model alkyltrimethylammonium surfactant ions (number of methylene groups in the tail is 3, 5, 8, 10, and 12) in mixture with NaF, NaCl, NaBr, and NaI salts, respectively. The SPC/E model is used to describe water molecules. Results of the simulation at 298 K are presented in form of the radial distribution functions between nitrogen and carbon atoms of CH₂ groups on the alkyltrimethylammonium ion, and the counterion species in the solution. The running coordination numbers between carbon atoms of surfactants and counterions are also calculated. We show that I- counterion exhibits the highest, and F- the lowest affinity to "bind" to the model surfactants. The results are discussed in view of the available experimental and simulation data for this and similar solutions. У роботi з допомогою методу молекулярної динамiки проведено моделювання низькоконцентрованого розчину iонiв алкiлтриметиламонiю (з кiлькiстю метиленових груп у ланцюгу 3, 5, 8, 10, 12) у сумiшi iз солями NaF, NaCl, NaBr або NaI при температурi 298 K. Для опису води використано модель SPC/E. Ре-зультати представлено у формi низки радiальних функцiй розподiлу мiж атомами азоту чи вуглецю (iз груп CH₂) алкiлтриметиламонiю та контрiонами розчину. Для детальнiшого висвiтлення результатiв також наведено бiжучi координацiйнi числа мiж атомами вуглецю та контрiонами. Виявлено, що контрiони I¡ демонструють найвищу, а F¡ найнижчу здатнiсть асоцiювати iз iонами алкiлтриметиламонiю. Огляд результатiв проведено у свiтлi наявних експериментальних та теоретичних даних для цих чи подiбних систем. 2013 Article Interaction of the model alkyltrimethylammonium ions with alkali halide salts: an explicit water molecular dynamics study / M. Druchok, Č. Podlipnik, V. Vlachy// Condensed Matter Physics. — 2013. — Т. 16, № 4. — С. 43603:1-10. — Бібліогр.: 32 назв. — англ. 1607-324X PACS: 61.20.Ja, 61.20.Qg, 82.20.Wt, 82.30.Rs, 82.35.Rs DOI:10.5488/CMP.16.43603 arXiv:1312.4495 http://dspace.nbuv.gov.ua/handle/123456789/120854 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| language |
English |
| description |
We present an explicit water molecular dynamics simulation of dilute solutions of model alkyltrimethylammonium surfactant ions (number of methylene groups in the tail is 3, 5, 8, 10, and 12) in mixture with NaF, NaCl, NaBr, and NaI salts, respectively. The SPC/E model is used to describe water molecules. Results of the simulation at 298 K are presented in form of the radial distribution functions between nitrogen and carbon atoms of CH₂ groups on the alkyltrimethylammonium ion, and the counterion species in the solution. The running coordination numbers between carbon atoms of surfactants and counterions are also calculated. We show that I- counterion exhibits the highest, and F- the lowest affinity to "bind" to the model surfactants. The results are discussed in view of the available experimental and simulation data for this and similar solutions. |
| format |
Article |
| author |
Druchok, M. Podlipnik, Č. Vlachy, V. |
| spellingShingle |
Druchok, M. Podlipnik, Č. Vlachy, V. Interaction of the model alkyltrimethylammonium ions with alkali halide salts: an explicit water molecular dynamics study Condensed Matter Physics |
| author_facet |
Druchok, M. Podlipnik, Č. Vlachy, V. |
| author_sort |
Druchok, M. |
| title |
Interaction of the model alkyltrimethylammonium ions with alkali halide salts: an explicit water molecular dynamics study |
| title_short |
Interaction of the model alkyltrimethylammonium ions with alkali halide salts: an explicit water molecular dynamics study |
| title_full |
Interaction of the model alkyltrimethylammonium ions with alkali halide salts: an explicit water molecular dynamics study |
| title_fullStr |
Interaction of the model alkyltrimethylammonium ions with alkali halide salts: an explicit water molecular dynamics study |
| title_full_unstemmed |
Interaction of the model alkyltrimethylammonium ions with alkali halide salts: an explicit water molecular dynamics study |
| title_sort |
interaction of the model alkyltrimethylammonium ions with alkali halide salts: an explicit water molecular dynamics study |
| publisher |
Інститут фізики конденсованих систем НАН України |
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2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120854 |
| citation_txt |
Interaction of the model alkyltrimethylammonium ions with alkali halide salts: an explicit water molecular dynamics study / M. Druchok, Č. Podlipnik, V. Vlachy// Condensed Matter Physics. — 2013. — Т. 16, № 4. — С. 43603:1-10. — Бібліогр.: 32 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT druchokm interactionofthemodelalkyltrimethylammoniumionswithalkalihalidesaltsanexplicitwatermoleculardynamicsstudy AT podlipnikc interactionofthemodelalkyltrimethylammoniumionswithalkalihalidesaltsanexplicitwatermoleculardynamicsstudy AT vlachyv interactionofthemodelalkyltrimethylammoniumionswithalkalihalidesaltsanexplicitwatermoleculardynamicsstudy |
| first_indexed |
2025-07-08T18:44:10Z |
| last_indexed |
2025-07-08T18:44:10Z |
| _version_ |
1837105419451891712 |
| fulltext |
Condensed Matter Physics, 2013, Vol. 16, No 4, 43603: 1–10
DOI: 10.5488/CMP.16.43603
http://www.icmp.lviv.ua/journal
Interaction of the model alkyltrimethylammonium
ions with alkali halide salts: an explicit water
molecular dynamics study¤
M. Druchok1, Č. Podlipnik2 , V. Vlachy2
1 Institute for Condensed Matter Physics, 1 Svientsitskii St., 79011 Lviv, Ukraine
2 Faculty of Chemistry and Chemical Technology, University of Ljubljana, 5 Aškerčeva St., 1000 Ljubljana, Slovenia
Received July 24, 2013, in final form August 29, 2013
We present an explicit water molecular dynamics simulation of dilute solutions of model alkyltrimethylammo-
nium surfactant ions (number of methylene groups in the tail is 3, 5, 8, 10, and 12) in mixture with NaF, NaCl,
NaBr, and NaI salts, respectively. The SPC/E model is used to describe water molecules. Results of the simu-
lation at 298 K are presented in the form of radial distribution functions between nitrogen and carbon atoms
of CH
2
groups on the alkyltrimethylammonium ion, and the counterion species in the solution. The running
coordination numbers between carbon atoms of surfactants and counterions are also calculated. We show that
I¡ counterion exhibits the highest, and F¡ the lowest affinity to “bind” to the model surfactants. The results are
discussed in view of the available experimental and simulation data for this and similar solutions.
Key words: surfactants, alkyltrimethylammonium salts, alkali halides, ion binding, molecular dynamics
PACS: 61.20.Ja, 61.20.Qg, 82.20.Wt, 82.30.Rs, 82.35.Rs
1. Introduction
It has long been known that properties of surfactant solutions, for example critical micelle concentra-
tion, depend on the nature of the counterion present in solution [1–7]. The latter effect being of particular
interest to us, it is further examined herein using the explicit water molecular dynamics method. In view
of our present study, important experimental results were presented by Rožycka-Roszak et al. [3]. This
group performed calorimetric measurements (see figure 1 of their paper) showing that upon dissociation
of the dodecyltrimethylammonium bromide micelle, the heat is consumed. In contrast to this, the disso-
ciation of dodecyltrimethylammonium chloride micelles is exothermic, i.e., heat is released. The experi-
ments also indicated that the two halide ions influence the process of micelle formation in a completely
different way.
The situation closely resembles the one observed in recent experimental studies of aliphatic x, y -
ionenes [8–10]. Ionenes are cationic polyelectrolytes with a different (x, y may vary from 3,3 to 12,12)
number of methylene groups between the quaternary ammonium groups. Notice that aliphatic ionenes
are similar in chemical structure to the alkyltrimethylammonium ions studied here. For example, the
monomer unit of the 12,12-ionene is actually the dodecyltrimethylammonium ion. The heats of dilution
of the x, y -ionenes indicate a strong difference between the salts with different counterions. The results
for x, y -ionene fluorides are exothermic and rather well follow the theoretical results based on the con-
tinuum solvent models. The salts with bromide, chloride, and iodide anions as counterions show different
behavior [8, 11]: heat of dilutionmay be either endothermic or exothermic depending on the length of the
hydrophobic portion of the charge. Moreover, the most recent experimental data indicated [12] that addi-
tions of extra methylene groups (transition from 6,12- to 12,12-ionene) affect the solutions with different
counterions differently.
¤It is a pleasure to dedicate this paper to our good friend and coworker Professor M.F. Holovko.
© M. Druchok, Č. Podlipnik, V. Vlachy, 2013 43603-1
http://dx.doi.org/10.5488/CMP.16.43603
http://www.icmp.lviv.ua/journal
M. Druchok, Č. Podlipnik, V. Vlachy
Among the theoretical methods of probing the hydration in the explicit water models, the molecular
dynamics simulations seem to be the most useful (see, for example, references [13–16]). In the present
explicit water molecular dynamics study we are interested in the effects of an increasing number of
methylene groups (i.e., the length of the surfactant tail) on the interaction between the various counterion
species in a solution and quaternary ammonium group of the surfactant. For this purpose, we performed
the study of mixtures of alkyltrymethylammonium surfactant ions with fluoride, chloride, bromide, and
iodide counterions in mixture with NaF, NaCl, NaBr, and NaI salts, respectively. The simulation is focused
on very dilute solutions with respect to surfactant. In this way, the counterion-charged group interaction
can be studied without possible complications of the polyion chain association. The study accordingly
applies to the conditions well below the critical micelle concentration. The surfactant molecules with the
tail, containing from three to twelve CH
2
groups, are probed.
2. Model and simulation details
A set of surfactant solutions containing alkylammonium ions, sodium co-ions, neutralizing halide
counterions, and water molecules are investigated. To obtain insights into the specific ion effects, we
examined a series of halide salts: fluorides, chlorides, bromides, and iodides. The respective counterions
are characterized by the same charge but different crystal size, so one can expect a somewhat different
interaction of the counterion with the surfactant (quaternary ammonium) ion. The latter ion consists of
the quaternary nitrogen, neighbored by three CH
3
-groups, a carbon chainwith CH
2
groups and a terminal
CH
3
group. As an example, in figure 1 we show the surfactant ion with five carbons in the tail. In the
present study we considered surfactants with five different tail lengths; i.e., with 3-, 5-, 8-, 10-, and 12
carbons denoted as C
3
, C
5
, C
8
, C
10
, and C
12
. The wide spectrum of chain lengths allows us to study the
effect of hydrophobicity on the counterion-quaternary ammonium interaction.
All the particles in the system were treated on equal footing. Water was described within the SPC/E
model [17]. The Lennard-Jones parameters for NaÅ ions were taken from reference [18], the ones for
the halide ions — from the work by Palinkas [19]. The Lennard-Jones parameters for the sites of a
surfactant were taken from the OPLS force field [20]. Charges at the atoms of surfactants were fit-
ted from the electrostatic potential calculated with DFT B3LYP/6-311G** using Jaguar 7.9 (Schrödinger
Suite) [21]. Listing these charges in the form of tables for the whole atom simulation is far from op-
timal. As an example, figure 1 shows the distribution of charges for C
5
, while all interested readers
are encouraged to request the full information from authors via e-mail. In order to preserve the in-
tramolecular geometry of the surfactants, we have utilized a set of bond and angular potentials in the
Figure 1. (Color online) Schematic representation of the alkylammonium ion with five methyl groups in
the tail. Nitrogen is indicated by blue, carbons by green, and hydrogens by white color. The numbers
show optimized atomic charges.
43603-2
Table 1. Model parameters.
species ² (kcal/mol) ¾ (Å)
water O 0.1554 3.1656
H 0.0 0.0
N 0.170 3.25
AA C 0.066 3.50
H 0.030 2.5
Na 0.0028 3.3304
F 0.0118 4.0
electrolyte Cl 0.0403 4.86
Br 0.0645 5.04
I 0.0979 5.40
form U Æ kbond(r ¡ r0)
2 and U Æ kangle(®¡®0
)
2. The carbon-carbon and nitrogen-carbon distances r
0
in the surfactant backbone are 1.5 Å with the corresponding kbond Æ 500 kcal/mol/Å2, the parameters
for the backbone angles — ®
0
Æ 111
± , kangle Æ 250 kcal/mol. The parameters for the carbon-hydrogen
bonds in CH
2
and CH
3
groups are 250 kcal/mol/Å2 and 1.1 Å. For the hydrogen-hydrogen distances in-
side CH
2
and CH
3
groups we used additional constraints with parameters 150 kcal/mol/Å2, 1.8 Å. As for
two off-backbone CH
3
groups, the corresponding carbon-nitrogen-carbon angle is controlled by the an-
gular potential 250(®¡109
±
) kcal/mol. Finally, for the surfactant rigidity we also applied a set of angular
potentials 250(®¡180
±
) kcal/mol between next but one backbone carbons (first-third-fifth atom, second-
fourth-sixth, . . . ).
The Lennard-Jones parameters (¾
i
, ²
i
) assigned to various atoms or ions are shown in table 1. For
unlike sites, the parameters were obtained using the mixing rules in the form ¾
i j
Æ
1
2
(¾
i
ž
j
) and
²
i j
Æ
p
²
i
²
j
. A standard DL_POLY [22] package was used for molecular dynamics simulations of model
solutions with the unit cell containing 2352 water molecules, one surfactant ion, one counterion X (X can
be F¡,Cl¡, Br¡, or I¡), and 6 NaÅX pairs modelling the added salt. The concentration
s
of the added low-
molecular electrolyte NaÅX¡ was ¼ 0.14 mol dm¡3. All the species were allowed to move freely across
the cubic cell with periodic boundary conditions. The long-range Coulomb interactions were taken into
account by the Ewald summation technique. The short-range interactions ware truncated at Rcut Æ 15 Å.
The pressure (1 bar) and temperature (298 K) were controlled by means of a Nose-Hoover barostat and
thermostat in an isotropic N , P , T ensemble within the Melchiona modification [23]. The number of
steps in the production runs ranged from 3.5 to 4.0£107 with the time step 5£10
¡16 s. Such a time step
is needed to satisfy the constraints imposed by the bond and angular intramolecular potentials for water
and surfactants. The radial distribution functions (RDF) between various sites on the molecule and ions
in solution are presented in the form of graphs.
3. Numerical results
3.1. Radial distribution functions
First, in figure 2 we consider the nitrogen-counterion radial distribution functions. Notice that in all
the solutions studied here an extra sodium salt (NaX, X¡ is the counterion) is present. The plots show
that fluoride counterions tend to be located in the bulk of the solution (away from the surfactant ion),
demonstrating poor correlation with the quaternary ammonium ion. This behavior is a consequence of
strong hydration of fluoride ion, preventing “association” of fluoride ions with the nitrogen group on
the surfactant, as we already know from the experimental [8–10] and theoretical [24, 25] studies of x, y -
ionene solutions. The halides of larger sizes, such as chloride, bromide, and iodide counterions, are less
strongly hydrated (their free energies of hydration are smaller in magnitude than that of fluoride ion)
and can, therefore, release some water molecules in interaction with the quaternary nitrogen group on
43603-3
M. Druchok, Č. Podlipnik, V. Vlachy
0
2
4
6
8
10
4 5 6 7 8 9 10
g(
r)
r, A
N(3)-F
N(3)-Cl
N(3)-Br
N(3)-I
0
2
4
6
8
10
4 5 6 7 8 9 10
g(
r)
r, A
N(5)-F
N(5)-Cl
N(5)-Br
N(5)-I
0
2
4
6
8
10
4 5 6 7 8 9 10
g(
r)
r, A
N(8)-F
N(8)-Cl
N(8)-Br
N(8)-I
0
2
4
6
8
10
4 5 6 7 8 9 10
g(
r)
r, A
N(10)-F
N(10)-Cl
N(10)-Br
N(10)-I
0
2
4
6
8
10
4 5 6 7 8 9 10
g(
r)
r, A
N(12)-F
N(12)-Cl
N(12)-Br
N(12)-I
Figure 2. (Color online) Nitrogen-counterion RDFs for molecule with (a) three methylene groups, C
3
, (b)
C
5
, (c) C
8
, (d) C
10
, and (e) C
12
. The results for fluorides are denoted by full red lines, for chlorides by
dashed green lines, bromides are denoted by short-dashed blue, and iodides by dotted magenta lines.
the surfactant. This causes the nitrogen-counterion peak height to follow the ordering: I¡ È Br¡ È Cl¡ È
F¡. This is valid for all the surfactants studied here, an exception being the shortest one, C
3
, where the
peak heights of the chloride and bromide ions are approximately the same.
Different halide ions follow different sequences of the first peak height with respect to the chain
length: for strongly solvated chlorides, the shortest, C
3
, surfactant has the highest peak. The peak height
then decreases in the order C
3
È C
5
È C
12
È C
8
È C
10
. In contrast with chlorides, the iodide salts, which
are known to release their hydration waters more easily, reveal a different dependence of the magnitude
of the first RDF peak. The highest value is obtained for C
8
: C
8
ÈC
5
¼C
12
ÈC
3
ÈC
10
. Here, the number of
methylene groups becomes more important; a higher number of CH
2
groups means a stronger attraction.
The balance between the Coulomb (charge density decreases with the chain length) and van der Waals
attraction, which increases with the number of methylene groups in the chain, produces the observed
sequence. Notice that, according to literature, the iodide ion is considered to have more affinity for hy-
drophobic surfaces than other halide ions [26]. The peak sequence for bromides reveals the lowest value
for C
12
, the others run close with a slight prevalence of the C
8
one, like it is found for the iodide solutions.
43603-4
0
0.5
1
1.5
2
2.5
3
3.5
4
3 4 5 6 7 8 9 10 11 12
g(
r)
r, A
C(3)-F
C(3)-Cl
C(3)-Br
C(3)-I
0
0.5
1
1.5
2
2.5
3
3.5
4
3 4 5 6 7 8 9 10 11 12
g(
r)
r, A
C(5)-F
C(5)-Cl
C(5)-Br
C(5)-I
0
0.5
1
1.5
2
2.5
3
3.5
4
3 4 5 6 7 8 9 10 11 12
g(
r)
r, A
C(8)-F
C(8)-Cl
C(8)-Br
C(8)-I
0
0.5
1
1.5
2
2.5
3
3.5
4
3 4 5 6 7 8 9 10 11 12
g(
r)
r, A
C(10)-F
C(10)-Cl
C(10)-Br
C(10)-I
0
0.5
1
1.5
2
2.5
3
3.5
4
3 4 5 6 7 8 9 10 11 12
g(
r)
r, A
C(12)-F
C(12)-Cl
C(12)-Br
C(12)-I
Figure 3. (Color online) Carbon-counterion radial distribution functions. The legend as for figure 2.
These results are complemented by the carbon-counterion radial distribution functions (figure 3).
Notice that only the carbons from the surfactant tails are included into this RDF calculation; the contribu-
tion of carbons of CH
3
groups neighboring to nitrogens is neglected. The sequence of carbon-counterion
peak heights is: I¡ È Br¡ È Cl¡ È F¡. Again an exception is the shortest molecule (C
3
), where the peak
heights of the chloride and bromide counterions are approximately the same. Peaks of these distribution
functions are generally lower than those of the counterion-nitrogen distributions, indicating a weaker
accumulation of counterions next to the surfactant tail. Similar to the nitrogen-fluoride radial distribu-
tion functions, the carbon-fluoride ones exhibit merely a weak correlation, confirming the conclusion
about marginal “association” of F¡ ions with the surfactant molecules. The carbon-chloride distribution
functions demonstrate a quite expected sequence of the RDF peak heights: the highest is C
3
peak, next
goes C
5
, then C
8
¼ C
10
¼ C
12
. This indicates that the relatively strongly solvated chloride counterions
exhibit little (or no) affinity for surfactants with longer tails. The carbon-iodide pair distribution func-
tions demonstrate a higher peak for C
3
than C
5
¼C
8
, while the lowest are the peaks for C
10
and C
12
. The
counterion-carbon interaction, as judged on the basis of these RDFs, is stronger for I¡ than for Cl¡, and
this effect is quite prominent for longer surfactants [26].
43603-5
M. Druchok, Č. Podlipnik, V. Vlachy
3.2. Running coordination numbers
Each of the surfactant species carries one charged group but a different number of methylene groups
(C
x
), which obscures the direct comparison (nitrogen-counterion vs carbon-counterion) of the RDFs dis-
cussed above. For this reason, we also present the so-called running coordination numbers as an alterna-
tive way of data analysis. This quantity, n
®¯
(r ), is defined as a number of particles ¯ in a sphere of radius
r around a certain particle ® in the center:
n
®¯
(r )Æ 4¼½
¯
r
Z
0
g
®¯
(r
0
)r
02
dr
0
, (3.1)
where ½
¯
is a number density of species ¯ in the system. We denote the counterion species with subscript
® and carbon of the methylene group with ¯, so the coordination numbers reflect the probability to find
a carbon atom in the sphere around a counterion (figure 4). This permits a more realistic presentation of
the counterion accumulation around the methylene groups, as it can be inferred from the relevant pair
distribution functions alone. The conclusion emerging from figure 4 is that fluoride ions are the least,
and iodide counterions the most strongly coordinated to carbon atoms, while the other counterions fit
in-between. Generally, the running coordination numbers for C
12
are the highest, with a decrease in the
direction toward C
3
. The present observation reflects the fact that C
12
solutions contain more carbons
than the C
3
ones. The running coordination numbers for fluorides demonstrate a monotonous depen-
dence on the length of the hydrophobic chain.
For less hydrated chlorides, the picture complicates: the C
8
running coordination number (for a region
of distances up to 8 Å) runs bellow the other corresponding functions. One should also note a relatively
small difference between C
12
and C
3
running coordination numbers for the fluoride and chloride solu-
tions. This finding is consistent with the suggestion drawn on the basis of the nitrogen-fluoride/chloride
0
0.2
0.4
0.6
0.8
1
4 5 6 7 8 9 10
n
(r
)
r, A
C(12)-F
C(10)-F
C(8)-F
C(5)-F
C(3)-F
0
0.2
0.4
0.6
0.8
1
4 5 6 7 8 9 10
n
(r
)
r, A
C(12)-Cl
C(10)-Cl
C(8)-Cl
C(5)-Cl
C(3)-Cl
0
0.2
0.4
0.6
0.8
1
4 5 6 7 8 9 10
n
(r
)
r, A
C(12)-Br
C(10)-Br
C(8)-Br
C(5)-Br
C(3)-Br
0
0.2
0.4
0.6
0.8
1
4 5 6 7 8 9 10
n
(r
)
r, A
C(12)-I
C(10)-I
C(8)-I
C(5)-I
C(3)-I
Figure 4. (Color online) Counterion-carbon running coordination numbers for the fluorides (top left),
chlorides (right), bromides (bottom left), and iodides (right hand panel). C
12
results are denoted by full
red lines, C
10
— dashed green, C
8
— short-dashed blue, C
5
— dotted magenta, and C
3
results are denoted
by dash-dotted cyan lines.
43603-6
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
4 5 6 7 8 9
g(
r)
r, A
O-N(12,F)
O-N(12,Cl)
O-N(12,Br)
O-N(12,I)
0
0.2
0.4
0.6
0.8
1
3 4 5 6 7 8
g(
r)
r, A
O-C(12,F)
O-C(12,Cl)
O-C(12,Br)
O-C(12,I)
Figure 5. (Color online) Oxygen-nitrogen (left-hand) and oxygen-carbon (right-hand) RDFs for molecule
with twelve methylene groups, C
12
. The results for fluorides are denoted by full red lines, for chlorides
by dashed green lines, bromides are denoted by short-dashed blue, and iodides by dotted magenta lines.
RDFs: the origin of the attraction between surfactants and counterions is mainly of electrostatic nature.
The picture changes if one considers bromide and iodide solutions. The gap between C
12
and C
3
values
becomes more significant, moreover, for the iodide case, the C
8
running coordination numbers exceed
C
10
values. This agrees with the jump seen above in the C
8
-iodide RDFs (figure 2).We ascribe this behavior
to the competition between Coulomb and van der Waals interactions; while the importance of the former
decreases with an increasing chain length, just an opposite is true for the van der Waals forces. We have
also calculated the counterion-nitrogen running coordination numbers. These data seem to merely con-
firm the insights obtained from the radial distribution functions presented in figure 2 and are, therefore,
not shown here.
3.3. Hydration of the quaternary ammonium and methylene groups
To document the effect of the counterion species on the hydration of the surfactant we collected the
oxygen-nitrogen and oxygen-carbon (methylene group) radial distribution functions. All the surfactans
studied here exhibit the same trends as far as the counterion species is concerned, so only the data for
the longest one, C
12
, are presented in more detail (see figure 5). Oxygen-nitrogen radial distribution func-
tions: the position of the first peak remains unchanged, but its height slightly decreases along the se-
quence F/Cl/Br/I. This result indicates that large and loosely hydrated counterions win against waters
in competition for the vacancies near surfactant ions. A similar effect has been earlier observed in the
studies of 3,3- and 6,6-ionene oligomers in water [24, 25].
The right hand panel of figure 5 presents the oxygen-carbon radial distribution functions. The dif-
ferences between the radial distribution functions belonging to different counterions are even smaller
here. It is the iodide radial distribution function which has the smallest peak, confirming the observation
mentioned above. Finally, the shapes of the oxygen-nitrogen and oxygen-carbon (methylene group) radial
distribution functions are the same as observed before for x, y -ionene oligomers in water [24, 25]. Much
weaker hydration (drying) of the methylene groups in comparison with the positively charged nitrogen
group is clearly visible.
We expect for the positively charged surfactant head to orient neighboring water molecules in such a
way that an oxygen points toward, and hydrogens away from the head. In addition, we are interested in
the orientation of water molecules near the hydrophobic tail. A water molecule is considered to be a part
of the surfactant hydration shell if the distance between oxygen and nitrogen is less than 6.3 Å, or the
distance between the oxygen and tail carbon is less than 4.3 Å. Notice that the carbons attached directly
to nitrogen are not included in the statistics. These distances are the positions of the corresponding first
minima of the nitrogen-oxygen and carbon-oxygen RDFs (figure 5). We monitored the angle between the
dipole moment of a (hydrating) water molecule and a vector pointing from oxygen to the nearest carbon
or nitrogen. Following this definition, we accumulated two types of angular distribution functions. The
first one describes orientations of hydrating waters in the vicinity of nitrogen (charged head), and the
43603-7
M. Druchok, Č. Podlipnik, V. Vlachy
second one near the carbons of hydrophobic tail. To illustrate the difference, we discuss these data in
terms of average angles. It is interesting that the angles averaged over the waters near the “nitrogen”
group show little dependence on the counterion type, or on the length of the hydrophobic tail. The vari-
ation of this angle is in the range between 97 to 100±. Contrary to this, the orientation distribution of the
waters near “carbons” demonstrates a spread from 91± for C
12
to 97± for C
3
. The result reflects the fact
that for shorter surfactants with higher charge density, hydrating waters are more affected than for the
longer (C
12
) ones.
4. Discussion
The quaternary ammonium group is a part of many important molecules. One such example are
aliphatic x, y -ionenes, where x and y denote the numbers of methylene groups between the two adjacent
quaternary nitrogens. These cationic polyelectrolytes can be synthesized with different charge density,
varying x, y numbers from 3 to 12 (see, for example [27–30]). Recently in a series of papers we had studied
aqueous solutions of x, y -ionenes using different experimental methods [8–10]. In addition, the molecular
dynamics simulations of the 3,3- and 6,6-ionenes were performed [24, 25].
The repeating monomer unit of the 3,3-ionene polyelectrolyte is composed of the quaternary am-
monium group followed by three methylene groups. Similarly, the repeating unit of 12,12-ionene is the
quaternary ammonium group followed by twelve CH
2
groups. It is quite clear from this that our model
C
12
surfactant can be “identified” as a monomer unit (with an exception of the terminal hydrogen) of
the 12,12-ionene polycation. With the same logic, the model C
3
surfactant is a building block of the 3,3-
ionene, while the C
5
and C
8
roughly correspond to the 6,6-ionene. This makes it worthwhile to compare
the present simulations with those for 3,3- and 6,6-ionene oligoions in explicit water. Unfortunately, no
molecular dynamic simulations for the 12,12-ionene solutions exist so far.
Here, we compare the pair distribution functions shown in figures 2 and 3 with those published in
references [24] (see figures 4 and 5 of that paper), and [25] (figure 3). Considering that the force field used
in both calculations is very similar, more or less similar results are expected. The eventually observed
differences between the two results could only be attributed to an accumulation of the charge on the
oligoion with six monomer units. The heights of the peaks in figure 4 (see reference [24]) follow the trend
NaF Ç NaCl Ç NaBr ÇNaI. The same holds true for the carbon-counterion RDFs shown in figure 5 of the
same paper, except that now the iodide and bromide peaks are very close to each other. In other words,
the trends exhibited by “monomers” are also reproduced by short oligoions in water. Useful information
on the specific ion effects in polyelectrolyte solutions may often be obtained by studying monomer sys-
tems, as it was demonstrated for salts of para-toluene(sulphonic) acid [31], and for tetraalkylammonium
halides in water (see reference [32], and the references therein). A word of caution is needed with re-
spect to this statement. Recent measurements by Čebašek and coworkers [12] show that for sufficiently
hydrophobic 12,12-ionenes, the trends with respect to the nature of counterion (Hofmeister series) may
be reversed in comparison with the more charged (less hydrophobic) 3,3-ionenes.
The experimental results for the alkyltrimethylammonium surfactant solutions, which partially in-
clude the pre-micellar region, have been presented by several authors [1, 2, 5, 7]. Since the critical micelle
concentrations for surfactants with long chains (C
12
and more) are very low, the data are not collected
systematically. Among these studies it is worth mentioning the work by Jakubowska [7] who used mass
spectrometry to investigate the affinity of counterions to surfactant monomers in the gas phase. She ex-
amined the sodium hexadecyl-N,N,N-trimethyl ammonium bromide in the presence of various salts. The
results suggested the following ordering in the affinity of counterions for this surfactant: F¡ ÇCl
¡
ÇNO
¡
3
.
Enthalpies of dilution of various surfactants have been measured in pre-micellar region by Birch and
Hall [1]; see figure 1 of their paper. The authors compare their results with the results by the Debye-
Hückel limiting law. Surfactant ions (alkyltrimethyl ammonium bromides, C
n
TAB) with a number of
carbon atoms n from 6 to 12 were examined. The surfactants exhibit both positive and negative devi-
ations from the limiting law. The ordering of the surfactants, from negative to positive deviations is:
C
6
TABÇC
8
TABÇC
10
TABÇC
12
TAB. This finding appears to be in qualitative agreement with the results
for counterion-carbon coordination number presented in figure 4.
43603-8
5. Conclusions
The explicit water molecular dynamics simulations of dilute solutions of model alkyltrimethylammo-
nium surfactant ions (the number of carbon atoms in the tail is 3, 5, 8, 10, and 12) in mixture with NaF,
NaCl, NaBr, and NaI, are performed. The results are presented in the form of relevant radial distribution
functions; in addition, the running coordination numbers for the counterion-carbon distributions are
evaluated. The nitrogen-counterion correlations seem to primarily depend on the Coulomb interaction.
On the other hand, the carbon-counterion distribution coordination numbers seem to be also affected
by the van der Waals forces. The molecular dynamics results presented here are consistent with the ex-
perimental data for alkyltrimethyl ammonium salts taken in the pre-micellar region. Furthermore, the
results agree with similar simulations performed for aliphatic x, y -ionene solutions, and with experimen-
tal findings for the surfactant and polyelectrolyte systems containing a quaternary ammonium group.
Acknowledgements
This study was supported by the Slovenian Research Agency fund (ARRS) through the Program 0103–
0201, and Project J1–4148.
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http://dx.doi.org/10.1007/BF00647799
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http://dx.doi.org/10.1002/cphc.200700763
http://dx.doi.org/10.1016/j.jcis.2009.06.027
http://dx.doi.org/10.1016/j.jcis.2010.03.043
http://dx.doi.org/10.1021/je101136a
http://dx.doi.org/10.1039/c2cp23137a
http://dx.doi.org/10.1039/C2CP40571G
http://dx.doi.org/10.1021/jp401313f
http://dx.doi.org/10.1016/S0301-4622(98)00237-3
http://dx.doi.org/10.5488/CMP.10.2.143
http://dx.doi.org/10.1016/j.molliq.2008.10.014
http://dx.doi.org/10.1016/j.bpj.2010.06.027
http://dx.doi.org/10.1021/j100308a038
http://dx.doi.org/10.1021/j100384a009
http://dx.doi.org/10.1021/ja9621760
http://dx.doi.org/10.1063/1.464304
http://www.ccp5.ac.uk/DL_POLY_CLASSIC/
http://dx.doi.org/10.1080/00268979300100371
http://dx.doi.org/10.1016/j.cplett.2007.11.024
http://dx.doi.org/10.1021/jp906727h
http://dx.doi.org/10.1103/PhysRevLett.100.258105
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M. Druchok, Č. Podlipnik, V. Vlachy
Взаємодiя модельних iонiв алкiлтриметиламонiю з iонами
лужногалоїдних солей: моделювання методом
молекулярної динамiки iз явно врахованими молекулами
води
М. Дручок1, Ч. Подлiпнiк2, В. Влахи2
1 Iнститут фiзики конденсованих систем НАН України, вул. I. Свєнцiцького 1, 79011 Львiв, Україна
2 Факультет хiмiї та хiмiчної технологiї, Унiверситет Любляни, вул. Ашкерчева 5, 1000 Любляна, Словенiя
У роботi з допомогою методу молекулярної динамiки проведено моделювання низькоконцентрованого
розчину iонiв алкiлтриметиламонiю (з кiлькiстю метиленових груп у ланцюгу 3, 5, 8, 10, 12) у сумiшi iз
солями NaF, NaCl, NaBr або NaI при температурi 298 K. Для опису води використано модель SPC/E. Ре-
зультати представлено у формi низки радiальних функцiй розподiлу мiж атомами азоту чи вуглецю (iз
груп CH
2
) алкiлтриметиламонiю та контрiонами розчину. Для детальнiшого висвiтлення результатiв та-
кож наведено бiжучi координацiйнi числа мiж атомами вуглецю та контрiонами. Виявлено, що контрiони
I¡ демонструють найвищу, а F¡ найнижчу здатнiсть асоцiювати iз iонами алкiлтриметиламонiю. Огляд
результатiв проведено у свiтлi наявних експериментальних та теоретичних даних для цих чи подiбних
систем.
Ключовi слова: сурфактанти, солi алкiлтриметиламонiю, лужногалоїднi солi, зв’язування iонiв,
молекулярна динамiка
43603-10
Introduction
Model and simulation details
Numerical results
Radial distribution functions
Running coordination numbers
Hydration of the quaternary ammonium and methylene groups
Discussion
Conclusions
|