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The Driving Force for the Association of Gemini Surfactants Kyeong-jun Jeong, and Arun Yethiraj J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b08936 • Publication Date (Web): 02 Nov 2017 Downloaded from http://pubs.acs.org on November 6, 2017

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The Journal of Physical Chemistry

The Driving Force for the Association of Gemini Surfactants Kyeong-Jun Jeong and Arun Yethiraj∗ Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706 E-mail: [email protected]

∗

To whom correspondence should be addressed

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Abstract The self-assembly of surfactants into lyotropic liquid crystalline phases is interesting from a fundamental and practical perspective. The propensity for self-assembly is particularly interesting in Gemini surfactants which have a very low critical micelle concentration. In this work we study the effect of head-group identity on the driving force for the self-assembly of Gemini surfactants, using computer simulations of the potential of mean force (PMF). We find that surfactants with sulfonate head-groups have a greater tendency to assemble than those with carboxylate head-groups. The minimum in the PMF is about a factor of two deeper and occurs at shorter distances. Interestingly, the driving force is entropic with the carobxylate and energetic with the sulfonate head-groups. Analysis of different contributions suggests that these differences arise from surfactant headgroup electrostatics and size. The results provide an explanation for why the morphology diagram of the sulfonate surfactants is insensitive to temperature.

1 Introduction Surfactants are composed of a hydrophobic tail and a polar head. In aqueous solution they aggregate in a manner to segregate the hydrophobic parts from the hydrophilic heads. The self-assembly of surfactants in aqueous media is important in a variety of practical applications 1 including solubilization, 2 micellar catalysis, 3,4 chemically selective delivery, 5,6 emulsification, 7,8 detergency, 9 and ion-exchange membranes. 10 This work is focused on twin-tailed Gemini surfactants, which make a variety of micellar and lyotropic liquid crystalline phases. Using computer simulations, we study the driving force for the association of two surfactants. The self-assembly in dilute solution can be characterized by the critical micelle concentration (CMC), which is the lowest concentration at which micelles appear. 1,11 Insight into the mechanism for self-assembly can be obtained by studying the dependence of the CMC on molecular details. 12 For example, the CMC decreases as the chain length of the hydrophobic group is increased which can be explained by noting that the hydrophobic interactions become stronger for 2 ACS Paragon Plus Environment

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longer tails. 1,13 The CMC increases when the charge on the head-group is closer to the α -carbon atom of tailgroup 14 or the size of the counterions is increased. 1,15–17 These features emphasize the importance of electrostatic correlations on the self-assembly - the weaker the binding between counterions and head-groups the lower the propensity for self-assembly. Of particular interest is the temperature dependence of the CMC because this sheds light on the driving force for self-assembly. The Gibb’s free energy of micelle formation, ∆GM , can be approximated by ∆GM ≈ RT ln CMC

(1)

where R is the gas constant and T is the temperature. If CMC decreases (increases) with decreasing temperature, it suggests the process is enthalpy (entropy) driven. Interestingly, for many surfactants, the temperature dependence of CMC is not monotonic,; 18–23 CMC decreases with temperature until some characteristic temperature, and then increases with a further increase of temperature. We are interested in twin-tailed Gemini surfactants, where two single tailed surfactants are covalently linked; this necessarily disrupts the energy/entropy balance of surfactant self-assembly. Most dramatically their CMC is two orders of magnitude lower than their analogous monomeric surfactants. 24–26 A number of experimental studies show that gemini surfactants do not follow the classical tendency of CMC with respect to molecular structure. 25–27 Zana 28 has proposed a formula to predict the CMC of gemini surfactants. By combining calorimetric measurements and temperature-dependent CMC values, this formula decomposes the enthalpy and entropy of micellization. 24 The model does not predict the the temperature dependence of the CMC or the nature of the thermodynamic driving force. Computer simulations provide a means of directly obtaining the driving force for self-assembly. Using simulations, one can determine the potential of mean force (PMF) between two surfactants in solution as a function of a reaction co-ordinate, which could be, for example, the distance between head groups. A study of the temperature dependence of the PMF allows one to decompose the PMF into energetic and entropic contributions. In their study of β -peptides 29 and diblock copolymers, 30 3 ACS Paragon Plus Environment


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Mondal et al. 29,30 showed that multi-body PMF calculations provide insight on the thermodynamic driving force for the association of molecules. One important physical insight from their work is that for amphiphilic molecules, the electrostatic interaction serves as dominant factor of driving force and assembly behavior. 30,31

Figure 1: Chemical formula of the gemini surfactant Na-74. The anionic headgroup X− stands for COO− for carboxylate, and SO− 3 for sulfonate. In this work, we examine how the identity of the headgroup of gemini surfactant affects the thermodynamic driving force of the PMF between molecular pairs. We study Na-74 with dicarboxylate and disulfonate head-groups (see figure 1) and show that the self-assembly is energetically driven in the former and entropically driven in the latter. We attribute these differences to the difference in electrostatic correlation between the head-groups and the counterions. To examine the origin of the entropic driving force we examine Na-14 with the dicarboxylate head-group, which has only one carbon atom in the tail. In this case the driving force is enthalpic suggesting that the entropic effect comes from the surfactant tails.

2 Computational Methods The GROMOS45a3 32 united atom force field is used for gemini surfactants and sodium counterion. In this model the methylene groups are treated using a united-atom (single site) approximation and all other species are treated atomistically. The only sites for which parameters are not available are the sulfonate head-groups. For these groups the partial charge on the oxygen atoms is set to be the 4 ACS Paragon Plus Environment

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same as in the carboxylate group, and the partial charge on the sulfur atom is chosen so that the sulfonate group has a net charge of -1e. The charges on the atoms are q(C)=+0.27, q(O)=-0.635 for carboxylate group, and q(S)=+0.905, q(O)=-0.635 for sulfonate group. The gemini surfactants have two chiral carbon centers at the ends of spacers. Among different stereoisomers, we consider the R-R configurations for two chiral centers. The SPC water model 33 is used with the SETTLE algorithm 34 to keep the molecules rigid. Lennard-Jones interactions are truncated at 1.4nm, and electrostatic interactions are calculated using the particle-mesh Ewald (PME) method. 35 PME parameters are: real space cutoff at 1.4 nm, sixth-order spline, maximum fast Fourier transform grid spacing of 0.12 nm. MD simulations are performed using GROMACS 4.5.5 package. 36 Initial configurations are generated with two surfactant molecules and 17075 water molecules in a cubic box of side length 8 nm. Three systems are considered: with two carboxylate surfactants, two sulfonate surfactants, and one carboxylate and one sulfonate surfactant. The energy of the system is minimized using a steepest descent algorithm and the configuration is equilibrated in the NPT ensemble (number of molecules, pressure, and temperature fixed) at a pressure of 1 bar. The final configurations from these simulations are used in the pulling simulations in the NVT (V is the volume) ensemble to create initial configurations for the umbrella sampling simulations. Parameters for pulling are 1000 kJ/mol nm2 for the harmonic force constant and pulling rate of 0.005 nm/ps. Temperature and pressure is kept constant using the Berendsen barostat and thermostat, 37 with which the GROMOS force field was parameterized. Details of the umbrella sampling simulations are as follows. There are a total of 39 windows in the umbrella sampling simulations. The reaction co-ordinate, ξ , defined as the distance between the middle points of spacer groups on the two different surfactants, varies from ξ =0.4 nm to ξ =1.1 nm with a spacing of 0.05 nm and ξ =1.1 nm to ξ =3.5 nm with a spacing of 0.1 nm. The harmonic potential in each umbrella sampling window has a force constant of 500 kJ/mol nm2 . In each umbrella sampling window, for all cases except Na-14 dicarboxylate, 45 ns of MD simulation with timestep of 4 fs are performed as a production run in the NVT ensemble at 300 K and 320 K. The



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Na-14 dicarboxylate has much shorter tail-groups than other surfactants in this study, so only 10 ns of production run for each umbrella sampling window is performed which is sufficient to sample its conformations. The potential of mean force(PMF) is obtained via the weighted histogram analysis method (WHAM), 38 and the WHAM analysis code provided by A. Grossfield. 39 For the PMF calculation with the intermolecular distance as the reaction coordinate, we add an entropic contribution by the rotation of two molecules, quantified as 40

Vpm f ,rot (ξ ) = −2kB T log ξ

(2)

in three-dimensional space. The depth of the free energy well of association with respect to the infinite separation limit is evaluated with this rotational component excluded. Statistical uncertainties in PMF profiles are obtained using block-averaging. Each production run is split into 3 blocks of equal length. Error bars are one standard deviation about the mean over three blocks. The entropic contribution to the PMF at a particular ξ is calculated from

∆S(ξ ) =

∆A(ξ , T + ∆T ) − ∆A(ξ , T ) ∆T

(3)

where A is the Helmholtz free energy, i.e., PMF, and ξ is the reaction coordinate, T is the temperature, and ∆T is finite difference between two temperatures. The energetic contribution is given by ∆U(ξ ) = ∆A(ξ ) − T ∆S(ξ ). We define the directional order parameter Sbb of the surfactant linkers as 1 Sbb = 2

~ ~ 2 b1 · b2 −1 3 |b~1 ||b~2 |

(4)

where b~1 and b~2 stand for the two end-to-end vectors of covalent linkers in two different molecules. For a perfectly aligned pair Sbb = 1, whereas completely random distribution of orientation leads Sbb = 0, and for a perpendicular arrangement Sbb = −0.5 . The rotational autocorrelation of water molecules hydrogen-bonded to surfactant headgroup


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atoms is calculated as follows. A water is considered to be hydrogen bonded if the distance between the water oxygen atom and the surfactant acceptor atom is less than 0.35 nm and the bond angle oxygen(water) - hydrogen(water) - acceptor(surfactant headgroup) is 180±30 degrees. The rotational autocorrelation function is defined as the cross product of two O-H bond vectors in a water molecule.

3 Results and Discussion 0.5

0.5 0

0

PMF (kcal/mol)

PMF (kcal/mol)

T = 300 K T = 320 K

-0.5

Na74 COO

-1

(a) -1.5

-0.5 T = 300 K T = 320 K

-1 -1.5

Na74 SO3

-2 (b)

-2.5 -3

-2

0.5

1

1.5

2 2.5 ξ (nm) 0.5

3

-3.5

3.5

0.5

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1.5

2 ξ (nm)

2.5

3

3.5

0

PMF (kcal/mol)

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T = 300 K T = 320 K

-0.5

Na74 COO,SO3

-1 -1.5

(c)

-2 -2.5

0.5

1

1.5

2 ξ (nm)

2.5

3

3.5

Figure 2: Potential of mean force between (a) two molecules for the carboxylate, (b) two molecules for the sulfonate and (c) one molecule of the carboxylate with one molecule of the sulfonate Na-74 surfactant, at temperatures of 300 K and 320 K.

For all surfactant pairs, the PMF shows a repulsion at a separation of ∼ 2 nm and then two attractive wells at 0.5 and 1 nm. Figure 2 (a), (b) and (c) depict the PMF for carboxylate, sulfonate, and the mixed pair of surfactants, respectively, at two temperatures. At a given temperature, the



qualitative behavior is similar in all cases although the attractive well at 1 nm is deeper than that at 0.5 nm for the carboxylate surfactant, and the opposite is true for the sulfonate surfactant. The PMF for the mixed pair is intermediate to those between carboxylate and sulfonate pairs, and the attractive well at 0.5 nm is stronger than that at 1 nm at 300 K. What is different is the temperature dependence: There is a stronger temperature dependence of the PMF in the carboxylate surfactant and the mixed pair, but not in the sulfonate surfactant. 9

9

PMF (kcal/mol)

∆U -T∆S

6 PMF (kcal/mol)

Na74 COO

3 0 -3

(a)

-6

6

∆U -T∆S

3

Na74 SO3

0 -3 -6

(b)

-9

-9 0.5

1

1.5

2 2.5 ξ (nm) 12

3

3.5

-12

1

0.5

1.5

2 ξ (nm)

2.5

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3.5

∆U -T∆S

8 PMF (kcal/mol)

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Na74 COO, SO3

4 0 -4

(c) -8 -12

0.5

1

1.5

2 ξ (nm)

2.5

3

3.5

Figure 3: Entropic and energetic contributions to PMF of association of (a) carboxylate pair, (b) sulfonate pair and (c) mixed pair of Na-74 surfactants for T=300 K. A consequence of the temperature dependence in figure 2 is that the association in the sulfonate pair is energy driven and that in the carboxylate pair and the mixed pair are entropy driven. Figure 3 depicts the energetic (∆U) and entropic (-T ∆S) contributions in the three cases and shows that the driving force is different for the surfactants. Interestingly the entropic (carboxylate, mixed) and energetic (sulfonate) contributions do not show two minima, which arise from a compensation of entropic and energetic contributions. 8 ACS Paragon Plus Environment

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The two minima in the PMF correspond to different relative conformations of the molecules, The predominant configuration for ξ =1 nm (for all cases) is one in which the linkers are perpendicular to each other and the tails point towards the other molecule. For ξ =0.5 nm, however, the conformations are different, with the linkers parallel in the case of the carboxylate and distributed similar to the bulk in the sulfonate and the mixed pair. These conclusions are obtained from examining the directional order parameter Sbb for the linkers as depicted in figure 4, and readily seen in typical snapshots shown in figure 5. 0.3 COO SO3 COO, SO3

0.2 0.1 Sbb

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0 -0.1 -0.2 -0.3

0.5

1

1.5

2 ξ (nm)

2.5

3

3.5

Figure 4: Directional order parameters of Na-74 surfactant linkers for T=300 K. The distribution of linker orientation is affected by bulkiness of headgroups. There is always a region at the vicinity of the smallest ξ where steric hindrance between headgroups forces perpendicular alignment. For the mixed pair and the sulfonate pair, ξ =0.5 nm is in the region of such steric constraint. The mixed pair makes transition into dominance of parallel conformation at ξ =0.6 nm to 0.7 nm, and for the sulfonate pair this small region of parallel configurations is eliminated. At farther distance region around ξ =1 nm, all cases prefers perpenticular orientation for more efficient hydrophobic association of tailgroups as shown in figure 5 (b), (d), and (f). The energetic contribution to the PMF is dominated by the electrostatic energy but there are compensations between different contributions. We decompose the total energy into various pair contributions from the three components (water, surfactant, counterions). A comparison between the carboxylate and sulfonate surfactants for these contributions is depicted in figure 6. The main differences arise from the surfactant-surfactant contribution. The surfactant-water interaction pro9 ACS Paragon Plus Environment


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vides a large stabilizing energy but is not different for the different head-group pairs. Even for the important contributions there is a large cancellation between positive and negative energy contributions, with energies of order 10 cancelling to give a total ∆U of order 1 (see figure 3). Note that although we can calculate these contributions in a unique manner, i.e., by calculating the energies between species, such a decomposition is not definitive because the presence of other species mediates the correlations between any two species. Note that the charge of the head-groups is not a dominant effect on surfactant orientation; the carboxylate pair sustains a parallel conformation at

ξ =0.5 nm despite strong electrostatic repulsion.

1.5

ξ = 0.5 nm ξ = 0.65 nm ξ = 1.0 nm Na74 COO

(a)

1

Probability Density

Probability Density

0.5

0 0

0.5

1

1.5 rtt (nm)

Probability Density

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1.5

2

2.5

ξ = 0.5 nm ξ = 0.65 nm ξ = 1.0 nm Na74 SO3

(b)

1.5

1

0.5

0 0

0.5

1

1.5 rtt (nm)

2

2.5

ξ = 0.5 nm ξ = 0.65 nm ξ = 1.0 nm

(c)

Na74 COO, SO3

1

0.5

0 0

0.5

1

1.5 rtt (nm)

2

2.5

Figure 7: Probability distribution of internal distance between two ends of tailgroups of (a) carboxylate pair, (b) sulfonate pair and (c) mixed pair of Na-74 surfactants at 300 K. It is not possible to decompose the entropic contributions in the same fashion as the energetic contributions. We do find, however, that the conformational distributions of the two surfactants are different. Figure 7 depicts the distribution of distance between two tail ends of a single surfactant molecule, sampled for windows ξ =0.5 nm, ξ =0.65 nm and ξ =1 nm. It shows that in the ξ =1 nm 11 ACS Paragon Plus Environment


window all cases have similar probability distribution, but in the ξ =0.5 nm window the carboxylate has a broader distribution than the others. Here we see that the probability distribution of distance between two tail ends is broader as the order parameter of linkers increases. The broadness of distribution of the mixed pair at ξ =0.5 nm more resembles the sulfonate, but when it comes to

ξ =0.65 nm it is closer to the distribution of carboxylate pair. Then it suggests the parallel alignment of linkers enables more conformational freedom of tailgroups than the perpendicular alignment. It appears possible, therefore that the entropic effect comes from the conformational entropy of the surfactant molecules. 2.5 T = 300 K T = 320 K

2 PMF (kcal/mol)

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Na14 COO

1.5 1 0.5 0

0.5

1

1.5

2 ξ (nm)

2.5

3

3.5

Figure 8: Potential of mean force between two molecules of Na-14 carboxylate surfactant at temperatures of 300 K and 320K. The major contribution to the entropy comes from the conformational entropy of the tail groups. Figure 8 depicts the PMF between two Na-14 carboxylate molecules at two temperatures. The local minimum of PMF does not show any significant change or lowering as temperature increases, which implies that the driving force is enthalpic, i.e., the entropic driving force of association is eliminated by cutting the tails of the surfactant molecules.

4 Conclusion We study the driving force for the self-assembly of Gemini surfactants in aqueous solution. By calculating the potential of mean force at two temperatures we can isolate entropic and energetic effects. We find that the driving force, i.e., entropic or energetic, depends on the nature of the 12 ACS Paragon Plus Environment

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head-group. The driving force is entropic for carboxylate head-groups and energetic for sulfonate head-groups. The simulations imply that the charge density and size of the surfactant head-groups determine the thermodynamic driving force of self-assembly. The energetic contribution is different with the different head-group pairs and this arises largely from the electrostatic interactions, mediated by the size of the head-groups, which controls the distance of approach. It appears likely that the entropic contributions arise from the conformations of the tails of the surfactants. Finally, our work provides the idea that temperature controlled studies of PMF serve as stepping stone to get insight into phase behavior of surfactant self-assembly. Particularly it helps estimating CMC and its temperature dependence by decomposing thermodynamic driving forces of PMF. A criterion for molecular design of anionic gemini surfactants can be suggested that as we make the headgroup smaller, it would drive the assembly to be favored as temperature increases.

5 Acknowledgements Computational resources are provided by the UW-Madison Center for High Throughput Computing (CHTC) and the UW-Madison Chemistry Department cluster under grant number CHE0840494.

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