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Thermodynamics, Transport, and Fluid Mechanics

Coarse-grained molecular dynamics simulations of the breakage and recombination behaviors of surfactant micelles Liu Fei, Dongjie Liu, Wenjing Zhou, Fei Chen, and Jinjia Wei Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b01490 • Publication Date (Web): 12 Jun 2018 Downloaded from http://pubs.acs.org on June 26, 2018

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Industrial & Engineering Chemistry Research

Coarse-grained molecular dynamics simulations of the breakage and recombination behaviors of surfactant micelles Fei Liu,† Dongjie Liu,† Wenjing Zhou,‡ Fei Chen,*, †, ‡ and Jinjia Wei*,†, ‡ †

State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University,

Xi’an 710049, China ‡

School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an

710049, China

*To whom correspondence should be addressed. E-mail: [email protected] (F.C.); [email protected] (J.J.W.). Telephone: +86-29-82665836 (F.C.); +86-29-82664375 (J.J.W.).

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ABSTRACT

Surfactant molecules can form micellar network structures that can be applied for turbulent drag reduction through their breakage and recombination behaviors. One of the mechanisms of turbulent drag reduction by surfactants is “viscoelastic theory” which proposed by DeGennes. However, evaluating the rupture and coalescence properties of network micelles is challenging. Here, we study the breakage and recombination behaviors of an individual rodlike micelle using Martini coarse-grained force field molecular dynamics simulations. The flexibility of an individual micelle can be measured by its breakage energy. Micelle recombination behaviors can be attributed to three mechanisms: the coalescence energy, zeta potential or hydrophobic driving effect of the surfactant micelles. Thus, an excellent micelle that is beneficial for turbulent drag reduction is difficult to rupture but easy to recombine. The breakage behavior should be considered prior to the recombination behavior, because the breakage energy of an individual micelle is approximately one to two magnitudes larger than its coalescence energy under various conditions. Organic counter ion salts, such as NaSal, favor micelle recombination because of their electrostatic screen effect and uneven distribution on the surfactant micelle surface. Furthermore, this work brings a novel approach to understanding the breakage and recombination behaviors of surfactant micelles, providing an essential and scientific guidance to the effective use of surfactants in turbulent drag reduction. And it also provides a direct evidence to support the “viscoelastic theory”.

KEYWORDS Coarse-grained molecular dynamics, Martini force field, Breakage and recombination behaviors, Surfactant micelles


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1. INTRODUCTION Gemini surfactants can self-assemble into a wide variety of micellar morphologies because of their hydrophobic tail and hydrophilic head groups1-5. Various micellar structures (e.g., spherical, rodlike, lamellar, vesicular, loop and branch, and long, flexible wormlike) can exhibit rich rheological properties6-9. These various rheological properties are beneficial for their use in numerous applications such as hydrofracking fluids in the oil industry, turbulent drag reducing agents, thickening agents in consumer products, drug carriers in targeted delivery, and templates to create functional nanofluids10-15. However, threadlike shear-induced structure (SIS) formation and shear banding can be observed in surfactant solutions due to the merging and reversible breaking motions of many individual, wormlike micelles16-19. The network of wormlike surfactant micelles are beneficial for turbulent drag reduction because of their ability to absorb and release stress from turbulent kinetic energy and change the turbulent spatial structure20-21. Therefore, understanding the mechanism of the breakage and recombination behaviors of surfactant micelles is essential for their applications. Since the early work of Xu, the coarse-grained molecular dynamics (CGMD) method has been used to study the relationships between the microstructures and rheological properties of polymers22. Regarding gemini surfactants in aqueous solutions, Castillo-Tejas established a relationship between the molecular structure and the spatial configuration with transport properties under a Couette simple shear flow23. However, the works of Xu and Castillo-Tejas are qualitative rather than quantitative because the CG force field was not accurate at that time. Thanks to Marrink and the Martini force field, which has been validated by thousands of papers, a reliable force field was provided to investigate gemini surfactant properties in aqueous solutions24-26.


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Since 2011, the structures, dynamics, and mechanical properties of self-assembled aggregates of surfactants have been extensively studied using the Martini CGMD method. Sureshkumar studied binary systems of cetyltrimethylammonium chloride (CTAC) and its counter ion salts (e.g., sodium chloride (NaCl), salicylate sodium (NaSal) and sodium 5-methylsalicylate (NamSal)). He determined the following aspects27-31: (a) the sphere-to-rod transition in surfactant micelles under various counter ion salts; (b) the salt-induced coalescence of spherical micelle properties using quantitative measurements via the potential of mean force (PMF) and Derjaguin-Landau-Verwey-Overbeek (DLVO) potentials; (c) the morphology, energetics and kinetics of surfactant micelles in aqueous solutions; (d) a quantitative description of the shearinduced orientation dynamics, stretching and scission of rodlike surfactant micelles; (e) the mechanism of anomalous diffusion in cationic surfactant micelles in the presence of an explicit salt and solvent-mediated interactions; and (f) the conformational dynamics in the uniaxial elongational flow of rodlike and U-shaped surfactant micelles. Furthermore, Zhang used the same binary system and provided further understanding with regard to three aspects: (a) the transformation mechanism from linear to branched wormlike micelles; (b) the morphology prediction method for micelles; and (c) the influence of pH on the self-assembly of surfactant micelles32-34. Although much is now understood about the self-assembly, dynamics, and rheology of micellar fluids, a few fundamental questions remain unanswered. First, how is the flexibility of surfactant micelles influenced by various solution temperatures, the concentration molar ratio (R) of the counter ion salt to the surfactant, or different types of counter ion salts? Second, what are the precise values of the breakage and recombination energies of an individual micelle in the breakage-recombination process under certain circumstances? Third, how do counter ion salts


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influence the recombination behavior of surfactant micelles, excluding the electrostatic screen effect? In the present work, we used the Martini CGMD method to investigate the breakage and recombination behaviors of surfactant micelles in an aqueous binary solution system, employing CTAC and NaCl/NaSal/NamSal as the surfactant and counter ion salts, respectively. The breakage energy of an individual micelle was investigated under various temperatures, concentration molar ratios and counter ion salts. The coalescence energy and zeta potential were computed to better understand the recombination behavior. Furthermore, the area of the surfactant micelle hydrophobic groups exposed to water was calculated to study the superimposed effect on thermodynamic random motion. The paper is organized as follows. Sec. 2 describes the computational methods, and Sec. 3 presents the analysis in two parts. Part one presents an analysis of the breakage energy for an individual micelle under various temperatures, concentration molar ratios and counter ion salts. Part two discusses the mechanisms of the recombination behaviors, including the coalescence energy of the micelles, a zeta potential analysis and the driving effect of the micelle hydrophobic groups superimposed on the thermodynamic random motion of an individual surfactant micelle. Finally, Sec. 4 provides the conclusions. 2. COMPUTATIONAL METHODS The Martini force field was employed to study the static equilibrium and shear-induced dynamics within the same system25. The Martini CGMD model is provided in the Supporting Information. The Lammps molecular package was employed for the breakage energy calculations35. Our simulations started from a cylindrical, pre-assembled distribution of the surfactant and counter


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ion salt molecules. Water molecules were randomly distributed in the simulation box. The initial configurations were prepared using the Packmol software. The canonical ensemble NPT was used for the density adjustment at the beginning of the simulations. After the initial equilibration, the motion equations were integrated for a constant NVT ensemble. The temperature was controlled via a Nose-Hoover thermostat, and the time step was set at 20 fs. The van der Waals interaction was shifted from 0.9 to 1.2 nm, and the electrostatic interaction was shifted from 0.0 to 1.2 nm as required by the Martini force field using the Lammps shifted potentials. The Particle-Particle Particle-Mesh (PPPM) solver was used to compute the long-range electrostatic interactions. To avoid freezing of the solvent beads, 10% of the water beads were modeled as antifreeze particles in each simulation, as described in the Martini force field model. Gromacs 4.5.5 package was employed for the calculation of solvent accessible surface area (SASA) which using “g_sas” command36. The canonical ensemble NPT was performed at 300 K and 1 atm with periodic boundary conditions along three directions. The integrated algorithm was set as the leapfrog algorithm, and the time step was set as 20 fs. The thermostat and barostat coupling were controlled by the Berendsen method37. The van der Waals interaction was shifted from 0.9 to 1.2 nm, and the electrostatic interaction was shifted from 0.0 to 1.2 nm as required by the Martini force field using the Gromacs shifted potentials. All simulations were performed for 100 ns to reach equilibrium. OVITO and VMD software were employed for visualizations38-39. 3. RESULTS AND DISCUSSION 3.1 Breakage behaviors for an individual surfactant micelle 3.1.1 Breakage energy and elongational strain rate


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Longer and less rigid micelles have additional "conformational entropy" because the micelle is not always nearly linear. For a surfactant aqueous solution, the hydrodynamic force of the turbulent flow must first overcome the additional "conformational entropy" before extensional rupture of surfactant micelles occurs. To investigate the breakage energy of micelles, the first step is to assemble a linear, rodlike micelle (see Supporting Information). After the pre-assembled micelle stress relaxation process, a uniaxial elongational flow is applied to the binary system to study the micelle breakage energy under various conditions. The periodic simulation box of the binary system deforms under a uniaxial tensile strain at a constant elongational strain rate in the z - direction with 1 atm pressure in the x - and y - directions. Therefore, the micellar fluid in the z - direction is stretched but compressed in the x - and y directions, and the volume of the box is invariable. In all simulations, the center of mass (COM) of the initial micelle structure is placed at the center of the simulation box so that the COM remains near the center of the simulation box over the entire course of the elongational strain simulations. We chose a 14-nm micelle binary system (see Table S1) to investigate the breakage energy of an individual micelle. The counter ion salt is NaSal, and the concentration molar ratio R is 1.0. The elongational strain rate, ε& , varies from 3e7 s-1 to 2e8 s-1, and these values are equivalent to stretching velocities of 0.6 m s-1 to 4 m s-1 in the macro-flow because the box length in the z direction is 20 nm. The extension energy for one micelle can be defined as the difference in the total pair potential energy between CTAC and its counter ion salt. From the micelle breakage process (Figure 1a), we can see that the maximum reasonable length of the micelle before rupture is approximately equal to the length when the elongational


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strain rate, ε& , varies from 3e7 s-1 to 2e8 s-1; the extension energy Eextension increases as the micelle gradually stretches (Figure 1b). Moreover, the breakage energy Eb is equal to the extension energy Eextension when an individual micelle stretches to its maximum reasonable length. A multimedia view of the micelle breakage process is provided in the Supporting Information (Animation S1). (a) (b)

Figure 1. (a) The 14-nm micelle breakage process. The binary system is CTAC/NaSal in an aqueous solution; the pre-assembled micelle length is 14 nm, the elongational strain rate, ε& , is 1.2e8 s-1, the concentration molar ratio, R, is equal to 1.0, and t represents the simulation time. Therefore, ε&t is the accumulated strains. (b) Extension energy, Eextension , versus the accumulated strain, ε&t . The accumulated strains, ε&t , are approximately 1.96 when micelle breakage occurs. Therefore, the breakage energy is 600 kJ mol-1 for the 14-nm rodlike micelle. Figure 1b shows that the extension energy increases with the gradually increasing micelle length before the micelle ruptures into two shorter micelles. The maximum reasonable elongation rate is the maximum reasonable micelle extension length before the rupture divides


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the initial length of the micelle. For the various lengths of our sample micelles, the maximum reasonable elongational rate gradually increases. This phenomenon is observed because the endcap of the short, rodlike micelle cannot be sufficiently stretched. We speculate that the ultimate maximum reasonable elongation for a long, threadlike micelle is close to 140%, as illustrated in Table S2. The maximum reasonable elongation rate can be validated by another method, i.e., by naturally applying stress relaxation on a stretched but not ruptured micelle. If the elongated micelle can retract to its initial length (Animation S2 in Supporting Information), the elongational length is not the ultimate rupture length for an individual micelle; on the contrary, if the micelle cannot retract to its initial length and breaks into two or more shorter micelles (Animation S3 in Supporting Information), the elongational length is longer than the rupture length. Therefore, the length at which the micelle ruptures is the maximum reasonable elongational length. Using this method, we can also conclude that the maximum reasonable elongation rate for our micelle samples is approximately 140%. When the elongational rate, ε& , ranges from 2e7 s-1 to 3e8 s-1, an individual, rodlike micelle will break into two micelles at its maximum reasonable elongational length; however, if the elongational rate surpasses 3e8 s-1, the extensional length of an individual micelle will exceed its maximum reasonable elongational length as the accumulated strains increase, and the micelle will break into several shorter, individual micelles. Alternatively, the overstretched micelle will break into many pieces and undergo stress relaxation after a few nanoseconds if the high elongational strain rate is suddenly removed (see Figure 2). Under this circumstance, we also regard the extension energy at the maximum reasonable elongational length of the micelle as the breakage energy because if an overstretched micelle surpasses this length, the micelle will break


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either via continual stretching or enduring a few nanoseconds of stress relaxation before breakage. These findings can explain why high-shear/extension devices, such as a centrifugal pump, can severely destroy micelle structures, resulting in a total failure of the drag-reduction effect on turbulent flows.

Figure 2. The breakage process of an overstretched micelle due to stress relaxation. This micelle breaks into 3 pieces after 3.0 nanoseconds of stress relaxation. The binary system is CTAC/NaSal in an aqueous solution; the pre-assembled micelle length is 19 nm; the temperature is 300 K; and the concentration molar ratio, R, is equal to 1.0. A low elongational rate has not yet been investigated because when the elongational rate is lower than 2e7 s-1 in our binary system, the hydrodynamic forces cannot overcome the elongational conformational entropy of the rodlike micelle because of its loose and flexible structure. However, this is a separate, important topic for a micelle system with a network structure.


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3.1.2 Breakage energy and micelle length The variation in the micelle extension energy as a function of the accumulated strains for the rodlike micelle is shown in Figure 3. We selected four rodlike micelles with lengths of 14 nm, 19 nm, 23 nm and 28 nm. The uniaxial elongational rate is set as 1e8 s-1; the surfactant aqueous solution temperature, T, is 300 K; the counter ion salt is NaSal; and the concentration molar ratio, R, is equal to 1.0.

Figure 3. Micelle extension energy versus the accumulated strains. The inset formulas show two forms of the linear Hookean elastic spring model. The black line represents the 14-nm micelle, red line is for the 19-nm micelle, blue line is for the 23-nm micelle and dark cyan line is of the 28-nm micelle. Figure 3 shows that the breakage energies for the four rodlike micelles are 600, 1100, 1450, and 1700 kJ mol-1 , respectively. Because the stretching process of individual micelles is nearly


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identical; i.e., the accumulated strains, ε&t , are proportional to the micelle stretching distances,

∆x , we can regard micelle behavior as a linear Hookean elastic spring. Then, the extension energy, Eextension , and the accumulated strains, ε&t , can be expressed as A ⋅ ε&t + B ⋅ (ε&t ) 2 , where A is a constant for each micelle’s initial length. For the above four rodlike micelles, the value of A is 81.1, 167.4, 173.5, and 199.0, respectively. B increases from 114.8 to 239.7 when the length of the micelle increases from 14 nm to 28 nm. When replace the micelle extension, ∆x , with ε&t in the linear Hookean elastic spring model, the stretching energy and stretching distance can be expressed as F0 ∆x + κ A∆x 2 . The stretching moduli of the rodlike micelles, κ A , are 25, 16, 14, and 12 kJ mol-1 nm−2 , respectively. The breakage energy can be calculated from the stretching energy at the maximum reasonable stretching distance using the linear Hookean elastic spring model, and 12 kJ mol-1 nm−2 is close to an accurate stretching modulus value for a long, wormlike micelle. In the “viscoelastic theory”, turbulent kinetic energy can be absorbed and stored by the micelles with network microstructure in a drag reducer solution at high shear rate40. When the high-shear-rate region diffuses or moves to the low-shear-rate region, the microstructures will relax to a random threadlike entanglement, and the stored energy will be released to low-wavenumber vortexes (large-scale vortexes) in the form of elastic stress waves, which greatly decrease the dissipation of turbulent kinetic energy and induce turbulent drag reduction40-41. Because a single wormlike micelle is the basic component of network micelles and its stretching modulus is invariable for a specific micellar fluid, if one network micelle system contains a larger length than the individual micelles, its extension energy will also be larger. After the long and flexible status of the network micelle is overcome by the kinetic vortexes, the micelle can consume more energy from the kinetic vortexes than a smaller network


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micelle system. Thus, a larger network micelle system will be more beneficial for turbulent drag reduction than a network micelle system with smaller micelle lengths. 3.1.3 Effects of the concentration molar ratio, temperature and counter ion salt on the breakage energy In our simulations, the 28-nm micelle acts as a long, wormlike micelle for its stretching modulus and breakage energy properties, and we studied the breakage energy of this micelle under various concentration molar ratios, R (see Figure 4a.).

(a)

(b)

Figure 4. (a) The effect of concentration molar ratio, R, on the breakage energy, Eb. The inset shows the stretching modulus as a function of the concentration molar ratio, R. The binary system is CTAC/NaSal; the temperature T is 300 K; the elongational strain rate, ε& , is 1e8 s-1. (b) Eb versus T. The binary system is CTAC/NaSal, R is 1.0, and the elongational strain rate, ε& , is 1e8 s-1. The breakage energy, Eb, increases from 600 kJ mol-1 to 1700 kJ mol-1 as R increases from 0.3 to 1.0 (see Figure 4a), corresponding to an increase from 4.23 to 12 kJ mol-1 nm−2 for the


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stretching modulus, κ A , in the micelle extension process (Figure 4a inset graph); however, as R increases from 1.0 to 2.0, the breakage energy is nearly constant within statistical error. Therefore, we regard R=1 as the minimum concentration molar ratio for the maximum breakage energy of an individual micelle in the CTAC/NaSal binary aqueous system. According to Sureshkumar, the cationic surfactant CTAC micelle can form only at R=1.2~1.5 concentration molar ratios with Sal- 27 because some Sal- anions penetrate the micelle core and screen the repulsive interactions among the CTA+ heads. Therefore, this explanation mutually verifies our minimum concentration molar ratio conclusion and Sureshkumar's studies. Our results also explain why the concentration molar ratio, R, is always equal to 2.0 but rarely below 1.0 for industrial applications and experimental processes, i.e., because the CTA+ micelle cannot capture all of the Sal- ions evenly dispersed in an aqueous solution. Therefore, some redundancy is necessary. However, if the concentration molar ratio, R, is below 1.0, the mechanical properties and micelle shape will be greatly influenced, and the additives might not result in a drag-reduction agent. Figure 4b shows the effect of the micellar solution temperature on the micelle breakage energy. We can see that the breakage energy of the micelle has small fluctuations at various temperatures, and the breakage energy value is 1750±100 kJ mol-1 . The micellar solution temperature can affect only the coalescence behavior of micelles, and the possibility of micelle recombination is enhanced by the increasing temperature, which is explicitly analyzed in Sec 3.3. For the different counter ion salts in the CTAC aqueous solution, such as NaCl, NaSal and NamSal, the breakage energies of the 28-nm micelle in CTAC/NaSal and CTAC/NamSal binary


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aqueous solutions are far greater than that of the micelle in a CTAC/NaCl aqueous solution (The details can be seen in the Supporting Information). For micelles with network structures, their length scale is approximately 1-100 µm , and the diameter of the micelles is approximately 4.5 nm. However, most turbulent vortex scales surpass O (10 µm ). Therefore, when the hydrodynamic forces of a turbulent vortex rupture the micelle network, extensional rupture is the only possibility for the many individual micelles within the vortex scale. This paper primarily discusses the breakage behavior of an individual micelle using the elongational flow in a surfactant/counter ion salt binary aqueous solution system without regard to the breakage and recombination behaviors of a complete micelle network, which should be studied further. 3.2 Recombination behaviors of surfactant micelles 3.2.1 Recombination behaviors and inter-micelle potential of mean force (PMF) The micelle self-assembly process is key to regain the turbulent drag-reduction property of surfactant additives. The micelle network can be reformed by many individual micelles because the diameter of an individual micelle is approximately defined by the surfactant/counter ion salt binary system. The recombination process of two single micelles can be divided into three types: 1) two spherical micelles coalescing into one rodlike micelle (Figure 5a); 2) a spherical/rodlike micelle and a rodlike/wormlike micelle merging into a branched micelle (Figure 5b); and 3) two wormlike micelles combining into an X-shaped micelle (Figure 5c).


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(a)

(b)

(c)

Figure 5. The recombination processes of two individual micelles. (a) Two spherical micelles coalesce into one rodlike micelle; (b) a spherical/rodlike micelle and a rodlike/wormlike micelle merge into a branched micelle; (c) two wormlike micelles unite into an X-shaped micelle. All micelles were generated using the CTAC/NaSal aqueous binary solution system at a temperature of 300 K and a concentration molar ratio, R, equal to 1.0. These three coalescence processes have a common feature. The coalescence process can be simplified as the coalescence process of two single spherical micelles because the dimension range of the junction point for the two micelles is approximately equal to one spherical micelle. We calculated the coalescence energy, Ec , of two spherical micelles to study the recombination behaviors of micelles. The coalescence energy can be computed using the different PMF values of two spherical micelles at the initial and coalesced positions. The detailed method for the PMF calculation can be seen in the Supporting Information.


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We first studied how the PMF values change with various concentration molar ratios. The counter ion salt is NaSal, and the temperature is 300 K (see Figure 6a).

(a)

(b)

Figure 6. (a) Potential of mean force (PMF) plotted as a function of separation, r, between the centers of mass of two micelles at varying concentrations of NaSal. The inset shows the coalescence energy, Ec, as a function of the concentration molar ratio, R. (b) The coalescence energy, Ec, as a function of the temperature, T. Figure 6a shows that the PMF value is always positive, indicating that the two cationic surfactant micelles are always mutually repulsive, and Sal- cannot screen all the repulsive effects of the CTA+ cationic charges. This result is another validation of the limited carrying ability of the cationic surfactant micelle for Sal- ions. Since the valence charges of CTA+ and Sal- are the same, the number of Sal- cannot surpass the number of CTA+ in the composition of a CTA+/Salmicelle, i.e., equivalent to R ≤ 1 . The coalescence energy, Ec, decreases as the concentration molar ratio, R, increases, indicating that the coalescence energy needed to overcome the repulsive force between two micelles decreases. This finding demonstrates that two micelles can more easily combine as the


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concentration molar ratio, R, increases. The coalescence energy also decreases as the temperature increases (see Figure 6b). With the increase in temperature, two micelles can be more easily merged; therefore, the increasing temperature benefits the recombination behaviors of micelles. When the counter ion salt is NaCl (temperature of 300 K and concentration molar ratio, R, of 1.0), the coalescence energy, Ec, for two micelles is 6 kcal/mol. When the counter ion salt NaSal is replaced with NamSal at the same temperature and concentration molar ratio, the coalescence energy, Ec, is 2.6 kcal/mol. Compared with 3 kcal/mol for NaSal, NamSal is slightly more beneficial for the recombination behavior of micelles. Additionally, NaCl makes the recombination process more difficult than the two organic counter ion salts, NaSal and NamSal. Considering the breakage energy and coalescence energy for micelles, the breakage energy is much larger than the coalescence energy for micelles. For the 28-nm micelle (with the counter ion salt NaSal, temperature of 300 K, and R=1), the breakage energy for one CTAC Martini molecule is approximately 1700/480=3.54 kJ mol-1. Under the same conditions, the coalescence energy of one surfactant molecule is approximately 3*4.182/80=0.156 kJ mol-1 for a spherical micelle. The breakage energy is approximately one magnitude larger than the coalescence energy for one surfactant molecule. However, the actual value gap between the breakage energy and coalescence energy might be even wider because the flexible and loose conformational entropy was not involved in the above calculation. However, the turbulent vortex hydrodynamic force should first overcome the flexible and loose conformational entropy of the micelle and nearly linearly stretch the micelle before the extensional stretching occurs. A long, wormlike micelle only has one or several junctions to merge. If we average the coalescence energy for a whole long wormlike micelle, the coalescence energy of the surfactant molecule is much smaller than its breakage energy.


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3.2.2 Recombination behaviors and zeta potential of micelles The coalescence process for various micelle shapes can be simplified as the coalescence process of two single spherical micelles, and an individual spherical micelle can be regarded as a charged colloid in an aqueous solution28. According to DLVO theory42-43, the repulsive force of two cationic micelles can be primarily attributed to the electrostatic repulsion between the charged surfaces of two spherical micelles as well as the overlap of their diffuse double layers. The zeta potential is a key indicator of the stability of a colloidal dispersion. The magnitude of the zeta potential indicates the degree of the electrostatic repulsion between adjacent, similarly charged particles in a dispersion. Therefore, we computed the zeta potential for a spherical cationic micelle to study whether micelles can easily recombine. Calculation details for the zeta potential calculations are in the Supporting Information. We chose a spherical micelle containing 80 CTA+ ions in an aqueous solution to study the absolute value of the zeta potential energy at different concentration molar ratios (see Figure 7). The counter ion salt is NaSal; the solution temperature is 300 K; and the box size and other parameters are the same as those used for the PMF calculation. Figure 7 shows that when R is less than 1.0, the absolute value of the zeta potential energy,

Ψzeta

, decreases as R increases,

indicating that micelles are more easily fused as the stability behavior of the colloid changes from good stability (R=0.3) to incipient instability (R=1.0)44-46.


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Figure 7. The absolute value of the zeta potential,

Ψzeta

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, at various concentration molar ratios of

NaSal to CTAC based on DLVO theory calculations. We synchronously studied the coalescence energy, Ec , and the absolute value of the zeta potential energy,

Ψzeta

, of the micelle (see Figure 8a). The coalescence energy, Ec , also

decreases as R increases, and the tendency is the same as that of the absolute value of the zeta potential energy,

Ψzeta

, versus R. This finding demonstrates that the electrostatic repulsion effect

on the charged surfaces of the micelles becomes weaker, and the electric potential difference between the diffuse double layers of the micelle and the bulk solution also decreases. Both circumstances can make the micelle fusion process easier.


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(b)

(a)

Figure 8. (a) The effect of concentration molar ratio, R, on the coalescence energy, Ec , and the absolute value of the zeta potential,

Ψzeta

. (b) The effect of solution temperature, T, on the

coalescence energy, Ec , and the absolute value of the zeta potential,

Ψzeta

.

When R is larger than 1.0, the absolute value of the zeta potential energy,

Ψzeta

, increases

with an increase in R, indicating that a high concentration of the counter ion salt can enhance the difficulty of micelle coalescence. This result can be explained by the variation in the value of the zeta potential,

Ψzeta .

When R is less than 1, the zeta potential energy is positive. If R is larger than

1.0, the zeta potential value is negative (see Figure 7), indicating that the electric potential value of the bulk solution is larger than that of the micelle diffuse double layers. For the application of drag-reduction additives on turbulent flow, however, the absolute value of the zeta potential, Ψzeta

, will always decrease as R increases from 0.3 to 2.0, and the fusion of micelles will be

easier as R increases. This effect occurs because the surfactant and counter ion salt concentrations are low (~O [1000 ppm]) compared with the 0.05 mol/L concentration used in our simulation settings; thus, the zeta potential value will always be positive in a turbulent flow. The absolute value of the zeta potential,

Ψzeta

, also decreases as the solution temperature increases

when the counter ion salt is NaSal and R=1.0 (see Figure 8b). This trend perfectly matches that


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of the coalescence energy versus the aqueous solution temperature. This finding shows that an increase in the solution temperature increases the random velocity of micelles and makes micelle merging easier. When NaCl is the counter ion salt, the absolute value of the zeta potential,

Ψzeta

,

(32 mV in our calculation) is larger than that with NaSal (12 mV) or NamSal (8 mV) as the counter ion salts, and micelle fusion is more difficult. When NamSal is used as the counter ion salt instead of NaSal, micelles can slightly more easily coalesce. 3.2.3 Recombination behaviors and the hydrophobic driving effect of the micelles In the CTAC/NaSal aqueous solution binary system, some of the aromatic rings of Sal- can penetrate the micelle core, and part of the Sal- can be absorbed on the surface of the hydrophobic group of CTA+ that is in direct contact with water molecules; this has been proven theoretically and experimentally27,47. Insight can be obtained from a calculation using the SASA of the micelle hydrophobic groups. We selected two spherical micelles, one composed of 80 CTA+ ions without Sal- and another composed of 80 CTA+ and 80 Sal- ions. The SASA of the two micelle hydrophobic groups as a function of the simulation time is illustrated in Figure 9. The SASA of the micelle hydrophobic groups increases from 60 to 85 nm2 after the addition of Sal-, indicating that the aromatic ring of Sal- is deeply embedded in the hydrophobic group of CTA+. Furthermore, if the Sal- ions can adsorb only on the surface of the hydrophobic group of CTA+, the SASA would absolutely decrease, as shown by the small fluctuations in the SASA in Figure 9. The location of the Sal- ions carried by the CTA+ cationic surfactant micelles is relatively fixed, regardless of whether the Sal- ions are embedded or absorbed. The only exception is when two micelles are close to their fusion position; in this case, a small amount of Sal- will jump from one micelle to the other and form a "salt bridge"32.


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Figure 9. The solvent accessible surface area (SASA) of micelle hydrophobic groups as a function of the simulation time. The aqueous solution temperature is 300 K. The distribution of Sal- on the surface of a surfactant micelle is uneven29 (see Figure S4). Consequently, this leads to an uneven distribution on the SASA of the micelle hydrophobic groups. The hydrophobic group driving force is the main driving force of protein folding. Therefore, we hypothesized that the CTA+/Sal- micelle can also be driven by hydrophobic driving forces, and the driving effect of the micelle hydrophobic groups can be superimposed on the thermodynamic random motion of the surfactant micelle. To test this hypothesis, two short, rodlike micelles with different distributions of hydrophobic areas in contact with water were designed by changing the concentration molar ratios of the counter ion salt to the surfactant while maintaining the same SASA values for the micelle hydrophobic groups (Table S4). Additionally, the two micelles have the same size to exclude the "scale effect". In Table S4, micelle A has a nearly even distribution of the hydrophobic area in contact with water due to less counter ion salt on its surface; micelle B has an uneven distribution of the hydrophobic area in


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contact with water. Theoretically, micelle A should not contain any Sal- because it has an even distribution of the hydrophobic area in contact with water. However, CTA+ surfactant micelles easily split when R=0 (no Sal-)28, resulting in unstable, rodlike micelles. Therefore, a minimum concentration molar ratio (R=0.3) was used to create stable, rodlike micelles, and the distribution of the hydrophobic area directly in contact with water for micelle A was nearly uniform. The velocity as a function of the simulation time for the COMs of the two micelles is shown in Figure 10.

Figure 10. The velocity of the COMs of the two micelles versus the simulation time. Figure 10 shows that the average velocity of micelle B is 125% times greater than that of micelle A, but the average velocities of micelles A and B significantly fluctuated over the simulation time. This result supports our hypothesis. A hydrophobic driving effect exists when an organic counter ion salt is added into the aqueous solution. Moreover, this driving effect can


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be superimposed on thermodynamic random motion to improve the micelle fusion possibility, which is beneficial to the recombination behavior of micelles. 4. CONCLUSIONS We studied the breakage and recombination behaviors of surfactant micelles by large-scale CGMD simulations. The extension energy, elongational strain rate, stretching modulus, and breakage energy were used to describe the breakage behaviors of an individual micelle. The extension energy increases with a gradual increase in the micelle length before the micelle ruptures into two shorter micelles. When the elongational strain rate is within a suitable range, an individual rodlike micelle will break into two micelles at its maximum reasonable elongational length, and the maximum reasonable elongation rate for a long, wormlike micelle is approximately 140%. The stretching modulus value of a long, wormlike micelle is approximately 12 kJ mol -1 nm −2 , and the breakage energy can be calculated from the extension energy at the maximum reasonable stretching distance using a linear Hookean elastic spring model. We have shown that R=1 is the minimum concentration molar ratio for the maximum breakage energy of an individual micelle; the temperature has a negligible influence on the breakage energy of micelles; and the micelle breakage energy in CTAC/NaSal and CTAC/NamSal binary aqueous solutions is far larger than that in a CTAC/NaCl aqueous solution. We present a novel viewpoint for understanding the recombination behaviors of surfactant micelles based on three factors: the coalescence energy, zeta potential and hydrophobic driving effect of the surfactant micelles. We demonstrated that the coalescence energy of the micelle and the absolute value of the zeta potential energy synchronically change by varying the concentration molar ratios and temperatures. Increasing the solution temperature and


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concentration molar ratio can enhance cationic surfactant micelle fusion by weakening the electrostatic effect on the micelle surface and in the diffuse double layers. The organic salts NaSal and NamSal show better performances in terms of recombination behavior than NaCl under the same conditions. Furthermore, the breakage energy of micelles is one to two magnitudes larger than their coalescence energy; therefore, the breakage energy should be given priority over the coalescence energy in the application of drag-reduction additives for turbulent flow. Finally, the CTA+/Sal- micelle can be driven by hydrophobic driving forces because of the uneven distribution of Sal- on the micelle surface, and its velocity contribution cannot be neglected from the thermodynamic random motion of a micelle. Notably, previous studies have rarely studied the breakage and recombination behaviors of micelles under the background of drag-reduction, turbulent-flow applications, and gave a direct evidence to support the “viscoelasticity” theory. Thus, our work provides molecular-level insight on the breakage and recombination behaviors of micelles, If we can study the flexible and relaxed "conformational entropy" of an individual micelle or even an entire network of micelles, the mechanism of turbulent-friction drag-reduction flow by surfactants will be further deciphered. ACKNOWLEDGMENTS The National Natural Science Foundation of China (No. 51636006, No. 51225601) and the Fundamental Research Funds for the Central Universities (No. cxtd2017004) supported the present work. NOTES The authors declare no competing financial interests.


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Table of Contents Graphic 1706x807mm (72 x 72 DPI)



Figure 1. (a) The 14-nm micelle breakage process. 538x526mm (72 x 72 DPI)


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Figure 1.(b) Extension energy versus the accumulated strain. 404x300mm (72 x 72 DPI)



Figure 2. The breakage process of an overstretched micelle due to stress relaxation. 270x261mm (96 x 96 DPI)


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Figure 3. Micelle extension energy versus the accumulated strains. 425x310mm (72 x 72 DPI)



Figure 4. (a) The effect of concentration molar ratio on the breakage energy. 396x294mm (72 x 72 DPI)


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Figure 4. (b) Breakage energy versus surfactant aqueous solution temperature 405x306mm (72 x 72 DPI)



Figure 5. The recombination processes of two individual micelles. 970x1001mm (72 x 72 DPI)


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Figure 6. (a) Potential of mean force (PMF) plotted as a function of separation between the centers of mass of two micelles at varying concentrations of NaSal. 327x291mm (72 x 72 DPI)



Figure 6. (b) The coalescence energy as a function of the temperature. 386x288mm (72 x 72 DPI)


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Figure 7. The absolute value of the zeta potential at various concentration molar ratios of NaSal to CTAC based on DLVO theory calculations. 387x299mm (72 x 72 DPI)



Figure 8. (a) The effect of concentration molar ratio on the coalescence energy and the absolute value of the zeta potential. 428x300mm (72 x 72 DPI)


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Figure 8. (b) The effect of solution temperature on the coalescence energy and the absolute value of the zeta potential。 415x302mm (72 x 72 DPI)



Figure 9. The solvent accessible surface area (SASA) of micelle hydrophobic groups as a function of the simulation time. 399x285mm (72 x 72 DPI)


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Figure 10. The velocity of the COMs of the two micelles versus the simulation time. 369x282mm (72 x 72 DPI)


Coarse-Grained Molecular Dynamics Simulations ... - ACS Publications

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