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DOI: 10.1039/C5RA26051E (Paper) RSC Adv., 2016, 6, 13442-13449

Vesicle formation of catanionic mixtures of CTAC/SDS induced by ratio: a coarse-grained molecular dynamic simulation study

Pan Wangab, Yunyun Maab, Zhibin Liuab, Youguo Yanab, Xiaoli Sun*a and Jun Zhang*ab
aCollege of Science, China University of Petroleum, 266580 Qingdao, Shandong, People's Republic of China. E-mail: sunxiaoli@upc.edu.cn; zhangjun.upc@gmail.com
bKey Laboratory of New Energy Physics & Materials Science in Universities of Shandong, China University of Petroleum, 266580 Qingdao, Shandong, People's Republic of China

Received 7th December 2015 , Accepted 11th January 2016

First published on 14th January 2016

Abstract

The formation of vesicles has been a hot topic because of their many potential applications, ranging from cell membranes to drug delivery. However, determining essential information for further development, such as molecular arrangement and interaction, is still experimentally challenging. In this study, coarse-grained molecular dynamics simulation (CGMD) was carried out to study the formation of vesicles in a cationic cetyltrimethylammonium chloride (CTAC) and anionic sodium dodecyl sulfate (SDS) system. In the mixtures, a series of morphologies was obtained as the mixed ratio changed. When the ratio of SDS was equal to that of CTAC, a vesicle was formed by disk-like bilayer curling and the entropy was the driving force. We hold that the bending energy of the bilayer is the resisting force and the electrostatic forces play a significant role in aggregate shape. Therefore, the surfactant distribution in different parts of disk-like bilayer aggregates were studied in the vesicle formation process. These studies put forward a new understanding of vesicle formation and brought to light the microscopic details of the bilayer–vesicle transition of catanionic mixtures.

1. Introduction

Vesicles, which have a bilayer membrane with an inner hollow structure, are concerned with many biological processes, and they can be exploited for wide-ranging applications such as drug delivery,1–3 templating nanochemistry4,5 and micro-reactors.6 Over the past few decades, a great deal of work about vesicles has been reported.7–11

In earlier studies, vesicles were produced by phospholipid molecules constituted by double-chained amphiphiles, and the formation of vesicles required mechanical methods, such as sonication or extrusion.12,13 However, these vesicles had a fatal drawback; they were unstable, which inherently restricted their potential applications. In 1989, Kaler et al.14 reported that stable vesicles could be found in aqueous mixtures of cationic–anionic (catanionic) surfactants that mimic the structure of phospholipids through the electrostatic interaction of their polar head groups. Unlike the phospholipids, catanionic surfactant vesicles can be formed spontaneously and exhibit high stability. Since then, more and more researchers have paid close attention to catanionic surfactant mixture systems,15–17 and a mountain of work about spontaneous vesicle formation in these mixture systems has been reported.9,18–20

Most of the investigations on catanionic surfactant mixture systems have been by experiment. Yatcilla et al.15 reported the phase behavior and aggregate morphologies of the cationic cetyltrimethylammonium bromide (CTAB) and anionic sodium octyl sulfate (SOS) mixture, and they found that the composition and chain length asymmetry had a great effect on the stability of the vesicles. After that, increasing interest was focused on the composition of the mixtures21–24 and the chain length asymmetry.25–29 Recently, some researchers began to investigate responsive vesicles via changing the external environments in the original basis of surfactant mixture systems, such as temperature30 and pH,31 which have more value in practical applications. In any case, self-assembly is one of the most fundamental scientific problems. In contrast to the continuous finds in environmental responsive vesicles, the essential answer on how the composition of the mixtures triggers distinct assemblies is still not clear. Atomic-level structural details of self-assembly processes and subtle molecular interactions are crucial to giving insight into self-assembly phenomena, but unfortunately, the information is challenging or impossible to probe experimentally.

Molecular dynamic (MD) simulation, which can provide microscopic details, has been applied in extensive fields.32–35 Mesoscopic molecular dynamics technologies, including coarse-grained molecular dynamics (CGMD) and dissipative particle dynamics (DPD) and so on, improve performance when handling larger lengths and timescales, and are powerfully exploited to investigate surfactant self-assembly in solutions. Wu et al.7 and Shillcock et al.8 applied CGMD and DPD, respectively, to studying the spontaneous vesicle self-assembly, and they both revealed the process of vesicle formation. Li et al.9 showed the effects of salt, temperature, and selective solvents on micelle–vesicle transition by DPD, and revealed the transition mechanism induced by various conditions from the microscopic point of view. de Vries et al.36 adopted CGMD models to analyze the properties of intermediate structures in detail and reflect the features of the vesicle formation processes. Markvoort et al.37 studied the bilayer–vesicle transition by CGMD, and revealed that the transition is entropy driven, after going deep into studying the potential energy. Although many simulation studies on vesicle formation or transition have been made, exploration of the mechanism of vesicle self-assembly by catanionic surfactant mixtures is still sparse, and further research on this topic is urgently needed.

In our work, we employed CGMD simulation to investigate vesicle formation in catanionic mixtures composed of sodiumdodecyl sulfate (SDS) and cetyltrimethylammoniumchloride (CTAC). Various morphologies of surfactant aggregates were obtained at different CTAC/SDS ratios and the vesicles were formed when the mixed ratio was 1[thin space (1/6-em)]:[thin space (1/6-em)]1. Furthermore, the formation process and mechanism were studied from the micro-perspective. These studies put forward a new understanding of vesicle formation, and brought to light the microscopic details of the bilayer–vesicle transition of catanionic mixtures.

2. Model and simulation methods

In this work, we performed CGMD simulation on CTAC/SDS surfactant mixture systems at different ratios, in which the total number of surfactants was fixed to 600. The ratios of SDS to CTAC are as follows: 6[thin space (1/6-em)]:[thin space (1/6-em)]0, 5[thin space (1/6-em)]:[thin space (1/6-em)]1, 3[thin space (1/6-em)]:[thin space (1/6-em)]1, 1[thin space (1/6-em)]:[thin space (1/6-em)]2, 1[thin space (1/6-em)]:[thin space (1/6-em)]1, 1[thin space (1/6-em)]:[thin space (1/6-em)]3, 2[thin space (1/6-em)]:[thin space (1/6-em)]1, 1[thin space (1/6-em)]:[thin space (1/6-em)]5, 0[thin space (1/6-em)]:[thin space (1/6-em)]6. For the convenience of expression, we defined these nine mixed systems as systems I to IX, respectively. In coarse-grained models, the most important feature is the new bead concept, involving several atoms or molecules. In accordance with the principle of the division of the Martini force field38 and the molecular structure, the coarse-grained structure of SDS and DTAB are shown in Fig. 1. Four hydrophobic alkyl groups were set as a single type C1 CG bead (blue), and three hydrophobic alkyl groups were treated as a C2 CG bead (blue). The hydrophilic head group (–SO4−) of SDS39 was represented by a Qa CG bead (yellow) with a negative charge. As a report by Sangwai et al.,40 the trimethylammonium head group combined with two neighboring alkyl groups was expressed as a Q0 bead with a positive charge. SDS was formed by three C1 beads and one Qa bead (Fig. 1(a)). CTAC was modelled by two C1 beads, two C2 beads and one Q0 bead (Fig. 1(b)). The same color rules have been used in the following figures. The CG water was mapped from four atomistic H2O molecules. There are two kinds of CG water, W and BW. The force field parameters for the interactions between CG beads are referred to as the Martini force field.38 On the basis of the Martini force field the presence of BW (named antifreeze particles, which replace 10% of all water beads) in the aqueous solution can disturb the lattice packing of the uniformly sized solvent particles and prevent unwanted freezing of the CG water. CG Cl− counterions were composed of three H2O molecules and one Cl−, the same as CG Na+.
image file: c5ra26051e-f1.tif
Fig. 1 Coarse-grain mapping for SDS (a) and CTAC (b). Four hydrophobic alkyl groups were set as a single type C1 CG bead (blue), and three hydrophobic alkyl groups were treated as C2 CG bead (blue). The trimethylammonium head group was represented by a Q0 CG bead (red) with a positive charge, and the sulphate head group was represented by a Qa CG bead (yellow) with a negative charge.

Our simulation work was performed by the Gromacs 4.5.5 (ref. 41) package. The simulations of the surfactant mixture in aqueous solution were accomplished in a cubic box with periodic boundary conditions along three directions. The side length of the box was 200 Å. The canonical ensemble NPT was performed at 298 K and 1 atm for each system, the integration step was set as 20 fs. The temperature was controlled by the Berendsen thermostat,42 and the pressure coupling was set by the Berendsen barostat.42 The cut-off for nonbonded interactions was set at 12 Å with the standard shift functions of Gromacs, where the van der Waals interaction was shifted from 0.9 to 1.2 nm, and the electrostatic interaction was shifted from 0 to 1.2 nm. All simulations were carried out for 1 μs to reach the equilibrium state.

3. Results and discussion

3.1. Mixed surfactant aggregates at different ratios

The self-assembly behavior of catanionic surfactant with different mixed proportions were studied. Compared with single surfactant aggregates in aqueous solutions, more and more kinds of complicated aggregates could be formed via varying the mixed proportions. In our simulation systems, spherical micelles, rod-like micelles, disc-like micelles and vesicles were obtained at different ratios of CTAC/SDS.

Fig. 2 shows the snapshots of equilibrium morphologies of surfactant aggregates at different CTAC/SDS ratios. If there was only CTAC in the solution, as in system I shown in Fig. 2(a), spherical micelles were formed. Once 1/6 CTAC was replaced by SDS in this system, in other words, when CTAC/SDS was 5[thin space (1/6-em)]:[thin space (1/6-em)]1, we got a spherical micelle and a rod-like micelle, as shown in Fig. 2(b). If there was more SDS in the system, a huge disc-like micelle was formed as shown in Fig. 2(c), when the ratio of CTAC/SDS was 3[thin space (1/6-em)]:[thin space (1/6-em)]1 in system III. Just like system III, a disc-like micelle was also obtained at the CTAC/SDS ratio 2[thin space (1/6-em)]:[thin space (1/6-em)]1 in system IV, shown in Fig. 2(d). Comparing the cross-section of the rod-like micelle with that of the disc-like micelle, the disc-like micelle was well-ordered and dense. When the ratio of CTAC/SDS was 1[thin space (1/6-em)]:[thin space (1/6-em)]1, a single vesicle was formed, as shown in system V. With the further increase of SDS content, we also got disc-like micelles at the CTAC/SDS ratio 1[thin space (1/6-em)]:[thin space (1/6-em)]2 and 1[thin space (1/6-em)]:[thin space (1/6-em)]3 in systems VI and VII, respectively, which was similar to systems III and IV. When the amount of SDS continued to increase, we got a “sandwich” micelle, which was stacked up by two disc-like micelles. From the cross-section of the sandwich micelle, a well-ordered bilayer arranged by SDS and CTAC formed between two disc-like micelles, which was considered to be due to the electrical charge effect. In the SDS system, we got the mixture of rod-like micelles and spherical micelles as shown in Fig. 2(g). Thus, it is concluded that a mixed ratio is a key factor in the shapes of aggregates in the mixed surfactant system. With the increase of the CTAC/SDS ratio from 6[thin space (1/6-em)]:[thin space (1/6-em)]0, 5[thin space (1/6-em)]:[thin space (1/6-em)]1, 3[thin space (1/6-em)]:[thin space (1/6-em)]1, 2[thin space (1/6-em)]:[thin space (1/6-em)]1, 1[thin space (1/6-em)]:[thin space (1/6-em)]1, 1[thin space (1/6-em)]:[thin space (1/6-em)]3, 1[thin space (1/6-em)]:[thin space (1/6-em)]2, 1[thin space (1/6-em)]:[thin space (1/6-em)]5 to 0[thin space (1/6-em)]:[thin space (1/6-em)]6, a number of aggregates with different morphologies can be formed, such as rod-like, disc-like, vesicle, and stacking disc-like micelles, and all these aggregates have been observed by experiment.15,43,44 It is worth mentioning that vesicles were formed, when the ratio of CTAC/SDS was 1[thin space (1/6-em)]:[thin space (1/6-em)]1.


image file: c5ra26051e-f2.tif
Fig. 2 The snapshot of equilibrium morphologies of surfactant aggregates in simulation systems I–IX. The bottom panels show the cross-sections of the max. aggregates in each system. The water beads are hidden for convenient observation. (a) System I, CTAC[thin space (1/6-em)]:[thin space (1/6-em)]SDS = 6[thin space (1/6-em)]:[thin space (1/6-em)]0. (b) System II, CTAC[thin space (1/6-em)]:[thin space (1/6-em)]SDS = 5[thin space (1/6-em)]:[thin space (1/6-em)]1. (c) System III, CTAC[thin space (1/6-em)]:[thin space (1/6-em)]SDS = 3[thin space (1/6-em)]:[thin space (1/6-em)]1. (d) System IV, CTAC[thin space (1/6-em)]:[thin space (1/6-em)]SDS = 2[thin space (1/6-em)]:[thin space (1/6-em)]1. (e) System V, CTAC[thin space (1/6-em)]:[thin space (1/6-em)]SDS = 1[thin space (1/6-em)]:[thin space (1/6-em)]1. (f) System VI, CTAC[thin space (1/6-em)]:[thin space (1/6-em)]SDS = 1[thin space (1/6-em)]:[thin space (1/6-em)]2. (g) System VII, CTAC[thin space (1/6-em)]:[thin space (1/6-em)]SDS = 1[thin space (1/6-em)]:[thin space (1/6-em)]3. (h) System VIII, CTAC[thin space (1/6-em)]:[thin space (1/6-em)]SDS = 1[thin space (1/6-em)]:[thin space (1/6-em)]5. (i) System IX, CTAC[thin space (1/6-em)]:[thin space (1/6-em)]SDS = 0[thin space (1/6-em)]:[thin space (1/6-em)]6.

In order to understand the processes of mixed surfactant self-assembly in aqueous solution, the evolution of the number of clusters (N) and max. cluster size (Nm) at different ratios were calculated as shown in Fig. 3. N and Nm were collected during 1 μs simulation and the flat line at each end of these curves demonstrated that our simulation systems were close to equilibrium. As shown in Fig. 3(a), N decreases sharply to a relatively stable value in the simulation process, which shows that clusters gather rapidly at first. In addition, Nm also shows a sudden increase in the initial stage. The evolution of Nm can be further divided into three stages, depending on the increase rate and number. In this first stage, Nm almost increases sharply, since randomly scattered surfactant molecules quickly gather into small clusters due to the hydrophobic effect of surfactant tails, and it only takes about 50 ns. In the second stage, Nm increases, which is owing to the fusion of small micelles. This stage lasts several hundred nanoseconds until the curve becomes flat, which is much longer than the first stage because the fusion of micelles needs a longer time than molecule aggregation. The final stage is the flat part of the curve, in which the system achieved “quasi-equilibrium”. Therefore, from this microscopic point of view, we think that the self-assembly of surfactants starts with the aggregation of molecules, followed by the formation and fusion of micelles.


image file: c5ra26051e-f3.tif
Fig. 3 Evolution of the number of clusters (a) and max cluster size (b) at different ratios. I to IX are the same as Fig. 2.

Compared with the equilibrium morphologies of surfactant aggregates at different CTAC/SDS ratios, not only the shapes of aggregates vary, but the numbers of aggregates are also different. Table 1 shows the number of clusters (N) and max cluster size (Nm) at different surfactant ratios. N and Nm changed significantly in different mixed surfactant systems. In system I, eight spherical aggregates were formed in cationic surfactant CTAC aqueous solution. When a little SDS was added to the cationic surfactant aqueous solution as shown in system II, N was reduced to 2, and Nm sharply increased to 408, which means that the aggregates that do form grow relatively large. As the ratio of CTAC/SDS reduced to 3[thin space (1/6-em)]:[thin space (1/6-em)]1, there was no change in N, while Nm increased to 528. When the ratio of CTAC/SDS was 2[thin space (1/6-em)]:[thin space (1/6-em)]1 or 1[thin space (1/6-em)]:[thin space (1/6-em)]2, all surfactants aggregated into disc-like micelles. In system V, where the number of cationic surfactants was equal to that of anionic surfactants, we got the unique morphology-vesicle, and all surfactants were self-assembled into a single vesicle. If the SDS content was increased continually, N increased to 2 and Nm decreased to 521 in system VII. From system VI to IX, with increasing SDS quantity, Nm became fewer and N was more. When there was only anionic surfactant SDS in system IX, six micelles were obtained. Thus, it was concluded that the ratio of cationic surfactants and anionic surfactants is a significant factor impacting surfactant self-assembly. We speculate that the electrostatic interaction between anionic surfactants and cationic surfactants leads to the behaviour of micellar aggregation. In the following, the process of the vesicle formation will be discussed in detail and the formation mechanism of the vesicles is analyzed from the view of charge distribution.

Table 1 The numbers of clusters (N) and max cluster sizes (Nm) at different surfactant ratios
System I II III IV V VI VII VIII IX
CTAC/SDS 6[thin space (1/6-em)]:[thin space (1/6-em)]0 5[thin space (1/6-em)]:[thin space (1/6-em)]1 3[thin space (1/6-em)]:[thin space (1/6-em)]1 2[thin space (1/6-em)]:[thin space (1/6-em)]1 1[thin space (1/6-em)]:[thin space (1/6-em)]1 1[thin space (1/6-em)]:[thin space (1/6-em)]2 1[thin space (1/6-em)]:[thin space (1/6-em)]3 1[thin space (1/6-em)]:[thin space (1/6-em)]5 0[thin space (1/6-em)]:[thin space (1/6-em)]6
Number of clusters (N) 8 2 2 1 1 1 2 2 6
Max cluster size (Nm) 106 408 528 600 600 600 521 343 216

3.2. The process of vesicle formation

Experimentally, the spontaneous formation of vesicles is too fast to be observed, and it is hard to record this procedure even with some precise instruments. By contrast, molecular dynamics simulation is a powerful tool to present the process of vesicle formation directly and clearly, as shown in Fig. 4.
image file: c5ra26051e-f4.tif
Fig. 4 Snapshots of vesicle self-assembly processes at different times.

Fig. 4 shows snapshots of the morphologies at different times. The process of vesicle formation shows three stages: the first is the nucleating stage, in which surfactant molecules aggregate to form small clusters and this stage only lasts a short time, about 20 ns. In the second stage, small micelles fuse into bilayer disk-like aggregates, and this lasts for a longer time than the first stage. Then, bilayer disk-like aggregates curl up into closed vesicles in the final stage. The duration of curling is about 30 ns, as shown in Fig. 4, which means that once the disk-like micelles formed, the vesicles soon turn out via curling. After that, the vesicles are kept at the steady state. Throughout the whole process, the fusion of micelles in the second stage takes the most time.

The self-assembly process for surfactants is always accompanied a change in energy. In order to understand this procedure, the energy of these systems was calculated. As shown in Fig. 5, the black line presents the system energy with time, which shows a clear downward trend, and the red line is the evolution of max cluster size (Nm) during simulation. In the fusion stage, the change in system energy also is shown as a “ladder”, which is consistent with the change in Nm. This means that the occurrence of fusion always goes with the decrease in energy. In the curling stage, the energy maintains a stable development until the end. We therefore think that the bilayer–vesicle transition is driven by entropy, and further analysis will be presented in the following.


image file: c5ra26051e-f5.tif
Fig. 5 Comparison diagram between system energy and max. cluster size at the ratio CTAC[thin space (1/6-em)]:[thin space (1/6-em)]SDS = 1[thin space (1/6-em)]:[thin space (1/6-em)]1.

To get further information about vesicles, the cross-sections of vesicles and the radial distribution functions (RDFs) of each group of surfactant and water as a function of distance from the vesicle's mass centre are shown in Fig. 6. Intuitively, the head groups at the inner surface are more compact than those at the outer surface (Fig. 6(a)). More quantitatively, the numbers of cationic and anionic surfactants are 62 and 66 in the inner, and 238 and 234 in the outer leaflets of the vesicle, respectively. The peaks of the head groups are found to be 1.7 nm and 4.1 nm for the inner and outer leaflets of the vesicle (Fig. 6(b)), respectively. Thus, the surface areas per head group are 0.28 nm2 and 0.45 nm2, respectively. The head group of the inner and outer leaflets have a different compactness due to the formation process of vesicles via the curling of bilayer disk-like micelles.


image file: c5ra26051e-f6.tif
Fig. 6 (a) A schematic representation of the structure of a vesicle. (b) The radial distribution functions g(r) of Q0, Qa, C1, C2 and water beads as a function of distance from the vesicle's center of mass.

3.3. The mechanism of vesicle formation

Interestingly, the vesicle is formed by the curling of the bilayer disk-like aggregate, which is an intermediate morphology during the formation of the vesicle. To analyze the mechanism of vesicle formation, the evolution of the total energy in the process of the bilayer–vesicle transition is plotted in Fig. 7. As seen in the figure, the total energy is slightly increased, which means that the bilayer–vesicle transition is driven by energy minimization of the bilayer's edge. Markvoort et al. reported that the transition is driven by entropy,45 and the entropy increase during the transition is due to the decrease of the effective excluded volume, which is similar to what occurs for helix formation.46 This conclusion is borne out by the reduction of the solvent accessible surface area (SASA) (Fig. 7), which multiplied by the excluded radius, is proportional to the excluded volume, as shown in the embedded diagram of Fig. 7.
image file: c5ra26051e-f7.tif
Fig. 7 The evolution of the total energy (black line) and the solvent accessible surface area (SASA) (blue squares) in the process of bilayer–vesicle transition, and the total energy processed by the linear regression (red line). The embedded diagram is the sketch map of the excluded volume (V) and excluded radius (r).

Since the driving force for the bilayer–vesicle transition is entropy, it was confusing that the bilayer disk-like aggregates in the systems III, V, VI, and VII did not curl into vesicles, even when the simulation time was extended. We therefore set out to determine what the resistance force was for the transition. We determined that the bending energy of the bilayer47 is the resistance force and the electrostatic repulsion interactions play a very important role. In order to make this clear and easy to be analyzed, we designed a pre-assembled bilayer disk-like aggregate, with a diameter of approximately 120 Å, as shown in Fig. 8; the length of the sides of the box was 200 Å. There were 59[thin space (1/6-em)]400 W beads and 6600 antifreeze particles (BW beads, colored in green). The total number of surfactants was 600. The pre-assembled aggregates contained three different proportions of CTAC and SDS, 3[thin space (1/6-em)]:[thin space (1/6-em)]1, 1[thin space (1/6-em)]:[thin space (1/6-em)]1, 1[thin space (1/6-em)]:[thin space (1/6-em)]3. In these initial configurations of bilayer disk-like aggregates, CTAC and SDS were arranged randomly. The simulation parameters were the same as those in the first section, except that the total simulation time was 500 ns.


image file: c5ra26051e-f8.tif
Fig. 8 (a) The pre-assembled structure of a disk-like bilayer membrane (the green points are water beads); (b) the top view of the disk-like bilayer membrane; (c) the side view of the disk-like bilayer membrane.

Fig. 9 shows the equilibrium morphology of the pre-assembled disk-like bilayer membrane at three different ratios. They are disk-like bilayer, vesicle, disk-like bilayer, as the ratio changes from 3[thin space (1/6-em)]:[thin space (1/6-em)]1, 1[thin space (1/6-em)]:[thin space (1/6-em)]1 to 1[thin space (1/6-em)]:[thin space (1/6-em)]3, respectively. As we have seen, the pre-assembled equilibrium morphologies consisted of self-assembled morphologies, which demonstrated the rationality of the pre-assembly method. Among these equilibrium morphologies, vesicles were only formed at the ratio of 1[thin space (1/6-em)]:[thin space (1/6-em)]1. The disk-like bilayer membranes were divided into several parts to study the effect of different molar fractions of surfactants on vesicle formation. A segmentation map of disk-like bilayer membranes is shown in Fig. 10. A disk-like bilayer with radius of 76 Å was divided into a cylinder with 19 equal intervals of concentric cylinders. Fig. 10(a) shows the top view, and Fig. 10(b) shows the side view of the segmentation map. The red cross is the center of the disk-like bilayer, the red line shows the central axis, and the yellow lines express the cylinder segmentation. In order to reveal the difference among these three disk-like bilayers, we compared the mole fractions of the two surfactants at different concentric cylinders.


image file: c5ra26051e-f9.tif
Fig. 9 The equilibrium morphology of the pre-assembled disk-like bilayer membrane at different ratios. (a) The ratio of CTAC/SDS is 3[thin space (1/6-em)]:[thin space (1/6-em)]1 (b) the ratio of CTAC/SDS is 1[thin space (1/6-em)]:[thin space (1/6-em)]1 (c) the ratio of CTAC/SDS is 1[thin space (1/6-em)]:[thin space (1/6-em)]3.

image file: c5ra26051e-f10.tif
Fig. 10 Segmentation map of the disk-like bilayer membrane. (a) The top view of the segmentation map. (b) The side view of the segmentation map.

We defined a parameter R to represent the mole fraction of SDS at each part. The relationship is as follows,

 
image file: c5ra26051e-t1.tif(1)
where NSDS and NCTAC are the numbers of SDS and CTAC in each part, respectively. We extracted the mole fraction of SDS at different disk-like bilayer membrane sections for different CTAC/SDS aggregates at different times, as shown in Fig. 11. The x-axis represents the distance to the central axis of the disk-like bilayer and the y-axis is the mole fraction of SDS. The visual process of the change of the mole fraction with the morphological transformation was acquired.


image file: c5ra26051e-f11.tif
Fig. 11 The evolution of the mole fraction of SDS at different disk-like bilayer membrane sections for different CTAC/SDS aggregates. (a) The ratio of CTAC/SDS is 3[thin space (1/6-em)]:[thin space (1/6-em)]1, (b) the ratio of CTAC/SDS is 1[thin space (1/6-em)]:[thin space (1/6-em)]1 and (c) the ratio of CTAC/SDS is 1[thin space (1/6-em)]:[thin space (1/6-em)]3.

Fig. 11(a) shows the evolution of the mole fraction at the ratio of 3[thin space (1/6-em)]:[thin space (1/6-em)]1. In the initial situation, the distribution of SDS in each section is homogeneous and the mole fraction remained at around 0.25 as shown in Fig. 11(a) by the black line. As time went on, the mole fraction of SDS in the center region rose to 0.5, while R near the edge of the disk-like bilayer remained at around 0.25. This was because the positively charged SDS and negatively charged CTAC attracted each other to form ion pairs, and they tended to gather in the center to lower the energy of the system. This rearrangement maintained the stability of the structure, while the excess CTAC was located in the edge region and did not form ion pairs. Thus, outer cylinders were positively charged to prevent the curling of the bilayer into a vesicle, so the electrostatic force played a significant role in the surfactant distribution and aggregate shape. In Fig. 11(b), the mole fraction of SDS was about 0.5 at the ratio of 1[thin space (1/6-em)]:[thin space (1/6-em)]1, and it was maintained at 0.5 during the whole simulation. This means that the disk-like bilayer membrane was in a neutral morphology before the vesicle was formed. The same quantity of SDS and CTAC made all surfactants form ion pairs. In Fig. 11(c), the evolution was similar to Fig. 11(a). Ion pairs were formed near the center, and excess SDS gathered in the edge region. The non-uniform distribution of excess surfactants was attributed to the initial maldistribution of headgroups (Fig. 12), which are denser in the central zones of the bilayer than in the edge regions. In this situation, the excess surfactants were much more vulnerable to gathering in the edge regions, due to the electrostatic repulsion effect, so the disk-like bilayer membrane was negatively charged. Eventually, we got three different disk-like bilayer membranes. While only the uncharged disk-like bilayer at the ratio of 1[thin space (1/6-em)]:[thin space (1/6-em)]1 could form vesicles, it verified that preventing electrostatic repulsion played an important role in the process of preventing the disk-like bilayer from curling into a vesicle.


image file: c5ra26051e-f12.tif
Fig. 12 The initial distribution of head groups. The head groups are displayed by the quicksurf method.

The disc-like bilayers formed in the systems III, IV, VI and VII did not curl into vesicles and electrostatic repulsion interactions played a key role. If the system is given enough surfactants, the bending energy and electrostatic repulsion interactions would be reduced and the disk-like bilayer could potentially be curled into vesicles. To illustrate this, a pre-assembled bilayer disk-like aggregate with more surfactants (N = 1200) was constructed and the proportions of CTAC and SDS were 3[thin space (1/6-em)]:[thin space (1/6-em)]1, 2[thin space (1/6-em)]:[thin space (1/6-em)]1, 1[thin space (1/6-em)]:[thin space (1/6-em)]2; and 1[thin space (1/6-em)]:[thin space (1/6-em)]3. The larger bilayers were converted into vesicles when the proportions were 2[thin space (1/6-em)]:[thin space (1/6-em)]1 and 1[thin space (1/6-em)]:[thin space (1/6-em)]2, but the proportions of 1[thin space (1/6-em)]:[thin space (1/6-em)]3 or 3[thin space (1/6-em)]:[thin space (1/6-em)]1 were not (data not shown). Hence, we obtained the following main results: firstly, in the process of bilayer–vesicle transition, the increase of entropy, which originated from the excluded volume overlapping itself, is the driving force. Secondly, the bending energy of the bilayer, in which preventing the electrostatic repulsion plays an important role, is the resistance force.

4. Conclusions

Cationic (CTAC) and anionic (SDS) surfactant aqueous mixture systems self-assembled into different morphologies of aggregates at different ratios. CG molecular simulation was used to investigate the formation of these aggregates, especially the vesicle formation, in detail. Our simulation results showed that the number and shapes of aggregates varied with different ratios of CTAC and SDS. When the number of CTAC was equal to SDS, we got vesicles formed by bilayer disk-like micelles, but not all disk-like bilayer membranes could curl into vesicles; it was closely related to the distribution proportion of SDS and CTAC. The mechanism of vesicle formation was analyzed and entropy was found to be the driving force, and the bending energy of the bilayer was the resistance force. Compared with the distribution of cationic (CTAC) and anionic (SDS) surfactants in the different parts of the disk-like bilayer, we found that the charge distribution had an important effect on vesicle formation. The same amount of cationic and anionic surfactants was beneficial to achieving a neutral structure; the non-equilibrium proportioned mixtures were more inclined to form a charged body, which went against curling into vesicles. In this work, we studied the formation mechanism of vesicles mainly from the point of view of the charge distribution. These simulation results brought to light new views on the understanding of vesicle formation, apart from the microscopic view. This is expected to generate further simulation studies on the explanations of vesicle formation and vesicle fusion. Further studies would be conducive to the development and application of the vesicles.

Acknowledgements

This work was supported by the National Program on Key Basic Research Project of China (2015CB250904), the Natural Science Foundation of Shandong Province (ZR2014EEM035), the Outstanding Innovation Team of China University of Petroleum (East China) (2015020008), the Fundamental Research Funds for the Central Universities (15CX02063A, 15CX05049A), China University of Petroleum (East China) start-up funding (2014010577).

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