A Dissipative Particle Dynamics Study - ACS Publications - American

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Phase Behavior of an Amphiphilic Block Copolymer in Ionic Liquid: A Dissipative Particle Dynamics Study Junlin Mai, Delin Sun, Libo Li, and Jian Zhou* School of Chemistry and Chemical Engineering, Guangdong Provincial Key Laboratory for Green Chemical Product Technology, South China University of Technology, Guangzhou 510640, P. R. China ABSTRACT: We systematically investigated the self-assembly behavior of poly(1,2-butadiene)-b-poly(ethylene oxide) (PB-bPEO) block copolymer in [Bmim][PF6] ionic liquid (IL) via dissipative particle dynamics simulations. An expanding scope of nanostructures, such as spherical micelles, rodlike micelles, entangled cylinders, sheets, branched lamellae, lamellae, platelets, tubes, and IL microphase structures, was observed under different polymer concentrations and polymer block ratios. When the polymer concentration was lower than 30 vol %, self-assembled morphologies transformed from spherical to rodlike or sheetlike micelles as the fraction of PEO block decreased. When the copolymer concentration was higher than 30 vol %, new morphologies such as wormlike micelles and branched lamellae emerged. Platelet and tube nanostructures were obtained when the concentration of PEO was lower than 10 vol %. In addition, lamellae structure was observed, represented as a triangular area in the phase diagram, and the IL microphase nanostructure appeared in the bottom right of the phase diagram. These various nanostructures observed in our study suggest a universal mechanism for the self-assembly of amphiphiles in given solvents. ([BMIM] [PF6]).17,18 It is speculated that the behavior of amphiphilic molecules in ionic liquid and that in water might be different. In fact, increasing numbers of experimental papers have investigated the phase behavior of ABCs in ILs. He et al.17 found that four kinds of amphiphilic poly(1,2-butadiene)-bpoly(ethylene oxide) (PB-b-PEO) diblock copolymers aggregated and formed different micelle structures in [BMIM][PF6], as observed by cryogenic transmission electron microscopy. Bennett et al.19 found that [emim]NTf2 additives tuned the domain size and different morphologies of polystyrene-bpoly(methyl propionate) (PS-b-PMMA) in water. Chen et al.20 studied the self-assembly of PEO-PPO-PEO (P123) in water/ ethylammonium nitrate (EAN) and methanol/EAN binary solvents. They found that, compared to the structure of representative system EAN, the EAN/water binary solvent did not affect the phase formation very much whereas EAN/ methanol did because of the difference of solubility in cosolutions. Madhavan et al.21 studied polystyrene-b-poly(4vinylpyridine) (PS-b-PV4P) as a film matrix by introducing different ionic liquids as additives and investigated the effect of IL on the film’s structure. Their results showed that nonprotic ionic liquids facilitated the formation of hexagonal nanoporous

1. INTRODUCTION The water-mediated self-assembly of amphiphilic molecules into various nanostructures and mesostructures, e.g., the formation of cell membranes and misfolded protein fibrillation, is a fundamental process in nature. Inspired by nature, selfassembly has been applied in many industrial fields, including microreactors,1 drug delivery,2 separation,3 dispersant technology,3 and nanolithography.4 Hence, thoroughly understanding the underlying force that determines the self-assembled structures is vital to designing new materials and nanodevices. Amphiphilic block copolymers (ABCs) are a class of functional materials that have attracted enormous attention in fabricating novel electronics and pharmaceutical delivery vehicles. The diversities of the building blocks make ABCs ideal candidates for investigating the effect of polymer compositions on the self-assembled morphology.5,6 The selfassembly process of ABCs in water is mainly driven by hydrophobic interactions,7 and the presence of cosolvent in water has considerable effect on the hydrophobic interactions and the resulting self-assembled morphology. Ionic liquids (ILs) are novel solvents with many attracting chemo-physical properties such as excellent ion conductivity, high thermal or electrochemical stability, and negligible vapor pressure, which have been widely used in many fields.8−14 Recently, ILs have been exploited to act as a medium for the self-assembly of biomolecules, polymers, and nanoparticles.15 Unlike water, the structure of ILs is usually heterogeneous on the nanoscale.16 Computer simulations and experimental studies have reported microphase separation phenomena for pristine ionic liquids such as 1-butyl-3-methylimidazolium hexafluorophosphate © XXXX American Chemical Society

Special Issue: Proceedings of PPEPPD 2016 Received: June 23, 2016 Accepted: October 17, 2016

A

DOI: 10.1021/acs.jced.6b00522 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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where Cs is the dimensionless spring constant between beads i and j, set to 4. In the DPD method, the interaction is a soft potential and beads have a probability to overlap in space. The charge must be spread out over a finite volume using a smearing charge distribution to avoid the collapse of beads on top of each other. We adopted the Slater-type distribution

structure whereas protic ILs led to membranes with lamella structures. Despite increasing attention on using ILs for copolymer selfassembly, theoretical studies have been rarely reported.22 It is thus imperative to explore the molecular details by using molecular simulations. Through extensive simulations, a deep understanding of the patterns and factors influencing the selfassembly process can be obtained, which has significant implications for relevant experiments carried out in the future. In the present work, we used dissipative particle dynamics (DPD) simulations to explore the phase behavior of amphiphilic polymer PB-b-PEO and ionic liquid [BMIM][PF6] mixtures.

f (r ) =

( 2r )

exp − λ .27 The electrostatic force between beads

i and j is described as FijE =

Γqiqj 4πr 2 ij

[1 − exp(− 2βrij)(1 + 2βrij(1 + βrij))]riĵ (7)

where Γ = e2/(kBTε0εrRc), elementary charge e = 1.602176565 × 10−19 C, permittivity of vacuum ε0 = 8.854187817 × 10−12 F· m−1, εr is the relative permittivity of the medium, q is the charge number, β = 5rc/8λ, and λ is the decay length of the charge. 2.2. Coarse-Grained Models. The CG models for [Bmim][PF6] and PB-b-PEO are illustrated in Figure 1. PB-

2. METHOD AND MODEL 2.1. DPD Method. DPD is a coarse-grained (CG) method for modeling complex multiphase systems. It was first introduced by Hoogerbrugge and Koelman,23 and later improved by Groot et al.24−26 In the CG system, one DPD bead can represent a group of atoms or even several molecules. Similar to molecular dynamics simulations, the time evolution of particles is governed by Newton’s equations of motion, dri dv = vi, mi i = fi dt dt

q πλ 3

(1)

where ri, vi, mi, and fi are the position, velocity, mass, and force of bead i, respectively. The DPD method uses the reduced unit, and the mass of bead is set to 1. The force fi acting on bead i can be described via conservative force FCij representing the excluded volume effect, the dissipative force FDij representing vicious drag, the random force FRij representing the stochastic impulse, spring force FSij, and the electrostatic force FEij as24,26 fi =

∑ (FCij + FijD + FijR + FSij + FijE) i≠j

(2)

Figure 1. Schematic illustration of molecular structures and coarsegrained models for PB-b-PEO and ionic liquid [Bmim][PF6].

The interaction between the DPD beads is determined by cutoff radius reduced unit Rc, and Rc is set to 1. Specifically, the first three forces are determined by the positions and velocities of beads i and j, as given by ⎧ ⎪ aij(1 − rij)riĵ (rij < 1) FCij = ⎨ ⎪ 0 (rij ≥ 1) ⎩

(3)

FijD = −γωD(rij)(riĵ ·vij)riĵ

(4)

FijR = σωR (rij)θijriĵ

(5)

b-PEO copolymers are composed of two kinds of beads, B and O. Beads B represent hydrophobic poly(1,2-butadiene), and beads O represent hydrophilic poly(ethylene oxide). The CG model is represented by BO(x−y). In BO(x−y), x is set to fixed value 7 while y is varied. [Bmim][PF6] is modeled by three beads P1, P2, and N. Bead P1 represents a hydrophobic alkyl chain, bead P2 represents a charged imidazolium, and bead N represents a PF6 anion. The CG scheme ensures that different beads have similar volume while the molecular topology is maintained. An important parameter in DPD simulation is dimensionless aij. Groot and Warren established a link between aij and Flory− Huggins parameter χij by mapping the DPD model onto Flory−Huggins theory. aij can be obtained via aij = aii + 3.27χij , ρDPD = 3 (8)

where aij is the repulsive parameter between two beads, rij = ri − rj, rij = |rij|, r̂ij = rij/|rij|, γ is the friction parameter, σ is the noise parameter, and θij is a randomly fluctuating variable with a Gaussian static and mean value of 0. ωD(rij) and ωR(rij) are weighting functions satisfying ωD(rij) = [ωR(rij)]2 = (1 − r/ Rc)2, σ2 = 2γkBT, kB is Boltzmann’s constant, kB = 1.3806488 × 10−23 J·K−1, and T is the thermodynamic temperature. In DPD simulation, kBT is chosen as the reduced unit of energy. In our simulation systems, the value of γ is set to 4.5 and σ is set to 3.24 The spring force between two adjacent beads of a certain molecule is expressed as FSij =

∑ Cs rij

where ρDPD is the number density of beads, i.e., the number of beads per unit of volume in a DPD simulation. aii is a dimensionless repulsive parameter between the same beads. For ρDPD = 3, aii is set to 25 on the basis of the compressibility of a pure liquid. We used aii = 25 as the value of the repulsive parameter between the same beads in this work. For binary components i and j, χij can be obtained through calculating the mixing energy between two molecular fragments,

(6) B



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⎛ E − 1 (E + E ) ⎞ ij jj 2 ii ⎟ χij = z⎜⎜ ⎟ RT ⎝ ⎠

interactions, electrostatic cutoff Rele c = 3, real-space convergence parameter α = 0.975, and reciprocal space (k-vector) range nmax = (5, 5, 5). A step size of Δt = 0.05τ was employed, where τ = 1 is the DPD reduced time unit.25 We judged the equilibrium of the system by observing the change in total energy over time in simulations. Different simulations require different times to reach equilibrium, and the longest simulation time was a total of 1 000 000 steps. All DPD simulations in this work were performed with the DL_MESO 2.5 package.30

(9)

where z is the coordination number, Eij is the mixing energy of a particular ij pair, R is the ideal gas constant, and T is the thermodynamic temperature. The Flory−Huggins parameters for eq 9 can be calculated by the Blends module in Materials Studio 7.0 with the model by Fan et al.28 To obtain a reasonable value, the averaged mixing energy of each pair was calculated with 2 000 000 samples by the Monte Carlo method. Table 1 shows DPD interaction parameter aij between different beads at 298 K.

3. RESULTS AND DISCUSSION 3.1. Assessment of the DPD Model in Predicting Copolymer Self-Assembly Structures in Ionic Liquids. To the best of our knowledge, this work represents the first simulation study to investigate the self-assembly behavior of block copolymers in ionic liquids. Thus, we validate the coarsegrained DPD models herein before discussing the selfassembled nanostructures observed in this work. Experimentally, the self-assembly of PB-b-PEO in [BMIM][PF6] ionic liquid was reported by He et al.17 It was found that the proportion of the PEO block had considerable effects on the self-assembled morphology. To be specific, the nanostructures would transform from spherical micelles to wormlike micelles and bilayered vesicles. In our simulations, we have systematically investigated the influence of the polymer concentration and PB/PEO (B/O) block ratio on the selfassembled nanostructures. The observed ternary phase diagram is shown in Figure 2. The phase diagram shows that when the polymer concentration is lower than 30 vol % the polymer forms a micelle structure in the ionic liquid, with structures determined by the polymer B/O ratio. The lines starting from

Table 1. DPD Repulsive Parameters aij of PB-b-PEO and [Bmim][PF6] at 298 K B O P1 P2 N

B

O

P1

P2

N

25 40.06 35.12 53.54 35.83

25 26.6 40.02 26.76

25 52.54 25.55

25 52.15

25

DPD simulations were carried out in a cubic box of 40Rc × 40Rc × 40Rc. The NVT ensemble and periodic boundary condition were applied. A Slater-type approach27 was used to treat electrostatic interactions. The relative permittivity εr of ionic liquid [Bmim][PF6] was set to 14.0,29 Γ = e2/(kBTε0εrRc) = 70.88, and β was dimensionless and was set to 0.929.27 The Ewald sum approach was used in long-range electrostatic

Figure 2. Ternary phase diagram in vol % and corresponding structures at 298 K by DPD simulations. Blue, PB beads; red, PEO beads; and yellow, [Bmim][PF6] beads. The concentration unit of the phase diagram is volume fraction (vol %). C



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the point in the lower-left corner represent different block ratios in the ternary phase diagram. As the length of the PEO fragment decreased, the self-assembled structure changed from spherical to rodlike micelles and then to double-layer vesicles. This trend is in excellent agreement with the experimental results reported by He et al.,17 suggesting that our coarsegrained DPD models are appropriate to describe the complex phase behavior of block copolymer in ionic liquids. In the following sections, we will discuss the morphologies shown in Figure 2 in more details. 3.2. Spherical Micelles and Vesicles. Spherical micelles are the most frequently observed structure during the selfassembly process, as Figure 3a,b shows. In the spherical micelle

Figure 4. Radial density profiles of spherical micelles and vesicles. The abscissa is the distance from the center of the sphere position (length of a DPD unit), and the ordinate is the number density (number of beads per unit volume) of the particles in that position.

and outer shell radius rout‑shell, respectively. Figure 4 shows that the number density of inner layers is higher than that of the outer layer. rin‑shell is 3, rout‑shell is 7, and thus the thickness of the shell is 4. We believe that inner PEO is mutually squeezed because the vesicles are small. With the increase in the diameter of the vesicles, the difference between the internal and external number densities decreases. 3.3. Rodlike and Wormlike Micelles. When the polymer concentration increases and the length of PEO is reduced, rodlike micelles form through the aggregation of spherical micelles, as Figure 5a illustrates. At low polymer concen-

Figure 3. Mesoscopic structures of PB-b-PEO in 90 vol % [Bmim][PF6] with different block ratios of PB to PEO. Blue, PB beads; red, PEO beads; and yellow, [Bmim][PF6] beads.

structure, the PB segment forms the core and the PEO segment forms the shell. Spherical micelles do not contact others because of the repulsions between the shells of PEO, and they are homogeneously distributed in the ionic liquid. The determining factor in forming a spherical micelle structure is the B/O ratio. According to the ternary phase diagram, this structure is dominant when the B/O block ratio is greater than 1. As the polymer concentration is increased, copolymers have a tendency to transform to a more continuous phase. To maintain the stability of the spherical micelle structure, an increase in the PEO ratio is required. It was found from Figure 2 that spherical micelles are mainly distributed in the phase diagram when the PB ratio is less than 18 vol %. The double-layered vesicle structure can also be formed under certain circumstances. As is shown in Figure 3c, the inner and outer parts of the vesicle are PEO, and the middle part is PB. By analyzing the phase diagram, the vesicular structure can be formed only at lower polymer concentrations (ratio of PB-bPEO < 10 vol %) and when the PEO block ratio is less than 0.38. When the block ratio of PEO become smaller, other impurity micelles will gradually form. We analyzed the size of the self-assembled structure. Figure 4 shows radial density profiles of spherical micelles and vesicles. In DPD simulations, the number density was set to 3. By comparison, it is clear in identifying the compatibility of different blocks with solvent. The number density of PB is higher than that of PEO, showing that the polymer chains of PEO are in an extended state in [Bmim][PF6]. In spherical micelles, we define that the horizontal axis of the cross-point of curves for PB and PEO is the average radius of core rcore and the horizontal axis on which the PEO curve begins to fall close to zero is the mean radius of the shell, rshell. The core radius rcore of spherical micelles BO(7−12) is 3 (length in DPD units, the same as below), and the outer radius rshell is 7. Vesicles BO(7−2) also define that the two horizontal axes of intersection for PB and PEO are inner shell radius rin‑shell

Figure 5. Mesoscopic structures of rodlike and wormlike micelles for PB-b-PEO in [Bmim][PF6]. Blue: PB beads; red: PEO beads; IL was not shown for the sake of clarity.

trations, PB-b-PEO is prone to self-assemble into rodlike structure when the B/O ratio is less than 1. However, at high copolymer concentrations, the structures are mainly determined by the length of PB. In fact, rodlike micelles may be of the strip form with a certain degree of flexibility. This work focuses on whether it is a cross-linked structure. Therefore, we called the rodlike and striplike micelles non-cross-linked micelles. Control of the growth of wormlike micelles has been reported.31−33 As Figure 5b,c shows, wormlike micelles are onedimensional, nonaxial, flexible, and cross-linked. In experiments, wormlike micelles were used as a template to synthesize fibrous mesoporous materials.34 By the analysis of the phase diagram, it was found that only if the B/O ratio reaches 50 vol % do the wormlike structures appear with a PB ratio of between 25 and 50 vol %, suggesting that the formation conditions of the wormlike structure are determined by the copolymer/block ratio. In Figure 5b,c, the concentrations of copolymer are similar but different in B/O ratio. At the same polymer concentration, the length of the PEO block is an important factor affecting the formation of wormlike micelles; as the block ratio of PEO decreases, the degree of cross-linking increases. The micelles can be formed as a network structure suitable for the use of porous template materials. D



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Figure 6. Time evolution of morphologies in the self-assembly process for wormlike micelles (BO(7−5), 37 vol % IL). Blue, PB beads and red, PEO beads. IL was not shown for the sake of clarity.

Figure 7. Time evolution of morphologies in the self-assembly process of sheets (BO(7−4), 90 vol % IL). Blue, PB beads and red, PEO beads. IL was not shown for the sake of clarity.

Because of the high concentration (PB-b-PEO > 50 vol %), PB-b-PEO copolymers readily form a continuous phase. Hence, the growth of wormlike micelles is different from that of rodlike micelles in terms of the formation mechanism. Figure 6 shows the time-dependent self-assembly process for wormlike micelles. Figure 6a shows that PB-b-PEO polymers are randomly dispersed in ionic liquid. After 800 time steps, copolymers begin to self-assemble into a cross-linked structure quickly (Figure 6b). After 40 000 time steps, copolymers selfassemble into the wormlike structure in Figure 6c and finally yield the cross-linked structure shown in Figure 6d. 3.4. Sheets and Branched Lamellae. Sheets are represented by bilayer structures. The inner layer is a PB block, and the outer layer is a PEO block. By an analysis of the ternary phase diagram, it is found that the main factor leading to the formation of this structure is the ratio of PB. The selfassembly process of the BO(7−4)/90 vol % IL system is shown in Figure 7. After 60 000 time steps, the PB-b-PEO copolymer forms spherical micelles as shown in Figure 7a). After a long DPD simulation time (390 000 time steps), copolymers form linear rodlike micelles, as shown in Figure 7b. At 400 000− 410 000 time steps, when the micelle (red circled) approaches the rodlike micelle (blue circle), they make contact but do not fuse, as shown in Figure 7c,d. After two micelles are separated, i.e., at 420 000−430 000 time steps, the attacking micelle (red circle) induces the rodlike micelle to deform and begins to bend in order to increases the contact area with the attacking micelle, as shown in Figure 7e,f. After the attacking micelle adjusts the position, it contacts the micelles again and finally

fuses with the micelle after 500 000 time steps, as shown in Figure 7g,h. The sheet structure overlapped, and finally a branched lamellae structure formed. In this case, the concentration of copolymers ranges from 30 to 70 vol %. As the concentration increases, structures of branched lamellae become more complex, as shown in Figure 8. The PB block forms the

Figure 8. Mesoscopic structures of branched lamellae for PB-b-PEO at different [Bmim][PF6] concentrations. Blue, PB beads and red, PEO beads. IL was not shown for the sake of clarity.

internal structure, whereas the PEO block constitutes the outer structure. Compared to sheets, there are obvious folds on the branched lamellae. Although the concentration is not extremely high, the formation mechanism is similar to that of wormlike micelles. 3.5. Lamellae. Lamellar structures are characterized by twodimensional extension and long-range order. The amphiphilic block units in copolymers and a simple topology are conducive E



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Figure 9. Time evolution of morphologies in the self-assembly process leading to the lamellae structure. Blue, PB beads and red, PEO beads. IL was not shown for the sake of clarity.

to the formation of ordered lamellae.35 Lamellar structures are distributed as a triangular area in the phase diagram. It appears that when the IL content is less than 50 vol %, the PB content is >40 vol % and the block ratio of PEO is >0.37. The selfassembly process of lamellae is shown in Figure 9. At high concentrations, copolymers are a continuous phase in the system. During DPD simulations, there is no sheet but only a cross-linked transition structure, as is shown in Figure 9a. The morphology then gradually transforms to the branched lamellaelike structure in which sheets are parallel to each other, as shown in Figure 9b. Eventually, the lamellar structure reaches equilibrium, forming a long-range-ordered structure after 150 000 DPD steps. Figure 10 shows the perpendicular

platelike structure will appear in the phase diagram. The platelet structure is shown in Figure 11. PEO evenly distributes

Figure 11. Mesoscopic structure of platelets for PB-b-PEO in [Bmim][PF6]. Blue, PB beads and red, PEO beads. IL was not shown for the sake of clarity.

on the surface of the platelet. Because of the amphiphilic property of PB-b-PEO, many microphase regions exist in the internal structure. Figure 12 shows the perpendicular density

Figure 10. Density profiles of PB, PEO, and IL for the lamellar structure.

density profiles of PB, PEO, and IL for lamellae. The abscissa is the distance from the reference plane (DPD units, the same as below), and the ordinate is the number density of particles in that position. From Figure 10, it is quantitatively studied with periodically layered ordered structures. The results showed that the size and structure of each layer are similar. The layer core is constituted by the PB block, the outer surface is constituted by PEO, and ionic liquid [Bmim][PF6] separates the two layers. Interestingly, the small pothole from the perpendicular density profile of PEO indicates that the layers are not perfectly overlapped, and there is a void in the area between layers. According to profiles of different components, the number density of PB is greater than the average value of 3, indicating that PB inner layers are dense. The number density of PEO is

A Dissipative Particle Dynamics Study - ACS Publications - American

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