Unraveling the Agglomeration Mechanism in Charged Block

Article pubs.acs.org/Macromolecules

Unraveling the Agglomeration Mechanism in Charged Block Copolymer and Surfactant Complexes Jose M. Borreguero,† Philip A. Pincus,∥ Bobby G. Sumpter,‡,§ and Monojoy Goswami*,‡,§ †

Neutron Data Analysis & Visualization, ‡Center for Nanophase Material Sciences, and §Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States ∥ Department of Material Science, University of California, Santa Barbara, Santa Barbara, California 93106, United States ABSTRACT: We report a molecular dynamics simulation investigation of self-assembly and complex formation of charged−neutral double hydrophilic and hydrophobic−hydrophilic block copolymers (BCP) with oppositely charged surfactants. The structure of the surfactant micelles and the BCP aggregation on the micelle surface is systematically studied for five different BCP volume fractions that also mimics a reduction of the surfactant concentration. The local electrostatic interactions between the oppositely charged species encourage the formation of core−shell structures between the surfactant micelles where the surfactants form the cores and the charged blocks of the BCP form the corona. The emergent morphologies of these aggregates are contingent upon the nature of the BCP neutral blocks. The hydrophilic neutral blocks agglomerate with the micelles as hairy colloidal structures while the hydrophobic neutrals agglomerate in lamellar structures with the surfactant micelles. The distribution of counterion charges along the simulation box shows a close-to-normal density distribution for the hydrophilic neutral blocks and a binodal distribution for hydrophobic neutral blocks. No specific surfactant concentration dependent scaling relation is observed as opposed to the simpler case of homo-polyelectrolytes.

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INTRODUCTION Since the introduction in the early 1980s, amphiphilic polymers have been synthesized in aqueous media for potential applications in optoelectronics,1 chemosensors,2 and biosensors.3 Similarly, surfactant-based systems have been used in solutions, colloids that can be found in everyday consumer products such as food additives, medicines, detergents, and cosmetics and have large-scale applications in biochemistry and biotechnology4 and drug delivery.5 The formation of various morphologies by spontaneous self-assembly of amphiphilic block copolymers (BCP) depends on a balance between the hydrophobic and hydrophilic interactions between the polymer and solvent.6−8 Recently, there have been an increased interest in amphiphilic BCP and surfactant complexes for applications in membrane technologies9 due to the increasing demand from petrochemical,10 pharmaceuticals11 and polymer electrolyte battery technologies.12,13 Cationic hydrophobic neutral block copolymers and protein coacervates have only been investigated by Fan et al.14 exhibiting steady state photonic responses. The unique combination of oppositely charged ionic−neutral BCP and surfactant complexes making it possible to form a variety of self-assembled structures. These complexes can be tuned15,16 via a large number of parameters such as the total concentration, the molecular weight of the BCP, charge ratio, backbone rigidity, ionic strength, polarity, and pH. The charged block copolymer with oppositely charged surfactants self© XXXX American Chemical Society

assembles at the nanoscale to form spherical and oblate spherical micelles, rodlike micelles, and vesicular and wormlike micelles.17,18 In a series of experimental works, Uchman et al.19,20 had shown that a surfactant induces a large variety of coassembled charged−neutral block copolymers. Most recently, it was shown that a double hydrophilic block polyelectrolyte, poly(sodium 2-sulfamate-3-carboxylisoprene) (PSCI)-blockpoly(ethylene oxide) (PEO), and cationic fluorosurfactant, N(heptadecafluorodecyl)pyridinium chloride (HFDCI), coassembled to form core−shell structures with the core formed by the PSCI/HFDCI complex and a shell of PEO blocks that were characterized by the cryo-transmission electron microscopy (cryo-TEM) and atomic force microscopy (AFM).19 Complexation of double hydrophilic block copolymer with a surfactant consisting of sodium (sulfamate-carboxylate)isoprene/ethylene oxide (SCIEO) and dodecyltrimethylammonium bromide (DTMAB) as well as quaternized poly(2-vinylpyridine) (QP2VP) was also studied by Pispas,21 exhibiting core−shell micellar structures of spherical and ellipsoid shape. Using small-angle neutron scattering, the aggregation of poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA)-block-poly(methyl methacrylate) (PMMA) hydrophobic−hydrophilic block copolymer at low concentration Received: October 26, 2016 Revised: January 12, 2017

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DOI: 10.1021/acs.macromol.6b02319 Macromolecules XXXX, XXX, XXX−XXX

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previous experiments/simulations rather than quantitative measurements. The article is organized as follows: we describe the simulation model in detail in the following section. In this section we explain the architecture and backbone charges of the BCP, the surfactants, and initial distribution of the counterions. In the Results section, we present the results, and on the basis of analysis of the potential of mean force and density distribution and various thermodynamic parameters, we detail the fundamental physics of the agglomerated structures. We conclude the article with a summary of the major findings and provide a brief discussion on potential future applications of these materials in polymer membranes and batteries.

of sodium dodecyl sulfate (SDS) surfactant has been shown to form dense PMMA core and a diffused coronal layer.22 A review of charged−neutral copolymer and surfactant selfassembly examined many different aspects of the nanoscale structure and shape of these complexes.17 Prior to examining the complex of charged−neutral BCP with a surfactant, it is reasonable to discuss polyelectrolyte− surfactant complexes in light of various simulation techniques. The self-assembly of double hydrophilic and mixed BCP, where one of the blocks is hydrophobic, has been studied extensively with dissipative particle dynamics (DPD) simulations in several recent studies. The DPD simulations were performed to investigate the coassembly of a set of amphiphilic polymers under various solvent properties, polymer architecture, and stoichiometric conditions. Posel23 et al. had shown that the dominant effect arises from the electrostatic interactions for pH-dependent self-assembly of P2VP−PEO BCPs where the slightly charged blocks form compact core−shell structures and the neutral blocks are not affected by the presence of other charge species. Furthermore, Šindelka et al. showed that the hydrophobicity of chain backbone and the presence of incompatible blocks in mixed BCP significantly affect the selfassembly of amphiphilic polymers, and the self-assembled structures range from core−shell particles to dissoluted single chain configuration.24 Very recently, the same group had performed DPD simulations to understand the electrostatic self-assembly of amphiphilic polymers in nonstoichiometric aqueous mixtures and found that the complex formation in nonstoichiometric environment differs from the stoichiometric counterpart in a variety of ways, e.g., lower association number, presence of charged core and excess free chains in nonassociated state.25 The self-assembly of mixed BCP with one hydrophobic and one polyelectrolyte block has also been studied by Lisal et al.,26 where the authors showed that the selfassembled core−shell micelles undergo massive dissociation with increasing degree of ionization of the polyelectrolyte (PE) chain. Despite these efforts to understand the agglomeration of charged−neutral BCP with surfactants, there is still a lack of comprehensive theoretical understanding of the effects of electrostatic versus entropic interactions. To address the structure−property relationship in these complexes, we investigate two sets of BCP−surfactant complexes: (i) hydrophilic neutral block and (ii) hydrophobic neutral block. The charged blocks remain the same for both systems. The presence of the charged block facilitates self-assembly of these polymer chains with surfactant micelles. The resulting agglomeration is investigated for their shape and structure. As discussed, the self-assembly of both mixed BCP and double hydrophilic systems has been studied earlier using experiment and simulation; however, surfactant-induced self-assembly of these polymers necessitates rigorous scrutiny that our work aims to provide. In this work, we have focused on probing the physics of self-assembly of a model charged BCP surfactant complex that has not been investigated either by experiments or by simulations earlier. Therefore, our central focus is a qualitative understanding of these self-assembled structures rather than quantifying these structures, even though we have compared our results with previous experimental and theoretical works wherever applicable and results are available. However, due to the lack of systematic data on surfactantmediated self-assembly of charged BCP, our best efforts relied on contrasting the fundamental trend of our simulation with

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SIMULATION METHOD We performed LAMMPS27 molecular dynamics simulations on a set of charged−neutral block copolymers (BCP) in implicit solvent following the Kremer−Grest bead−spring polymer model.28 We introduced an anionic surfactant moiety as a physically functionalizable group so that the anionic surfactants can electrostatically interact with the cationic charged blocks of the BCP. The charged−neutral BCP and surfactant models are shown in Figure 1. Two groups of 50−50 charged−neutral

Figure 1. Model system.

BCP are considered in this study: (I) hydrophobic neutral block and (II) hydrophilic neutral block, with varying BCP concentration. The BCP chain length and the charge states on the backbone of the cationic blocks are unchanged for both sets of simulations. To preserve the overall electroneutrality of the system, equal numbers of negative and positive counterions corresponding to the cationic BCP charges and anionic surfactants are incorporated into the simulation system. The surfactants are modeled as 12-mer bead−spring polymer chains with 11 tail groups and one anionic headgroup, architecturally similar to a SDS-type surfactant. The initial configurations are created from randomly generated BCP chains of chain length Nm = 60 for different concentrations of BCP chains, 1000 surfactants, and negative and positive counterions to render the system with no net charge. The BCP, surfactant, and the counterions are placed in a periodic box of volume 100 × 100 × 100σ3, where σ is the monomer diameter. The monomer sizes of the BCP, surfactant, and counterions are assumed to be the same to address the selfassembly of different species of comparable monomer sizes. For each set, as shown in Figure 1, five different systems are simulated differentiated by the total number of BCP chains given by Nc = 50, 100, 200, 300, and 400 with the charged blocks containing six cations each. The choice of these set of Nc number of chains allows us to investigate the BCP−surfactant complexes (BPSC) at different BCP volume fraction, ϕBCP, B


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Macromolecules such that the surfactant volume fraction, ϕS, is higher than, equal to, or lower than ϕBCP. The volume fraction of the BCP chains and the surfactant for different Nc are shown in Table 1.

was used to model the cross-interactions between the monomers. Each ionic monomer has explicit charge on it; the anionic surfactant heads occupy −q charges and the cationic charges on the ionic blocks of the BCP occupy +q charges, and the corresponding counterions have opposite charges. The ionic species interact via Coulomb force given by

Table 1. Volume Fractions of BCP Chains and Surfactants for Different Nc Nc

ϕBCP

ϕS

50 100 200 300 400

0.184 0.306 0.458 0.549 0.609

0.736 0.612 0.458 0.366 0.305

UijCoulomb(rij) =

Uij = − 0.5κR 0

, where ε = 1.0 is the dielectric constant

of the medium and ε0 is the vacuum permittivity. qi and qj are the effective interacting electronic charges. The simulations were performed at a fixed reduced temperature given by T* = kBT/εLJ = 1.0, where kB is the Boltzmann constant and T is the temperature at variable BCP volume fractions as shown in Table 1. As we change the number of overall charges in the system (by changing the ϕBCP), the ratio of the Coulomb energy relative to the thermal energy becomes increasingly important. This ratio is coupled to an important length scale parameter, known as the Bjerrum length, in electrostatic systems. The Bjerrum length is given by λB = e2/4πε0εkBT, where e is the elementary charge. A typical Bjerrum length calculation further elucidates the significance of the λB length scale. For example, in water, where ε = 80 at 22C, λB is only 0.7 nm while for a low ε solvent (ε = 1.0), the Bjerrum length is approximately 57 nm, which is approximately 80 times larger than water. Therefore, the range of electrostatic interaction in a low ε solvent will have a potentially stronger effect than water. It should be noted, however, that varying the BCP concentration changes the charge states and the number of negative counterions and thereby affects the dielectric constant of the solution,32 giving rise to a change in λB. We will not elaborate on the effect of PE charge states on ε and λB as we are focusing on the direct relationship between variable BCP concentration and the BPSC structures. Apart from this, a separate factor influences the Bjerrum length and the Debye screening length of the backbone charges. The concentration of counterions changes as the number of chains increases from Nc = 50 to 400. The negative counterion volume fraction, ϕncion, ranges from 0.018 to 0.061. While the change in counterion concentration is ≈200% between simulations, the change in backbone charge concentration increases the same amount. Moreover, the total counterion concentration is a tiny fraction compared to the overall concentration of the solution. Therefore, the effect of change in Bjerrum length (or effective Debye screening radius) on these simulations is negligible as the number of charges on the chain backbone increases. Our assumption is corroborated in the Results section where we observe that the majority of the counterions are released to counterbalance the loss of configuration entropy caused by the electrostatic interactions between BCP charges and surfactant headgroup. Counterions in the solution remain free or in a doublet state with another oppositely charged counterion. In a salt-free environment this is typically observed scenario; however, in the presence of salt the Bjerrum length and hence Debye screening effect should be dealt with extreme caution.33−35 The time steps used for integrating the equations

The total number of monomers is low compared to the volume of the simulation box, and hence the simulation systems are all at dilute condition, the number density, ρ, varying from 1.63 × 10−2σ−3 to 4.0 × 10−2σ−3 for 50 to 400 chain lengths, respectively. The highly dilute solution allows us to carefully investigate the dynamical transitions associated with the BPSC. Moreover, the total number of surfactants is constant for all systems, leading to a surfactant concentration, ρsurf = 1.2 × 10−2σ−3. Pool et al.29 had shown that the critical micelle concentration (CMC) for Lennard-Jones surfactants with anionic or cationic heads is within the concentration range of ρCMC * = 10−5−10−6 at T* = 1.0. Therefore, surfactant concentration in the present case is well above the CMC, allowing all the surfactant to form micelles. It should also be noted that the presence of charged block copolymer affects the CMC.30 However, this does not hinder micelle formation and is largely unaffected as we will show later in the Results section. The bond between monomer beads of both polymer chains and surfactants is modeled by the finitely extensible nonlinear elastic (FENE) springs 2

qiqj

4πε0εrij

⎡⎛ ⎞12 ⎛ ⎞6 ⎤ ⎡ ⎛ rij ⎞2 ⎤ σ σ ⎢ ⎥ ln 1 − ⎜ ⎟ + 4εLJ⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ + εLJ ⎢⎣ ⎥ r ⎝ R0 ⎠ ⎦ ⎝ rij ⎠ ⎦ ⎣⎝ ij ⎠ (1)

with κ = 30εLJ/σ being the spring constant and R0 = 1.5σ is the finite extensibility. The first term in the FENE bond potential is attractive with a maximum extent to R0. The attractive FENE has a singularity at rij = R0 that prevents the bond length stretch beyond R0. The second term is repulsive LJ potential with a cutoff at rcut = 21/6. The repulsive LJ potential prevents the monomers from overlapping each other. While performing simulations with bonded polymer models, the polymer chains cannot be allowed to cross as it is one of the key physical characteristics of polymer chains. This requires maintaining separation between bonded beads enough so that the chains are not allowed to cross. The FENE potential inherently achieves this. In eq 1, rij is the distance between two monomers, and εLJ is the LJ interaction (energy) parameter. The energy parameters, εLJ = 1.0, are set for all the monomeric interactions except for the surfactant tail. For hydrophobic surfactant tails, εLJ = 2.0 are used as a higher ϵLJ is reasonable for modeling the strongly hydrophobic surfactant tails.31 The energetic interaction between any pair of nonbonded monomers is modeled by a truncated and shifted LJ potential. The nonbonded interactions between hydrophilic neutral monomers are modeled by repulsive LJ potential while the nonbonded hydrophobic interactions are modeled by attractive LJ interactions. The Lorentz−Berthelot mixing rule

of motion are Δt * = Δt / miσ 2/εLJ = 0.012 , while the reduced energy and reduced distance are defined as U* = U/ kBT and r* = r/σ.

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RESULTS AND DISCUSSION The simulations were carried out in the canonical ensemble (NVT) with a Langevin thermostat for temperature control. All C


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Figure 2. Snapshot of the self-assembled structures of charged BCP surfactant complex for the double hydrophilic BCP. Top panel: (a) Nc = 50 and (b) Nc = 400 are plotted to represent the full system where the surfactant micelles form complexes with the charged BCP chains. Bottom panel: (c) Nc = 50 and (d) Nc = 400 show only the surfactant micelle. (c) and (d) plots are same as (a) and (b) with the only exception that the BCP chains are not shown in these plots to clearly demonstrate the distribution and shape of the surfactant micelle. For these plots, cyan and black spheres represent the neutral and charged monomers from the charged BCP block, respectively. Magenta represents the neutral block of the BCP chain. Red and yellow represent the head and tails of the surfactant. The light gray and blue background monomers are positive and negative counterions. The charged BCP blocks surround the surfactant micelle and the neutral block trail from the micelle surface similar to “hairy colloid” structure (top panel). The bottom panel shows spherical and almost equal number of micelle for low and high Nc.

simulations were run for 50 million LJ time steps to enable equilibration and the analysis were based on the statistics of another 10 million times steps. There are several approaches to evaluate equilibrium in MD simulation. In our case, the thermodynamic equilibrium of the system was verified from the mean-square-displacement (MSD) calculations. It was observed that the MSD reaches diffusive regime even for the longest molecule of the system, i.e., the BCP chains. The two different set of simulations for hydrophilic− hydrophilic and hydrophobic−hydrophilic will be referred to as double hydrophilic and mixed BCP systems, respectively. For the double-hydrophilic BCP, the snapshots are shown in Figure 2 for Nc = 50 and 400. The full system is shown in the top panel (Figure 2a,b) where the BCP chains decorate the surface of the micelle. In Figure 2c,d, the surfactant micelle structures are plotted, and spherical micelles are observed for both the BCP volume fractions. Therefore, the charged block of the BCP chain has no significant observable effect in modifying the spherical surfactant micelle. The anionic head groups of the surfactant are distributed on the surface layer of the micelle. The negative micelle surface attracts the cationic monomers of the charged BCP blocks that decorate the surfactant micelle as can be seen in Figure 2a,b. In Figure2b, it is not obvious as the crowding of BCP due to the higher concentration impedes discernment. Additionally, the neutral hydrophilic block of the

BCP dangles from the micelle surface similar to hairy colloidal nanoparticle structures as has been observed in colloidal nanoparticles made from amphiphilic polymers.36−38 In previous studies the interfacial behavior of surfactant polyelectrolyte complexes has been analyzed; however, the location and arrangement of the PE chains could not be established.39 In the present self-assembled structures, we have established the location and arrangement of the BCP chain. The other noticeable feature comes from the self-assembly and formation of the surfactant micelles. The distribution and the number of surfactant micelles do not vary considerably with the number of BCP chains in the system as can be observed in Figure 2c,d. In Figure 3, we show snapshots of the mixed BCP systems for two BCP volume fractions, Nc = 50 and 400. The morphologies of double hydrophilic (Figure 2) and mixed BCPs are comparatively different. The full system for both BCP volume fractions is shown in the top panel, and the surfactant micelles are separately shown in the bottom panel of Figure 3. The charged block of the BCP decorates the surfactant micelles forming a coronal layer whereas the hydrophobic neutral blocks form a layer between adjacent surfactant micelles, identical to a lamellar morphology. A dense coronal hydrophilic block and a dense layer of hydrophobic blocks have been previously observed by Wesley et al.22 using small-angle neutron D


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Figure 3. Self-assembled structures of the hydrophobic neutral block of the charged BCP. Top panel, (a) and (b): full system for Nc = 50 and 400. respectively. Bottom panel, (c) and (d): same as (a) and (b) but without the BCP chains. In (a) and (c), the BCP chains form lamellar style 50−50 BCP morphology along with the surfactant micelles. The hydrophobic interactions between the BCP and surfactant are primary contributing factors for these morphologies. At low BCP concentration, surfactants form nonspherical micelles with all the surfactant molecules agglomerated into one large micelle as is observed in (c) and (d). Color scheme is the same as Figure 2.

Figure 4. Closeup look of the mixed BCP system (Figure 3). The red and yellow are the surfactant heads and tails, respectively. The magenta colors are the hydrophobic neutral blocks of the BCP chain. All the other monomers such as the charged blocks of the BCP are shown in transparent color to make it easier to focus on the structures formed by hydrophobic blocks and surfactant micelles. Color schemes are the same as the previous two figures. The counterions are not shown in this figure for clarity.

scattering. We also observe the coronal layer made of surfactant heads and the charged BCP and a dense lamellar layer formed by the hydrophobic blocks. At a higher volume fraction of the BCP (Figure 3b), the total number of cations on the BCP exceeds the total number of anionic surfactant heads. Therefore, a small percentage of the excess charged blocks in the coronal region are found to be dangling in solution, unlike

the double hydrophilic case, where almost all the charged blocks dangle from the micelle. The surfactant micelles form oblate spheres at low Nc (Figure 3c) instead of spheres, in contrast to the hydrophilic neutral blocks (Figure 2c). The oblate spherical shape of surfactant micelles in the presence of hydrophobic moieties is well-known, and it is also observed that different surfactants tend to form oblate to prolate shapes.40,41 E


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Figure 5. Comparison of radial distribution function g(r) for different charge species in the system. (a, b) The black, red, green, blue, and magenta lines represent Nc = 50, 100, 200, 300, and 400, respectively. The RDF between BCP backbone charges and surfactant head are shown for doublehydrophilic and mixed BCP system in (a) and (b), respectively. Weaker aggregates are observed for larger number of aggregates. The insets in (a) and (b) show the RDF with respective counterions. The top panels of the insets are for charges with the negative counterions, and bottom panels are RDF of the surfactant head with positive counterions. (c) RDF for counterions only for two Nc values, Nc = 50 and 400, are shown in top and bottom panel, respectively. The solid lines are for positive counterions (released from the BCP backbone charges), and the dashed lines are for negative counterions (released from surfactant head). The blue and red colors represent double hydrophilic and mixed BCP systems, respectively. (d) RDF between positive and negative counterions. The circle and square blue symbols double hydrophilic for Nc = 50 and 400, and solid and dashed lines represent mixed hydrophobic Nc = 50 and 400 systems, respectively. The black vertical line is drawn at the only observed peak at r = 1.1σ, a signature of positive and negative counterion doublet formation. No long-range structures are observed for the counterions.

interact with the oppositely charged surfactant head. The surfactant heads, being on the surface of the micelle, aid the charged blocks decorating the micelle in a coronal layer. The microphase-separated hydrophobic blocks, in effect, form the dense lamellar structures.22 The second effect comes from the van der Waals interactions between the hydrophobic blocks of the BCP and surfactant tails at the micellar core that induce deformations on the surfactant spherical shape. To obtain a clear insight into the monomer organization of the different charge species of the BCP, surfactants, and counterions, we investigate the radial distribution function (RDF) of the charged species only as shown in Figure 5. The radial charge distribution function examines the position of charges with respect to each other. In Figure 5a,b the RDF between backbone charges and head groups for double hydrophilic and mixed BCP system show a large peak a distance close to the distance between two monomers. The charge−head association shows that the charge BCP blocks

A lamellar morphology, similar to 50−50 BCP morphologies, is not quite evident in Figure 2; hence, to show the underlying morphologies more prominently in a crowded environment, we take a closer look at the mixed BCP system in Figure 4. The BCP lamellar structures are clearly seen. The surfactant micelle exhibits a pronounced oblate shape instead of totally spherical surfactant, as expected from surfactant aggregation, even at highest BCP volume fraction. The deformation of these micelles is similar to the oblate structures observed in shearinduced deformation of single surfactant multilamellar vesicle42 in aqueous solution of anionic surfactant linear alkylbenzenesulfonic acid (HLAS) as visualized by microscopy. In the present study, we take advantage of two dominating forces of mixed BCP to emulate shearlike effects. The first effect deals with the steric repulsion between the hydrophobic neutral block and hydrophilic charged block of the BCP which allows the microphase separation between the charged block and hydrophobic blocks rendering the charged blocks availability to F


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Figure 6. Potential of mean force between charged monomers of the BCP and surfactant heads (top panel, a and b) and neutral monomers and surfactant head (bottom panel, c and d). The left panel, (a) and (c), represents the double hydrophilic BCP chain; the right panel, (b) and (d), represents the mixed BCP chain with hydrophobic neutral blocks. The color schemes are shown in the legend. For both systems the BCP charge− heads show a sharp attractive potential well representing strong attraction, whereas the BCP neutral block−heads show a relatively shallow potential well.

occupy the area near the micelle surface. The first peak heights are reduced for higher BCP concentration, and hence the agglomeration between charge and the head groups is weaker as Nc increases. This shows that more number of chains dangle inside the implicit solvent. Competition between electrostatics (from charged species) and entropic (from neutral species) forces is responsible for the self-assembly of these aggregates. As the BCP concentration increases, the entropic contribution from the neutral blocks is higher than the electrostatic interactions between charged species which results in a higher number of dissociated blocks from the surface of the surfactant micelle. As a consequence, the agglomeration between BCP charges and surfactant head weakens, which is clearly visible in the reduction of the first peak of g(r) in Figure 5a,b. The peak heights in Figure 5b are distinctively larger, indicating a stronger agglomeration in mixed BCP system than the double hydrophilic (Figure 5a) system. Therefore, the charges are more crowded on the mixed BCP system than the hydrophilic system. As we will discuss later in this section, entropic interactions between the hydrophobic neutral blocks and hydrophobic surfactant and electrostatic interaction between the oppositely charged surfactant head and backbone charges both favor a stronger agglomeration. The insets of Figure 5a,b show the RDF between the charge species with oppositely charged counterions; the top panel shows BCP backbone charges with negative counterions, and the bottom panel shows the head with positive counterions. Both of the insets show

weakly aggregated structures. The counterions are barely associated with the charges or the head; instead, they are all released into the solvent medium. Further structural information on counterions can be revealed by plotting the counterions RDF as displayed in Figure 5c,d. Here we plot the RDF of negative and positive counterions for the lowest (Nc = 50, top panel) and highest (Nc = 400, bottom panel) BCP concentration in Figure 5c, and the RDF of negative and positive counterions are plotted in Figure 5d. In Figure 5c, both double hydrophilic (blue lines) and mixed BCP (red lines) systems, the first peak is observed at a distance between two monomers. The first peak is dominant only for positive counterions in mixed BCP systems, and thereafter negligible structural changes are observed. This suggests that individual counterions prefer to be dispersed in the central simulation box (implicit solvent). While both the systems show weaker agglomeration of counterions compared to the charge−head, the top panel exhibits a higher peak compared to the bottom panel representing the presence of a larger number of positive counterions. At low BCP concentration (low Nc), the number of positive counterion (corresponding to the surfactant) is higher compared to the negative counterion (corresponding to the BCP). The excess positive counterions dissolute in the system, giving rise to a stronger peak. Figure 5d exhibits the relative position of the oppositely charged counterions. In this plot, the negative and positive counterion pairs peak at r = 1.1σ, approximately the G


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for Nc = 50 to 400 (Figure 6b). This shows that the BCP charged blocks in the mixed BCP systems require ≈0.5kBT excess free energy to dissolve from the micellar surface for any BCP volume fraction. The 0.5kBT excess free energy is purely an entropic effect subjected to the hydrophobicity of the neutral block. Both Figures 6a and 6b show an energy barrier, measured at the knee of the PMF plots, which spreads in the range −4.0kBT to −2.0kBT from the highest to lowest Nc. This energy barrier is essentially the amount of free energy required to dissociate only the BCP charges from the surfactant head and hence from the micelle surface. Additionally for LJ surfactant system in aqueous media, the surfactant desorption free energy can be estimated from the CMC as F = −kBT ln(CMC), which is between −6.0kBT and −5.0kBT,46,47 and hence this is the amount of free energy required to pull a surfactant molecule far from the micelle. These estimates show that the dissociation of the BCP charges from the surfactant head on the micellar surface is more favorable than dissolving the surfactant molecule from the micelle as the free energy in the first case (−4.0kBT to −2.0kBT) is lower than the free energy in the latter case (−6.0kBT to −5.0kBT). Therefore, the surfactant micelles formed in both the systems are comparatively stable and hardly affected by the architecture of the BCP chain. One noticeable difference is observed though for mixed BCP complex with higher volume fraction of the BCP chain, Nc = 300 and 400 (blue and magenta curves in Figure 6b). The PMF well is of the order of −6.0kBT and is comparable to the free energy of desorption of surfactant. At higher BCP volume fraction, therefore, the surfactant can be dissolved fairly easily. It would be interesting to see whether this technique of dissolving surfactant molecules, thereby forming porous structures, in a polymer−surfactant complex can be used to synthesize polymer membranes. Figures 6c and 6d represent the PMFs between the neutral BCP block and surfactant heads for the double hydrophilic (c) and mixed BCP (d), respectively. The neutral−head PMFs in both cases show a lower minimum, less than −2.0kBT, representing weaker confinement of the neutral blocks on the micellar surface (anionic surfactant head decorates the micelle surface) compared to the charged blocks on the micellar surface (Figure 6a). The PMF minimum becomes increasingly weaker as more chains are added to the system. This is the result of overcrowding of the miceller surface by the cationic charges of BCP near the anionic surfactant heads initiated by stronger electrostatic interactions. Another feature observed in the neutral−head PMF is their broad distribution, representing weaker entropic interactions between the neutral blocks with the surfactant molecule as a whole, with an exception for the mixed BCP systems. In Figure 6c, the broad distribution and hence the weaker interactions between neutral blocks and surfactant molecules result in the neutral blocks locating outside of the agglomerated micelle−charge BCP structures as observed in Figure 2. Increasing the number of chains decreases the potential minima, and more neutral chains are found outside the micelle BCP−charge aggregates. The PMF can examine the system’s energy changes as a function of the distance between two monomers. The PMFs in Figure 6 show a larger barrier beyond r = 20σ. A small dip at r = 1.1σ, the distance between two monomers in contact, is also observed in the PMF for the mixed BCP system, representing the position of neutral monomers next to anionic surfactant head. The large barrier thereafter extends to ≫20σ. The dip along with the extended PMF barrier is representative of the

distance between two counterion centers with absolutely no long-range structures. This means the counterion pairs form a doublet. The doublets are more pronounced for higher BCP concentration (Nc = 400). This explains the absence of a large peak in the “only” counterion RDF in Figure 5c (bottom panel). The accessibility of a large number of oppositely charged counterions helps form the doublets with no longrange structures. From these structural analyses it is evident that most of the counterions are dissociated from the BCP chains and surfactants and are dispersed in the solvent (central simulation box). Oppositely charged counterions always pair in doublets without forming long-range structures. The association between the BCP charge and the surfactant heads is strong due to electrostatic interactions that assists releasing the counterions in the medium. To make a comparison of the energetic penalty associated with the self-assembly of different charged species, it is important to know the changes in free energy as a function of distance between two charged monomers. In the dilute system, the PMF incorporates explicit/implicit solvent effects as well as the intrinsic interactions between two different monomers. An investigation of PMF can qualitatively explain the changes of free energy, thereby providing a comprehensive insight of the self-assembly of the charge species.43 Consequently, we investigate the PMF, W(r), between different sets of charged monomers as shown in Figure 6. We follow the standard procedure of PMF calculation44,45 from the radial distribution function, g(r), in dilute solution given by W(r) = −kBT ln[g(r)]. In Figure 6a,c, the PMF between the BCP cationic charges and the surfactant anionic head shows a sharp decrease at r = 1.1σ. This is the representative contact distance between two monomers of the same size 1.0σ. The PMFs for the double hydrophilic and mixed BCP systems show a similar attractive PMF well that reconciles the opposite charge of the monomers from the BCP chain and the surfactant heads at the coronal layer. In the case of double hydrophilic BCP, the PMF between BCP charge and surfactant heads (Figure 6a) shows a potential barrier “knee” around r = 20σ, indicating a high potential barrier for escaping agglomeration. This distance can be considered as the average micelle size. For hydrophobic neutral blocks (mixed BCP in Figure 6b), two upward twists in the PMF are observed: the first one at r ≈ 15σ and the second at r ≈ 25σ. The presence of two potential barriers implies the presence of two escape boundaries for the agglomerated charged monomers. This can be explained using the knowledge of structures seen before in Figure 4. As the hydrophobic BCP deforms the spherical micelles, the asymmetrical structure relocates the micelle boundaries along the major and minor axis of the oblate sphere. Hence, the charge−head PMF shows two potential barriers of the PMF situated at the major and minor axis of the oblate sphere located at distances 25σ and 15σ, respectively. As discussed earlier, this deformation of the spherical micelle is the result of strong entropic interactions between the hydrophobic neutral chains and surfactant tails. The oblate spherical structures have been observed earlier in surfactant micelles under shear.42 In the present work, we established that spherical surfactant micelles in dilute solution can be deformed by incorporating a mixed BCP with hydrophobic neutral block without any extraneous intervention, e.g., shear. The PMF minimum changes from −4.3kBT to −2.1kBT for Nc = 50 to 400 in double hydrophilic BCP (Figure 6a) while the change in mixed BCP systems is from −4.9kBT to −2.6kBT H


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Figure 7. Comparison of PMFs for counterions with other charge species. The negative (ncions) and positive (pcions) counterions correspond to the cationic charges on the BCP chains and anionic head groups of the surfactants, respectively. (a, b) PMF between positive and negative counterions for double hydrophilic and mixed BCP systems, respectively. The color scheme for (a, b) is the same as Figure 6. Comparison of the PMFs between (c) BCP cationic charge and negative counterions and (d) anionic surfactant head and positive counterions for both systems and two different BCP volume fractions, Nc = 50 and 400. The solid and dashed lines in (c) and (d) represent double hydrophilic and mixed BCP systems, respectively.

negative and positive counterions complement the electrostatic neutrality of the cationic BCP charges and anionic surfactant heads, respectively. It is interesting to observe that none of these plots show noticeable long-range structures. Figure 7a,b shows the PMF for negative with positive counterions. In both cases, the PMF shows no oscillations at long length scales, suggesting a lack of long-range order and hence fluidlike response. A well-defined, sharp minimum of the potential well is observed around r = 1.1σ, the distance between two counterions in contact. With a potential barrier (from potential minima to maxima) of the order of −3.0kBT to −2.0kBT at r ≈ 1.1σ, this is the only coordination sphere where the negative and positive counterions form structures. Furthermore, no other ordered structures can be derived from these PMF plots. Therefore, the only possible packing is a doublet formation with negative and positive counterions. No secondary coordination sphere is observed, and hence the counterions are mostly free and in a disordered state, similar to simple liquids. Figure 7c,d shows the PMFs for BCP charge with negative counterions and head with positive counterions for Nc = 50 (in blue) and Nc = 400 (in red). The solid and the dashed lines represent systems with hydrophilic (double hydrophilic) and hydrophobic (mixed BCP) neutral chains, respectively. In Figure 7c, the PMF shows a shallower potential barrier but a stronger potential minima, compared to the counterion− counterion potential barrier and minima observed in Figure

agglomeration of the neutral blocks on the surface of the micelle (surfactant head) and then expanding to a distance r > 20σ with strong barrier that will prevent dissociation of the mixed BCP−surfactant agglomerated structures (Figure 6d). The PMFs show a decrease with increasing r for higher number of chains, Nc = 300 (blue line) and 400 (magenta line). The decrease is an entropic effect arising from the larger available phase volume with increasing distance47 in an overcrowded environment with oppositely charged monomers. The loss of contact between the hydrophobic neutral monomers and surfactant tails due to the higher number of charged blocks on the micelle surface gives rise to an overall repulsive interaction between surfactant molecule and the neutral hydrophobic monomers that results in the lower barrier in PMF for higher number of chains. From Nc = 50 to 100 (red and black lines in Figure 6d), a long-range net attractive tail of explicit many-body origin emerges with decreasing BCP volume fraction which favors the mixed BCP clustering with all surfactant molecules and results into agglomeration of BCP with a few surfactant micelles as can be seen in Figure 4. In polymeric systems with explicit electrostatic interactions, the role of counterions is critical for understanding the microphase separation and molecular self-assembly at longer length scales.31,48 In this regard, we analyze the PMFs between positive and negative counterions and their respective the charge species on the BCP and surfactants in Figure 7. The I


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Figure 8. Distribution of charges across the length of the simulation box obtained by calculating the density of the charged block (BCP) around the surfactant head (a) double hydrophilic and (b) mixed BCP systems. The size of the simulation box is 100σ centered around zero. Hence, the density distribution spreads from −50σ to +50σ across an arbitrary axis of the simulation box.

Figure 9. Radius of gyration and end-to-end distance. For comparison the Rg2/N and Re2/N are plotted along with the 6Rg2/N. The green circles indicate Rg2/N; red squares and blue triangles represent Re2/N and 6Rg2/N values, respectively. (a) represents the complex with hydrophilic neutral blocks, and (b) represents the hydrophobic neutral blocks.

heads cover the miceller surface, we plot the distribution of BCP charges around the surfactant heads in Figures 8a and 8b for double hydrophilic and mixed BCP blocks systems, respectively. The attractive electrostatic interactions between negative heads and positive charges inhibits the aggregation of the BCP charged monomers near the surfactant heads that are next to each other if no other interactions play a major role in the self-assembly of the BCP charged block on the coronal layer of the surfactant micelle. As a result, the BCP charged blocks are distributed evenly on the surface of the micelle, and hence the BCP charged blocks around the heads approach a normal distribution. For double hydrophilic systems, the charged blocks in Figure 8a exhibit close to normal distribution around the micelle surface (surfactant head) except for Nc = 50 and 300. The deviations are small and can be explained as due to the entropic effect of the hydrophilic neutral blocks which is extended out to the solution and thus dragging along some of the charged blocks. On the other hand, the distribution of BCP charges around the micelle surface shows larger deviation from a normal distribution for all BCP concentrations for mixed BCP systems as shown in Figure 8b. The distributions are bimodal for Nc = 50 and 100; thereafter, the bimodal distribution disappears with increasing Nc, and the spread (width) of the distribution increases compared to double hydrophilic systems. This suggests that the charged blocks of the BCP are not evenly distributed on the surface of the micelle, and for low Nc there is

7a,b. For both the double hydrophilic (solid lines) and mixed BCP (dashed lines) systems, the potential barriers show a variation in W(r) between −0.5kBT and −1.0kBT (Figure 7c). The potential minimum is observed at a distance of r = 1.1σ, typical charge separation distance. This represents that some of the negative counterions form doublets with the BCP charges. However, these counterions in the agglomerated structures can easily be detached (the potential barrier is weaker) and released into solution. The PMF between positive counterions and the surfactant heads shows a stronger potential minima, − 3.0kBT to −4.0kBT in Figure 7d for both double hydrophilic (solid lines) and mixed BCP (dashed lines) systems. The “knee” in the potential well for lower volume fractions (at r = 15σ) represent the extension of the reach of positive counterions with a strong attractive potential that in turn screens most of the electrostatic interactions arising from the surfactant heads. From these plots, it can be concluded that the counterions are weakly attached to the BCP charged blocks or to the surfactant heads and hence mostly free (well-dispersed) in the system. It is well established that the release of the counterions from their condensed states (on the BCP chains or surfactant head in this case) aids a formation of the multilevel BCP−surfactant complex.17 In order to understand the relative likelihood of the BCP charges being around the micelle surface, we focus our attention to the distribution of charges. Because the surfactant J


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This results in an entropic drag-enforced deformation and hence a protruded micellar structure as has been observed in Figure 4, which allows the charged blocks to spread across the larger surface area of the oblate micellar structures, resulting in an increase in Rg and Re. The increase in charges on the BCP increases the coverage area on the surfactant micelles and the entropic interactions are reduced, thus reducing the oblate structures that in turn reduces the Rg and Re of the BCP chain.

an asymmetric charge distribution on the micelle surface, resulting in an oblate micelle structure. In this case, BCP charges asymmetrically distribute according to the major and minor axis of the oblate micelle. As has been observed earlier (Figures 4 and 6), the hydrophobic blocks form lamellar structures with the surfactant micelles distorting their spherical geometry toward the lamellar hydrophobic blocks, giving rise to the probability of finding high number of BCP chains toward the lamellar direction. Thus, a higher number of BCP charges distribute in this direction due to purely entropic effects. This becomes more pronounced at low BCP volume fractions as the entropic penalty to carry a low number of charge blocks toward the lamellar direction is small compared to high BCP volume fractions, as can be seen in Figure 4a. While the deformation of the surfactant micelles is caused by entropy driven agglomeration of the charged BCP (with hydrophobic neutral blocks), this class of structural organization shares analogy with shear deformation of surfactant micelles,42 emulsion droplets,49 and biopolymers.50 To identify the range of the size of the BCP polymer coil as a function of BCP volume fraction, we examine the radius of 1 N gyration, R g2 = N ∑i ⟨(ri − rCM)2 ⟩, where rcm is the center-ofmass and the end-to-end distance R2e = ⟨(rN − r1)2⟩ , where N is the chain length and is shown in Figure 9. The double hydrophilic and the mixed BCP Rg and Re show different features as a function of polymer volume fraction. For convenience, we plotted Rg2/N and Re2/N. To compare with a typical ideal chain of same chain length, we plotted the 6 times the respective Rg2/N values. In both the cases, the Re2/N is smaller than the 6 times radius-of-gyration values (ideal chain value), implying that the BCP chain shrinks in size as compared to an ideal BCP chain of the same size. For the double hydrophilic system (Figure 9a), there is no substantial change of the Rg and Re with the change in BCP volume fraction. As shown earlier (Figures 2 and 6) the hydrophilic blocks generally trail from the surfactant micelle surface while the charged blocks are attached. This distinct self-assembled structure does not change significantly with the BCP volume fraction. Consequently, there is hardly any change in the Rg and Re of the polymer (Figure 9a) with ϕBCP where the neutral blocks are hydrophilic. In homo-polyelectrolyte surfactant complexes, it has been observed that Rg and Re follow a scaling law with the change in total number of charges of the system either by modifying the charge states of the polyelectrolyte31 or by changing salt concentration.51 The current work suggests that designing complexes of constrained shape and size can be obtained more precisely by using charged BCP rather than neutral polymers or homo-polyelectrolytes. The Rg and Re for the BCP chains in double hydrophilic system show a large drop from Nc = 50 to 100; thereafter, there is a slight increase in the Rg and Re values. For these two chain lengths, ϕBCP (0.184 and 0.306) ≪ surfactant volume fraction, ϕS (0.736 and 0.612) (Table 1). Additionally, the cationic charges on the BCP chains are 300 and 600, respectively, which is lower than the number of oppositely charged surfactant heads (1000). Particularly for Nc = 50, the charged blocks cover the smaller surface area of the micelles, and hence there is adequate gaping between the hydrophobic surfactant tails of the micelle and BCP hydrophobic blocks, through which they can interact. The total entropic interactions between the hydrophobic blocks and surfactant tails is stronger than the electrostatic interactions between the oppositely charged heads and BCP charged blocks.

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CONCLUSIONS We have performed a detailed structural analysis of micelle formation and aggregation of the anionic surfactants with cationic charged−neutral BCP using large-scale MD simulations. Two sets of charged−neutral BCP, one with hydrophilic neutral blocks and other with hydrophobic neutral blocks, show different agglomeration behavior with surfactant micelles. The micelle structures adopt spherical or oblate sphere structures depending on the physical property of the neutral block, i.e., hydrophilic and hydrophobic. The electrostatic interactions between the charged blocks and the surfactant heads and the entropic interactions between the neutral blocks and surfactant tails are responsible for the morphologies observed in this study. The distribution of the charge species on the spherical aggregate is qualitatively determined by the radial distribution function of different charge species as shown in Figure 5. The backbone charges and the surfactant heads show close association while the counterions are completely dissociated from the BCP chain and surfactants. The close association between the BCP and the surfactant charges helps form nanodmains, prompting the BCP and surfactant molecules self-assemble into separate nanostructured aggregates. The similar self-assembled structures have been observed in experiments recently by Wang et al.52 By using small-angle neutron scattering (SANS), Wang et al.52 showed that the addition of SDS increases the mobility of the polymer chains in mixed BCP, N,N-dimethylacrylamide (DMA), and 2-(N-ethylperfluorooctane-sulfonamido)ethyl methacrylate (FOSM) hydrogels, thereby freeing the polymer chains from associating hydrogels, and helps rearrange themselves to form smaller kinetically stable nanodomains. The nature of the interactions determines the final morphology of the charged block copolymer surfactant complex. In the hydrophilic neutral block environment, the surfactants form typical spherical micelles as driven by free energy. However, the BCP hydrophobic neutral blocks distort the micelles toward oblate sphere structures purely due to entropic effects. The structural details (snapshots in Figures 2−4) were further investigated by calculating the potential of mean force between the different species. The PMF results also confirm the existence of spherical and oblate structures in hydrophilic and hydrophobic neutral block surroundings. While deformation of the spherical micellar structures has been previously observed under shear flow,42 we have presented a study in which it could be possible to obtain the deformed surfactant micelles by introducing charged−neutral BCP. Also, it would be interesting to test whether the large BCP volume fraction polymer−surfactant complexes can used to develop membranes by dissolving the surfactant molecules. The hydrophilic neutral blocks, on the other hand, form hairy colloid structures with the surfactant micelle as the core. Both experimentally and theoretically, the core−shell microstructures are commonly observed in charged BCP−surfactant complexes.17,36,53 Most recently, Uchman et al. observed the K


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by the Office of Science of the U.S. DOE under Contract DEAC02-05CH11231. Research by M.G. and J.M.B. is supported by the Center for Accelerated Materials Modeling (CAMM) funded by the U.S. DoE, BES, MSED.

same core−shell structures using cryo-TEM and AFM on double hydrophilic block polyelectrolyte and fluorosurfactant.19 The multilevel structures of all these observations are driven by a competition between electrostatic interactions between charge species and entropic interactions between neutral species and by the release of the condensed counterions. The charged−neutral BCP surfactant aggregation is dominated by the interaction between charged and neutral blocks with the surfactant heads and tails. As observed in Figure 9, the BCP shrinks in size influenced by surfactants for all the BCP volume fractions and from the neutral blocks hydrophilicity or hydrophobicity. The BCP polymers are either continuously adsorbed on the surfactants or the polymers are adsorbed on the discrete micelles depending on the interactions between the blocks and surfactant heads and tails. When the hydrophobic interactions are dominant, the polymers entropically drag the surfactant molecules to form oblate spherical structures. If the electrostatic interactions are dominant, then the surfactant micelles adsorb the charged group of the polymers, giving rise to hairy micelle structures. This observation is consistent with previous simulations of polymer−surfactant complex.54 In a follow-up work, we will show the dynamics of different molecules and relaxation of the polymer chains and surfactants in the aggregate. In this article, the aggregate size and shape are examined qualitatively to understand the fundamental physics of the charged BCP surfactant complex. However, for the comparison of experimental data and real world designs, a thorough investigation of shape and sizes with actual size, shape, and count of the surfactant micelle is desirable. Also, mutual orientation of the BCP chains with respect to the micelle can provide an understanding of the shape and sizes of the aggregates. Moreover, the calculation of density distribution around the surfactant micelle will also be beneficial understand overall aggregate structures and its complex shapes. In conclusion, we opine that preference should be given to the charged−neutral BCP while designing materials with constraint in shape and size for specified set of applications instead of homo-polyelectrolytes or neutral polymers. These findings could open up new opportunities for polymeric colloidal nanoparticles and membrane design research targeting applications in polymer batteries, separation technologies, and drug delivery.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (M.G.). ORCID

Bobby G. Sumpter: 0000-0001-6341-0355 Monojoy Goswami: 0000-0002-4473-4888 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy (DoE), Office of Basic Energy Sciences, Materials Science and Engineering Division. The research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract DEAC05-00OR22725. Part of this research used resources of the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Scientific User Facility supported L


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