Dynamics of Charged Species in Ionic-Neutral Block Copolymer and

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Dynamics Of Charged Species in Ionic-Neutral Block Copolymer and Surfactant Complexes Jose M. Borreguero, Philip A. Pincus, Bobby G. Sumpter, and Monojoy Goswami J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b05047 • Publication Date (Web): 21 Jun 2017 Downloaded from http://pubs.acs.org on June 23, 2017

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The Journal of Physical Chemistry

Dynamics Of Charged Species in Ionic-Neutral Block Copolymer and Surfactant Complexes Jose M. Borreguero,† Philip A. Pincus,‡ Bobby G. Sumpter,¶,§ and Monojoy Goswami∗,¶,§ †Neutron Data Analysis & Visualization, Oak Ridge National Laboratory, Oak Ridge, TN, 37831 ‡Department of Material Science, University of California, Santa Barbara, CA ¶Center for Nanophase Material Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, 37831 §Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831 E-mail: [email protected]

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Abstract Structure-property relationships of ionic block copolymer (BCP) surfactant complexes are critical towards the progress of favorable engineering design of efficient charge transport materials. In this article, molecular dynamics simulations are used to understand the dynamics of charge-neutral BCP and surfactant complexes. The dynamics are examined for two different systems, charged-neutral double hydrophilic and hydrophobic-hydrophilic block copolymers with oppositely charged surfactant moieties. The dynamics of the surfactant head, tails and charges are studied for five different BCP volume fractions. We observe that the dynamics of the different species solely depend on the balance between electrostatic and entropic interactions between the charged species and the neutral monomers. The favorable hydrophobichydrophobic interactions and the unfavorable hydrophobic-hydrophilic determine the mobilities of the monomers. The dynamical properties of the charge species influence complex formation. Structural relaxations exhibit length-scale dependent behavior, with slower relaxation at the radius of gyration length-scale and faster relaxation at segmental length-scale consistent with previous results. The dynamical analysis correlates ion-exchange kinetics to the the self-assembly behavior of the complexes.

Introduction Relaxation dynamics of ionic polymers have garnered a great deal of interest because of its importance in understanding charge-transport mechanisms in polymer batteries, 1–3 bulk heterojunction polymer solar cells 4 and membranes. 5,6 The combination of polyelectrolytes with oppositely charged surfactants bring additional useful properties 7–9 that can be exploited to design novel materials in a variety of applications such as consumer products, 10 oil recovery, 11 surface modifications 12 and colloidal stabilization. 13 Polyelectrolyte surfactant complexes have been well studied since the pioneering work by Kataoka et al. and Kabanov et al. 14–16 In addition, Langevin 17 and Kogej 18 published a series of detailed reviews on the complexation of oppositely charged polyelectrolytes and surfactants in aqueous solution. Starting from this seminal set of studies, a large 2 ACS Paragon Plus Environment

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array of experimental and theoretical research resulted in hundreds of papers published on polyelectrolyte complexation 10,19 with oppositely charged surfactants. It is, therefore, difficult to list all relevant articles in this field. Despite the large number of studies, the dynamics of the different species in surfactant mediated charged-neutral BCP complexes lacks a fundamental theoretical understanding of the dynamical behavior of the charged-neutral BCP surfactant complex. In spite of challenges, recent developments in this direction can have direct impact on designing novel materials using charged-neutral BCP surfactant complex. While polyelectrolyte-surfactant complexes have a broad range of applications, a new class of materials, ionic-neutral block copolymers, 20–22 show promising materials properties for applications in high energy density batteries, 23,24 fuel cells, 25 separation membranes, 26 and BCP photonics in protein-BCP coacervates for protein delivery. 27 Due to the presence of the charged block in the ionic-neutral BCP, these complexes form microphase separated morphologies/structures that are compliant with both better mechanical performance and higher charge transport 20,22,28 for high throughput applications. The charged BCP nanostructures in conjunction with oppositely charged surfactants can significantly modulate their functional properties. 29,30 The properties of charged BCP-surfactant complexes can be tuned 31,32 via a large number of parameters such as, the total concentration, the molecular weight of the BCP, charge ratio, backbone rigidity, ionic strength, and polarity and pH, resulting in the formation of various different structures that lead to distinct structural relaxation and dynamics. Recently a series of experimental works were performed by Uchman et al. 33,34 on the complexation of poly(ethylene oxide) - block poly(methacrylic acid), PEO-PMAA, with an oppositely charged surfactant, N-dodecylpyridinium chloride, DPCI. The self-assembly, complex formation and surfactant diffusion were analyzed in their works. These investigations of the dynamics of surfactants revealed a non-monotonic dependence of self-diffusion coefficients with surfactant concentration. An important aspect of their study reflects the kinetics of the complex formation, in which, they found that structural development consists of two steps, (i) a fast initial step which is < 50ms and (ii) a slower relaxation process in the 10−1 s to 100 s time scale. To establish a structure-property relationship that enhances the properties of



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these complexes, it is necessary to first understand the fundamental physics of the kinetics driven self-assembly. A fundamental understanding will provide key information to lay out the design principles for high charge transport yield. However, many of the dynamical properties and the mechanism of the self-assembly of charged BCP-surfactant complex are either poorly understood or not clearly established. To address the dynamical properties in these complexes, we investigate two sets of BCPsurfactant complexes, where the architecture of the BCP consists of one partially charged block and a neutral block that is either (i) hydrophilic or (ii) hydrophobic. Each system contains of the same number of surfactant molecules with one anionic hydrophilic head and a long hydrophobic tail. The charged blocks of the BCP were kept the same for both systems. In many circumstances, a qualitative understanding of the structure and properties of these complex materials stimulates further experimental investigation that can have profound effects in materials design. While the volume fraction, chain composition and architecture are all imporatant factors in designing materials for future applications, we have focused on developing a simplified model system for a qualitative understanding of the physics of the underlying relaxation dynamics in charged BCP surfactant complexes that have not previously been investigated either by experiments or by simulations. Moreover, the charge separation on the charged block of the BCP backbone can have significant effect on the dynamics of different species in the complex. 35–37 However, in this work we will discuss only one of the aspects that can influence the dynamics of the system, i.e., the concentration of the overall BCP in the complex. Prior structural studies 38 demonstrated that the surfactant induced self-assembly of charged-neutral BCP require a scrutiny of the relaxation dynamics and its effect on the self-assembly of the complexes. We aim to provide a comprehensive physical understanding of the relaxation and diffusion of the different species of the complex and compare our results with previous experimental and theoretical works wherever applicable. However, due to the lack of systematic data on relaxation and dynamics of surfactant mediated charged BCP complex, our best efforts relied on contrasting the trends of these simulations with previous experiments/simulations. The merit of these simulations lies in understanding the fundamental


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physics underlying the observed dynamics. The article is organized as follows: The model polymer architecture and the simulation details are described in the next section. In the Results section, we report the formation of a chargenetwork that induces special structures in the system, followed by the diffusion and structural relaxation of the different species leading to the self-assembly or complex formation. We conclude the article with a brief discussion on the importance of dynamics on potential applications in developing materials with enhanced charge transport properties.

Simulation Method Molecular dynamics (MD) simulations are performed for a randomly generated mixture of 5050 charged-neutral BCP chains and surfactant molecules. The degree of polymerization of the charged-neutral BCP and anionic surfactants is Nm = 60 and 12 respectively. The BCP chains contain a 30-monomer neutral block and a 30-monomer charged block with each charged block containing 6 cations. The anionic surfactant is architecturally equivalent to sodium dodecyl sulfate (SDS) surfactant. Equal number of negative and positive counterions are added to render a system with no net charge. The two sets of charged-neutral BCP contain (i) hydrophobic and (ii) hydrophilic neutral blocks. These two sets will be referred as (i) “mixed BCP" and (ii) “doublehydrophilic" BCP in this article. The BCP chain length and the charge states on the backbone are unaltered for both sets. The simulations are performed using LAMMPS 39 MD package in a periodic box of volume, 100 × 100 × 100σ 3 , where σ is the monomer diameter. The monomer sizes of the BCP, surfactant and counterions are assumed to be the same in order to address the dynamics of different species of comparable monomer sizes. For each set, five different systems are simulated for number of BCP chains, NC = 50, 100, 200, 300 and 400 that corresponds to the BCP volume fraction, φBCP = 0.18, 0.31, 0.46, 0.55 and 0.61. The surfactant volume fraction, φS for the five systems are, 0.74, 0.61, 0.46, 0.37 and 0.31 respectively. As can be observed from these volume fractions, the choice of this set of NC number of chains allows us to investigate the dynamics at



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different φBCP such that the φS , is higher, equal and lower than φBCP . For polyelectrolyte surfactant complexation driven by electrostatics, the charge ratio, Z, which is the stoichiometric ratio for chargeable groups, is a crucial parameter for electrostatic complexation. The charge ratio, Z, is defined by the number of charges on the surfactant to the number of charges on the charged-neutral BCP. In our simulations, Z = 0.3, 0.6, 1.2, 1.8 and 2.4 respectively. The isoelectric case, Z = 1.0, equal number of negative surfactant charges and positive BCP charges is carefully omitted as it is not relevant for electrostatic complexation. 40,41 While the charge ratio is crucial in the dynamics of electrostatic complexation, in this article though, we will discuss the results in terms of volume fraction for being consistent with our earlier work. 38 The simulations are performed at dilute condition under implicit solvent at monomer number densities, ρ , varying from 1.63 × 10−2 σ −3 to 4.0 × 10−2 σ −3 for 50 to 400 chain lengths respectively. The highly dilute system allows us to carefully investigate the dynamical transitions associated with the complex. The surfactant concentration is kept constant for all systems at ρsur f = 1.2 × 10−2 σ −3 . Pool et al. 42 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 to 10−6 at T ∗ = 1.0. Hence the surfactant concentration in these simulations is above

the CMC, thus spontaneous micelle formation in all of these simulations is guaranteed. In a system where one or more polyelectrolyte chains can be adsorbed on the surfactant micelle, 43,44 another important factor, the critical aggregation number (CAC) plays a significant role in self-assembly of polyelectrolyte-surfactant complex. Typically CAC is of the order of 100-1000 times lower than the regular CMC. 40,45 At CMC, unassisted micelization occurs in pure surfactant systems, while assisted (by the polyelectrolyte) micelization occurs at CAC. While a surfactant concentration lower than CMC can form assisted micelles, the primary focus of this work is to understand the dynamics of BCPs in the presence of unassisted micelles. 46 Therefore, all of our simulations are performed at surfactant concentrations higher than CMC, that also satisfies the condition where the total concentration is well above CAC. Once the necessary condition (concentration above CAC) is satisfied, the complexation and self-assembly of the charged-neutral BCP and surfactant are


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assured for all the simulations in this work. The charged-neutral BCP and surfactants are modeled following the Kremer-Grest bead spring polymer model. 47 The bond between monomer beads for both polymer chains and surfactants are modeled by the finitely extensible nonlinear elastic (FENE) springs, "

ri j Ui j = −0.5κ R20 ln 1 − R0

2 #

+ 4εLJ

"

σ ri j

12

σ − ri j

6 #

(1)

+ εLJ

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 extension to R0 . The attractive FENE

has a singularity at ri j = R0 that prevents the bond length stretching beyond R0 . The second term 1 6 is the repulsive LJ potential with a cutoff at rcut = 2 σ . The repulsive LJ potential prevents the monomers from overlapping each other. The separation between bonded beads must prevent the

chains from crossing, which is inherently achieved by the FENE potential. In Equation 1, ri j 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 recommendable to model the strongly hydrophobic surfactant tails. 37,48 The energetic interaction between any pair of non-bonded monomers is modeled by a truncated and shifted LJ potential. The non-bonded interactions between hydrophilic neutral monomers are modeled by a repulsive LJ potential while the non-bonded hydrophobic interactions are modeled by attractive LJ interactions. The LorentzBerthelot mixing rule 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 BCP blocks occupy +q charges, and the corresponding counterions have opposite qq

charges. The ionic species interact via the Coulomb force given by, UiCoulomb (ri j ) = 4πεi0 εrj i j , where j

ε = 1.0 is the dielectric constant of the medium and ε0 is the vacuum permitivity respectively. qi , q j are the effective interacting electronic charges. The simulations are performed at a fixed temperature, T ∗ = kB T εLJ = 1.0 (T ∗ in reduced 7 ACS Paragon Plus Environment


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unit), where kB is the Boltzmann constant and T is the temperature. The Bjerrum length, a length scale parameter equivalent to the ratio of the Coulomb energy to the thermal energy, is given by, λB = e2 4πε0 ε kB T , where e is the elementary charge, εk is the dielectric constant and ε0 is the

vacuum permitivity. Since in this work, the temperature and εk of the system is constant, the dependence of the Bjerrum length will not be discussed in this article. However, it should be noted that varying BCP concentration changes the charge states and the number of negative counterions, thereby it may affect the solution’s dielectric constant, 49 giving rise to a change in ε . We will not

elaborate on the effect of PE charge states on ε since we are focusing on the effects of variable BCP concentration on the dynamics. Apart from this, the counterion concentration and the solvent properties also influence the Bjerrum length. The concentration of counterions increases as the number of chains increases from Nc = 50 to 400. For instance, the negative counterion volume fraction, φncion , increases from 0.018 to 0.061. While the changes in counterion concentration is ≈ 200% between simulations, the same changes in average charge density occur due to an increase in the backbone charges. Moreover, the total counterion concentration is a tiny fraction compared to the overall concentration of the solution, and most of the counterions are released into the solution. 38 Therefore, the change in Bjerrum radius due to change in counterion concentration is negligible. Counterions in the ‘implicit’ solvent remain either free or in doublet states with another oppositely charged counterion. In a salt free environment especially with ‘implicit solvent’, as in this article, this is a valid assumption, however in the presence of salt or explicit solvent the Bjerrum length needs to be dealt carefully 50,51 that can affect dominate the behavior of the polyelectrolytesurfactant complex. All simulations were carried out in the canonical ensemble (NV T ) with a Langevin thermostat for temperature control. The Langevin thermostat ensures interaction with the background implicit solvent. All simulations were run for 50 million LJ time steps and the results are based on the statistics collected for another 10 million times steps after equilibration. The time step used for q ⋆ integrating the equations of motion is, ∆t = ∆t mi σ 2 εLJ = 0.012, while the reduced energy and reduced distance are defined as, U ∗ = U kB T and r∗ = r σ . 8 ACS Paragon Plus Environment

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Results and Discussion In a recent work, 38 structural issues and thermodynamics of the complexation has been discussed in detail. This article deals with the dynamics of the charge species and their relation to the selfassembled structures reported earlier. Therefore, we will not elaborate on the structural issues in this article, but concentrate on the kinetics of the self-assembly. However, before going into the details of the dynamics, the self-assembly of charges requires a short discussion due to their many-faceted electrostatically driven self-assembling behavior. Ionic networks play a critical role in determining and controlling the ion transport in chargedneutral block copolymers. The distribution of the charged species plays a crucial role in determining the mechanical and transport properties of these systems. 1,52–54 Hence, we discuss the charge distribution inside the system prior to discussing the dynamics of the same. The snapshots (structures) of only the ionic species formed by the BCP charges and surfactant heads are shown in Figure 1(a) and (b). A visual inspection of the charge distribution shows an evenly distributed network of charges in the double hydrophilic system (Figure 1(a)) and a concentrated charge-distribution near the surfactant heads (red dots) for the mixed BCP system (Figure 1(b)). In Figure 1(c) we show the number density distribution (Type of monomer/Volume) for the double hydrophilic (blue) and the mixed BCP system (red) for the charges and the surfactant head. The sparse charge distribution (blue circles) of the double hydrophilic system is manifested in the broad radial dependence of the number density distribution in Figure 1(c) whereas a stronger local agglomeration of the charges on the surfactant head (blue squares). The surfactant head density distribution for mixed BCP system (red squares) shows a bimodal distribution representing a varying size distribution of the surfactant micelles. In the mixed BCP system, the micelle interface is dominated by the electrostatic interactions retaining the charged blocks with the hydrophobic neutral blocks residing side-by-side. In the double hydrophilic environment, the majority of the charged blocks are solvated away from the surface of the surfactant micelle resulting in hairy nanoparticle structures as has been observed in our previous work. 38 The effect of the electrostatic interactions in hydrophobic and/or hydrophilic media leading to the formation of concentrated and sparse charge distribution is not limited to 9 ACS Paragon Plus Environment


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(a)

(b)

(c)

Figure 1: Snapshot of the self-assembled nanoionic structures of the polymer and surfactant charged species are shown for an intermediate polymer volume fraction, Nc = 300. The snapshots represent (a) double hydrophilic and (b) mixed BCP systems. The red and blue spheres represent surfactant head and charges on the polymer chains respectively. In (a) the double hydrophilic system does not allow agglomeration of all the polymer charges on the surfactant head. On the other hand, (b) in the mixed BCP system polymer charges agglomerate on the surfactant micelle interface. (c) Number density distribution radially for NC = 300 and for the double hydrophilic (blue) and mixed BCP system (red). The circles and the squares represent the BCP charge and the surfactant head respectively.


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charged-BCP surfactant systems. A similar self-assembled ionic network of concentrated charges has also been observed in a recent simulation study by Aryal et al. 1 In their work, ionic nanostructures of different size and shapes were generated by mediating the electrostatic interactions between charged species of ionic polymers in hydrophilic and hydrophobic environments. As the primary focus of this article is understanding the dynamics of the charge species, we restrict the discussion in dynamical properties only. Additional details regarding the thermodynamics of the ionic nanostructures and structural details have already been reported elsewhere 38 and hence require no further discussion. Hereafter, we focus on the dynamics of the different species in the model system by calculating the mean-square-distance (MSD) and dynamic structure factor from the equilibrated trajectories and investigate the self-diffusion and structural relaxation of these species. The mean square displacement (MSD) for the charged species only are shown in Figure 2 and Figure 3 for double hydrophilic and mixed BCP systems, respectively. A comprehensive structural information can be found in Ref.

38

For both systems, MSD (calculated by subtracting

the center-of-mass motion drift) for positive and negative counterions show fast diffusive motion compared to the charges and surfactant head. The counterions are released into the solution and are ‘mostly free’ or in a doublet state with oppositely charged counterions. The ‘mostly free’ counterions consequently exhibit diffusive dynamics of free particles in a dilute solution. There is a decrease in the mobility of the counterions with reduced number of chains. However, for positive counterions, a slight increase in the mobility is observed from NC = 50 to NC = 100 followed by a decrease in mobility. The number of positive counterions is fixed at N pcions = 1000 while the number of negative counterions increase from Nncions = 300 to 2400. The trend in counterion mobility is related to the number of positive counterions being either larger or smaller than the number of negative counterions. In the regime Nncions < N pcions , the slight increase mobility from NC = 50 to 100 can be attributed to the increase in φBCP . In the low φBCP case, the positive counterions are associated with the surfactant head. As more BCP is added to the system, a greater number of charged blocks of the BCP are adsorbed on the surfactant head of the spherical micellar



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(a)

(b)

(c)

(d)

Figure 2: Mean-Square Displacement (MSD) for the double hydrophilic system for the selected charged species. The MSD are plotted for (a) negative counterions, (b) positive counterions, (c) charges on the BCP charged block and (d) surfactant head. Color scheme: black lines represent NC = 50, red lines represent NC = 100, green lines represent NC = 200, blue lines represent NC = 300 and magenta lines represent NC = 400 respectively. The black two-sided arrow represents the diffusive region used to calculate the diffusion constant shown later in this section.


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structure, releasing more positive and negative counterions into the solution and hence there is a slight increase in mobility from NC = 50 − 100. On the other hand, for N pcions < Nncions , the slight decrease is related to the overall decrease in free counterions. In this regime there are more Nncions that can form doublets with the N pcions and that results in fewer free counterions and hence a decrease in the counterion motion. A similar behavior has been observed in the transport of Na+ and Br− in a mixture of sodium poly(acrylic acid) and alkyltrimethylamonium bromide (CnTAB) (NaPAA-C1 2TAB) at the air/water interface. 55 In a related investigation, Qi et al. 44 had shown that the dilution down below the CAC leads to a disassembling of the complex in a hydrophilic-neutral BCP and surfactant complex and hence a complete desorption. In our simulation, we have not observed the disassembly behavior as the simulations are performed in implicit solvent condition and no dilution experiments (simulation) were performed that would require addition of water. In Figure 2(c)-(d) and Figure 3(c)-(d), MSD for the charges and head are plotted for double hydrophilic and mixed BCP systems. The mobilities of the BCP charges increase with an increase in the number of BCP chains for both systems. An increase in BCP chains increases the total number of charges, of which, there is a maximum number of charges that can associate with the surfactant heads on the micelle surface. The unassociated charges or the residual charges increases with NC thereby the MSD increases with NC . The mobilities are much faster for the double hydrophilic system (Figure 2(c)) than for the mixed BCP system (Figure 3(c)). The negatively charged surfactant heads sit on the surface of the surfactant micellar surface for both systems. The negatively charged heads attract the positive BCP charges due to strong electrostatic interactions. In the mixed BCP system, the hydrophobic neutral blocks favor entropic attraction between the hydrophobic core of the surfactant micelle thereby pulling both blocks of the BCP towards the surfactant micelle and has been observed in Ref. 38 Along with the strong electrostatic interactions between the BCP charge and the head, the dynamics are restricted for both the charge and head as can be observed in Figure 3(c) and (d). On the other hand, the double hydrophilic BCP forms hairy nanoparticle like structures in which the surfactant micelle forms the core and the BCP forms the corona. The unfavorable interactions between the hydrophilic block and the surfactant tail help to push the BCP



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(a)

(b)

(c)

(d)

Figure 3: Mean-square displacement for the mixed BCP system for the charged species only. The MSD are plotted for (a) negative counterions, (b) positive counterions, (c) charges on the charged block and (d) surfactant head. For all the plots, black lines represent NC = 50, red lines represent NC = 100, green lines represent NC = 200, blue lines represent NC = 300 and magenta lines represent NC = 400 respectively.


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away from the surfactant micelle. This enthalpic repulsion causes a large part of the BCP charges to move away from the micellar surface and hence show comparatively less agglomeration. The manifestation of this effect is visible in Figure 2(c) and (d) where the charges show faster dynamics compared to the mixed BCP system. Alternatively, the surfactant heads mobility is comparatively less affected as the surfactants are in micellar states.

(a) Double Hydrophilic

(b) Mixed BCP

Figure 4: Diffusion coefficient as calculated from the MSD for (a) double hydrophilic and (b) mixed BCP systems. The color schemes are shown in the legends. One of the main objectives of the MSD analysis is to extract the self diffusion constant of the molecular species. The self-diffusion coefficients for the various charged species are shown in Figure 4. Figure 4(a) and (b) show the results for the double hydrophilic and the mixed BCP system respectively. The self-diffusion coefficients, Dc , Dh , Dnc and D pc are derived from the Ein . t t→∞

stein relation, Dspecies = 16 lim

The subscripts c, h, nc and pc represent four different

charge species: BCP charge (green), surfactant head (blue), negative counterion (black) and positive counterion (red), respectively. Since only one diffusion constant is extracted in the limit t → ∞, it is important to note that if a particular species is undergoing multiple types of diffusion during the t → ∞ limit, the calculated Dspecies will be an average in that time limit. 56 The slope of the MSD is calculated from the diffusive regime as shown in Figure 2(a) by the double-sided arrow. For consistency, we used the same region from different MSD to derive the diffusion constants of different species. The diffusion coefficients of counterions Dnc (black) and D pc (red) show 15 ACS Paragon Plus Environment


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relatively fast diffusion. The addition of BCP increases the total number of charges and hence encourages adsorption of the BCP charged block on the surfactant head. The same distribution of BCP charges can also be seen in the number density distribution shown in Figure 1 and our prior structural studies. 38 The distribution of BCP charges on the surface of the micelle screens out both the positive and negative counterions from the surfactant head and the charged block of the BCP, releasing the counterions ’mostly free’ into the solution. The dynamical properties of the counterions along with the structural analysis performed earlier, 38 indicate that the formation of these charged BCP−surfactant complexes is an ion-exchange process. In this ion-exchange process, the charged BCP with high concentration of positive charges bind to the negatively charged surfactant head of the micelle surface by replacing the monovalent counterions. These results are consistent with earlier theoretical 55 and experimental 57 reports on the formation of polyelectrolyte-surfactant complexes by an ion-exchange process. Slow diffusive behaviors are observed for the BCP charges and head (Figure 4(a) and (b)). The double hydrophilic system (Figure 4(a)) shows a slight increase in Dc (green) from NC = 50 to 200 and remains constant thereafter for higher NC . With an increase in the number of BCP chains, mobility increases in both the charged blocks and the hydrophilic blocks. As discussed in the previous section, the entropic mismatch between the hydrophobic tail and hydrophilic neutral block pushes the charged block away from the head which results into an extra freedom for the movement of the charged blocks until all the heads are neutralized by the BCP charges. This is manifested in the slight increase in self diffusivity from NC = 50 to 200 and a slow increase thereafter. In contrast, Dh (blue) remains roughly constant throughout the BCP concentration range. The steady value of Dh is explained by the surfactant heads being attached to the more compact surface of the surfactant micelle. Thus the self-diffusion of the heads are limited due to their relatively rigid structural property. 38 For the mixed BCP systems, the diffusive behavior of the surfactant head exhibits similar response, i.e., little or no change in Dh as shown in Figure 4(b). In Figure 4(b), Dc shows a minimal drop in value and stays constant for the whole NC range. The addition of charged BCP blocks increases the total number of charged and hydrophobic neutral monomers.


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The increase hydrophobic neutral block strengthens the interaction between surfactant micelle core and the hydrophobic neutrals of the mixed BCP. The charges on the BCP replace the monovalent counterions on the head until the surfactant and BCP charge concentration become equal. This results in a modest drop in Dc until NC = 200. The favorable interaction between the surfactant micelle core and hydrophobic neutrals of the mixed BCP brings the two molecules together and the charges on the BCP decorate the surface of the micelle as was observed in Figure 1(b). The strong electrostatic correlation between the surfactant head and the BCP charges manifests in a Dc behavior similar to Dh at higher NC . Similar behavior of charge transport has been observed in poly(thylene-oxide) − poly(propylene oxide) − poly(ethylene oxide) block copolymer and ionic surfactant complexes. 58 The increase in Dc in Figure 4(a) and the modest drop in the Dc value Figure 4(b) until NC = 200, once again, corroborates the fact that the formation of these complexes rely on an ion-exchange process. 55,57

(a)

(b)

Figure 5: Dynamic structure factor (Intermediate scattering function), S(Q,t), for one BCP concentration, NC = 100, and one scattering wave vector, Q = 0.3142 representing largest length scale, L = 20.0σ . The figures in (a) and (b) are plotted for double-hydrophilic and mixed-BCP systems respectively. The plots of S(Q,t) shown here are typical representation of relaxation of different species of the simulating systems and is required to calculate the relaxation time. Color scheme represents, negative counterions (red), positive counterions (black), surfactant head (green), surfactant tail (blue), charged block of the BCP (orange), neutral block of the BCP (magenta) and charges on the polymer chains (cyan). For all the systems, the system specific S(Q,t) was calculated to determine the relaxation time shown in Figure 6 In Figure 5, we show the typical dynamic structure factor, S(Q,t), for a particular set of BCP 17 ACS Paragon Plus Environment


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concentration and wave number, NC = 100 and Q = 0.3142 respectively. The S(Q,t) for all the systems (not shown here) are observed to follow similar decay pattern. The fastest relaxation is observed for the counterions (red and black) for both the systems as they are either in ‘mostly’ free or in doublet state giving rise to faster free molecular relaxation. Relaxations of the charged block of the BCP and charges on the BCP chains (orange and cyan) show similar decay pattern as they are part of the same block. The surfactant tails (blue) show the slowest relaxation followed by the surfactant head (green). Surfactant molecules are part of the aggregated micelle and hence the motion of both the head and tails are restricted within the micelle. Therefore, the surfactant molecules are expected to exhibit slow dynamics as observed here. Interestingly, the neutral block of the BCP (magenta) show slower dynamics in mixed BCP case (Figure 5(b)) and faster dynamics in double hydrophilic case (Figure 5(a)). As observed in the structural analysis, 38 the neutral blocks agglomerate between the surfactant micelle in mixed BCP system while the neutral blocks freely dangle in solvent in the double hydrophilic case. The dynamics shows the same neutral BCP relaxation behavior for these two systems. For double hydrophilic system (Figure 5(a)), the neutral BCP relaxation is faster than the surfactant as the dangling neutral blocks are free to move in the solvent. However, in the mixed BCP system the neutral BCP relaxation is comparable with the surfactant molecules. For the mixed BCP system (Figure 5(b)), the surfactant agglomerate in between the surfactant micelles consequently their movements are restricted to the surfactant relaxation. For all the systems the S(Q,t) are calculated and the S(Q,t) data are used to obtain the structural relaxation time presented in Figure 6. The structural relaxation time, τ , is determined from the dynamic structure factor, S(Q,t), and is defined as the time the structure factor reaches to 1 e of the S(Q,t = 0). In Figure 6, the p relaxation times (in reduced units), τ ∗ = τ mi σ 2 /εLJ , are plotted for two different Q values, Q =

0.3142 and Q = 1.2566 for double hydrophilic and mixed BCP systems respectively. These two Q values correspond to the length scales, L = 20.0σ and L = 5.0σ (Q = 2π L), respectively and align

closely with the radius of gyration, Rg of the BCP. It has been observed in a previous structural study 38 that Rg ≈ 20σ or slightly greater than 20σ across all the systems. The relaxation dynamics


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(a)

(b)

(c)

(d)

Figure 6: Relaxation time, τ ∗ , for two different Q values. Left panel, (a) and (c) are plotted for the double hydrophilic system and the right panel, (b) and (d) are plotted for the mixed BCP system. Relaxation times are obtained for two different Q values; (a)-(b) for Q = 0.3142 and (c)-(d) for Q = 1.2566 representing two different length scales associated with the radius of gyration of the BCP chain. The black and red colors represent the head and tail of the surfactant. Green and blue colors represent the neutral polymer (polymer A) and neutral monomers of the charged block (polymer B) respectively and the magenta color represents the charges on the charged block (ACharge). Lines are guide to the eye only.



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at Rg would represent typical long length-scale dynamics while the intermediate length scales or segmental length-scale dynamics can be represented by the dynamics at a distance between the charge monomers, i.e. 5σ . Therefore, the choice of the above two Q values corresponds to long and intermediate length scales. At the monomeric length scale, L = 0.97σ corresponding to Q ≈ 6.5, no compelling physics can be observed in these type of strongly correlated systems, therefore the relaxation dynamics at the monomer length scale is omitted from the present discussion. In Figure 6(a) and (c), the surfactant head and tails show a dip at NC = 100 followed by an increase. For the double hydrophilic systems and in the limit φBCP < φS , the surfactant heads are not all screened by the polymer chains. Moreover, the fewer the BCP charges, there are more unscreened heads, resulting in a stronger electrostatic repulsion between the micelles. Therefore, the surfactants are stiffly bound to the micelle. This results in a higher τ ∗ for low BCP concentration. From NC = 100 onward, as it approaches φBCP ≥ φS limit, while the increase in BCP charges screen more heads thereby reducing electrostatic repulsion, the chains proximity to the micelle surface reduces the surfactant movement. That is reflected in an almost flat τ ∗ from NC = 200 onward (Figure 6(a) and (c)). The slight decrease in τ ∗ from NC = 200 to 400 causes decreased micellar stability due to higher BCP charges which drag the neutralizing positive charges from the negative head of the surfactant micelle. The effect of surfactant concentration, chain length compatibility on micelle surface properties, and relaxation behavior for different solvent has been investigated extensively and the results presented here are in agreement with earlier investigations on surfactant dynamics in an aqueous or polyelectrolyte environments. 59,60 The neutral BCP blocks form the micellar corona with hairy NP structure and hence they dangle from the micelle and are loosely bound to the micelle. 38 This results in a faster relaxation for the neutral blocks. On the contrary, the relaxation of the BCP charges follows the charged BCP block. The charged blocks are attached to the micelle surface (surfactant head), however, the weak attachment due to the repulsive BCP neutral block reduces the binding between the micelle and BCP charges. The slower relaxation of the charged blocks is a consequence of the weakly bound charges with the micelle. In the mixed BCP systems, the head and tail relaxation times decrease with an increase in


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NC for both length scales (Figure 6(b) and (d)). In these systems, in addition to the electrostatic attractions between the anionic surfactant head and cationic BCP charges, the attraction between the hydrophobic groups and the surfactant tails also influences the relaxation of the surfactant molecules and BCP chains. The tails form lamellar type structures with the surfactant micelle. This causes an additional constraint to the surfactant micelle stability. The attractive hydrophobic interactions between the hydrophobic groups and tails results in a pull of the surfactant tail at the micelle core. Thus the rigid packing of the surfactant micelle is loosened as the number of BCP increases, giving rise to a faster relaxation of the surfactant molecules (head and tail). Similarly, the relaxation of the BCP neutral block becomes faster as more BCP chains are introduced to the system. The same can be observed for the heads and tail molecules in Figure 6(b), but not in Figure 6(d). The lower length scale, L = 5σ , is approximately five monomeric units, i.e., the segment between two charge sites of the charged block. Therefore, the relaxation time at this length scale is governed by the likelihood of the charges associating with the micellar surface and the hydrophobic interactions between the neutral BCP block and surfactant tails of the micellar core. If the number of surfactants is higher than the number of BCP charges, screening will increase with an increase in number of BCP chains. With the increase in screening, the BCP charges will form a rigid, stable agglomerated structure 59 with the micelle that increases the relaxation time. Alternatively, an over-saturated screening will relax some of the BCP charges that cannot associate with the surfactant head (on the micelle surface). Thus lower relaxation time (faster relaxation) with an increase in BCP charges, in the regime where number of surfactant is less than the BCP charges, is observed in Figure 6(d). The length scale dependence of τ ∗ for the double hydrophilic system is shown in Figure 6(a) and (c). At longer length scales (Figure 6(a)-(b)), the relaxation time is more than an order of magnitude higher than the smaller length scales for both double hydrophilic and mixed BCP (Figure 6(b)-(d)) systems. The longer length scales (L = 20σ ) represent the relaxation of the micelle and BCP agglomerated structures. Due to the strongly bound large compact structures, all of the



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relaxation dynamics slow down at this length scale. As discussed earlier the structural relaxation at lower length scale ( 5σ ) corresponds to relaxation dynamics at the segmental length scale. As the smaller length scale is comparable to the segmental length scale, the BCP charges form an ion-pair with a some of the surfactant heads (on micelle surface) and can easily change its interaction partner to another surfactant head. Hence the segmental relaxation mechanism can be much faster, as it is indeed observed in the drop in relaxation times, τ ∗ in Figure 6(c) and (d) compared to Figure 6(a) and (b). In the polyelectrolyte-surfactant complexes, the fastest relaxation mode was assigned to the motion of the surfactant molecule grafted onto a polymer, a length scale comparable to the segmental length scale and is attributed to the unassociated polymers at the polymer-micelle interface. 61 This is consistent with our finding in BCP-surfactant complex at the lower length scale.

Conclusions The dynamics of charged species in a charged-neutral BCP surfactant complex were thoroughly examined using MD simulations. Two sets of charged-neutral BCPs, one with hydrophilic neutral blocks and the other with hydrophobic neutral blocks exhibit complex dynamics at different length scales. We first examined the structures formed by the ionic species only. Ionic structures are crucial to determining and controlling the charge transport in these systems. Our results indicate that the ionic structures (Figure 1) are fairly distributed and connected in the double hydrophilic system while the ionic structures are more concentrated in the mixed BCP system. The charges form the backbone skeleton of the nanostructured complex. The interactions between the neutral hydrophobic/hydrophilic monomer and the electrostatic interactions between the charges compete energetically compete with each other giving rise to the characteristic structures observed for these complexes. These ionic structures are not limited to only charged-neutral BCP surfactant complexes, but have also been observed in colloidal systems, 1,13,62–64 where it forms distinct ionic networks. The mobility of the ‘mostly free’ counterions and/or counterions in doublet states with oppo-


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sitely charged counterions exhibits faster dynamics. The counterion MSD also provides support for the counterion release scenario observed in earlier works. 55 The dynamics (MSD) of the BCP charges and surfactant heads demonstrates balance between the entropic and enthalpic forces inherent to these complexes. The resulting MSD for the double hydrophilic and mixed BCP systems align ideally with the nature of the hairy structures and lamellar structure of the two different systems. The monovalent counterions are replaced by the BCP charges as the charges favorably bind with the surface of the surfactant micelle resulting in the formation of the complex that is driven by ion-exchange process. The ion-exchange process has been well established in the selfassembly of PE surfactant complexes resulting in release of counterions. 55,57 In these simulations, we have shown that the formation of the charged BCP and surfactant complex is also driven by ion-exchange processes. The structural relaxation time as obtained from the dynamic structure factor, S(Q,t), shows length-scale dependent relaxation times for the neutral and charged species. The neutral blocks of the BCP chains show close to two orders of magnitude faster relaxation for the double hydrophilic system (τ ∗ < 102 ) than for the mixed BCP system (τ ∗ ≈ 104 ) . This compliments the structural finding of hairy and lamellar structures formed by the neutral blocks of these two systems, where the hairy structures have more degrees of freedom to relax faster compared to molecules tightly attached to the lamellae. With an increase in NC the relaxation times of the surfactant heads and tails decrease for the mixed BCP system while the head and tail relaxation times remain unchanged in the double hydrophilic system (except a small dip at NC = 100). The decrease in τ ∗ in mixed BCP systems is due to the combined effect of the electrostatic interactions, screening of the surfactant head and the hydrophobic interactions between the BCP neutral block and surfactant tail. 59–61 At lower length scale the relaxation dynamics are comparable to the dynamics at the segmental length scale of the charged BCP. Additionally, the relaxation dynamics provides confirmation of the ion-exchange process in controlling self-assembly. In combination with the structural investigation, 38 this study helps establish a comprehensive understanding of the structure-property relationship of the charged-neutral BCP surfactant com-



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plex. Our studies strongly favor design of high-throughput charge transfer materials using chargedneutral BCPs with surfactant moieties for structurally steady, enhanced dynamical capability materials instead of using homo-polyelectrolytes or neutral polymers. While no advanced experimental outlook is detailed in this theoretical study, the fundamental understanding of the charged-neutral BCP and surfactant complexes could open opportunities for designing better polymer membranes, colloidal suspensions research targeting water separation technologies, drug delivery systems and polymer batteries.

Acknowledgements 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 DE-AC05-00OR22725. Part of this research used resources of the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Scientific User Facility supported by the Office of Science of the U.S. DOE under Contract No. DE-AC02-05CH11231. A portion of this research was conducted at the Center for Nanophase Materials Sciences (CNMS), which is a DOE Office of Science User Facility.

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Dynamics of Charged Species in Ionic-Neutral Block Copolymer and

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