Structure and Dynamics of Ionic Block Copolymer ... - ACS Publications

Sep 6, 2017 - independent of the degree of sulfonation of the C block with no long-range order. The cluster cohesiveness and .... associate to form io...
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Structure and Dynamics of Ionic Block Copolymer Melts: Computational Study Dipak Aryal,† Anupriya Agrawal,†,‡ Dvora Perahia,*,† and Gary S. Grest*,§ †

Department of Chemistry and Department of Physics, Clemson University, Clemson, South Carolina 29634, United States Department of Mechanical Engineering and Materials Science, Washington University in St. Louis, St. Louis, Missouri 63130, United States § Sandia National Laboratories, Albuquerque, New Mexico 87185, United States ‡

S Supporting Information *

ABSTRACT: Structure and dynamics of melts of copolymers with an ABCBA topology, where C is an ionizable block, have been studied by fully atomistic molecular dynamics (MD) simulations. Introducing an ionizable block for functionality adds a significant element to the coupled set of interactions that determine the structure and dynamics of the macromolecule. The polymer consists of a randomly sulfonated polystyrene C block tethered to a flexible poly(ethylene-rpropylene) bridge B and end-capped with poly(tert-butylstyrene) A. The chemical structure and topology of these polymers constitute a model for incorporation of ionic blocks within a framework that provides tactility and mechanical stability. Here we resolve the structure and dynamics of a structured polymer on the nanoscale constrained by ionic clusters. We find that the melts form intertwined networks of the A and C blocks independent of the degree of sulfonation of the C block with no long-range order. The cluster cohesiveness and morphology affect both macroscopic translational motion and segmental dynamics of all the blocks.

I. INTRODUCTION Introducing distinctive blocks into one macromolecule constitutes an effective path to tailor microdomain geometries that offer a portfolio of desired properties.1,2 As the complexity of the copolymer increases, the ability to tailor properties and design new materials is enhanced. However, increasing number of blocks with distinctively different chemistries results in a set of new challengesparticularly, controlling the overall structure and dynamics from segmental to macroscopic motions. Of particular technological significance are polymers that consist of ionizable blocks. Their role as ion and charge carriers enables selective transport, opening new directions for biotechnology3,4 and clean energy.5−7 These ionizable blocks that enable functionality impact the dynamics of macromolecules through ionic clustering.8−14 While some of these ionic polymers have found industrial applications, the interplay between factors that control the structure and dynamics of highly segregating blocks with compound topology remains a critical open question. Of particular significance is resolving the effect of clustering of ionic blocks on phase structure and dynamics on atomistic to nanometer length scales. These length scales present an experimental and computational challenge since the ionic clustering often traps the polymers in intermediate states that remain stable over extended time scales, often exceeding that of device lifetimes. Here using fully atomistic molecular dynamics (MD) simulations, we have obtained a distinctive molecular insight into the structure and © XXXX American Chemical Society

dynamics of one structured copolymer with polystyrene sulfonate (PSS) as the ionic block. We show that the ionic clustering not only dominates the macroscopic dynamics of copolymer melts as previously observed in PSS15,16 but also impacts the local packing and segmental dynamics of all constituents of the copolymer, including those that are not tethered to the ionic clusters. The dynamics of macromolecules across a broad time and length scales underline their unique viscoelastic behavior. Specifically, the dynamics is controlled by the molecular weight of the polymers, their rigidity, and their topology. Further complexity may arise from long-range ordering induced by connecting multiple blocks into a macromolecule.2 Incorporating ionic groups into block copolymers drives association of the ionic blocks that, in turn, changes the structure and dynamics of the macromolecules.17−20 One such macromolecule is a symmetric pentablock copolymer (ABCBA). The center block (C) consists of randomly sulfonated atactic polystyrene (PSS). It is symmetrically tethered to a poly(ethylene-rpropylene) (PErP) (B) and terminated on both sides by bulky atactic tert-butylpolystyrene (t-b-PS) (A). This structured polymer was initially designed with the rational that the ionizable blocks would facilitate transport and the others would Received: April 8, 2017 Revised: August 24, 2017

A

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between the chemistries and physical behavior of polymers. Further the time scales accessible to MD simulations are those that overlap cluster formation experimentally and are well correlated with neutron spin echo and backscattering experimental studies. The polymer chemical structure as well as examples of chains depicted from melts of sulfonation fractions f = 0 and f = 0.55 are given in Figure 1. This strong segregation has been

provide tactility (PErP) and mechanical stability (t-b-PS). While being a complex macromolecule, in contrast to lower order copolymer topologies of di- and triblocks, this ABCBA macromolecule constitutes the simplest system that does not disintegrate when the cohesiveness of the ionic clusters decreases. This together with the fact that its separate blocks have been well studied9−14 makes this copolymer an optimal model system to probe the correlation of ionic cluster behavior and structure and dynamics of macromolecules where the transport channels coexist with mechanical stabilizing groups. Polystyrene sulfonate, which constitutes the ionizable block of this structured polymer, has been well studied. Numerous groups have established a correlation between the presence of ionic clusters and constrained dynamics.9−14 Experimentally, Weiss et al.9 have demonstrated that it is sufficient to incorporate small numbers of ionizable groups in PS to drive high viscosities and entangled-like rheology. Using atomistic MD simulations, Agrawal et al.15,16 have recently provided molecular insight into clustering in PSS and demonstrated a direct correlation of the association of the sulfonated groups and the dynamics of the aromatic rings within PSS. Tethered to potentially mechanical stabilizing blocks, this pentablock has been the focus of several studies including those of solution structure and transport in membranes.21−25 This copolymer provides a model system where experimentally anionic polymerization offers a well-defined modifiable macromolecule to probe the effects of complexity tailored into copolymers in the high segregation limit on their structure and dynamics. Significant insight into the behavior of this ABCBA copolymer has been obtained from solution studies where a variety of micellar shapes that depend on the solvent have been identified including spherical and elliptical core−shell arrangements.20,26 Recent MD simulations have revealed that the core of these micelles consists of soft nanonetworks formed by the ionic segments, constituting a new type of soft responsive nanoparticle.19,27,28 The degree of cohesiveness of the ionic clusters in solution is translated to the membranes and determines the path to formation of their structure. The significance of understanding the detailed interrelation between the blocks is manifested in recent comprehensive studies that demonstrated the impact of nature of the co-ion transport across membranes.21,22,29 The current study is set to resolve the structure and dynamics of melts of this ABCBA copolymer. Particularly, it probes the interrelation between the sulfonated block that associate to form ionic clusters and the nonionizable blocks across sulfonation fractions varying from a nonionic copolymer through the ionomer regime to the polyelectrolyte one. The results are compared with those previously obtained atomistic simulation for PSS.15,16 The fully atomistic MD simulations, presented here, allow capturing the nanosecond scale dynamics which is the time scale for segmental motion in polymers. Similar to physical ionic membranes (i.e., experimental), the membranes may consist of long-lived states, dictated by the time of assembly of the ionic clusters. Here, atomistic MD simulations provide an insight into a critical length scale, essential for controlling local structure and dynamics of a system confined by formation of ionic clusters. This length scale is not accessible by models such as bead− spring30,31 and DPD and coarse-grained models.32−37 While coarse-grained models probe phase behavior and transport at large scales, by their construction, these techniques average over ca. 0.1−3 nm, a range that depicts direct correlation

Figure 1. (a) Chemical structure of poly(tert-butylstyrene)-b-ethylener-propylene-b-styrene-r-styrenesulfonate-b-ethylene-r-propylene-bpoly(tert-butylstyrene) pentablock molecule. Images of single chain of pentabock from melts with (b) f = 0 and (c) f = 0.55 at 500 K. Blue represents the center PS block, orange the t-b-PS block, and green the PErP block. Oxygen atoms are red, sulfur atoms are yellow, and sodium atoms are gray. The letters x, y, and z correspond to the polarization numbers of each of the blocks, and r denotes random. For the PErP 1.1% of the monomers are propylene.

previously observed experimentally20,25 and computationally19,28 in solutions and in micelles. Here, the understanding attained on ionic clustering on the structure and dynamics of PSS15,16 is translated to structured copolymers that contain ionizable blocks. We find that both the structure and dynamics of the melt are strongly impacted by the size and shape of the ionic clusters, as was previously observed for PSS.15,16 The ionizable groups associate within the polystyrene domains and impact the macroscopic dynamics of the entire copolymer. Surprisingly, the formation of ionic clusters within the PSS domain impacts the packing and segmental dynamics of all blocks. Following a detailed account of the model and methodology, the paper introduces structure and dynamic studies of the ABCBA polymer. Both sections begin with studies of dielectric constant ε = 1, as dictated by the force field chosen. The dielectric constant is then increased to tune the cohesiveness of the ionic clusters.

II. MODEL AND METHODOLOGY Pentablock copolymers were modeled using the Optimized Potentials for Liquid Simulations−All Atoms (OPLS-AA) framework of Jorgensen et al.38,39 The OPLS-AA potential includes both bonded and nonbonded interactions. The bonded potential is sum of intermolecular bond, angle, and dihedral interactions. The nonbonded interaction Unb(rij) is a combination of the 12−6 Lennard-Jones (LJ) potential and electrostatic potential B

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Macromolecules ⎡⎛ ⎞12 ⎛ ⎞6 ⎤ qiqj σij σij Unb(rij) = 4εij⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ + r ⎝ rij ⎠ ⎦ 4πεrij ⎣⎝ ij ⎠

maintained by using a Langevin thermostat with a 100 fs damping constant. The melt for f = 0.15 was prepared in two ways. In the first, the 30 chains were run at constant volume at T = 500 K without any solvent for 40 ns followed by compression to melt densities at a constant pressure of P = 1 atm and temperature T = 700 K using the Nosé−Hoover barostat/thermostat for 30 ns. Alternatively, the 30 chains were immersed in a 1:1 mixture of cyclohexane:heptane (a commercial solvent) for 40 ns, after which the solvent was removed over 10 ns and the system was compressed at constant pressure of P = 1 atm for 30 ns. The ion cluster distributions were then calculated for both systems and were found to be identical as shown in Figure S1. Equilibrating in the cyclohexane:heptane mixture and then removing the solvent is equivalent to the process used industrially to cast membranes of the polymers. In this solvent the ionic blocks segregate from the rest of the blocks and the tb-PS collapses, as has been shown in both experimental and computational studies.20,28 As both the cluster distribution and the scattering function of both systems are found to be the similar, we used the one made without the solvent to make the other three melts, since it is computationally faster. After running at constant pressure for 30 ns, the mass densities of the system at 700 K were 0.84, 0.86, 0.88, and 0.90 g/cm3 for f = 0, 0.15, 0.30, and 0.55, respectively. The resulting size of the simulation cell L is ∼160 Å. Each of these systems was then run for 400 ns. 700 K was chosen since it is well above the glass transition of PSS. The system was then cooled to 500 K at a rate 60 K/ns at constant pressure P = 1 atm and then run at constant volume at mass densities 0.87, 0.89, 0.91, and 0.93 g/ cm3 for f = 0, 0.15, 0.30, and 0.55, respectively, for 150 ns. It is important to note that the ionic clusters in membranes formed by both methods evolve during the preparation in the first 100 ns or so. All clusters remain dynamic throughout the simulation. To understand the effect of the electrostatic interactions on the structure and dynamics, the dielectric constant was increased from ε = 1 to 2, 5, 10, and 20 for f > 0 after 400 ns at 700 K and then run for an additional 200 ns. The f = 0.15 was also run at 500 K for the same four values of ε. Tuning the dielectric constant is a path to affect the ionic clusters. It bears similarities to effects of minute amounts of polar solvents on the ionic clusters experimentally as shown for Nafion and PSS, where the majority of humidity resides in the ionic region. The dielectric constant changes hardly affect the neutral blocks but strongly impacts the ionic regions. Simulations with ε > 1 were run at the same volume as that of the corresponding ε = 1 system to facilitate comparison. This results in a slight increase of pressure of 3.9−47.5 atm as ε increased from 2 to 20 at 700 K. To ensure that we allow sufficient time for the ionic cluster to evolve, the dielectric constant of the polymer at ε = 20, where PSS exhibit no ionic clusters,15,16 was switched to ε = 1, and the formation of ionic clusters was followed. We find that it took 100−150 ns for the ionic clusters to re-form after the dielectric constant is reduced. The static structure factor S(q) of the melt was calculated as a function of q for all f

(1)

where rij is the distance between atoms i and j. εij is the LJ energy and σij is the LJ diameter for atoms i and j, and qi is the partial charge for atom i. Berthelot’s rule εij = (εiεj)1/2 and Good−Hope’s geometric mixing rule σij = (σiσj)1/2 are used for the LJ energy and LJ diameter, respectively. The dielectric constant ε in the OPLS-AA model is set to ε = 1. Nonbonded interactions are calculated between all atom pairs of different molecules and all pairs on the same molecule separated by three or more bonds, though the interaction is reduced by a factor of 1/2 for atoms separated by three bonds. The cutoff rc = 1.2 nm is used for all LJ interactions. Coulomb interactions are treated with long-range particle−particle particle-mesh algorithm (PPPM)40 Ewald with a real space cutoff of 1.2 nm and a precision of 10−4. The cutoff value was chosen to optimize computational efficiency while maintaining precision. Thirty unique, randomly sulfonated pentablock molecules with f = 0, 0.15, 0.30, and 0.55 were built using Polymer Builder, and their energy was minimized using the Amorphous Cell modules in Accelrys Materials Studio41 and placed in a cubic periodic simulation cell of initial size L3 with L = 300 Å. The energy of each molecule was initially minimized with the polymer consistent force field (pcff) to remove overlaps, available in Materials Studio, followed by conversion to OPLSAA potentials, using an in-house code. OPLS-AA potentials, which are not available in Materials Studio, were used for production runs since they are optimized for alkanes and capture well the properties of hydrocarbon chains.45 OPLS-AA parameters for sulfonated groups and alkane are taken from refs 42−45. The pentablock molecules, A-B-C-B-A (Figure 1a), had a total molecular weight of ∼50 000−53 000 g/mol depending on the degree of sulfonation with a center block (C) of randomly sulfonated atactic polystyrene tethered to polyethylene with randomly substituted 1.1% propylene (B) and end-capped by atactic poly-tert-butyl blocks (A). The total number of atoms Nch in each chain varied from 11 896 to 12 181 depending on f. The total number of atoms in the simulation cell is N = 30Nch. The total wt % of the center sulfonated block is ∼40%, while each of the randomly substituted polyethylene blocks is ∼20% and each of polytert-butylstyrene blocks is ∼10%. The counterion is Na+ in all cases. Experimentally, a small fraction of propylene is introduced to prevent PE crystallization. The ratio of the blocks was chosen to match experimental studies.20 This ratio was optimized by Kraton Polymers LLC for balancing transport and tacticity of this polymer. The total molecular weight of the polymers in the current study is ∼33% less than the experimental one, as a compromise with computational cost. The fraction of sulfonated aromatic rings was chosen to propagate from a neutral copolymer through the ionomer regime to the polyelectrolyte region. LAMMPS classical MD code46 was used to carry out all the simulations. Newton’s equations of motions were integrated using a velocity-Verlet algorithm. The reference system propagator algorithm (RESPA)47 with multi-time scale integrator with a time step of 1.0 fs for the bond, angle, dihedral, van der Waals interactions, and direct interactions part of the electrostatic interactions, and time steps 4.0 fs for f = 0 and 2.0 fs for f > 0 for long-range electrostatic interactions were used to the accelerate the simulation. Temperature was

N

S(q) =

N

∑ bibj exp(iq(ri − rj))/ ∑ bibj i,j=1

i,j=1

(2)

where N is the number of atoms in the melt. The scattering lengths of each element for neutrons are b = −3.7406 × 10−15 C

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Macromolecules m for H, b = 6.6511 × 10−15 m for C, b = 2.804 × 10−15 m for S, b = 5.803 × 10−15 m for O, and b = 3.63 × 10−15 m for Na. S(q) for the individual blocks was determined by setting bi = 0 for all atoms in the other blocks. The q vectors are chosen to be commensurate with the simulation cell, q = 2π/L (nx, ny, nz), where ni are integers. The results for S(q) are averaged over the last 200 ns of the run. The mobility of the pentablocks was measured by the meansquare displacement (MSD) for the entire pentablock and each of the three blocks using eq 3. MSD =

1 N

N

∑ ⟨⌊ri(t ) − ri(0)⌋2 ⟩

(3)

i=1

Segmental motion of polymer was determined by measuring the dynamic structure factor S(q,t) of the melt N

S(q , t ) =

Figure 3. (a) Melts of the pentablock at the indicated sulfonation fractions; (b) PSS center block from the melts in (a). All results are for 500 K with ε = 1. Blue represents the center PS, orange the t-b-PS, and green the PErP. Oxygen atoms are red, sulfur atoms are yellow, and sodium atoms are gray.

N

∑ bibj exp[iq(ri(t ) − rj(0))]/ ∑ bibj i,j=1

i,j=1

(4)

where N is the total number of atoms in each melt. S(q,t) for the individual blocks was determined by setting bi = 0 for atoms in the other blocks. S(q,t) results are fitted with either a single exponential

S(q , t ) S(q , 0)

independent of the sulfonation fraction, the blocks are locally phase segregated with the aliphatic block percolating across the melts. The end block appears segregated from both the PSS and the PErP block. In contrast to copolymers with blocks of volume fractions close to each other, neither the nonionic nor the ionic polymer melts exhibit long-range correlations. The melt of the nonionic copolymer, shown in Figure 2, consists of intertwined domains of segregated PS and t-b-PS in a continuum of PErP. While the two aromatic blocks segregate from the PErP, they do not intermix. These domains propagate across the melt. Similar structures have been recently reported experimentally by Zuo et al.2 for tetra- and heptablock nonionic copolymers. Using X-ray scattering, they have demonstrated that microphase separation occurs between incompatible blocks leading to a morphology which consists of a continuous region of poly(ethylene-r-propylene) and a mixture of poly(cyclohexylethylene) and polyethylene blocks. Increasing f from 0 to a finite value only slightly affects the overall distribution of the different blocks as shown in Figure 3. The size of these ionic clusters increases with increasing f, eventually forming an ionic network which percolates across the sample along the styrene domains for f = 0.55. The clusters include ionic groups from multiple polymer chains for all f studied. These results are in good agreement with the experimental observations of Choi et al.,25 who found that membranes of this polymer with f = 0.10 and 0.26 form isolated ionic microdomains whereas membranes with high f ( f = 0.39 and 0.52) exhibit a bicontinuous microphase-separated morphology of ionic groups. These clusters are typical of PSS as has been shown experimentally10,18 and computationally.15,16 However, the presence of the additional blocks impacts the shape, size, and distribution of these clusters and their cohesiveness. Beyond the formation of ionic clusters, increasing f affects the overall dimensions of the copolymers in the melt as reflected in their mean-squared radius of gyration ⟨Rg2⟩1/2, which at T = 500 K is 44.3 ± 0.3, 40.2 ± 0.2, 38.5 ± 0.2, and 37.5 ± 0.2 for f = 0, 0.15, 0.30, and 0.55, respectively. These changes are a first indication that clustering of ionic groups impacts the packing of the entire polymer. The effects of ionic clustering on the structure were extracted from the calculated static structure factor S(q) for all melts, following eq 2. S(q) as a function of q for different f values are

= A(q)e−Γ(q)t , where Γ(q) is the effective

diffusion coefficient, or a double exponential S(q,t)/S(q,0) = A1(q)e−Γ1(q)t + A2(q)e−Γ2t, where Γ1(q) and Γ2(q) are effective diffusion coefficients. To analyze the ionic clusters, we measured the distribution of ionic clusters and the mean cluster size. Two ionic groups SO3− are considered to be in the same cluster if the two S atoms are separated by less than a prescribed distance.

III. RESULTS AND DISCUSSION A. Structure. Pentablock melts were probed as the sulfonation fraction was varied from f = 0 to 0.55. This range of f depicts the crossover from nonionic copolymer to an ionomer center block and to a polyelectrolyte one. Images of the melts at 500 K are shown in Figure 2 for the nonionic polymer and in Figure 3 for the ionic ones. In all melts,

Figure 2. Nonionic pentablock melt ( f = 0) at 500 K for (a) entire melt, (b) PS and t-b-PS, (c) PS, and (d) t-b-PS. Box length L ∼ 160 Å. Blue represents the center PS, orange the t-b-PS, and green the PErP. D

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Macromolecules presented in Figure 4. The pattern for f = 0 consists of a broad signature at low q range. This liquid−liquid correlation

distribution of intermolecular packing. While the intensity of the signature that corresponds to the ionic domains increases with increasing f, the intensity of the peak centered around a distance of 4 Å decreases and the line broadens. This change in line shape with increasing f is attributed to disruption in packing arising from the presence of the ionic aggregates. The static structure factor S(q) shows that the ionic clusters dominate the nanometer length scale in these melt. The effects of cluster cohesiveness, size, and morphology on the cluster size and its distribution were probed by tuning the dielectric constant.15,16 The average ionic cluster size for ε = 1, 5, 10, and 20 for f = 0.15 is shown in Figure 5 where two ionic groups are considered to be in the same cluster if the sulfur atoms are separated by less than 6 Å. The closest distance between two sulfur atoms in a multiplet is 4.6 Å, accounting for the dimensions of the sulfur, the oxygen, and the counterion. Results for the cluster size distribution are the same for a maximum separation between two sulfur atoms to be in the same cluster of 5 and 6 Å. The ionic clusters are of highly correlated dipoles. The association of the counterions within the ionic clusters is shown in the inset of Figure 5a. With increasing dielectric constant, less of the counterions are condensed as expected for ion pairs in high dielectric media, though the counterions remain within the PS domains for all ε. Surprisingly, however, a larger fraction of the Na+ cations are condensed with increasing f for the same value of ε. This is attributed to the fact that with increasing the fraction of sulfonated groups the polarity of the PS domains increases, making it “an electrostatic trap” for the cations. Similar to melts of PSS,16 increasing the dielectric constant results in a decrease of the average cluster size. Above ε = 10 hardly any clusters are formed. As electrostatic interactions are long-range and decay with inverse the distance between the charges, we have probed cluster percolation across the membrane as the cutoff radii were varied between 6 and 10 Å. An ionic cluster is considered to percolate when there is a continuous path across the sample in all three directions.48,49 Figure 5b describes the largest cluster in a melt of f = 0.30 at ε = 1. Melts with f = 0.30 are on the border of isolated/percolated clusters. For a maximum distance of 6 Å between two S atoms, isolated clusters are observed. Increasing the cutoff to 7 Å hardly affect the results. However, following the clusters across the sample for 8 Å shows one percolating

Figure 4. S(q) as a function of q for melts of pentablock at the indicated f with ε = 1 at 500 K. Inset shows the peak intensity Imax at the ionic peak (left axis) (full symbols) and the corresponding dimension d (right axis) (open symbols) as a function of f.

quantifies the average thickness of the PS and tert-butyl-PS domains as depicted in Figure 2c. With increasing f, the liquid− liquid correlation translates to a well-defined peak that shifts to lower q values (larger dimensions), and concurrently its intensity increases. The peaks correspond to average dimensions of ∼32, 40, and 42 Å for f = 0.15, 0.30, and 0.55, respectively. The changes in intensity and dimensions are captured in the inset of Figure 4. These changes in line shape depict the formation of denser packing of the ionic groups and, concurrently, a decrease in the domain size distribution. At higher q values, a signature centered around q ∼ 0.7 Å−1 (9 Å) is observed. This signature that does not appear in S(q) for only the PErP block and is not impacted by f. It is attributed to the intramolecular dimension associated with the aromatic rings. An additional peak, centered around q ∼ 1.2−1.5 Å−1 (5−4 Å), corresponds to intermolecular packings including that of the PErP block and those of the aromatic rings. The peaks are broad and thus overlapping. They reflect the wide

Figure 5. (a) Average cluster size as a function of ε for f = 0.15 (red) and 0.30 (blue) at 500 K (full) and 700 K (open). Inset shows percent of Na+ condensed as a function of function of ε for f = 0.15 (circles), 0.30 (triangles), and 0.55 (stars). (b) Largest cluster (red) for f = 0.30 with ε = 1 and T = 500 K at the indicated cutoff distances between two S atoms, used to determine if two ionic groups are in the same cluster. (c) Largest cluster for f = 0.30 with ε = 10 at the indicated cutoff. E

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Figure 6. S(q) as a function of q for (a) copolymer, (b) PSS block, (c) PErP block, and (d) t-b-PS block for f = 0.15 at indicated ε for T = 500 K.

Figure 7. (a) Mean-square displacements for the indicated block. (b) Distance over which the indicated species moves over 200 ns as a function of f for T = 700 K.

cluster, where at 10 Å the ionic cluster percolates. Using 6−7 Å as the maximum distance between two sulfur atoms in the same cluster, we detect only tightly packed multiplets, as was observed in PSS,16 whereas increasing the distance to 8−10 Å, we also detect correlations of more loosely correlated ionic groups. Increasing ε to 10 allows the sulfonated group to rearrange as is shown in Figure 5c. In contrast to PSS, the ionic clusters are confined into one of the blocks forming an assembly with different cohesiveness that include both the dipole arrangements and the distance in between adjacent dipoles. The static structure factor for the melt is depicted in Figure 6a and for the individual blocks in Figure 6b−d as ε is varied. The ionic signature of the pentablock and PSS is highly sensitive to changes in the dielectric constant. With increasing ε, the intensity decreases however the position of the peak hardly changes (Figure 6a). As the clusters dissociate, the peak

broadens significantly; however, the ionic block remains largely segregated, as indicated by the broad signature in S(q). While no tightly associated ionic groups remain above ε = 5, the PSS block stays segregated from the rest of the polymer, forming a noncohesive ionic domain as is further emphasized in S(q) for the PSS block in Figure 6b. The chain packing for both the PSS and the PErP chains broadens with increasing the dielectric constant as reflected in the peak in S(q) centered around q ∼ 1.2 Å−1. While the packing of both the PSS and PErP blocks is affected by the dissociation of the ionic clusters, the terminal t-b-PS block remains unchanged. This decrease in intensity with increasing ε of the packing signature in the PSS is a signature of increasing disorder within the PS domain. Surprisingly, we find that the packing of the rubbery block is affected by the ionic clusters, where packing of the chains signature is higher in intensity for melts with ionic F

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Figure 8. Distance indicated species move over 200 ns as a function of dielectric constant ε at T = 700 K. (a) PSS for f = 0.15 (circles), f = 0.30 (up triangles), and f = 0.55 (stars). (b) PErP (left triangles) and t-b-PS (down triangles) for f = 0.15 (full symbols) and 0.55 (open symbols).

Figure 9. S(q,t)/S(q,0) as a function of time for the indicated q values at T = 700 K for (a) pentablock (full symbols) and PSS (open symbols), (b) PErP (full symbols) and t-b-PS (open symbols), at indicated q values, (c) effective diffusion coefficients Γ(q) of the copolymer and PSS, and (d) effective diffusion for t-b-PS and PErP. In S(q,t) the symbols correspond to the data and the solid lines to the fitting. In (c) and (d), the dotted line is a guide to the eye.

copolymer while tuning the ionic clusters. The first indication of arrested dynamics was observed in the MSD of the center of mass of the blocks compared with that of the individual chains. The results are presented in Figure 7 for T = 700 K. The mobility of the entire copolymer follows that of the PSS block, which is considerably slower than the other blocks for all f. During these measurements the polymer did not move its own dimensions. Not surprisingly, the mobility of the center block is further reduced as f increases as the addition of a small amount of ionic groups significantly reduces the mobility of chains. Both the flexible and end blocks move larger distances than the center blocks for all f values. Increasing the fraction of ionic groups has a measurable effect on the dynamics of flexible and end blocks. Over the time of the measurement, the copolymer did not move its own dimensions; however, while the diffusion is

clusters than that when the clusters dissociate. We attribute the impact of ionic groups on packing to local stretching of the PErP by the clustered PSS which is denser, inducing a more homogeneous packing of the aliphatic domains. With increasing ε, the PSS domains relax and the PErP becomes less correlated. Here we show a direct correlation between cluster formation within one polymeric domain and packing of another block. The origin of the ionic cluster effects on the PErP however is yet to be understood. The terminal block is unaffected by changes in ionic clustering. B. Dynamics. B.1. Macroscopic Dynamics. The dynamics of flexible and semiflexible polymer melts is dictated by a conjunction of their molecular weight, their Kuhn length, and their entanglement length.50 In ionomer melts where ionic clusters add constraints, the dynamics become yet more complex. Here we follow the dynamics of the pentablock G

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Figure 10. S(q,t)/S(q,0) as a function of time for f = 0.15 (symbol) and f = 0 (line) at q = 0.2 Å−1 for (a) pentablock, (b) PSS (c) PErP, and (d) t-bPS block at indicated ε values at T = 700 K.

The results for S(q,t) are further analyzed to extract the time constants for each of the constituents. At short times, 1−3 ns, a fast component is detected for some of the q ranges. It is attributed to fast rotations of nonconfined aromatic rings, which lowers the intensity of the entire pattern but is not directly measured within the q range studied. S(q,t) was analyzed with a sum of exponentials, starting from a single exponential. Alternatively, the KWW51 is used where multiple coupled dynamics is captured by a stretched exponentials. Here a single exponential was sufficient only for q values below the ionic peaks. A double exponential was able to capture the dynamics above this value. The effective diffusion coefficients Γ1(q) and Γ2(q) (by definition Γ1(q) < Γ2(q)) as a function of q are shown in Figure 9c,d. Both Γ1(q) and Γ2(q) increase linearly with q for q < 0.5 Å−1 with a crossover to a faster increase for larger q around the Rg = 13 Å of the individual blocks. While Γ1(q) is significantly slower than Γ2(q), it is essential to include both to fit the data for all blocks. It is attributed to the proximity of segments to the sulfonated groups; however, the origin of these slow components remains an open question. As seen in Figure 9d, the segmental motion of the t-b-PS is slower than that of the polyethylene segments in the PErP block. This is consistent with the fact that the t-bPS is collapsed compared to the PErP block, constraining its segmental dynamics. To further probe the effects of clustering on segmental dynamics, S(q,t) was calculated at different ε values. Figure 10 depicts S(q,t) for five values of ε for the pentablock, the PSS, the PErP, and the t-b-PS blocks for f = 0.15 at q = 0.2 Å−1 for T = 700 K. The corresponding plot on a semilogarithmic scale is shown in Figure S3. The values measured for the nonionic pentablock copolymers at the same q values are plotted as well. At this q range, dynamics reflected around the dimensions that correspond to the ionic peak is captured. In this q range, with increasing the dielectric constant, the dynamics of the entire copolymer and the ionic blocks increase (Figure 10a,b). The dynamics of the t-b-PS becomes faster as well, as the

impacted by the ionic block, the nonionic segments are moving slightly larger distances. Experimental neutron spin echo studies have shown that the time scale of dynamics for noncharged polymers is of the order of 300−400 ns. Here the results point to confined dynamics, where the copolymer motion is constrained either by the ionic clusters, as observed for PSS,15 or by structural features including domain boundaries and entanglements. To separate the two factors, the cluster’s cohesiveness was tuned via changing the dielectric constants and the MSD was extracted. The results are shown in Figure 8 for f = 0.15, 0.30, and 0.55. While the actual ionic clusters have dissociated, and the MSD slightly decreases with increasing f, the overall translation of the polymer remains rather small. These observations suggest that the arrest of the macroscopic dynamics is a result of convoluted structure−ionic cluster effects. B-2. Segmental Dynamics. Further insight into dynamics obtained by measuring the dynamic structure factor S(q,t) as a function of time, at different length scales manifested in the different q values, is shown in Figure 9. S(q,t) crosses a q range of 0.1−0.7 Å−1. The corresponding semilogarithmic presentation is presented in Figure S2. This q range encompasses the length scales of the ionic domains and chain packing. S(q,t) has been calculated for the entire polymer and for each of the blocks. This quantity captures well the motion in the intermediate scattering function and can be compared with experimental data. For q < 0.2 Å−1, S(q,t) hardly decays over the time scale of the measurement, signifying constraint of motion as observed in the MSD. Below these q values (i.e., probing larger dimensions) no dynamics is observed. With increasing q, zooming into the segmental motion regime, the intensity decays with characteristic time constants that describe the motion captured at different q values. The overall relaxation of S(q,t) for the entire pentablock and the ionizable one are rather similar, as shown in Figure 9a where the rubbery and end block relax significantly faster as shown in Figure 9b. H

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dielectric constant ε reduces the average cluster size and their cohesiveness. Both the segmental and macroscopic motions of the polymer molecules significantly decrease as f increases. We find that, similar to PSS, the addition of a small fraction of ionic groups significantly slows the mobility of the center of mass of the copolymer. Surprisingly, the segmental dynamics, as determined from the decay of the dynamic structure factor S(q,t), slows down for not only the entire pentablock and the center block but also the flexible and end blocks as f increases. Reducing the strength of the electrostatic interactions, by increasing the dielectric constant, breaks up the ionic clusters, thereby increasing the mobility of the entire pentablock as well as all three blocks. Similar to experiment and previous computational studies, the ionic clusters constrain the macroscopic dynamics of the copolymer; however, the segregation between the blocks play a critical role is retaining the membrane stability as the clusters dissociate. In contrast to ionic homopolymers, in these symmetric pentablock copolymers the ionic groups are segregated to one of the domains, where their cohesiveness affects the structure and dynamics of the entire copolymer.

overall dimensions of the collapsed block are reflected in this q range. The dynamics of the PErP is initially faster than the rest of the blocks. Its faster dynamics with increasing ε is predominantly manifested at higher q range where chain packing is manifested. There is very limited contribution of the PErP to the scattering function in this q range. The dynamics for all components however is slightly slower in comparison with that of the nonionic copolymers. This difference is attributed to the electrostatic interactions within the PS domain that persist even when the actual ionic clusters are dissociated. With breakup of the ionic clusters, the data were now well described by a single exponential. The effective diffusion constants Γ extracted from a single-exponential fit of the data are shown in Figure 11. For both the entire polymer and the

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b00724. Additional figures, including the distribution of ionic clusters for f = 0.15 for the two preparation methods (Figure S1) and the dynamic structure factor S(q,t)/ S(q,0) for the copolymer and the individual blocks (Figures S2 and S3) (PDF)

Figure 11. Effective time constant for pentablock, PSS, PErP, and t-bPS block for f = 0.15 (full) as a function of ε and for f = 0 (open) with ε = 1 for q = 0.2 Å−1 at T = 700 K.

ionic blocks, the effective diffusion increases with increasing ε and levels off at around ε = 5. The other two blocks are hardly affected. With increasing ε and dissociation of the ionic clusters, both the center block and the entire pentablock become significantly more mobile. These dynamic measurements show that the ionic clusters dominate the motion of the entire copolymer and affect segmental dynamics within all blocks. While unlocking of the ionic clusters enhances dynamics and S(q,t) can be described by one time constant; the inherent segregation between the blocks remains a barrier for motion.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (D.P.). *E-mail: [email protected] (G.S.G.). ORCID

Gary S. Grest: 0000-0002-5260-9788

IV. CONCLUSIONS The study revealed the effect of ionic clustering on the structure and dynamics in structured symmetric ionic copolymer on multiple length scales. No long-range ordering is observed in either the nonionic or the ionic copolymers where intertwined domains of PS and t-b-PS, segregated from each other, form cocontinuous domains across the melt which are segregated from the PErP domains. This type of cocontinuous structure was previously observed by Zuo et al.2 and co-workers. For f = 0, this structure is attributed to the incompatibility of the aliphatic and aromatic blocks coupled with the relatively high volume fraction of PErP compared to the two PS based blocks which are not miscible, as shown in Figure 2. The ionic groups associate within the PSS domain and enhance segregation of the PSS block with the t-b-PS block. For f = 0.15 isolated ionic clusters are formed. Increasing f to 0.30 results in ionic clusters which are near the percolation threshold whereas melts with f = 0.55 exhibit percolating ionic networks. The ionic clusters show a well-defined signature in S(q), whose intensity increases and line width decreases with increasing f as a result of the tightly packed ionic groups. Reducing the electrostatic interactions by increasing the

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge financial support from DOE Grant DE-FG02-12ER46843. This support has enabled to develop computational techniques for computational preparation of the membranes. Under this support, melts were made and the static structure was calculated. We gratefully acknowledge NSF Grant DMR 1611136. This funding has enabled the study of dynamics in these melts. This research used resources at the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the United States Department of Energy under Contract DEAC02-05CH11231. This work was made possible in part by advanced computational resources deployed and maintained by Clemson Computing and Information Technology. This work was performed, in part, at the Center for Integrated Nanotechnologies, a U.S. Department of Energy and Office of Basic Energy Sciences user facility. Sandia National Laboratories is a multimission laboratory managed and I

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