Microscopic Structure of Compacted Polyelectrolyte Complexes

Letter Cite This: ACS Macro Lett. 2019, 8, 123−127

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Microscopic Structure of Compacted Polyelectrolyte Complexes: Insights from Molecular Dynamics Simulations Diddo Diddens,*,‡ Jörg Baschnagel, and Albert Johner* Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 Rue du Loess, Strasbourg 67034 Cedex 2, France

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S Supporting Information *

ABSTRACT: We utilize atomistic molecular dynamics (MD) simulations to study local structural changes inside a polyelectrolyte complex consisting of poly(styrenesulfonate) (PSS) and poly(diallyldimethylammonium) (PDADMA) upon densification, in analogy to ultracentrifugation in experiments. In particular, we focus on the water content and on the reinforcement of the PSS−PDADMA network for various external accelerations. We demonstrate that apart from the formation of mesoscopic pores observed experimentally also the microscopic structure and the local relaxation processes likely affect the unique rheological properties of compacted polyelectrolyte complexes, as densification increases both the number of PSS− PDADMA coordinations and the intermixing of PSS and PDADMA. These processes slow down local rearrangements, thus further stabilizing the compacted state. We find that the concept of binary PSS−PDADMA salt bondsrelevant for theoretical modelsis not strictly valid in the dense limit.

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created from poly(acrylic acid) and poly(allylamine) have selfhealing properties,12 and their properties can additionally be tuned via the pH.13 Nonetheless, several open questions remain regarding the local structure inside PECs and CoPECs. Here, we elucidate the microscopic structure of a native PEC and a model CoPEC consisting of PSS/PDADMA via fully atomistic MD simulations. Particular focus lies on the local structure of water channels, coordinations between polyions, dynamical correlations between charged moieties, and the evolution of these quantities during compaction. The simulation details are given in the Supporting Information (SI). In short, randomly mixed complexes from PSS and PDADMA oligomers with N = 16 monomers in 2.5 molar NaCl solution were simulated with GROMACS5.0.414,15 using the force fields from refs 16−19. To model the centrifugation, a constant external acceleration g = 0.001− 0.01 nm/ps2 was applied to the PEC in an elongated tetragonal simulation box (see SI for the rationale behind this setup). Eight independent runs were performed for statistical averaging. Proper equilibration of the relevant quantities during the centrifugation simulation is validated in section S4.1. During compaction, the water content of the PEC decreases as shown in Figure 1a (here, all water molecules within the spatial extent of the complex were counted). For g = 0.002− 0.005 nm/ps2, the final water content is 53−58%, similar to the

ecently, polymeric materials with tunable properties came into focus, vitrimers being the most prominent example.1 Vitrimers are covalently cross-linked polymer gels that can change their topology by bond switching exchange reactions whose rate is sensitive to temperature. Furthermore, the glass transition of these gels can be tuned by catalysts, such that the material can be transiently put out of its glassy state into a state with high exchange rate in which it is easy to process. In this context, it is natural to think about salt bonds, which occur in complexes of polyanions and polycations, as another example of labile cross-links. Polyelectrolyte complexes (PECs) form spontaneously when mixing equimolar amounts of polyanions and polycations and hence have the appeal of simplicity.2,3 Unfortunately, they are brittle in the dry state and difficult to process further.4,5 Recently, Porcel and Schlenoff6 transformed PECs consisting of PSS and PDADMA into processable materials via ultracentrifugation in concentrated NaCl solutions (about 2.0−2.5 mol/L). The obtained compact PECs (CoPECs) could subsequently be cured in salt solutions to tune their mechanical properties, for which reason they have been termed saloplastics.7 Alternatively, PECs immersed in concentrated salt solutions can be densified in an extruder.7 Experimentally, CoPECs were characterized at several length scales: From rheology measurements, it was found that the shear modulus in the rubbery plateau lies in the kPa range and decreases slightly with increasing salt concentration,7 whereas confocal microscopy revealed a porous structure.8 At the mesoscopic level, neutron scattering indicated Gaussian9 or slightly swollen10 statistics of labeled polyelectrolyte chains. From a rheological point of view, CoPECs are promising candidates for biomedical applications.8,11 Moreover, CoPECs © XXXX American Chemical Society

Received: August 18, 2018 Accepted: January 7, 2019

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DOI: 10.1021/acsmacrolett.8b00630 ACS Macro Lett. 2019, 8, 123−127

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ACS Macro Letters

Figure 1c shows the size distribution function of small isolated clusters consisting of Nw water molecules that are not part of the larger channels. Two water molecules were defined to belong to a cluster if their oxygen atoms were no more than 0.33 nm apart.17 We find that although the vast majority of all water molecules belongs to bulk water percolating through the channels (see above), a minor fraction of small isolated clusters with Nw ≤ 30 water molecules is nonetheless present, even without centrifugation (Figure 1c). In total, we find about 30− 40 truly isolated water molecules with Nw = 1 in the entire simulation box. For clusters consisting of 10 ≤ Nw ≤ 30 molecules, the size distribution is apparently exponential. Centrifugation seems to increase the fraction of clusters with 10 ≤ Nw ≤ 30 (possibly also due to merging), as evident from the comparison of the curves for the first (solid) and last 50 ns (dashed) of the simulation. The transient network of polyelectrolyte chains within the complex, formed by monomer coordinations, is crucial for the gel’s rheological properties (note that CoPECs are physical gels, in which cross-link formation is in principle reversible). The evolution of the average coordination number between PSS and PDADMA monomers and between monomers and counterions is shown in Figure S5 (SI). In particular, the PSS− PDADMA network becomes denser, which manifests itself by an increase of the average coordination number from about 1.8 to 1.9−2.2, depending on g. Simultaneously, the coordination numbers for the respective counterions decrease by a comparable fraction. Despite the increase of PSS−PDADMA contacts, the relative orientation of the involved monomers largely remains the same, as observed from the spatially resolved coordination probability densities (Figure S6). Figure 2a shows the probability distribution function that a given polyelectrolyte chain (PSS or PDADMA) coordinates to

Figure 1. Time evolution of (a) the water content (in weight percent) and (b) the area-to-volume ratio of the channels inside the CoPECs for various g. The size distribution function of isolated water clusters of size Nw is shown in (c). Solid and dashed lines correspond to the first and last 50 ns of the simulation. The typical structure of the water channels is shown in (d).

experimental value of about 57% at 2.5 M NaCl,6 which corresponds to a relative decrease of the complex size (i.e., its spatial extent) of 65−80% in the simulations. We found a linear relation between both quantities with slight deviations for g = 0.001 nm/ps2, indicating that in this case the effective barriers related to compaction are not always overcome. In the simulation, water essentially builds a single branched channel (Figure 1d and Figure S4 in the SI) apart from the disconnected pores observed on mesoscopic scales.6 To determine the aspect ratio of the channel, we measured its area-to-volume ratio (Figure 1b) by partitioning the system into small cubes of size a = 0.14 nm, roughly the size of a water molecule, and counting those cubes occupied by polymer atoms.20−22 Assuming locally cylindrical channels, we estimate the channel radius to be about 1 nm from Figure 1b, decreasing upon compaction. Moreover, the channels are markedly poorer in salt than the supernatant solution, and the channel walls are slightly enriched in PDADMA relative to the unprocessed state. We may loosely divide the CoPEC water into two classes: bulk water filling the channels and surface water in direct contact with the polymer, the latter approximately corresponding to hydration water. A rough estimate of the fraction of hydration water is obtained by multiplying the area-to-volume ratio by a (the cube size, see above), which ranges from about 0.25 to 0.33 with increasing g. These values compare well to the experimentally estimated ratio of hydration water6 (about 0.25 at 2.5 mol/L NaCl), even though the pores observed experimentally on mesoscopic scales are substantially larger than the channels in the simulations.

Figure 2. Distribution function of (a) the number NPE of distinct, oppositely charged polyelectrolyte chains a given polyelectrolyte chain (either type) coordinates to and (b) of the number of coordinating monomer pairs Nc for a given pair of a PSS and a PDADMA chain binding to each other. The arrows indicate the averages.

NPE chains of the oppositely charged polyelectrolyte (averaged over the last 50 ns). With increasing g, the average ⟨NPE⟩ (arrows in Figure 2a) becomes larger, meaning that the network structure is tightened and that the chains interpenetrate more strongly. A similar observation is made from Figure 2b, which shows the probability distribution function that a given pair of a PSS and a PDADMA chain that are in contact has Nc coordinating monomer pairs. For all g, a PSS− PDADMA pair mainly involves only a few coordinating monomers, although in some cases basically all monomers of both chains are involved in the coordination. With increasing g, 124

DOI: 10.1021/acsmacrolett.8b00630 ACS Macro Lett. 2019, 8, 123−127

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ACS Macro Letters

This clearly demonstrates that the compaction process favors rearrangements (ultimately leading to reshaping of the complex), although about 70−80% of all bonds are not or only temporarily disrupted during the first 50 ns. However, even in comparative simulations with g = 0, a certain degree of rearrangements takes place (Figure 3). At the final stage of compaction, the situation is opposed to the findings from Figure 3a. Here, the local salt-bond breaking events (PS) become less frequent for large g due to the increased densification, whereas the occurrence of long-time rearrangements (PH) is similar for all g. After the entire simulation length of 200 ns, only 58−66% of the initial contacts are still intact (i.e., in the spirit of PH). The formation of contacts (Figure 2) and the structural rearrangements (Figure 3) necessarily involve the motion of the polyelectrolyte chains. However, at all times, the PEC network is rather dense, thus clearly restricting the dynamics. One scenario that is compatible with these constraints is the sticky Rouse/reptation mechanism.27−29 Here, each chain performs ordinary polymer motion; however, an energy barrier has to be overcome for each microscopic displacement. In principle, this energy should be related to the relaxation time of PS for elementary dissociation events. However, since the CoPEC structure is stabilized by multiple PSS−PDADMA contacts (Figure 2) and since free monomers establishing the renewal of a salt bond are not necessarily available, the overall structural relaxation times related to PH are substantial (Figure 3). Thus, with respect to the sticky Rouse/reptation mechanism, rather the true recombinations contained in PH lead to an ef fective dissociation with time τ*B in the spirit of the analytical model of ref 29, which also is a purely local process independent of N. Although our simulations are too short to fully capture sticky-Rouse dynamics, the analytical model can be employed to bridge microscopic rearrangements (probed in simulations) and macroscopic relaxation (probed by rheology), at least on a qualitative level. We roughly estimate via extrapolation of PH from Figure 3b that τB* is at least on the order of 1 μs (see section S6 in the SI). Recent viscosity measurements of CoPECs doped with potassium bromide30 lead to 50 ns < τB* < 1 μs when interpreted within the same theoretical framework29 (the largest time corresponding to the lowest salt-to-polyion ratio of 1:2), which nicely falls into the same range as the estimates from Figure 3b for sodium chloride, even though the salt concentration is about four times higher. It is important to stress that KBr suppresses cross-links more efficiently than NaCl and that ion-specific effects play a role,31 such that the overall agreement clearly is reasonable.32 We find that a given monomer (either PSS or PDADMA) moves on average by about 2−3 monomers along the oppositely charged polyelectrolyte chains it coordinates to (i.e., relative motion in terms of monomer indices, see Figure S13) during the simulation. Here, PDADMA diffuses more slowly than PSS, as expected from its larger rigidity. Interestingly, the respective motions of either chain are essentially uncorrelated and thus compatible with local Rouse dynamics (Figure S13). While our aim was to provide a truly microscopic picture, coarse-grained models retaining some chemical details33,34 seem highly promising for future studies. We performed chemically realistic MD simulations of the compaction of PSS/PDADMA complexes (CoPECs) at high salt concentrations (2.5 mol/L). The simulated CoPECs displayed water contents of 50−60 wt % and fractions of

the latter fraction becomes less populated, as the polyelectrolytes become progressively intermixed, such that each PSS− PDADMA pair is formed by fewer individual coordinations. Consistently, the average number of involved monomer pairs (arrows in Figure 2b) decreases. For longer chains, one would on the one hand expect that distant binary contacts along the chains become more dilute, while on the other hand the organization of several locally correlated contacts should essentially be independent of N, although the total number involved in a set of correlated contacts may clearly exceed the range of Figure 2b. In context with locally correlated contacts, we only observe a moderate degree of ladder structures, i.e., sequences of monomers on either chain of a PSS−PDADMA pair that coordinate to each other23 (Figure S11), which might be related to the different persistence lengths of PSS and PDADMA. Besides the connectivity, the lifetime of the salt bonds is crucial for the CoPEC’s rheological properties. This is reflected by Figure 3, which shows the fraction of initial PSS−PDADMA

Figure 3. Decay of PSS−PDADMA coordinations as a function of time t at (a) the first 50 ns and (b) the final 50 ns of the centrifugation simulation. The solid curves indicate the fraction of contacts/salt bonds still present after t (irrespective if the bond was temporarily broken), whereas the dashed lines show the decay if bond reforming is excluded.

coordinations formed by monomers n and m that are still intact after observation time t. We defined the function Hnm(t0) which is one if n and m are coordinated at starting time t0 (as determined on the basis of the neighbor distances in Figure S2a) and zero otherwise, and calculated the correlation function PH(t) = ⟨Hnm(t0)Hnm(t0 + t)⟩/⟨H2nm⟩.24−26 Of course, events in which the monomer pair is broken and reformed during t also contribute to PH. Thus, we additionally defined Snm(t0,t), which is only one if n and m are coordinated to each other for all frames in [t0:t0 + t], and analogously PS(t) = 2 ⟨Hnm(t0)Snm(t0,t)⟩/⟨Hnm ⟩.24−26 While PS (dashed curves) measures the average waiting time until a primary dissociation event occurs (irrespective of its long-term success), PH (solid curves) is susceptible to successful dissociation events leading to long-time structural relaxations.26 Both observables have been computed for the first and the last 50 ns of the simulation (Figure 3a and 3b, respectively). We find that at the initial stage of compaction the elementary dissociation events expressed by PS are independent of g (relaxation time of about 1 ns), suggesting that this process is related to purely local relaxations. In contrast, the rearrangement of PSS− PDADMA coordinations (PH) is several orders of magnitude slower; nonetheless, we observe that permanent bond breaking becomes more efficient at large g during initial compaction. 125

DOI: 10.1021/acsmacrolett.8b00630 ACS Macro Lett. 2019, 8, 123−127

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hydration water of about 25%, similar to experimental data.6 Most importantly, the microscopic PSS/PDADMA network is reinforced during complexation, as reflected by an increase of both the connectivity and the progressive intermixing of polyelectrolyte chains. In this context, the concept of binary salt bonds or PSS−PDADMA monomer pairs does not strictly hold, as in the dense medium each monomer is on average coordinated by two monomers of the oppositely charged polyelectrolyte species. This structural feature has important consequences for the relaxation dynamics of the complex: While individual PSS−PDADMA coordinations display a rather fast local relaxation (about 1 ns), the rearrangement of PSS−PDADMA coordinations is orders of magnitude slower, especially due to the tight network formed by multiple monomer coordinations. Therefore, microscopic relaxation times entering analytical models29 should rather be interpreted as a characteristic time scale for the complicated local reorganization of the monomeric environment instead of a dissociation time of binary salt bonds. When introducing such an ef fective dissociation time, the simulation results indeed show reasonable agreement with recent rheology measurements.30 It also seems worthwhile to simulate subsequent curing at lower salt concentrations with regard to rheological properties, although analytical theory captures the main effects.30

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ASSOCIATED CONTENT

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsmacrolett.8b00630. Simulation details, formation of the complex structure, structure of water channels, evolution of contacts during centrifugation, ladder structures, fitting procedure of contact lifetimes, and polymer motion (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Diddo Diddens: 0000-0002-2137-1332 Present Address ‡

Helmholtz Institute Münster (IEK-12), Ionics in Energy Storage, Forschungszentrum Jülich GmbH, Corrensstraße 46, 48149 Münster, Germany. Notes

The authors declare no competing financial interest.

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REFERENCES

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ACKNOWLEDGMENTS

The authors would like to thank Pierre Schaaf, Fouzia Boulmedais, Michel Rawiso, Fabien Gaudière, and Iuliia Konko as well as Christian Holm and Jens Smiatek for helpful discussions. We are especially grateful to Joseph Schlenoff for providing rheological data prior to publication. D.D. would also like to thank the German Research Foundation (DFG) for funding (grant DI 1959/1-1). A.J. benefitted from the support of the Agence Nationale de la Recherche (ANR-12-BS080006-01). 126

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