doi.org/10.26434/chemrxiv.9876395.v2

Spatiotemporal Formation Kinetics of Polyelectrolyte Complex Micelleswith Millisecond ResolutionHao Wu, Jeffrey Ting, Boyuan Yu, Nicholas Jackson, Siqi Meng, Juan de Pablo, Matthew Tirrell

Submitted date: 25/07/2020 • Posted date: 27/07/2020Licence: CC BY-NC-ND 4.0Citation information: Wu, Hao; Ting, Jeffrey; Yu, Boyuan; Jackson, Nicholas; Meng, Siqi; de Pablo, Juan; et al.(2019): Spatiotemporal Formation Kinetics of Polyelectrolyte Complex Micelles with Millisecond Resolution.ChemRxiv. Preprint. https://doi.org/10.26434/chemrxiv.9876395.v2

We have directly observed the in situ self-assembly kinetics of polyelectrolyte complex (PEC) micelles bysynchrotron time-resolved small-angle X-ray scattering, equipped with a stopped-flow device that providesmillisecond temporal resolution. A synthesized neutral-charged diblock polycation and homopolyanion that wehave previously investigated as a model charge-matched, core-shell micelle system were selected for thiswork. The initial micellization of the oppositely charged polyelectrolytes was completed within the dead time ofmixing of 100 ms, followed by micelle growth and equilibration up to several seconds. By combining thestructural evolution of the radius of gyration (Rg) and aggregation number (N) with complementary moleculardynamics simulations, we develop new information on how the self-assemblies evolve incrementally in sizeover time through a two-step kinetic process: first, oppositely-charged polyelectrolyte chains pair to formnascent aggregates that immediately assemble into spherical micelles, and second, these PEC micelles growinto larger micellar entities. This work has determined one possible kinetic pathway for the initial formation ofPEC micelles, which provides useful physical insights for increasing fundamental understandingself-assembly dynamics driven by polyelectrolyte complexation that occur on ultrafast timescales.

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Spatiotemporal Formation Kinetics of Polyelectrolyte Complex Mi-celles with Millisecond Resolution Hao Wu,†,# Jeffrey M. Ting,†,‡,# Boyuan Yu,† Nicholas E. Jackson,†, ‡ Siqi Meng,† Juan J. de Pablo,†,‡ and Matthew V. Tirrell†,‡* † Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States. ‡ Center for Molecular Engineering and Materials Science Division, Argonne National Laboratory, Lemont, Illinois 60439, United States.

ABSTRACT: We have directly observed the in situ self-assembly kinetics of polyelectrolyte complex (PEC) micelles by synchrotron time-resolved small-angle X-ray scattering, equipped with a stopped-flow device that provides millisecond temporal resolution. A synthesized neutral-charged diblock polycation and homopolyanion that we have previously investigated as a model charge-matched, core-shell micelle system were selected for this work. The initial micellization of the oppositely charged polyelectrolytes was com-pleted within the dead time of mixing of 100 ms, followed by micelle growth and equilibration up to several seconds. By combining the structural evolution of the radius of gyration (Rg) and aggregation number (N) with complementary molecular dynamics simula-tions, we develop new information on how the self-assemblies evolve incrementally in size over time through a two-step kinetic process: first, oppositely-charged polyelectrolyte chains pair to form nascent aggregates that immediately assemble into spherical micelles, and second, these PEC micelles grow into larger micellar entities. This work has determined one possible kinetic pathway for the initial formation of PEC micelles, which provides useful physical insights for increasing fundamental understanding self-assembly dynamics driven by polyelectrolyte complexation that occur on ultrafast timescales.

Under selective solution conditions, amphiphilic block poly-mers can be designed to self-assemble into an assortment of di-verse morphological structures, depending on the relative length, chemical nature, and molecular architecture of the hy-drophilic and hydrophobic polymer blocks.1,2 Equilibrium structures have received far more attention than the time-de-pendent phenomena of their formation. Theoretical works by Aniansson and Wall,3-5 Halperin and Alexander,6 and Dormi-dontova7,8 have proposed two possible mechanisms for the ki-netics of polymeric self-assemblies toward equilibrium: (i) sin-gle-chain insertion/expulsion and (ii) micelle fusion/fission. Experimental evidence has tested these model frameworks by adjusting solvent quality to induce micelle formation. For in-stance, using millisecond time-resolved small-angle X-ray scat-tering (TR-SAXS) under stopped-flow to provide nanoscale spatial resolution and temporal resolution, Lund and coworkers reported that the initial micellization kinetics of poly(ethylene-alt-propylene)-block-poly(ethylene oxide) (PEP-b-PEO) can be viewed as a fast nucleation (within 10 ms) and a slow growth process, where the elemental PEP-b-PEO aggregate growth fol-lows a single-chain insertion mechanism akin to the Aniansson-Wall theory.9 By comparison, Kalkowski et al. investigated mi-cellization kinetics of poly(ethylene glycol)-block-poly(capro-lactone) (PEG-b-PCL) with synchrotron X-ray scattering equipped with a microfluidic device.10 In this system, they dis-tinguished three successive stages of the micellization (nuclea-tion, micelle fusion, and polymer insertion), evident by the tem-poral evolution of the radii of gyration (Rg). From 0-250 ms, the Rg increased steadily as free unimers coupled into nuclei. Im-mediately after 250 ms, the Rg abruptly doubled in size, indicat-ing that nascent nuclei began merging together, followed by

steady structural growth from free PEG-b-PCL chains. While distinct from the Halperin-Alexander and Lund reports, the for-mation kinetics are in good agreement with the particle-particle fusion model described by Dormidontova.8 Further advanced techniques such as in situ liquid-cell transmission electron mi-croscopy and in silico simulations have captured such collision events in solution.11 In short, understanding kinetic formation in terms of tunable fundamental variables (e.g., polymer size/composition, concentration, interfacial tension) has un-locked design principles to more easily prepare nanoparticle as-semblies with greater fidelity, control, reproducibility, and sta-bility over time for intended applications.

However, compared to the advances in understanding the as-sembly kinetics of micelles formed by uncharged amphiphilic polymers over the past decade,6,8,12-18 little is known about the initial moments of self-assembly of polyelectrolyte complexa-tion-driven systems. Polyelectrolyte complexes (PECs) are pre-pared from an associative phase separation (i.e., coacervation) process between oppositely charged polyelectrolytes in water; for block polyelectrolytes, the process is thought to be more complicated due to the interplay among multiple components, including the polycation/polyanion pairing (e.g., polymer polar-ity, charge density, sequence effect, chirality, asymmetric block length ratios, etc.), high water content and related excluded vol-ume considerations, and the presence of salts in physiological settings.19-21 Since the formation of PEC micelles is believed to be strongly driven by the entropically favorable liberation of counterions between oppositely charged moieties, it is reasona-ble to infer that there are parallels to the thermodynamics of ho-mopolyelectrolyte complexation.22,23 Takahashi and coworkers

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investigated the complexation kinetics of oppositely charged homopolyelectrolytes, sodium poly(acrylate) and poly(allyla-mine hydrochloride), in aqueous NaCl solutions with TR-SAXS coupled with a stopped-flow device.24 They reported the evolu-tion of the complex droplet size, structure, and molar mass in a time range from 2.5 to 8733 ms, following (i) an immediate (< 2.5 ms) pairing step where oppositely charged chains pair by electrostatic interactions; (ii) a complexation step where the ion pairs further coalesce into nearly neutral aggregates, driven by van der Waals and hydrophobic effects; (iii) a growth step where aggregates grew analogously to the Brownian-coagula-tion kinetics of spherical colloidal particles. The same group also later revealed morphological transitions of cylindrical-to-spherical PEC micelles with salt by TR-SAXS,25 similarly to amphiphilic micelles.26

In general, the self-assembly process of PEC micelles from well-defined polyelectrolyte systems has remained unclear. In this Letter, by employing in situ TR-SAXS with millisecond temporal resolution, we experimentally investigate the self-as-sembly of one set of well-defined PEC micelles as a starting point toward building more quantitative predictions of for-mation kinetics. The constituents of this model PEC micelle system are poly(ethylene oxide)-block-poly(vinyl benzyl trime-thylammonium chloride) (PEO-b-PVBTMA) and sodium poly(acrylate) (PAA), shown in Figure 1-A. We have previ-ously demonstrated the controlled fabrication of polyelectro-lytes in parallel synthesis27 and interrogated aspects of the well-defined equilibrium structures of this pairing in the dilute re-gime.28,29 TR-SAXS experiments were carried out on the Bio-logical Small Angle Scattering Beamline BL 4-2 at the Stanford Synchrotron Radiation Lighthouse (SSRL), SLAC National Accelerator Laboratory.30,31 The TR-SAXS facility at the SSRL BL4-2, equipped with a customized Bio-Logic 4 syringe stopped-flow mixer (SFM 400), provides access to solution ki-netics on the millisecond time scale. Briefly, a typical TR-SAXS experiment proceeds in the following manner, shown schematically in Figure 1-B. First, aqueous solutions of posi-tively-charged polymers and negatively-charged polymers were loaded in two separate syringes. Second, equal volumes of pol-ycation and polyanion solutions were pumped into the mixer by the motors, corresponding to the equimolar concentration of the cationic and anionic monomer units. The dead time was ~ 4 ms. Third, 30 µL of mixed solution was further dispensed into the capillary cell, where the incident X-ray radiates through. The sample solution was sealed and buffered by solvent on the two ends of the capillary cell. The exposure time for each measure-ment was set to 20 ms. Automated capillary cleaning assisted in checking for potential radiation damage between experiments. Additional details are provided in the Supporting Information.

The time evolution of the SAXS curves is presented in Figure 2. Three independent kinetic experiments were carried out from the 5K53-158 sample, where the diblock polycation was PEO5K-b-PVBTMA53 (molar mass of PEO = 5000 g mol-1; de-gree of polymerization of PVBTMA = 53), the polyanion was PAA158 (degree of polymerization of PAA = 158), and the total polymer concentration was 2.5 mg mL-1. To achieve high time resolution, we used a low exposure time of 20 ms, which may reduce the quality of the scattering curves due to noise. To avoid this, we independently repeated the same experiment three

times. It is shown that the scattering data are reliable and repro-ducible even under a very low exposure time of 20 ms. Collec-tively, all TR-SAXS patterns exhibited features of isolated par-ticles with spherical morphology, well fitted by a polydisperse core-shell sphere model (see the Supporting Information). The increase in the scattering intensity over time reflects the micelle growth captured in real time. Due to the limitations of the in-strument setup and experimental conditions, the lower limit of the experimentally probed time period remained 100 ms. Thus, the nucleation event for chain complexation was completed by 80 ms and was not experimentally observable.

Figure 1. (A) Polyelectrolyte complex micelles consist of a poly-cation, PEO-b-PVBTMA, and polyanion, PAA. (B) Schematic rep-resentation of the time-resolved small-angle X-ray scattering ex-periments equipped with a stopped-flow setup.

Nevertheless, the structural evolution of the 5K53-158 PEC

micelles provided insightful information in the time range from 100 to 5000 ms. At 100 ms, well-formed micellar aggregates with a spherical geometry were already present in solution. The scattering intensity values increased steadily over time while maintaining the overall shape until 5000 ms, when the change in scattering intensity was barely discernable and indicated that the micelle growth became exceptionally slow relative to the prior state. The final state of micelles formed after injection in the stopped-flow path was sampled with SAXS after several minutes and did not differ (see Supporting Information). We also investigated the effects of block length and polymer con-centration on the formation kinetics of PEC micelles, particu-larly on the growth rate. This involved a longer polycation, PEO10K-b-PVBTMA100 with PAA158 (10K100-158) at 2.5 and 3.75 mg mL-1. In anticipation of slower growth kinetics, the ex-posure time was set to 80 ms in order to extend experimental time window for TR-SAXS characterization. The recorded time was 19,200 s and 38,400 s for the 2.5 and 3.75 mg mL-1 polymer concentrations, respectively. We observed that qualitatively, 10K100-158 samples formed larger micellar aggregates at a slower overall rate at both concentrations.

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Figure 2. TR-SAXS curves showing the formation of PEC micelles by (A) 5K53-158 at 2.5 mg mL-1 total polymer concentration, and (B) 10K100-158 at 2.5 and (C) 3.75 mg mL-1 total polymer concentration, respectively. Data points represent experimental data; see Figure S-X for fittings to a polydisperse core-shell model.

To better understand the assembly mechanism, the micelle

size evolution over time was quantified. The Rg of the micellar aggregates over time was extracted via the Guinier approxima-tion using the GNOM package32 as we have previously de-scribed28 The aggregation number (N) was determined from fit-ting to a polydisperse core-shell sphere model. Three independ-ent measurements of 5K53-158 formation showed a similar time dependence. As seen in Figure 3, we observe that at within the initial 100 ms, PEC micelles have already formed with Rg = 10.5 nm. Afterward, these micellar aggregates continued to grow in size, steadily increasing by 14% in Rg over 5000 ms. By dynamic light scattering (see Supporting Information), pre-assembled micelles prepared from these polyelectrolytes gener-ally exhibit an apparent hydrodynamic radius (Rh) of ca. 30.0 nm, corresponding to a shape factor (Rg/Rh) of 0.4. This corre-sponds to a highly water solvated structure, well below the con-ventional reference of a solid sphere (Rg/Rh = !3/5 ~ 0.77).33 For comparison, Heo et al. have reported molecular confor-mation measurements of multiple post-polymerization func-tionalized PEC micelles, which comprised roughly 80% water by neutron scattering. 34 A similar trend in Rg and N versus time was found in the 10K100-158 samples in Figure 4. The kinetic equilibration process appears slower for the micelles with longer polycation block lengths. For the 5K53-158 micelle, the Rg values plateaued around 5000 ms, whereas for the 10K100-158 system, the Rg increased by 27% from 11.0 nm at 5000 ms to 14.0 nm at 38,400 ms. We attribute this delay to the higher activation energy barrier and longer time involved with polymer rearrangement in longer chains.

From the aforementioned amphiphilic block polymer litera-ture, there are two conventional mechanisms for micelle for-mation: single-chain insertion/expulsion or micelle fusion/fis-sion. Micelles formed by oppositely charged polymers have features that are distinct from uncharged polymers. According to the current theories of polyelectrolyte complexation, free in-dividual chains are driven to form complexes with their oppo-sitely charged counterparts due to predominately entropic con-tributions,35-37 even at extremely low concentrations. Under this established framework, free chains are unlikely to exist as

unbound chains when micelles have already formed. In align-ment with time-resolved formation kinetics using homopoly-electrolytes,38 it is reasonable to infer that a similar entropi-cally-driven process occurs with block polyelectrolytes: imme-diately upon mixing, oppositely charged blocks pair with each other to form effectively neutralized clusters within a few mil-liseconds. Chain exchange events may happen immediately af-ter complexation, but given the short time and length scales, this is not experimentally observable, even with advanced synchro-tron capabilities. However, in the hundred-millisecond time pe-riods, the experimental data suggests that it is unlikely that mi-celle fusion/fission took place. Otherwise, the Rg values of the micellar aggregates would have exhibited an abrupt jump in magnitude, as Kalkowski et al. have observed in the (1) nucle-ation, (2) fusion, and (3) insertion stages of PEG-b-PCL micelle formation; here, the Guinier Rg correspondingly evolved from (1) ~2-5 nm to (2) ~5-9 nm, before (3) plateauing at ~10 nm.10

Figure 3. The evolution of the fitted Guinier Rg for 5K53-158 (red circles) in TR-SAXS experiments over the time range of 0 to 5000 ms. Error bars denote the standard deviation of each measurement.

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Figure 4. The evolution of the fitted Guinier Rg for 10K100-158 (red circles) at (A) 2.5 mg mL-1 and (B) 3.75 mg mL-1 over the time range of 0 to 40,000 ms. Error bars denote the standard deviation of each measurement. The final Rg and N are X and X, respectively.

Furthermore, when we repeated TR-SAXS measurements at a higher 3.75 mg mL-1 total polymer concentration, the slow growth of Rg remained invariant over time (Figure 4B). This implies that the formation of dilute PEO-b-PVBTMA/PAA mi-celles is largely concentration-independent. Previous work on electrostatic assemblies have shown a strong dependence on polymer concentration due to fusion-fission mechanisms.39

Because the PEC micelles were highly solvated and com-pletely hydrophilic, this result was initially puzzling. However, we have previously shown that this PEO-b-PVBTMA/PAA system exhibits repulsive interparticle effects at dilute condi-tions using SAXS.28 Physically, we demonstrated that when two micelles approach, the PEO coronas may be compressed to some extent, but the depth of the compressed area is only half of the corona thickness. In other words, the micelle cores were unable to reach each other, which supports the observations that PEC micelle fusion/fission is improbable during the formation process. Similar steric arguments have been made by theories for certain amphiphilic block polymer micelles that do not ex-hibit fusion-based growth mechanisms.6 At some critical stage the cluster insertion becomes dominant when micelle coronas are too large and dense to be penetrated.

To complement the experimental TR-SAXS kinetics condi-tions and assess the relationship between Rg and N in this time regime, a charged Kremer-Grest model40 was employed for the coarse-grained molecular dynamics (MD) simulation of poly-electrolyte coacervates. Polymers were simulated as bead-spring chains. For simplicity in maintaining electroneutrality, the 5K53 chain was simulated as a diblock with 110 and 50 monomer beads for the neutral and positively charged blocks, respectively; the homopolyanion comprised 150 negatively-charged monomer beads. Each bead was identical in size and interacted via the shifted and truncated Lennard-Jones potential. The connectivity of polymer beads was maintained by the fi-nitely extensible nonlinear elastic (FENE) potential. The salt-

free solvent was treated implicitly with a dielectric constant ε = 78.5, and counterions were neglected. Spherical micelles at given aggregation numbers were pre-assembled and placed at the center of the simulation box. Pre-assembly was achieved by first uniformly placing the polymer chains on a spherical sur-face of given radius with the charged blocks pointing towards the center of the sphere. An energy minimization of the system was then performed using a conjugated gradient algorithm im-plemented in a large-scale atomic/molecular massively parallel simulator (LAMMPS41) with 106 MD steps for equilibration. Afterward, a production run of 106 timesteps was used to collect data every 104 timesteps to calculate the Rg, radial density pro-file, and radial distribution function of the micelles. A detailed simulation methodology is provided in the Supporting Infor-mation.

The MD simulation results in Figure 5 show how the Rg and asphericity parameter (k2) ofthe PEC micelle correlates to the change in specified N. Given three selected aggregation num-bers (N = 75, 105, and 135), it is observed that the Rg increased from 8.25 ± 0.98 nm to 9.66 ± 0.88 nm (i.e., a 17% difference), which is qualitatively consistent with experimental estimates of a 14% increase in Rg growth. Differences in the absolute Rg val-ues from experiment can be attributed to the coarse-grained and implicit solvent nature of the simulations. Near zero values of the asphericity parameter (Figure 5) combined with the com-puted radial distribution functions (Figure S-5) indicated that at all molecular weights micelles exhibit spherical morphologies with similar internal structures. Further computational efforts can help capture the initial micellization kinetics that are not experimentally observable. For instance, Bos and Sprakel re-cently employed Langevin dynamics simulations to study fast exchange dynamics.42 In the early simulation time steps of the micellization stage, they found that initially, polyelectrolyte chains adopted a relatively stretched configuration before rap-idly forming aggregates by both expulsion/insertion and fu-sion/fission events, revealed by the decrease of size and release of counterions. Fusion and fission events were defined by the expulsion of small neutralized clusters containing a few poly-electrolytes from one micelle into another micelle.

Figure 5. MD simulation results of the Rg (orange data with dashed arrow to the left axis) and asphericity (green data with dotted arrow to the right axis) as a function of aggregation number for the 5K53-158 system. The inset shows a snapshot of the micelle using LAMMPS analysis.

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Combining the experimental and simulation results with lit-erature evidence, we propose that a possible kinetic pathway of micellization can be described in a two-stage process, as illus-trated in Scheme 1. First, immediately upon mixing in the stopped-flow apparatus, oppositely charged polyelectrolytes form charge-neutralized clusters. From these cluster aggregates, although the ultrafast time scale of the PEC micellization pro-cess was not commensurate with TR-SAXS, well-defined spherical micelles with Rg ~10-11 nm. Second, the micelle products equilibrate by exchanging either unimer chains or ion-paired clusters, as evident by incremental growth in Rg and N. During this process, we believe that fusion events are highly unlikely due to repulsive interparticle interactions that this sys-tem has been shown to exhibit. The universality of this kinetic pathway is the subject of ongoing investigations. In the former step, the mixing method of the stopped-flow apparatus and the ionic strength of the solution may play key roles in adjusting the timescale of cluster formation proceeding the PEO-b-PVBTMA and PAA micellization. For the latter step, greater scrutinization of the polyelectrolytes’ physical attributes, e.g., varying the ra-tio and the total chain lengths of blocks, may reveal differences in the likelihood of micelle fusion/fission, and therefore, alter the spatiotemporal evolution of micelles upon equilibration.

Scheme 1. Illustrated kinetic pathways of the investigated PEC

micelles.

Furthermore, the formation kinetics may be strongly depend-

ent on the chemical nature of the polymer constituents them-selves. Charged heteropolymers and sequence-defined macro-molecules give rise to distinct hierarchical assemblies at equi-librium,43 depending on the local interactions and sequence var-iation of the primary structure. By extension, the dynamics of PEC micelle formation, chain exchange, and equilibration are also likely highly influenced by how oppositely-charged poly-electrolytes associate at the molecular level. With this vast pa-rameter space, greater systematic exploration of different poly-electrolytes is vital for more quantitative prediction capabilities and theories of complex coacervation. Recently, Amann et al. reported kinetic pathways for PEC micelle formation using TR-SAXS using PEO-b-PVBTMA (2K6, 2K8, 2K12, and 2K19) and poly(styrene sulfonate) (PSS19).44 Their data shows the for-mation of metastable aggregates, followed by rearrangement and pinch-off into smaller micellar-like entities. We hypothe-size that this additional kinetic step arises because of the choice of the strongly-charged PSS polyanion. We have previously shown that upon complexation, PEO-b-PVBTMA forms mi-cron-scale, kinetically frozen aggregates with PSS, in contrast to the spherical micelles with PAA.45 Furthermore, direct com-parison of the homopolymer PVBTMA with PAA and PSS

reveal liquid and solid complexes, respectively, by optical mi-croscopy and SAXS (Figure S-1), which may account for subtle differences in the initial pairing step. Amann and coworkers also provide evidence that during the growth and equilibration step, fusion/fission events were not observed, in agreement with the subsequent behavior of PEO-b-PVBTMA/PAA. A direct comparison of formation pathways suggests that the early-stage micellization kinetics might be challenging to fully generalize, with the exact pathway likely to be highly dependent on the en-vironmental and polymer parameters.

Altogether, this Letter provides an early study in understand-ing the ultrafast kinetics of ionic polymer assemblies. Further effort is underway to compare the kinetic pathway dependency of molecular attributes that are known to affect complex coac-ervation, such as the neutral-to-charged block lengths, the strength and type of the charged moieties, counterion valency, solvent quality, and other orthogonal association effects. Un-covering the underlying polymer physics from a fundamental molecular engineering standpoint can lead to new insights in an array of bioapplications. Such endeavors can potentially im-prove the loading capacity, robustness, and stability of non-viral vector formulations for proteins,46 peptides,47 and nucleic ac-ids48 in the future.

ASSOCIATED CONTENT

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Materials, Methods (file type, i.e., PDF)

AUTHOR INFORMATION

Corresponding Author * E-mail: mtirrell@uchicago.edu (M.V.T.)

ORCID Hao Wu: 0000-0001-6276-6114 Jeffrey M. Ting: 0000-0001-7816-3326 Boyuan Yu: 0000-0002-8200-4413 Nicholas E. Jackson: 0000-0002-1470-1903 Siqi Meng: 0000-0002-2238-9278 Juan J. de Pablo: 0000-0002-3526-516X Matthew V. Tirrell: 0000-0001-6185-119X

Notes The authors declare no competing financial interest. #These authors contributed equally to this work.

Author Contributions All authors contributed to proofreading the manuscript. H.W. con-ceived and implemented the project, carried out the micelle for-mation and scattering experiments, drafted the initial manuscript, and analyzed the scattering data. J.M.T. performed the polymer synthesis, carried out polymer characterization, and conducted the scattering experiments. B.Y. conducted the molecular dynamics simulations and analysis. N.E.J. assisted with the development and interpretation of the simulations. S.M. assisted with the scattering experiments and analyzed the bulk complex materials. J.J.d.P. was the principle investigator and contributed to the data analysis and interpretation. M.V.T. was the principal investigator of the project and directed the research, managed the project, and contributed to the data analysis and interpretation of the experiments.

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Funding Sources This work was performed under the following financial assistant award 70NANB19H005 from U.S. Department of Commerce, Na-tional Institute of Standards and Technology (NIST) as part of the Center for Hierarchical Materials Design (CHiMaD).

ACKNOWLEDGMENT We gratefully thank Artem M. Rumyantsev, PhD, for helpful dis-cussions. J.M.T. acknowledges support from the NIST-CHiMaD Postdoctoral Fellowship. Parts of this work were carried out at the Soft Matter Characterization Facility of the University of Chicago. The authors also thank Thomas Weiss, PhD, Ivan Rajkovic, PhD and Tsutomu Matsui, PhD, at the Stanford National Accelerator Laboratory for their assistance in scattering experiments and in-sightful discussions. Use of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. The SSRL Structural Molecular Biology Program is supported by the DOE Office of Biological and Environmental Research, and by the National Institutes of Health, National Institute of General Medical Sciences (including P41GM103393). The contents of this publication are solely the responsibility of the authors and do not necessarily represent the official views of NIGMS or NIH.

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8

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Supporting Information for:

Spatiotemporal Formation Kinetics of Polyelectrolyte Complex Micelles

with Millisecond Resolution

Hao Wu,†,# Jeffrey M. Ting,†,‡,# Boyuan Yu,† Nicholas E. Jackson,†, ‡ Siqi Meng,† Juan J. de

Pablo,†,‡ and Matthew V. Tirrell†,‡*

†Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States.

‡Center for Molecular Engineering and Materials Science Division, Argonne National Laboratory, Lemont, Illinois

60439, United States.

#These authors contributed equally to this work.

*Corresponding Email: mtirrell@uchicago.edu

(1) Materials and Methods

Materials. The following materials were reagent grade and used as received, unless stated

otherwise: poly(ethylene oxide) methyl ether (2-methyl-2-propionic acid dodecyl trithiocarbonate)

(Sigma, Reported Mn = 5,000 g/mol; 10,000 g/mol), (vinylbenzyl)trimethylammonium chloride

(VBTMA, Sigma, 99%), 2,2'-azobis[2-(2-imidazolin-2-yl)propane]dihydrochloride (VA-044,

Wako Chemicals, USA), poly(acrylic acid sodium salt) (PAA, Polymer Source, 14,800 g/mol),

acetic acid (glacial, Sigma, ≥99.85%), sodium acetate trihydrate (Sigma, ≥99%), and SnakeSkin

dialysis tubing (MWCO 3.5K, 22 mm, Thermo Scientific). Acetate buffer solution was prepared

using 0.1 M acetic acid and 0.1 M sodium acetate trihydrate (0.1 M) (42/158, v/v), adjusted to pH

5.2 for RAFT polymerizations. Unless otherwise stated, all water was used from a Milli-Q water

purification system at a resistivity of 18.2 MΩ-cm at 25 °C.

Certain commercial equipment and materials are identified in this paper in order to specify

adequately the experimental procedure. In no case does such identification imply

recommendations by the National Institute of Standardsand Technology (NIST) nor does it imply

that the material or equipment identified is necessarily the best available for this purpose.

Polyelectrolyte Synthesis and Characterization. PEO-b-PVBTMA was synthesized

using aqueous RAFT polymerization from the reagents listed above, according to our previous

work.1 All samples were characterized by aqueous size-exclusion chromatography with multi-

angle light scattering and 1H NMR spectroscopy prior to scattering studies.

Polyelectrolyte Complex (PEC) Preparation. PECs were prepared under 1:1

stoichiometric charge-matched conditions between homopolycation and homopolyanion. The “as

prepared” polymer concentration was fixed at 1 wt%. Stock solutions of each polymer were added

sequentially to a 1.5 mL microcentrifuge tube solution with the premeasured amount of NaBr stock

solution (5 M) and Milli-Q water. Samples were then sealed, immediately vortexed for at least 30

s, and stored until further use.

PEC Micelle Preparation. Polyelectrolyte stock solutions (5 mg/mL) were prepared with

direct dissolution of polymers in filtered Milli-Q water. Pre-formed micelle assemblies were

prepared at targeted total polymer concentrations by mixing the oppositely-charged polyelectrolyte

solutions. Total polymer concentrations were set to be dilute enough to avoid interparticle effects

of this system.2 Unless otherwise noted, the charged monomer concentration was maintained at

2.45 µmol/mL.

Pre-assembled micelle solutions were made at room temperature in dust-free 12 x 75 mm

borosilicate glass tubes. To Milli-Q water, the calculated volume of polycation was added first,

followed by the calculated volume of polyanion from their respective stock solutions

(corresponding to charged-matched conditions, comprising equimolar concentrations of the

cationic and anionic monomer units). Reversing the order of addition had no effect on the final

morphology of the electrostatic assembly. The resulting micelle solution was vortexed for at least

30 s and set aside for at least 1 h before any measurement.

Optical Light Microscopy Imaging. Optical phase contrast microscopy (Leica DMI

6000B + Leica Application Suite (LAS) image acquisition software; Wetzlar, Germany) was used

to directly visualize PEC samples prepared from homopolyelectrolyte pairings. 100 µL of the PEC

samples were transferred into ultra-low attachment 96-well plates (Costar, Corning Inc.). To

prevent water evaporation, the plates were carefully sealed. Imaging was performed one day after

the sample preparation in order to ensure that phase separation was complete and in equilibrium

states. The contrast of the acquired images was then enhanced with ImageJ software for clarity.

Dynamic Light Scattering. Experiments were carried out on a Brookhaven Instruments

BI-200SM Research Goniometer System with a λ = 637 nm incident laser at 23 °C. A dust-free

decalin bath was used to match the refractive index of glass. The apparent hydrodynamic radius

(Rh) of scatters under Brownian diffusion were calculated using the Stokes-Einstein relationship.

The correlation function at 90° was fitted to a first-order single exponential using MATLAB, and

the apparent hydrodynamic radius distribution was also determined using REPES analysis.3

High-throughput solution SAXS. SAXS experiments of the pre-formed micelles were

performed at the Stanford Synchrotron Radiation Lightsource (SSRL) Beam-Line 4-2 (Menlo

Park, CA). In-house autosampler robotics enabled high-throughput data collection for

temperature-controlled 96-well plate datasets (average rate of 3-5 min/sample, or 96 samples in 5-

8 h). Briefly, approximately 30 µL sample aliquots were pumped to a 1.5 mm quartz capillary cell,

which underwent sample oscillations upon exposure to minimize radiation damage. In between

sample runs, extensive washing of the capillary, needle, and tubing was programmed to be

performed by dispensing water and detergent. Data acquisition was conducted using Blu-Ice

software with a customized Bio-Logic 4 syringe stopped-flow mixer (SFM400).

Time-resolved small angle X-ray scattering (TR-SAXS). The TR-SAXS experiments

were performed at the Stanford Synchrotron Radiation Lightsource (SSRL) Beam-Line 4-2 (Menlo

Park, CA). The sample-to-detector distance was set to 3.5 m; the X-ray wavelength λ0 was set to

1.38 Å (9 keV) for all measurements. 2D scattering patterns were collected using a Dectris Pilatus3

X 1M pixel array detector system (Dectris Ltd, Switzerland) over the range of momentum transfer

q ~ 0.0025-0.17 Å-1, where q is defined as the magnitude of the scattering vector. For each

scattering pattern during the stopped-flow TR-SAXS experiment, the X-ray exposure time was set

to 20 and 80 ms for the 5K53-158 and 10K100-158 micelle samples, respectively. Signals and

timing were monitored using Oscilloscope; solutions were oscillated in the stationary quartz

capillary cell during data collection to maximize the exposed sample volume and minimize the

radiation dose per unit volume of sample. The capillary was washed in between experiments. The

collected data was radially integrated, checked for potential radiation damage or air bubbles, and

buffer subtracted using the automated data reduction pipeline at the beamline. Only data that did

not show sign of radiation damage were included in the final averaging for each sample. Further

resources on the experimental setup and data treatment are available elsewhere.4,5

To the polyelectrolyte stock solutions, glycerol (1 wt%) was included to prevent potential

beam damage. All polyelectrolyte stock solutions were degassed prior to loading into syringes. We

emphasize the importance of this to minimize the formation of air bubbles for each TR-SAXS run.

The intensity of identical particles with spherical symmetry can be expressed as:

I(q)=P(q)S(q), where P(q) is the form factor associated with the size and shape of scatterers, and

S(q) is the structure factor that characterizes the interparticle interactions and approaches unity at

sufficiently dilute conditions. Micelle samples in this study were fitted using a combination of a

polydisperse core-shell sphere model and a polydisperse Gaussian coil function.6,7 The equation

of the form factor can be expressed as:

𝑃(𝑞) =𝜙'()𝑉+

,3𝑉.(𝜌. − 𝜌1)𝑗(𝑞𝑟.)

𝑞𝑟.+3𝑉1(𝜌1 − 𝜌+567)𝑗(𝑞𝑟+)

𝑞𝑟189

+ 𝜙:65:2[(1 + 𝑈Ξ)@A B⁄ + Ξ − 1]

(1 + 𝑈)Ξ9 + 𝑏𝑘𝑔 (S-1)

𝑗(𝑥) =𝑠𝑖𝑛𝑥 − 𝑥𝑐𝑜𝑠𝑥

𝑥9 (S-2)

Ξ =N𝑞𝑅P,:65:R

9

1 + 2𝑈 (S-3)

𝑈 =𝑀T

𝑀U− 1 (S-4)

Here, VS, VC, and VS are the volumes of a single micelle, the micelle core, and the micelle shell,

respectively; ρS, ρC, and ρsolv are the scattering length densities of the micelle shell, micelle core

and solvent, respectively; rS is the radius of the micelle shell and rC is the radius of the micelle

core. The scale is a factor that equals to the volume fraction when the scattering data is on an

absolute scale. The bkg term denotes the background level. Additional information on the use of

this chosen model, along with relevant information on extracting the Guinier Rg values of the

samples, is provided in our previous works.1,2

(2) Supplemental Polyelectrolyte Complex (PEC) Characterization

Figure S-1 shows the solution characterization of oppositely-charged homopolymers

PVBTMA and PAA, PVBTMA and PSS, and PVBTMA and PSS at 2.5 M NaBr. The SAXS

profiles and optical microscopy image suggest that PVBTMA and PAA form liquid coacervates,

while PVBTMA and PSS form solid complexes. More detailed information can be found in

references that examine bulk coacervate/complex systems. 8

Figure S-1. Small-angle X-ray scattering (left) and optical microscopy imaging (right) analysis of

the homopolymer pairings: (A) PVBTMA + PAA at 0 M NaBr, (B) PVBTMA + PSS at 0 M NaBr,

and (C) PVBTMA + PSS at 2.5 M NaBr.

Pre-assembled micelles comprising PEO5K-b-PVBTMA53 and PAA158 were prepared and

characterized prior to TR-SAXS experiments. Using a cumulant expansion fitting method,9 the

hydrodynamic radius (Rh) of the PEC micelles was determined to be 30.0 nm at 90°, with a

colloidal polydispersity (µ2/Γ2) of 0.14 (Fig. S-2). In addition, REPES analysis3 of the

autocorrelation function at 90° corresponded to a Rh of 28.8 nm (Fig. S-3). Thus, the pairing of

PEO-b-PVBTMA and PAA provides access to a uniform, well-characterized PEC micelle system

that can be investigated with TR-SAXS studies.

Figure S-2. Fitting of the autocorrelation function of a representative 5K50-158 micelle sample at

90° via cumulant expansion.

Figure S-3. Size distribution of a representative 5K50-158 micelle samples via REPES analysis at

90° angle.

In the TR-SAXS experiments, to assess whether the PEC micelles had reached a near-

equilibrium state, final state products were examined over the course of several minutes. Scheme

S-1 describes this process by comparing illustrations of these two protocols. For monitoring

formation kinetics, pumps were motorized to inject the diblock polycation and homopolyanion to

the mixer and capillary, in between buffer solvent. After we observed minimal increase in the

scattering intensity of the SAXS curves over time, we motorized the pumps to examine PEC

micelles along the capillary path (since over several minutes, the final state products were free to

diffuse in solution).

Scheme S-1. Illustration of stopped-flow setup for measuring the formation kinetics (t = 0) and

measuring the final state products (t >> 0).

(3) Molecular Dynamics Simulations

A charged Kremer-Grest model10 is employed for classical molecular dynamics

simulations of polyelectrolyte coacervates. The solvent is treated implicitly with a dielectric

constant 𝜖 = 78.5, and counterions are not included since we are focusing on understanding the

equilibrium structures of PEC micelles at the salt-free limit, with the total system charge being

neutral. Each monomer bead has the same size 𝜎 and interacts through the shifted and truncated

Lenneard-Jones potential,

𝑈\] = ^4𝜀\]a(𝜎/𝑟(c)A9 − (𝜎/𝑟(c)d − (𝜎/𝑟(c)A9 + (𝜎/𝑟(c)de𝑟(c < 𝑟)0𝑟(c > 𝑟)

(S-5)

where 𝑟) = 2A/d𝜎, 𝜀\] = 1.0𝑘j𝑇.

The connectivity of polymer beads is maintained by the finitely extensible nonlinear elastic

(FENE) potential,

𝑈lmnm = −0.5𝑘𝑅o9𝑙𝑛(1 − (𝑟(c/𝑅o)9)

(S-6)

where the spring constant 𝑘 = 30𝑘j𝑇/𝜎9 and the maximum extension 𝑅o = 1.5𝜎.

The electrostatic interactions between charged beads are described by the Coulomb

potential,

𝑈.5q65': = 𝑘j𝑇𝑙j𝑞(𝑞c/𝑟(c (S-7)

where the Bjerrum length, 𝑙j, is set to 2.0𝜎. Correspondingly, in real units 𝜎 = 0.35𝑛𝑚. The

particle-particle particle-mesh (PPPM) technique11 is used to evaluate the Coulomb interactions,

where the cutoff for short range part is 5.0𝜎 and the error threshold is set to 10-4.

A cubic box of length 100𝜎 is used with periodic boundary conditions applied to each

dimension. A Langevin thermostat is coupled to the system to maintain the NVT ensemble with

reduced 𝑇 = 1, timestep of 0.006𝜏\] , and damping constant 𝛾 = 1.0𝜏\]@A . The simulations are

carried out using LAMMPS. 12,13

A spherical PEC micelle of given aggregation number is pre-assembled and placed in the

center of the simulation box. The aggregation number here refers to the number of polycation

chains inside the PEC micelle. The pre-assembly is achieved by first uniformly placing the

polymer chains on a spherical surface of given radius with the charged blocks pointing towards

the center of the sphere. Then an energy minimization of the system is performed using conjugated

gradient algorithm implemented in LAMMPS.11,12 The stopping tolerance for energy and force is

10-4𝑘j𝑇 and 10-6𝑘j𝑇/𝜎, respectively. The pre-assembled PEC micelle is equilibrated using 106

MD timesteps. The equilibration is ensured by monitoring the temperature, potential energy, and

radius of gyration (𝑅P) of the micelle for the system. After equilibration, a production run of 106

timesteps is used to collect data every 104 timesteps to calculate the 𝑅P, radial distribution function,

and radial density profile of the micelle.

Figure S-4. Radial density profiles of the PEC micelles at the specified (A) N = 75, (B) N = 105,

and (C) N = 135. Within each plot, curved lines depict the total (purple), core (orange), positively

charged (red), negatively charged (dark blue), and corona (light blue) contributions.

Figure S-5. Representative radial distribution function of the N = 105 micelle system.

(4) Supporting Information References

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Assembly of Designer Styrenic Diblock Polyelectrolytes. ACS Macro Lett. 2018, 7, 726–

733.

(2) Wu, H.; Ting, J. M.; Weiss, T. M.; Tirrell, M. V. Interparticle Interactions in Dilute

Solutions of Polyelectrolyte Complex Micelles. ACS Macro Lett. 2019, 8, 819–825.

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Angle X-Ray Scattering Facility at the Stanford Synchrotron Radiation Laboratory. J.

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Throughput Data Acquisition System for Biological Solution X-Ray Scattering Studies.

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(accessed July 19, 2020).

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Dynamics Simulation. J. Chem. Phys. 1990, 92, 5057–5086.

(11) Plimpton, S.; Pollock, R.; Stevens, M. Particle-Mesh Ewald and rRESPA for Parallel

Molecular Dynamics Simulations.; Minneapolis, 1997.

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