doi.org/10.26434/chemrxiv.9876395.v1

In situ Time-Resolved Small-Angle X-ray Scattering Reveals theFormation Kinetics of Polyelectrolyte Complex MicellesHao Wu, Jeffrey Ting, Siqi Meng, Matthew Tirrell

Submitted date: 18/09/2019 • Posted date: 23/09/2019Licence: CC BY-NC-ND 4.0Citation information: Wu, Hao; Ting, Jeffrey; Meng, Siqi; Tirrell, Matthew (2019): In situ Time-ResolvedSmall-Angle X-ray Scattering Reveals the Formation Kinetics of Polyelectrolyte Complex Micelles. ChemRxiv.Preprint.

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. This work has elucidated one general kinetic pathway for the process of PECmicelle formation, which provides useful physical insights for increasing our fundamental understanding ofcomplexation and self-assembly dynamics driven by electrostatic interactions that occur on ultrafasttimescales.

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In situ Time-Resolved Small-Angle X-ray Scattering Reveals the For-mation Kinetics of Polyelectrolyte Complex Micelles Hao Wu,†,= Jeffrey M. Ting,†, ‡,= Siqi Meng,† and Matthew V. Tirrell†, ‡,* † Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States. ‡ 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 core-shell mi-celle system were selected for this work. The initial aggregation of the oppositely charged polyelectrolytes was completed within 80 ms, followed by evidence of micelle growth up to several seconds. Analysis of experimental data over time shows that, contrary to self-assemblies formed by uncharged polymers, PEC micelles exhibit neither classical unimer exchange nor micelle fusion phenom-ena during the coacervation-driven self-assembly. By combining the structural evolution of the radius of gyration (Rg) with theoretical considerations, we hypothesize that the formation of these PEC micelles proceeds via a three-step process: first, oppositely charged polyelectrolyte chains pair to form effectively neutral clusters comprising a few polymer chains; second, these nascent clusters form larger micellar aggregates (Rg ~10 nm); and last, micelles continue to grow from merging clusters by ~14-27% in Rg, depending on polymer molar mass. We demonstrate that larger PEC aggregates are more energetically favored than the smaller clusters, with cluster-micelle insertion emerging as the predominant mechanism over micelle-micelle fusion. This work has elucidated one general kinetic pathway for the process of PEC micelle formation, which provides useful physical insights for increasing our fundamental understanding of complexation and self-assembly dynamics driven by electrostatic interactions that occur on ultrafast timescales.

Block polymers are macromolecules comprising segments of chemically distinct repeat units covalently linked together. Un-der selective solution conditions, amphiphilic block polymers can be designed to self-assemble into an assortment of diverse morphological structures, depending on the relative length, chemical nature, and molecular architecture of the hydrophilic and hydrophobic polymer blocks.1,2 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 millisecond 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 aggre-gate growth follows a single-chain insertion mechanism akin to the Aniansson-Wall theory.9 By comparison, Kalkowski et al. investigated micellization kinetics of poly(ethylene glycol)-block-poly(caprolactone) (PEG-b-PCL) with synchrotron X-ray scattering equipped with a microfluidic device.10 In this sys-tem, they distinguished three successive stages of the micelliza-tion (nucleation, micelle fusion, and polymer insertion), evident by the temporal evolution of the radii of gyration (Rg). From 0-250 ms, the Rg increased steadily as free unimers coupled into nuclei. Immediately after 250 ms, the Rg abruptly doubled in

size, indicating that nascent nuclei began merging together, fol-lowed by steady structural growth from free PEG-b-PCL chains. While distinct from the Halperin-Alexander and Lund reports, the formation kinetics are in good agreement with the particle-particle fusion model described by Dormidontova.8 Further advanced techniques such as in situ liquid-cell transmis-sion electron microscopy and in silico simulations have cap-tured such collision events in solution.11 In short, understanding kinetic formation in terms of tunable fundamental variables (e.g., polymer size/composition, concentration, interfacial ten-sion) has unlocked design principles to more easily prepare na-noparticle assemblies with greater fidelity, control, reproduci-bility, and stability over time for intended applications.

However, compared to the remarkable advances in under-standing the assembly 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 polyelec-trolyte complexation-driven systems. Polyelectrolyte com-plexes (PECs) are prepared from an associative phase separa-tion (coacervation) process between oppositely charged poly-electrolytes in water; for block polyelectrolytes, the process is thought to be more complicated due to the interplay among mul-tiple components, including the polycation/polyanion pairing (i.e., polymer polarity, charge density, sequence effect, chiral-ity, asymmetric block length ratios, etc.), high water content and related excluded volume considerations, and the presence of salts in physiological settings.19,20 Since the formation of PEC micelles is believed to be strongly driven by electrostatic inter-action between oppositely charged moieties, it is reasonable to infer that the formation kinetics of PEC micelles is related to

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the thermodynamics of homopolyelectrolyte complexation.21,22 Takahashi and coworkers investigated the complexation kinet-ics of oppositely charged homopolyelectrolytes, sodium poly(acrylate) and poly(allylamine hydrochloride), in aqueous NaCl solutions with TR-SAXS coupled with a stopped-flow de-vice.23 They reported the evolution 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 oppo-sitely 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 hydro-phobic effects; (iii) a growth step where aggregates grew anal-ogously to the Brownian-coagulation kinetics of spherical col-loidal particles. The same group also later revealed morpholog-ical transitions of cylindrical-to-spherical PEC micelles with salt by TR-SAXS,15 qualitatively similar to amphiphilic mi-celles.24

To the best of our knowledge, the kinetics associated with the self-assembly process of PEC micelles at the millisecond time-scale has never been reported to date. In this Letter, by employ-ing in situ TR-SAXS with millisecond temporal resolution, we experimentally investigate the nonequilibrium self-assembly of one set of well-defined PEC micelles as a starting point toward building more quantitative predictions of formation kinetics. The constituents of this model PEC micelle system are poly(ethylene oxide)-block-poly(vinyl benzyl trimethylammo-nium chloride) (PEO-b-PVBTMA) and sodium poly(acrylate) (PAA), shown in Figure 1(A). We have previously demon-strated the facile controlled fabrication of polyelectrolytes in parallel synthesis25 and interrogated the self-assembly behavior and well-defined equilibrium structures of this pairing in the di-lute regime.26 All TR-SAXS experiments were carried out on the Biological Small Angle Scattering Beamline BL4-2 at the Stanford Synchrotron Radiation Lighthouse (SSRL), SLAC National Accelerator Laboratory.27,28 The TR-SAXS facility at the SSRL BL4-2, equipped with a customized Bio-Logic 4 sy-ringe stopped-flow mixer (SFM 400), provides access to solu-tion kinetics on the millisecond time scale and above. Briefly, a typical TR-SAXS experiment proceeds in the following man-ner, shown schematically in Figure 1(B). First, aqueous solu-tions of positively-charged polymers and negatively-charged polymers are loaded in two separate syringes. Second, equal volumes of polycation and polyanion solutions are pumped into the mixer by the motors, corresponding to the equimolar con-centration of the cationic and anionic monomer units. The dead time is ~4 ms. Third, 30 µL of mixed solution is further dis-pensed into the capillary cell, where the incident X-ray radiates through. The sample solution is sealed and buffered by solvent on the two ends of the capillary cell. The exposure time for each measurement was set to 20 ms. Automated capillary cleaning assisted in checking for potential radiation damage between ex-periments. Additional experimental 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 is 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) Schematic representation of the time-resolved small-angle X-ray scattering experiments integrated with a stopped-flow setup. (B) Formation of polyelectrolyte complex micelles upon mixing of a polycation, PEO-b-PVBTMA, and polyanion, PAA.

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 surprisingly 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 in-dicated that the micelle growth became exceptionally slow rel-ative to the prior state. The final state of micelles formed after injection in the stopped-flow path was sampled with SAXS af-ter several minutes and did not differ (see Supporting Infor-mation). We also investigated the effects of block length and polymer concentration on the formation kinetics of PEC mi-celles, particularly 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 kinet-ics, the exposure time was changed to be 80 ms in order to ex-tend experimental time window for TR-SAXS characterization. The recorded time was 19,200 seconds and 38,400 seconds 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 for both pol-ymer concentration samples.

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Figure 2. TR-SAXS curves showing the formation of PEC micelles by (A-C) PEO5K-b-PVBTMA53 and PAA158 at 2.5 mg mL-1 total polymer concentration, repeated three times independently, and (D-E) PEO10K-b-PVBTMA100 and PAA158 at 2.5 and 3.75 mg mL-1 total polymer concentration, respectively. Data points represent experimental data while red lines denote fittings to a polydisperse core-shell model.

To better understand the assembly mechanism and structural

evolution, the micelle size evolution was directly quantified. The radius of gyration (Rg) of the micellar aggregates over time was extracted via the Guinier approximation using the GNOM package (described in the Supporting Information). The three independent measurements of 5K53-158 formation showed a similar time dependency on the evolution of the Guinier Rg in Figure 3. We observe that at first, the PEC micellar aggregates with a Rg of 10.5 nm have formed within the initial 100 ms. Afterward, these micellar aggregates continue to grow as their size increases steadily by 14%, starting from 10.5 nm at 100 ms to 12.0 nm at 5000 ms. By dynamic light scattering (shown in the Supporting Information), pre-assembled micelles prepared from these polyelectrolytes generally exhibit an apparent hy-drodynamic radius (Rh) of ca. 30.0 nm, corresponding to a shape factor (Rg/Rh) of 0.4. This corresponds to a highly water solv-ated structure, well below the conventional reference of a solid sphere (Rg/Rh = !3/5 ~ 0.77).29 For comparison, Heo et al. have reported molecular conformation measurements of various PEC micelles comprising post-polymerization functionalized poly(ethylene oxide)10K-block-poly(allyl glycidyl ether)52 di-blocks, ranging in shape factor values from 0.1 to 0.27.30 A sim-ilar trend in Rg versus time was found in the 10K100-158 sam-ples at both polymer concentrations in Figure 4. However, it is evident that the formation process is much slower for the mi-celles with polycations containing longer block lengths. For ex-ample, for the micelle sample 5K53-158, Rg values plateaued around 5000 ms, whereas for the 10K100-158, the Rg increases 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. We note that this gradual change in Rg has no marked dependence on polymer concentration.

From the aforementioned amphiphilic block polymer litera-ture, there are two conventional mechanisms for micelle for-mation: single-chain insertion or micelle fusion. In the time pe-riod from 100 to 5000 ms, the data suggests that it is unlikely that micelle fusion 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 formation of PEG-b-PCL micelles.10 Thus, by process of elimination the incremental growth of the micellar aggregates should follow a Aniansson/Wall-like chain insertion mechanism. However, this classical single-chain insertion mechanism can be reasonably excluded as well. According to the current theories of polyelec-trolyte complexation, free individual polyelectrolytes are driven to form complexes with their oppositely charged counterparts due to a balance of entropic and enthalpic contributions,31-33 even at extremely low concentrations. In other words, free cat-ionic or anionic chains are unlikely to exist as unbound chains at a time when micellar aggregates with a Rg of 10 nm have already formed. In alignment with the formation kinetics of ho-mopolyelectrolyte complexes,23 it is reasonable to infer that a similar process occurs with block polyelectrolytes. Immediately after mixing, oppositely charged blocks pair with each other to form effectively neutral clusters within a few milliseconds. Then, these incipient clusters start to aggregates into larger mi-cellar structures.

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

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.

It is important to emphasize that the formation of intercon-nected mesoscopic structures is hindered in diblock polymers due to favorable stretching of the hydrophilic neutral blocks in water, and the lack of bridging chains is experimentally verifi-able among discrete micelles. The core and corona of PEC mi-celles have been shown to be highly solvated with water.19 In micelle systems containing triblock polyelectrolytes as a con-stituent component, gel phases and macroscopic phase separa-tion have been reported in dilute solutions under SAXS analysis and molecular dynamics simulations.34 Although the exact ki-netic pathway of these PEC micelles in the initial 100 ms un-fortunately cannot be addressed at this moment with the work-ing conditions of the synchrotron instrument, the collected ex-perimental data from this well-characterized system does ena-ble us to outline the likely formation mechanism using theoret-ical considerations.

Thus, we hypothesize that in the probed experimental time period, the growth pathway of PEC micelles occurs mainly through a cluster-micelle insertion mechanism. We define a “cluster” as a limited number of individual polyelectrolyte chains associated by “sticky” intermolecular ion complexation to form effectively neutral mesostructures. These are transitory precursors to the well-defined, spherical micelles – a subtle but important distinction to establish compared to amphiphilic block polymer chains. From a thermodynamic perspective, we rationalize why micelle fusion is not favored to explain the in-crease in Rg. Consider two micelles with radii 𝑅& and 𝑅' merg-ing into a larger micelle assembly with a radius of 𝑅(. When they merge, one micelle has to penetrate the dense outer corona of the other. The change in free energy (∆𝐹) is incurred by the change of the free energy of the solvent-core interface 𝐹+,-./012.34 . Mathematically, this can be expressed as: reference

𝐹+,-./012.34 ≅ 4𝜋𝑅+'𝛾 (1)

∆𝐹 = 4𝜋𝛾(𝑅(' − 𝑅&' − 𝑅'') (2) 𝑅(( = 𝑅&( + 𝑅'( (3)

where 𝛾 is the interfacial tension and P is the aggregation num-ber of the micelle, respective to each micelle by the subscript number. ∆𝐹 is always negative and reaches its maximum abso-lute value when 𝑅& = 𝑅' . However, before the complex core fusion occurs, the micelles have to overcome the energetic bar-rier from the corona chains adopting more extended confor-mations as the two micelles penetrate each other. Clusters of a few chains do not pay this additional energetic penalty. When micelle 1 with 𝑃& chains penetrates micelle 2 with 𝑃' chains, each chain loses 𝑃'

& '⁄ free energy, and the total energy, Ufusion, can be given by:

𝑈0BC+D, ≅ 𝑃&𝑃'&/' (4)

From the above expression, it is clear that Ufusion is propor-

tional to the aggregation numbers of the two merging micellar aggregates, and the energetic barrier of micelle-micelle fusion is higher than that of the cluster-micelle insertion. Thus, the cluster-micelle insertion mechanism is energetically favored over the micelle-micelle fusion mechanism. Yet, at the begin-ning of micelle growth, when the aggregation numbers are

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Scheme 1. Illustration of the proposed kinetic pathway in the self-assembly formation process of PEC micelles.*

* Counterions not shown for simplicity. In the cluster aggregation, the red “X” denotes micelle-micelle fusion, which may be possible

only at short times when micelles are sufficiently small to not have a dense corona shell.

sufficiently small, micelle-micelle fusion may be possible. At some critical stage the cluster insertion becomes dominant when micelle coronas are too large and dense to be penetrated. This phenomenon has been recently verified in our previous work using this PEO-b-PVBTMA/PAA system at dilute condi-tions via SAXS analysis, where we observed that when two equilibrium micelles approach, the PEO coronas may be com-pressed to some extent, but the depth of the compressed area is only half of the corona thickness.26 The micelle cores are unable to reach each other, which makes PEC micelle fusion highly improbable. Similar steric arguments have been made by theo-ries for certain amphiphilic block polymer micelle systems that do not exhibit fusion mechanisms.6,35 Again, we note that in the analysis above, the polyelectrolyte clusters and intermediate micelles are assumed to be electrostatically neutralized.

Therefore, we speculate that the observed kinetic pathway of these PEC micelles can be described as a three-stage process, as illustrated in Scheme 1. First, immediately upon mixing in the stopped-flow apparatus, oppositely charged polyelectrolytes form effectively neutral clusters within a few milliseconds. Alt-hough this may be experimentally challenging to probe, we an-ticipate that continued simulation efforts36-38 can be a powerful avenue to explore the nature of these small complex clusters. The mixing method and ionic strength may also play a key role in adjusting the timescale of cluster formation proceeding mi-cellization; selecting different polyelectrolyte pairings may re-sult in nonequilibrium aggregates that can be processed in a path-dependent manner.39 Second, the incipient clusters aggre-gate into sphere-like micellar aggregates. Both cluster insertion and micelle fusion are viable pathways until the particles exhibit intermicellar repulsive interactions from steric hinderance. Third, as the spherical micelles grow larger in size, cluster in-sertion becomes the main pathway, accounting for the incre-mental growth in Rg observable by stopped-flow TR-SAXS.

In summary, by employing in situ TR-SAXS technique with millisecond time resolution, we detailed the spatiotemporal evolution and kinetic pathways of a well-studied PEC micelle candidate. It is shown that micelles with an average Rg of 10 nm have been completely formed within 100 ms. These PEC mi-celles continued to grow in a steady manner to ca. 12-14 nm. By applying a quantitative physical model, we concluded that neither the classical single chain insertion nor the micelle fusion mechanism stands. Instead, PEC micelle formation is likely to proceed via a cluster-micelle insertion mechanism. We believe

that this work provides a unique springboard to better under-stand related ionic soft matter systems that exhibit unclear phe-nomena from fast structural dynamics. For instance, based on these results, materials genome-driven studies can be leveraged to explore the kinetic rate dependency of molecular attributes that affect coacervation, such as the neutral and charged block lengths, the strength and type of the charged moieties, the coun-terion valency, the hydrophobicity of the polyelectrolyte chain backbone, and the ratio between the neutral and charged blocks for complexation.40 Uncovering the underlying polymer phys-ics of complex formation from a molecular engineering ap-proach can also lead to new insights in biology.41 Physiologi-cally-relevant external parameters like solution pH, tempera-ture, and salt salinity can be easily studied in a systematic man-ner, especially in terms of evaluating micelle stability and dis-assembly.42 For practical bioapplications, TR-SAXS experi-ments with PEC micelles containing nucleic acids43,44 or bioac-tives45,46 can lay the foundation for translating biopharmaceuti-cal formulations into future medical products with greater reli-ability in efficacy, robustness, and safety.

ASSOCIATED CONTENT

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Materials and Methods, Supplemental Polyelectrolyte Complex Micelle Characterization (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

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

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formation and scattering experiments, drafted the manuscript, ana-lyzed the data, and assisted the material synthesis and characteriza-tion. J.M.T. performed the polymer synthesis, carried out polymer characterization, and assisted with the scattering experiments. S.M. assisted with the TR-SAXS experiments. 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.

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 as part of the Center for Hierarchical Materials Design (CHiMaD).

ACKNOWLEDGMENT The authors gratefully acknowledge the financial support from the U.S. Department of Commerce, National Institute of Standards and Technology (NIST), through the Center for Hierarchical Materials Design (CHiMaD). 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 Raj-kovic, PhD and Tsutomu Matsui, PhD, at the Stanford National Ac-celerator Laboratory for their assistance in scattering experiments and insightful discussions. Use of the Stanford Synchrotron Radia-tion Lightsource, SLAC National Accelerator Laboratory, is sup-ported 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 Re-search, and by the National Institutes of Health, National Institute of General Medical Sciences (including P41GM103393). The con-tents 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

Table of Contents artwork

download fileview on ChemRxivFormation Kinetics_fin.pdf (2.85 MiB)

Supporting Information for:

In situ Time-Resolved Small-Angle X-ray Scattering Reveals the Formation Kinetics of Polyelectrolyte Complex Micelles

Hao Wu,†,# Jeffrey M. Ting,†,‡,= Siqi Meng,† and Matthew V. Tirrell†,‡,*

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

‡ Argonne National Laboratory, Lemont, Illinois 60439, United States, *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) 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.

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) Micelle Characterization

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

characterized prior to TR-SAXS experiments. Using a cumulant expansion fitting method, 8 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-1). In addition, REPES analysis3 of the

autocorrelation function at 90° corresponded to a Rh of 28.8 nm (Fig. S-2). 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-1. Fitting of the autocorrelation function of a representative 5K50-158 micelle sample at 90° via cumulant expansion.

Figure S-2. 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) Supporting Information References

(1) Ting, J. M.; Wu, H.; Herzog-Arbeitman, A.; Srivastava, S.; Tirrell, M. V. Synthesis and

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.

(3) J, J. Regularized Positive Exponential Sum (REPES) Program-a Way of Inverting Laplace

Transform Data Obtained by Dynamic Light Scattering. Collect. Czech. Chem. Comm.

1995, 60, 1781–1797.

(4) Kline, S. R. Reduction and Analysis of SANS and USANS Data Using IGOR Pro. J Appl

Crystallogr 2006, 39, 895–900.

(5) Smolsky, I. L.; Liu, P.; Niebuhr, M.; Ito, K.; Weiss, T. M.; Tsuruta, H. Biological Small-

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

Cryst 2007, 40, s453–s458.

(6) Martel, A.; Liu, P.; Weiss, T. M.; Niebuhr, M.; Tsuruta, H. An Integrated High-Throughput

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

Rad. 2012, 19, 431–434.

(7) Jackson, A. J. “Introduction to Small-Angle Neutron Scattering and Neutron

Reflectometry” NIST Center for Neutron Research, Gaithersburg, MD, 2008

(8) Koppel, D. E. Analysis of Macromolecular Polydispersity in Intensity Correlation

Spectroscopy: the Method of Cumulants. J. Chem. Phys. 1972, 57, 4814–4820.

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