Non-equilibrium phenomena and kinetic pathways in self-assembled polyelectrolyte complexes

The formation of hierarchical self-assembled structures is often driven by non-covalent interactions, such as hydrogen bonding, hydrophobic effects, and electrostatic interactions.^1–5 On the energy landscape, these physical interactions are much weaker than chemical covalent bonds. Thus, for complex systems that comprise many modes of non-covalent interactions, the molecular assemblies resulting from specific formation pathways can be kinetically trapped in non-dissipative (i.e., metastable non-equilibrium) states rather than reaching equilibrium states.^7–9 Kinetic trapping is related to the origin of complex behaviors in many biological systems, such as protein folding,¹⁰ hemostasis,¹¹ and ribosome assembly.¹² The transitions between kinetic traps and thermodynamically stable states lead to a non-equilibrium assembly,¹³ which may be useful in itself and has been employed to build transient structures that are inaccessible for conventional equilibrium approaches.^14–18 For example, Korevaar et al.¹⁷ reported that the supramolecular assemblies that were polymerized from π-conjugated oligomers formed a short-lived kinetically favored metastable assembly before reaching the thermodynamically favored configuration. Using a chiral tartaric acid as an auxiliary to change the thermodynamic preference, they were able to obtain the metastable assemblies exclusively. Xu and co-workers¹⁹ demonstrated the construction of kinetically trapped ultralong ordered polyion nanoladders by ionic self-assembly. They designed a coordination complex of a stiff bisligand that can self-assemble slowly into cocoon-like structures. These structures immediately transformed into uniform nanoladder morphology upon the addition of an oppositely charged polymer.

Polyelectrolyte complexes (PECs) are a major class of macromolecular self-assembled materials based on electrostatic interaction. These materials are usually formed from combining solutions of oppositely charged polymeric macroions, where the process is believed to be initiated by electrostatic interactions and facilitated by the entropic gain from the release of counterions.^20–26 However, polyelectrolyte complexation is often frustrated by many factors such as conformational constraints, chain immobility, a lack of charge complementarity, and the competition between short-range attraction and long-range repulsion.^6,27,28 As a consequence, PECs are usually intrinsic out-of-equilibrium structures.²⁹ The static and dynamic properties of non-equilibrium PEC are determined by not only the chemical nature of constituting polymers and environmental elements, e.g., solution ionic strength, but also by physical processing pathways. The important roles of these factors have been undervalued in the experimental details of many complex coacervation reports to date. Consequently, challenges in the structural reproducibility of complex materials may arise upon scale-up or extension to end-use applications. Recently, Vitorazi and co-workers³⁰ stressed the importance of the mixing order in coacervation by investigating the thermodynamics of poly(diallydimethylammonium chloride) (PDADMAC)/poly(sodium acrylate) (PAA) complexation. Using isothermal titration calorimetry, they found a two-step coacervation process by adding PDADMAC to PAA or vice-versa and revealed that the phase separation exhibited an exothermic profile upon addition of PDADMAC to PAA but an endothermic profile for the reverse in terms of titration calorimetry response.

Furthermore, the morphological evolution of non-equilibrium PEC assemblies over a wide range of time and length scales is not well understood. The majority of effort has been devoted to finding conditions that circumvent non-equilibrium states in the assembly of coacervate core micelles in a reproducible manner.^31–36 As a consequence, little effort has been expended to understand the underlying factors governing the morphological transformation and complex internal structures in polyelectrolyte aggregates. Laaser et al.³⁷ investigated the structural stability and temporal evolution of micelleplexes, comprising poly(dimethylaminoethyl methacrylate)-block-poly(styrene) and poly(styrenesulfonate) homopolymers and emphasized the roles of charge imbalance and ionic strength in the interplay between kinetic and thermodynamic products in these systems. Wang et al.³⁸ proposed an effective method to stabilize the structures and fluorescent performance of reversible coordination polymers by kinetically trapping their local concentrations in polymeric complex micelle cores. Using a kinetic Monte Carlo simulation, Zhang and co-workers³⁹ investigated the structure and evolution kinetics of non-equilibrium ionic assemblies of oppositely charged nanoparticles and elucidated the determinative roles of ion correlations in non-equilibrium cluster formation. Overall, contemporary research on accessing non-equilibrium states of soft matter via an ionic self-assembly is scarce and case dependent. Advancements in such areas may create new avenues from a molecular engineering viewpoint to achieve novel functionalities and ultimately to mimic non-covalent macromolecular self-assembly motifs that are omnipresent in nature.

We have investigated the formation pathways and non-equilibrium phenomena in electrostatic aggregates that were formed by two oppositely charged styrenic diblock polyelectrolytes, namely, poly(ethylene oxide)-block-poly(vinyl benzyl trimethylammonium chloride) (PEO-b-PVBTMA) and poly(ethylene oxide)-block-poly(styrene sulfonate sodium) (PEO-b-PSS) [Figs. 1(a) and 1(b)]. The PVBTMA block is a strong cationic polyelectrolyte and has been demonstrated to be effective in DNA encapsulation,⁴⁰ while the PSS block is a strong anionic polyelectrolyte and has been widely used as a proxy for DNA molecules.^41–44 In order to elucidate the role of processing pathways, two distinct approaches were designed to probe the metastable morphologies of the resulting electrostatic assemblies. The temporal dependence of the structural evolution and the prolonged salt annealing kinetics was revealed by time-dependent light-scattering experiments, and the intermediate morphologies were visualized by cryogenic transmission electron microscopy (Cryo-TEM). Furthermore, the nuanced transformations of the internal structures in the non-equilibrium assemblies were investigated by small-angle X-ray scattering (SAXS). Our results elaborate the internal structures and the morphological transition of PEC assemblies from kinetic traps to equilibrium states in a spatiotemporal manner.

The following chemicals were reagent grade and used as received, unless stated otherwise: poly(ethylene oxide) methyl ether (2-methyl-2-propionic acid dodecyl trithiocarbonate) (PEO, Sigma, Reported M_n = 5000 or 10 000), sodium 4-vinylbenzenesulfonate (SS, Sigma, ≥90%), (vinylbenzyl) trimethylammonium chloride (VBTMA, Sigma, 99%), 2,2′-azobis[2-(2-imidazolin-2-yl)propane]dihydrochloride (VA-044, Wako Chemicals, USA), acetic acid (glacial, Sigma, ≥99.85%), and sodium acetate trihydrate (Sigma, ≥99%). SnakeSkin^™ dialysis tubing (MWCO 3.5K, 22 mm, Thermo Scientific) was used to purify crude products. The acetate buffer solution was prepared with 0.1M acetic acid and 0.1M sodium acetate trihydrate (0.1M) (42/158, v/v) at pH 5.2 for all reactions. All water was filtered through a Milli-Q water purification system at a resistivity of 18.2 MΩ cm at 25 °C.

A detailed description of the chemistry for reversible addition-fragmentation chain transfer (RAFT) polymerization is provided in Ting et al.⁴⁵ In a typical reaction, to a dried 25 ml round bottom flask, the styrene sulfonate monomer (6.7 mmol at 1.0M monomer concentration), RAFT PEO macromolecular chain transfer agent (0.067 mmol), and VA-044 (0.0067 mmol) were added to an aqueous acetate buffer solution (pH 5.2, 6.7 ml). The reactor was then sealed, degassed via three cycles of freeze-pump-thaw, and heated at 50 °C under nitrogen and constant stirring for at least 21 h. Afterward, the reaction was quenched by cooling to room temperature and opening to air. Crude yellow mixtures were dialyzed against Milli-Q water for 3 cycles of 8 h each, followed by lyophilization to yield ca. 2 g free-flowing yellow powder. The details of the polymer characterization are available in Table SI of the supplementary material.

Polycation and polyanion stock solutions were prepared in Milli-Q water at the concentration of 5.0 mg/ml and were filtered through 220 nm Polyvinylidene fluoride (PVDF) filters before use. All samples were prepared following the direct dissolution protocol or the salt annealing protocol. Electrostatic assemblies were made by mixing the stock solutions under stoichiometric conditions, with the presence of various salt types and salt concentrations. Each charged monomer had a concentration of 2.45 mmol/L. All micelle solutions were made at room temperature.

In the protocol of direct dissolution, a certain amount of salt solution was added into pure water, and then polycation stock solution and polyanion stock solution were added corresponding to the equimolar concentration of the cationic and anionic monomer units. The resulting micelle solution was set aside for at least 1 h before any measurement. Meanwhile, in the protocol of salt annealing, polycation and polyanion stock solutions were mixed prior to the addition of salt. Three salt types (NaCl, NaBr, and NaI) and a wide range of salt concentrations were selectively investigated. The effect of salt types is shown in Figs. S1 and S2 and Table SII of the supplementary material.

Dynamic light scattering (DLS) was carried out on a Brookhaven Instruments BI-200SM Research Goniometer System with a 637 nm incident laser at room temperature. The hydrodynamic radius (R_h) of scatters under Brownian diffusion can be calculated via the Stokes-Einstein relationship: $Rh=kBT/6πηD$⁠, where k_B is the Boltzmann constant, T is the absolute temperature, and η is the viscosity of the solution, here as taken that of water. The size and size distribution were obtained using a regularized positive exponential sum (REPES) algorithm⁴⁶ and the build-in non-negative least-squares (NNLS) algorithm⁴⁷ in the Brookhaven software. Time-resolved dynamic light scattering experiments were conducted using a script that is written by Cmm scripting language. Time delay and time duration were tailored for different samples and the time resolution. Intensity and correlation functions were recorded right after salt addition. The dead time was ca. 1 s. All of the DLS experiments were conducted at the angle of 90°.

Small-angle X-ray scattering (SAXS) experiments were carried out on beamline 12-ID-B at Advanced Photon Source, Argonne National Laboratory. The sample-to-detector distance was about 4 m, and the q range covered 0.002–0.5 Å⁻¹. Samples were loaded in thin-walled quartz capillaries or flow cells; 1 wt. % of glycerol was added to each sample to prevent potential beam damage. Using the SAXSLee package at Sector 12-ID-B, the experimentally generated 2D SAXS image was converted into the scattering vector defined as $q=4πλsinθ2$⁠, where λ is the incident X-ray wavelength and θ is the scattering angle. Then the 2D image was azimuthally averaged into a one-dimensional scattering curve. The absolute scattering intensity was calibrated with glassy carbon. The SAXS data were analyzed using the Irena package⁴⁸ and fitted by the two-level Beaucage model.⁴⁹ 

Cryogenic transmission electron microscopy (Cryo-TEM) was used to image particles. A Field Electron and Ion (FEI) Tecnai^™ G2 Spirit BioTWIN TEM was used to image samples set at an accelerating voltage of 120 kV onto a LaB6 emitter at −178 °C. A droplet of about 3 µL samples containing electrostatic assemblies was pipetted onto a carbon/Formvar grid that is cleaned by a PELCO easiGlow glow discharge instrument. The grid was blotted for 3 s and was quenched rapidly in liquid ethane and subsequently transferred to a single-tilt cryo holder. Images were taken using an EagleTM 2k CCD camera (up to 4 megapixels) and analyzed with the FEI TEM Imaging and Analysis (TIA) software. Phase contrast was enhanced by imaging at 8-12 µm under focus.

It is well studied that for amphiphilic polymers, the physical preparation protocols in solution have a marked effect on the dynamics of self-assemblies.^50–53 For electrostatically driven assemblies, in addition to the hydrophobic-hydrophilic balance and the chemical properties of the constituent monomers, the ionic character of charged segments and the presence of counterions and water throughout the assembly influence the kinetics and thermodynamics of coacervation. As a first approach to clarifying the mechanism of ionic self-assembly in a simple manner, we investigated the assembly of PEO-b-PVBTMA and PEO-b-PSS using two protocols shown in Fig. 1. In Protocol 1, the direct dissolution method, we prepared samples by sequentially combining the predetermined quantities of water, salt solution, polycation solution, and polyanion solution in this order. In Protocol 2, the salt annealing method, assemblies were first made by adding the predetermined quantities of water, polycation solution, and polyanion solution in this order, followed by salt solution. In other words, salt was distinctly added before the complex formation in the former protocol, while salt was added after complexation in the latter protocol [Fig. 1(c)].

Following these procedures, electrostatic assemblies of two polymer pairs of different chain lengths (PEO_5K-b-PVBTMA₅₀/PEO_5K-b-PSS₅₀ and PEO_10K-b-PVBTMA₁₀₀/PEO_10K-b-PSS₁₀₀) were prepared with 500 mM NaBr; the size and size distribution were compared by DLS over two months, shown in Fig. 2. It was observed that, for the direct dissolution method, both samples formed PEC-core micelles with relatively low colloidal polydispersities (<0.20 by cumulant fitting) and mean hydrodynamic radius (R_h) of ∼25 nm [Figs. 2(a) and 2(b)]. The size distribution broadened over the course of 70 days with sealed quiescent samples at room temperature. For the salt annealing method, however, the resulting electrostatic assemblies have a mean R_h of 100 nm with broad distributions [Figs. 2(c) and 2(d)], which apparently exceeded the polymers contour length (⁠$Lc≈0.40NPEO+0.26NPVBTMA$⁠). Surprisingly, after 70 days, the sizes and polydispersity metrics of these assemblies evolved into smaller narrower values, which largely matched the micellar products created by the direct dissolution method. As a result, we speculate that these assemblies were likely kinetically trapped aggregates, facilitated by the interplay between strongly charged PVBTMA and PSS blocks.

This convergence can be understood in light of our conceptual understanding of the steps of complex formation.²¹ Polyelectrolyte complexation is probably driven by the electrostatic attraction between oppositely charged groups and promoted by the entropy gain from the release of counterions. In the direct dissolution method, salt was added to the stock solutions of polycation and polyanion before the complex formation step. The presence of salt may have suppressed the release of counterions upon complexation, which hindered the initial formation of the kinetically trapped aggregates. Thus, equilibrium micellar structures are formed via the pathway 2 described in Fig. 7. In comparison, in the salt annealing process, the PEC assemblies were preemptively formed before the addition of salt. The oppositely charged polyelectrolyte chains interconnected with each other rapidly due to the large entropy gain from the counterion release. These chains may have not reached their optimal configurations, and thus some PEO chains may be buried in interconnected complex domains. In other words, we posit that the rearrangement of the hydrophilic chains was retarded by the large Debye screening length and the large entropic penalty associated with it. This results in the failure of forming uniform micelles with a hydrophilic corona and complexed core. After the salt was added, the interconnected complexes gradually equilibrated, and at over sufficient time, these electrostatic assemblies made from the two methods reached the similar micellar products because they were technically the same thermodynamic process. These observations motivated us to explore the underlying mechanism of structural evolution with additional complementary techniques.

It should be noted that the salt concentration and salt type were chosen based on our findings about the anion’s abilities to affecting the formation and stability of the polyelectrolyte complex assemblies. Our observation suggests that the heavier anions (i.e., I⁻ > Br⁻ > Cl⁻) have stronger effect on the screening of the electrostatic interactions in the polyelectrolyte complex assemblies. A similar phenomenon has been reported in bulk complexes forming from two homo-polyelectrolytes.⁵⁴ This trend follows the Holfmeister series, which views Cl⁻ as a moderately inert anion and I⁻ as a chaotrope that increases polymer solubility. The details are elaborated in Figs. S1 and S2 and Table SII of the supplementary material.

The time dependence of the structural evolution of the electrostatic assemblies is shown in Fig. 3. The sizes and size distributions were interpreted from the correlation functions in DLS and represented by intensity-averaged values using the NNLS algorithm. Compared with REPES, the NNLS algorithm used here is more sensitive with respect to multi-modal distributions; results analyzed with REPES are available in Figs. S1 and S2 of the supplementary material. It was observed that both of the two samples PEO_5K-b-PVBTMA₅₀/PEO_5K-b-PSS₅₀ and PEO_10K-b-PVBTMA₁₀₀/PEO_10K-b-PSS₁₀₀ showed two-population distributions within a short time after salt addition. As time elapsed, the sizes of the two polyelectrolyte-assemblies became smaller and reduced to a single peak after 25 min or 130 min for the PEO_5K-b-PVBTMA₅₀/PEO_5K-b-PSS₅₀ or PEO_10K-b-PVBTMA₁₀₀/PEO_10K-b-PSS₁₀₀, respectively. The PEO_5K-b-PVBTMA₅₀/PEO_5K-b-PSS₅₀ sample evolved into a narrow single-peak distribution with an average diameter of 38 nm after 50 min, and the PEO_10K-b-PVBTMA₁₀₀/PEO_10K-b-PSS₁₀₀ sample showed a single population with an diameter of 75 nm with low polydispersity after 400 min. It should be noted that at 400 min, the PEO_10K-b-PVBTMA₁₀₀/PEO_10K-b-PSS₁₀₀ sample had not reached its equilibrium state since the mean size continued to decrease to 50 nm after 21 hours (see Fig. S2 of the supplementary material).

Based on the phenomena we observe, we hypothesize that the overall structural evolution can be described into two stages: (1) disassembly of interconnected aggregates, followed by (2) redistribution of the incipient individual assemblies. In the initial state, polyelectrolyte chains are kinetically trapped due to the interplay between electrostatic interaction, hydrophilic-hydrophobic balance, and entropic penalty association with counterion relocation. Upon salt addition, the electrostatic interactions are weakened because the charged sites on the polymer chains are screened by the abundant counterions. Consequently, the irregularly shaped aggregate complexes broke apart, which was evidenced by the size reduction detected by DLS. The time scale of the structural evolution of this step was relatively fast and dependent on the molecular weight of the polyelectrolytes—the PEO_5K-b-PVBTMA₅₀/PEO_5K-b-PSS₅₀ evolved into a single distribution after 25 min [Figs. 3(a)–3(e)] and the PEO_10K-b-PVBTMA₁₀₀/PEO_10K-b-PSS₁₀₀ transformed to a sole peak after 220 min [Figs. 3(g)–3(k)]. At the second stage, the nascent individual PEC assemblies redistributed to smaller sizes and narrower distribution over a wide range of time, as the data shown in Figs. 3(e)–3(f) for PEO_5K-b-PVBTMA₅₀/PEO_5K-b-PSS₅₀ and Figs. 3(k)–3(l) for PEO_10K-b-PVBTMA₁₀₀/PEO_10K-b-PSS₁₀₀. This process was time consuming compared to the disintegration of interconnected aggregates in the first stage. The prolonged redistribution kinetics may probably be attributed to the entropic penalty to breaking down the paired charged sites in the complex cores as well as the additional energetic penalty resulting from the steric repulsion provided by the hydrophilic corona blocks. This size redistribution may be directly associated with the chain exchange process in self-assembled polymeric nanoparticles, which are subject to micelle collision and fragmentation over long periods of time. Similar observations have been reported in the amphiphilic block copolymer^55–57 and cationic polyelectrolyte micelles,⁵⁸ although the exact mechanism of chain exchange kinetics may be somewhat different for polyelectrolyte complex micelles in the present work.

SAXS was employed to further investigate the structural evolution of the non-equilibrated electrostatic assemblies as a function of NaCl from 100 mM to 1000 mM concentration. All curves exhibited an upturn at the low q regime (q < 0.01 Å⁻¹), which suggested the presence of large aggregates with R_g > 200 nm (⁠$Rg=2π/qmin$⁠) (Fig. 4). More information was obtained by fitting the SAXS data using the two-level Beaucage model^49,59 characterized by three parameters: a Guinier scaling factor G, a radius of gyration R_g, and a Porod exponent P. The scattering intensity is given by

This Beaucage model is used to fit SAXS data with levels composed of a Guinier part and a power law tail. It can handle SAXS features for which an exact scatter model is difficult or impossible. Here, the two levels were divided at the q = 0.01 Å⁻¹, and each length level was represented by an R_g and a power law slope. The fitting parameters were shown in Tables I and II. The R_g values of the q < 0.01 Å⁻¹ regimes were not given because of the absence of the corresponding Guinier regions. Details of the fitting are available in Fig. S4 of the supplementary material.

The second columns of Tables I and II contain the Porod exponents that correspond to mass fractals of the large electrostatic assemblies. At the low to intermediate salt concentration of 100-600 mM, the Porod exponents were close to 2.0, which is a signature of Gaussian chains.⁶⁰ However, at high salt concentration of 1000 mM, the Porod exponent reduced to 1.63, close to the 5/3 signature of fully swollen coils.⁶⁰ We attribute this to the breakup of kinetically trapped aggregates at high ionic strength, which allows the polymer chains to transform into more swollen and extended configurations. This transition was in line with the discussion of chain rearrangements in the DLS experiments. Figure 7 also shows a schematic representation of the breakup of aggregates upon the addition of external salt in the salt annealing pathway. Column 4 showed the evolution of the radius of gyration of the internal structures, and it decreased from 11.1 nm to 9.0 nm over the salt concentration range. The Porod exponents corresponding to surface fractals in column 5 in Table I between 3.5 and 3.9 (and these in Table II between 3.1 and 3.9) represented the internal structures and indicated the existence of rough spherical surfaces. Taking the above information into consideration, it is reasonable to infer that the electrostatic assemblies were constructed by local fuzzy globular complexes and interconnected segments between them. The similar results were founded in the PEO_5K-b-PVBTMA₅₀/PEO_5K-b-PSS₅₀ sample [Fig. 4(a) and Table II]. It should be noted that, in the high q region of the PEO_10K-b-PVBTMA₁₀₀/PEO_10K-b-PSS₁₀₀ sample with 1.0M salt, there was an approximate Guinier plateau, which might be caused by the smaller structures in the system.

Cryo-TEM was further employed to visualize the intermediate metastable morphologies of the electrostatic assemblies (Fig. 5). As expected, without salt, the non-equilibrium assemblies adopted the morphology of polydispersed interconnected aggregates; at high ionic strength, the aggregates were broke apart, as depicted in Fig. 7. For instance, the mean geometric diameter of the PEO_10K-b-PVBTMA₁₀₀/PEO_10K-b-PSS₁₀₀ assemblies decreased from 83 ± 44 nm (95% CI = 67, 98) at no salt to 34 ± 17 nm (95% CI = 31, 38) with 1.0M NaCl, a near 2.5 reduction in size. Furthermore, the overall spread of the particle distribution was affected by salt. The interquartile range (IQR) and corresponding outliers were calculated. In the same PEO_10K-b-PVBTMA₁₀₀/PEO_10K-b-PSS₁₀₀ example, the IQR of each respective sample was 56 nm and 21 nm, with remaining larger particles at 1.0M NaCl identified as outliers. At 1.0M NaCl, the IQR of PEO_5K-b-PVBTMA₅₀/PEO_5K-b-PSS₅₀ was similarly 14 nm. Overall, these results were consistent with the aforementioned SAXS data. One can observe that, even at high salt concentration where NaCl > 1.0M, the shape of the electrostatic assemblies was non-spherical. This might be attributed to the chemical nature of the strongly charged PVBTMA and PSS blocks—they formed precipitate bulk complexes, and due to the low contrast between the PEO and the background, the observed objects were primarily polyelectrolyte complexes. A similar morphology has been found in metal containing complex coacervate core micelles.⁶¹ The shape of the complexes might become more globular at higher ionic strength where PVBTMA and PSS blocks form soluble coacervates. The results of PVBTMA/PSS bulk complexes were given in Fig. S19 of the supplementary material.

The kinetics of the salt annealing process was investigated by time-resolved dynamic light scattering, where the average intensity was collected as a function of time immediately after salt was added. The relaxation functions were shown in Fig. 6 and were best fitted using the Kohlrausch-Williams-Watts (KWW)⁶² equation that can be expressed as

where I is the intensity, τ is the characteristic relaxation time, and β is the KWW exponent ranging from 0 to 1 and is used to describe a distribution centered about the mean relaxation time, which is calculated as the first moment of the stretched exponential by

where is Γ the gamma function. The KWW stretched exponential function is often used as a phenomenological description of relaxation in disordered systems, such as glasses,⁶³ polymer melts,^64–66 and protein gels.⁶⁷ For instance, Tang et al.⁶⁷ used the KWW model to discriminate the broad rheological relaxation behaviors in associative protein hydrogels. Because the interesting parallels between temperature and salt have been previously demonstrated for PEC assemblies (e.g., time-salt superposition of rheological properties⁶⁸), we attempted to use the KWW model to elucidate the relaxation behaviors of the PEO-b-PVBTMA/PEO-b-PSS assemblies prepared with the salt annealing method.

The KWW fitting parameters are shown in Table III. It is apparent that the decay rate is strongly dependent on the molecular weight of the polyelectrolytes, with the PEO_5K-b-PVBTMA₅₀/PEO_5K-b-PSS₅₀ micelles (τ = 8.90 min) decaying much faster than the PEO_10K-b-PVBTMA₁₀₀/PEO_10K-b-PSS₁₀₀ micelles (τ = 56.6 min). This matched well to the time scales of the size evolution of the assemblies in the aforementioned DLS results. Moreover, two stretched exponents β of 0.82 and 0.30 were obtained, which suggested the presence of wide spectrum relaxation behaviors in the salt annealing process. This broadly distributed relaxation was, to a large extent, originated from the heterogeneous kinetically trapped electrostatic assemblies such as the non-uniform distribution of charged sites and chain entanglement, which was supported by the observation that the PEO_10K-b-PVBTMA₁₀₀/PEO_10K-b-PSS₁₀₀ sample (containing more charged sites and longer chain blocks) exhibited a much longer and broader relaxation kinetics than those of the PEO_5K-b-PVBTMA₅₀/PEO_5K-b-PSS₅₀ sample. To the best of our knowledge, this is the first demonstration of how the KWW model might describe the relaxation kinetics of self-assembled polyelectrolyte complexes that are subjected to salt.

Self-assembled polyelectrolyte complexes with metastable morphologies were formed from strongly charged polyelectrolytes. The morphological transformation and relaxation behaviors of the resulting non-equilibrium aggregates were examined upon the addition of salt. These non-equilibrium assemblies had a significant structural inhomogeneity and consisted of moderately salt-resistant internal complexes and salt-susceptible interconnected components. The irregularly shaped interconnected electrostatic aggregates started to disintegrate in the presence of strong salts and high ionic strengths. The temporal disintegration of the kinetically trapped assemblies can be discriminated as a two-step process: a fast mode of the breakdown of the interconnected parts and a slow mode of the redistribution of the nascent individual assemblies. The whole process is schematically represented in Fig. 7. This feature of generating nano-scale soluble polyelectrolyte micelles from kinetically trapped microscopic assemblies over time can be potentially exploited for the controlled release of therapeutics.^69–71  Future work will be emphasized on the chain conformational transition in polyelectrolyte precipitates and soluble complexes, the role of chain exchange in the electrostatic assembly redistribution, and the production of polyelectrolyte complex micelles from non-equilibrium polyelectrolyte complexes in a controlled manner. A relevant study about kinetic trapping reversible coordination supramolecules in polyelectrolyte assemblies will also be investigated. We anticipate that the results presented here will attract attention and encourage effort to the non-equilibrium phenomena of polyelectrolyte complexes and will bring new insights into design ideal charged macromolecule-based systems for various applications.⁶⁹ 

See supplementary material for the details on polymer characterization (Table SI), effect of salt types (Figs. S1 and S2 and TABLE SII), size evolution characterized by REPES (Fig. S3), SAXS modeling (Figs. S4, S6–S17), Cryo-TEM size distribution (Fig. S18), and bulk complexes (Fig. S19).

The authors gratefully thank Tera Lavoie, Ph.D. for her assistance at the Advanced Electron Microscopy Facility at the University of Chicago and Xiaobing Zuo, Ph.D. for his assistance at the Advanced Photon Source at Argonne National Laboratory. The use of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory, was supported under Contract No. DE-AC02-06CH11357. J.M.T. acknowledges support from the NIST-CHiMaD Postdoctoral Fellowship, which is supported by the U.S. Department of Commerce, National Institute of Standards and Technology (NIST) through the Center for Hierarchical Materials Design (CHiMaD) under financial assistant Award No. 70NANB14H012. 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 Standards and Technology (NIST), nor does it imply that the material or equipment identified is necessarily the best available for this purpose.