# The Kinetic Pathways for the Formation of Complex Coacervate Micelles of Antimicrobial Peptides and Block Copolymers

Thomas D. Vogelaar, Henrik Torjusen, Theyencheri Narayanan, Reidar Lund

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Thomas D. Vogelaar, Henrik Torjusen, Theyencheri Narayanan, Reidar Lund. The Kinetic Pathways for the Formation of Complex Coacervate Micelles of Antimicrobial Peptides and Block Copolymers. Macromolecules, 2025, 58 (1), pp.158-168. 10.1021/acs.macromol.4c02077. [hal-05122157](https://hal.science/hal-05122157v1)

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# The Kinetic Pathways for the Formation of Complex Coacervate Micelles of Antimicrobial Peptides and Block Copolymers

Thomas D. Vogelaar, Henrik Torjusen, Theyencheri Narayanan, and Reidar Lund*

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Cite This: *Macromolecules* 2025, 58, 158–168

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Supporting Information

**ABSTRACT:** The conceptual application of complex coacervate core micelles (C3Ms) as drug delivery vehicles has obtained significant interest over the past several decades. Although C3Ms show promise in targeting specific body areas and improving drug circulation times, their low reproducibility and limited stability have hindered their progression to clinical trials and commercial viability. One of the major obstacles is the lack of understanding of the formation and growth kinetics of C3Ms. Since their structure is often controlled kinetically rather than thermodynamically, this insight is essential for achieving good reproducibility and stability of C3M drug delivery vehicles. Time-resolved small-angle X-ray scattering (TR-SAXS) offers excellent insights by resolving spatiotemporal kinetic processes on nanometer/millissecond scales. Here, we investigate the formation kinetics of C3Ms comprised of the antimicrobial peptide, colistin, and poly(ethylene oxide)-b-poly(methacrylic acid) (PEO-b-PMAA). Using TR-SAXS coupled to stopped-flow mixing, we have identified three distinct steps in the mechanism of this complex coacervation system: nucleation, fusion, and single chain/ion-pair insertion. Nucleation cannot be experimentally resolved as it is completed during the mixing process. The fusion kinetics proceed as a first-order reaction with relaxation times of approximately 50–85 ms. The driving force for fusion is larger at increased concentrations. Chain/pair insertion occurs at relaxation times of 15–25 s, where larger remaining size mismatches (higher dispersity) drive the final equilibration process. As expected, the structural formation is concentration-dependent, providing a handle to acquire control over the size and dispersity of these kinetically trapped C3Ms. These findings contribute to a deeper understanding of C3M formation and stability, potentially advancing the development of C3M-based drug delivery systems.

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## 1. INTRODUCTION

Over the past several decades, the conceptual use of complex coacervate core micelles (C3Ms) as nanomedicine in the form of drug delivery vehicles has been thoroughly assessed.¹⁻⁴ C3Ms, otherwise referred to as polyelectrolyte or polyion complex micelles (PIC/PEC/PCM), belong to the class of self-assembled structures.¹,³,⁵⁻⁷ These complexes are formed after liquid–liquid phase separation, induced by electrostatic interactions between oppositely charged polyelectrolytes in aqueous solutions.³,⁵,⁸ The self-assembly is driven by a combination of an enthalpic term due to electrostatic charge attraction with the entropic gain related to counterion release and polyelectrolyte hydration effects.⁵ To design formulations of C3Ms suitable for drug delivery systems, a charged drug, or DNA is usually complexed with other polyelectrolytes, which can be oppositely charged lipids, (block-)copolymers, or other biomacromolecules.⁹⁻¹² One of the biggest challenges in the practical application of these complex coacervates is macroscopic phase separation i.e. low stability.⁵,¹³,¹⁴ This can be detrimental to the therapeutic potential of a drug delivery system if it is not adequately taken into account.³,¹⁵ To create stable systems, often a neutral block is conjugated to one of the polyelectrolytes.⁸,⁹,¹³,¹⁶ The neutral block, e.g. poly(ethylene

oxide) (PEO), poly(acryl amide) (PAA), or the polypeptoid poly(sarcosine) (pSar),²,¹⁷,¹⁸ provides steric repulsion and acts as a shell around the highly charged polyelectrolyte core.²,⁸,¹⁹,²⁰ These C3Ms most often exhibit a core–shell morphology with their size dependent on multiple factors like polyelectrolyte block length, ionic strength, charge density, and number of polyelectrolyte moieties, among others.²,³,⁸ The interplay of these factors emphasizes the complexity involved in ensuring the stability and reproducibility of C3Ms as a drug delivery vehicle.

If designed well, C3M systems can increase drug circulation times by protecting its load along with targeting certain areas in the body.²⁰,²¹ In this respect, some applications have been aimed at the delivery of DNA, drugs, proteins, and peptides.²,¹¹,¹²,¹⁷,²²⁻²⁴ Even though multiple efforts have

Received: August 31, 2024

Revised: November 12, 2024

Accepted: December 18, 2024

Published: December 31, 2024

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been made, neither commercially available nor clinical tests have been conducted on any of the systems thus far.<sup>3,20</sup> Generally, this can be attributed to the time-consuming empirical analysis done on the equilibrium versions of various systems.<sup>20</sup> Most systems suffer from difficulties in reproducibility and optimization, making analysis tedious and creating drug delivery vehicles that are not suitable for upscaling and clinical testing.<sup>20,25</sup>

Currently, one of the major knowledge gaps in this field is the understanding of the formation and growth kinetics of such micellar systems.<sup>17,19,20,26</sup> Investigating these formation kinetics more fundamentally can significantly improve the control of the release and stability for several C3Ms drug delivery systems at once.<sup>10</sup> Little is known about the complete micellization process, but there is a consensus that the formation of C3Ms starts with ion pairing/nucleation.<sup>5,19,26</sup> The following kinetic processes are unclear, as they are highly dependent on multiple factors, e.g. concentration, charge density of block lengths, charge fractions, and ionic strength.<sup>2,5,13,27</sup> In addition, the kinetics of the formation of C3Ms is complicated to measure, as they occur in a millisecond to second range.<sup>26,28-30</sup> Most studies investigating these systems employ time-resolved turbidity, light scattering, or small-angle X-ray/neutron scattering (TR-SAXS/SANS) coupled to fast mixing techniques like the stopped-flow apparatus.<sup>8,20,28,31-33</sup> These techniques have been used to investigate the self-assembly and disassembly kinetics of several different types of amphiphiles, like surfactants<sup>34,35</sup> or block copolymers,<sup>19,26,36</sup> that can result in a multitude of structures, e.g., (cylindrical) micelles, vesicles, or disks.<sup>37</sup> Only recently, the formation kinetics of the complexation of different C3M-forming systems has been investigated using spatiotemporal high-resolution TR-SAXS.<sup>2,19,26,38</sup>

Wu et al.<sup>19</sup> investigated the kinetic formation of poly-(ethylene oxide)-*b*-poly(vinyl benzyl) trimethylammonium chloride (PEO-*b*-PVBTMA) with poly(acrylic acid) (PAA) and could follow the growth of spherical particles from 100 ms to 5 s, where spherical entities grew over time. In contrast to the kinetic formation complexing with PAA, Amann et al.<sup>26</sup> analyzed the C3M formation of PEO-*b*-PVBTMA with poly(styrene sulfonate) (PSS). They found the quick formation of metastable micellar aggregates after 2.6 ms, which rearranged into individual micelles as charge equilibration was attained, which typically occurred over a time scale of 30 s. These examples are only two of the many possible pathways of C3M formation.<sup>2,37</sup>

Next to the kinetics of block copolymer C3M formation, similar studies have been performed on the formation and exchange kinetics of polyelectrolyte complexes (PECs)<sup>29</sup> (complexation from oppositely charged homopolymers)<sup>16</sup> and noncharged block copolymer (BCP) micelles.<sup>2,20,39</sup> Takahashi et al.<sup>29</sup> investigated the formation kinetics of sodium poly(acrylic acid) (PAA) and poly(allylamine hydrochloride) (PAH) into PECs, where the authors elucidated three stages in complexation: nucleation, coalescence/fusion, and growth/insertion. Similar findings were also reported by Kalkowski et al.<sup>20</sup> where they investigated poly(ethylene oxide)-*b*-poly(caprolactone) (PEO-*b*-PCL) BCP micelle formation employing microfluidic mixing. These fusion and insertion processes (and their opposite counterparts, fission, and expulsion) were also found highly relevant in the exchange and dissociation kinetics observed in BCP micelles.<sup>40-43</sup> Building on the kinetic mechanisms observed in PECs and

BCP micelles, models for C3Ms can be further developed and refined to more accurately capture their complex formation and growth kinetics.

Previously, we have investigated static<sup>44</sup> and timed (by prodrug hydrolysis)<sup>45</sup> C3Ms consisting of the cationic antimicrobial peptide colistin together with the partially anionic block copolymer poly(ethylene oxide)-*b*-poly-(methacrylic acid) (PEO-*b*-PMAA). The C3Ms, characterized by SAXS modeling, consist of a colistin and PMAA core, where the PEO polymer brush acts as a protective shell by entropic (steric) repulsions. The formed C3Ms with a size of 35 nm were found to be stable and reproducible along a wide range of charge ratios and retained their bacterial activity.<sup>44</sup> Herein, we show the in-detail study of the formation kinetics of the complex coacervates containing antimicrobial peptides. We address the kinetic pathways, varying several important parameters such as block lengths, charge stoichiometry, and ionic strength effects. Using a detailed SAXS model, taking into account the dispersity and mass balances,<sup>44</sup> we obtained information on the evolution of structural parameters such as aggregation numbers and radii. Through the analysis of the time-dependent parameters, we find that the kinetics occurs via three main steps: (i) nucleation, (ii) fusion/fission of premicelles, and (iii) ion-pair/single-chain exchange leading to metastable, final micelles.

## 2. EXPERIMENTAL SECTION

2.1. Materials. Three different versions of PEOₓ-*b*-PMAAᵧ (where x and y are the degrees of polymerization for the PEO and PMAA blocks respectively) with block lengths of PEO₄₅-*b*-PMAA₄₁; *D* = 1.20, PEO₄₅-*b*-PMAA₈₁; *D* = 1.15, and PEO₁₁₄-*b*-PMAA₈₁; *D* = 1.15 were purchased from Polymersource Inc., Canada. Colistin Sulfate (PHR1605), Trizma base, Trizma hydrochloride, and sodium chloride (NaCl) were purchased from Sigma-Aldrich/Merck, Germany. All chemicals were used without further purification.

2.2. (Time-Resolved) Small-Angle X-ray Scattering (TR-SAXS). PEO-*b*-PMAA with differing block lengths and colistin sulfate were dissolved in 0.05 M TRIS buffer at pH = 7.4. To obtain the static small-angle X-ray scattering (SAXS) profiles of complex coacervate structures, the components were “hand-mixed” at stoichiometric charge matching concentrations, at a fixed total concentration of 0.50 wt %. This was achieved by adding the polymer solution to the colistin solution in equal volumes while the mixture was then thoroughly mixed by repeatedly pipetting up and down for about 30 s. The mixes were then measured at 20 °C using the BioSAXS beamline BM29 at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France.<sup>46</sup> For each sample, the automatic sample changer injected 50 µL of the sample into a quartz glass capillary with a diameter of 1 mm. Subsequently, 10 scattering frames of 1.0 s each were recorded using a Pilatus 3 × 2 M detector (energy of 12.5 keV, sample–detector distance = 2.81 m, Q-range = 0.007–0.45 Å⁻¹). The background samples (0.05 M TRIS buffer, pH = 7.4) were measured between each sample measurement and the capillary was cleaned between every measurement.

To determine the formation kinetics, the solutions were mixed using an SFM-4000 stopped-flow device adapted for *in situ* TR-SAXS (Bio-Logic Science Instruments, France). TR-SAXS measurements were performed at 20 °C at the TRUSAXS beamline ID02 at the European Synchrotron Radiation Facility (ESRF) (Grenoble, France).<sup>47</sup> The mixing was done in a 1:1 volume ratio at a total flow rate of 6.0 mL/s, resulting in a dead time of 2.9 ms. TR-SAXS patterns of PEO-*b*-PMAA-colistin mixtures were collected on an Eiger2-4 M detector placed at 2.0 m from the stopped-flow capillary (size ~ 1.25 mm), covering a Q-range of 0.003–0.40 Å⁻¹. To obtain more insights about the larger/aggregated structures, some samples were also measured at a sample–detector distance of 15.0 m, resulting in a Q-range of 0.0005–0.0040 Å⁻¹. Subsequently, the Q-ranges were
combined using the software SAXSUtilities2⁴⁸ and restricted to 0.0015–0.40 Å⁻¹.

The total concentrations of polymer-colistin mixtures were fixed at either 0.50 wt %, 0.25 wt %, or 0.125 wt % at colistin charge fractions ($f_+$) of 0.44 ≤ $f_+$ ≤ 0.67, while the corresponding PEO-b-PMAA and colistin concentrations varied for each $f_+$. 31 frames were in total collected for each sample for 8 to 10 reproducible shots. For every shot, 30 successive frames with 5 ms X-ray exposure time were measured with the interval between frames varied in a geometric progression (common ratio = 1.35) spanning a time range from 2.9 ms to 86 s. A final frame was taken with an exposure time of 0.1 s when the formation of the micelles was completed (manually checked in advance, confirmed by final state reproducibility checks), roughly 2 min (set to t = 120 s in this work for simplicity) after mixing. In Figure 4, we added one more point at different points in time to show the kinetic completion within 2 min. The background sample (0.05 M TRIS buffer, pH = 7.4) was measured before each set of time-resolved measurements. For both SAXS and TR-SAXS, the data was scaled to absolute intensities using water as a reference. Every frame was analyzed for radiation damage and bubbles, followed by averaging of the shots at all 31-time points, buffer subtraction, and binning (from ≈1000 points for SAXS and ≈1600 points for TR-SAXS both to ≈280 points), resulting in the final scattering curves that are presented in this paper.

**2.3. (TR-)SAXS Data Modeling.** To analyze the SAXS data on an absolute scale, we modeled the data using a simplified version of a previously reported fuzzy-surface complex coacervate model.⁴⁴ This model includes broad interfaces and dispersity and consists of three contributions to describe the micellar scattering: fuzzy-core complex coacervates, free colistin, and PEO-b-PMAA scattering, and an additional internal pseudo-structure factor ($S(Q)_{\text{internal}}$) to account for the interactions between the charged polyelectrolytes in the core. The total scattering function is given in eq 1:

$$I(Q) = \varphi \cdot f_{\text{Coa}} \left( I_{\text{Coa}}(Q) + \frac{\text{blob}(Q)}{V_{\text{Coa}}} \right) + \varphi (f_{\text{Poly}} \cdot I_{\text{Poly,free}}(Q) \cdot f_{\text{mix}} + f_{\text{Col}} \cdot I_{\text{Col,free}}(Q) \cdot (1 - f_{\text{mix}})) + f_{\text{Coa}} \cdot S(Q)_{\text{internal}} \quad (1)$$

Where $\varphi$ is the volume fraction (which is the total concentration divided by the average density of colistin and PEO-b-PMAA), $f_{\text{Coa}}$ is the fraction of material that forms coacervates/C3Ms, $V_{\text{Coa}}$ is the volume of one micelle, $f_{\text{Poly}}$ is the fraction of nonincorporated polymer, $f_{\text{Col}}$ is the fraction of nonincorporated colistin and $f_{\text{mix}}$ is the molar fraction of polymer in the aqueous (dilute) phase. For C3M scattering, we assume charge-matching in the core and use a fuzzy sphere form factor (spheres with graded interfaces based on radius R and its interface width, $\sigma$). The form factor for fuzzy spheres ($P(Q) = A_{\text{core}}(Q)^2$) is described by eqs 2–5, and the following C3M scattering function is given in eq 6.⁴⁹,⁵⁰

$$F_0 = \left( \frac{R}{\sigma^2} + \frac{1}{\sigma} \right) \frac{\cos(Q \cdot (R + \sigma))}{Q^4} - \frac{3\sin(Q \cdot (R + \sigma))}{Q^5 \cdot \sigma^2} + \left( \frac{R}{\sigma^2} - \frac{1}{\sigma} \right) \frac{\cos(Q \cdot (R - \sigma))}{Q^4} \quad (2)$$

$$F_1 = \frac{-3 \cdot \sin(Q \cdot (R + \sigma)) + 6 \cdot \sin(Q \times R)}{Q^5 \cdot \sigma^2} - \frac{2 \cdot R \cdot \cos(Q \cdot R)}{Q^4 \cdot \sigma^2} \quad (3)$$

$$V_n = \frac{R^3}{3} + \frac{R \cdot \sigma^2}{6} \quad (4)$$

$$A_{\text{core}}(Q) = \frac{F_0 + F_1}{V_n} \quad (5)$$

$$I_{\text{Coa}}(Q) = \frac{\Delta\rho_{\text{average}}^2 \cdot P^2 \cdot V_{\text{tot}}^2 \cdot A_{\text{core}}(Q)^2}{V_{\text{Coa}}} \quad (6)$$

Where $I_{\text{Coa}}(Q)$ is the scattering contribution from the C3Ms, $\Delta\rho_{\text{average}}$ is the average scattering length density, P is the aggregation number (number of molecules per micelle), and $V_{\text{tot}}$ is the total volume of the blobs. The blob scattering of the polyelectrolytes in the core of the C3Ms was also taken into account (eq 7):

$$\text{blob}(Q) = V_{\text{tot}}^2 \cdot P \cdot \Delta\rho_{\text{average}}^2 \cdot \frac{|f_{\text{blob}}|}{(1 + Q^2 \cdot \xi^2)} \quad (7)$$

Where the $f_{\text{blob}}$ is the fraction of blobs, and $\xi$ is the blob correlation length. For the free scattering contributions of polymer and colistin, the Debye form factor for polymers and polyelectrolytes is used (eq 8).⁵¹

$$P(Q)_{\text{Debye}} = \frac{2(e^{-Q^2 \cdot R_g^2} - 1 + Q^2 \cdot R_g^2)}{(Q^2 \cdot R_g^2)^2} \quad (8)$$

In which the $R_g$ is the radius of gyration of the polyelectrolyte. The last contribution is the internal pseudo-structure factor $S(Q)_{\text{internal}}$ related to the charge correlations between the blobs of anionic PMAA and cationic colistin (eq 9).⁴⁴,⁵²⁻⁵⁴

$$S(Q)_{\text{internal}} = \frac{|C(Q)| \cdot e^{-(Q-Q_{\text{local}})^2 / 2 \cdot (W \cdot Q_{\text{local}})^2}}{W \cdot Q_{\text{local}} \cdot \sqrt{2\pi}} \quad (9)$$

Where $C(Q)$ is the fractal scattering, W is the relative width at high $Q$, and $Q_{\text{local}}$ is the internal scattering location. With the fuzzy-surface complex coacervate model, a quantitative analysis can be made on C3M structures (more details in the Supporting Information). For the (simultaneous) fit analysis of all 31 frames at once, first, least-squares fit was performed keeping the following parameters free: the total aggregation number (P) and the radius of the core, including its density distribution and dispersity ($R$, $\sigma$, $D$). As these parameters do not describe the high Q region, we fixed the previously mentioned parameters and floated the blob scattering parameters, including the free fraction of colistin ($f_{\text{Col}}$), blob fraction ($f_{\text{blob}}$), blob correlation length ($\xi$), the relative width at high Q ($W$), the internal scattering location ($Q_{\text{local}}$), and fractal scattering ($C(Q)$). Finally, the P, R, $\sigma$, and $D$ were floated again and fitted, resulting in the fit results presented here. The standard deviation for the fit parameters was based on the changes of 10% in $\chi^2$ for the fits. To be sure that the analysis of the kinetics from the scattering data is independent of the model, we obtained the aggregation number P using a model-independent Guinier analysis based on the fits of the Q-range of 0.0047–0.009 Å⁻¹ (eqs 10 and 11).

$$I(Q) = \frac{I(0)}{1 + (Q \cdot R_g/3)^2} \quad (10)$$

$$P = \frac{I(0) \cdot d^2 \cdot N_A}{c \cdot \Delta\rho^2 \cdot M_{w0,\text{average}}} \quad (11)$$

In which $R_g$ is the radius of gyration, d is the average density of the colistin-polymer mixture, c is the total concentration, $M_w$ is the average molecular weight of one polymer-colistin molecule, and $N_A$ is Avogadro's number.

# 3. RESULTS AND DISCUSSION

**3.1. Static SAXS Patterns of Complex Coacervates.** It is already well documented that the initial ion pairing and formation kinetics is rather fast.⁵,¹⁹,²⁶ By examining several different systems with the same cationic counterpart, colistin, we can elucidate a selection of potential outcomes of the complexation kinetics based on the different degrees of polymerization. To review these systems, we first elucidate the final states of several different colistin coacervation complexes from the static SAXS measurements. Three different PEO-b-PMAA polymers (PEO₄₅-b-PMAA₄₁, PEO₄₅-b-
PMAA<sub>81</sub>, and PEO<sub>114</sub>-b-PMAA<sub>81</sub>) were analyzed as potential candidates for colistin complexation at stoichiometric charge matching conditions (f<sub>+</sub> = 0.50) (Figure 1).

<figure><img src="image_10.png" /><figcaption>**Figure 1.** SAXS patterns of three PEO-b-PMAA polymers: PEO<sub>45</sub>-b-PMAA<sub>41</sub> (orange squares), PEO<sub>45</sub>-b-PMAA<sub>81</sub> (blue circles), PEO<sub>114</sub>-b-PMAA<sub>81</sub> (green triangles), and colistin (gray rhombuses) at 0.25 wt % (A). Fits in A were made using the Debye model for polymer chain scattering (eq 8). SAXS profiles of the complexation of these anionic polymers with colistin at stoichiometric charge matching at 0.50 wt % total concentration (B). Fits in B are made using the fuzzy-surface complex coacervate model (eq 1).</figcaption></figure>

**Figure 1A** shows the scattering patterns of the initial, unmixed components: colistin and the different block copolymers. As can be seen, they all display a Guinier region that appears flat in the log-log presentation at low Q. At high Q, we observe a weak $Q^{-2}$ scattering, resembling polymer coils. Therefore, we employed the Debye model (eq 8) for Gaussian chains and obtained good fits (solid lines). For the mixed samples where complex coacervate micelles are formed, the data were described by the “fuzzy-sphere” model (eq 1) (Figure 1B). Based on the fits (detailed fit parameters in Table S1), the complexes of PEO<sub>45</sub>-b-PMAA<sub>41</sub> and PEO<sub>114</sub>-b-PMAA<sub>81</sub> show core-shell micellar features with total diameters of 32 ± 1 nm and 82 ± 4 nm, respectively. PEO<sub>45</sub>-b-PMAA<sub>81</sub> coacervates also display core-shell-like features and are 72 ± 6 nm in diameter but are in a slightly aggregated state, shown by the upturn at low Q. Based on the differences in sizes there is a clear link between the size/aggregation numbers and the fraction of water within the micelles. The more charge present per micelle core, the more water is drawn in due to the lower hydrophobicity in these systems and the bigger the size.<sup>8,55,56</sup> In addition, the polymers with a higher degree of polymer-

ization are found to form more polydisperse C3Ms (18% versus 24–25%), resulting in an increased effective range of sizes. All micelles show a correlation peak at high Q around 0.20 Å<sup>-1</sup>, indicating a certain optimal packing distance between colistin and PMAA in the core, similar to what has been previously observed in C3M systems.<sup>52,57</sup> These packing conditions can be attributed to positional charge correlations between electrostatic blobs within the complex coacervates.<sup>44,52</sup> The PEO chains sticking outside the core are thought to cause steric repulsion between the micelles, resulting in higher stability over a long time (several months). Another factor contributing to its high stability is the fractions of free colistin and PEO-b-PMAA. These fractions are estimated to be constant and lay around 15 ± 1%, based on the fit analysis. Here, we show three systems that form stable complex coacervate systems at several different sizes, relevant to elucidate kinetic processes through TR-SAXS analysis.

**3.2. TR-SAXS Analysis of Multiple C3M Systems.** We analyzed the time-resolved complexation of these same systems through TR-SAXS for a selected number of frames encompassing the complete complex coacervation kinetics (Figure 2). For the polymers with larger molecular weights, a more extended Q-range was used, as an attempt to capture the overall larger structure.

All components already form complexes at time scales less than 2.9 ms, the dead time of the stopped-flow apparatus (Figure 2). Within the dead time of mixing, we observe the formation of rather large micelles as seen by the high intensity at low Q, followed by a steep decay at intermediate Q. For PEO<sub>45</sub>-b-PMAA<sub>41</sub> and PEO<sub>114</sub>-b-PMAA<sub>81</sub> coacervates we observe a Guinier-like region that appears at a near plateau in log-log plots. However, for PEO<sub>45</sub>-b-PMAA<sub>81</sub> and some frames of the PEO<sub>114</sub>-b-PMAA<sub>81</sub>, a significant upturn at the lowest Q is observed, signifying complex coacervates that are partially aggregated into larger clusters. To take these aggregated structures into account, we implemented a structure factor in the fuzzy-surface complex coacervate model, describing the cluster formation of micelles (*Supporting Information*).

All PEO-b-PMAA coacervates grew over 86 s to the final end-state and were found to be similar to the static SAXS patterns (Tables S2–S4). However, due to the effect of mixing on the final metastable (kinetically arrested states), the stopped-flow coacervates were found to be slightly smaller compared to the hand-mixed C3Ms (Tables S1 and S2).<sup>17</sup>

<figure><img src="image_11.png" /><figcaption>**Figure 2.** SAXS patterns of the time-resolved complexation by combining colistin with three different PEO-b-PMAA polymers at stoichiometric charge matching: PEO<sub>45</sub>-b-PMAA<sub>41</sub> (A), PEO<sub>45</sub>-b-PMAA<sub>81</sub> (B), and PEO<sub>114</sub>-b-PMAA<sub>81</sub> (C) at 0.50 wt % total concentration. In these plots, we show 8 of the 31 frames that were measured over time, spanning from the first frame to the final state. Fits are made using the fuzzy-surface complex coacervate model given in eq 1.</figcaption></figure>
Interestingly, we see that the system attains a near-optimal packing as seen by the development of a structure factor peak at high Q already within the dead time of mixing. This can be attributed to rapid nucleation into micelles within 2.9 ms. This nucleation phase is followed by a growth phase, as the scattering patterns show a 5 to 10-fold complex increase in the forward scattering intensity for these complexes. In the transition from small micellar structures in the first 25 ms toward the final state, the slope at intermediate Q steepens (increase of radii), and the Guinier plateau intensity increases (increasing aggregation number). This is supported by the fit results, where we observe increases in both aggregation number and size over time for the PEO-b-PMAA-colistin C3Ms. The time evolution of the most important structural parameters, i.e. the aggregation number (the number of molecules in one micelle, *P*) and the total radius growth ($R_{tot}$) is shown in Figure 3.

<figure><img src="image_12.png" /><figcaption>**Figure 3.** Evolution of aggregation numbers *P* (orange squares) and total radii ($R_{tot}$) (blue circles) over time, including error bars for PEO<sub>45</sub>-b-PMAA<sub>41</sub> (A), PEO<sub>45</sub>-b-PMAA<sub>81</sub> (B), and PEO<sub>114</sub>-b-PMAA<sub>81</sub> (C) coacervates. The dispersity (*D*) changes are included as insets for each polymer (green triangles). The *P*, $R_{tot}$, and *D* values were based on the fits of the SAXS data using the fuzzy-surface complex coacervate model, including a cluster formation structure factor for PEO<sub>45</sub>-b-PMAA<sub>81</sub> and PEO<sub>114</sub>-b-PMAA<sub>81</sub> coacervates.</figcaption></figure>

The growth profiles of the aggregation number and the total radius show that the time scale of the kinetics of coacervation is significantly different for each degree of polymerization of PEO-b-PMAA (Figure 3). To account for model-dependent effects on the kinetic analysis, we performed model-free Guinier analysis and found a similar evolution of aggregation number therefore similar kinetics as expected (Figure S1). PEO<sub>114</sub>-b-PMAA<sub>81</sub> coacervates reach a plateau for $R_{tot}$ *P*, and

*D* at around 10 s (Figure 3C), whereas PEO<sub>45</sub>-b-PMAA<sub>41</sub> coacervates only reach the plateau around 120 s (Figure 3A). PEO<sub>45</sub>-b-PMAA<sub>81</sub> coacervates do not show clear trends, neither in aggregation number nor the total radii fits (Figure 3B). For the two largest polymers (Figure 3B,C), the clustering effect introduces larger uncertainties in the parameters *P*, *D*, and $R_{tot}$. Moreover, for PEO<sub>45</sub>-b-PMAA<sub>81</sub> and PEO<sub>114</sub>-b-PMAA<sub>81</sub> coacervates, the parameters *P* and $R_{tot}$ appear to be directly linked and show a power-law relationship with exponents of roughly 1/3, indicating growth at an equal internal density (Figure S2). PEO<sub>45</sub>-b-PMAA<sub>41</sub> coacervates have a more complex *P* and $R_{tot}$ relation, consisting of several stages of growth. Considering the quality of the fit analysis on the micelle formation and the independence of *P* and $R_{tot}$ growth, PEO<sub>45</sub>-b-PMAA<sub>41</sub> micelles are the best fit for a comprehensive investigation (Figure 3A).

The formation kinetics of this system appears to be comprised of three different stages (most important fit parameters in Table S5). First, nucleation was completed during mixing, shown by an average *P* of 380 ± 11 molecules at the start of the kinetic measurements. Here, the kinetics is especially fast due to the very low or absence of an enthalpic barrier for nucleation as the chains complex due to electrostatic attraction.

In the second stage, we observe a slower but still rather fast growth of the total radius to a stable value of 11.5 ± 0.3 nm. In this step, the initial growth of *P* is steep and then proceeds with moderate growth while the *D* decreases to its minimum (16%) (Table S5). Third, the final growth of the total radius and *P* to its final state of $R_{tot}$ = 13.2 ± 0.3 nm and *P* = 1170 ± 35. Even though the free fractions of colistin/PEO-b-PMAA remain around 12–15% in the fit analysis, it should be noted that the exchange of colistin/PEO-b-PMAA from the coacervate to the aqueous phase and the opposite way cannot be excluded. In addition, the fit analysis of the free fractions is relatively imprecise, as the scattering contributions of free chains are minor to those of micelles. We thereby could not use these parameters directly to investigate the kinetics. In further kinetic analysis, the *f*<sub>Col</sub> parameter was reported, but not used for kinetic modeling. To obtain more insight into the underlying mechanism for complex formation, we investigated the dependence on concentration, pH (effective charge), and ionic strength on the kinetics of PEO<sub>45</sub>-b-PMAA<sub>41</sub> coacervates.

**3.3. Kinetic Quantification of Stoichiometric Charge Matching and Off-Ratio Effects.** The thermodynamics and kinetics of complex coacervate are complicated and dependent on many factors, like charge, pH, and ionic strength.<sup>8,58</sup> It is thought that during nucleation, the majority of the energy contribution comes from the electrostatic interactions, whereas at a later stage, the polyelectrolyte hydration effects and counterion release also facilitate the growth of complex coacervate micelles.<sup>8,13,59</sup> Combining theories of the kinetics of uncharged polymeric micelle assemblies (BCP micelles) with complex coacervation thermodynamics can be essential for a better understanding of the formation of these C3M systems. For amphiphilic micelle assembly, which is mostly driven by hydrophobicity (reduced hydration), the mechanisms commonly responsible for micellization are nucleation (described by conventional nucleation theory), fusion/fission, and single chain/ion-pair exchange (Aniansson-Wall model).<sup>2,5,40,42,43,60–62</sup> Johnson and Prud’homme<sup>63</sup> described that the fusion mechanism is mainly driven by large mismatches in size. These mismatches can also be highly
<table><caption>Table 1. Kinetic Parameters from the Fits of the Different Charge Fractions of PEO₄₅-b-PMAA₄₁ Coacervates Based on eqs 12 and 13 at Three Concentrations (0.50, 0.25, and 0.125 wt %)ᵃᵇ</caption><thead><tr><th>f<sub>+</sub></th><th>φ (wt %)</th><th>α (-)</th><th>⟨τ<sub>1</sub>⟩ (ms)</th><th>⟨τ<sub>2</sub>⟩ (s)</th><th>P<sub>0</sub> × 10<sup>2</sup> (-)</th><th>P<sub>∞</sub> × 10<sup>2</sup> (-)</th></tr></thead><tbody><tr><td rowspan="3">0.44</td><td>0.50</td><td>0.27 ± 0.01</td><td>66 ± 6</td><td>22 ± 2</td><td>6.4</td><td>19</td></tr><tr><td>0.25</td><td>0.31 ± 0.01</td><td>68 ± 6</td><td>19 ± 2</td><td>5.9</td><td>25</td></tr><tr><td>0.125</td><td>0.31 ± 0.01</td><td>65 ± 6</td><td>22 ± 2</td><td>4.9</td><td>25</td></tr><tr><td rowspan="3">0.50</td><td>0.50</td><td>0.29 ± 0.01</td><td>67 ± 6</td><td>24 ± 2</td><td>3.8</td><td>12</td></tr><tr><td>0.25</td><td>0.31 ± 0.01</td><td>63 ± 6</td><td>22 ± 1</td><td>4.0</td><td>14</td></tr><tr><td>0.125</td><td>0.30 ± 0.01</td><td>73 ± 7</td><td>28 ± 5</td><td>2.8</td><td>14</td></tr><tr><td rowspan="3">0.54</td><td>0.50</td><td>0.36 ± 0.01</td><td>54 ± 5</td><td>20 ± 1</td><td>3.6</td><td>11</td></tr><tr><td>0.25</td><td>0.32 ± 0.01</td><td>57 ± 5</td><td>23 ± 2</td><td>3.3</td><td>12</td></tr><tr><td>0.125</td><td>0.30 ± 0.01</td><td>62 ± 6</td><td>20 ± 1</td><td>2.6</td><td>11</td></tr><tr><td rowspan="3">0.60</td><td>0.50</td><td>0.35 ± 0.01</td><td>53 ± 5</td><td>23 ± 2</td><td>3.7</td><td>12</td></tr><tr><td>0.25</td><td>0.35 ± 0.01</td><td>57 ± 6</td><td>21 ± 1</td><td>3.4</td><td>12</td></tr><tr><td>0.125</td><td>0.33 ± 0.01</td><td>76 ± 7</td><td>16 ± 1</td><td>2.3</td><td>10</td></tr><tr><td rowspan="3">0.64</td><td>0.50</td><td>0.35 ± 0.01</td><td>53 ± 5</td><td>22 ± 1</td><td>3.7</td><td>11</td></tr><tr><td>0.25</td><td>0.33 ± 0.01</td><td>60 ± 6</td><td>22 ± 1</td><td>2.9</td><td>11</td></tr><tr><td>0.125</td><td>0.31 ± 0.01</td><td>83 ± 8</td><td>16 ± 1</td><td>2.3</td><td>10</td></tr><tr><td rowspan="3">0.67</td><td>0.50</td><td>0.36 ± 0.01</td><td>57 ± 5</td><td>24 ± 2</td><td>3.7</td><td>12</td></tr><tr><td>0.25</td><td>0.35 ± 0.01</td><td>55 ± 5</td><td>20 ± 1</td><td>3.1</td><td>12</td></tr><tr><td>0.125</td><td>0.34 ± 0.01</td><td>65 ± 6</td><td>16 ± 1</td><td>2.3</td><td>11</td></tr></tbody></table>

ᵃβ₁ and β₂ were fixed to 1 and 0.5, respectively. ᵇThe standard deviation for the fit parameters was based on the changes of 10% in the sum of squares.

relevant for complex coacervation processes.⁶⁰,⁶³⁻⁶⁵ Veis' symmetrical aggregation model,⁶⁴,⁶⁶ concludes that a large thermodynamic effect due to the mismatch of charges drives charge equilibration. Using Langevin dynamic simulations, Bos and Sprakel¹³ found that this charge neutrality plays a major role in the micellization kinetics of C3Ms. Additionally, they found that in the initial micellization phase fusion events could occur. This is in contrast with the findings of Wu et al.¹⁹ where the authors stipulate that it is unlikely that bigger micelles collide and fuse, considering the steric repulsion between these micelles. They found that the kinetics was dominated by ion-pair or single-chain exchange (expulsion/insertion).¹⁹ It is however possible that in their measurements initial fusion events were not resolved experimentally due to the relatively long dead time of 100 ms. Moreover, Bos and Sprakel¹³ found that increased nonelectrostatic contributions, i.e. hydrophobicity effects, at later timescales in the formation kinetics of C3Ms, will cause domination of chain expulsion/insertion over fusion/fission events. Based on these findings, we hypothesize that the first growth phase can be mainly attributed to the fusion of less sterically hindered (smaller) micelles.¹³,²⁹,⁶⁰,⁶³ The second growth phase we believe can be attributed to the slow insertion of single chains/ion pairs, in line with the findings of Wu et al.¹³,¹⁹,⁶⁰,⁶³ After the initial trial-and-error model fit exercise, we found that the use of only one kinetic process (in addition to nucleation) could not describe the data.

Therefore, we modeled the aggregation number over time with a double-stretched exponential expression,⁴³,⁶⁷ including an exponential for the “experimentally invisible” nucleation process (eq 12). We included the following three contributions that may represent the following processes: (0) nucleation, (1) fusion, and (2) slower chain insertion (exchange) kinetics. From the parametrization, we can calculate the mean relaxation times of the kinetic processes (eq 13).

$$P(t) = (P_0 - 1) \cdot e^{-(t/\tau_0)} + (P_\infty - P_0) \cdot \left( 1 - \left( \alpha \cdot e^{-(t/\tau_1)^{\beta_1}} - (1 - \alpha) \cdot e^{-(t/\tau_2)^{\beta_2}} \right) \right) + 1 \quad (12)$$

$$\langle \tau \rangle = \frac{\tau}{\beta} \Gamma \left( \frac{1}{\beta} \right) \quad (13)$$

Where $P_\infty$ is the final state aggregation number, $P_0$ is the aggregation number from the first frame at $t = 2.9$ ms, and $\alpha$ is the amplitude weighing factor of the two continuous kinetic processes, giving the fraction of the first kinetic process contribution. $\tau_0$, $\tau_1$, and $\tau_2$ are the relaxation times from the nucleation (0) and the two different growth processes (1 and 2), and $\beta_1$ and $\beta_2$ the corresponding stretching exponents. Using the apparent relaxation times from the fit, the mean relaxation times can be calculated using eq 13. As the nucleation process is not resolved experimentally through TR-SAXS, we fixed $\tau_0$ to ≪2.9 ms, as this process occurred during the mixing before the first measurement frame. Initial parameter determination showed that the exponentials for both processes can be fixed to $\beta_1 = 1$ and $\beta_2 = 0.5$, respectively.

To understand the kinetic mechanisms in more detail, we investigated the concentration dependency.¹⁹,²⁰,²⁶ Previously, only the stoichiometric charge matching cases were addressed, in which PEO-b-PMAA and colistin had equal charges (1:1 charge, charge fraction $f_+ = 0.50$). Based on previous research on this system, stable micelles of the same composition (confirmed in Figure S3) can be formed in a colistin charge fraction range of $f_+ = 0.40$ and $f_+ = 0.83$.⁴⁴ Within the range of $f_+ = 0.40$ to $f_+ = 0.83$, we found that C3Ms exhibit charge neutrality in the core, with any excess charges residing in the dilute phase.

Six different stoichiometric charge fractions within this range were analyzed using TR-SAXS at three concentrations. Subsequently, least-squares fitting was performed to obtain the evolution of P using eqs 12 and 13, while the amplitude weighing factor $\alpha$ and relaxation times $\tau_1$ and $\tau_2$ were fitting
parameters. In Figure 4, the kinetic fits are shown for stoichiometrically charge-matched complex coacervates, including an illustration of the potential mechanisms underlying the kinetic processes. Additionally, the total radii over time were plotted to observe additional concentration effects on the kinetic processes (inset in Figure 4). In Table 1, the kinetic fit parameters are presented for $0.44 \le f_+ \le 0.67$ of which the TR-SAXS are presented in Figure S3 for 0.50 wt %.

As can be seen, there is a substantial concentration dependence in the formation kinetics (Figure 4 and Table 1). These findings are indications of the presence of metastable, kinetically frozen micelles whose final structural characteristics depend on the concentration.⁶³,⁶⁸ The nucleation stage, even though not directly resolved experimentally, was found to be highly dependent on concentration. Higher concentrations were found to result in the formation of larger polydisperse nuclei (higher $P_0$ and $R_{tot}$), while the final compositions appeared to be less correlated to the concentration (Figure 4 and Table 1). In situations where the polymer is in excess ($f_+ = 0.44$), the aggregation seems to be quicker than at charge matching or colistin-in-excess systems ($f_+ \ge 0.50$).

<figure><img src="image_13.png" /><figcaption>**Figure 4.** Growth of stoichiometrically charged-matched $PEO_{45}$-b-PMAA$_{41}$ coacervates at three concentrations: 0.50 wt % (orange squares), 0.25 wt % (blue circles), and 0.125 wt % (green triangles) coacervates over time, based on aggregation number $P_i$ including fits from the kinetic modeling, and total radius ($R_{tot}$) over time (inset). Fits were made using the fuzzy-surface complex coacervate model to obtain the $P$ and $R_{tot}$ over time. The kinetics of $PEO_{45}$-b-PMAA$_{41}$ coacervates is illustrated and can be divided into three steps: nucleation (green background), fusion (yellow background), and chain insertion (purple background).</figcaption></figure>

We observe that increased concentrations lead to faster initial kinetics (for nucleation and fusion), probably due to increased collision frequency for nucleation and number of fusion events. The fusion reactions are fast and result in a quick decrease in dispersity. These fusion kinetics are likely driven by charge mismatches in smaller micelles, causing them to fuse with larger micelles, significantly reducing the total dispersity

of the system⁶³ (Tables S5–S7). After the process of fusion, we observe an equilibration process, probably dominated by chain exchange, which takes a longer time.⁶⁹ This process is faster at higher concentrations (Table 1), potentially due to the lower dispersity in these systems (Tables S5–S7), leading to more equilibrated systems that facilitate easier insertion of single chains or ion pairs.

When the dispersity is decreased and stabilizes to 16–18%, the metastable final states are reached, where lower concentrations are found to have a lower final dispersity. Even though several different final (meta)states could be observed, the different kinetically frozen states are similar to each other and show long-term stability.⁷⁰

In summary, the kinetic processes involved in the complexation of $PEO_{45}$-b-PMAA$_{41}$ with colistin were found to be relatively similar at other charge fractions and highly depended on concentration. In general, around 30–35% increase in the aggregation number for each system can be explained by the first-order fusion of small micellar entities with a typical time scale of 50–85 ms (Table 1). After the fusion-dominated regime, the slower insertion of single chains or ion pairs drives the remaining growth, characterized by relaxation times of 15–25 s and a stretching exponent $\beta_2 \approx 0.5$.

### 3.4. Ionic Strength Effects: Formation versus Salt Shock.
An increase in solution ionic strength is known to reduce the electrostatic interactions by charge-screening.⁸,⁷¹ As previously discussed, electrostatic interactions play a key role in the initial formation kinetics of C3Ms and are therefore expected to be highly affected by ionic strength changes.⁸,¹³,⁵⁸ The formation of C3Ms in salt solutions usually results in swelled structures due to the screening of charges.⁸ Generally, there are two ways to assess the effects of increased ionic strength, either by formation in salt solutions or the salt addition after the formation of C3Ms, causing micellar rearrangement. First, we analyzed the former, where stoichiometrically charge-matched $PEO_{45}$-b-PMAA$_{41}$-colistin-C3Ms were formed in the presence of different concentrations of sodium chloride (NaCl) at 0.50 wt % (Figure 5). To model the growth of the aggregation number, we used the double-

<figure><img src="image_14.png" /><figcaption>**Figure 5.** Growth of 0.50 wt % stoichiometrically charged-matched $PEO_{45}$-b-PMAA$_{41}$ coacervates at four ionic strengths: 0.00 M NaCl (orange squares), 0.05 M NaCl (blue circles), 0.10 M NaCl (green triangles), and 0.15 M NaCl (gray rhombuses) over time, based on aggregation number $P_i$ including fits from the kinetic modeling. Fits were made using the fuzzy-surface complex coacervate model to obtain the $P$ over time.</figcaption></figure>
<table><caption>Table 2. Kinetic Parameters from the Fits of PEO<sub>45</sub>-b-PMAA<sub>41</sub> Coacervates Formation in the Presence of NaCl Based on eqs 12 and 13 at Three Concentrations (0.50, 0.25, and 0.125 wt %)<sup>a,b</sup></caption><thead><tr><th>I<sub>s</sub> (M) from NaCl</th><th>φ (wt %)</th><th>α (-)</th><th>⟨τ<sub>1</sub>⟩ (ms)</th><th>⟨τ<sub>2</sub>⟩ (s)</th><th>β<sub>2</sub> (-)</th><th>P<sub>0</sub> × 10<sup>2</sup> (-)</th><th>P<sub>∞</sub> × 10<sup>2</sup> (-)</th><th>f<sub>w</sub> (-)</th><th>Đ<sub>∞</sub> (%)</th></tr></thead><tbody><tr><td rowspan="3">0.00</td><td>0.50</td><td>0.29 ± 0.01</td><td>67 ± 6</td><td>24 ± 2</td><td>0.50 ± 0.02</td><td>3.8</td><td>12</td><td>0.68 ± 0.02</td><td>17</td></tr><tr><td>0.25</td><td>0.31 ± 0.01</td><td>63 ± 6</td><td>22 ± 1</td><td>0.50 ± 0.02</td><td>4.0</td><td>14</td><td>0.65 ± 0.02</td><td>16</td></tr><tr><td>0.125</td><td>0.30 ± 0.01</td><td>73 ± 7</td><td>28 ± 5</td><td>0.50 ± 0.02</td><td>2.8</td><td>14</td><td>0.65 ± 0.02</td><td>16</td></tr><tr><td rowspan="3">0.05</td><td>0.50</td><td>0.23 ± 0.01</td><td>49 ± 4</td><td>11 ± 1</td><td>0.59 ± 0.02</td><td>1.7</td><td>7.5</td><td>0.82 ± 0.02</td><td>19</td></tr><tr><td>0.25</td><td>0.21 ± 0.01</td><td>52 ± 5</td><td>12 ± 1</td><td>0.56 ± 0.02</td><td>1.5</td><td>8.4</td><td>0.79 ± 0.02</td><td>17</td></tr><tr><td>0.125</td><td>0.20 ± 0.01</td><td>63 ± 6</td><td>15 ± 1</td><td>0.60 ± 0.02</td><td>0.9</td><td>8.6</td><td>0.81 ± 0.02</td><td>17</td></tr><tr><td rowspan="3">0.10</td><td>0.50</td><td>0.18 ± 0.01</td><td>54 ± 5</td><td>22 ± 4</td><td>0.64 ± 0.02</td><td>1.0</td><td>9.2</td><td>0.88 ± 0.02</td><td>21</td></tr><tr><td>0.25</td><td>0.17 ± 0.01</td><td>53 ± 5</td><td>27 ± 6</td><td>0.58 ± 0.02</td><td>0.8</td><td>9.4</td><td>0.86 ± 0.02</td><td>20</td></tr><tr><td>0.125</td><td>0.17 ± 0.01</td><td>60 ± 6</td><td>18 ± 3</td><td>0.63 ± 0.02</td><td>0.6</td><td>10</td><td>0.86 ± 0.02</td><td>19</td></tr><tr><td rowspan="3">0.15</td><td>0.50</td><td>0.10 ± 0.01</td><td>140 ± 12</td><td>31 ± 3</td><td>0.86 ± 0.03</td><td>0.6</td><td>35</td><td>0.85 ± 0.02</td><td>23</td></tr><tr><td>0.25</td><td colspan="9">Inconclusive model fits</td></tr><tr><td>0.125</td><td colspan="9">Inconclusive model fits</td></tr></tbody></table>

<sup>a</sup>β<sub>1</sub> was fixed to β<sub>1</sub> = 1.<sup>b</sup>The standard deviation for the fit parameters was based on the changes of 10% in the sum of squares.

stretched exponential expression (eq 12). Initial parameter determination revealed a correlation between β<sub>2</sub> and ionic strength, which was subsequently used as a fitting parameter. The stretched exponent for the "fusion" process was fixed to β<sub>1</sub> = 1. The fit parameters, including measurements at 0.25 and 0.125 wt % total concentration, are listed in Table 2.

Similar to what was found in salt-free solutions, we see two clear processes for I<sub>s</sub> ≤ 0.10 M (Figure 5 and Table 2). If we assume that the first process again corresponds to fusion, we see that the kinetics is faster and that the initial aggregation number (P<sub>0</sub>) decreases with increasing ionic strengths (below the CIC, I<sub>s</sub> < 0.30 M NaCl (Figure S4)). The stretched exponential also increases, indicating a narrower distribution (Table 2). These observations are probably caused by reduced electrostatic interactions. This electrostatic interaction-dependency is 2-fold: (1) an increase in the barrier driving nucleation, resulting in a smaller P<sub>0</sub>, and (2) an increase in the rate of fusion.<sup>8,58</sup> Moreover, at increased I<sub>s</sub>, C3Ms get closer to their thermodynamic equilibriums as they are less prone to end up in kinetically arrested states.<sup>8</sup> Therefore, this generally results in increased overall rates at higher ionic strengths.<sup>72</sup> However, for this system, this effect is more nuanced, as the electrostatic interactions also affect the dispersity of the system and thereby, the second process of insertion of chains/ion pairs as well. At increased I<sub>s</sub>, the Đ of the C3Ms is increased (Table 2), resulting in a dampening effect on the otherwise expected faster exchange kinetics.

At high concentrations of salt, above the critical ionic concentration (CIC), complex coacervate micellization does not occur as the electrostatic interactions have become too weak (see Figure S4 for the TR-SAXS patterns of the data presented in Figure 5 and Table 2).<sup>8</sup> Based on the TR-SAXS data, the CIC lies slightly above I<sub>s</sub> = 0.15 M NaCl as at 0.15 M NaCl, C3Ms still form, but in a more undefined (poly-disperse), unstable, and aggregated state for the highest concentration (Figures 5 and S4) as indicated by an anomalous increase of apparent P. This effect might also be related to reduced colloidal stability of the stabilizing PEO chains. In general, the C3Ms swell at increased ionic strengths due to osmotic pressure, as reflected by the increase in the volume fraction of water (f<sub>w</sub>) and size (R<sub>tot</sub>).

In addition to the effect of ionic strength on the formation of C3Ms, it is also highly relevant to assess the stability, dissociation, and rearrangements of C3Ms upon salinity shocks. Generally, there are multiple potential outcomes of

salinity shocks: swelling, rearrangements, complete annealing into single chains, or a combination of them. The latter two are also referred to as dissociation kinetics and are relevant in the development of drug C3Ms systems, as the control of drug release is crucial.<sup>36</sup> Research on the dissociation kinetics of C3Ms with salt shocks exists but is limited.<sup>17,36</sup> Through time-resolved static light scattering (TR-SLS), Wu et al.<sup>36</sup> and Zhang et al.<sup>17</sup> found that the dissociation kinetics of C3Ms is most likely dependent on a combination of fusion/fission processes combined with single-chain expulsion/insertion. To shine a light on the salt shock stability of stoichiometrically charge-matched PEO<sub>45</sub>-b-PMAA<sub>41</sub>-colistin-C3Ms, we exposed beforehand hand-mixed C3Ms to different concentrations of NaCl spiked TRIS buffer solutions with TR-SAXS (Figure 6). Inducing shocks with I<sub>s</sub> = 0.60 M NaCl resulted in the nonquantifiable dissociation of complex coacervates within 25 ms (Figure S5).

<figure><img src="image_15.png" /><figcaption>Figure 6. Evolution of aggregation number (P) after exposing 0.50 wt % (A) and 0.25 wt % (B) stoichiometrically charged-matched PEO<sub>45</sub>-b-PMAA<sub>41</sub>-colistin coacervates to salt shocks: 0.05 M NaCl (orange squares), 0.10 M NaCl (blue circles), and 0.15 M NaCl (green triangles). Fits were made using the fuzzy-surface complex coacervate model to obtain the P.</figcaption></figure>

The salt shocks mostly induced rearrangements that were highly dependent on the concentrations of both C3Ms as well as the strength of the salt shocks (Figure 6). The rearrangements occurred in three steps. (1) Reduction of the mean aggregation number until the minimum P-value is reached in the time frame between 2.9 and 300 ms. (2) P stabilization, where the duration depends on the severity of the salt shock. (3) Growth, where the higher the concentration of salt added, the faster and larger the growth of P.
The sudden addition of salt mainly results in decreased electrostatic interactions, as seen by the increase of the fraction of water in the C3Ms ($f_w$) (Tables S8–S10). This screening of electrostatic charges initially causes swelling and destabilization, resulting in some dissociation in step 1. Fusion/fission reactions are more likely to be affected by the concentration of C3Ms due to the collision frequencies varying with concentrations.<sup>10,32</sup> Fusion events are likely to be increased in occurrence at higher concentrations, which can also result in a higher probability for fission since the micelles may overgrow leading to splitting into smaller entities. Insertion and expulsion on the other hand are less related to the concentration but more on the dispersity in the presence of increased ionic strengths for these systems.<sup>32,69</sup> Dispersity effects for these systems were found to be minor (Tables S8–S10), and the decisive factor of the dispersity lies in the mixing before salt addition. Considering the concentration effects, the dissociation process mainly seems to be dominated by fission reactions, assisted by minor expulsion contributions in step 1.

In the subsequent stabilization (step 2) and growth phase (step 3) that follow the dissociation, the kinetics appears to be more complicated. Several contributions play a role at the same time and distort the observation of the kinetic processes: increased aggregation numbers, aggregation, and increased dispersity effects (Tables S8–S10). The stabilization and growth are most probably comparable to the previously discussed formation kinetics in the presence of salt.

## 4. CONCLUSION

TR-SAXS enabled the elucidation of the formation kinetics of the complex coacervation of PEO-b-PMAA with colistin into C3Ms. Using model fitting, we obtained a detailed insight into the structural parameters and growth mechanism, revealing a three-step mechanism: (0) nucleation, (1) fusion/fission, and (2) single-chain/ion-pair exchange kinetics toward a metastable state. The nucleation phase was found to be completed during the mixing phase, and could therefore not be resolved experimentally. The fusion kinetics was first-order and concentration-dependent at relaxation times of $\langle\tau_1\rangle = 50-85$ ms, while higher concentrations resulted in faster fusion kinetics. Insertion kinetics was found to be slower with $\langle\tau_2\rangle = 15-25$ s and in addition concentration-dependent. The chain/ion-pair insertion was mostly affected by remaining micellar size mismatches, where larger mismatches (higher dispersity) resulted in a slower equilibration step as more chains needed to exchange to reach metastable state kinetics. The presence of salt reduced the electrostatic interactions, resulting in faster kinetics that were more dominated by chain exchange. By controlling the concentration, charge ratios, and ionic strengths, different metastable end states could be achieved. As direct measurements of the micellization kinetics of complex coacervation systems are crucial for their optimization, we believe this research contributes to potential advances in the development of C3M-based drug delivery systems for biomedical applications.

## ASSOCIATED CONTENT

### Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.macromol.4c02077.

Additional SAXS model explanation, SAXS model fits, Guinier analysis comparison, power law behavior, kinetic

parametrization fits, critical ionic concentration determination, SAXS patterns of complete ionic dissociation, and SAXS fits on dispersity effects (PDF)

## AUTHOR INFORMATION

### Corresponding Author

Reidar Lund – Department of Chemistry, University of Oslo, Oslo NO-0315, Norway; Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, Oslo NO-0315, Norway; orcid.org/0000-0001-8017-6396; Email: reidar.lund@kjemi.uio.no

### Authors

Thomas D. Vogelaar – Department of Chemistry, University of Oslo, Oslo NO-0315, Norway

Henrik Torjusen – Department of Chemistry, University of Oslo, Oslo NO-0315, Norway

Theyencheri Narayanan – European Synchrotron Radiation Facility, Grenoble 38043, France; orcid.org/0000-0003-1957-1041

Complete contact information is available at: https://pubs.acs.org/10.1021/acs.macromol.4c02077

### Notes

The authors declare no competing financial interest.

## ACKNOWLEDGMENTS

We gratefully acknowledge funding from the Norwegian Research Council (Project No. 315666). We are indebted to the complete ID02 staff at the European Synchrotron Radiation Facility (ESRF) for technical support and the ESRF for providing beam time through proposals SC-5313 and SC-5459. The static SAXS data collected at the BioSAXS beamline at BM29 at the ESRF (Grenoble, France) was obtained with the assistance of M. Tully, P. Pernot, and D. Moussaoui. The authors are in general grateful to the ESRF for beam time through the “Norwegian BAG” and for providing the infrastructure through the PSCM lab for sample preparation. In addition, we thank local contact L. Matthews and colleagues V. Koynarev and O. Krogseth for assisting in the TR-SAXS measurements at ID02. Lastly, we acknowledge the use of the Norwegian Centre for X-ray Diffraction, Scattering and Imaging (RECX) for access to SAXS, supported by the Norwegian Research Council (NRC).

## ABBREVIATIONS

<table><tr><td>AMP</td><td>antimicrobial peptides</td></tr><tr><td>C3Ms</td><td>complex coacervate core micelles</td></tr><tr><td>CMC</td><td>critical micelle concentration</td></tr><tr><td>DLS</td><td>dynamic light scattering</td></tr><tr><td>f<sub>+</sub></td><td>charge fraction of colistin</td></tr><tr><td>f<sub>w</sub></td><td>fraction of water in the complex coacervate</td></tr><tr><td>M<sub>w</sub></td><td>molecular weight</td></tr><tr><td>P</td><td>aggregation number</td></tr><tr><td>PEO-b-PMAA</td><td>poly(ethylene oxide)-b-poly(methacrylic acid)</td></tr><tr><td>Đ</td><td>dispersity</td></tr><tr><td>R<sub>g</sub></td><td>radius of gyration</td></tr><tr><td>R<sub>tot</sub></td><td>total radius</td></tr><tr><td>TR-SAXS</td><td>time-resolved small-angle X-ray scattering</td></tr></table>
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