Entropic charge separation as a general mechanism arresting nanoscale condensate coarsening

Abstract

Classical liquid–liquid phase separation (LLPS) predicts that droplets grow continuously via Brownian coalescence or Ostwald ripening, yet many nanoscale biomolecular condensates remain stable for hours or days without active regulation. Such condensates often arise through complex coacervation between oppositely charged macromolecules, making this interaction motif broadly relevant in biology and soft matter. Here we combine experiments, theory, and simulations to identify a merging-limited coarsening (MLC) regime in which merging of condensates decreases sharply below a critical droplet size. Chain-length asymmetry between oppositely charged polymers drives entropic interfacial charge separation even at globally neutral stoichiometry, imparting net droplet charges and generating long-range electrostatic repulsion. These size-dependent barriers produce exponential rather than classical power-law growth and trap droplets in long-lived metastable states. Our framework unifies suppressed MLC and classical Brownian coalescence within a single predictive model and provides a general mechanism for condensate stability in both reconstituted systems and living cells.

Introduction

Droplet coarsening is a ubiquitous process in natural and industrial processes. In classical liquid–liquid phase separation (LLPS), coarsening typically proceeds through two main mechanisms (1): Brownian motion–induced coalescence (BMC) (2, 3) and Ostwald ripening (4, 5). These mechanisms predict continuous, rapid droplet growth with well-established scaling laws. Analogous coarsening phenomena occur in living cells, where biomolecular condensates display liquid-like behaviors, coalescing and growing over time (6–9).

However, unlike liquid droplets, many condensates in cells remain stable in size for hours or days (7, 8, 10–12). This stability has been attributed to various cellular factors: active biochemical reactions that regulate droplet size (13–16), physical hindrance by cytoskeletal networks or chromatin (7, 8, 11), and adsorption of protein–RNA complexes at interfaces (10, 17). While these mechanisms are important, they depend on specific cellular components and cannot account for recent in vitro observations showing that compositionally simple nanoscale condensates remain stable for extended periods (12, 18–22) (Fig. 1a). This raises a fundamental question: what physical mechanism stabilizes nanoscale condensates in the absence of cellular complexity?

Fig. 1.

Nanoscale complex coacervates formed at low concentrations exhibit suppressed coarsening behavior. (b) The initial mean hydrodynamic diameter d_h0 measured immediately after mixing as a function of monomer concentration of polyelectrolyte c_m. (c) The absorption values of coacervate solutions as a function of monomer concentration, measured at 300 nm and 600 nm wavelengths. (d) Schematic illustration of distinct coarsening dynamics of condensates in cells and in synthetic systems. In cells, condensates remain stable over time, while in synthetic systems, they often merge and rapidly grow into larger structures. (e) At c_m = 16 mM, the hydrodynamic diameter d_h of microscale coacervates exhibits a power-law increase with time, with the exponent α ≈1/3. (f) At c_m = 2 mM and c_m = 5 mM nanoscale coacervates are initially stable, but their d_h increases abruptly at later times with power-law exponents seemingly larger than 1/3. (d) At c_m = 0.1 mM and c_m = 0.3 mM, nanoscale coacervates remain stable over 12 hours, demonstrating completely arrested growth.

Here, we combine experiments, theory, and simulations to uncover a general merging-limited coarsening (MLC) mechanism that explains this anomalous size stability. We show that coacervates formed by oppositely charged polyelectrolytes at a neutral stoichiometry ratio exhibit a strong size dependence in merging efficiency: while larger coacervates follow classical BMC, nanoscale coacervates merge extremely slowly. This inefficiency arises from chain-length asymmetry between the oppositely charged polymers, driving entropic charge separation at interfaces and generating strong, size-dependent electrostatic barriers. This framework reframes LLPS as a kinetically constrained process evolving over a rugged energy landscape, with direct implications for controlling condensate stability in both biological and synthetic systems. It further unifies suppressed MLC and classical BMC regimes within a single minimal predictive model.

Results

Many biological condensates form through the complex coacervation between proteins and nucleic acids via multivalent interactions (23, 24). To understand the physical principles underlying biological phase separation, complex coacervates comprised of oppositely charged polyelectrolytes have served as model systems due to their simplified physicochemical properties (25–27). Here, we investigate the coarsening dynamics of coacervates, formed by negatively charged poly(methacrylic acid, sodium salt) (PMA) and positively charged poly(diallyl dimethylammonium chloride) (PDDA) at a 1:1 stoichiometric ratio of monomer concentrations. Dynamic light scattering (DLS) shows that the initial hydrodynamic diameters (d_h0) increase monotonically with monomer concentration of polyelectrolytes (c_m) (Fig. 1b). Turbidity measurements also reveal a sharp rise above a threshold, followed by a plateau regime (Fig. 1c). Coacervates spanning nano- to microscale sizes are observed by optical microscopy and transmission electron microscopy (TEM) (Fig. S2-S3 (28)). In particular, TEM shows nanoscale condensates with polymer brushes surrounding a dense core, indicating a gradual density gradient (Fig. S3d (28)). These results align with recent studies about forming stable nanoscale clusters at low concentrations (21, 29–31). However, the time evolution of nanoscale droplets has not been thoroughly investigated.

We further use DLS to track the hydrodynamic diameter d_h of coacervates formed at various concentrations over periods exceeding 12 hours. Because nucleation and spinodal decomposition are typically fast (18, 32, 33), our measurements primarily capture the later coarsening stage (3, 34). At c_m = 16 mM, microscale coacervates exhibit a power law growth with an exponent close to 1/3 (Fig. 1d), consistent with predictions by classic theories, such as Brownian motion-induced coalescence (BMC) or Ostwald ripening (3, 34). Surprisingly, at intermediate concentrations (c_m = 2 mM and 5 mM), nanoscale coacervates (~200 nm) initially remain stable, yet undergo abrupt, rapid growth in later stages, with exponents deviating from 1/3 (Fig. 1e). Moreover, at even low concentrations (c_m = 0.1 mM and 0.3 mM), nanoscale coacervates remain stable over 12 hours with d_h constant at ~80 nm and ~150 nm, respectively (Fig. 1f). These results reveal three distinct concentration-dependent coarsening regimes: (i) classical power-law growth, (ii) delayed growth, and (iii) long-term arrested growth.

Similar trends are observed using another coacervate system formed by poly (vinyl sulfonic acid, sodium salt) (PVS) and poly (diallyl dimethylammonium chloride) (PDDA) at a neutral monomer ratio. Coacervates have concentration-dependent sizes d_h0 ranging from tens of nanometers to a few microns (Fig. S4-S6 (28)) and exhibit three similar coarsening regimes across different sizes (Fig. S7 (28)). Beyond synthetic coacervates, suppressed coarsening has been recently observed for nanoscale protein condensates that are formed at low protein concentrations (12, 18–22). Together, these results suggest a general mechanism underlying the suppressed coarsening of nanoscale condensates.

To understand these unexpected results, we first consider two basic coarsening mechanisms: Brownian motion-induced coalescence (BMC) and Ostwald ripening. Both mechanisms predict a power-law scaling, $\frac{d{r}^3}{dt}=k$, where r is the mean radius of droplets, t is the duration time, and k is the growth rate. The rates of BMC (k_BMC) and Ostwald ripening (k_OR) depend on distinct physical parameters (Supplementary Note 1 (28)). Given physical parameters of our coacervates, we find that k_BMC ≳ 3.9 × 10⁻⁶ μm³/s and k_OR ≈ 1.1 × 10⁻⁷ μm³/s. This suggests that BMC dominates coarsening, consistent with previous studies showing Ostwald ripening is generally negligible in coacervate systems (7, 14). Therefore, we mainly focus on BMC as the dominant mechanism in the following sections. As a result, the coarsening behavior of microscale coacervates can be described by the BMC mechanism (Fig. 2a and Fig. S8 (28)); not only does the power-law exponent closely match 1/3, but the rate coefficient k aligns with the theoretical estimate k_BMC. However, nanoscale coacervates formed at low concentrations deviate significantly from the curves predicted by BMC (Fig. S8 (28)).

Fig. 2.

Merging-limited coarsening of nanoscale coacervates. (a) The mean droplet hydrodynamic diameter d_h as a function of time, with experimental data represented by hollow circles and the theoretical results from Eq. (1) shown as solid lines. The parameters used in solving Eq. (1) are summarized in Table S1. (b) The variation of pseudo-exponent α as a function of d_h0/d_c. The values of α are extracted from linear fitting of the experimental results during an initial period (1–100 min) (purple triangles represent PMA/PDDA coacervates and orange triangles denote PVS/PDDA coacervates). The theoretical value of α (solid dark blue line) is obtained similarly by fitting the theoretical curves during an early stage.

Why is the coarsening of nanoscale coacervates suppressed? To answer this, we calculate the growth rate $\frac{d{(d_h)}^3}{dt}$ as a function of coacervate size based on our experiments (Fig. S9 (28)). Results show that k increases substantially with the coacervate size d_h (Fig. S10 (28)). Therefore, the results suggest that smaller coacervates merge much slower than larger ones. This steep increase in k over d_h are captured using a phenomenological exponential expression, $k=k_{0}exp{[(d_h/d_c)}^n]$, where k₀, d_c, n, are fitted constants (Fig. S10 (28)).

To theoretically elucidate the underlying mechanism and capture our experimental observations, we develop a theoretical model that incorporates both droplet diffusion and size-dependent merging efficiency (See Supplementary Note 2 for details (28, 35)). The evolution of the droplet radius r is described by:

$$\frac{d{r}^3}{\mathit{\text{dt}}}=\frac{3{\varphi }_0}{8\pi }\frac{k_{\text{diff}}{k}_{\text{act}}(r)}{k_{\text{diff}}{k}_{\text{act}}(r)},$$ (1)

Here, ϕ₀ is the droplet volume fraction, and k_diff = 16πDr is the encounter rate of diffusive droplets based on the Smoluchowski theory, where D is the diffusion constant of a droplet of radius r (36). The term k_act denotes the size-dependent merging rate of two colliding droplets (37). Based on the fitting in Fig. S10 (28), we adopt a phenomenological form for the merging rate as, $k_{\text{act}}(r)=k_0{e}^{{-(r_c/r)}^2}$, where r_c is a critical size that sets the merging barrier. This functional form is rationalized by considering droplet merging as an energetically restricted process, in which the merging rate follows an Arrhenius equation, $k_{\text{act}}~\mathit{\text{exp}}(-\frac{V_E}{K_{B}T})$, where V_E represents an energetic barrier of merging (See Supplementary Note 3 for details). In the limit where merging is much faster than diffusion, i.e., k_act ≫ k_diff, Eq. (1) reduces to the classic BMC model (3),

$$\frac{d{r}^3}{dt}=\frac{k_{\text{B}}T{\varphi }_0}{\pi {\eta }_0}$$ (2)

which leads to r~t^1/3. In the opposite limit, where merging is extremely slow k_act ≪ k_diff, we derive a merging-limited coarsening (MLC) model:

$$\frac{d{r}^3}{dt}=\frac{3{\varphi }_0}{8\pi }{k}_{\text{act}}(r).$$ (3)

In the limit where k_act → 0, Eq. (3) simplifies to log r ~k_actt, implying an exponential growth over time (Supplementary Note 2 (28)). This is validated by replotting coarsening data within semi-logarithmic coordinates, which shows that d_h of nanoscale coacervates increases linearly over time (Fig. S11 (28)). By contrast, microscale coacervates that coarsen via BMC do not exhibit such linear growth in semi-logarithmic plots (Fig. S11 (28)).

Fitting experimental data with Eq. (1) yields theoretical curves that quantitatively capture coacervate coarsening behaviours across different initial sizes (Fig. 2a), including the anomalous growth at intermediate concentrations where growth shifts from MLC to BMC. By extracting a pseudo-exponent α from early-stage fits (~ 2 hours) of experimental results, we find α < 1/3 for small coacervates and plateau at ~1/3 for larger ones (Fig. S12 (28)). The theoretical curve likewise shows a rapid rise of α over d_h0/d_c in capturing experimental results (Fig. 2b). Monte Carlo simulations with size-dependent merging efficiency also reproduce experimental and theoretical observations: droplets grow slowly when small but exhibit BMC growth when large (Fig. S13 (28)).

Similar to our observations with complex coacervates, a recent study shows that condensates formed by intrinsically disordered proteins (IDPs), such as hnRNPA2 LCD, resist growing under various conditions (20). To test the generality of our framework, the theoretical model is applied to analyze the coarsening data from this study (20). The BMC model effectively captures the rapid coarsening dynamics of condensates, but deviates significantly when describing condensates with low growth rates (Fig. S14 (28)). In contrast, our proposed MLC model successfully captures these slow coarsening dynamics (Fig. S14 (28)). These results highlight the broad applicability and physical relevance of the MLC mechanism across diverse condensate systems.

Having demonstrated MLC, we further discuss potential mechanisms that may reduce the merging rate of small coacervate droplets. The MLC identified in this study shares similarities with merging-limited aggregation in colloidal particles, where charge-induced electrostatic repulsion reduces aggregation and stabilizes particles (38). Similarly, condensates or coacervates formed by charged macromolecules experience electrostatic repulsions that contribute to their size stability (18, 39). To test the effect of electrostatic repulsion, we measure zeta potentials of PMA/PDDA coacervates. We find that these coacervates exhibit significant surface charge, while zeta potential slightly decreases as concentration increases (Fig. 3a). In addition, as the size of nanoscale coacervates increases (c_m = 2 mM), the absolute value of zeta potential decreases following a power-law relationship with a fitted exponent of ~0.74 (Fig. 3b and Fig. S15 (28)).

Fig. 3.

Chain length asymmetry-induced entropic charge separation and electrostatic barriers. (a) Plot of the zeta potential of complex coacervates as a function of the monomer concentration c_m. (b) Logarithmic plot of Zeta potential Ψ_c of coacervates as a function of their size. Different colors represent different independent tests with coacervates formed at c_m = 2 mM. Plots of solution absorption (c), hydrodynamic diameter (d), and Zeta potential Ψ_c (e) of coacervates (c_m = 2 mM) at different salt concentrations. Plots of solution absorption (f), hydrodynamic diameter (g), and Zeta potential Ψ_c (h) at different PDDA to PMA monomer ratios. A transition is observed when the stoichiometric ratio is approximately 1.3/1.

To further verify the effect of electrostatic repulsion, we add salt to screen electrostatic interactions. As anticipated, increasing salt concentration increases the turbidity of the coacervate solution, revealed by spectroscopy measurement and bulk-phase turbidity in microcentrifugation tubes (Fig. 3c and Fig. S16 (28)). Concomitantly, higher salt concentrations lead to larger initial coacervate sizes (Fig. 3d) and a decrease in the absolute value of zeta potential (Fig. 3e). Notably, at salt concentrations beyond 50 mM, microscale coacervates form and grow rapidly through BMC with a power-law exponent close to 1/3 (Fig. S17-S18 (28)). These results provide strong evidence that electrostatic repulsion among coacervate droplets underlies their long-term size stability.

Previous studies have only shown that condensates or coacervates are charged when stoichiometric ratios of oppositely charged polymers are imbalanced (40, 41). In that case, an excessive portion of charged polymers will attach to condensate surfaces and generate an electrostatic potential. However, in our study, coacervates are all formed under conditions of neutral stoichiometry, which in principle promotes efficient phase separation and minimizes net charge within condensates. This, therefore, raises a critical question: what causes the strong surface charge observed in coacervates formed at neutral stoichiometry?

To answer this question, it is noted that the polyelectrolytes used to form our coacervates have unequal chain lengths, with PDDA chains substantially longer with n ≈ 1700 repeated units than those of PMA n ≈ 47. Similar chain length asymmetry is also presented in PVS/PDDA coacervates (Fig. S7) as well as condensates formed by the complexation of IDPs and counterions (20).

We thus hypothesize that chain-length asymmetry promotes entropic partitioning, whereby shorter chains preferentially partition into the dilute phase to maximize their configurational entropy. This asymmetric distribution induces interfacial charge imbalance even at globally neutral stoichiometry, leading to electrostatic repulsion that stabilizes the coacervates. To test this, we systematically varied the PDDA/PMA monomer ratio to tune the surface charge. When the ratio exceeds 1—indicating an excess of PDDA—coacervates retain high surface charge density and exhibit pronounced stability (Fig. 3f–h). In contrast, ratios below 1 reduce the stability of coacervates, yielding higher turbidity, larger initial sizes, and lower zeta potentials (Fig. 3f–h). Notably, a distinct peak emerges near a ratio of ~1/1.3, suggesting that coacervates are least stable under this condition. These experimental results imply a strong entropic contribution, where chain-length asymmetry leads to asymmetric partitioning and interfacial charge separation.

To further validate our hypothesis, we perform fluid particle dynamics (FPD) simulations (42–45) that incorporate both many-body hydrodynamic and long-range electrostatic interactions (see Supplementary Methods for details (28)). In asymmetric configurations, each positively charged chain contains 100 monomers, whereas each negatively charged polymer chain contains 10 monomers. All other parameters, such as monomer concentration, size, and valency, are kept constant. The negative-to-positive chain ratio is set to 10 to maintain global charge neutrality.

Simulations at a monomer concentration of 92.5 mM show power-law growth with an exponent approaching 1/3, consistent with the conventional BMC mechanism (Fig. 4a, yellow points, and Fig. S19 (28)). However, at c_m=27.4 mM, the coacervates exhibit slower coarsening, particularly with an exponent smaller than 1/3 during the late stage (Fig. 4a, blue points, and Fig. S19 (28)). Although the early-stage growth superficially resembles classical BMC, it may not strictly follow the standard mechanism. The resulting associative complexation imposes microscopic kinetic constraints that reshape the coarsening pathway into a two-step process: (1) rapid formation of ionically bound complexes and (2) their mesoscale growth and coalescence. Consequently, the early-stage growth captured in our FPD simulations may reflect this non-classical pathway rather than conventional BMC.

Fig. 4.

The suppressed coarsening behavior of coacervates is attributed to the combination of asymmetric chain length and low molecular concentration. (a) Temporal evolution of characteristic wavenumber <q>, defined as the first moment of the structural factor S<q, t> in FPD simulations. σ is the diameter of spherical particles connected by harmonic bonds to form polyelectrolytes. Simulations include two asymmetric cases: c_m=92.5 mM and N₊/N₋=100:10; c_m =27.4 mM and N₊/N₋=100:10, and one symmetric case: c_m =27.4 mM and N₊/N₋=10:10. (b) Plot of the charge density of individual coacervates as a function of size R_g. (c) Representative structural configurations of coacervates formed under the three conditions. Freely dispersed polyanion chains are observed mostly in case (i). (d) Schematic illustrations of coacervates with asymmetric chain lengths that have unsaturated charged groups at the interface. In contrast, coacervates with symmetric chain lengths have a neutralized interface, characterized by balanced electrostatic interactions at the interface

These two comparison simulations align closely with experimental observations, showing that coarsening suppression is exclusive to relatively low monomer concentrations. To prove the necessity of chain length asymmetry, we perform an additional simulation in which both positively and negatively charged polymer chains comprise 10 monomers. As a result, the simulation shows a typical rapid coarsening with an exponent close to 1/3 (Fig. 4a, green points, and Fig. S20 (28)). This confirms that chain length asymmetry is critical for inducing suppressed coarsening.

Simulations also reveal that nanoscale coacervates formed with asymmetric chain lengths and low concentrations exhibit more unsaturated charged groups at the interface, along with shorter polyanions in the dilute phase (Fig. 4c). This confirms entropic partitioning driven by chain-length asymmetry, where shorter chains favor the dilute phase to maximize their configurational entropy and lead to interfacial charge separation even under globally neutral stoichiometry. Analysis of coacervate charge densities shows that most coacervates under these conditions carry net positive charge, with charge density and net charge decreasing over size (Fig. 4b and Fig. S21-S22 (28)). This simulation result aligns with zeta potential measurements in Fig. 3b. In contrast, coacervates formed with symmetric chain lengths exhibit near-zero net charge density regardless of size (Fig. 4b). These results underscore the critical role of chain length asymmetry in activating the MLC mechanism.

Moreover, analysis of the asphericity A of coacervates shows that coacervates with asymmetric chain lengths adopt non-spherical morphologies, including “tadpole”-like and “fold”-like shapes, during the early growth phase (Fig. S23 (28)). These deviations from spherical globules reflect the weak shrinking tendency of nanoscale droplets, inducing the formation of loosely packed, extended structures with net charges (44). Analogous cluster geometries have also been observed in symmetric charged coacervates when the stoichiometry is not neutral (40, 41). Overall, the FPD simulations qualitatively capture our experimental observations and clarify the molecular mechanisms underlying the chain length asymmetry-induced merging-limited coarsening of coacervates. Since this mechanism acts on length scales significantly larger than solvent molecules, the coarse-grained model remains a valid approach for capturing long-time phase separation dynamics, even though it omits atomic-level solvent details (46).

In conclusion, we reveal that nanoscale condensates can be stabilized for extended periods by size-dependent electrostatic merging barriers arising from chain-length asymmetry—a general principle that reframes liquid–liquid phase separation (LLPS) as a kinetically constrained process evolving on a rugged energy landscape (Fig. S24 (28)). We combined experiments, theory, and simulations to show that these barriers enable nanoscale condensates to remain in long-lived metastable states. In contrast to conventional LLPS purely driven by free-energy minimization, nanoscale complex coacervates form via molecular-level electrostatic interactions between oppositely charged polymers. These interactions impose microscopic kinetic constraints, leading to distinctive coarsening behaviors that are sensitive to chain-length asymmetry, entropic charge separation, and thus size-dependent electrostatic barriers. Importantly, our results indicate that nanoscale condensates are more stable at relatively low concentrations. This low-concentration regime maximizes entropic charge separation and matches the subsaturation conditions of many cellular LLPS systems (18). Therefore, our work may provide mechanistic insight into the widespread size stability of condensates observed in living cells and in vitro reconstituted systems (18, 19, 21, 30, 47). By uncovering a non-classical coarsening pathway governed by entropic electrostatics, we extend the physical framework of liquid-liquid phase separation, offering a general principle for controlling metastability across soft matter, biology, and nanotechnology.