Heterogeneous Charged Complexes of Random Copolymers for the Segregation of Organic Molecules.

Nature harnesses the disorder of intrinsically disordered proteins to organize enzymes and biopolymers into membraneless organelles. The heterogeneous nature of synthetic random copolymers with charged, polar, and hydrophobic groups has been exploited to mimic intrinsically disordered proteins, forming complexes with enzymatically active proteins and delivering them into nonbiological environments. Here, the properties of polyelectrolyte complexes composed of two random copolymer polyelectrolytes are studied experimentally and via simulation with the aim of exploiting such complexes for segregating organic molecules from water. The anionic polyelectrolyte contains hydrophilic and hydrophobic side chains and forms self-assembled hydrophobic domains. The cationic polymer is a high-molecular-weight copolymer of hydrophilic and charged side groups and acts as a flocculant. We find that the polyelectrolyte complexes obtained with this anionic and cationic random copolymer system are capable of absorbing small cationic, anionic, and hydrophobic organic molecules, including perfluorooctanoic acid, a compound of great environmental and toxicologic concern. Importantly, these macroscopic complexes can be easily removed from water, thereby providing a simple approach for organic contaminant removal in aqueous media. MARTINI and coarse-grained molecular dynamics simulations explore how the microscale heterogeneity of these random copolymer complexes relates to their segregation functionality.

Introduction

Random copolymers have a statistical distribution of two or more types of monomers, leading to spatial heterogeneity in local composition as different regions of a copolymer chain may have different average composition. This type of heterogeneity from disordered polymer sequences is thought to be important in achieving biomimetic functions such as molecular-scale pattern-matching.[1−4] Membraneless organelles, which are spatiotemporal aggregates of nucleic acids, enzymes and their substrates, and oppositely charged, intrinsically disordered proteins with rather random sequences of amino acid monomers,[5] likely utilize such concepts of disorder and heterogeneity. Because these membraneless organelles are analogous to polyelectrolyte complexes of oppositely charged random copolymers, the behavior of such complexes could provide insight into the behavior of membraneless organelles. This analogy has inspired research into the use of synthetic random copolymers to interact with enzymes, forming what can be considered to be a type of polyelectrolyte complex.[6,7] Concentrating small-molecule substrates is also a crucial function of membraneless organelles. Here, we explore the possibility of using polyelectrolyte complexes of random copolymers as mimics of disordered proteins in membraneless organelles with an aim to segregate small organic molecules from aqueous solution.

Polyelectrolyte complexes are generally formed when oppositely charged polymers are mixed in aqueous solution.[8,9] Depending on factors including charge ratio, degree of polymerization, monomer sequence,[10,11] ionic solution conditions,[12−15] or solvent quality,[16] a wide range of phase behaviors for the polyelectrolyte complex can be observed, including the formation of colloidal suspensions, liquid coacervates, and solid precipitates.[17−20] Colloidal suspensions of polyelectrolyte complexes have been investigated for their ability to encapsulate bioactive molecules and deliver such molecules in a biological environment.[21−23] Liquid coacervates of polyelectrolyte complexes have been shown to encapsulate and concentrate enzymes from solution,[24−26] similar to the capabilities of membraneless organelles.

The formation of solid precipitates with polyelectrolyte complexes can be particularly useful in separating particles from aqueous solution and removing contaminants from water through a flocculation process.[27,28] Traditionally, flocculation is used to remove negatively charged colloids such as fine clay particles from water via the addition of a single species of a high-molecular-weight cationic polymer, which neutralizes the surface charge of the particles, acts as a bridge between them, and coagulates the particles into macroscopic flocs.[29,30] However, polyelectrolyte complexes have also been used for flocculation purposes,[27] and solid polyelectrolyte complexes can also be effective at removing ionic compounds such as metal ions or charged organic compounds from water.[31]

This flocculation behavior provides a relatively simple experimental approach to measure the segregation of organic molecules into polyelectrolyte complexes. There have been studies demonstrating the ability of polyelectrolyte complex coacervates to partition and segregate small organic molecules,[32−35] and separating the coacervates from the supernatant generally requires centrifugation techniques. In contast, solid polyelectrolyte complexes that segregate organic molecules can be removed from solution through simple filtration. Segregation efficiencies can then be obtained by measuring the concentration of organic molecules in the filtered solution.

Building upon a rational design principle outlined in earlier work involving complexes of random copolymers and enzymes,[6] we hypothesize that a random anionic copolymer with hydrophilic, hydrophobic, and anionic monomers will form micellar-like structures in aqueous solution and flocculate with a random cationic copolymer, with the heterogeneity of the resulting complex providing favorable interactions with a wide range of organic molecules. Previously, others have shown that random copolymers with hydrophilic and hydrophobic groups exhibit protein-like folding and form single-chain micelles while segregating dye molecules in aqueous solution.[36] It is reasonable to expect that the addition of an anionic component would allow the three-component copolymer to form similar structures and encapsulate organic molecules, with the additional benefit of being able to remove the copolymer and dye in a flocculation-like process, which may enable applications in industrial water remediation.

Here, we develop a method to segregate and remove organic molecules from water using two oppositely charged random copolymers through experiments, simulations, and analysis. The anionic copolymer is comprised of hydrophilic, hydrophobic, and anionic methacrylate groups. (Figure a) The cationic copolymer is composed of hydrophilic and cationic methacrylate groups. (Figure b) These random copolymer polyelectrolytes were synthesized using free radical polymerization and form macroscopic complexes when mixed (Figure c), successfully encapsulating several organic dyes with varying degrees of effectiveness. Three dyes, crystal violet, methyl orange, and phenolphthalein, were chosen as model molecules for their respective cationic, anionic, and hydrophobic natures as well as ease of quantification via UV–vis spectroscopy. Perfluorooctanoic acid was also chosen to demonstrate the relevance of this system in filtering difficult-to-remove chemicals from aqueous systems (Figure d).

Figure 1

(a) Chemical structure, MARTINI parametrization, coarse grain model, illustration, and simulation snapshot of the anionic random copolymer. (b) Chemical structure, illustration, and coarse grain model of the cationic random copolymer. (c) Illustration and simulation snapshot of complexation between the anionic random copolymer and the cationic random copolymer. (d) Chemical structure of organic molecules used in experiments. (e) Coarse grain model of organic molecules used in simulations. Red and green beads correspond to positive and negative charges respectively, while tan beads are hydrophobic, and blue beads are hydrophilic.

We use coarse-grained molecular dynamics at two different length scales to study how the heterogeneous nature of these random polyelectrolyte complexes affects their ability to flocculate dyes. The simulations show complexes that are highly heterogeneous in composition with hydrophobic domains as well as heterogeneities in the charge distribution throughout the complexes. We explain the origin of these heterogeneities using statistical analysis that has been used previously to explain compositional heterogeneities observed in strongly incompatible random copolymers[37] and in random ionomers, which are molten state (dry) systems.[38,39] Models of the dyes are also included in the simulations (Figure e), and we analyze the roles that hydrophobicity and charge play in the removal of the dyes.

Results and Discussion

Polymerization and Characterization of Random Copolymers

We synthesized the anionic and cationic copolymers via free radical polymerization. Aqueous size exclusion chromatography was used to determine apparent weight-average molecular weight (Mw), apparent number-average molecular weight (Mn), and apparent dispersity (Mw/Mn) values (Table ). The values are apparent, as polymers that form hydrophobic domains can exhibit intermolecular aggregation in aqueous media via hydrophobic interactions.[40] This aggregation behavior can be confirmed for the anionic copolymer, as we obtained higher apparent Mw values with higher concentrations of polymer solution. (See SI, Table S4.) This interpolymer aggregation behavior likely explains the low measured dispersity of 1.1, which is significantly different from the dispersity of roughly 2 that we would expect for polymers produced by free radical polymerization of methacrylate monomers.[41] We note that such a very low apparent dispersity has also been observed in another charged polymer system with interchain aggregates that was synthesized by free radical polymerization.[42]

Table 1

Copolymer Characterization: Mole Fractions, Apparent Average Molecular Weights, Apparent Dispersity, and Apparent Average Degrees of Polymerization

	anionic random copolymer	cationic random copolymer
component 1 mol fraction	PEGMEMA: 0.51	HEMA: 0.54–0.60
component 2 mol fraction	EHMA: 0.44	TMAEMA: 0.40–0.46
component 3 mol fraction	SPMA: 0.05	N/A
apparent Mw (g/mol)	290 000	10 000 000
apparent Mn (g/mol)	260 000	4 300 000
apparent dispersity (Mw/Mn)	1.1	2.3
apparent DPw	820	60 000–62 000
apparent DPn	770	26 000–27 000

The cationic polymer also shows an anomalously high Mw value for a polymer synthesized by free radical polymerization, which is likely due to the fact that the hydroxyethyl methacrylate (HEMA) monomer used in the cationic polymer is susceptible to effects of chain transfer to the polymer and monomer and may act as a branching unit.[43] Thus, it is likely that the cationic polymer is highly branched in structure. This branching may be beneficial in the complexation process, as some studies suggest that highly branched flocculants exhibit better flocculation performance.[30] However, quantifying the degree of branching in polymers is not a simple process[44] and is not explored further in this study. We note that the dispersity of this polymer was measured to be 2.3, which is in line with expected values.

We analyzed the copolymer compositions via 1H NMR spectroscopy. (Peak assignments are shown in SI, Figures S3 and S4.) The anionic polymer has a molar composition of 51% polyethylene glycol methyl ether methacrylate (PEGMEMA), 44% (ethylhexyl methacrylate) (EHMA), and 5% sulfopropyl methacrylate (SPMA). From this information and the apparent Mw, we can calculate an apparent weight-average degree of polymerization (DPw) of 820. The peak assignments for the cationic copolymer cannot be exactly determined without knowing the branching ratio of the polymer, but upper and lower bounds can be determined for the strictly linear case and strictly branched case (one branch per HEMA monomer). Thus, a reasonable estimate for the molar composition of the cationic polymer is 54–60% HEMA and 40–46% TMAEMA, with an apparent DPw between 60 000 and 62 000. From this analysis, we can conclude that the cationic copolymer has a substantial charge fraction and is much longer than the anionic copolymer, potentially making it an effective flocculant. The anionic copolymer has a significant hydrophobic composition while being slightly charged. See Table for a summary of copolymer characterization.

Polyelectrolyte Complex Formation and Dye Filtration

We formed solid polyelectrolyte complexes by mixing 300 μL of 66 ± 2 mg/mL aqueous anionic copolymer solutions and 220 μL of 15.0 ± 1.5 mg/mL aqueous cationic copolymer solution in 10 mL of distilled water, which leads to a 6 to 1 ratio by weight of anionic copolymer to cationic copolymer. Initially, the mixture of copolymer solutions turns turbid and cloudy, indicating that polyelectrolyte complexes have grown to a size comparable to the wavelength of visible light. In less than a minute, macroscopic flocs can be observed, indicating the complexes have favorable interactions and a strong tendency to aggregate and coalesce into larger and larger structures. However, we also observe that the solution tends to be slightly turbid after macroscopic flocculation, indicating that there are colloidal polyelectrolyte complexes remain in solution. These are likely charge-stabilized colloids, as there is an excess of positive charge in the complexes. At this point, we add 20 μL of a 50 mg/mL magnesium sulfate solution, and this addition appears to coagulate the remaining polyelectrolyte complexes within a few minutes and leaves the solution clear. We believe this coagulation process is analogous to how multivalent cations are used to coagulate anionic colloids from solution.[45] The final aggregate sizes are usually on the order of millimeters and are robust to mechanical perturbation. When the mixture is stirred with a magnetic stir bar, the aggregates do not break apart even at stirring speeds exceeding 1000 rpm. After filtration through a 0.22 μm membrane filter, the measured solid concentration in the filtered solution is 0.17 ± 0.02 mg/mL. This concentration corresponds to a polyelectrolyte complexation efficiency of ∼92%.

The amounts of copolymer solution that we mixed in the above description are determined by using a titration procedure. Starting with an initial mixture of distilled water and anionic copolymer solution, corresponding to a 10.3 mL solution containing 1.90 ± 0.05 mg/mL of anionic copolymer, we add the 15.0 ± 1.5 mg/mL cationic polymer solution in 20 μL increments. We consistently find that macroscopic flocculation occurs at 220 mL of cationic solution added, which may correspond to a sort of equivalence point. However, this is not a traditional equivalence point for polyelectrolyte complexes, as the molar ratio of positive charges to negative charges of the complexes is not 1:1 but has a significant excess of positive charge with a ratio of 2.9–3.3:1. This amount of copolymer solution added to form macroscopic complexes does not change when adding dyes or contaminants at a concentration of 2 μg/mL, except for the case of phenolphthalein, where 240 μL of cationic solution was needed for flocculation. This difference is likely due to a slight salt concentration of about 1 mM NaCl from the preparation procedure and suggests that there is a salt concentration dependence on the formation of these complexes, which is normally observed in systems of aggregating polyelectrolyte complexes.[46] This effect may be explored further in a future study.

The removal efficiency for the dyes is determined by comparing the peak visible light absorption of the filtered samples with complexes removed to a calibration curve from stock solutions of the dye. We find that the removal of crystal violet, the cationic dye, is quantitative with a single filtration removing over 99.5% of the dye, reaching the detection limit of the instrument used. We obtain similar results for phenolphthalein, a hydrophobic dye, with a removal efficiency of >98%. It should be noted that filtration experiments for phenolphthalein were performed in its colorless, neutral form, whereas quantification experiments were performed in its colored, charged form. The removal efficiency with a single filtration of methyl orange, the anionic dye, is 65 ± 5%. We determine the removal efficiency of PFOA in a manner similar to the dyes, except using liquid chromatography with mass spectrometry using electrospray ionization. A value of 63.0 ± 0.5% is obtained for a single filtration. We also perform repeated filtrations for a sample of perfluorooctanoic acid, with the process of adding anionic copolymer solution, and then cationic copolymer solution and magnesium sulfate being repeated twice for a total of three filtrations. In total, 89.0 ± 0.5% of the perfluorooctanoic acid was removed in this experiment, demonstrating that this system can significantly reduce the concentration of environmentally relevant contaminants from aqueous systems. These results are shown in Figure (a).

Figure 2

(a) Filtration results. For each of the three dyes, the results are averages from three separate filtration samples. Crystal violet and phenolphthalein are quantitatively removed. For perfluorooctanoic acid, results for one and three filtrations on a sample of perfluorooctanoic acid are shown. Error bars are standard deviations from three runs of a single sample. (b) Images of 2 μg/mL aqueous solutions of crystal violet before (left vial) and after (right vial) addition of 100 μL of anionic copolymer solution (66 mg/mL). (c) Images of 2 μg/mL aqueous solutions of crystal violet before (left vial) and after (right vial) encapsulation in a polyelectrolyte complex of anionic and cationic copolymer. (d) Visible absorbance spectra of a 2 μg/mL solution of crystal violet in water as a function of added anionic copolymer solution (66 mg/mL). A significant solvatochromic shift is observed upon addition of trace levels of copolymer solution.

Confirmation of Dye Encapsulation and Micelle Formation in an Anionic Copolymer

Crystal violet and methyl orange are solvatochromic dyes, exhibiting visible absorbance spectral shifts with changes in the hydrophobicity of the local environment.[47] We leverage this behavior to obtain information on the interactions of the dyes with the copolymer and resulting complex. Figure (b,d) shows that solutions of crystal violet exhibit a solvatochromic red shift when mixed with small amounts of anionic copolymer solution, with a peak absorbance shift from 593 to 598 nm. As the small amount of copolymer added does not change the overall polarity of the solvent, the crystal violet must be interacting strongly with the local hydrophobic domains of the anionic copolymer. This spectral shift is similar to the shift shown when anionic micelles of sodium dodecyl sulfate are formed in solution with crystal violet.[48] This shift is retained when complexes of the anionic and cationic copolymers are formed as shown in Figure (c), indicating that crystal violet is located near the hydrophobic pockets that exist within the polyelectrolyte complex. No solvatochromic shift is observed in absorbance spectrum when anionic copolymer is added to a solution of methyl orange nor does the resulting complex exhibit a visual color shift. These results indicate that methyl orange does not interact strongly with the hydrophobic domains of the polyelectrolyte complex, possibly due to a weaker hydrophobic character and/or the same charge repulsion from the anionic copolymer. This may explain the lower removal efficiency of methyl orange compared to crystal violet. We turn to molecular dynamics simulations in order to differentiate more clearly the effects that charge or hydrophobicity have in the segregation and removal of these organic molecules and their molecular-scale interactions with the polyelectrolyte complexes.

Simulations of Polymers and Dyes

We use coarse-grained molecular dynamics at two different length scales to study the interactions of crystal violet, methyl orange, and variations of these molecules with the polymer complexes. The MARTINI model provides information on the conformation of the anionic random copolymer, while a more coarse, implicit solvent model is developed to study the formation of complexes and interactions with the dyes. Using the MARTINI model, we first perform simulations of only the anionic copolymers and their counterions without cationic copolymers or dyes. The monomer fractions for the anionic copolymers match the fractions used in experiments (EHMA: 0.44, PEGMA: 0.51, SPMA: 0.05), and each copolymer has a degree of polymerization (DP) of 100. We observe that the anionic copolymers form micelles with both models, and the distribution of hydrophobic, hydrophilic, and negatively charged beads from the micelle center of mass for the MARTINI model can be found in the SI (Figure S2). These distributions are also shown for the two different states we observe using the coarse-grained model when the cationic copolymers are also included in the simulations. Like the anionic copolymers, we use monomer fractions that correspond to experiments (HEMA: 0.54, TMAEMA: 0.46). In this case, DP = 200 is chosen in order to represent the larger molecular weight of the cationic polymer used in experiment. In both models, the anionic copolymers that are not interacting with the cationic copolymers take on micellar configurations due to the hydrophobic side chains and backbone. When interacting with the cationic polymers, the anionic copolymers take on much more stretched conformations that still feature hydrophobic domains.

The two models confirm that the anionic copolymer forms a hydrophobic core with a hydrophilic corona and charges sitting at the edge of the hydrophobic core. This demonstrates the ability of the coarse-grained model to capture the conformation of the methacrylate-based, random, charged copolymers.

As was noted above, the experimental polymer charge ratio, i.e., the total ratio of positive charges on all of the copolymers to the total number of negative charges on all of the copolymers, was 2.9–3.3. (As in the simulations, counterions make the system charge neutral overall). Earlier experimental work done of complex coacervation has suggested that only polymer charge neutral systems form macroscopic phases whereas noncharge neutral systems should form smaller dispersions.[49] Some studies even presuppose that this condition should be met.[50] Even when studies have extended the modeling to include charge anisotropy and short-range attractions, the models include only fluctuations via linear response theory (or random phase approximation), and when ionic correlations are included, they are assumed to be local using a binding energy of ions to the chain backbone.[16,51]

The distribution of charge on the polymers, along with the formation of hydrophobic domains for the anionic copolymer, likely plays a role in the nonstoichiometric polymer charge ratio of the complexes. The polymers used in this study are nearly ideal random copolymers, as the reactivity ratios of the methacrylate monomers are nearly 1.[6] Thus, the charges are randomly distributed, and we can calculate the number fraction or probability of finding a sequence of N charged units on the polymer[52]where fc is the charge fraction of the polymer. The cationic copolymer has a much higher charge fraction of 0.46, compared to the anionic copolymer charge fraction of 0.05. We can conclude that on average that the cationic copolymer has considerably longer and more frequent positive charge sequences than the anionic copolymer has negative charge sequences. We also note that the average distance between charge sequences is the reciprocal of the charge fraction, being 20 for the anionic copolymer and 2.2 for the cationic copolymer. Compounded with the fact that anionic charges are spread out over the surface of hydrophobic domains, regions of the cationic copolymer with longer charge sequences will require interactions with multiple hydrophobic domains to effectively compenstate the charge. Steric effects will limit the number of hydrophobic domains that can aggregate in a local area, at times leading to uncompensated positive charges.

The coarse-grained simulations support this hypothesis, and a polymer charge ratio near 3 was required to create a percolated structure, in reasonable agreement with the experimental polymer charge ratio (2.9–3.3). In Figure , we explore the percolation (counting only the hydrophobic beads) of the system as more cationic polymer is added by examining the probability of finding a polymer in a cluster of a certain size as a function of the polymer charge ratio. This probability is a weight-average probability, as opposed to a number-average probability, meaning that the probabilities are normalized by the total number of polymers in a cluster of a certain size as opposed to the total number of clusters of a certain size. Thus, a delta function for a cluster size of 1 signifies a single cluster of all the components. At polymer charge ratios below 1, large clusters constituting up to 60% of all polymers are observed. In these clusters, cationic copolymers serve as high-valency cross-linkers, forming hydrophobic connections with on average eight anionic copolymers in a “pearl-necklace”-like structure.[53] The ratio of charges on the average cationic polymer to the average anionic polymer is 9.2, meaning that the charge on the average cationic polymer is incompletely compensated by the 8 anionic copolymers on average to which it is connected. Consequently, free micelles and smaller clusters containing both cationic and anionic polymers are also observed. For the same reason, these smaller clusters always have a net positive charge even though the system is net negatively charged. As the charge ratio is increased above 1, more cationic polymer is added, and there is an electrostatic driving force for the free micelles to enter the densely connected phase. However, smaller dispersions are still observed, and only when the charge ratio continues to increase to the observed experimental ratio of ∼3 do we see the smaller dispersion completely incorporated into one large cluster.

Figure 3

Probability of a chain being in a certain sized cluster, where the cluster size is measured as a fraction of the finite sized simulation, as a function of polymer charge ratio, which is defined as the ratio of the number of positive charges to the number of negative charges in polymer clusters (the system is electrically neutral due to counterions). At low charge ratio, free micelles, small clusters, medium-sized clusters, and large clusters comprised of nearly every chain are observed (left). As the polymer charge ratio is increased above 1, there is an electrostatic driving force for the free micelles to enter the dense phase; the free micelles should be incorporated in the dense phase even if it is not connected through hydrophobic interactions (center). As the charge ratio is further increased to 2 and above, the medium-sized clusters effectively disappear, leaving the polymers in one dense phase (red test tube). This agrees well with experiments where a polymer charge ratio above 3 is necessary to drive all the polymers into a macroscopic phase.

The use of positively and negatively charged polymers combined with the statistical nature of copolymerization creates a system where individual polymers have a range of compositions in terms of charge sign, fraction, and hydrophobicity. It has been shown that amphiphilic copolymers with a distribution of compositions should phase separate into many phases with different compositions.[37,54] However, we do not observe this in simulation or experiment due to the addition of the charged monomers and the energetic cost of creating many interfaces. Instead, we observe local charge heterogeneity as shown in Figure . This is shown by splitting the simulation box into many smaller cells of a certain size, L, and calculating the effective charge in those cells, Zeffwhere N+ is the number of positive charges in the cell and N– is the number of negative charges in the box. In Figure (a), N+ and N– are restricted to be charges on the polymers; in Figure (b), they can be any charge including those from the counterions. At small cell sizes, we observe two peaks at ±1 with and without the inclusion of counterions in the effective charge of the box. That is, the system develops domains with different fractions of charge. The energy penalty, Fc, associated with this charge heterogeneity is proportional to the square of the effective charge, divided by the cell size, L, in terms of the Bjerrum length, lB = e2/(4πε0εKBT) with ε0 being the permittivity of vacuum, ε being the relative permittivity of the media, e being the elementary charge, KB being Boltzmann’s constant, and T being absolute temperature. Here, we use the Bjerrum length in water, 0.7 nm, which comes from its bulk dielectric constant, ε = 80.

Figure 4

(a) Calculations of charge heterogeneity for charges on polymers. The simulation box is split into smaller cells of different lengths, L, and then the effective charge from the polymers in these boxes is calculated according to eq . Box sizes of 2.5 and 5 nm show two peaks where the effective charge is ±1. This shows how the hydrophobic energy of the polymers leads to local charge segregation in these polyelectrolyte complexes. (b) Calculations of charge heterogeneity for charges on polymers and counterions. The same calculation is performed as described above. Free counterions help to negate some of this charge segregation, but at small length scales, the two peaks are still observed. At larger length scales, with a Gaussian distribution centered at 0, effective charge is observed. (c) Electrostatic driving force for dye segregation. The electrostatic energy of different dyes when they are free in solution and segregated in the complexes as well as the energy difference between the states.

As the cell size increases, the effective charge scales with the number of charges, which scales with the volume of the cell or the cell size cubed. Thus, the overall charge energy scales with the cell size to the fifth power.The compensation for this charge heterogeneity must come from the hydrophobic interactions of the anionic and cationic copolymers. The energy of these hydrophobic interactions, FH, comes from the interface between the solvent and hydrophobic domains. It scales with the surface tension, γ, and, by dimensional analysis, the cell size squared.Thus, the charged term has a much stronger scaling with the cell size, and as a result, the two peaks at ±1 are observed only at small length scales, obtained by minimizing the sum of eqs and 4 giving Lhetero ≈ (γ/lB)1/3. Free counterions help to compensate the charge on the polymers, decreasing this length scale in Figure (b). Above this length scale, the population of cells with different numbers of charges tends toward a Gaussian distribution with zero average net charge, while the distribution width becomes broader as L increases. This is due to the stretched conformations of the copolymers in complexes as described in Figure S2. We note that when L increases beyond a critical value, the width of the charge distribution should shrink again, because there is no system with macroscopic excess charge. Finally, when L approaches the system box size, we observe a delta function at zero given the electroneutrality condition imposed in the simulations.

The charge heterogeneity also impacts the absorption of the dyes. In order to explore the generality of the method to segregate different molecules, we used seven variations of crystal violet and methyl orange coarse grain dyes shown in Figure . These molecules were added into the simulations with a polymer charge ratio of 3.25 at a ratio of 1 dye molecule to 130 polymer monomers. A dye is considered segregated if any of its hydrophobic beads is within a certain distance of a hydrophobic bead belonging to a polymer. Following experimental trends in removal rate, the crystal violet has a higher condensation rate than methyl orange. This makes sense given the additional hydrophobic benzene ring in the crystal violet that effectively increases its hydrophobic interaction with the complex. Overall, for purely hydrophobic dyes, the more hydrophobic beads it contains, the higher the percentage of segregated contaminants in the sample. This dependence of segregation to hydrophobicity is in line with experimental results in related polymer–micelle complexes.[35] We also see that adding a charged bead to a given hydrophobic structure decreases the percentage of molecules segregated. These segregation results are shown in Figure (a).

Figure 5

(a) Percentage segregation for the seven simulated dyes. The ratio of dyes to polymer monomers is 1:130, and the volume fraction of polymers is ∼10%. Segregation is defined as any hydrophobic dye bead being within a cutoff distance from a hydrophobic polymer bead. Almost all condensation occurs on the anionic polymers, which form stretched micelle-like structures with hydrophobic cores. The more hydrophobic a dye is, as measured by the number of hydrophobic beads, the higher the percentage segregated. Adding a charged bead to a hydrophobic dye always decreases the percentage segregated. (b) Circular variance as a measurement of dye location within hydrophobic domains. The circular variance is used to measure the degree of hydrophobic burial of a dye. It is calculated by taking the length of the vector sum of all the unit vectors from the dye to hydrophobic beads that are within the cutoff distance. This is then divided by the number of vectors and subtracted from 1. Thus, 1 is the maximum burial, and 0 is the minimum. (c) The position of dyes within hydrophobic domains as measured by circular variance. Left and center show specific comparisons for dyes with and without charges. The uncharged dyes are always much more buried. The right shows how the degree of burial continues to increase as the number of hydrophobic beads in the dye is increased.

As expected for the net positively charged polymer complex, the negative methyl orange dye is more readily segregated than its positive counterpart. This is supported by Figure (c), which shows that the electrostatic driving force is stronger for methyl orange than its positive counterpart. That is, for the negative dye, the electrostatic energy decreases upon condensation into the polymer complex, whereas for the positive dyes, there is almost no difference in electrostatic energy despite the polymer charge ratio of 3.25. Figure (c) also shows that, due to the charge heterogeneity demonstrated in Figure (a), the absorption of the positive dyes is not adversely impacted by the net positive charge on the complexes. The heterogeneity of the charges in the complex makes it possible for both negative dyes to reduce their energy upon condensation. In contrast, the positive dyes are relatively unaffected, because there are areas of net positive and net negative charge in the polymer complex, which is net positive. This encouraging generality of the method is not anticipated by simple intuition, which shows the importance of the heterogeneities in charge and composition caused by the random copolymers (some domains have positive charge and some negative) as shown in Figure (a,b).

This generality is explained by examining the location of condensed dyes within the hydrophobic cores present in the polymer complexes. To this end, we measure the hydrophobic circular variance. A full explanation of the circular variance is given in Figure (b), but it is used as a measure of the degree of burial of the dyes. Maximum burial by hydrophobic beads corresponds to a circular variance of 1, and minimum burial corresponds to a circular variance of 0. The distribution of circular variances for the different dyes is shown in Figure (c). There are two basic distribution shapes, one for charged and one for uncharged dyes. The distribution for charged dyes skews to lower values meaning that these dyes are restricted to be closer to the surface of the hydrophobic region due the charges preferring the ionic solvent environment. However, we notice a difference in the segregation behavior of oppositely charged dyes, with 10% of the segregated anionic methyl orange condensed to a hydrophobic bead on the cationic copolymer, compared to 1% for the segregated crystal violet. Despite the fact that both dyes reside at the interface of hydrophobic and hydrophilic regions of the polyelectrolyte complex, their hydrophobic interactions can be significantly different given that the methyl orange is more likely to interact with the cationic copolymer than the crystal violet. This discrepancy may help explain why we do not observe a solvatochromic shift in experiments where methyl orange was segregated into complexes.

The distribution for the uncharged dyes tends toward higher values of burial, and the distributions indicate more burial as more hydrophobic beads are added. This burial means a stronger overall interaction between the hydrophobic portion of the dye and the hydrophobic domain of the complex, explaining the trend of lower percent segregated for charged dyes despite no adverse effects observed in the electrostatic potential (see Figure c). The stretched conformations of the anionic copolymers could be contributing to the removal of the charged dyes, because they have a higher surface area to volume ratio than spherical micelles and thus allow more low circular variance sites for the charged dyes to condense.

Future Outlook

We developed a method to segregate organic molecules from water into complexes formed by two oppositely charged, random copolymer species. We demonstrated that the heterogeneity of the complex plays an important role in providing favorable interactions to a wide variety of small molecules, as shown by our analysis of positively charged, negatively charged, and hydrophobic molecules. Hydrophobic interactions from hydrophobic cores play a dominant role for segregation into the complexes, and charged molecules undergo relatively favorable electrostatic interactions due to nanoscale charge segregation in the complexes. There are still many interesting aspects of this system to explore. The sizes and distribution of the hydrophobic domains, and whether such domains are formed primarily through interactions between multiple polymer chains, are another aspect of heterogeneity in our system, which likely affects molecule uptake. We also claim that the hydrophobic domains, along with differences in charge distribution of the polyelectrolytes, leads to nonstoichiometric charge ratios for macroscopic complexes. It may then be possible to tune the charge distribution and hydrophobic content to change this charge ratio, which may also affect molecule uptake. Investigating how different copolymer compositions affect these various parameters and molecule uptake could be an active field of research.

Our work has implications for disordered systems such as membraneless organelles to concentrate small-molecule substrates necessary for enzymatic biological processes. Combining this result with the ability of synthetic random copolymers to form complexes with enzymes,[6] we expect that it may be possible to replicate the function of membraneless organelles in optimizing enzymatic activity by colocalizing an enzyme and its substrate, with potential industrial applications.

This method has the potential to provide an economical approach to remove a wide range of dye and contaminants from water on a large scale, as random copolymers can be synthesized inexpensively via free radical polymerization. The basis of favorable interactions between various molecules lies within the statistical distribution of monomers that leads to heterogeneity at the nanoscale, and controlling dispersity or other structural features of the polymer through more expensive techniques such as controlled radical polymerization is not necessary. This technique could be incorporated into existing water remediation processes via addition of a well-designed anionic random polyelectrolyte during a flocculation step. The flocculation behavior of these polyelectrolyte complexes also has the potential to lead to the removal of hydrophobic particles from water such as enzymes and nanoparticles including nanoplastics,[55] something which traditional flocculants may have difficulty accomplishing, as they lack a significant hydrophobic interaction. Further studies on interactions between these heterogeneous polyelectrolyte complexes and bulk polymer surfaces are planned to explore such a possibility.