Molecular Dynamics Simulations of Adsorption of Poly(acrylic acid

Sep 10, 2015 - We have investigated the interaction of dodecyltrimethylammonium chloride (DoTA) micelle with weak polyelectrolytes, poly(acrylic acid)...
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Molecular Dynamics Simulations of Adsorption of Poly(acrylic acid) and Poly(methacrylic acid) on Dodecyltrimethylammonium Chloride Micelle in Water: Effect of Charge Density Muralidharan S. Sulatha* and Upendra Natarajan Molecular Modeling and Simulation Lab, Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, India S Supporting Information *

ABSTRACT: We have investigated the interaction of dodecyltrimethylammonium chloride (DoTA) micelle with weak polyelectrolytes, poly(acrylic acid) and poly(methacrylic acid). Anionic as well as un-ionized forms of the polyelectrolytes were studied. Polyelectrolyte− surfactant complexes were formed within 5−11 ns of the simulation time and were found to be stable. Association is driven purely by electrostatic interactions for anionic chains whereas dispersion interactions also play a dominant role in the case of un-ionized chains. Surfactant headgroup nitrogen atoms are in close contact with the carboxylic oxygens of the polyelectrolyte chain at a distance of 0.35 nm. In the complexes, the polyelectrolyte chains are adsorbed on to the hydrophilic micellar surface and do not penetrate into the hydrophobic core of the micelle. Polyacrylate chain shows higher affinity for complex formation with DoTA as compared to polymethacrylate chain. Anionic polyelectrolyte chains show higher interaction strength as compared to corresponding un-ionized chains. Anionic chains act as polymeric counterion in the complexes, resulting in the displacement of counterions (Na+ and Cl−) into the bulk solution. Anionic chains show distinct shrinkage upon adsorption onto the micelle. Detailed information about the microscopic structure and binding characteristics of these complexes is in agreement with available experimental literature.

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INTRODUCTION Intermolecular interaction of surfactants with ionic and nonionic polymers in aqueous solution holds significant importance for applications in various biological and industrial processes.1−8 Polymer−surfactant systems are widely applied in industrial processes such as water treatment as flocculant− water insoluble mixtures, powder processing as dispersion agents, and in food technology as rheological modifiers. Polymer surfactant complexes (PSC’s) which are complex structures formed by surfactants and polymers exhibit properties different from those observed in their respective pure solutions. Scattering techniques have revealed that structures prevailing in these complexes can be described by a necklace model of surfactant aggregates formed around the polymer chain. The nature and strength of polymer−surfactant interactions are dictated to a large extent by the chemical structure of polymer and surfactant molecules. There exist two such types of polymer−surfactant interactions. When an ionic surfactant interacts with an ionic polymer or a polyelectrolyte (PE) of opposite charge as the surfactant, a strong favorable polymer−surfactant interaction is exhibited due to electrostatic interactions between surfactant and polymer molecules. The aggregates are formed at very low critical aggregation concentration (CAC) values which are usually orders of magnitude lower than the critical micelle concentration (CMC) values of the surfactants. When an ionic surfactant © XXXX American Chemical Society

interacts with a nonionic polymer, hydrophobic and ion-dipole interactions influence the structure of the complex. Association of ionic surfactants with oppositely charged PE’s has been a subject of considerable interest and invigorating research due to importance in biological systems as well as many industrial applications.4,5 Applications using oppositely charged particles include coatings where coprecipitation can be achieved and encapsulation where small polymer−surfactant complexes are used.2−5 Many biomacromolecules such as DNA are also polyelectrolytes, and the formation of complexes with proteins and membranes are expected to play critical roles in biological regulation processes with applications in therapeutic delivery systems.3 A considerable number of experimental efforts have brought out a significant progress in our current understanding of the general principles of association between charged polymers and charged surfactants in solutions and at interfaces.4−7 PE chain properties are determined by charge density, chain flexibility, and hydrophobicity which in turn are dictated by structure of the polymer backbone and by the nature of the side groups. Charge density and charge strength also contribute to variable long-range electrostatic interactions. However, the typical structural properties of these PSC’s do not depend exclusively on the electrostatic interaction between Received: May 16, 2015 Revised: September 2, 2015

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binding force, while a surprising observation is the increase in CAC with pH. One would expect an enhanced tendency for binding with increase in charge and a resultant lowering of the CAC. This behavior has been attributed to the difference in flexibility and conformation of PAA chains at different values of pH.15 The onset of surfactant binding being shifted to lower free surfactant concentration for polyelectrolyte charge density less than 0.26 as compared to higher value has been observed in the interaction of PAA and PMA with tetradecyltrimethylammonium bromide surfactant as well.16 It is also understood that electrostatic force by itself is not responsible for binding of cationic surfactants to poly(carboxylic acid)s. These experimental studies have been reviewed by Wang and Tam in their paper on the investigations of binding of DoTA with PAA at different values of the degree of neutralization (α) using isothermal titration calorimetry (ITC) and laser light scattering techniques,17 where binding of surfactant to the PE chain was observed at all values of α. For α < 0.3, and at very low DoTA concentration, binding was attributed to hydrophobic interactions of the surfactant alkyl tails with the apolar segment of PAA. ITC profile for α < 0.3 exhibits a significant exothermic peak with the precipitation of the resultant mixture which has been attributed to interchain complexation via hydrogen bonding induced by the binding. The precipitate was found to resolubilize with further addition of surfactant as more micelles are bound to the chain with their ionic headgroups pointing outward. With increase in α, electrostatic forces become predominant in the binding of anionic PAA with the micelle. These authors have also reported the existence of an endothermic peak in the ITC profile for α above 0.3, which was attributed to the release of condensed counterions on PAA via an ion-exchange process. The aggregation number of the PAAbound micelle was found to be close to that of the free micelle. Other experimental studies have also indicated that the aggregation number of DoTA is essentially independent of PE as well as salt concentration.2,18,19 Experimental studies involving the association of PAA with alkyltrimethylammonium bromides based on five different surfactant chain lengths (C6− C16) and different polyion lengths (30 and 6000 repeat units) have been investigated by visual inspection and small-angle Xray scattering experiments.20 The attraction between oppositely charged surfactant aggregates and polyions was found to decrease with decrease in surfactant chain length and with decrease in polyion length, thus resulting in increased miscibility with water. A weak attraction due to binding of short polyions with short surfactant chains leads to a complex that could swell to a disordered micelle structure. Long polyions and long surfactant chains form a structural complex that aggregates until the hexagonal phase. In one of the earlier studies, the interaction of PMA with decyltrimethylammonium bromide (DeTA) has been reported.21 Binding of cetylpyridinium chloride (CPC) onto PE’s PAA and PMA in their atactic and syndiotactic forms is known. 22,23 The interaction strength of this series of polycarboxylates (fully ionized, f = 1) showed the strongest binding, i.e., the lowest CAC with PAA. Binding of CPC to fully ionized PMA (atactic and syndiotactic) was shifted to higher CAC values in comparison to PAA, implying that less surfactant binds to PMA chains. Another study on the binding of dodecylpyridinium chloride to PAA and PMA at low charge density also showed the cooperativity of surfactant binding to PMA as being significantly less than that of PAA.24 Interactions of PAA and PMA with cationic surfactants like decylammonium

chain and surfactant. Several solution properties are dictated by a complex interplay between short-range hydrophobic attraction, long-range electrostatic effects, and entropic degrees of freedom. The fine balance between these factors decides the solubility and equilibrium conformation of molecules present in these complexes in solution. Hydrophobic and ion-dipole interactions drive the association of nonionic polymers with ionic surfactants.1,2,4 The studies on the interaction between nonionic polymers such as poly(ethylene oxide) (PEO), poly(propylene oxide) PPO, poly(N-vinylpyrrolidone) (PVP), and poly(N-isopropylacrylamide) (PNIPAM) with ionic surfactants in dilute aqueous solution are available in the literature.9−13 Examples include association between PEO and anionic sodium dodecyl sulfate (SDS) whereas no such interaction was found between PEO and cationic surfactants.10 In a similar manner, interaction of PNIPAM with SDS is found to be more favorable than with cationic surfactants.14 Different aspects of binding and physical properties of PSC’s are available through a considerable volume of experimental work. Despite numerous studies in the literature, it has been difficult to convincingly demonstrate a microscopic picture of PE−surfactant aggregation phenomenon, since most experimental studies are limited to measurement of macroscopic phase behavior such as lowering of CMC through changes in viscosity and conductivity. New insight into mechanisms governing PE−surfactant interaction can be provided by computer simulations. Simulation studies by far have utilized coarse-grained Monte Carlo techniques with exclusion of the chemical details of the polyelectrolyte and surfactants. The present study aims to provide a detailed picture of the aggregation complex that is inaccessible through experiments alone and allows us to understand the association mechanisms postulated in experimental and theoretical studies. Computer simulations proposed are such that chemical details of the PE, surfactant, solvent, and ions are included. In this paper we present an atomistic MD simulation study of the interaction of two poly(carboxylic acid)s with a cationic surfactant DoTA. Poly(carboxylic acid)s represent an important class of weak PEs whose charge density can be varied by a change in pH and this study focuses on two chemically different PE’s, poly(acrylic acid) (PAH) and poly(methacrylic acid) (PMH), which differ in their hydrophobicity. The charge density of the poly(carboxylic acid) is varied such that we study complexes of DoTA with fully ionized polycarboxylate (corresponding to anionic PEs PAA and PMA where all the acid groups are in COO− form) and with un-ionized poly(carboxylic acid)s (corresponding to PAH and PMH as nonionic polymers where all the acid groups are intact as COOH). This would serve to clearly distinguish the association mechanisms between ionic and nonionic polymers as well as the effect of hydrophobicity in the formation of PSC’s. Interaction between weak synthetic polyelectrolytes and a cationic surfactant can serve as simplified models for more complex biological systems and has potential applications in drug delivery and control of chemical reactivity. The properties of complexes of surfactants with PE’s as well as nonionic polymers have been studied experimentally as well as by theoretical methods and computer simulations. Experimental studies involving the binding of PAA with DoTA have relied on pyrene labeled PAA as the fluorescent probe at different pH and salt conditions.15 The addition of salt increases the CAC owing to the reduction of the electrostatic B

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The Journal of Physical Chemistry B chloride have been explored.25,26 In the case of PMA, micellar aggregates bound to the PE chain were observed at higher concentrations when compared to the analogous PAA systems. Weaker interactions with surfactants were observed with PMA than PAA, on the basis of an estimation of the polymer− surfactant interaction strength.26 A significant amount of literature is available on the nature of PE−surfactant interactions explored by theory and computations27−36 where in complex formation has been described as a molecular association process in which the polyions act as counterions by wrapping around the surfactant micelle. This association is also attributed as an ion-exchange process where the condensed counterions on the PE are replaced by the surfactant molecule. Different aspects including the strength of hydrophobic interactions between the polyion and the micelles, polyion-mediated electrostatic interactions, and the forces between the micelles induced by polyions have been the subject of investigations in the literature. Theoretical studies include complexation of anionic PE with positively charged spherical macroions in salty water27 which have shown that the PE chain binds to spheres by winding around them while spheres repel each other and form periodic necklace. At the isoelectric point where the total charges of the spheres and PE are equal, the necklaces condense into macroscopic bundles. Complexation of long thin PE chains with oppositely charged spheres have been investigated in the limit of strong and weak adsorption.28 Critical conditions for PE adsorption were derived in this work and also showed that overcharging of the complexes is not observed as often predicted. Critical adsorption of long weakly charged PE in salt solution onto oppositely charged colloids have been studied, the expressions provided being valid for any sphere radius.29 A universal critical line for the sphere radius as a function of the screening length was derived which distinguishes adsorbed states from desorbed ones. The ground state dominancy approximation has been used to study the encapsulation of a PE chain by an oppositely charged spherical surface, and it was shown that the electrostatic attraction between the PE and the surface along with the entropy loss of the encapsulated chain dictates the optimum conditions for encapsulation.30 A simple model for the binding of PE to an oppositely charged macroion with radius of the same order as the polymer persistence length has been derived.31 In the model, the finite radius of curvature of the macroion imposes the stability limits on the bound state. The model predicts transitions to bound state stability in the same conditions (PE charge density, macroion radius, salt concentration) under which these are observed in experiments involving binding of PE with oppositely charged micelles. A scaling analysis of PE adsorption due to short-range interactions at oppositely and similarly charged surfaces can be found in studies by Dobrynin et al.32−34 Polymer surface coverage, layer thickness, and surface overcharging were calculated as a function of surface charge density, the strength of the short-range interactions, and the ionic strength of the solution. A brief overview of the theroretical and simulation work on complexes of linear macroions (flexible and semiflexible PEs) with oppositely charged spherical macroions (colloids, globular proteins) is available.35 A comprehensive description of these studies can be found in a recent article,36 wherein a correlation of the binding strength of surfactants to PEs in salt-free mixtures as a function of polyion charge density and surfactant hydrophobicity, applicable to a broad range of PEs, is given. This particular correlation was developed on the

basis of the analysis of the experimental reports in the literature. According to the model, cooperative binding strength increases as the square of the PE charge density and in proportion to the surfactant’s hydrophobicity. The relationship predicts the binding strength in PE−surfactant mixtures based on mesoscale parameters determined from chemical composition. Molecular simulation studies of PSC’s available in the literature have primarily used coarse-grained models.37−46 Wallin and Linse have investigated the behavior of PE−micelle complex by varying the chain flexibility, linear charge density, and micelle radius.38−40 Complexes formed between several PE chains and spheres have also been looked at.41 Adsorption of chains with varying flexibility on spheres has been investigated with specific details such as curvature effects, overcharging issues, and adsorption limits.42,43 Monte Carlo simulations of PSC’s by varying the hydrophobic and electrostatic interactions have also been reported.44 Surfactant was treated as a flexible molecule consisting of a hydrophobic tail and hydrophilic headgroup in yet another study which showed that in the absence of surfactant the PE chain is rigid, and it wraps around the micelle once the surfactant is added.45 In a recent work, coarse-grained MD simulations have been applied to investigate PE−surfactant interaction with a focus on the effect of hydrophobicity (or hydrophilicity) and charge density of the PE chain and the concentration of the surfactant.46 The aggregation of surfactants on the hydrophilic PE is significantly different from that of the hydrophobic PE. It has been found that the hydrophilic PE wraps around the micelle surface, resulting in a rod-like micelle. In the case of hydrophobic PE, spherical micelles are formed, and the chain penetrates into the hydrophobic core of such a complex. A study of the complexation of a neutral polymer PEO with anionic surfactant SDS using atomistic MD simulations in explicit water showed that the association is mainly driven by hydrophobic interaction between polymer chain and surfactant tails.47 The preferential interaction of PEO with SDS and not with cationic surfactants has been revealed by atomistic MD simulations.48 By this study preferential interaction of PEO with anionic micelles was shown to be due to the direct electrostatic interactions between the micelle and the polymer even though the polymer carries no charge. The four PSC’s in the present study are PA1-S (PAADoTA), PA0-S (PAH-DoTA), PM1-S (PMA-DoTA), and PM0-S (PMH-DoTA). We use 30 repeat unit PE chain following the experimental study in which such short chains were used to study the interaction between PAA and DoTA.20 The chemical structures of the repeat unit of PAH and PMH are given in Scheme 1. The schematic and atom numbering of a single DoTA surfactant is provided in Scheme 2. Scheme 1. Chemical Structure of the Repeat Unit of Unionized PAH and PMHa

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Fully ionized PAA and PMA are in which the COOH groups are present as COO−.

C

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reported for this surfactant (Nagg = 47).56 The simulated system consists of a cubic box containing the preassembled DoTA micelle centered in the box with periodic image distance of 6 nm. The system was then solvated with 6300 SPC water molecules.58 An adequate number of Cl− counterions were added to maintain electroneutrality of the solution. Energy minimization was performed on the system subsequent to the addition of water molecules and ions to maintain the maximum energetic force on any atom to be less than 1000 kJ mol−1 nm−1. This was followed by 100 ps each of NVT simulations at 300 K and NPT simulations at 1 atm with position restraints on surfactant molecules so as to enable structural relaxation of water molecules. The final sampling simulations were carried out for 40 ns in the NPT ensemble with position restraints on surfactant headgroups using a force constant value 1000 kJ mol−1 nm−2 and water geometry constrained using the Settle algorithm.59 For analysis, coordinates were written after every 500 steps. The radial distribution functions, the radial density profiles measured outward from the micelle center of mass, the micelle radius, and the solvent accessible surface area (SASA) were calculated and compared with data available in the literature from experiments and prior simulation studies. Simulations of Free PE Chains in Aqueous Solution. Atactic polymeric chains with a degree of polymerization (n = 30) were constructed by a random assignment of dihedral angle values at the backbone bonds. The degree of ionization was varied by deprotonation of the carboxylic acid groups along the chain. The charge density (f) was set as nc/n, where nc is the number of charged monomers for the PE chain. Two types of chains, differing in f, were used: the fully ionized chain ( f = 1) where all the carboxyl groups are in COO− form and the unionized chain ( f = 0) where all the carboxyl groups are in the COOH form. The initial configuration of the chain in aqueous solution was generated by the placement of a fully stretched (all trans) PE chain in a cubic box (edge length 7 nm) along with around 7500 SPC water molecules. In the case of chains with f = 1 (PAA and PMA), an adequate number of Na+ ions were added to maintain charge neutrality. For un-ionized chains with f = 0 (PAH and PMH), the Na+ ions were not added as the chain has zero charge and all carboxyl groups are in the COOH form. The solvated system was subjected to energy minimization without any constraints using the steepest descent method to keep the maximum force on any atom in the system to values below 1000 kJ mol−1 nm−1. This was followed by NVT and NPT simulations with position restraints on the polymer chain, with no constraints on the degrees of freedom of water molecules so that these are relaxed and the temperature and pressure are at their equilibrium values. The final simulations were performed in the NPT ensemble with the water geometry constrained using the Settle algorithm.59 For analysis, coordinates were written after every 500 steps. All MD simulations were performed at a temperature of 300 K. Typically 25−30 ns simulations were performed for the ionized chains and 20 ns for the un-ionized chains, from which the last 10 ns was used for the sampling and analysis during which the potential energy and Rg of the chain remained stable, showing sufficient trans−gauche conformational transitions indicating appropriate sampling. Simulations of DoTA Micelle with PE Chain. The procedure used here follows those in practice used for earlier studies.47,48 The PE chains with varying charge densities ( f = 1 and 0) were used in the simulation with the cationic DoTA surfactant micelle (Nagg = 47). To prepare the PE−micelle

a

N is the N atom, and HM is the methyl group belonging to the surfactant head along with the C1 carbon. C2 to C12 carbons correspond to the tail of the surfactant.

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SIMULATION METHODOLOGY AND DETAILS All simulations were carried out using GROMACS 4.0.7 molecular dynamics package49 with GROMOS96 45a3 force field50 parameters which has been used extensively for aqueous solution of polar polymers and PEs. In an earlier study, conformational chain properties of PAA and PMA in dilute aqueous solution with varying charge density were reported using GROMOS 53a6 force field by atomistic molecular dynamics (MD) simulations.51 Solvent molecules and the Na+ counterions were taken into account explicitly in the simulations by which the conformational properties like the radius of gyration (Rg) were calculated in agreement with experimental values. Notably, the difference in the distribution of the counterions with regard to the PE backbone structure was brought forth. Na-PMA in water showed a stronger correlation with counterions in comparison to Na-PAA. This is in accordance with the effect of solvent quality on the PE chain wherein water is a poor solvent for PMA (with hydrophobic methyl groups) as compared to PAA. It is known that in poor solvents counterions tend to correlate with the polyion chain relatively stronger than in good solvents.6 The force field parameters for PAA and PMA are similar in both GROMOS 45a3 and 53a6 force fields and are provided in the earlier work on PEs.51 GROMOS 45a3 force field has been used here following the earlier reports on the simulations of alkylammonium surfactants using this particular force field.48,52 The partial charges on DoTA+ cation were taken from the literature on molecular dynamics of these micelles which were modeled using GROMOS 45a3 force fields.48,52 The CH3 and CH2 groups of the surfactant as well as the polymer chains were described by united atoms. The polar hydrogens of the poly(carboxylic acid)s PAH and PMH were treated explicitly. The Ryckeart−Bellemans torsion potential53 was used to quantify the dihedral angle rotation about the aliphatic backbone bonds in the PE chains and the surfactant. For other torsional angles in the PE chains, the proper torsion potential of the GROMOS parameter set was used. The headgroup of the surfactant was defined as C1, N, CHM1, CHM2, CHM3, and the tail comprised C2−C12 atoms (Scheme 2). The initial coordinates of surfactant molecules and polymer chains were generated using the Materials Studio Visualizer.54 Final trajectories were visualized using VMD.55 In all simulations the minimum image criteria were followed so as to avoid unwanted contacts between periodic images during the course of the simulation. Simulations of DoTA Micelle. Initially atomistic MD simulations for spontaneous micelle formation of DoTA were carried out for simulation trajectory of 200 ns which gave aggregation number (Nagg) of 38, which was lower than the experimental values.56 Hence, we used a preassembled micelle structure (Nagg = 47) which was generated using the PACKMOL program,57 the aggregation number for packing the DoTA micelle being similar to the experimental value D

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of the micelle water is completely expelled beyond which the distribution function is nonzero. The DoTA micelle−water interface starts at a distance of 1 nm. The distribution of the surfactant headgroups around the COM shows a maximum at 1.9 nm. The appearance of this peak corresponding to the surfactant headgroups indicates the transition between the hydrophobic micelle core and the hydrophilic micelle shell. Figure S1 also shows that Cl− ions are distributed on the micellar surface near the headgroups. This can be observed in a better way in the radial distribution function (RDF) between the N atoms (micelle) and the Cl− ions as shown in Figure S2a with a broad peak at around 0.5 nm corresponding to the counterion layer located on the micelle exterior. This layer extends up to a distance of about 0.65 nm from the nitrogen atoms. The interaction between water and the surfactant head methyl group atoms (CHM) and the atoms adjacent to it (C1 and C2) can be deciphered from the RDF’s also given in Figure S2b. Water interacts strongly with headgroup atoms showing a peak at around 0.36 nm followed by a shallow peak at 0.54 nm. The aliphatic groups which connect the tail with the headgroup show two peaks in the same position as that of the headgroup atoms, thereby suggesting that water molecules are able to migrate past the headgroup layer in order to establish close interaction with atoms of the inner headgroup carbons (C1 and C2). To summarize, Cl− ions are mainly located on the outside of the micelle surface in close contact with the surfactant headgroups. These results are in agreement with the atomistic simulations of alkyltrimethylammonium surfactant micelles reported in the literature.48,52 Conformations of Free PE Chains. PE chains having 30 repeat units at two different conditions of f were simulated in dilute aqueous solution. Equilibrium conformations of the chains were then established after sufficient sampling. The fully ionized chains (PAA and PMA) are in bent conformations due to electrostatic repulsions between ionized units. The unionized chains (PAH and PMH) are in coiled form due to the presence of COOH groups all along the chain, thereby lowering of electrostatic repulsions between the adjacent residues. The evolution of Rg for the single PE chains as a function of time during the MD simulation is given in Figure S3. The averaged Rg values obtained from the simulations are 1.48 ± 0.09 nm (PAA), 1.43 ± 0.06 (PMA), 0.70 ± 0.01 nm (PAH), and 0.79 ± 0.01 nm (PMH). Rg of fully ionized PAA chain with variation in number of repeat units were calculated from atomistic and coarse-grained MD simulations and compared with results from dynamic light scattering experiments by Wiegand et al.65 An extrapolation of these values for a PAA chain of 30 repeat units gives a value in the range of 1.45 nm, which is in agreement with the Rg value derived from MD simulation of the present study. Polyelectrolyte−Surfactant Complexes. Snapshots of the PSC’s formed between the PE chains and the DoTA micelle during the simulations are shown in Figure 1. Visual inspection shows that PAA being anionic is strongly adsorbed onto the DoTA micelle surface in the complex PA1-S. The PAA chain is able to wrap around the micelle within 5 ns of the simulation time and thereafter remains as a stable complex. The un-ionized chain, PAH, also forms a stable complex (PA0-S) with the cationic DoTA micelle. PAH chain which is in a coiled form gets adsorbed on to the micellar surface in the coiled form itself. In the PM1-S complex, the anionic PMA chain is not fully in contact with the micellar surface, and a part of the chain

systems, an equilibrated conformation of a 30 repeat unit equilibrated PE chain was added within 10 Å of the surface of an equilibrated DoTA micelle. A cubic box (edge length 6.5 nm) with around 6800 water molecules was used. An adequate number of Na+ and Cl− ions were added to maintain charge neutrality in the system. The initial energy minimization was performed by restraining the surfactant and the PE chain, thus permitting structural relaxation of water molecules. This was followed by 100 ps each of NVT and NPT simulations at 300 K with position restraints on the surfactants as well as the PE chain. Final simulations were done in the NPT ensemble with position restraints used only on the headgroups (surfactants) and by use of the Settle algorithm to constrain water geometry.59 Equilibration of the system was monitored using Lennard-Jones (LJ) and electrostatic potential energy of interaction between the micelle and the PE chain. The dispersion interactions were calculated as the sum of pairwise LJ interactions between all micelle atoms and PE atoms. The electrostatic Coulombic potential between the micelle and the PE chain was also calculated in a similar way. The total simulation time was typically 40 ns with the last 20 ns used for sampling and analysis. For analysis, coordinates were written after every 500 steps. Simulation Specifications. The equations of motion were integrated using leapfrog algorithm with a time step of 2 fs. Final sampling simulations were carried out in the NPT ensemble, with the temperature and pressure maintained at 300 K and 1 atm respectively using the Berendsen coupling scheme.60 Periodic boundary conditions were applied with the minimum image convention.61 LJ interactions were terminated beyond 1.4 nm along with the use of continuum correction for the longer range contributions. Long-range electrostatic interactions were calculated with the particle mesh Ewald (PME) method with a real space cutoff of 1 nm and maximum FFT grid spacing of 0.12 nm and cubic interpolation order.62,63 Trajectory snapshots were collected at intervals of 4 ps. Neighbor lists were updated and utilized every tenth integration step. Bonds involving hydrogen were constrained with the LINCS64 algorithm, and SPC water was kept rigid using the Settle algorithm.59

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RESULTS AND DISCUSSION DoTA Micelle Structure. The Rg value of the simulated micelle is 1.59 nm. The radius of the spherical micelle Rsp is defined as the root-mean-square (rms) distance of the nitrogen (N) atoms from the micelle COM, which is 1.90 nm. The radius of the hydrocarbon core Rc measured by the rms distance from the C1 atoms to the micelle center of mass is 1.86 nm. The solvent accessible surface area (SASA) of the DoTA micelle was calculated and compared with the results available in the literature. The total SASA of DoTA micelle (Nagg = 47) is found to be 110.5 ± 2 nm2, which is comparable to the value 105.9 nm2 (Nagg= 40) reported for the DoTA micelle.48 The snapshot of equilibrated preassembled micelle is given in Supporting Information Figure S1 along with the density profiles measured in spherical shells radiating from the micelle center of mass (COM). The density profile shows that the tail atoms cluster near the center, the head atoms are near the micellar surface, and the Cl− counterions are loosely dispersed around the head region. A hydrophobic environment is created in the region of the tail atoms from where water molecules are completely excluded. Water density increases while moving toward the micellar surface. Up to about 1 nm from the COM E

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Energetics. The LJ and electrostatic Coulombic energies between the PE chain and the micelle during the formation of the PSC’s were monitored during the MD simulation trajectory and are given in Figure 2. The energies are found to gradually drop during the initial period of the simulation and beyond 10 ns remain constant for PA1-S, PA0-S, and PM1-S complexes (Figures 2a, 2b, and 2c, respectively). In the case of PM0-S (Figure 2d), it is found that the energies remain unchanged until about 10 ns and drop drastically at around 11 ns where the association between the PMH chain and micelle starts and thereafter remains constant. Visual inspection shows that the complex PM0-S is formed between 10.5 and 11 ns of the simulation time and thereafter remains stable. One can also find out the distinct differences in the energy characteristics between the complexes formed with the cationic surfactant micelle in the case of ionized versus un-ionized chains. For PA1-S and PM1-S, there is a sharp as well as an appreciable reduction of Coulomb energy between the PE and the micelle with time as compared to the LJ potential. The reverse holds true for the un-ionized chains in the complex formation in which case there is a steep decrease in the LJ potential with time, as compared to the Coulomb potential, as in the case of PA0-S and PM0-S. This sheds light on the difference in the driving force of association of the ionized vs un-ionized PE chains with DoTA micelle. For the fully ionized PAA and PMA chains, intermolecular association with the DoTA micelle is driven by electrostatic interactions whereas for the un-ionized PAH and PMH chains the association is largely due to van der Waals interactions. This observation is consistent with the interpretations derived from ITC experiments on PAA−DoTA interactions at different f values of the PAA chain,17 which have pointed to the electrostatic interaction predominantly being responsible for

Figure 1. Snapshots of the PSC’s derived from the MD simulations. For the surfactant micelle, the headgroup atoms are blue and the tail atoms are green. For the PE chain, carbon atoms are yellow, oxygens are red, and hydrogens of PAH and PMH are white. Water and counterions are not shown here for clarity.

forms a tail in the aqueous solution. In the PM0-S complex as well, PMH chain binds to the micelle in the coiled form.

Figure 2. Nonbonded energy contributions between the DoTA micelle and the PE chain in the PSC’s as a function of time during the MD simulation. F

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Figure 3. Radial density profiles measured outward from the micellar COM in the PSC’s derived from MD simulations. The graph for Cl− ions is multiplied by 5 for clarity.

the association in the case of ionized PAA interacting with DoTA micelle (charge density, α > 0.3) and hydrophobic forces leading to complex formation between PAA chains (α < 0.3) and DoTA micelle. Thus, our simulations highlight the importance of van der Waals forces in the association between neutral polymers and cationic micelles as found here for PAH/ PMH with DoTA. The energy terms (LJ and Coulomb) obtained from the MD simulations reveal important insights into the molecular forces responsible for the formation of the complexes. The energy terms corresponding to the interaction between (1) micelle and solvent medium and (2) PE chain and solvent medium are given in Figures S4 and S5, respectively. An increase in the electrostatic potential between the micelle and solvent medium (water and ions) with time is observed due to the dehydration of the micelle surface. This is appreciable only in the case of PA1-S and PM1-S whereas for the corresponding micelles interacting with un-ionized chains the energies are fairly constant. With regards to PE−solvent interactions, PA1-S shows an increase in the electrostatic energy suggesting dehydration of the polymer, whereas for the other cases the values are unchanged. For PA1-S and PM1-S, LJ energy is constant during the entire simulation period. For PA0-S and PM0-S a slight increase in the LJ energy is observed, which remains constant once the complexes are formed. Structure of Polyelectrolyte−Surfactant Complexes. Figure 3 shows the radial density profiles measured in spherical shells radially outward from the micelle COM for the PSC’s obtained from the MD simulation trajectories. The profile for the PA1-S complex (Figure 3a) suggests complete adsorption of the chains on to the charged head groups, i.e., the micellar surface and away from the hydrophobic hydrocarbon surface.

The structural characteristics of the DoTA micelle are otherwise unchanged. The tail atoms exclude water until about 1 nm from the micelle COM, and the peak corresponding to the headgroup atoms is located at 1.9 nm, in a manner similar to that shown in Figure S1 for the free micelle. The radial density profiles in Figure 3a for PA1-S show that the PE adsorption is in the hydrophilic micellar surface (headgroups) region where the peak intensity is at its maximum. The PAA chain is near the surface of the micelle or in other words near the headgroups. It does not penetrate the hydrocarbon−water interface and remains adsorbed mainly on the micellar hydrophilic headgroups throughout the simulation time. The adsorption of the PAA chain on the micelle starts at about 1.5 nm from the micelle COM and extends up to 2.8 nm. The headgroup distribution from the micelle COM starts at 1.2 nm and extends up to 2.7 nm. Thus, the PAA chain and headgroups have a very similar radial density profile, therefore confirming the association of the anionic PAA chain onto the cationic micellar headgroups. This also confirms that the association is purely due to electrostatic interaction in the case of the PA1-S complex. The density profile peak for the PA0-S complex (Figure 3b) shows that the maximum intensity is at the periphery of the headgroup peak for the PAH chain. The un-ionized PAH chain is adsorbed on to the micellar surface, but with lower interaction strength as compared to PA1-S complex. This is described in detail in the later sections on the binding characteristics of the complexes. It is seen that in the case of PM1-S complex (Figure 3c) as well the PMA chain starts adsorbing on the micelle at about 1.5 nm from the micelle COM, and the adsorption extends up to about 3 nm. However, unlike the case of PA1-S complex, the radial density profile for PM1-S shows two peaks: one within the profile G

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Figure 4. RDF of the various atoms of the surfactant and the PE chain in the PSC’s with respect to the micellar COM.

corresponding to the headgroup and one outside the headgroup. The peak intensity for the chain is found to be higher at locations away from the micellar surface. Although there is electrostatic association between the PMA chain and the cationic surfactant headgroups, a portion of the chain forms a tail extending into the bulk aqueous solution. In the case of the PM0-S complex (Figure 3d) as well the PMH chain gets adsorbed on the micelle as well in the coiled form. Another feature that emerges from the density profiles is the release of Cl− ions from the micelle surface due to association with the PE chains. On a comparison of the density profiles of the free micelle with that of micelles having adsorbed PE chains, it is clearly seen that the PE chain is now positioned closer to the micelle headgroups, resulting in the displacement of Cl− ions into the bulk solution. This is evident in the RDP corresponding to only the micellar surface of the PSC’s where the profiles corresponding to the micellar surface of the PSC’s consisting of the head groups, Cl− ions, and the PE chains are shown (Figure S6). The maximum reduction of Cl− ion density is observed in the case of PA1-S complex, wherein the PAA chain acts as an efficient counterpolyion and wraps around the micelle surface. In summary, there is stronger electrostatically driven association seen for PA1-S complex as compared to the other three complexes. The whole PAA chain is wrapped around the micellar surface and in close binding with the micellar head groups in PA1-S. In all four complexes the PE chain (whether anionic or neutral) is positioned mainly near the hydrophilic head groups on the micelle surface and does not penetrate into the micelle. So the PE chain in association with DoTA micelle is positioned on the micellar surface and is neither at the hydrocarbon−water interface nor solubilized in the interior of the micelle. The radial density profile of the

PM1-S complex also indicates a part of the chain adsorbed on to the micellar surface and a part of the chain that forms a tail in the aqueous solution. The RDF’s of the various atoms in the PE chain and surfactant atoms with respect to the micellar COM in the various PSC’s given in Figure 4 show that the adsorbed polymer chain is located above the headgroups and in particular close to the N atoms. The distribution of the various atoms of the micelle and the PE chain clearly sheds light on the nature of binding of the complex where in carboxyl oxygens (O of the PE chain) are closer to the N atoms (micelle). The PE chain does not penetrate into the micelle interior into the hydrophobic core and is found to reside on the micellar surface for anionic as well as neutral chains studied in the present work. The binding occurs through interaction between the N (DoTA)−carboxyl oxygens (O) of the PE chains. For the PA1-S complex the peaks corresponding to N atoms (micelle) and carboxyl oxygens (PE chain) overlap each other, suggesting strong intermolecular interaction. In summary, there is a stronger binding in the case of the PA1-S complex as compared to the other three complexes. The whole PAA chain is woven around the micellar surface and in close association with the micellar headgroups. Binding of PMA chain to DoTA is weaker than that of PAA even though the chain is fully ionized and is anionic. The strength of interaction of the PE with the micelle is found to be PAA > PMA for the anionic chains and PAH > PMH for the neutral chains. The RDP’s also suggest the displacement of Cl− counterions from the micellar surface. In the PSC, PE chains are in proximity to the headgroups when compared to the Cl− ions. This is discussed in a later section on the RDF between the atoms of the PE chain and those of the micelle. The results of the MD simulations also confirm that H

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Figure 5. RDF’s showing the binding of chain onto the micelle. (a) Upper panels: atom-based RDF between the N (micelle) and O (PE). (b) Lower panels: RDF between the center-of-mass of the PE residues and the N atoms.

Figure 6. Atom-based RDF’s between the N and Cl− ions in the free micelle and in the PSC’s.

anionic PAA interacts with DoTA more favorably than anionic PMA, which is in agreement with the experimental data available in the literature.23−26 The RDF’s for the intermolecular pairs formed between the atoms in PE with those from micelle in the PSC’s are shown in Figures 5. Plots corresponding to N−O pair (Figure 5a) show interaction between the headgroup N atoms of the micelle with the carboxyl oxygens of the PE chains. The graph shows a peak at 0.35 nm followed by shoulder peaks at 0.55 nm. The binding strength is almost double in anionic chains as compared to the corresponding neutral chains, or in other words, a stronger binding is observed in PA1-S when compared to PA0-S. This pattern is followed in the PM-S complexes as well. The RDF for the intermolecular pair constituted by the COM of the PE residues and the N atoms (Figure 5b) also shows a peak at 0.5 nm corresponding to the binding of the PE with N of the

micelle. The residue-based RDF’s between the COM of the PE units and the head methyl group atoms (Figure S7) also underline similar characteristics. In this case the peak is at 0.4 nm followed by a shoulder peak at 0.6 nm. Irrespective of the charge density, it is seen that that there is an attractive force that leads to formation of PSC with the contacts between the micelle and the PE chain starting at ∼0.5 nm. The RDF’s clearly illustrate stronger binding of anionic PE chains to the micelle as compared to the neutral PE chains. The Cl− ions are loosely distributed at around 0.5 nm from the micelle N atoms as seen from the RDF for all the PSC’s (Figure 6,) but the peak intensity varies depending on the PE chain charge density. Cl− ion distribution in the free micelle is also given for a comparison in Figure 6 along with those corresponding to the different PSC’s. In the case of PA1-S and PM1-S complexes, although the counterions are at about 0.5 nm from the micelle I

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Figure 7. RDF’s between carboxyl oxygens and Na+ ions in the free anionic chains and adsorbed chains in the PSC’s.

Figure 8. Number of PE repeat units adsorbed onto the DoTA micelle. Dotted line indicates the theoretical maximum adsorption, i.e., the adsorption of all the 30 repeat units in the PE chain.

the case of RDF for the pair constituting the COM of the chain residues and the Na+ ions two peaks are seen at 0.32 and 0.52 nm (Figure S8). The positions of the peaks are similar for free as well as the adsorbed chains, but the peak intensity values differ. Na+ ion binding to the PE chain is stronger for the free chains PAA and PMA in aqueous solution as compared to adsorbed chains in the PSC’s PA1-S and PM1-S. The key feature arising from these plots is the release of Na+ ions into the solvent medium upon PE adsorption. Binding of the anionic carboxyl oxygens of the PE chain with the cationic head groups in the micelle leads to a reduction in the correlation between the Na+ ions and the PE chain which otherwise neutralizes and stabilizes the anionic PE chains. It should be noted here that the PMA chain is relatively hydrophobic as compared to PAA. In aqueous solution a higher density of the counterions in the vicinity of PMA chain backbone than PAA is observed.51 Even in the PSC’s the Na+ counterion density remains higher for PMA than PAA. The lower binding strength observed in PM1-S as compared to PA1-S could be due to the difference observed in Na+ distribution in the two complexes. The relatively hydrophobic nature of the PMA chain leads to a lowering of the strength of interaction with the cationic DoTA micelle. This is shown in Figure S9 where a direct comparison is given for the interaction strength for complexes PA1-S and PM1-S. Now for the PA0-S and PM0-S complexes, since the PE chains are neutral, the interaction is understandably weaker when compared with the anionic counterparts. While making a comparison between the un-ionized chains PAH and PMH (Figure S10), we find that the binding strength is not appreciable, and PAH shows only marginally higher affinity for binding with cationic DoTA in comparison with PMH.

N atoms, the intensity of the curve is considerably lowered when compared to that in the free micelle, suggesting that the correlation between the N atom (micelle) and Cl− ions is weakened now due to the presence of the anionic PE chain. In the case of PA1-S and PM1-S, the Cl− ions are released from the micellar surface due to adsorption of the anionic PE chain which acts as a polymeric counterion. Increase in entropy due to release of counterions from the micelle and the polyion has been suggested as an important driving force for association between the PE and micelles with opposite charges.7,8 For the PA0-S and PM0-S complexes, there is a slight increase in the Cl− ion density when compared to that in free micelle. For the PA0-S and PM0-S complexes, a slightly higher correlation between the N atoms and the Cl− ions is seen due to the adsorption of the un-ionized PAH and PMH chains. Cl− ions move closer to the headgroup atoms when compared with the free micelle due to favorable interaction with the un-ionized chains. This suggests that adsorption of the un-ionized chains on the micelle leads to a slightly higher counterion density near the headgroups. Such an increase in the counterion binding as compared to the situation of the free micelle has been previously observed in MD simulations of adsorption of PEO onto SDS (anionic) micelle.47 The distribution of Na+ ions (counterions for the anionic PE chains, PAA and PMA) is shown in Figure 7 with respect to the carboxylate oxygens as well as the PE repeat units. The RDF’s between the carboxylate oxygens and the Na+ ions in the free PE chain as well as the adsorbed PE chains in the PSC’s (viz., PA1-S and PM1-S, respectively) are shown. In this case two sharp peaks are seen at 0.24 and 0.44 nm corresponding to condensed Na+ ions and solvent-separated ions, respectively. In J

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Figure 9. (a) Snapshot of the PA1-S complex derived from the simulation with no position restraints on the surfactant head groups. The headgroup atoms are blue, and the tail atoms are green. For the PE chain, carbon atoms are yellow and oxygens are shown in red. Water and Cl− ions are excluded in the image for better clarity. (b) Radial density plot of the PA1-S complex measured outward from the micellar COM. The graph corresponding to Cl− ions is multiplied by 5 for clarity.

Solvent Accessible Surface Area (SASA). The SASA values of the free micelle as well as the micelle in the PSC’s observed from the simulations are given in Table 1S. Rg values of the free micelle as well as those in the PSC’s are also given in Table 1S. It is seen that Rg of the DoTA micelle is unchanged upon PE adsorption. SASA values of the micelles as a function of simulation time in the course of the trajectory are presented in Figure S11 where a reduction in the hydrophilic surface area of the micelle upon polymer adsorption occurs, and this is clearly observed in the case of PA1-S. PM1-S and PA0-S show a similar extent of reduction in hydrophilic area, and PM0-S shows the least. Because of PE adsorption, a reduction in the exposed surface area to water is observed in the case of PA1-S. For PA1-S, there is a noticeable decrease in the hydrophilic surface area (4.4 nm2) and increase in the hydrophobic surface (2 nm2) area of the micelle upon polymer adsorption. This can be interpreted as the masking of the hydrophilic headgroups of the micelle by the adsorbed PAA chain by which they are rendered unavailable for solvent. PM0-S shows the least extent of reduction in the hydrophilic SASA, as only a few charged headgroups are blocked by PMH chain and the total SASA of the polymer adsorbed micelle in PM0-S is similar to the free micelle. Number of Repeat Unit Adsorption with the Micelle. Figure 8 shows a rough approximation of the number of contacts between the micelle and the PE chain in the PSC during the MD simulation. A repeat unit is taken to be adsorbed on the micelle if the distance between the carboxyl oxygens of the PE chain and the N atoms of the micelle are within a distance of 0.5 nm. The averaged number of repeat units adsorbed in the complexes in the last 10 ns of the simulation was obtained as 30.0 ± 1.0 (PA1S), 13.5 ± 1.0 (PA0S), 16.7 ± 1.0 (PM1S), and 10.9 ± 0.9 (PM0S), respectively. Thus, the repeat unit adsorption is 100% and 55% for anionic PAA and PMA chain, respectively. The corresponding values are 45% and 36% respectively for PAH and PMH. Interaction with Water. The RDF’s representing the interaction of the headgroup atoms of the DoTA micelle with water in the PSC’s are given in Figure S12. The RDF for the pair consisting of N atoms of the micelle and water oxygens shows a peak at 0.45 nm for the free micelle and for the complexes. For PA1-S, the peak intensity is only slightly lower,

suggesting a marginal reduction in the interaction of the N atoms of the micelle with water upon complex formation. The interaction of poly(methacrylic acid)-based complexes PM1S and PM0-S with water, in particular for the N atom, is similar to that in the free micelle. The RDF’s corresponding to methyl groups in the surfactant head with respect to water show a lower interaction with water oxygens upon complex formation, thus implying a very small amount of dehydration of the micelle upon chain adsorption. Now considering the interaction of C1 carbons with water oxygens, no change is seen as a result of complex formation. A direct comparison between the free chains and adsorbed chains (in the PSC’s) with regards to their interaction with water is shown in Figure S13. The backbone carbon atoms of the chain are dehydrated in the complex PA1-S where there is a strong interaction between the PAA chain and the micelle. PAH chain in the PA0-S complex also shows less hydration by water. The hydration of the adsorbed chains in the PM1-S and PM0-S complexes is similar to that seen for the free chains in solution. Conformation of PE Chains in PSC’s. The Rg values for adsorbed chains obtained from the simulations are 1.26 ± 0.03 nm (PA1-S), 1.13 ± 0.04 nm (PM1-S), 0.711 ± 0.01 nm (PA0S), and 0.803 ± 0.03 nm (PM0-S). The evolution of Rg and end-to-end distance of the PE chains during the formation of PSC’s are shown in Figures S14 and S15, respectively. Anionic chains PAA and PMA show significant shrinkage upon adsorption on to the micelle. The Rg value of the free chains PAA and PMA in water obtained from the simulations are 1.48 ± 0.09 and 1.43 ± 0.06 nm, respectively. Ionized chains shrink due to adsorption as the negative charges are neutralized by the positively charged cationic headgroups of the micelle. This observation is consistent with the experimental and theoretical data on polyelectrolyte−micelle interactions of opposite charge.1,2,4,17 The shrinkage of the anionic PAA chain due to adsorption on DoTA micelle has been observed before, and this has been attributed to the electrostatic binding of the surfactant molecules onto the carboxylate groups of anionic PAA.17 This process results in charge neutralization of the chain leading to its shrinkage. Binding of the PAA chain onto the DoTA micelle is also accompanied by the release of counterions from the micelle (Cl−) as well as the PAA chain (Na+). During formation of the PSC, the condensed Na+ counterions on the ionized PAA chain are released, and charge neutralization occurs now K

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Simulations with Different Starting Conformation for Anionic PE Chains. We have also carried out additional simulations for complex formation in the case of PA1-S and PM1-S. Here the anionic PE chain in a coiled conformation was placed on the cationic DoTA micelle. The final snapshots of PA0-S and PM0-S were used respectively as starting conformations for PA1-S and PM1-S by removal of the protons and thereby balancing the charge. The final snapshots of PA1-S and PM1-S derived from these simulations are given in Figure S19 and are seen to be similar to those shown earlier as in Figures 1a and 1c for PA1-S and PM1-S, respectively. The anionic PAA chain wraps around the cationic DoTA micelle whereas the PMA chain adsorbs partially onto the micelle and forms a tail extending into the bulk solution.

through association with the oppositely charged surfactant head groups, which leads to PE chain shrinkage. A similar behavior is seen in the case of anionic PMA chain in PM1-S complex. The un-ionized chains PAH and PMH in the complexes PA0-S and PM0-S, respectively, remain in the coil form and do not exhibit any change in conformation. The decay of the autocorrelation functions of the backbone torsion angles of the chains during the association process is given in Figure S16. The decay of the adsorbed chains is slower than that of the corresponding free chains in aqueous solution. The change in the backbone torsional angle of one of the repeat unit (middle of the chain) as a function of time is also given in Figure S17. The torsion angle change along with the change in Rg shows that the chain undergoes conformational transition while getting adsorbed on to the micelle from solution. Simulation of PA1-S with No Position Restraints on the Surfactant Headgroups. An additional simulation was carried out in which the position restraints on the surfactant headgroups were removed during the production run for the PA1-S system. Here also we observe that the PAA chain wraps around the micelle and is adsorbed on the surfactant headgroups. The final snapshot of the PA1-S complex and the radial density profile obtained in this case are given in Figure 9. The tail atoms exclude water up to a distance of about 0.8 nm from the micelle COM, and the peak corresponding to the headgroup atoms is located at 1.7 nm. The PAA chain is located near the micelle headgroups, and the adsorption of the PAA chain on the micelle starts at about 1.5 nm from the micelle COM and extends up to 2.8 nm. The headgroup distribution from the micelle COM starts at 1 nm and extends up to 2.3 nm. The Cl− ions are distributed on the micellar surface and is seen at around 1.5−3 nm from the COM of the micelle. There are slight differences in the radial density profiles obtained for the PA1-S complexes derived from the simulations with and without position restraints on the head groups. Notably the peak corresponding to the head groups is broader as seen in Figure 9b when compared to the one in Figure 3 for PA1-S. The final conformation of the complex (Figure 9a) obtained is similar to the one shown in Figure 1a for PA1-S. Simulation of PSC’s with Anionic DoTA Micelle. We also simulated DoTA micelles with inverted charges (i.e., anionic DoTA micelle) in order to probe further the influence of the charge of the headgroups on the interaction between the PE chain and the DoTA micelle. The charges used for the anionic DoTA micelle were taken from ref 48. The simulations showed that there is no association between the anionic PAA and PMA chains with the anionic DoTA micelle. However, the un-ionized chains PAH and PMH associate with the anionic DoTA micelle to form stable complexes. This is clearly seen in the plot showing the adsorption of PE monomers on to the anionic DoTA micelle given in Figure S18. The weak interactions seen in the case of PA1-S and PM1-S are largely due to thermal fluctuations and have been observed previously in the case of interaction of SDS with cationic DoTA micelle.48 These simulations of the anionic and neutral poly(carboxylic acid)s with the anionic DoTA micelle highlight the observation that the driving force for the association between the anionic PE chains and cationic DoTA micelle is electrostatic interactions. There is no interaction with the anionic chains when the charges on the micelle are flipped so that it becomes anionic. In the case of PA0-S and PM0-S (with anionic DoTA), the numbers of monomers adsorbed are approximately 7 ± 1.31 and 6.5 ± 1.5, respectively.

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CONCLUSIONS Atomistic MD simulations presented in this study pertain to PSC’s formed between weak polyelectrolytes and a cationic micelle in aqueous solution without added salt. It is observed that the anionic PAA chain wraps around the micelle with all monomers strongly adsorbed on to the micelle, and the binding is found to be dominated by electrostatics. PAA chain is strongly adsorbed on to the headgroups, i.e., the micellar surface. In the PM1-S complex, a part of the anionic PMA chain, not in contact with the micellar surface, forms a tail that extends into the aqueous solution. The binding strength of PAA is higher than that of PMA. Irrespective of the charge density on the PE chain, it is observed that there is an attractive force that binds the complex with the contacts between the micelle and the PE chain at ∼0.5 nm. Fully ionized chains show more affinity for complex formation as compared to the corresponding un-ionized forms. Predominantly, electrostatics driven association along with favorable dispersion energy lead to complex formation for PSC’s involving anionic chains and the cationic micelle. For the un-ionized chains, vdW type dispersion forces are significant and dominant toward complex formation. The simulations show that due to adsorption of the anionic PE chains on to the DoTA micelle, Cl− ions are released into the bulk solution. The maximum reduction of Cl− ion density near the micellar surface is seen for PA1-S complex wherein the PAA acts as an efficient counter polyion. A reduction in the correlation between the Na+ ions and the chain backbones (in PAA and PMA) is also observed in the PSC’s. This is expected as the anionic PE chains minimize the electrostatic repulsion between its charged residues by binding with the cationic head groups of the micelle. Thus, the entropy gained by the release of counterions (Cl− and Na+) into the medium also facilitates strong interaction between the micelle and the anionic PE chains. Even in the PSC’s the Na+ counterion density remains higher for PMA than PAA. The relatively hydrophobic nature of the PMA chain leads to a higher counterion correlation with Na+ ions, thus lowering its interaction with the cationic DoTA micelle. We see a reduction in the hydrophilic SASA of the micelles upon PE adsorption, and the maximum reduction is observed in the case of PAA. Anionic chains PAA and PMA show distinct shrinkage upon adsorption on to the micelle as compared to the corresponding free chains in solution where as no conformational change is observed in the case of the corresponding neutral chains. The information obtained from the simulations is consistent with the experimental data on these systems. It also sheds light on the nature of binding and association in these PSC’s. The differences in the affinity for L

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complex formation between the two PE’s PAA and PMA are also correctly brought forth.

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ASSOCIATED CONTENT

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b04680. Figure S1: (a) snapshot of the equilibrated DoTA micelle and (b) radial density plot of the DoTA micelle measured outward from the micellar COM; Figure S2: RDF’s between the (a) DoTA micelle N atoms and Cl− counterions and (b) DoTA headgroup atoms and the water oxygens; Figure S3: Rg of the free PE chains in aqueous solution; Figure S4: nonbonded energy contributions between the DoTA micelle and solvent medium; Figure S5: nonbonded energy contributions between the PE chain and solvent medium; Figure S6: radial density profiles of the micellar surface in the PSC complexes; Figure S7: RDF between the center-of-mass of the PE residues and the head methyl group atoms; Figure S8: RDF between the center-of-mass of the PE residues and the Na+ ions; Figure S9: RDF’s showing the comparison of PSC’s formed between anionic chains PAA and PMA with DoTA; Figure S10: RDF’s showing the comparison of PSC’s formed between un-ionized chains PAH and PMH with DoTA; Figure S11: solvent accessible surface area of the DoTA micelle in the PSC’s; Figure S12: interaction of the headgroup atoms of the DoTA micelle with water before and after chain adsorption; Figure S13: interaction of the PE chain backbone carbon atoms with water in the PSC’s before and after chain adsorption; Figure S14: Rg of the adsorbed chain in the PSC’s; Figure S15: end-to-end distance of the adsorbed PE chains in the PSC’s; Figure S16: autocorrelation functions of the backbone torsions of the PE chain as a function of simulation time; Figure S17: backbone dihedral (RB) of the 15th repeat unit of the adsorbed PAA chain in the PA1-S complex as a function of simulation time; Figure S18: number of PE repeat units adsorbed onto the anionic DoTA micelle; Figure S19: snapshot of the PSC’s derived from anionic chains (with a different starting conformation); Table S1: Rg (DoTA) and the solvent accessible surface area (SASA) of the PSC’s derived from the MD simulations (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected], [email protected]; Tel 091-044-22574184; Fax 091-044-22574152 (M.S.S.). Notes

The authors declare no competing financial interest.

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REFERENCES

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ACKNOWLEDGMENTS

M.S.S. thanks DST, New Delhi for Research Funds (DSTWOS-A/CS-63/2008), under the Woman Scientist Scheme. We thank the High Performance Computing Facility (HPCE) at IIT-Madras for the computer time. M

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