Molecular Dynamics Simulations of PAA–PMA Polyelectrolyte

Aug 10, 2012 - (2) All minimization and molecular dynamics simulations were performed using GROMACS ..... For the same charge density, PAA showed high...
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Molecular Dynamics Simulations of PAA−PMA Polyelectrolyte Copolymers in Dilute Aqueous Solution: Chain Conformations and Hydration Properties 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: Atomistic molecular dynamics simulations of copolymers of poly(acrylic acid) (PAA) and poly(methacrylic acid) (PMA) in dilute aqueous solution were performed as a function of charge density, in explicit solvent medium and counterions. The studied polyelectrolytes follow a general behavior of chain expansion with charge density until a point where the repulsion between the electrostatic charges between the anionic residues is effectively neutralized by the counterions. The average persistence length is found to increase and levels off at higher charge densities, and the values imply the chains to be flexible. With increase in PMA content in the chain, counterions show increased correlation with chain backbone and a systematic reduction in the number of water molecules in the first hydration shell. The intermittent hydrogen-bond correlation function for the hydrogen bonds between the chain residues and water decays faster for PAA chain as compared to PMA, indicating a rigid hydration layer for the latter. The shorter H-bond lifetimes coupled with the slower relaxation indicate that MA−water H-bonds break more easily than those of AA−water H-bonds, but the water molecules remain in the vicinity of the chain because of slow diffusivity and can easily reform the bonds.

I. INTRODUCTION Polyelectrolytes are polymers that are soluble in polar solvents with release of ions. Classic examples of synthetic polyelectrolytes with intrinsically flexible and linear backbones are poly(acrylic acid) (PAA), poly(methacrylic acid) (PMA), and sodium poly(styrene sulfonate). PAA and PMA are weak anionic polyelectrolytes for which the dissociation of acid groups can be adjusted with pH. The solution properties of polyelectrolytes are characterized by complex interactions involving poly ions, counterions, and the solvent molecules. In neutral polymers, the dilute solution properties are controlled by excluded volume interactions between polymer chains and the solvent. In the case of polyelectrolytes, there are additional electrostatic interactions that occur between the charged species and the solvent molecules. The different atomic level electrostatic interactions arising from the presence of charges pertaining to chemically different species along the chain are responsible for the peculiar behavior observed in polyelectrolyte systems. Water-soluble synthetic polyelectrolytes are employed in a wide range of industrial and biomedical applications and have been studied extensively as simple prototypes of natural polyelectrolytes such as nucleic acid, proteins, etc. Application of pH-responsive synthetic polyanions including PAA, PMA, and polyethacrylate (PEA) in drug delivery systems has been reviewed.1 These polyanions have been studied as complexes with biomolecules or in the preparation of liposomal formulations, which are pH-sensitive. Electrostatic interactions between these charged molecules dictate a wide range of molecular processes. An example is the use of flexible synthetic polyelectrolytes in the precipitation of proteins from aqueous solution.1 PAA has tremendous applications in industry as dispersing agents, scale inhibitors © 2012 American Chemical Society

in laundry processes, thickening agents in water borne formulations, water absorbants, etc. The study of these systems is also fundamentally important, and a polyelectrolyte such as Na−PAA (sodium polyacrylate) serves as a prototype for the study of the behavior of natural polyelectrolytes. In a recent paper, we presented the conformational behavior of PAA and PMA in dilute aqueous solution with varying charge density using atomistic molecular dynamics (MD) simulations.2 In that study, the 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 polyelectrolyte backbone structure was brought forth; evidently Na−PMA (sodium polymethacrylate) 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 polyelectrolyte chain wherein water is a poor solvent for PMA (with hydrophobic methyl groups) as compared to PAA.3 It is known that in poor solvents counterions tend to correlate with the poly ion chain relatively stronger than in good solvents.4 In continuation of that work, in this Article we present atomistic MD simulations of atactic PAA−PMA random copolymers in dilute aqueous solution in the entire range of charge density with explicit solvent medium and counterions. We present a detailed analysis of the hydration properties and conformational Received: Revised: Accepted: Published: 10833

May 14, 2012 July 31, 2012 August 1, 2012 August 10, 2012 dx.doi.org/10.1021/ie301244n | Ind. Eng. Chem. Res. 2012, 51, 10833−10839

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Lennard-Jones interactions were truncated and shifted at a cutoff rc = 0.9 nm. The Coulomb potential with a reactionfield10 correction was employed for the calculation of the electrostatic energy (cutoff at 1.4 nm), with the reaction field dielectric constant εRF taken as that equal to the value for water (εRF = 78.5). Bond lengths were held constant using the Shake procedure.11 Time step of 2 fs was used to integrate the equations of motion with a leapfrog algorithm. The neighbor list was updated every 10 steps with a list cutoff of 1 nm. Other parameters include a weak coupling to a temperature (T = 300 K) and pressure (p = 1 atm) bath with coupling times of τt = 0.1 ps and τp = 0.5 ps (water compressibility 4.5 × 10−10 kPa−1).12 Typically 15 ns simulations were performed, from which the last 10 ns was used for sampling and analysis. For analysis, coordinates were written every 500 steps. All MD simulations were performed at 300 K.

behavior of these copolymer chains in aqueous solution specifically looking at PAA−PMA copolymers, which can serve as potential candidates for polymeric dispersant systems in which the units of the relatively hydrophobic PMA can be used to vary or control the interactions with other organic molecules, surfactants, etc., present in water.

II. METHODOLOGY AND COMPUTATIONAL DETAILS The detailed description of the methodology and the parameters employed in the simulations are provided in the earlier study.2 All minimization and molecular dynamics simulations were performed using GROMACS simulation engine (version 4.0.7).5 The GROMOS 53a6 parameter set was used for the MD simulations.6 The RB torsion potential was used to describe the dihedral angle rotation about the aliphatic backbone bonds.7 For other torsional angles, the proper torsion potentials belonging to the GROMOS parameter set were used. The force field parameters used in this set of simulations are provided in ref 2. Atactic random copolymer chains with different mol % of PAA and PMA content were studied. These are referred to as CP-1 (30 mol % PMA), CP-2 (50 mol % PMA), CP-3 (75 mol % PMA), and CP-4 (90 mol % PMA). Copolymeric chains were modeled as one atactic strand, with 20 repeat units solvated in 5500 water molecules. The degree of ionization was varied by deprotonation of the carboxylic acid groups at random positions along the chain. The charge density is given as f = Nc/N, where Nc is the number of charged monomers for the polymeric chain. The uncharged form has all carboxyl groups as COOH (f = 0), and the fully ionized chain has all carboxyl groups in the COO− form ( f = 1). Three different ionized forms were simulated and analyzed separately in dilute solutions, by having 5, 10, and 15 carboxylate groups (COO−) along the chain ( f = 0.25, 0.5, and 0.75, respectively). An adequate number of Na+ ions were added to the solvated system to maintain charge neutrality. The homopolymers PAA and PMA are also included in this study for comparison (taken from ref 2), and we present additional analysis of these with inclusion of the detailed H-bonding analysis, intermittent hydrogen-bond (H-bond) autocorrelation functions, and persistence length (Lp). These homopolymers were studied at different charge densities (f = 0, 0.2, 0.4, 0.6, 0.8, and 1).2 The concentration of the polyelectrolyte studied was 0.01 mol/L, and the Na+ counterion concentration is determined to be in the range 0−0.28 mol/L depending upon the charge density of the chain. The United-Atom model was used for the aliphatic carbon atoms and the polar hydrogens treated explicitly in the simulations. The initial structure of the polyelectrolyte chain was taken as an extended conformation. The initial configuration representing the copolymer chain in aqueous solution was generated by placing a fully stretched polyelectrolyte chain in a cubic box along with randomly distributed Na+ counterions and SPC water molecules (simple point charge model).8 This solvated system was subjected to energy minimization without any constraints by using the Steepest Descent method to keep the maximum force on any atom in the system to values below 100 kJ/nm mol. This was followed by NVT and NPT simulations with position restraints on the chain, with no constraints on the degrees of freedom of water molecules so that these are relaxed and the system 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.9 The

III. RESULTS AND DISCUSSION A. Chain Conformational Properties. The radius of gyration (Rg) of the copolymer chains from the MD simulations is provided in Figure 1. The values for the

Figure 1. Variation in Rg for PAA−PMA random copolymers in aqueous solution as a function of charge density. Values for PAA and PMA are from ref 2. (The standard deviations are within 5% for all of the polymers studied here.)

homopolymers PAA and PMA are also given for comparison.2 Snapshots of the copolymer chain conformations at different charge densities are provided in Figure 1S in the Supporting Information. The uncharged chains are in the coiled form with an Rg value of ∼0.65−0.73 nm and expand with an increase in charge density, reaching a limiting value above f = 0.5. This suggests effective screening of the charges along the chain by the counterions, thereby preventing any further chain expansion. The simulations give a Rg value of ∼1 nm for the fully ionized chains of PAA, PMA as well as the copolymers. It is seen that maximum chain expansion occurs around f = 0.5, beyond which there is very little change in the conformation of the chains. The uncharged forms of all of these copolymers are present as tight coils that expand upon ionization. With ionization, these chains expand to relieve the electrostatic repulsion between the charged monomer residues. Fully ionized chains are more or less in a “bent” conformation, which is farther from a truly extended rod form. Variations in local polymer chain flexibility can be directly evaluated by a calculation of the persistence length, Lp, of the chains. Lp was calculated for the polyelectrolytes from the atomistic simulations as a function of charge density. It is derived from the information on the cosines of the angles between the consecutive bonds along the main chain, as the number of bonds where the average cosine value reaches a 10834

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Table 1. Computed Average Persistence Length (nm) of the Polyelectroloytes as a Function of Charge Density f

PAA

CP-1

CP-2

CP-3

CP-4

PMA

0 0.2 0.25 0.4 0.5 0.6 0.75 0.8 1.0

0.35 ± 0.02 0.43 ± 0.08

0.43 ± 0.05

0.55 ± 0.08

0.55 ± 0.03

0.53 ± 0.03

0.64 ± 0.05 0.66 ± 0.05

0.60 ± 0.07

0.57 ± 0.03

0.56 ± 0.13

0.62 ± 0.06

0.64 ± 0.08

0.73 ± 0.10

0.72 ± 0.09

0.70 ± 0.10

1.1 ± 0.16

1.04 ± 0.19

1.1 ± 0.20

0.96 ± 0.18

1.15 ± 0.09

1.04 ± 0.15

1.21 ± 0.27

1.07 ± 0.14

0.45 ± 0.08

0.67 ± 0.04

0.46 ± 0.08 0.86 ± 0.24 1.05 ± 0.19

0.66 ± 0.06 0.93 ± 0.15 1.10 ± 0.14

varied in the range 6.2 nm ( f = 1), 2.9 nm (f = 0.5), to 0.46 nm ( f = 0). The values were found to increase with decrease in salt concentration. It suffices to state in this context that in a dilute aqueous solution where the electrostatic interactions between the chains are completely absent, the chain dimensions must be represented by those derived from the present simulations, which correspond to isolated polyelectrolyte chains. The ionized PAA−PMA copolymers as shown by the simulations for relatively short chains here, as well as the homopolymer PAA and PMA chains studied earlier,2 are found to behave like flexible chains, as is known experimentally for the corresponding homopolyelectrolytes. Of course, it must be borne in mind that the bare (neutral, intrinsic without the electrostatic contribution) persistence length of PAA21 is 1.1 nm in a theta solvent (1.5 M NaCl at 25 °C, a concentration higher than what we have simulated for the ionic strengths here in salt-free aqueous solutions). The simulated persistence length values for PMA chain simulated here agree well with experimental values17 for f > 0.5. What emerges from our present study on the copolymers, as a function of charge density, is that these relatively short chains under dilute simulated conditions as in here behave like flexible macro-ions showing strong ionic-strength dependence (much stronger than that given by Debye−Huckel limiting expression with counterion condensation, as has been indicated also by approximate theoretical studies by Le Bret22 and Fixman23). However, as pointed out by Fixman,23 calculations in those earlier theoretical studies were in good agreement (as tailored specifically for the rigid-rod polyelectrolyte DNA) with experiment, except for very low ionic strength conditions (which is also the case of our present systems) with no added salt or very little added salt. The increase and leveling-off of persistence length has been clearly established for partially neutralized PAA in dilute aqueous salt-free solutions.24 The simulated ionic strength dependence of persistence length in the present work, in that Lp increases with an increase in charge density and levels off, reflects an opposite trend as compared to that shown by experiments21 on K−PAA (potassium salt of PAA) with typically sufficiently high salt concentration. At low ionic strengths, as is the case for chains we have studied here, it is known that flexible polyelectrolytes such as PAA show an increase in Rg and hydrodynamic radius (i.e., chain expansion) accompanying an increase in charge density due to unscreened repulsion between repeat units (i.e., residues) facilitated by the condensed counterions (in this case Na+). As it is well-known that counterions are condensed for PAA and PMA, clearly one must expect these counterions to be condensed onto the backbone for the copolymers as well. The qualitative trend observed for the chain expansion shown by our simulations is in agreement with that successfully shown theoretically by Odijk25

value of 1/e (where e is the unit vector corresponding to the orientation of the ith bond along the backbone), and this point is determined by a linear interpolation of log(cos). The Lp values given in Table 1 are in units of length (nm) obtained as the number of bonds multiplied with the bond length (0.154 nm used for the C−C bond length in the simulations). It is seen that Lp increases with charge density for the chains. With increase in the mol % of the PMA monomers, Lp is found to increase up to a charge density of 0.6. Above f = 0.6, the persistence length values are similar irrespective of the copolymer. Lp of semidilute PAA solutions in the presence of salt have been measured by Muroga et al. using SAXS, and the values were essentially independent of the charge density as well as salt concentration.13 The values reported were in the range 0.8−1.4 nm for PAA, for uncharged as well as ionized chains. Walczak et al. used polarized Raman spectroscopy to investigate the local conformation of PAA in salt-free semidilute solutions as a function of the degree of ionization.14 Their first study14a (Lp values in the range 1.4−1.7 nm with varying charge density) was in agreement with that of Muroga et al., but a second study14b with renewed spectroscopic methods showed that Lp increases with charge density. Tricot et al. have reported 1.2 nm for Na−PAA chain in highly concentrated NaBr solution (theta solvent for PAA) as calculated from viscosimetry methods,15 while in dioxane (theta solvent) it is 1.4 nm as observed from SAXS measurements.16 Pletsil et al. via SAXS studies of semidilute solutions of PMA as a function of degree of neutralization have reported Lp values to be in the range 0.8−1.2 nm.17a,b In a recent report, Lp for un-ionized PMA (in HCl) is found to be 3.6 ± 2.2 nm, and for Na−PMA it is 11 ± 3 nm (studied concentration range of 2−10 g/L).18 It should be noted here that the values reported in the literature for PAA and PMA are in a wide range, and it is not possible to draw a conclusion about the precise experimental values corresponding to these polyelectrolytes. From the simulations presented here, in the case of a 20 repeat unit oligomeric chain of PAA (or PMA), the Lp value increases with charge density, and for the fully ionized chains the value is in the range of 1− 1.2 nm. In a Monte carlo simulation representing polyacrylate in aqueous solution, Carnie et al.20 have reported finite Lp = 1 nm and Rg = 1 nm for a 20 bead fully ionized chain (f = 1), where each bead corresponds to a repeat unit, the results of which are in agreement with our present study. Carnie et al. have also presented the Lp values for chains having up to 320 beads (monomers) in salt concentrations ranging from 0.1 to 0.0001 mol dm−3. Infinite chain persistence lengths were obtained in that study by extrapolation of the distribution of angles of the chain bonds relative to the central bond. For a 320 bead chain at a salt concentration of 0.1 mol dm−3, the values 10835

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for solutions in which the molar poly ion concentration does not exceed the critical value (Cp*) at which the electrostatic persistence length Le becomes equal to and beyond which it exceeds the contour length of the chain. The contour length for the chains in our simulations is 3.1 nm. B. Distribution of Counterions. From the simulated distribution of Na+ ions around the carboxylate oxygens (Figure 2), we find that there is a sharp first peak at 0.21 nm that

Figure 3. Radial distribution function between the center of mass of the polyelectrolyte residues and the water oxygens in the case of fully ionized ( f = 1) chains.

copolymer, the simulations show that the number of H-bonds decreases. The integration of the first peak corresponding to the RDF of the chain residues with respect to the water oxygens gives the coordination number of water molecules at any given time in the first solvation shell. These values are listed in Table 2 and have been obtained by integration of the RDF peak up to

Figure 2. Radial distribution function between the carboxylate oxygens of the polyelectrolyte residues and the Na+ ions.

Table 2. Average Coordination Number of Water Molecules in the First Solvation Shell of the Polyelectrolyte Residues

increases in intensity accompanying an increase in PMA content in the chain. In a comparison of the radial distribution functions (RDF’s) corresponding to the copolymer residues with respect to the Na+ ions (Figure 2S in the Supporting Information), for CP-1, CP-2, and CP-3, we observe that there are only two peaks, one at 0.5 nm and a broad peak around 1 nm, which correspond to ions present closer to the polymer backbone and the solvent separated ion-pairs, respectively. For CP-4, there is an additional peak at 0.35 nm due to condensation of Na+ ions onto the chain backbone. This has been noted previously for Na−PMA also.2 This is due to the relatively stronger correlation of the Na+ ions to the PMA residues in comparison to the PAA residues. This has been ascribed to water being a poor solvent for PMA due to the hydrophobic methyl groups3 and hence the presence of a stronger correlation of PMA with the counterions in aqueous solution. With increase in the interaction strength (MA content in the chain), the peak intensity becomes more pronounced, which is an indication of the localization of the ions near the chain. C. Hydration Behavior. The RDF’s between the center of mass of polyelectrolyte residues to the water oxygens show a well-defined first solvation shell (Figure 3S in the Supporting Information). The number of water molecules within the solvation shell increases with an increase in charge density of the chain. A well-defined hydration shell is observed, irrespective of the charge density, in all systems studied here. With increase in the MA content in the copolymer, a lowering of the peak intensity pertaining to the hydration shell is observed, which is shown in Figure 3 for the fully ionized chains of the copolymers. This is expected as the methyl groups contribute toward the hydrophobicity of the chain and water molecules are gradually displaced from the vicinity of the chain with increase in the MA content. We use a geometric criteria for the definition of a H-bond. A H-bond is assumed to be present if the two oxygens are within a distance of less than 0.35 nm and the O---O−H angle is less than 30°. Regarding the H-bonds between the chain residues and water molecules with an increase in the MA content in the

f

PAA

CP-1

CP-2

CP-3

CP-4

PMA

0 0.2 0.25 0.4 0.50 0.6 0.75 0.8 1

4.6 5.4

4.2

3.9

3.6

3.5

3.4 4.3

5.2

5.0

4.6

4.4

6.2

6.0

5.4

5.2

7.0

6.7

6.5

6.1

7.7

7.4

7.3

6.8

6.1

5.0

6.5 7.2 7.9

5.8 6.3 6.7

a separation distance 0.45 nm. It is observed that as the mol % of MA units increases in the copolymer chain, the number of water molecules in the solvation shell is reduced. The effect of ionization is evident from the increase in the number of water molecules in the hydration shell, across all of the polyelectrolyte chains. Analysis of the structural relaxation of the H-bonds26−29 between the polyelectrolyte and water is described in this section. The simple model proposed by Luzar and Chandler to analyze the hydrogen-bond kinetics in water is used here, which describes the kinetics of protein−water hydrogen-bond breaking and formation.26,27 There is an inter conversion between a “bound state” in which the water molecule is hydrogen-bonded to the polymer residue and a “quasi-free state” in which the hydrogen bond is broken but the water molecule remains within the first solvation shell of the residue site. The dynamics of the H-bonds is characterized by the intermittent H-bond time correlation function, C(t), which is defined as:26

C(t ) =

h(0)h(t ) h

(1)

where h(t) is a hydrogen-bond population operator, which is equal to 1 if a H-bond is present at time t and 0 otherwise. C(t) is the probability that a H-bond present at time t = 0 is also Hbonded at time t and is independent of possible breaking of Hbonds at intermediate times and allows reformation of broken 10836

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bonds. In other words, it measures correlations in time series of bonds independent of possible bond-breaking events. Therefore, it is the intermittent H-bond correlation function. It allows recrossing the barrier separating the bonded and nonbonded states as well as the long time diffusive behavior. Therefore, the relaxation of C(t) provides information about the structural relaxation of a particular type of H-bond. The correlation function corresponding to water−water Hbonds in the bulk is given for a comparison in Figure 4 along

Figure 5. Decay of the intermittent H-bond time correlation function for the hydrogen bonds between the polyelectrolyte residues and water for the fully ionized chains as a function of copolymer composition.

The use of Luzar−Chandler description of H-bond kinetics enables the calculation of rate constants for the breaking and reformation of H-bonds between polyelectrolyte chain and water molecules. The kinetics of the H-bond breakage and reformation is derived from chemical dynamics analysis. According to this formalism, from the reactive flux correlation function K(t), a forward rate constant for H-bond breakage (k1) and a backward rate constant for H-bond formation (k2) are derived.

Figure 4. Decay of the intermittent H-bond time correlation function for the hydrogen bonds in (1) bulk water; and for the fully ionized chains of (2) PAA and water, and (3) PMA and water.

with those for the polyelectrolyte−water H-bonds for the fully ionized chains of PAA and PMA. Figure 4 shows the structural relaxation of the polyelectrolyte−water H-bonds to be much slower than the water−water H-bonds in the bulk. In the case of bulk water, a rapid initial decay in the bond correlation function due to the fast librational and vibrational motion of the H-bonded sites has been observed.30 Water molecules in the hydration layer of the polyelectrolyte chain form stronger Hbonds with it, and hence the relaxation of the polyelectrolyte− water H-bonds is much slower than those corresponding to bulk water. The dynamics of H-bonds is also coupled with the diffusion of molecules. Water diffusion is relatively slow in the presence of polymers, and this allows the reformation of broken H-bonds, and hence leads to slower relaxation of the polyelectrolyte−water H-bonds. While comparing fully ionized PAA and PMA chains, a differential relaxation behavior is observed. It is found that the structural relaxation of PMA− water H-bonds is slower than those of the PAA−water system. A reason for this could be the reduced mobility of water molecules near PMA due to a rigid hydration layer as compared to PAA, and hence a much slower decay of the H-bond correlation function. SAXS studies on semidilute solutions of PMA point to the existence of a monomolecular hydration shell, the density of which for a fully ionized chain is about 10% higher than that of bulk water.17b For a dense hydration layer, the diffusion is slow, and this could lead to a slower relaxation of PMA−water H bonds. In the case of PAA (which is more hydrophilic), the hydration layer could be much less dense, which helps in faster diffusion of water molecules and to the relaxation of the PAA−water H-bonds. Also shown in Figure 5 is the decay of polyelectrolyte−water H-bond correlation function with increase in PMA content in the copolymers, which is found to be consistently slower with increase in MA content (shown here in the case of fully ionized chains). Relaxation of the polyelectrolyte−water H-bonds for the fully ionized chains is slower than those corresponding to partially ionized ones (Figure 6).

−dC(t ) dt

(2)

K (t ) = k1C(t ) − k 2n(t )

(3)

K (t ) =

where n(t) is the time-dependent probability that a H-bond is broken that existed at t = 0 but that the two hydrogen-bonding groups are still within hydrogen-bonding distance. The forward and the backward rate constants for this process are k1 and k2, respectively. The H-bond lifetime in this scheme is given by the inverse forward rate constant: 1 τHB = k1 (4) The values corresponding to the average lifetime of the Hbond between the polyelectrolyte and water are given in Table 3 and are in the range of 1.2−3.4 ps. These values portray a significantly longer lifetime than that for the water−water Hbonds (0.3−0.7 ps).30 The H-bond lifetime is independent of the MA content in these copolymers, and it follows a general trend of increase in lifetime with charge density of the chain. The ability to form H-bonds with water is higher for the charged residues. The presence of relatively strong H-bonds also correlates with higher hydrophilicity of the residues. Water molecules could be bound stronger to the COO− groups than the COOH groups, which result in higher lifetime of the Hbonds formed with the former. The copolymers showed lower H-bond lifetime as compared to the homopolymers bearing the same charge density. For the same charge density, PAA showed higher H-bond life times as compared to the copolymers. We find that polyelectrolyte−water H-bond lifetimes for MAcontaining polymers are shorter than that of PAA-water Hbonds along with a slower decay of the intermittent H-bond correlation function. This suggest that PMA-water H-bonds break more easily than those of PAA−water H-bonds, but the water molecules remain in the vicinity of the PMA chain because of slow diffusivity and can easily reform the bonds. 10837

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Figure 6. Decay of the intermittent H-bond time correlation function for the hydrogen bonds between the polyelectrolyte residues and water as a function of charge density.

■

Table 3. Average Lifetime (τHB, ps) of the H-Bonds between the Polyelectrolyte Residues and Water f

PAA

0.2 0.25 0.4 0.50 0.6 0.75 0.8 1

1.28

CP-1

CP-2

CP-3

CP-4

1.20

1.03

1.33

1.41

1.65

1.84

1.39

2.05

2.00

1.62

2.22

1.97

2.10

1.97

1.91

2.02

1.64

3.74 3.86 3.33

Snapshots of the conformation of the copolymers at varying charge densities (Figure 1S), RDF between the center of mass of the polyelectrolyte residues and Na+ ions (Figure 2S), and RDF’s between the center of mass of the polyelectrolyte residues and water oxygens for the copolymers (Figure 3S). This material is available free of charge via the Internet at http://pubs.acs.org.

PMA 1.02

2.53

ASSOCIATED CONTENT

S Supporting Information *

2.44

■

2.5 3.23

AUTHOR INFORMATION

Corresponding Author

*Tel.: 091-044-22574184. Fax: 091-044-22574152. E-mail: [email protected], [email protected].

IV. CONCLUSIONS Atomistic MD simulations of PAA−PMA copolymers in dilute aqueous solution under the condition of no added salt, as a function of charge density, are presented here taking into account counterions and solvent medium explicitly. The chains expand with increase in charge density from a coiled form to a bent form, in agreement with experimental behavior at low ionic strength. The electrostatic interactions between the adjacent monomers in the fully ionized (f = 1) chains are effectively screened by the Na+ counterions, and hence the chain adopts a bent conformation (Figure 1S) rather than an elongated (rod-like) conformation. The values of persistence length increase with charge density and are in the range 0.35− 1.2 nm for the polyelectrolytes studied in dilute aqueous solution, thus depicting them as flexible chains. With increase in the MA content, a reduction in the coordination number of water molecules around the polyelectrolyte residues is noted. Increase in the charge density leads to an increase in the extent of hydrogen bonding with water. The H-bonds between the polyelectrolyte chain and water molecules are longer-lived than those between water molecules themselves, in agreement with the existing literature from simulations on other polymers and proteins. Intermittent H-bond correlation function decays slower for PMA as compared to PAA, signifying the difference in the H-bonding interactions present in aqueous solution. A denser hydration layer surrounding the PMA chain as compared to that around the PAA chain could be responsible for a slower decay of the H-bond corrleation function in the former. In the context of the application of synthetic polyanions, which undergo conformational transition with pH in solution, for drug delivery, such studies would provide valuable information regarding the interaction of these macromolecules with water and other biomolecules.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.S.S. thanks DST, New Delhi, for Research Funds under the Women-Scientist Scheme (Grant: DST-WOS-A/CS-63/2008). REFERENCES

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