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Conformations and hydration structure of hydrophobicpolyelectrolyte atactic poly(ethacrylic acid) in diluteaqueous solution as a function of neutralisationPraveenkumar Sappidia, Sulatha S. Muralidharana & Upendra Natarajana

a Molecular Modelling and Simulation Laboratory, Department of Chemical Engineering,Indian Institute of Technology (IIT) Madras, Chennai, 600036IndiaPublished online: 08 Jul 2013.

To cite this article: Molecular Simulation (2013): Conformations and hydration structure of hydrophobic polyelectrolyteatactic poly(ethacrylic acid) in dilute aqueous solution as a function of neutralisation, Molecular Simulation, DOI:10.1080/08927022.2013.803551

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Molecular Simulation, 2013 http://dx.doi.org/10.1080/08927022.2013.803551

Conformations and hydration structure of hydrophobic polyelectrolyte atactic poly(ethacrylic acid) in dilute aqueous solution as a function of neutralisation

Praveenkumar Sappidi, Sulatha S. Muralidharan1 and Upendra Natarajan*

Molecular Modelling and Simulation Laboratory, Department of Chemical Engineering, Indian Institute of Technology (IIT) Madras, Chennai 600036, India

(Received 8 October 2012; final version received 3 May 2013)

Chain conformations, counter-ion structure, intermolecular hydrogen bonding structure and dynamics of atactic polyethacrylic acid (PEA) in salt-free aqueous dilute solution at 258C are studied via molecular dynamics (MD) simulations with explicit-solvent and explicit-ion description for the first time. The intermolecular structure was analysed by the radial distribution functions (RDF) for specific atom types between PEA chain, water molecules and Naþ counter-ions, as well as by the hydration near the PEA chain in the solvated system. An increase in f provides an increase in kRgl of the chain, consistent with the existence of the compact form of PEA. The simulations show expansion for radius-of-gyration with increase in f, as expected for flexible polyelectrolytes under salt-free condition. The extent of intermolecular hydrogen bonds (H-bonds) between PEA and water is enhanced by increase in f. Chains having a higher counter-ion density show higher values of kRgl, influenced by intermolecular interactions between PEA and water. The coordination of Naþ counter ions and water molecules to carboxyl oxygens of polyacrylic acid (PAA) increases with charge density of the chain. A comparison of the structure aspects is made with PAA and PMA polyelectrolytes in dilute solution, which brings out the hydrophobic effect of the ethyl side-groups in PEA on conformational properties and counter-ion condensation structure.

Keywords: polyelectrolyte; hydrophobic; aqueous; hydrogen bonding; molecular dynamics

1. Introduction a great depth of knowledge on the chemical physics

Polyelectrolytes are charged macromolecules containing aspects, which has been made available via pioneering

ionisable groups,[1,2] having a wide range of technologi- computational simulation studies as well.[9–12] There

cal applications cutting across the disciplines of physics, exist very few studies on polyelectrolyte solutions with

chemistry, chemical and materials engineering.[3,4] explicit description of ions in the simulations,[13–16] and

Examples of polyelectrolytes include vinyl-based poly with an atomistic description of the polyelectrolyte chain

(carboxylic acids) such as polyacrylic acid (PAA), (PAA [16–18] and PMA [17,18]), notwithstanding having

polymethacrylic acid (PMA), polyethacrylic acid (PEA) looked at only dilute polymer conditions. In one study, an

and polystyrenesulfonate (PSS), and DNA and other atomistic description of the polyelectrolyte (PAA) has

polymeric acids and bases. Ionisable groups on these been used in a Monte Carlo scheme for investigation of

polyelectrolytes can dissociate depending on the solution chain conformational properties in comparison with conditions and leave charges on the polymer chains with experiment.[16] However, most of these studies in the release of counter ions in polar solvents such as water. literature have not looked at the important aspect of The dissociation of the polymer chain is generally hydrogen-bonding effects, given that most simulation accompanied by oppositely charged counter-ions that studies have not investigated atomistic systems with tend to neutralise the charge on the repeating unit.[2] The explicit chemistry; there being very few recent references physical and chemical behaviour of polyelectrolytes in the field in this regard specifically as applied to PAA differs from that of uncharged or neutral polymers due and PMA systems.[17,18] Scaling relationships valid for to the presence of electrostatic interactions between sufficiently high molecular weight polyelectrolytes in charges, be it weak or strong depending on the nature of solution, for their static structure and key thermodynamic the chemical structure.[2] property (osmotic pressure) and dynamic properties such

Sufficient level of fundamental and applied knowledge as macromolecular diffusion, are available over a wide exists on the unusual behaviour of the unique class range of polyelectrolyte concentration (from dilute to pertaining to the polyelectrolyte type of macromol- semi-dilute regime) and salt concentration.[19–21] ecules.[5] The theoretical models and advances in the By changes in the chemical substituent group on the field of polyelectrolytes have been exemplified to great polycarboxylate, its affinity for water can be varied. The detail in several reviews.[1,2,6,7,8] At present there exists widely investigated chemical PAA can be considered as

*Corresponding author. Emails: unatarajan@iitm.ac.in, upen.natarajan@gmail.com

q 2013 Taylor & Francis

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hydrophilic. On the other hand, PMA and PEA have hydrophobic group as well as ionisable groups and their corresponding salts sodium poly(methacrylate) (Na-

PMA), sodium poly(ethacrylate) (Na-PEA) show mark­

edly different properties in aqueous solutions as compared to PAA.

PEA is a hydrophobic anionic polyelectrolyte that shows propensity for interesting behaviour such as self-assembly into nanoparticles in solution [22] and for pH tuning in microgels.[23–26] PEA may be used as pH-responsive material in advanced drug delivery system for tissue engineering application and towards synthetic modelling of biological membranes.[26–29] Fundamental experimental studies have investigated the behaviour of PEA dilute solution.[30–33] There are extremely few investigations on the dilute solution properties of salt-free PEA–water system leading to conclusions about the conformational properties using results from potentiometric titrations in aqueous NaCl at ionic strengths in the range 0.01–0.3 at temperatures 5–358C (278–308K),[30,31] and by viscometric, optical and 1H NMR studies.[32]

PEA also exhibits the compact form at low degree of ionisation and an extended coil at higher degree of ionisation.[31–33] PEA and PMA in their extended coil form show a similar molecular structure that can be described by the worm-like chain model. However, the compact forms in present in acidic medium, of PEA [33] and PMA [34] are different, with the form for PEA describable by a swollen-gel network while the form for PMA represented by the worm-like chain in a u-solvent (or medium).[33,34] This behavioural difference has been ascribed to the structural difference between ethyl and methyl side-groups and to the proposal of a significant extent of intramolecular association between the ethyl groups leading to the hydrophobic effect being more significant in PEA than in PMA.[34] The very recent experimental study by Pelijhan et al. [35] has shown evidence of strong intermolecular association between short PEA chains in salt-free water; this effect ascribed to the formation of hydrogen bonding contributed by the unionised groups as well as plausible hydrophobic self-association driven by the ethyl side-groups in this polyelectrolyte. Therefore, not only is the behaviour of PEA chains different from that of PMA and PAA in aqueous solution, there is also a strong motivation to undertake simulation studies in order to provide funda­mental understanding of known behaviour and to enquire about possible novel behaviour in solution.

The work presented in this paper focuses on the application of molecular dynamics (MD) simulations to study local and chain-level structure and conformations of PEA in dilute aqueous solution under salt-free condition (no added salt), as a function of the charge density (equivalently the degree of neutralisation in the present context). To our knowledge, this is the first report of a

molecular simulation study on polyelectrolyte PEA in solution, atomically detailed with explicit description of all species. The detailed understanding of the molecular structure of atactic PEA (a-PEA) in aqueous solutions is the objective of this study. We focus on conformational and structural properties, hydration behaviour and auto correlation function of hydrogen bonds and the spatial distribution of counter ions in dilute aqueous solutions of PEA.

2. Methodology and computational details

The structural formula for the repeating unit of PEA as per the force-field typing is shown in Figure 1. PEA was modelled as an atactic polymer strand, with 20 repeat units solvated in 5500 water molecules (concentration excluding counter ions, 0.01 mol/l). The simulated chain had the tacticity (dyads) sequence: R-M-M-M-M-R-R-R-R-R-R-M-R-R-R-R-R-M-M. This sequence containing the largest block of 6 racemic dyads out of 19 is within 30% number fraction, which is reasonable. The acid form of the residue has the carboxyl group as COOH with an explicit hydrogen and the fully ionised residue has the carboxyl group in the COO2 form. The charge density was varied for the polyelectrolyte chain by replacement of COOH groups with COO2 along the chain. Different ionised forms were studied separately in solution, by having 0, 5, 8, 10, 12, 15, 16 and 20 COO2

along the chain (charge density, f ¼ Nc/N ¼ 0, 0.25, 0.4, 0.5, 0.6, 0.75, 0.8 and 1, respectively, where Nc is the number of ionised residues and N is the total number of residues). An adequate number of Naþ ions were added to the solvated system in order to maintain overall charge neutrality. Results from earlier recent MD simulations on PAA and PMA have shown that 20 repeat units are sufficient to capture the local conformations, hydrogen bonding and counter-ion structure in dilute polymer concentration aqueous solution even for atactic chains [17, 18 and references therein], which in particular becomes feasible for flexible polyelectrolytes such as these due to their relatively low electrostatic persistence length in salt-free solution. In the repeating unit of the polymer, the tetrahedral backbone carbon atom bonded to four carbons including the ones part of the carboxyl (COOH) and the ethyl (ZCH2CH3) side-groups was designated as the chiral centre (C2* per the force field) and the carbon atom

Figure 1. Chemical structure formula of the PEA repeat unit with force-field typing.

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of the aliphatic (CH2) group of the repeat unit was designated as the non-chiral carbon.

With this specification, the dyads and triads can be specified in going across the chain from either end of the chain as per standard (IUPAC) convention. The generation of the initial state of the chain would require a generation of the tacticity sequence and the torsion angle states at the backbone bonds. The chain was generated via Materials Studio interface [36] using Monte Carlo simulation,[37, 38] which would result in the typical near Bernoullian distribution of dyads [39] in vinyl polymers constituted by short as well as bulky side-groups. The details of the generation methodology for the dyad tacticity sequence are known from earlier seminal studies.[37,38] For the choice of the rotational (torsion) angles at each backbone bond, the chain configurations were specified during the chain generation by using the probabilities based on the ‘equivalent Markov process’ for Monte Carlo generation of correctly weighted (based on local repeat unit level conformational energy weights) chain under the unper­turbed condition. The generated chain used in the simulation has 40% meso dyads, 60% racemic dyads, and the percentages of MM, RR and MR triads are 22, 50 and 27, respectively. Even though the tacticity sequence in the PEA chain as used would not pertain to a perfectly random sequence, the sequence was found to be sufficiently random for such short chains, and in being able to acceptably distinguish itself from isotactic or syndiotactic PEA chains for overall chain dimensions. The longest stereospecific block consisted of six repeating units (for racemic dyads), which was significantly lower than 50% (i.e. 10 repeating unit block) for diblock copolymer (the one extreme for the regular arrangement of the repeating units), while it was very different for an alternating (i.e. other extreme for a regular or non-random) sequence of M and R dyads. Given this, the stereochemical sequence along the chain used in the simulations is reasonable, in order to derive properties for a sufficiently random chain. The tacticity sequence was maintained the same for all values of the respective different extent of ionisation.

GROMOS 53a6 parameter set was used in the simulations.[40] Dihedral rotation about the aliphatic back bone bond was represented by the Ryckaert–Belle­mans (RB) torsion potential, while the proper torsion potentials belonging to the GROMOS parameter set was used for describing energy of the other torsion angles in the chain. The force-field parameters used in this set of simulations are taken from our earlier study.[17] All potential energy minimisation and MD simulations were performed using GROMACS (version 4.0.7).[41] Ali­phatic carbon atoms are treated as united atoms and polar hydrogens explicitly in the simulations. The initial configuration was generated by placing a fully stretched polyelectrolyte chain in a cubic periodic box along with

Molecular Simulation

randomly distributed Naþ counter-ions and single-­

point-charge water molecules.[42] Water geometry was constrained using the SETTLE algorithm.[43] Lennard-­Jones interactions described by a 6–12 potential form were truncated and shifted at 0.9 nm. Electrostatic interactions were computed using a Coulomb potential (cut-off at 1.4 nm) along with a reaction field correction, with the reaction field dielectric 1RF equal to the value for water (1RF ¼ 78.5).[44] Bond lengths were held constant using the SHAKE procedure.[45] Equations of motion were integrated using a leapfrog algorithm using a time step of 2 fs. Other simulation parameters included the following: a neighbour list, which was updated every 10 steps with a list cut-off 1 nm; weak coupling [46] to temperature (T ¼ 300 K) and pressure ( p ¼ 1 atm) baths with coupling times tt ¼ 0.1 ps and tp ¼ 0.5 ps (water compressibility 4.5 £ 10210 kPa21). The solvated system was subjected to energy minimisation without any constraints using Steepest Descent method. NVT simu­

lation run of 100 ps was performed, followed by a 100 ps NPT run with position restraints on the polymeric chain, with no constraints on the water molecules, so that temperature and pressure are at their equilibrium values. This was then followed by NPT MD simulation for 20 ns and the data was recorded at every 500 steps. The last 5 ns of the trajectory were used for the analysis. All MD simulations were performed at a temperature 300 K.

3. Results and discussion

3.1 Conformational properties

The chain conformations of the PEA chains at different values of charge density f as obtained at the end of the 20 ns simulation trajectories are given in Figure 2. Figure 3 shows the variation in radius-of-gyration (Rg) with increase in chain charge density and also the Rg

distribution for the chains. The unionised PEA chain is in coiled form with an average kRgl value 0.74 nm (std dev. ^ 0.027). With increase in charge density, the chain expands to minimise the electrostatic repulsion between the charged residues and is accompanied by an increase in Rg. This qualitative behaviour is in agreement with experimental observations on neutralised weak polyelec­trolytes (e.g. PAA and PMA) supported also by polyelectrolyte theory [1,2] in dilute salt-free aqueous solution. It is seen that maximum chain expansion occurs when the charge density is 0.5 beyond which there is very little change in Rg. The fully ionised chain is in a bent conformation (Figure 2) and has an average kRgl value 0.985 nm (std dev. ^ 0.031). The mean Rg value changes by 34% over the ionisation range studied here (0–100%). The standard deviation in the Rg value is 2.9–4.8% across 0–100% ionisation range, given the sufficiently long duration of the simulated trajectories, thereby indicating

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Figure 2. (Colour online) Chain conformation of PEA at different charge density, f. Water molecules and ions are not shown here; aliphatic backbone carbon (grey), carboxylic acid hydrogen (white), oxygen (red) and ethyl side groups (yellow).

good statistics for equilibration and the properties thus derived. The higher value of the standard deviation occurs at f ¼ 0.5, while the deviations are less at low degree and high degree of ionisation. The experimental [33] values shows that the Na-PEA chain in aqueous solution would

give an Rg of 2.3 nm for the molecular weight of (Mw ¼ 1–2 £ 105) g/mol at 20% degree of ionisation and it went up to 3.7 nm for 80% degree of ionisation (i.e. f ¼ 0.8). The PEA chain in aqueous solution forms a compact structure for f , 0.25. Upon increase in charge density along the chain, for f . 0.5, the chain unfolds showing an expansion. This is in accordance with the experimental observation of PEA chain transition from a compact coil at low degree of ionisation to an extended chain upon increase in the degree of ionisation.[32,33] The nature of this simulated curve is qualitatively similar to that observed for a PEA chain having a significantly higher molecular weight (,100 times) in the experiment, under similar condition of solvent quality (inclusive of dipolar interactions and electrostatic effects due to ions) in dilute condition.

Our earlier MD study [18] on chains of PAA and PMA has also shown similar behaviour of a chain expansion with an increase in charge density. Chain expansion followed by a leveling off beyond f ¼ 0.5 seen here for a-PEA is similar to that observed for a-PMA. As a function of the charge density, the qualitative variation of Rg seen by the simulations here for PEA is found to be very similar to the qualitative variation in the intrinsic viscosity [32] of dilute PEA solution containing low NaCl concentration (0.01 M), and this is in agreement with experimental observation. The experimental study [32] with which we have compared our simulation result pertains to a high molecular weight PEA dilute solution (intrinsic viscosity 0.29 dl/g in a buffer at pH < 7).

3.2 Na1 counter-ion distribution

The distribution of Naþ counter ions adjacent to the PEA chain can be obtained from the RDFs as given in Figure 4(a),(b). Figure 4(a) shows the distribution between the centre of mass of the PEA residues and Naþ ions. The first peak at ,0.35 nm is due to the condensed counter-ions

Figure 3. (a) Computed conformationally temporally averaged kRgl. (b) Probability distribution of Rg with varying charge density (degree of neutralisation) for a-PEA chain.

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(a) (b)

g(r)

[PE

A-N

a+]

50

40

30

20

10

0

200

160

120

80

40

0

g(r)

[O

1O2-

Na+

]

f = 1.0 f = 0.8 f = 0.6 f = 0.4

f = 1.0 f = 0.8 f = 0.6 f = 0.4

0.3 0.6 0.9 0.1 0.2 0.3 0.4 0.5 r (nm) r (nm)

Figure 4. RDF between (a) the centre-of-mass of PEA residues and the counter ions (Naþ) and (b) carboxylate oxygens and Naþ ions at different charge densities.

and the peak at , 0.55 – 0.65 nm is due to the solvent-separated ions. The RDF between the carboxylate oxygens and Naþ ions (Figure 3(b)) also is in accordance with this behaviour. A prominent first peak is observed at 0.25 nm corresponding to condensed counter-ions and a broader peak at 0.45 nm due to solvent-separated ions. With increase in charge density, more counter-ions are condensed on to the chain backbone (as shown by increase in first peak intensity with increase in charge density in Figure 4(a),(b)). As observed from our earlier study [17] for a-PAA, the first peak corresponding to the location of the nearest-neighbour counter-ions with respect to the polyelectrolyte was observed at 0.55 nm (a-PAA) and 0.35 nm (a-PMA) from RDFs calculated between the centre of mass of the monomer units with respect to the Naþ ions. For the RDFs calculated between the carboxylate oxygens and Naþ ions, for PAA, there are only two peaks, one at 0.46 nm caused by Naþ ions near to the carboxylate group and a broader second local maximum at around 1 nm due to solvent-separated ion-pairs.[17] In the case of PMA,[17] in addition to the two peaks, (at 0.44 and 1 nm) there is a sharp first peak at 0.24 nm which is similar to the peaks observed in this study for PEA. In Figure 5(a),

(b) a comparison of the counter-ion distribution in the case of fully ionised chains ( f ¼ 1) for PAA, PMA and PEA is given. The nature of counter-ion distribution observed here for PEA resembles to that of PMA observed from our earlier report, although PEA exhibits much stronger correlation with the counter-ions as compared to PMA. Thus, the correlation between the chain backbone and counter-ions becomes stronger with increase in hydro­phobicity of the polyelectrolyte chain. The RDFs for water–water interactions are not presented here; however, those would provide the specific information on the steric effect of the presence of Naþ counter-ions especially so at higher degree of ionisation in spaces where water molecules would otherwise be present in the absence of ionisation.

The conformation of polyelectrolytes in solution is influenced by the solvent quality for the chain backbone. The earlier MD simulation studies on polyelectrolyte conformations under poor solvent conditions have shown that correlations between the counterions and the polyions becomes stronger as the solvent quality is decreased.[1, 47–49] A higher percentage of nearest-neighbour counter-ions is indicative of strong correlation induced attraction

Figure 5. A comparison of the RDF between (a) centre of mass of monomer residues and the counter ions (Naþ) and (b) carboxylate oxygens and Naþ ions for fully ionised chains of PAA, PMA and PEA.

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between the polyion and the counterions which leads to weakening of the electrostatic repulsions between the ionised residues along the chain. The difference in the counter-ion distribution between PAA on one hand and PMA and PEA chains on the other as derived from the MD simulations here indicate that water is a poor solvent for PMA and even more so for PEA as compared to what is observed in the case of PAA. This leads to stronger correlation of counter-ions with the chain backbone for PMA and PEA. PEA due to the presence of hydrophobic ethyl groups shows greater correlation with Naþ ions than that for PMA. Condensation of counter-ions on the chain backbone for PMA and PEA can also lead to a mutual attraction between the monomers that in turn resist futher chain expansion due to ionisation. Based on the computed Rg values from the MD simulations here and from earlier work,[17,18] we see that for fully ionised chains PAA, PMA and PEA alike show a similar averaged value of ,1 nm. The similar Rg values for PMA (and PEA) when compared to PAA suggests that electrostatic repulsion between the neighbouring charged residues in completely ionised chains is adequately balanced by the counter-ions in the case of PMA and more so in the case of PEA. The charge density of the polyion is considerably reduced in case of PMA and PEA when compared to PAA. This lower level of charge density of PEA chain does not pose an appreciable influence for the polyion to stretch itself to its full possible extension length when completely ionised. The counter-ion condensation reduces the charge density on the chain and promotes chain shrinkage.

3.3 Hydration behaviour

The RDF between the centre of mass of the PEA residues with water oxygens is provided in Figure 6. The plots are given for PEA chains with varying charge densities. The slight increase in the affinity for water molecules with charge density is due the presence of more hydrophilic COO2 groups along the chains with ionisation. The un-ionised PEA chain is in a coiled form which excludes water from its vicinity. With chain expansion due to ionisation, there is a slight increase in the number of water molecules next to the chain. The water distribution profiles here show that g(r) is less than 1, which suggests a reduced probability of finding water molecules in the PEA chain vicinity as compared to the uniform distribution in the bulk region. Figure 7 shows a comparison of the solvation shell of fully ionised ( f ¼ 1) PAA, PMA and PEA chains. In the case of PAA and PMA, a well-defined solvation shell is observed at 0.35 nm irrespective of the chain charge density. In the case of PEA, the first solvation shell is absent in comparison to PAA and PMA. The distribution of water molecules near the PEA chain is lower than that in the bulk as seen from the RDFs. Due to the presence of hydrophobic

Figure 6. RDF between centre of mass of PEA residues and the water oxygens at a function of charge density (degree of ionisation of chain).

ethyl groups in the chain, relatively less number of water molecules are present in the vicinity of the chain as compared to PAA and PMA. The distribution profiles clearly show the exclusion of water molecules from the chain vicinity with increase in hydrophobicity of the chain units.

The COO2 and COOH groups along the PEA chain can form intermolecular H-bonds with water. In addition, intramolecular H-bonds are possible between COOH groups (for unionised and partially ionised chains). A geometric criteria is used for the definition of 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 OZOZH angle is less than 308. The simulations show that the extent of intermolecular hydrogen bonds between PEA residue and water molecules is enhanced by an increase in the charge density. The number of PEA–water intermolecular

Figure 7. A comparison of the RDF for the pair consisting of centre of mass of the monomer residue and the water oxygen for fully ionised chains ( f ¼ 1) of PAA, PMA and PEA. Data for PAA and PMA taken from earlier study.[17,18]

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hydrogen bonds increases with charge density, as presented in Figure 8, clearly showing a linear variation. The number of H-bonds (values rounded off to relevant significance) is 43 ^ 3 at f ¼ 0 and 104 ^ 4 at f ¼ 1, respectively (% std dev. , 7 over 0 , f , 1). The intramolecular H-bonds between the chain residues show a slight increase with ionisation due to the greater possibility of H-bond between a COOH group and a neighbouring COO2 group than between two adjacent COOH groups.

The hydrogen bonding dynamics is of importance in polar polymer systems [50–52] especially based on the earlier studies conducted on non-electrolytic polymer solutions. In our present investigation, an analysis of the structural relaxation of the H-bonds [53–55] between the polyelectrolyte and water has been carried out via the simple model proposed by Luzar and Chandler.[53,54] According to that model, 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 vicinity of the residue site. The dynamics of the H-bonds is characterised by the intermittent H-bond time correlation function [53] C(t), which is defined as

CðtÞ ¼ khð0

khÞh

lðtÞl

; ð1Þ

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 ¼ 0 is also H-bonded at time t and is independent of possible breaking of H-bonds at intermediate times and allows reformation of broken bonds. In other words, it measures

Molecular Simulation

correlations in time series of bonds independent of possible bond breaking events. Therefore, the relaxation of C(t) provides information about the structural relaxation of a particular type of H-bond. A comparison of the relaxation of the polyelectrolyte–water H-bonds is given in Figure 9. The relaxation of water–water H-bonds in the polyelec­trolyte system is given for a comparison. H-bonds between water molecules themselves decay faster than the polyelectrolyte–water H-bonds. In the case of bulk water, a rapid initial decay in the H-bond correlation function due to the fast librational and vibrational motion of the H-bonded sites has been observed,[56,57] as well as a slowing down of water H-bond dynamics in presence of halogen anions (Cl2 and Br2).[57] From our results, we find that water molecules in the hydration layer of the polyelectrolyte chain form stronger H-bonds with it and hence the relaxation of the polyelectrolyte–water H-bonds are 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. We see a distinct difference in the structural relaxation of the polyelec­trolyte–water H-bonds between the three different chains, PAA, PMA and PEA. It is found that the structural relaxation of PEA–water H-bonds is slower than those of PMA followed by those corresponding to PAA. In an earlier report while comparing PAA and PMA, this was attributed to 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. Small angle X-Ray scattering studies on semi-

Figure 9. A comparison of the decay of the intermittent correlation function of the H-bonds with water for the fully ionised ( f ¼ 1) chains of PAA, PMA and PEA. The relaxation of the water–water (W–W) H-bonds in the bulk is also given.

Figure 8. Variation of the number of PEA–water hydrogen Data for PMA and PAA taken from earlier study for a bonds as a function of degree of ionisation of the chain. comparison.[17,18]

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dilute solutions of PMA also point to the existence of a monomolecular hydration shell, the density of which for a fully ionised chain is about 10% higher than that of bulk water.[58] For a dense hydration layer, the diffusion is slow and this could lead to a slower relaxation of PMA–water H-bonds. We see here much slower relaxation of PEA–water H-bonds than those for PMA. The hydration layer surrounding the PEA with hydrophobic ethyl groups could be much denser than for PMA and this must be leading to the slower diffusion of water molecules surrounding the chain and hence a slower relaxation. 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.

The structural relaxation of the PEA–water H-bonds as a function of charge density is shown in Figure 10. The relaxation of polyelectrolyte–water H-bonds for the fully ionised chains is found to be slower than those corresponding to partially ionised ones. In the fully ionised chain, maximum number of COO2 groups are present which bind strongly to the water molecules compared to the COOH groups (present in partially ionised chains together with COO2 groups) and these result in slower relaxation of the resulting H-bonds. The H-bond relaxation curves and the relaxation time values obtained from our simulations do not show monotonic behaviour. For f , 0.5, the relaxation curves decrease but not mono­

tonically. However, for f . 0.5 there is a clear monotonic behaviour indicating that the relaxation is slowed down. This is also corroborated by presence of a sufficient number of condensed-ions near the charged groups of the polymer, as being the correct behaviour that should be expected. The steric effect due to counter-ions filling the places where water should otherwise be also bears influence on the local structure and dynamics, as reflected by its effect on (a) the backbone dihedral angle distribution

Figure 10. Decay of the intermittent H-bond time correlation function for the hydrogen bonds between the PEA residues and water molecules as a function of charge density of the chain.

(discussed in Section 3.4) as well as (b) H-bond dynamics and the PEA–water H-bonding coordination number (Figure 8).

The results obtained here for f , 0.5 could likely fall short of sufficient statistics for this particular dynamic property, as we have calculated the property over the entire simulation box, given the low absolute number of neutralised groups and counter-ions, and this aspect has been discussed in brief in earlier report.[18] The relaxation time values for decay function of PEA–water H-bonds averaged across the chain, in the ionisation range 0.5 , f , 1 obtained (in ps) from our simulations are 19.9 ( f ¼ 0.5), 24.0 ( f ¼ 0.6), 29.7 ( f ¼ 0.75), 33.4 ( f ¼ 0.8) and 43.2 ( f ¼ 1). As the H-bond dynamics at room temperature in water is a very local phenomenon, the use of longer chains in a larger periodic simulation box, under dilute conditions, would not provide worthwhile information at low values of f. The difference between the relaxation times (and the associated curves) for H-bonds in dilute system with PEA and for those bonds in pure water is quite significant as seen from the results. This has been observed for PAA and PMA from earlier work.

3.4 Dihedral angle distribution

The dihedral angle (torsion angle) distributions are presented in Figure 11(a)–(c) for the backbone and side-groups (ethyl and carboxylic acid on each side of the backbone bonds). The carbon atoms in the repeating unit are defined using the symbols C1 (for CH2 group) and C2* (for chiral tertiary carbon atom bonded to the two side-groups). For the backbone angle C1ZC2*ZC1ZC2* (Figure 11(a)), three states exist in reasonable proportion of probability: gaucheþ (g þ at 08), gauche2 (g 2 at 2608) and trans (t at 1808). The trans peak increases with degree of ionisation. The backbone torsion angles show increase in trans states relative to gauche states, thus presenting chain extension with increase in degree of ionisation. The side-group dihedral angles show a different behaviour. The ethyl group torsion angle C1ZC2*ZC3ZC4 (Figure 11(b)) pertaining to the CZC bond connecting this group to the backbone does not show a systematic trend in the variation of the trans and gauche states, while these three conformational states do exist. The gauche g þ state at 608 show a high probability when the chain in not ionised. For the other side-group dihedral angle pertaining to the CZC bond connecting the carboxyl carbon to the backbone C1ZC2*ZCAZO2 (Figure 11(c)) only gauche (g þ, g 2) states are present, and the probability of g þ and g 2 are found to be unaffected by ionisation. Interestingly, these torsion angles on the opposite sides of the PEA backbone prefer opposite states. While the interesting observation on the lack of occurrence of trans state at the rotatable bond connecting the carboxyl side-group to the backbone is not

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0.012

9 Molecular Simulation

backbone bond as obtained from the simulations on(a) 0.016 f = 1.0 relatively short chains of 20 repeat units is different as f = 0.8 shown in Figure 11(a). A longer atactic chain of PEA f = 0.6 could circumvent this disparity, given that both symmetric f = 0.4

dist

ribu

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(b)

f = 0.0

0.008

0.004

0 –180 –120 –160 0 60 120 180

Angle

0.025

gauche states would be expected to occur with equal probability along the chain. However, the chain used here is sufficiently non-atactic, which is supported by the observed level of agreement of the overall chain dimensions (i.e. Rg) with experiment, which would have not been possible with a purely isotactic or a syndiotactic chain in the case of PEA, due to the ethyl side-groups present, even for a chain of only 20 repeating units.

4. Conclusions f = 1.00 f = 0.80 The simulations show an increase in kRgl with degree-of­

0.02 f = 0.60 f = 0.40 ionisation (or neutralisation) f of the PEA chain with the

dist

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tion

(c)

0.015 f = 0.00

0.01

0.005

0 –180 –120 –60 0

Angle

60 120 180

0.025

chain expansion arising from occupancy of trans conformational states along the backbone torsion angles, with the kRgl value somewhat levelling off beyond f ¼0.5. This behaviour is qualitatively commensurate with experimental observation of intrinsic viscosity as a function of chain-ionisation under dilute conditions for PEA observed in the literature. We note that even the distribution of kRgl shows expansion with increase in the degree of neutralisation (i.e. charge density of the chain).

Results of the RDF with respect to the centre-of-mass of the PEA residues and water molecules show a distinct

0.015

0.02

f = 1.00 f = 0.80 f = 0.60 f = 0.40 f = 0.00

0.01

0.005

0 –180 –120 –60 0

Angle

60 120 180

peak at 0.42 nm, but the intensity of the peak is less than that of 1 (corresponding to a long-range value of g(r)). The results for the RDF for atom-pairs consisting of centre of mass of the PEA units and Naþ ions shows peak at 0.35 nm corresponding to counter-ion shell near the chain, and at 0.65 nm corresponding to solvent-separated ion-pairs. The RDFs for the carboxyl oxygen atoms with respect to Naþ

counter-ions shows a systematic increase in coordination number with increase in f along with the systematic increase in the coordination number for the water molecules surrounding the immediate shell of the carboxyl side-group oxygen atoms. From the RDFs for the counter-ion distributions with respect to the fully ionised

dist

ribu

tion

Figure 11. Dihedral distribution: (a) backbone dihedral (averaged over C1ZC2*ZC1ZC2* and C2*ZC1ZC2*ZC1), (b) C1ZC2*ZC3ZC4, ethyl side group and (c) C1ZC2*Z CAZO2 dihedral for the carboxyl side-group.

of concern, and the reasons for this, whether this could arise solely due to presence of water (hydrogen bonding) and ions, and whether this behaviour should be true for vinyl polyacrylates or polymethacrylate chains that do not bear charges, are not clear at this time. This would be a matter of future investigation.

The peak intensity for the probability of occurrence of symmetric gauche (g þ, g 2) conformational states at the

polyelectrolyte chain (as indicated either by the function with respect to the centre of mass of PEA repeating unit or the carboxyl side-groups), we observe a higher coordi­nation of Naþ ions in the case of PEA in comparison with PMA and PAA.

The number of intermolecular H-bonds between PEA chain and water molecules increases with f showing a linear variation. For the fully ionised PEA chain ( f ¼ 1), the number of intermolecular H-bonds is lower than that of corresponding PAA and PMA chains in comparison, and in the order PAA . PMA . PEA. For intramolecular H-bonding, we observe that for unionised PEA case it is 1 and ,4–5 for the ionised chains ( f in the range 0.25–0.8).

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The intermittent hydrogen bonds of fully ionised polyelectrolyte PEA is seen to decay slower than that observed for other anionic polyelectrolytes PMA and PAA from previous investigations in the literature, thus pointing to the clear influence of the hydrophobic ethyl side-group in PEA chain. The decay of the intermittent hydrogen bond correlation function between PEA units and water molecules shows a slowing down of the dynamics with increase in the degree of neutralisation.

The conformational distributions of the two backbone and two side-group torsion angles shows the existence of both gauche and trans states except for the angle within the carboxyl side-group for which only gauche states exist. The probability of the trans states at the backbone bonds increases with the degree of ionisation concomitantly leading to chain expansion and increase in kRgl.

Acknowledgement MSS thanks DST, New Delhi for a research fellowship under the grant DST-WOS-A/CS-63/2008.

Note 1. Emails: mssulatha@iitm.ac.in, mssulatha@gmail.com

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