Ion Valence and Concentration Effects on the Interaction Between

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C: Physical Processes in Nanomaterials and Nanostructures

Ion Valence and Concentration Effects on the Interaction Between Polystyrene Sulfonate-Modified Carbon Nanotubes in Water Prasad Rama, Arup Ranjan Bhattacharyya, Rajdip Bandyopadhyaya, and Ajay Singh Panwar J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b10467 • Publication Date (Web): 03 Apr 2018 Downloaded from http://pubs.acs.org on April 3, 2018

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The Journal of Physical Chemistry

Ion Valence and Concentration Effects on the Interaction between Polystyrene Sulfonate-modified Carbon Nanotubes in Water Prasad Rama†, Arup R. Bhattacharyya‡, Rajdip Bandyopadhyaya§, Ajay S. Panwar*,‡ †

Centre for Research in Nanotechnology and Science

Indian Institute of Technology Bombay, Powai, Mumbai – 400076, INDIA ‡

Department of Metallurgical Engineering and Materials Science

Indian Institute of Technology Bombay, Powai, Mumbai – 400076, INDIA §

Department of Chemical Engineering

Indian Institute of Technology Bombay, Powai, Mumbai – 400076, INDIA

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Abstract We use molecular dynamics simulations and the adaptive biasing force method to evaluate potential of mean force between two carbon nanotubes (CNTs), each surface-modified by an adsorbed sodium-polystyrene sulfonate (Na-PSS) polyanion, in aqueous electrolyte media. Changes in electrolyte concentration and counter-ion valence can lead to qualitative changes in the interactions between polyelectrolyte-modified CNTs. We show that in presence of monovalent NaCl salt, a long-range screened electrostatic repulsion exists between CNTs. This repulsion can be described by a generalized Derjaguin−Landau−Verwey−Overbeek (DLVO) interaction that accounts for anisotropy of charged cylindrical colloids. In contrast, an attraction between CNTs is observed in presence of divalent MgCl2 salt. The attraction is attributed to ion-

pair correlations between anionic SO3 groups, on different PSS chains, induced by Mg2+ counter-

ions acting as bridges between the SO3 groups. However, for the salt-free case where divalent Mg2+ counter-ions are considered instead of the Na+ counter-ions, condensation of Mg2+ counterions on the adsorbed PSS chain results in neutralization of surface charge and leads to a shortrange steric repulsion between the CNTs. Thus, our simulations show that qualitatively different interactions, either short-range steric repulsion, long-range repulsion or attraction, can arise between PSS-modified CNTs based on counter-ion valence and electrolyte concentration. ⃰ Corresponding

author. Email: [email protected]

Phone: (+91)22-25767644


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1 Introduction Often, effective dispersion of carbon nanotubes (CNTs) in an aqueous media is achieved by noncovalent modification of CNT surfaces with polyelectrolytes.1,2 This is very relevant to a number of polyelectrolyte-based self-assembly approaches for fabrication of functional coatings, containing CNTs.2,3 These have potential applications as antimicrobial films,4 electrodes,5 biosensors,6,7 conductive papers8 and as separation membranes.9 In this context, it is extremely pertinent to understand the role of polyelectrolytes in mediating interactions between CNTs in an aqueous medium. Polystyrene sulfonate (PSS) is a commonly used polyelectrolyte for non-covalent surface modification of CNTs and is also a component of conductive polymer blends, such as PEDOTPSS. It displays a low pKa value in water, which leads to a high degree of ionization over a wide pH range.10,11 In presence of the sodium salt of PSS (Na+-PSS), extremely stable dispersions of multi-walled CNTs (MWCNTs) are obtained, due to the adsorption of the PSS polyanion onto the MWCNT surfaces.12 A negative electric surface potential develops at the MWCNT surfaces due to the adsorption of PSS, and the resulting dispersion stability can be ascribed to a combination of steric and electrostatic effects. Given its widespread use as an ionic modifier for CNTs, PSS is a model polyelectrolyte for understanding polyelectrolyte-mediated interactions between CNTs in an aqueous medium. There exist several simulation studies which examine different aspects of interactions between charged spherical nanoparticles in aqueous electrolytes, such as, many-body effects, like-charge attraction, and salt valence.13–16 In contrast, there are only a limited number of molecular simulation studies that investigate the role of electrolyte and solvation effects, in controlling the dispersion of anisotropic colloids (such as CNTs), in presence of ionic modifiers.17–24 However, to our knowledge, a systematic simulation or theoretical study of polyelectrolyte mediated interactions between cylindrical colloids in aqueous electrolyte medium has not been reported in the literature. Such an investigation is important because it can potentially address several questions relevant to the electrostatic stabilization of CNTs in the presence of polyelectrolyte surface modifiers. The first question is related to the description of long-range interactions between two hydrophobic anisotropic colloids (or cylindrical CNTs), with surfaces 3 ACS Paragon Plus Environment


modified by a charged polyelectrolyte (PSS polyanion) in an aqueous electrolyte medium. Although the classical DLVO theory25 predicts an isotropic long-range interaction between charged spherical particles, it has also been generalized for rod-like charged colloids (representing rigid polyelectrolytes)26,27 accounting for anisotropy through an anisotropic interaction factor. However, most of the studies, whether for spherical13–16 or anisotropic26 colloids, assume uniform surface charge densities and do not seem to account for hydrophobic colloidal surfaces modified by adsorbed polyelectrolyte molecules. The second aspect is related to the surface charge density of the polyelectrolyte-modified CNT surface, which will depend on the degree of ionization of the polyelectrolyte. This in turn will be strongly dictated by the valence of the counter-ion. Finally, ion-correlation effects in presence of multi-valent counterions can lead to attractive interactions between particles of like-charge.28–31 Based on the understanding of this phenomena, attraction between like-charged colloids and polyelectrolytes have been reported in simulations,13–16,29 and in experiments on latex spheres,32 DNA28 and viruses.33 Thus, an attractive interaction may arise between two polyelectrolyte-modified CNTs in the presence of multi-valent counter-ions. However, the adsorbed polyelectrolyte also provides a steric barrier ahead of the CNT surface, which will influence the overall interaction between the CNTs. Molecular dynamics (MD) simulations have shown that the solvation behavior of PSS is quite complex, as it would depend on a number of factors including chain length, both degree of sulfonation and its distribution along the chain contour, the type and valence of the added electrolyte.19 The same simulations have also shown evidence of likecharge attraction between sulfonate groups on different PSS chains. This has been done in presence of divalent and trivalent salts, arising from counter-ion mediated bridges between sulfonate groups. In combination, all of the above phenomena would likely influence the stability of PSS-modified CNT dispersions in an aqueous electrolyte media. The aim of the present study is to provide mechanistic insight into polyelectrolyte-mediated interactions between CNTs with surfaces modified by PSS (used here as a model polyelectrolyte), in an aqueous electrolyte medium as a function of salt concentration and counter-ion valence. The interaction is evaluated by calculating the potential of mean force between two PSS-modified CNTs using molecular dynamics simulations and complementary free energy calculations.


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2 Simulation method Fully-atomistic representations of a PSS molecule and a single walled CNT used in our simulations are shown as simulation snapshots in Figs. 1(a) – (d). A PSS molecule in our simulation is a short-chain polyelectrolyte consisting of 22 monomer units. Carbon nanotubes with armchair geometry of (7, 7) bearing a length, l = 30 Å and a diameter, 2 r = 9.41 Å are considered for the study. The necessary coordinate data files for CNT and PSS molecules were created using Visual Molecular Dynamics (VMD)34 and the Marvin suite,35 respectively. Equilibrated structures of CNT/PSS complexes were obtained via adsorption of a PSS polyanion onto a CNT surface as shown in Figs. 1(c), (d). The distance-dependent interaction between PSS modified CNTs is simulated by placing two such CNT/PSS complexes at a separation distance, d, as shown in Fig. 1(e). All solutes were solvated with water molecules corresponding to a density of 1 g/cc. The effect of added salt was simulated by adding the appropriate number of either monovalent (Na+) or divalent (Mg2+) counter-ions, to the simulation box for respective salt concentrations. In order to make the system charge-neutral, equivalent numbers of either Na+/Mg2+ counter-ions (salt-free case) or Cl- co-ions (finite salt concentrations) were also added. All simulations were carried out by using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) package.36 Periodic boundary conditions were applied along all three directions. The CHARMM force-field was used to represent all inter-atomic potentials, and the TIP3P model was used to describe water molecules. Electrostatic interactions were evaluated using a ‘particle-particle particle-mesh’ Ewald solver37 with an accuracy of 10-4. Inner and outer cutoffs of 8 and 10 Å, respectively, were used for both electrostatic and Lennard-Jones interactions. Equations of motion were integrated using the velocity Verlet algorithm. Whereas, a simulation box size of 78 × 78 × 40 Å3 (nearly 24000 atoms including water) was used for equilibrating CNT/PSS complexes, a box size of 74 × 143 × 74 Å3 (nearly 77000 atoms including water) was used for evaluating the interactions between two CNT/PSS complexes. Simulations were performed in an NPT ensemble at a temperature of 300 K and a pressure of 1 atm. The Langevin thermostat and Berendsen barostat were used with damping time constants of 100 fs and 1000 fs, respectively. A time step size of 1 fs was used for all simulations. The rigidity of O-H bonds and H-O-H angles in water molecules were maintained using the SHAKE algorithm. In all our simulations, the orientation of a CNT axis was constrained along the Z5 ACS Paragon Plus Environment


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direction using the collective variable analysis (Colvars)38 module. Our simulation protocol involves first equilibrating isolated PSS polyanions in water for a duration of 10 ns (Figs. 1 (a), (b)). An equilibrated PSS polyanion was then made to adsorb over a bare CNT surface in a 15 ns long simulation (Figs. 1 (c), (d)). This process resulted in the formation of stable CNT/PSS complexes in water. The potential of mean force (PMF) between two CNT/PSS complexes (generated using the method described above), as a function of the distance, d, between the centers of masses of the two CNTs, was evaluated using the adaptive biasing force (ABF) method. According to the ABF method, the free energy along a transition coordinate can be seen as a potential resulting from the average force acting along the coordinate (ξ).39,40 = −〈 〉 = 〈

( )

−

ln||

() =

〉

(1) (2)

Where, || is the determinant of Jacobian for the transformation from Cartesian to generalized coordinates, and ( ) is the potential energy function. Equation (1) gives the instantaneous force applied along the transition coordinate to overcome the free energy barrier and this force was integrated to yield the potential given in Eq. (2). In our simulations, the distance, d, between the centers of masses of two CNTs is the transition coordinate and the PMF between the two CNT/PSS complexes is obtained as a function of d. Thus, d is the only unconstrained coordinate, while all rotations of the CNTs and translations of the CNT centers-of-mass in the X- and Zdirections are constrained through harmonic constraints. However, we do not constrain any degrees of freedoms corresponding to the adsorbed PSS molecules. Two CNT/PSS complexes were placed at a separation of d along the Y-axis in the larger simulation box of dimensions 74 × 143 × 74 Å3 for the ABF simulations (Fig. 1(e)). Systems corresponding to different salt concentrations of NaCl, = 0.05 M, 0.1 M, 0.5 M, and MgCl2 , !" # = 0.1 M. 0.5 M respectively, were considered for the ABF simulations. The sampling range along d spanned from 20 to 55 Å. This range was split into 7 equal windows of width 5 Å each. The lower bound of the sampling interval was fixed at d = 20 Å, since the CNT radius was nearly 5 Å, and the thickness of the adsorbed PSS layer was also found to be close to 5 Å. A given system was equilibrated for a period of 1 ns before the biasing force is applied. Run times for ABF


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simulations for different cases and windows varied between 10 – 30 ns, and their duration was decided by the extent of sampling in a particular run. The PMF over the entire range of d for a set of conditions was reconstructed using gradients, ∇A(), obtained from runs for individual windows. Electric potential maps were constructed using the PME Electrostatics module of the VMD package41, which uses the Ewald summation method to compute electric potentials at any location in the simulation box. VMD was also used for all visualization tasks.

3 Results and Discussion 3.1 Degree of ionization Simulation snapshots in Figs. 1(a), (b) show states of ionization for an isolated PSS polyanion in water, in presence of Na+ and Mg2+ counter-ions, respectively, obtained after 10 ns simulation (in absence of CNT). Over the course of another 15 ns simulation, the PSS polyanion was allowed to adsorb onto the hydrophobic CNT surface via its hydrophobic backbone, leading to the formation of a stable CNT/PSS complex. A back-of-the-envelope estimate, based on thermogravimetric analysis data of adsorbed PSS on MWCNTs,42,43 shows that approximately 15 monomers of styrene sulfonate adsorb onto the surface of the CNT (see Section S1 in Supporting Information for the calculation). This number is not too different from the 22-mer PSS segments that are allowed to adsorb onto the CNTs in our simulations. Hence, the PSS:CNT weight ratio used in the simulations is very close to typical PSS:CNT weight ratios commonly observed in aqueous CNT/PSS dispersions. Stable CNT/PSS complexes are formed both in the cases of Na+ and Mg2+ counter-ions, as shown in Figs. 1(c) and (d), respectively. For a PSS polyanion, whether isolated in solution or in a bound state with the CNT, the Na+ counter-ions do not appear to be strongly associated with -

the SO3 functional groups, possibly leading to a highly charged PSS backbone. In contrast, and -

as expected13,14,32,44 for a multi-valent ion, Mg2+ counter-ions are very strongly bound to the SO3 groups, whether in solution or bound with the CNT.



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Figure 1. Simulation snapshots illustrating ionization of PSS in aqueous media as an isolated polyelectrolyte and as a polyelectrolyte adsorbed onto a CNT surface, for the cases of (a) isolated NaPSS polyelectrolyte, (b) isolated MgPSS polyelectrolyte, (c) NaPSS adsorbed onto the CNT surface, (d) MgPSS adsorbed on to the CNT surface. (e) Snapshot of the simulation setup showing two CNT/PSS complexes in presence of Na+ counter-ions separated by a distance of 55 Å. Water molecules are not shown here for clarity. Table 1. Degree of ionization values for NaPSS and MgPSS in an aqueous medium for the cases of an isolated polyelectrolyte and a polyelectrolyte adsorbed onto a CNT surface.

Trial number

Na-PSSH2 O

Na-PSS-CNTH2 O

Mg-PSSH2O

Mg-PSSCNT-H2O

1

0.84

0.77

0.00

0.00

2

0.78

0.70

0.00

0.00

3

0.78

0.79

0.00

0.00

4

0.79

0.68

0.00

0.00

Avg. degree of ionization

0.80

0.74

0.00

0.00


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Degree of ionization (doI) calculations for all four cases in Figs. 1 (a) – (d) are shown in Table 1, where the doI value has been averaged over four independent simulations for each case. A -

proximity criterion between a sulfonate group, SO3 , and a Na+/ Mg2+ counter-ion, based on a cutoff distance of 6 Å, was used to determine whether a counter-ion is condensed onto the PSS polyanion. As expected, the isolated PSS polyanion appears in a highly ionized state in presence of Na+ counter-ions, with the doI value decreasing slightly once PSS adsorbs onto the CNT. The decrease in the doI values could be due to the reduced entropy of the PSS backbone which leads to a slight increase in the condensation of Na+ counter-ions on the PSS polyanion. However, Mg2+ counter-ions are found to strongly condense onto the PSS polyanion, both for the isolated PSS and CNT/PSS complex, resulting in doI values of zero. These findings are consistent with previous reports in the literature. Langevin dynamics simulations45 of flexible bead-spring polyelectrolyte chains have shown lower degrees of ionizations in presence of divalent and trivalent counter-ions as opposed to monovalent counter-ions. Molecular dynamics simulations of 20-mer polyacrylic acid (PAA) oligomers46 show rapid dissociation of monovalent Na+ counter-ions within a few picoseconds after introducing the PAA polyanion in water. However, when CaCl2 is added to solution, divalent Ca2+ counter-ions are found to come in direct contact with the carboxylate groups on the PAA polyanion after 2 ns of simulation time. Similarly, using MD simulations combined with metadynamics, Bulo et al.47 have demonstrated a strong “site binding” of Ca2+ counter-ions to carboxylate groups in a short PAA polyanion. The strong -

condensation of Mg2+ counter-ions occurs because the average separation between two SO3 groups on a PSS chain is approximately 4 Å which is less than the Bjerrum length of 28 Å for divalent counter-ions at 300 K.48 The doI calculations are also corroborated by radial distribution -

functions describing the correlation of counter-ions with the SO3 groups. Figures S1 and S3 in the Supporting Information discuss the adsorption of PSS onto CNTs and counter-ion condensation, through plots of radius of gyration and radial distribution functions, respectively. Though, we consider only one type each of monovalent (Na+) and divalent (Mg2+) counter-ions in our simulations, counter-ion affinities to the anionic sulfonate group can vary for different types of either monovalent (Na+ vs K+) or divalent (Ca2+ vs Mg2+) cations. For instance, MD simulations49 have shown that carboxylate (a small anionic group) has a greater affinity for Na+ over K+, and methylsulfonate (a large anionic group) has a greater affinity for K+ over Na+. The 9 ACS Paragon Plus Environment


specificity of cation-anion interactions in water can be explained phenomenologically by a law of matching water affinities proposed by Collins50,51 which predicts that the spontaneous association of oppositely charged ions in water is related to free energies of ion hydration. Using a combination of fully-atomistic MD simulations and ab initio calculations with polarizable continuum water models, Jungwirth and co-workers have constructed Hofmeister-like series where different cations can be arranged in decreasing order of affinities with respect to an anionic functional group. Cation-anion interactions were considered for various large anions, including acetates, formates and methylsulfonates, commonly present in proteins, surfactants and polyelectrolyte systems.49,52–54 Using thermodynamic and spectroscopic data, Kherb and coworkers could order various monovalent and divalent cations in Hofmeister-like series for acetate-cation interactions, and found that all divalent cations showed much stronger association with acetate in comparison to monovalent species.55

3.2 Potential of mean force As described in the Methods section, Step 2 of our simulation protocol is used to generate stable CNT/PSS complexes, as shown in Fig. 1(c), (d). Their dispersion stability is determined by computing the PMF between two parallel CNT/PSS complexes in an aqueous medium for different salt concentrations. Figure 1(e) shows a typical simulation setup for determining the PMF between two parallel CNT/PSS complexes as a function of their separation, d. Figure 2 shows snapshots from simulations corresponding to different salt concentrations, with the two CNT/PSS complexes separated by a distance of approximately 50 Å. The top row (Figs. 2(a) – (d)) represents CNT/PSS complexes in presence of Na+ counter-ions, with the NaCl concentration, , increasing from 0 M to 0.5 M from left to right. Figures 2(e), (f) show

CNT/PSS complexes with Na+ counter-ions with added MgCl2 salt, corresponding to !" # = 0.1 M and 0.5M, respectively. One should note that both Na+ and Mg2+ counter-ions are visible

in these figures. Figure 2(g) in the bottom row represents a simulation with no salt but Mg2+ counter-ions. Consistent with the findings of Fig. 1, Na+ counter-ions do not appear to be strongly condensed onto the PSS polyanion in presence of monovalent NaCl salt (Figs. 2 (a) – (d)), which effectively renders the CNT surface negatively charged. Also, consistent with expected counter-ion behaviour next to charged colloidal surfaces, Na+ concentration next to the CNT surfaces is seen to increase with increasing NaCl concentration. This strongly indicates 10 ACS Paragon Plus Environment

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increasing double layer thickness with increasing NaCl concentration. In presence of MgCl2 salt, the concentration of Mg2+ counter-ions next to the CNT surfaces increases with salt concentration. Although it is not very clear from the two-dimensional representations in Figs. 2(e), (f), some Mg2+ counter-ions do condense onto the PSS polyanion. Figure 2(g) shows that Mg2+ counter-ions are condensed onto the PSS polyanion, which suggests that the surface of the CNT/PSS complex will be devoid of any surface charge.

Figure 2. Simulation snapshots showing Na+ counter-ions in the vicinity of two CNT/Na-PSS complexes separated by 50 Å at different NaCl concentrations, (a) 0 M, (b) 0.05 M, (c) 0.1 M, and (d) 0.5 M. Similarly, both Na+ and Mg2+ counter-ions are shown for added MgCl2 salt in (e) 0.1 M MgCl2 , and (f) 0.5 M MgCl2 , (g) considers the case of no added salt and two CNT/MgPSS complexes showing complete condensation of Mg2+ counter-ions onto PSS. Water molecules are not shown here for clarity. The computed PMFs for a system of two CNT/PSS complexes for different electrolyte concentrations and varying ion types are discussed in Fig. 3. The reference state for all PMF calculations is fixed at d = 55 Å (maximum separation distance considered in the simulations), where the PMF is assumed to be zero. This separation is nearly four times the Debye length (13.6 Å at 0.05 M NaCl) for the lowest electrolyte concentration considered here, hence it is



reasonable to expect that interactions between the two CNT/PSS complexes are weak at d = 55 Å. To be precise, counter-ion densities peak at approximately 10 Å from the CNT axis (Fig. 6), which translates to a peak-to-peak separation of 35 Å. This separation is still nearly three times the largest Debye length (13.6 Å at 0.05 M NaCl) considered in our simulations. Figure 3(a) compares the PMF between two CNTs for the following three cases; (i) unmodified bare CNTs, (ii) CNTs modified with the Na-salt of PSS, and (iii) CNTs modified with the Mg-salt of PSS. The interaction between two bare CNTs in water is marked by a strong attraction, which is characteristic of hydrophobic colloids in water. The well-depth is nearly -40 kcal/mol and the equilibrium separation is close to 12.5 Å (which is approximately equal to the van der Waals diameter of the CNT, 9.41 Å + 3.4 Å = 12.81 Å), and clearly points to aggregation of CNTs in water. Upon adsorption of the PSS polyanion onto the CNT surface, there is a qualitative change in the interaction between the two CNTs. The PMF shifts to the right and is repulsive over the entire range studied here. However, the counter-ion valence seems to have a strong influence on the range of the interaction potential between the two CNT/PSS complexes. For the case of the Na+ counter-ion, where the doI is quite high and the surfaces are charged, a long-range character to the decay of the PMF (d > 25 Å) is noticed, suggesting a Coulombic repulsion between the two CNTs. In contrast, for Mg2+ counter-ions, the long-range character nearly disappears, and the repulsion seems to be a result of a strong, but short-range steric interaction (active at separations below 30 Å). Based on the observations in Figs. 1(b) and (d), the short-range steric repulsion, in presence of divalent counter-ions, can thus be attributed to the quenching of surface charges on the CNT/PSS complex resulting from Mg2+ condensation onto the PSS polyanion. (A plot of the surface electric potentials next to CNT/PSS complexes shown in Fig. S8 also confirms the neutralization of surface charge in presence of the Mg-salt of PSS.) Hence, the results suggest that, whereas CNT dispersions are electrostatically stabilized in presence of Na-PSS, they are sterically stabilized in presence of Mg-PSS. Next, we systematically study the interaction between CNT/PSS complexes as a function of salt concentration. Figure 3(b) shows the PMF between two CNT/PSS complexes for four different NaCl (1:1 salt) concentrations, = 0 M, 0.05 M, 0.1 M and 0.5 M. The first observation is that the interaction between the CNT/PSS complexes is repulsive and appears to be long-ranged for all salt concentrations. However, the range of interaction potential decreases with increasing salt concentration, indicating a screening effect, due to increased concentration of Na+ counter12 ACS Paragon Plus Environment

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ions in front of the negatively charged CNT/PSS complexes. Visual evidence from Figs. 2(a) – (d) also clearly shows increasing accumulation of Na+ counter-ions next to the CNT/PSS complexes with increasing NaCl concentration. This is discussed in greater quantitative detail later in Fig. 6. As a result, the electric potential decays over shorter distances with increasing salt concentration, thereby reducing the range of repulsive PMF in the medium. This lends further credence to the conclusion that the repulsive interaction between two CNTs has an electrostatic origin.

Figure 3. Calculated PMF as a function of separation, d, between two CNT/PSS complexes which varies from 20 Å to 55 Å. (a) PMF curves for bare CNTs, and salt-free cases with NaPSS and Mg-PSS, respectively. (b) Variation of PMF for CNT/PSS complexes in presence of monovalent NaCl salt at concentrations of 0 M, 0.05 M, 0.1 M, and 0.5 M, respectively. (c) Variation of PMF for CNT/PSS complexes in presence of divalent MgCl2 salt at concentrations of 0 M, 0.1 M, and 0.5 M, respectively. (d) PMF curves in (b) fitted to a generalized DLVO interaction between charged cylindrical colloids predicted from the theory by Chapot et al.27



However, the interaction between CNT/PSS complexes is very different in presence of divalent MgCl2 (2:1 salt) and is discussed in Fig. 3(c). One should note that the Na-salt of PSS is considered here, with additional Mg2+ and Cl- ions being added, corresponding to two MgCl2 concentrations, !" # = 0.1 M and 0.5M, respectively. Figure 3(c) shows three plots corresponding to the salt-free case of Na-PSS/CNT complexes, !" # = 0.1 M and !" # = 0.5

M. In contrast with the salt-free Na-PSS/CNT case, which is used as a reference here, the PMF at !" # = 0.1 M does not seem to show a long-range repulsive character. Instead, the repulsion appears to be short-ranged and mostly of a steric nature. Interestingly, at !" # = 0.5 M, the

PMF has an attractive well over the range 30 Å < d < 45 Å. The well has a depth of approximately 3.0 kcal/mol and a minimum located at d = 36 Å (see inset in Fig. 3(c)). MD simulations of cation binding with carboxylate groups in polyacrylate oligomers by Bulo et al.47 have shown that direct coordination of Ca2+ with a COO- group leads to a decrease of more than 10 kcal/mol in free energy when compared to the direct binding of Na+ with a COO- group. Moreover, a Ca2+ ion has to overcome a large barrier of approximately 11 kcal/mol to detach from the COO- group, implying a very strong binding of Ca2+ ions to the polyacrylate chains. In contrast, a low detachment barrier of 1 kcal/mol and a preference for water-mediated indirect binding were observed for a Na+ ion. Based on the Hofmeister series proposed by Vlachy et al.,54 one would expect the Na+ ion to have an even weaker affinity for the sulfonate groups in PSS. It is well known that ion-correlation effects and counter-ion condensation in presence of multivalent ions can lead to attractions between like-charged particles. These effects can be understood in the context of theories predicting like-charged attractions for rigid rods, in presence of divalent counter-ions.29–31 Attraction between like-charged polyelectrolytes, such as DNA, in presence of multi-valent counter-ions has been shown in several experiments.28 Moreover, experiments have shown that divalent counter-ions can lead to lateral assembly of viruses in solution.33 In addition, several molecular dynamics and Monte Carlo simulations have also demonstrated attractive interactions in presence of multi-valent salts for spherical particles.13–16 In an interesting MD study, Wu and Yang56 have shown increased repulsion between two sodium dodecyl sulfate modified graphene sheets in presence of a very high concentration (4 M) of CaCl2, even though they observe Ca2+ binding with negatively charged -

SO4 groups. They attributed the repulsion to a combined effect of steric repulsion between 14 ACS Paragon Plus Environment

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adsorbed surfactants and Coulombic repulsion between surfactant headgroups and Cl- ions confined between the graphene sheets. However, to the best of our knowledge, this is the first time that attraction between polyelectrolyte-modified CNTs has been predicted in presence of divalent counter-ions. In Fig. 3(d), we compare the simulation results from Fig. 3(b) with theoretical predictions made by Chapot et al.

26

for the DLVO interaction between two highly charged cylinders. The dashed

lines corresponding to the theoretical predictions are obtained by assuming certain parameters, such as Debye length, surface potential and cylinder radius. The calculation of the fitting curves based on the predictions of Chapot et al. are discussed in greater detail in section S3 (Supporting Information). We find very good qualitative and quantitative match for our simulation results, with theoretical predictions for = 0.05 M and 0.1 M. For = 0.5 M, the simulation results are qualitatively similar to the theoretical predictions but predict higher values when compared to the theory. The difference between simulation and theory can be attributed to a variety of factors, the most significant of them being that the surface charge density is nonuniform in our simulation. The most important conclusion from this comparison is that interaction between CNT/PSS complexes in a monovalent salt can be described by a generalized DLVO interaction, which accounts for anisotropy of charged cylindrical colloids. Polarizable water models are also employed in simulations to better incorporate polarization effects associated with solvation shells next to charged interfaces. Jungwirth and co-workers17,49 have used ab initio calculations with polarizable continuum water models to calculate the association free energies for cation-anion pairs. Kamath et al.57 compared solvation dynamics of water in nano-confinement between two MgO slabs using a polarizable shell water model and a non-polarizable three-site water model in molecular dynamics simulations. Interestingly, both models predicted a similar interfacial structure, but the polarizable model seemed to over predict the orientational order and under predict transport properties of water in confinement. Using coarse-grained MARTINI models with a polarizable description for coarse-grained water, Vögele et al. simulated58,59 polyelectrolyte complexes of polystyrene sulfonate and polydiallyldimethylammonium (PDDA), and demonstrated good agreement with data from fully atomistic simulations using non-polarizable three-site water models.60,61



-

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-

3.3 Inter-chain SO3 - SO3 correlations in presence of MgCl2 In order to test the prediction of attraction between CNT/PSS complexes induced by divalent counter-ions, we ran a 5 ns long “unconstrained” simulation, where two CNT/PSS complexes are placed at a separation of approximately 40 Å in a 0.5 M MgCl2 solution. Only the orientation of the CNTs are constrained along the Z-axis via a harmonic constraint. The distance of 40 Å is chosen because it is close to the location of the energy minimum (d = 36 Å) for the PMF curve corresponding to the case of 0.5 M MgCl2 (Fig. 3(c)).

Figure 4. (a) Simulation snapshots over a 3 ns interval showing the close association of two -

-

CNT/PSS complexes at 0.5 M MgCl2 salt resulting from inter-chain SO3 - SO3 correlations due to bridging by divalent Mg2+ counter-ions. (b) Separation distance between the two CNT/PSS complexes remains nearly constant over the 3 ns interval. (c) Radial distribution functions -

-

-

between two SO3 groups on different CNT/PSS complexes show that inter-chain SO3 - SO3 correlations are stronger at 0.5 M MgCl2 in comparison to 0.1 M MgCl2 . Figure 4(a) shows simulation snapshots over the course of first 3 ns of simulation. The two CNT/PSS complexes appear to maintain their original separation distance and remain in registry 16 ACS Paragon Plus Environment

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with respect to each other. Quantitatively, this is shown in Fig. 4(b), where the separation distance between the two CNT/PSS complexes remains nearly constant over the 3 ns period. This clearly points to an attractive interaction between the two complexes, and thus validates the prediction of the PMF curve in Fig. 3(c). Although, the diffusivity of CNTs is expected to be low, our estimates (see Supporting Information, section S5) based on a translational diffusion constant indicate root mean square displacements of nearly 2 nm which are 4 – 5 times larger than the fluctuations in distance (less than 5 Å) observed in Fig. 4(b). Hence, the relative displacement of the CNT/PSS complexes is influenced most strongly by the attraction induced by Mg2+ ions. A comparison of the “unconstrained” simulation of Fig. 4 with two “unconstrained” simulation scenarios discussed in section S5 of the Supporting Information clearly shows that CNT-CNT attraction is induced by Mg2+ ions. The first “unconstrained” simulation is a hypothetical case of two CNT/PSS complexes interacting in the presence of Mg and Cl atoms, each bearing zero charge, added to the simulation box corresponding to a salt concentration of 0.5 M MgCl2 . In this case, Mg and Cl atoms interact only through Lennard-Jones interactions. PSS polyanions and Na+ counter-ions carry their respective charges. For the second simulation, Na+ and Clions bearing their respective charges are added to the simulation box corresponding to a salt concentration of 0.5 M NaCl. It is found that the CNT-CNT distance remains more or less constant only in presence of divalent Mg2+ ions, and diverges for the other two cases (Figs. S4 and S5).

A limitation of the small CNT length and low degree of polymerization of the PSS, considered in the simulation is that, the surface coverage of the CNT is non-uniform. Over the course of a simulation, CNTs can rotate about their axes, and result in the two adsorbed PSS polyanions falling out of registry. This reduces the attraction, and beyond 3 ns the separation distance was found to slowly increase because CNTs would begin to slide along the Z-axis. In our opinion, if one were to consider larger CNTs and longer PSS molecules which would possibly wind around the CNTs upon adsorption, it would be possible to stabilize the lateral assembly of two CNT/PSS complexes for longer durations over the course of the simulation. However, this would entail considering a much larger simulation box and a more expensive computational effort. Figure 4(c) -

shows radial distribution function plots representing the inter-chain correlations between SO3 groups on the two PSS chains, adsorbed on either CNTs, for !" # = 0.1 M and 0.5 M. From -

these plots, one can conclude that a stronger correlation exists between SO3 groups of the two 17 ACS Paragon Plus Environment


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apposing PSS chains at 0.5 M MgCl2 , in comparison to the correlations at the lower MgCl2 -

concentration of 0.1 M. For the 0.5 M case, correlations between the SO3 groups start becoming significant at separation distances of 5 Å, whereas at 0.1 M MgCl2 , no significant correlations are observed for separation distances less than 9 Å. This result further contributes to our claim -

that, Mg2+ induced correlations between SO3 groups on the two PSS chains lead to a net attraction between the CNT/PSS complexes in 0.5 M divalent MgCl2 salt solution. Figure 5(a) is a more detailed view of the snapshot at 2.5 ns from Fig. 4(a) and shows Mg2+ ions forming bridges between anionic SO3 groups on the two PSS chains. Measured distances of SO3 − Mg*+ -

-

ion pairs correlate well with the peaks in the radial distribution function plot, ,

-

SO3 0Mg

(3), in Fig.

5(b).

Figure 5. (a) Detailed view of the snapshot at 2.5 ns from the simulation in Fig. 4(a) showing divalent Mg2+ ions forming ion bridges between two SO04 groups on the two CNT/PSS complexes at 0.5 M MgCl2 . (b) Radial distribution function representing distribution of Mg2+ ions around sulfonate group on the CNT/PSS complexes in (a). In Figs. 6 – 9, we discuss the distribution of counter-ions and water around the CNT/PSS complexes, and the variation of electric potential away from the CNT surfaces. These quantities were calculated from data obtained from simulations, where two CNT/PSS complexes were held at a fixed separation of 50 Å. More specifically, atoms corresponding to the CNTs and the PSS 18 ACS Paragon Plus Environment

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polyanions are held rigid and not allowed to move during the course of the simulation. However, atoms corresponding to water and all ions are allowed to move in simulations. Simulations of 4 ns duration each are then carried out for different salt concentrations of NaCl and MgCl2 . Ion densities, water densities and electric potential values corresponding to a particular salt concentration were generated by time-averaging values of the respective quantities, over the final 1 ns of that simulation. This way, we ensure that the results correspond to a well-equilibrated system. The evaluation of the electric potential takes into account all the charges that are present in the simulation box, including PSS polyanions, co-ions, counter-ions and all partial charges of water molecules.

3.4 Counter-ion density distributions Counter-ion densities for Na+ and Mg2+ ions as functions of the radial distance from centers of CNT/PSS complexes are plotted in Figs. 6(a) and (b), respectively, for different salt concentrations of NaCl and MgCl2 . Vertical dashed lines in Figs. 6(a) and (b) represent the location of the CNT surface at approximately 5 Å from the CNT axis, at r = 0 Å. In presence of added NaCl salt [Fig. 6(a)], we observe that Na+ concentration next to the CNT surface increases with increasing bulk NaCl concentration for all values of r. As expected, for counter-ion distributions next to charged surfaces, Na+ counter-ions accumulate near the negatively charged CNT/PSS surface with a maximum density appearing at r ≈ 12 Å. Beyond this, Na+ density decays over a certain distance, to approach a bulk value. Ion density profiles beyond r = 25 Å are not shown here, because this is half of the 50 Å separation between the two complexes. Figure S6 shows the profiles at larger radial distances. This behavior is qualitatively consistent with the classical Poisson-Boltzmann description of counter-ion distribution next to a charged surface.



Figure 6. Radial distributions of counter-ion density around a CNT for different molar concentrations of salt. (a) Na+ ion distribution from center of a CNT extending radially outward for different NaCl concentrations, and (b) Mg2+ distribution from center of a CNT extending radially outward for different MgCl2 concentrations. Dashed vertical lines in (a) and (b) indicate the CNT surface at 5 Å from its axis.

Deserno et al.62 investigated counter-ion condensation on a rigid-rod polyelectrolyte in the context of a cell-model by comparing numerical solutions of the Poisson-Boltzmann equation and MD simulation results. Their calculations of fractional number of counter-ions, distributed in a cylindrical domain surrounding the polyelectrolyte, showed that screening effects dominate in presence of added monovalent salt. A smaller peak in Na+ density is also observed for NaCl concentrations close to r ≈ 16 Å. This peak becomes more prominent with an increase in the overall NaCl concentration. It is most likely a result of the tail end of the adsorbed PSS extending radially outward in the solution. The Mg2+ ion density profiles for the case of divalent MgCl2 salt [Fig. 6(b)] are qualitatively similar to the Na+ profiles. However, there are some differences. In addition to the maximum ion density occurring at r ≈ 12 Å, there is a smaller but significant peak at r < 10 Å, suggesting a strong affinity of Mg2+ ions to the PSS polyanion. Also, ion density values at the maxima (r ≈ 12 Å) turn out to be comparable for equal concentrations of NaCl and MgCl2 , respectively. However, Mg2+ ions carry double the quantum of charge in comparison to Na+ ions, thereby leading to a 20 ACS Paragon Plus Environment

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much greater screening of surface potential by the Mg2+ counter-ions. It is observed that Mg2+ ion densities decay to a slightly lower value in comparison to Na+ ion densities, for same values of and !" # . This could be because of the fact that, for the case of NaCl, both Na+-PSSand NaCl contribute to the overall number of Na+ ions in solution. A comparison of the Mg2+ and Na+ profiles for the same MgCl2 concentration provides insight into the competitive adsorption of two cations on the negatively charged CNT/PSS surfaces. Concentration profiles for Na+ counter-ions are also plotted in Fig. 6(b) for the two MgCl2 concentrations as dashed lines, and clearly indicate that Mg2+ ions bind preferentially to the PSS polyanion when compared to the Na+ ions. As the MgCl2 concentration increases, the larger Na+ peak shifts rightward from 11 Å at 0.1 M to 16 Å at 0.5 M, and also diminishes greatly in intensity indicating that the sulfonate groups have a higher affinity for the divalent cations. In simulations of short-chain Li+-PSSaqueous solutions next to graphene surfaces in presence of BaCl2 and LaCl3 salts, Chialvo and Simonsen63 demonstrated that the negatively charged sulfonate groups have a greater binding affinity to Ba2+ and La3+ in comparison to the smaller monovalent Li+ ion.

3.5 Water density distributions Water density distributions are shown in Fig. 7, both as polar plots (Figs. 7(a) – (d)) and as radial density plots (Fig. 7(e) – (f)), for the cases of = 0 M and 0.1 M. Figures 7(a) and (b) are polar plots of water densities for the two apposing CNT/PSS complexes, placed at a separation of 50 Å for the case of = 0 M. Similarly, Figs. 7(c) and (d) correspond to polar plots of water

densities for the two apposing CNT/PSS complexes for the case of = 0.1 M. The polar

plots clearly show the anisotropy in water distribution arising from asymmetric adsorption of PSS polyanion onto the CNT surfaces. The black colored areas in the polar plots are regions devoid of water and correspond to the -

hydrophobic CNT and the PSS backbone. Water density is higher around the ionized SO3 groups (indicated by blue color), which are hydrophilic in nature. In contrast to the CNT/PSS complexes, water distribution is symmetric for the case of bare CNTs as shown in Fig. S7.1(a), (b). Far away from the CNT/PSS complexes, water density is expected to be invariant with



respect to salt concentration. In addition, based on visual observations, water density in the vicinity of the CNT/PSS complex does not seem to drastically change with the addition of NaCl. This observation is also confirmed, when we plot water density profiles as a function of the radial distance from the centers of two CNTs, at two values of in Figs. 7 (e), (f). The radial density plots at the two NaCl concentrations are practically indistinguishable, thus confirming for the range of NaCl concentrations examined here, that added salt does not alter the water density significantly in the vicinity of the CNT/PSS complex. The same is found to be true for water distributions around CNT/PSS complex in presence of divalent MgCl2 salt (Fig. S7.2).


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Figure 7. Distribution of water around two CNT/PSS complexes (denoted by CNT1 and CNT2) separated by 50 Å at different NaCl concentrations. (a) and (b) Polar plots of water distribution at 0 M NaCl next to (a) CNT1 and (b) CNT2. (c) and (d) Polar plots of water distribution at 0.1 M NaCl next to (c) CNT1 and (d) CNT2. (e) and (f) Radial density distributions at 0 M and 0.1 M NaCl next to (e) CNT1 and (f) CNT2. Dashed vertical lines in (e) and (f) indicate the CNT surface at 5 Å from its axis. 23 ACS Paragon Plus Environment


3.6 Electrostatic potential maps Figures 8(a) – (f) show anisotropy in the description of electric potential around the CNT/PSS complexes at different NaCl concentrations of = 0 M, 0.1 M and 0.5 M. Whereas, Figs. 8(a), (b) show the electric potential variation around the two CNT/PSS complexes placed at a distance of 50 Å, at = 0 M; Figs. 8(c), (d) and 8(e), (f) show the same for two CNT/PSS complexes at = 0.1 M and 0.5 M, respectively. We have superimposed the atomic

representation of individual CNT/PSS complexes (corresponding to average position from the simulations) on top of the electric potential plots. Now, one can clearly see that regions in the vicinity of the adsorbed PSS polyanion acquire a negative electric potential due to the ionized -

state of the SO3 groups. These are indicated by blue shaded regions, which are localized around the polymer. Addition of salt to water leads to increased screening of surface charge and may also reduce the electric potential at the CNT/PSS surface. This is observed in Figs. 8(e), (f), where the extent of blue shaded regions comes down significantly in comparison to the salt-free cases of Figs. 8(a), (b) and 0.1 M of Fig. 8(c), (d). Observations from the plots of Fig. 8 are important because they conclusively prove that, the adsorption of PSS polyanion onto CNTs leads to formation of CNTs with negatively charged surfaces. This in turn results in a long-range electrostatic interaction between two CNT/PSS complexes which contributes to their excellent dispersion stability in aqueous media.


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Figure 8. Polar plots of electric potential distribution around two CNT/PSS complexes (denoted by CNT1 and CNT2) separated by 50 Å at different NaCl concentrations. Electric potential at 0 M NaCl next to (a) CNT1 and (b) CNT2. Electric potential distribution at 0.1 M NaCl next to (c) CNT1 and (d) CNT2. Electric potential distribution at 0.5 M NaCl next to (e) CNT1 and (f) CNT2.



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Figures 9(a) – (d) show anisotropy in the description of electric potential around CNT/PSS complexes at two different MgCl2 concentrations of !" # = 0.1 M, 0.5 M. From these plots, one can clearly see that regions in the vicinity of the adsorbed PSS polyanion acquire a positive -

electric potential due to overcharging, in presence of Mg2+ ions, which condense onto the SO3 groups of the polyelectrolyte chain. These are indicated by grey shaded regions, which are localized around the polymer. Addition of a divalent salt to water leads to increased screening of surface charge and may also reduce the electric potential at the CNT/PSS surface.

Figure 9. Polar plots of electric potential distribution around two CNT/PSS complexes (denoted by CNT1 and CNT2) separated by 50 Å at different MgCl2 concentrations. Electric potential at 0.1 M MgCl2 next to (a) CNT1 and (b) CNT2. Electric potential at 0.5 M MgCl2 next to (c) CNT1 and (d) CNT2. 26 ACS Paragon Plus Environment

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Figures 10(a), (b) show variation of the electric potential as a function of separation between two CNT/PSS complexes. Electric potential values are calculated in the X-Y plane cutting through the middle of two CNT/PSS complexes, and the variation along a line in the Y-direction is plotted in Fig. 10. This is described schematically in the inset of Fig. 10(a). The dashed lines indicate the location of the centers of the two CNTs at d = -25 Å and d = 25 Å. The adsorbed PSS polyanions are localized on the inside edges of the CNTs (see Fig. 8).

Figure 10. Variation of electric potential between two CNT/PSS complexes along the direction of separation (Y-axis) at d = 50 Å for (a) NaCl concentrations of 0 M, 0.05 M, 0.1 M and 0.5 M, and (b) MgCl2 concentrations of 0 M, 0.1 M and 0.5 M. From Fig. 10(a), we observe that, the surface potentials of CNT/PSS complexes are negative at all concentrations of NaCl. The electric potential shows a large negative value, approximately 10 Å away from the center of the CNTs at 5 615 Å, which should correspond to the surface potential that develops at the CNT/PSS surface. This is also consistent with the maxima in Na+ ion density plots observed at 5 10 Å in Fig. 6(a). With increase in , the surface potential values decrease, from approximately 180 mV at 0 M NaCl to 70 mV at 0.5 M NaCl, as a result of increased condensation of counter-ions onto the CNT/PSS surface. In addition, the characteristic decay length of the electric potential also decreases with increasing NaCl concentration. This observation is consistent with the idea of increased electrostatic screening of the surface potential with increasing salt concentration. We note that the electric potential variation is not symmetric with respect to the two CNT/PSS complexes, which is a manifestation 27 ACS Paragon Plus Environment


of the asymmetric adsorption of PSS onto the CNTs. However, for a given NaCl concentration, the surface potential values for the two CNT/PSS complexes are quantitatively very similar. The effect of a divalent salt is shown in Fig. 10(b), where the electric potential for the two cases of !" # = 0.1 M and 0.5 M are plotted with the salt-free CNT/Na-PSS case. Further, the electric potential curves are asymmetric with respect to the two CNT/PSS complexes and show increased screening with increase in an MgCl2 concentration. However, these plots differ qualitatively with those for NaCl in a significant way. The surface potential for the CNT/PSS complexes becomes positive, in comparison to the negative surface potential, observed in presence of NaCl. This is because of charge reversal at the CNT/PSS surface resulting from condensation of divalent Mg2+ ions, as shown in Figs. 2(e), (f) and Fig. S3(b).

4 Conclusions In this study, we have used fully atomistic molecular dynamics simulation and free energy calculations to calculate the PMF between two CNT/PSS complexes, in an aqueous electrolyte medium under varying conditions of added-salt concentration and counter-ion valence. The calculated PMF provides a quantitative measure of the interaction between polyelectrolytemodified CNTs, in aqueous electrolyte media at the molecular level. This can be used to determine the colloidal stability and aggregation behavior of CNT/PSS complexes in water. Our simulation results lead us to the following important conclusions: •

PSS polyanions adsorb onto CNT surfaces via their hydrophobic backbones, and their aromatic side-groups also display a strong registry with the CNT surface. Although the model description and force-field used in the simulations do not account explicitly for π-π interactions, the registry possibly suggests that π-π interactions could, in part, enable PSS adsorption onto CNT surfaces. This leads to the formation of stable CNT/PSS complexes. The degree of ionization of adsorbed PSS and consequently the surface potential of CNT/PSS complexes is dependent on both counter-ion valence and electrolyte concentration in the medium. This leads to a long-range electrostatic repulsion between CNT/PSS complexes in presence of monovalent Na+ counter-ions and also a short-range steric repulsion in presence of divalent Mg2+ counter-ions.


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•

In presence of NaCl, interaction between two CNT/PSS complexes is electrostatic in origin and is characterized by increasing screening of the potential, with an increase in salt concentration. By comparing our simulation data to previously published theoretical results on colloidal interactions between charged cylinders, we show that the interaction between CNT/PSS complexes can be understood in terms of a generalization of the classical DLVO theory, which accounts for anisotropy in the shape of the colloids.

•

The effect of ionic valence is clearly observed in simulations, through condensation of divalent Mg2+ counter-ions onto the PSS polyanion, leading to CNT/PSS complexes with nearly zero surface electric potential. In presence of divalent MgCl2 salt in aqueous medium, strong ion-correlation effects lead to a net attraction between two like-charged CNT/PSS complexes. To the best of our knowledge, this is the first time that an attraction between two polyelectrolyte-modified cylindrical colloids has been shown in presence of multivalent salt.

Hence, our simulations address fundamental mechanistic questions regarding the colloidal stability of PSS-modified CNTs in an aqueous electrolyte media. In our opinion, the most important contribution of this study is that qualitatively different interactions, either short-range steric repulsion, long-range repulsion or attraction, can arise between PSS-modified CNTs based on counter-ion valence and electrolyte concentration. The results provide insight into tuning the range and strength of the effective interactions between CNT/PSS complexes in water, by the introduction of mono- and multi-valent counter-ion species. In addition, our results suggest that attraction between like-charged CNT/PSS complexes in divalent salt can lead to lateral assemblies of CNTs in an aqueous medium, which can be useful for a bottom-up design of CNT superstructures for supercapacitor applications.

Supporting Information Available Data for estimation of CNT surface coverage with PSS, radius of gyration, electrostatic potential calculation for anisotropic cylindrical colloids, radial distribution functions, water density distribution profiles and electric potential distribution were made available. This information is available free of charge via the Internet at http://pubs.acs.org/.



Acknowledgements The authors would like to acknowledge Grant SR/S3/ME/0016/2011 from the Department of Science and Technology, Ministry of Science and Technology, India for funding support, and National PARAM Supercomputing Facility at Centre for Development of Advanced Computing (CDAC), Pune, India for giving us access to use PARAM Yuva II.

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TOC Graphic



Figure 1. Simulation snapshots illustrating ionization of PSS in aqueous media as an isolated polyelectrolyte and as a polyelectrolyte adsorbed onto a CNT surface, for the cases of (a) isolated NaPSS polyelectrolyte, (b) isolated MgPSS polyelectrolyte, (c) NaPSS adsorbed onto the CNT surface, (d) MgPSS adsorbed on to the CNT surface. (e) Snapshot of the simulation setup showing two CNT/PSS complexes in presence of Na+ counter-ions separated by a distance of 55 Å. Water molecules are not shown here for clarity. 89x46mm (300 x 300 DPI)

ACS Paragon Plus Environment

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Figure 2. Simulation snapshots showing Na+ counter-ions in the vicinity of two CNT/Na-PSS complexes separated by 50 Å at different NaCl concentrations, (a) 0 M, (b) 0.05 M, (c) 0.1 M, and (d) 0.5 M. Similarly, both Na+ and Mg2+ counter-ions are shown for added 〖"MgCl" 〗_"2" salt in (e) 0.1 M 〖"MgCl" 〗_"2" , and (f) 0.5 M 〖"MgCl" 〗_"2" , (g) considers the case of no added salt and two CNT/Mg-PSS complexes showing complete condensation of Mg2+ counter-ions onto PSS. Water molecules are not shown here for clarity. 138x86mm (300 x 300 DPI)



Figure 3. Calculated PMF as a function of separation, d, between two CNT/PSS complexes which varies from 20 Å to 55 Å. (a) PMF curves for bare CNTs, and salt-free cases with Na-PSS and Mg-PSS, respectively. (b) Variation of PMF for CNT/PSS complexes in presence of monovalent NaCl salt at concentrations of 0 M, 0.05 M, 0.1 M, and 0.5 M, respectively. (c) Variation of PMF for CNT/PSS complexes in presence of divalent 〖 "MgCl" 〗_"2" salt at concentrations of 0 M, 0.1 M, and 0.5 M, respectively. (d) PMF curves in (b) fitted to a generalized DLVO interaction between charged cylindrical colloids predicted from the theory by Chapot et al.27 77x61mm (300 x 300 DPI)


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Figure 4. (a) Simulation snapshots over a 3 ns interval showing the close association of two CNT/PSS complexes at 0.5 M 〖"MgCl" 〗_"2" salt resulting from inter-chain 〖"SO" 〗_"3" ^"-" - 〖"SO" 〗_"3" ^"" correlations due to bridging by divalent Mg2+ counter-ions. (b) Separation distance between the two CNT/PSS complexes remains nearly constant over the 3 ns interval. (c) Radial distribution functions between two 〖"SO" 〗_"3" ^"-" groups on different CNT/PSS complexes show that inter-chain 〖"SO" 〗_"3" ^"-" 〖"SO" 〗_"3" ^"-" correlations are stronger at 0.5 M 〖"MgCl" 〗_"2" in comparison to 0.1 M 〖"MgCl" 〗 _"2" . 180x125mm (300 x 300 DPI)



Figure 5. (a) Detailed view of the snapshot at 2.5 ns from the simulation in Fig. 4(a) showing divalent Mg2+ ions forming ion bridges between two 〖"SO" 〗_3^- groups on the two CNT/PSS complexes at 0.5 M 〖 "MgCl" 〗_"2" . (b) Radial distribution function representing distribution of Mg2+ ions around sulfonate group on the CNT/PSS complexes in (a). 145x73mm (300 x 300 DPI)


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Figure 6. Radial distributions of counter-ion density around a CNT for different molar concentrations of salt. (a) Na+ ion distribution from center of a CNT extending radially outward for different NaCl concentrations, and (b) Mg2+ distribution from center of a CNT extending radially outward for different 〖"MgCl" 〗 _"2" concentrations. Dashed vertical lines in (a) and (b) indicate the CNT surface at 5 Å from its axis. 76x35mm (300 x 300 DPI)



Figure 7. Distribution of water around two CNT/PSS complexes (denoted by CNT1 and CNT2) separated by 50 Å at different NaCl concentrations. (a) and (b) Polar plots of water distribution at 0 M NaCl next to (a) CNT1 and (b) CNT2. (c) and (d) Polar plots of water distribution at 0.1 M NaCl next to (c) CNT1 and (d) CNT2. (e) and (f) Radial density distributions at 0 M and 0.1 M NaCl next to (e) CNT1 and (f) CNT2. Dashed vertical lines in (e) and (f) indicate the CNT surface at 5 Å from its axis. 195x230mm (300 x 300 DPI)


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Figure 8. Polar plots of electric potential distribution around two CNT/PSS complexes (denoted by CNT1 and CNT2) separated by 50 Å at different NaCl concentrations. Electric potential at 0 M NaCl next to (a) CNT1 and (b) CNT2. Electric potential distribution at 0.1 M NaCl next to (c) CNT1 and (d) CNT2. Electric potential distribution at 0.5 M NaCl next to (e) CNT1 and (f) CNT2. 216x282mm (300 x 300 DPI)



Figure 9. Polar plots of electric potential distribution around two CNT/PSS complexes (denoted by CNT1 and CNT2) separated by 50 Å at different 〖"MgCl" 〗_"2" concentrations. Electric potential at 0.1 M 〖"MgCl" 〗 _"2" next to (a) CNT1 and (b) CNT2. Electric potential at 0.5 M 〖"MgCl" 〗_"2" next to (c) CNT1 and (d) CNT2. 144x125mm (300 x 300 DPI)


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Figure 10. Variation of electric potential between two CNT/PSS complexes along the direction of separation (Y-axis) at d = 50 Å for (a) NaCl concentrations of 0 M, 0.05 M, 0.1 M and 0.5 M, and (b) 〖"MgCl" 〗 _"2" concentrations of 0 M, 0.1 M and 0.5 M. 76x35mm (300 x 300 DPI)


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