Influence of Counterion Valency on the Conformational Behavior of

Using a dissipative particle dynamics approach, we study the conformations and interactions of a cylindrical polyelectrolyte brush (CPB) with added sa...
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J. Phys. Chem. B 2009, 113, 5104–5110

Influence of Counterion Valency on the Conformational Behavior of Cylindrical Polyelectrolyte Brushes Li-Tang Yan,*,† Youyong Xu,‡ Matthias Ballauff,§,| Axel H. E. Mu¨ller,‡,| and Alexander Bo¨ker*,†,|,⊥ Physikalische Chemie II, Makromolekulare Chemie II, Physikalische Chemie I, and Bayreuther Zentrum fu¨r Kolloide and Grenzfla¨chen, DWI an der RWTH Aachen e.V. and Lehrstuhl fu¨r Makromolekulare Materialien and Oberfla¨chen, RWTH Aachen UniVersity, 52056 Aachen, Germany ReceiVed: December 3, 2008

Using a dissipative particle dynamics approach, we study the conformations and interactions of a cylindrical polyelectrolyte brush (CPB) with added salt. The effects of counterion valency on the conformational behaviors of the CPB are analyzed in detail by considering various parameters like the distribution of bond lengths, the mean distance between two grafting points, the order parameter of side chains, etc. The lyotropic behavior of the CPB is also investigated through examining the backbone persistence. Our simulations demonstrate that the presence of the multivalent counterions can induce the collapse of the CPB, leading to various conformations. We identify a horseshoe to helical to coil-like conformation transition with increasing counterion valency. An important factor for the collapse of the CPB is the fact that the strong condensation of counterions induced by the higher electrostatic correlations decreases the osmotic pressure inside the brush. It is found that the ratio of the backbone persistence to the diameter of the CPB, lp/d, can only be affected to a slight extent by changing the counterion valency and the side chain length. These results may provide a valuable guideline that can be used to tailor the microstructure of the systems and to yield desired macroscopic behaviors. 1. Introduction Attaching long polyelectrolyte (PE) chains to the solid surface leads to planar1–3 or spherical PE brushes,4–6 depending on the geometry of the surface. The investigation on PE brushes has become one of the most active fields in polymer science7–10 due to the entirely new properties of PE brushes compared with brushes of uncharged polymers and their importance in a wide range of areas, such as colloid stability,11 rheology control,12 and membrane modification.13 A major point of interest is the investigation of conformational transitions in PE brush systems. The conformational behavior of planar brushes with added salt has been explored experimentally and theoretically.3,14–16 For instance, theoretical mean-field approaches predict the collapse and weak swelling regimes of the brush layer, depending on the valency and the concentration of added salt.16 The conformational dependence on ionic strength and valency of counterions has also been investigated for spherical PE brushes (SPBs).17–21 Upon addition of multivalent counterions, a collapse of SPBs occurs because the replacement of monovalent counterions by multivalent ones reduces the number of counterions inside the brush.18,19 In combination with a strong condensation of the multivalent counterions on the PE chains, the osmotic pressure inside the brush, which is balanced by the chain’s elastic energy, is significantly reduced, also leading to the collapse of SPBs.18,19 * Corresponding authors. E-mail: [email protected] (L.-T.Y.); [email protected] (A.B.). † Physikalische Chemie II. ‡ Makromolekulare Chemie II. § Physikalische Chemie I. | Bayreuther Zentrum fu¨r Kolloide and Grenzfla¨chen. ⊥ DWI an der RWTH Aachen e.V. and Lehrstuhl für Makromolekulare Materialien and Oberflächen.

Recent advances in synthetic polymer chemistry have made it possible to produce macromolecules of complex and well defined topology with precise control of molecular parameters, e.g., the cylindrical polymer brushes, i.e., polymer chains, densely grafted with multiple side chains.22–24 Cylindrical polymer brushes can present different conformational behaviors in response to various external conditions, for example, temperature,22 the selectivity of the solvent,23 etc. When the side chains are PE chains, this leads to the cylindrical polyelectrolyte brush (CPB), which could potentially be used in the fields of nanotechnology and biomedicine, e.g, as a drug carrier.25–28 In contrast to the uncharged cylindrical polymer brushes, CPBs are more complex due to the additional length scales set by the long-range Coulomb interaction. There is also a delicate interplay between the electrostatic interactions between the counterions and the charged groups of CPBs, which in turn are governed by the short-range potential. Moreover, compared to the planar and spherical PE brushes, more conformational degrees of freedom from the main chain (backbone) render the study of CPBs more difficult. There have been few systematic investigations concerning the conformational behaviors of CPBs in the presence of added salt, which are almost limited within the experimental observations.1,25–28 Recently, we found experimentally that CPBs can exhibit helical structures in the presence of multivalent counterions.35 In contrast to spherical polymer brushes, the simulation results for CPBs are scarce, although computational simulations can provide a unique way to elucidate the properties of charged system.23,29,30 In the present paper, by employing a dissipative particle dynamics (DPD) approach, we simulate the systems of a CPB with added salt, which enables us to discern the conformations of the CPB and the distribution of the ions in depth. The correlation effect which is expected to be relevant for multivalent counterions is investigated. The conformational behaviors of

10.1021/jp810648z CCC: $40.75  2009 American Chemical Society Published on Web 03/23/2009

Conformational Behavior of CPBs

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the CPB with respect to various counterion valencies are analyzed in detail by considering different parameters, e.g., the distribution of bond lengths, the mean distance between two grafting points, the order parameter, etc. It will be demonstrated that such an approach reveals many new aspects of the conformation behaviors of CPBs.

When modeling polymers, the chains are constructed by connecting the adjacent particles via an extra harmonic spring31

2. Model and Simulation Details

where the constant C is -4.0. The electrostatic force FEi exerted on beads i is analyzed as reported in Groot’s work.32 According to this study, the electrostatic field is solved by smearing the charges over a lattice grid whose size is determined by a balance between the fast implementation and the correct representation of the electrostatic field. In the present simulations, the grid size is set to a. For each charged bead, a charge proportional to fn(ri) ) 1 - rin/Re is assigned to every grid node within a radius of Re ) 1.6a in such a way that the sum of all charged nodes is equal to the charge of the bead, where rin denotes the distance between the grid node n and the ion i.32 The electric field is solved according to the following equation:

DPD is a coarse-grained molecular dynamics (MD) approach that can capture effectively the hydrodynamics of complex fluids while retaining essential information about the structural properties of a system’s component.31 An advantageous feature of DPD is that it utilizes soft repulsive interactions between the beads which represent cluster of molecules or repeat units in a polymer chain. Consequently, one can use a significantly larger time step between successive iterations than those required by MD. In DPD, the pairwise interactive force acting on a bead i by the bead j contains three parts: the conservative force (FijC), the dissipative force (FijD), and the random force (FijR).

FijC ) RijωC(rij)eij

(1)

FijD ) -γωD(rij)(Vij · eij)eij

(2)

FijR ) σωR(rij)ξij∆t-1/2eij

(3)

where rij ) ri - rj, rij ) |rij|, Vij ) vi - vj, and eij ) rij/rij. ri and vi denote the position and velocity of bead i, respectively. γ is the dissipative strength which controls the heat dissipated in a time step, and σ is the noise strength with σ ) 3.67. ξij is a random number which has zero mean and unit variance. The conservative force FijC of eq 1 is derived from a soft interaction potential within a certain radius a. Rij is the maximum repulsion between bead i and bead j, which can relate to the Flory-Huggins χ-parameter.31 In the present simulations, the interaction between like species Rii is chosen to be 78.33 The hydrophilic nature of the side chains is captured by setting the repulsion parameter Rij between water and the monomer ions of the side chains to be 72, while a repulsion parameter between water and the monomers of the backbone with 83 is selected to specify the hydrophobic nature of the backbone. The counterions and other ions are set to have the interaction parameters of water. In order to ensure that the conservative force is soft and repulsive, the weight function ωC(rij) is chosen as ωC(rij) ) 1 - rij/a for rij < a and ωC(rij) ) 0 for rij g a.31 The dissipative (FijD) of eq 2 and random forces (FijR) of eq 3 have to be coupled, since thermal heat generated by the random force must be balanced by the dissipation force. The precise relationship between these two forces is determined by the fluctuation-dissipation theorem, which sets conditions for both of the weight functions, i.e., ωD(rij) and ωR(rij)31

ωD(rij) ) [ωR(rij)]2

(4)

and the amplitudes of these forces

σ2 ) 2γkBT

(5)

where T is the canonical temperature of the system. The form of ωR(rij) is a simple function like that of ωC(rij).

FijS )

∑ Crij

(6)

j

(

∇

)

ε ∇φ ) -F¯ e,nΓ εrε0 n

(7)

where ε, εr, and ε0 are the values of the dielectric permittivity of the medium, the vacuum, and the water, respectively.32 Fje,n is the averaged charge density, Γ ) 13.87 is the coupling constant which corresponds to the Bjerrum length of water at room temperature, and ∇φn is the electric gradient at grid node n. The same smearing distribution, fn(ri), that is used to solve the electrostatic field, is consistently used to evaluate electrostatic force on an ion. Then, the electrostatic force on ion i can be calculated from

FiE ) -qi

∑ fn(ri)∇φn

(8)

n

where qi is the charge of ion i.32 Again, the sum over n is limited to grid nodes within the distance Re from ri. Similar to MD simulations, DPD captures the time evolution of a many-body system through the numerical integration of Newton’s equation of motion. Here, we use a modified velocityVerlet algorithm according to Groot and Warren31 to solve the motion equation. The CPB used in the simulations consists of the backbone with M ) 80 beads of which every second carries a side chain of L charged beads. Although the model-CPB is much smaller than the real one, the essential physical effects are captured.18,19 Each bead in the side chain carries a charge of +1, forming the monomer ions. The number of counterions of added salt is obtained with Nc ) |ML/2q|, where q (-1, -2, -3, or -4) is the counterion valency. Thus, the charge ratio between the monomer ions and the counterions is 1:1. Consequently, the concentration of added salt can be determined on the basis of the counterion number, which is not repeated here for simplicity. The other monovalent ions, i.e., the monovalent counterions from CPBs and the monovalent positive ions from added salt, always ensure the neutrality in the system. The volume of the simulation box is set as (32a)3 such that the CPB can be considered to be independent and the finite size effects can be avoided. In the simulations, the radius of interaction, the bead mass, and the temperature are set as unity, i.e., a ) m ) kBT ) 1. A characteristic time scale is then defined as τ ) (ma2/kBT)1/2. The time step ∆t ) 0.06τ and a total bead number

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Figure 1. Radius of gyration, Rg, as a function of the counterion valency. The characteristic conformations for every counterion valency are also listed. (a) |q| ) -1, (b) |q| ) 0, (c) q ) -1, (d) q ) -2, (e) q ) -3, and (f) q ) -4. |q| ) -1 and 0 indicate the cases of the neutral cylindrical polymer brush and the CPB without added salt, respectively. The pink and cyan spheres in the simulation images indicate the beads of the backbone and the side chains, respectively.

density of 3/a3 are selected. The physical length and time scales in the present simulations are a ≈ 0.646 nm and τ ≈ 88 ps.33 The system is equilibrated for 2 × 105 time steps; the desired quantities are produced during further 2 × 105 time steps. 3. Results and Discussion In this section, we present the results of the DPD simulations concerning equilibrium conformations of isolated CPB with added salt. Figure 1 shows the typical conformations of a CPB consisting of a backbone with M ) 80 and 40 sidechains with L ) 9. For convenience, the absolute values, |q|, of the negative charges of the counterions, q ) -1, -2, -3, or -4, are used when each corresponding figure is plotted in this paper. Note that here and in the following figures we use |q| ) -1 and 0 only to indicate the cases of the neutral cylindrical polymer brush and the CPB without added salt, respectively. Thus, the results of both of these cases can be put together with other points in the same figure which is convenient for comparison. Already, the presentation in Figure 1 illustrates some striking differences in the conformational behavior of the structures depending on the counterion valency. For the neutral cylindrical polymer brush (|q| ) -1), it exhibits a rod-like conformation which is one of the characteristic conformations of the neutral cylindrical polymer brush with hydrophilic side chains and a hydrophobic backbone.34 When the beads in the side chains are charged and no salt is added (|q| ) 0), the value of Rg increases because the monomer ions will repel each other due to their charges. In this case, the CPB presents the horseshoe-like conformation with adequately extending side chains, corresponding to the experimental observations.25–28 When the salt is added, both the backbone and the side chains of the CPB will collapse, and a higher counterion valency corresponds to a smaller value of Rg. What is more interesting is the fact that various conformations can be identified from Figure 1 with increasing counterion valency, q. The CPBs with q ) -1 and -2 still present horseshoe-like conformations but with smaller curve and size. When the valency of the counterions is equal to -3, the CPB collapses further and the curvature of the backbone increases. The corresponding quantitative characterization for the structure of the backbone can be found in Supporting Information Figures S1 and S2. After quantifying the structure of the CPB, we find that it really exhibits a helical conformation at q ) -3. Moreover, this helical conformation

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Figure 2. Asphericities, µ, of the CPB as a function of counterion valency.

has also been observed in the experiments for the CPBs with multivalent counterions at q ) -3.35 By creating a helix, the CPBs can generate an overlap of the excluded volume from successive turns.35,36 When the value of q reaches -4, the collapse of the CPB is so strong that it even exhibits a coil-like conformation. Clearly, the CPB undergoes a horseshoe to helical to coil-like conformational transition with increasing counterion valency. To quantify the conformational transitions, we calculate the asphericity (µ) of the CPB, which is defined as37,38

µ ) 1 - 3〈I2〉/〈I12〉

(9)

where I1 and I2 are the first two invariants

I1 ) λ1 + λ2 + λ3

(10)

I2 ) λ1λ2 + λ2λ3 + λ1λ3

(11)

and λ1, λ2, and λ3 are the eigenvalues of the gyration tensor

GuV )

1 N

N

∑ (rui - Rg )(rVi - Rg ) i

u

V

(12)

where u and V ) x, y, z. The summation runs over the N positions ri of every bead of the CPB. µ is a quantifiable description of how deformed from a reference spherical shape. When the object exhibits a standard spherical shape, µ is equal to 0, while µ ) 1 indicates an object with line shape. Figure 2 illustrates the asphericities of the CPB with the increasing counterion valency. It can be found that the value of µ for the neutral cylindrical polymer brush is larger than that for the CPB without added salt, because the neutral cylindrical polymer exhibits a rod-like conformation while the conformation of the CPB without added salt is horseshoe-like. With the increasing counterion valency, µ grows, indicating that the conformation of the CPB presents more anisotropy due to the collapse of the CPB. Within this scale, the collapse of the CPB is mainly due to the side chains, while the backbone has a relatively smaller change. However, when |q| is larger than 2, the higher counterion valency leads to an extreme collapse for both side chains and the backbone. Thus, the CPB becomes more isotropic and µ turns to decrease.

Conformational Behavior of CPBs

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Figure 3. Density profiles of monomer ions (black line), multivalent counterions (red line), monovalent counterions from the CPB (blue line), and monovalent positive ions from added salt (green line), with respect to the backbones of the CPB. The valencies of the counterions are (a) q ) -1, (b) q ) -2, (c) q ) -3, and (d) q ) -4.

In Figure 3, the density profiles of the monomer ions, multivalent counterions, the monovalent counterions from the CPB, and the monovalent positive ions from added salt are shown, all measured with respect to the minimum distance of each bead from the backbone. The mutual repulsion of the monomer ions due to their charge not only leads to a larger size of the CPB but also enables the counterions to diffuse into the brushes as well, which can be seen from their density profiles. When the valency of the counterions from added salt is equal to that of the monovalent counterions from the CPB, i.e., q ) -1, the peaks of these two species within the brushes are very similar (Figure 3a). However, the peak of the monovalent counterions from the CPB will decrease with increased counterion valency, q. It reveals that a replacement of monovalent counterions by the multivalent ones takes place inside the brushes. The replacement can lead to the reduction of the total number of counterions within the brushes, which can also be discerned from Figure 3. Similar phenomena have also been observed in the studies of SPBs which demonstrate that the reduction of the number of the counterions inside the brushes is one of the important factors for the collapse of the brushes.16–19 To gain insight into the collapse of the CPB, we calculate the correlation functions, g(r), among the monomer ions in the side chains and the trivalent counterions, monovalent counterions from the CPB, and the monovalent positive ions from added salt, which are illustrated in Figure 4. The peak of trivalent counterions is much higher than those of all other ions. It reveals that the correlation of trivalent counterions is stronger than those of other ions and a strong condensation takes place for the trivalent counterions. One can note that even harmonic peaks occur in a large scale of the correlation function of trivalent

Figure 4. Pair correlation function g(r) between monomer ions and trivalent counterions (black line), monovalent counterions from the CPB (red line), and the monovalent positive ions from added salt (blue line), where q ) -3.

counterions, demonstrating more structure is established around each condensed trivalent counterions. The strong condensation induced by the higher electrostatic correlations can decrease the osmotic pressure, also leading to the collapse of the brushes.18,19 In Figure 5, we present a comparison of the mean-square displacement (MSD) of the monomers in the backbone, the monomer ions in the side chains, the trivalent counterions, and the monovalent counterions from the CPB in the system with q ) -3. Due to the stronger binding, the mobility of trivalent counterions is much smaller than that of the monovalent ones. The self-diffusion coefficient D0 can be obtained from the relation 〈∆r2〉 ) 6D0t.39 The diffusion coefficient of the monomers in the backbone is much smaller than that of the monomer ions in the side chains, revealing that the formation

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Figure 5. MSD 〈∆r2〉 of the backbone monomers (black line), monomer ions (red line), trivalent counterions (blue line), and monovalent counterions from the CPB (green line) in a system with q ) -3. The diffusion coefficients D0 are obtained from the slope of the lines above τ ) 10.

Figure 7. Characteristic bond length of the monomer ions Sb and the ratio of Sb to the characteristic bond length of the monomers Mb. Lines are only to guide the eye. |q| ) 0 indicates the case of the CPB without added salt.

Figure 6. Probability distribution of bond lengths for monomers in the backbone (black circles) and the monomer ions in the side chains (red circles), with q ) -3. Fitting the data yields the solid lines.

Figure 8. Distance of bg between main chain grafting points of the CPB as a function of the counterion valency. The line is only to guide the eye. |q| ) 0 indicates the case of the CPB without added salt.

of the equilibrium conformation for the backbone may be slower than the collapse of the side chains. The diffusion of the trivalent counterions is faster than that of the monomer ions. However, it is still in the same order of magnitude. In contrast, the D0 value of the monovalent counterions is much larger than that of the trivalent ones. It reveals that the trivalent counterions are osmotically inactive due to their binding to the side chains, and the transitional contribution to the osmotic pressure is mainly determined by the monovalent counterions. A detailed description of the internal structures of the CPBs can be obtained by analyzing the bond length b, shown in Figures 6 and 7. The bond length probability distributions, P(b), for the monomers in the backbone and the monomer ions in the side chains are illustrated in Figure 6. A clear shift to longer bond lengths in the distribution of lengths is found for the monomer ions, demonstrating that the bond lengths of the side chains are more extended than those of the backbone. This is not surprising, since the bond length of side chains is directly affected by the mutual charge repulsion of the monomer ions, although both side chains and the backbone will collapse in the presence of counterions. To analyze P(b) quantitatively, we determine the characteristic bond length of the monomers in the backbone, Mb, and that of the monomer ions in the side chains, Sb, through a Lorentz line fit.40 Figure 7 plots Sb and the ratio of Sb to Mb against various counterion valencies. Clearly, Sb decreases with increasing counterion valencies because the higher counterion valency induces a stronger collapse of the CPBs. Moreover, one can find that a higher counterion valency corresponds to a smaller ratio of Sb to Mb.

It reveals that the side chains with charged beads have a more sensitive response to the change of the counterion valency than the backbone. Let us next consider in more detail the local short length scale behavior of CPB. Figure 8 presents the average distance between main chain grafting points bg as a function of the counterion valency. The result shows a striking difference in the bg for various q. This difference is directly related to the fact that the side chains with a weaker collapse have a stronger interaction with the backbone, which fully agrees with the Monte Carlo simulations for the neutral cylindrical polymer brushes with flexible or rigid side chains.41 A similar phenomenon is also illustrated in Figure 9, which shows the order parameter η ) 1/2〈3 cos2 θ - 1〉 of the side chains as a function of the counterion valency, where θ is the angle between side chain direction (end-to-end vector) and the local backbone direction. Here, we use a local direction defined by main chain beads separated by 10 beads. η characterizes the orientation of the side chains with respect to the cylinder axis. As expected, the data imply that the side chains orient more and more perpendicular to the backbone as the counterion valency is decreased. Concerning the possibility of lyotropic behavior of the cylindrical polymer brushes in solutions, the critical parameter is the ratio of the persistent length, lp, to the diameter, d, of the cylindrical polymer brushes. Here, we also apply this parameter to study the effects of counterion valency and side chain length on the possibility of lyotropic behavior of the CPB. To obtain lp, the bond-bond correlation function, Cbb ) 〈β(i) β(i+m)〉,

Conformational Behavior of CPBs

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Figure 9. Order parameter η of side chains of the CPB as a function of the counterion valency. The line is only to guide the eye. |q| ) 0 indicates the case of the CPB without added salt.

Figure 10. Persistent lengths of the backbone, lp, as a function of the counterion valency, where the line is only to guide the eye. Inset: ratios of lp to the diameter of the CPB (d ) 2λ) as a function of q, where λ is the root-mean-square end-to-end distance of the side chains.

defined as the average over all pairs of bond vector β separated by m other bonds in the backbone, is calculated first. Then, the backbone persistence can be measured by42 M

lp )

∑ Cbb(m)

(13)

m)0

It should be pointed out that lp is not the real persistence length and stays always smaller or equal to the number of segments constituting the chain. However, it is still an effective parameter to characterize the persistence length of the backbone. For the diameter of the CPBs, we use d ) 2λ, where λ is the rootmean-square end-to-end distance of the side chains. The calculated results about lp and lp/d are illustrated in Figures 10 and 11. Figure 10 plots the change of lp against various counterion valencies, q, and the inset shows the value of lp/d as a function of q. The persistence length of the backbone decreases with increasing counterion valency. This is due to the fact that a stronger collapse of the CPB takes places for a higher counterion valency. From the inset, it can be seen that the ratio of lp/d increases from about 2.1 to 2.5, revealing that the size of side chains with charged beads is more sensitive to the change of the counterion valency than that of the backbone, corresponding to the previous results. It has been demonstrated that the side chain length has great effects on the lyotropic behavior of the neutral cylindrical polymer brushes.42,43 In Figure 11 and its inset, we present lp and lp/d of the CPB as a function of the

Figure 11. Persistent lengths of the backbone, lp, as a function of the contour side chain length L with trivalent counterions, where the line is only to guide the eye. Inset: ratios of lp to the diameter of the CPBs (d ) 2λ) as a function of L, where λ is the root-mean-square end-toend distance of the side chains.

contour side chain length (equal to the bead number of each side and with unit a). Similar to the results of the neutral cylindrical polymer brushes,34,41 the lp of the CPB increases for a longer contour side chain length. However, the growth of lp is much smaller than that of d, which leads to the decrease of lp/d with increasing L. For our particular system, lp/d decreases about from 3 to 1 by increasing side chain length. Decreasing L further to 3 does not lead to much higher ratios (lp/d ≈ 5). An important result of our investigations on the influence of the counterion valency and the side chain length of the CPB is that the ratio lp/d can only be affected to a slight extent by varying these two parameters. However, lp/d has to be large enough to obtain lyotropic phase transition before interpenetration of the brushes leads to screening of the excluded interactions at elevated polymer concentrations. As an estimate deduced from predictions for semiflexible cylinders with hard-core interaction, the ratio lp/d should be of the order of 10 in order to lead to lyotropic behavior at reasonable concentrations. 43 Thus, we conclude that lyotropic behavior should be more difficult to reach for the CPBs especially with lower counterion valency and longer side chains, although the interactions of the charges in the CPB system may be helpful to reach the screening of the excluded interactions. 4. Conclusions On the basis of a DPD model, we investigate the conformations and interactions of a CPB in the presence of added salt with multivalent counterions. The conformational behaviors of the CPB with respect to various counterion valencies are analyzed in detail by considering different parameters, i.e., the distribution of bond lengths, the mean distance between two grafting points, the order parameter, and the persistent length of the backbone. Our simulations demonstrate that the presence of the multivalent counterions can induce the collapse of the CPB, leading to various conformations. We identify horseshoehelical-coil-like conformation transition with increasing counterion valency. An important factor inducing the collapse of the CPB is the fact that the strong condensation of counterions induced by higher electrostatic correlations decreases the osmotic pressure inside brushes. The results demonstrate that the multivalent counterions are osmotically inactive due to their binding to the side chains, and the transitional contribution to the osmotic pressure is mainly determined by the monovalent ones. It is found that the side chains with a weaker collapse have a stronger interaction with the backbone. The investigations

5110 J. Phys. Chem. B, Vol. 113, No. 15, 2009 on the influence of the counterion valency and the side chain length of the CPB show that the ratio of the backbone persistence to the diameter of the CPB, lp/d, can only be affected to a slight extent by varying these two parameters. The results reveal that the lyotropic behavior may be found less for CPB especially with lower counterion valency and longer side chains. These results may provide a valuable guideline that can be used to tailor the microstructure of the systems and to yield desired macroscopic behaviors. Acknowledgment. This work was supported by DFG within SFB 481. L.-T.Y. acknowledges the support from the Alexander von Humboldt Foundation. A.B. is grateful for financial support by the Lichtenberg-Program of the VolkswagenStiftung. Supporting Information Available: The quantification for the helical conformation of the CPB at q ) -3. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Ru¨he, J.; Ballauff, M.; Biesalski, M.; Dziezok, P.; Grohn, F.; Johannsmann, D.; Houbenov, N.; Hugenberg, N.; Konradi, R.; Minko, S. AdV. Polym. Sci. 2004, 165, 79. (2) Bendejacq, D.; Ponsinet, V.; Joannicot, M. Eur. Phys. J. E 2004, 13, 3. (3) Csajka, F.; Seidel, C. Macromolecules 2000, 33, 2728. (4) Ballauff, M. Prog. Polym. Sci. 2007, 32, 1135. (5) Zhang, L.; Yu, K.; Eisebgerg, A. Science 1996, 272, 1777. (6) Fo¨ster, S.; Hermsdorf, N.; Bottcher, C.; Lindner, P. Macromolecules 2002, 35, 4096. (7) Pincus, P. Macromolecules 1991, 24, 2912. (8) Borisov, O. V.; Birshtein, T. M.; Zhulina, E. B. J. Phys. II 1991, 1, 521. (9) Ni, R.; Cao, D.; Wang, W.; Jusufi, A. Macromolecules 2008, 41, 5477. (10) Zhou, F.; Huck, W. T. S. Phys. Chem. Chem. Phys. 2006, 8, 3815. (11) Das, B.; Guo, X.; Ballauff, M. Prog. Colloid Polym. Sci. 2003, 121, 34. (12) Amoskov, M.; Birshtein, T. M.; Belyaev, D. K. J. Polym. Sci., Ser. A 2007, 49, 851. (13) Jain, P.; Dai, J.; Grajales, S.; Saha, S.; Baker, G. L.; Bruening, M. L. Langmuir 2007, 23, 11360. (14) Sirchabesan, M.; Giasson, S. Langmuir 2007, 23, 9713.

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