Reentrant Variation of Single-Chain Elasticity of Polyelectrolyte

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Reentrant Variation of Single-Chain Elasticity of Polyelectrolyte Induced by Monovalent Salt Miao Yu, Lu Qian, and Shuxun Cui J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b00696 • Publication Date (Web): 30 Mar 2017 Downloaded from http://pubs.acs.org on March 31, 2017

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The Journal of Physical Chemistry

Reentrant Variation of Single-Chain Elasticity of Polyelectrolyte Induced by Monovalent Salt

Miao Yu, Lu Qian, Shuxun Cui* Key Laboratory of Advanced Technologies of Materials (Ministry of Education), Southwest Jiaotong University, Chengdu 610031, China * Email: [email protected]

ABSTRACT The interactions between monovalent counterions and polyelectrolyte are important in chemical and biological systems. The condensation and screening effect of counterions complicate the polyelectrolyte solutions. By means of single-molecule AFM, the single-chain mechanics of a strong polyelectrolyte, poly(sodium styrenesulfonate) (PSSNa), in KCl aqueous solutions over almost whole concentration range have been studied. The M-FJC model has been used to describe the single-chain elasticity of PSSNa in KCl solutions with a parameter of single-chain modulus (K0). Along with the increase of the concentration of KCl from zero to almost the saturation concentration, a reentrant variation of K0 of single PSSNa chain can be observed. When [K+] is between 0.01 M to 3 M, the charges on the PSSNa backbone are almost completely screened, i.e., the PSSNa chain is virtually neutral in this case. Because K0 has a positive correlation with the net charge of the polymer chain, the increased K0 at very high KCl concentrations (≥ 3.5 M) indicates that the chain is charged again. Due to the negative charges on the backbone of PSSNa, only the positively charged counterions (K+) can be adsorbed on the chain. Thus, the PSSNa chain should be positively charged when KCl concentrations ≥ 3.5 M. That is, the charge inversion occurs in this case, which is induced by a monovalent salt. This finding may lay the foundation for the future applications of drug delivery and gene therapy. 1

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INTRODUCTION Polyelectrolytes are ion-containing polymers, which will ionize and show an extended conformation when dissolved in water or other polar solvent.1-4 As an important class of functional polymers, polyelectrolytes have been explored and applied for several decades. Because of the good physical properties, such as flocculability and thickening property, polyelectrolytes have been used in food, cosmetics, medicines and other important areas. Furthermore, the most important categories of macromolecules in biology, such as DNA, RNA, and proteins, are polyelectrolytes too, whose function cannot be understood without taking into account the contributions of electrostatic and other forces.5-7 Therefore, the behaviors and properties of polyelectrolytes are significantly different from those of the uncharged polymers. In spite of extensive research of polyelectrolytes, scientists have not yet achieved a similar level of understanding to the uncharged polymers. It is well known that, there are various inorganic ions in a cell. These ions are important for the cell osmotic pressure and acid-base balance. A channel with a door of protein located on the surface of a cell is the only way for ions go through in and out of the cell, which is known as the ion channel.8 As mentioned above, protein is a kind of polyelectrolyte. Thus, the study of the interactions between ions and polyelectrolyte is particularly important. The interactions between small ions and charged macroions had been studied by many researchers. Among them, a counterintuitive phenomenon named charge inversion had attracted the attentions of many scientists. In general, external ions can be introduced into polyelectrolyte solution as counterions to screen the electrostatic repulsion. By condensing on the surface of a single polyelectrolyte chain, these counterions will cause the collapse of polyelectrolyte chains.9 However, excess counterion condensation will lead to reverse of the net charge symbol, which is called charge inversion. This counterintuitive phenomenon has been reported in diverse systems that are in contact with an aqueous solution containing multivalent ions, such as electric double layers,10 colloids,11 polyelectrolytes,12 nanochannels,13 Langmuir monolayers,14

and

electrolyte

solutions.15

Theoretically,

due

to

the

counterion-counterion correlation, the multivalent counterions can form a strongly 2


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correlated “liquid” layer on the polyelectrolyte surface, which will overcompensate the charges of the polyelectrolyte backbone at high salt concentrations.16 The computer simulations indicated that the association of counterions and co-ions will cause collapse at first and then redissolution of polyelectrolytes by further addition of multivalent ions.17 Experimentally, Zhang and his coworkers studied the reentrant behavior of a grafted polyelectrolyte with a quartz crystal microbalance (QCM).18 Their results showed that even a low concentration of multivalent salt can cause charge inversion of polyelectrolyte chains. In the condition of monovalent salt, however, the condensation will be limited in a certain amount, which was not enough to cause charge inversion. On the other hand, charge inversion can be also found in a protein channel or hydrophobic colloids in the presence of monovalent ions.19 The data obtained in these experiments suggested that charge inversion can be induced by two different mechanisms (specific adsorption and competitive binding) in the condition of monovalent ions.19 Recently, this phenomenon has attracted more and more attentions for its potential application in gene therapy, and etc. Especially, it may be applied to carry DNA (genes) into living cells.20, 21 Three experimental methods, i.e., electrophoresis,11 streaming currents13 and QCM,18 have been exploited to study the interactions between small counterions and polyelectrolyte. In those measurements, a polyelectrolyte solution with a relatively high concentration is used.22-26 In this condition, the interactions among polyelectrolyte chains may greatly affect the behavior of chains, which should be considered in the analysis. Furthermore, the entanglement of polyelectrolyte chains undoubtedly makes the problem more complicated. On the other hand, compared to electrostatic interactions, dispersion force and hydrophobic force are relatively weak, which are often ignored in data analysis. In this work, the atomic force microscopy (AFM)-based single molecule force spectroscopy (SMFS)27-49 is used to investigate the interactions between counterions and single polyelectrolyte chain. The essential advantage of SMFS is that it allows the study and analysis of a single chain. In the very dilute polyelectrolyte solution (the case of SMFS), the intermolecular interactions between polyelectrolyte chains can be ignored due to relatively long distance between them. Only the intrachain interactions and the interactions between a single polyelectrolyte chain and the surrounding 3



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environment need to be considered. This method not only simplifies the situation but also reflects the real status of a single polyelectrolyte chain more clearly. In this paper, we have investigated the single-chain mechanics of a typical polyelectrolyte by SMFS in a KCl solution over almost the whole range of concentrations. Along with the increase of the concentration of KCl from zero to almost the saturation concentration, a reentrant variation of single-chain modulus (K0) of single PSSNa chain can be observed. Due to charge screening, the value of K0 obtained in a moderate concentration of KCl solution is lower than that in DI water. The value of K0 obtained in a nearly saturation concentration of KCl is larger than that obtained in a moderate concentration, which may indicative of charge inversion of the polyelectrolyte chain at the single-molecule level. MATERIALS AND METHODS Materials and Chemicals. Poly(sodium styrenesulfonate) (PSSNa) is purchased from Sigma-Aldrich, which has a typical MW of 1000 kDa. The polydispersity index (PDI) of PSSNa is 1.2. Other chemicals are analytically pure and used without further treatment, unless specified otherwise. Deionized (DI) water (>18 MΩ•cm) is used when water is involved. Sample Preparation. PSSNa is dissolved in DI water to a concentration of 5 mg/L. In the force measurements, the glass slides are used as the substrates. Before use, the glass slides are treated by a hot piranha solution (98% H2SO4 and 35% H2O2, 7:3, v/v) for 30 min, followed by rinsing with abundant DI water and dried by air flow. (Warning: Piranha solution is extremely oxidizing and should be handled with care!) Then, the prepared glass slides are immersed in the (3-aminopropyl)triethoxysilane (APTES) solution (2 mM, CH2Cl2 solution) for 20 min. The glass slides are then rinsed in an ultrasonic bath with CH2Cl2, ethanol and DI water for 5 min, respectively. In order to prepare the sample for SMFS, a few drops of the PSSNa solution are deposited onto the treated substrate for 30 min. Then, the substrate is rinsed with abundant DI water to remove the loosely adsorbed polymers. Finally, the sample is immediately used in the force measurements.

4


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Force Measurements. All the force measurements are performed on the commercial MFP-3D AFM (Asylum Research, CA). Prior to the measurements, a drop of liquid is introduced between the V-shaped Si3N4 AFM cantilever (Bruker Corp., CA) and the sample surface. The spring constant of each AFM cantilever is obtained by the thermal excitation method, which is around 45 pN/nm. The instrumentation details of the SMFS can be found elsewhere. 27, 33, 34

RESULTS AND DISCUSSION In a nonpolar organic solvent, the van der Waals forces between solvent molecules and polymer are very weak, which can be ignored in SMFS studies.50 Previous studies have shown that the inherent elasticity of a single polymer can be obtained in a nonpolar solvent.51 Figure 1A shows the typical force-extension (F-E) curves of PSSNa obtained in octylbenzene. In the F-E curves, the force rises monotonically with the extension, corresponding to the increasing restoring force during the elastic elongation. When the polymer bridge between the substrate and the AFM tip is broken, the F-E will drop to the noise level (~ 10 pN). Because of both the polydisperse nature of polymer and the random stretching point of an AFM tip, the apparent contour lengths of PSSNa vary (Figure 1A). To compare the F-E curves of polymer chains of different contour lengths, the F-E curves are normalized by their extension corresponding to the same force (e.g., 500 pN). The superposition of the normalized F-E curves (Figure 1B) indicates that the elastic force signals present the single-chain inherent elasticity of PSSNa. It is interesting to make a comparison of the F-E curves obtained in DI water (Figure S1) and octylbenzene, since PSSNa is not ionized in octylbenzene. As can be seen from Figure 2, the F-E curve of a single PSSNa chain in DI water is steeper than that corresponds to the single-chain inherent elasticity, which is obtained in octylbenzene. This result shows that upon elongation by an external force, the ionized polyelectrolyte chain will present a higher single-chain enthalpic elasticity than that of the unionized polymer. The two environments, i.e., DI water and organic solvent, are simpler than those will be discussed below. Therefore, we can take the F-E curves obtained in these two conditions as the criteria for further comparisons. 5



2000

2000

(A)

1500

Force / pN

Force / pN

1000 500

(B)

1500 1000

0

500 0

0

100 200 300 Extension / nm

400

0.0

0.4 0.8 1.2 Normalized Extension

Figure 1. (A) Typical single-chain F-E curves of PSSNa obtained in octylbenzene, and (B) the normalized single-chain F-E curves of those shown in (A).

1200 Force / pN

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

octylbenzene DI water

800 400 0 0.90 0.95 1.00 1.05 Normalized Extension

Figure 2. Comparison of the normalized single-chain F-E curves of PSSNa obtained in octylbenzene (solid line) and DI water (dotted line).

The ionization makes PSSNa backbone negatively charged and present an extended conformation.52 It is expected that the chain flexibility can be restored by introducing external salt (KCl in this study), which can effectively screen the electrostatic force. Therefore, the concentration of monovalent salt solution is increased gradually to investigate how the concentration of monovalent ions affects the enthalpic elasticity of a single PSSNa chain. It is worth noting that the 6


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single-chain elasticity of PSSNa cannot be remarkably affected even if the surface charge density is changed (see Supporting Information for details).53

0.01M KCl 0.1M KCl 1.0M KCl 2.0M KCl 3.0M KCl

Force / pN

1500 1000 500 0 0.0


Figure 3. Comparison of the normalized single-chain F-E curves of PSSNa obtained in different concentrations of KCl.

1200

(A)

800

(B)

DI water 1M KCl

1200 Force / pN

Force / pN

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


400

octylbenzene 1M KCl

800 400

0

0 0.7


0.7

0.8 0.9 1.0 1.1 Normalized Extension

Figure 4. (A) Comparison of the normalized single-chain F-E curves of PSSNa obtained in DI water (dotted line) and 1 M KCl (solid line). (B) Comparison of the normalized single-chain F-E curves of PSSNa obtained in 1 M KCl (solid line) and octylbenzene (dashed line).

As shown in Figure 3, no remarkable difference can be observed among the F-E curves obtained in KCl solution, though the concentration spans two orders of magnitude (from 0.01 M to 3 M) (Figure S2). The superposition of these F-E curves 7



indicates that they show the identical single-chain elasticity, suggesting that the states of the single PSSNa chain are similar in this range of KCl concentrations. This state is defined as equilibrium state I in this paper. Another possible reason for the superposition in Figure 3 is that the difference among the F-E curves obtained in this broad range of KCl concentrations is rather slight, which can be shielded by the noise of AFM (~ 10 pN). An F-E curve under equilibrium state I (e.g., 1 M KCl) is chosen to make a comparison with that obtained in DI water. As shown in Figure 4A, the single-chain enthalpic elasticity of PSSNa in equilibrium state I is smaller than that in DI water. The comparison of the F-E curves obtained in equilibrium state I (e.g., 1 M KCl) and octylbenzene (Figure 4B) shows that the single-chain enthalpic elasticity obtained in equilibrium state I is still larger than the inherent elasticity, even if the electrostatic force is almost completely screened. Seen from Figure 4B, the high force region of the two curves cannot be superposed well, implying that after screening the electrostatic force between repeating units of a single PSSNa chain, there still exist other forces that influence the single-chain enthalpic elasticity.

1600 Force / pN

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

3.5M KCl 4.0M KCl

1200 800 400 0 0.0


Figure 5. Comparison of the normalized single-chain F-E curves of PSSNa obtained in high concentrations of KCl (3.5 and 4.0 M).

Then, the salt concentration is raised until close to the saturation concentration of KCl solution (4.5 M, at 25 oC), so as to confirm whether this kind of relatively stable equilibrium structure I is the final state for single PSSNa chains. Interestingly, single 8


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polyelectrolyte chains tend to stay in another relatively stable structure at higher concentrations, which indicates the formation of a new dynamic equilibrium (noted as equilibrium state II), see Figure 5, 6 and S3. There is an interesting phenomenon in the relatively high concentration of KCl solution: The flexible chain, which has returned to a random coil structure (in equilibrium state I) from an extended sate (in DI water), turns to a rigid one again, when the KCl concentration reached 3.5 M or higher (Figure 6A). (A)

1200

1.0M KCl 3.5M KCl

Force / pN

1200 Force / pN

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


800 400

(B) DI water 3.5M KCl

800 400

0

0 0.7


0.7


Figure 6. (A) Comparison of the normalized single-chain F-E curves of PSSNa obtained in equilibrium state I (1 M KCl) (solid line) and II (3.5 M KCl) (dotted line). (B) Comparison of the normalized single-chain F-E curves of PSSNa obtained in DI water (solid line) and equilibrium state II (3.5 M KCl) (dotted line).

As mentioned above, four kinds of conformations of a single PSSNa chain can be observed through the variation of the surrounding environment. In the nonpolar organic solvent, the single-chain elasticity of a polymer is dominated by its backbone. Recently, we studied the inherent elasticity of a single uncharged polymer chain with a Carbon-Carbon (C-C) backbone (e.g., polystyrene (PS)).51 It is interesting to find that in a nonpolar solvent, the single-chain elasticity of PSSNa is identical to that of PS, see Figure 7. In addition, the QM-FRC model with a freely rotating unit length (lb) of 0.154 nm can be used to describe the single-chain inherent elasticity of PSSNa (see Supporting Information for details).51 It has been shown that polymers with the same backbone but different side chains have the same single-chain inherent elasticity.51 Because PSSNa cannot be dissolved in a nonpolar solvent, the counterions are closely 9



attached to the polyelectrolyte backbone.54 It is expected that a polyelectrolyte chain will show a similar behavior to that of an uncharged polymer chain in this condition. This result indicates that the inherent elasticity of the single polymer will not be influenced by the side chains of PSSNa.51 On the other hand, the superposition of fitting curve and experimental curves (Figure 7) also verify that PSSNa are dispersed into single chains on the substrate. As a result, the forementioned complicated problems can be simplified by the single-chain condition (Figure S4).

2000 Force / pN

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1500

PSSNa PS QM-FRC

1000 500 0 0.0 0.4 0.8 1.2 Normalized Extension, R/L0

Figure 7. Normalized single-chain F-E curves of PSSNa (red line) and PS (blue line) obtained in octylbenzene, and the QM-FRC fitting curve with lb = 0.154 nm (dotted line).

Strong polyelectrolytes tend to be fully ionized when dissolved in DI water.2, 4, 55 Part of counterions diffuse into the solvent, which causes the backbone charged. The charges of polyelectrolyte system are composed of the fixed ionized groups on the backbone and the movable counterions in the solution.56 Because the Coulomb force acts stronger and longer than van der Waals forces, electrostatic force plays a dominant role in the dilute polyelectrolyte solution. It changes the essence of the solution, and leads to an important phenomenon of the polyelectrolyte solution: Diffusion of counterions makes polyelectrolyte repeating units charged and repelling each other by electrostatic force. In this case, the polymer backbone is stretched to an extended conformation by repulsive Coulomb forces, even if there is no external

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stretching force.55 Therefore, the single-chain enthalpic elasticity obtained in DI water is larger than that obtained in octylbenzene. With the introduction of KCl, the single PSSNa chain tends to stay in a equilibrium sate (hereafter referred as equilibrium sate I, see Figure 3). Figure 4A shows that the single-chain enthalpic elasticity of PSSNa obtained in equilibrium sate I (1 M KCl) is smaller than that obtained in DI water. This is reasonable because external ions are introduced into the system, which can screen the electrostatic force effectively. In this case, the conformation of single PSSNa chains returns to random coil from an extended state. In other words, with the screening of electrostatic force, a single PSSNa chain will convert back into a flexible one, which has a smaller enthalpic elasticity than that in DI water. In equilibrium state I, the salt concentration spans two orders of magnitude, but no remarkable difference can be found in their F-E curves. It can be speculated that at least two forces take effect in this sate. In a polyelectrolyte solution, there are two basic phenomena: Condensation and screening of charges. In general, counterions will not be completely diffused from the chain but be condensed around the polyelectrolyte partially.55 Counterions seem to keep a certain length away from the backbone, which is defined as Bjerrum length ( l B ), see Eq. 1.57 Some counterions will form a rod with a radius of l B , others will be diffused with a distance larger than l B (Figure S5).58

lB 

e2 4 r 0 kBT

(1)

In Eq. 1,  r is the relative dielectric constant which is determined by the property of the solution,  0 is the vacuum dielectric constant. Their product represents the ability of separating ions or the solvation capacity of solvents. With the introduction of external monovalent ions, part of free water molecules are trapped by forming the hydration layer of the ions. Thus, for the whole system, the number of free water molecules are reduced, which weakens the solvation capacity of solvents and reduces the dielectric constant.59 It is expected that the relative dielectric constant

 r will decrease with addition of monovalent ions, which leads to the increase of l B . 11



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The radius of rod distribution ( l B ) around the single polyelectrolyte chain increases, meaning that the surface area of the rod increases. Thus, there will be more space for the incoming counterions condensed around the PSSNa backbone. However, the condensation can be hardly quantified up to date. Here in this paper, information of how a single PSSNa chain behaves in those conditions can be obtained qualitatively by observing the variation of the single-chain elasticity of PSSNa in different concentrations of monovalent salt solution. It is expected that in equilibrium state I, the counterion condensation effect on the surface of a single polyelectrolyte chain leads to accumulation of counterions. With further condensation, the screening effect between counterions and backbone-fixed charges is enhanced. The Debye length,  D , will be decreased with the increase of counterion condensation. When the Debye length is smaller than the electrostatic blob size, the behaviors of polyelectrolytes become similar to that of an uncharged polymer.55 This uncharged polymer is not sensitive to the salt concentrations, which is shown in Figure 3. Ninham et al. pointed out that the dispersion force between ions and the surface of a single polyelectrolyte chain cannot be ignored.60 Moreover, their calculation results also showed that the dispersion force had significant influence on the distribution of ions as well as the potential energy: The dispersion force will be increased with the increase of salt concentration.60 Because of the forementioned two basic phenomena, the counterion concentration near polyelectrolyte backbone is higher than other parts in the solution. This situation makes the disperse force so large that the single-chain enthalpic elasticity is affected (Figure 4B). With the increase of counterion condensation, the dispersion force increases while the electrostatic repulsion gradually decays because of the screening effect. It is expected that these two forces reach an equilibrium state to a certain extent, where the single PSSNa chain shows a relatively stable state of the structure in a wide range of KCl concentrations in SMFS study, as reflected by the superposition of the single-chain force curves in Figure 3. The existence of non-ignorable dispersion force makes the enthalpic elasticity of the single PSSNa chain larger than its inherent elasticity (obtained in octylbenzene),60 see Figure 4B.

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As the salt concentration further increase, the single PSSNa chain tends to stay in another equilibrium sate (hereafter referred as equilibrium sate II, see Figure 5). Figure 6 shows that the single-chain enthalpic elasticity of PSSNa obtained in equilibrium sate II (3.5 M KCl) is larger than that obtained in other conditions. It is well known that the modified freely joint-chain (M-FJC) can be used to describe the rigidity (elasticity) of many single polymer chains semiquantitatively though they are only a simple approximation (see Supporting Information for details).30 The M-FJC parameters of PSSNa in DI water suggests the single-chain modulus, K0 = 35 000 pN, which shows that PSSNa is stiff in DI water (Figure S6A). The M-FJC fitting of PSSNa in 1M KCl suggests K0 = 29 700 pN, which is smaller than that obtained in DI water (Figure S6B). However, the M-FJC fitting parameter of PSSNa obtained in 4M KCl is K0 = 50 000 pN, which indicates that PSSNa is very stiff in this condition (Figure S6C). It can be assumed that there is a positive correlation between K0 and net charge of the polymer chain.30 Thus, K0 can be used as an indicator for the net charge of the chain: The increase of K0 corresponds to the increase of net charge of the polymer chain. The curves of single PSSNa chain and K0 in different KCl concentrations are shown in Figure 8, where a remarkable reentrant behavior of K0 can be observed.

800

(A)

0

-

Equilibrium state II (C) DI Water (A) Equilibrium state I (B)

0.01 0.1

1

2

3

~ neutral

4

+

Net charge of the chain

50000

K0 / pN

1200 Force / pN

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


400

40000

0

30000


0

0.01 0.1

1

2

3

KCl concentration / M

4

Figure 8. (A) Normalized single-chain F-E curves of PSSNa in three states: The initial state of ionization in DI water (solid line), the flexible state in equilibrium state I (dotted line), and the charge inversion state in equilibrium state II (dash dot line). (B) The reentrant variation of K0 in different concentrations of KCl and the schematic sketch of the net charge on the PSSNa backbone (blue line).

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The blue line on the top of Figure 8B shows that as the KCl concentration increases, the net charge of single PSSNa chain has been changed. In DI water, there is no doubt that the single PSSNa chain is negatively charged. In the equilibrium state I region, K0 keeps constant and is smaller than that in DI water, which means that the single PSSNa chains tend to be virtually neutral. In the equilibrium state II region, K0 is larger than that obtained in the equilibrium state I region, which indicates that the net charge of the chain in the II region is larger than that in the I region. Due to the negative charge on the backbone of PSSNa, only the counterions with a positive charge (K+ in this study) can be adsorbed on it. The larger net charge in the II region implies that the single PSSNa chain is positively charged. That is, the charge inversion of the PSSNa chain occurs when KCl concentration is very high, see Figure 8B. As the degree of the counterion condensation increases, the interactions between counterions and polyelectrolyte surface exclude the co-ions (Cl- in this study).19 The extreme case might lead to charged inversion of the polyelectrolyte chains, which is reported mostly when multivalent ions are used as counterions.16, 18 In chemical and biological systems, charge inversion occurs even in low concentrations when the counterions are multivalence ions: Due to strong interactions with polyelectrolytes surface and with each other, multivalence counterions, which are utilized to screen the electrostatic repulsion, do not position themselves randomly in three-dimensional space, but form a strongly correlated “liquid” on the surface of the polyelectrolytes.16 As a consequence, the counterions close to the polyelectrolyte chain surface cause the polarization of the surface under the “liquid” layer and produce “image” charges with opposite sign on the polyelectrolyte surface.16 Meanwhile, the repulsion between the adsorbed counterions and the incoming counterions would create some correlation holes.16 As the ionic strength increases, the attractions between the “image” charges and the incoming counterions lead to further counterion condensation on the polyelectrolyte chains through the correlation holes, which finally causes the reverse of the net charge symbol.18 According to the analysis for multivalent ions, it is expected that the following two factors will be helpful to realize charge inversion: A) A driving force which makes the counterions approach to the surface of a single

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polyelectrolyte chain and B) a surface with “correlation holes” which can provide more adsorption sites for the counterions. In our experiments with monovalent salt, the increase of K0 can be observed only when the concentration is high enough. Recent experiments showed that the uncharged polymer can also adsorb ions under high salt concentrations by the non-electrostatic interactions.24 One possible driving force for this adsorption is the dispersion force, which is observed only at high salt concentrations. It is expected that this might be a reason for charge inversion. Furthermore, Faraudo and his coworkers have studied the colloid surface by MD simulations.61 They found that monovalent ions caused charge inversion only on a hydrophobic colloid surface, but not on a hydrophilic colloid surface. This finding shows that the hydrophobic surface also plays a significant role in charge inversion if the counterions are monovalent ions.62 It can be seen from the structure of PSSNa backbone that only the sulfonic acid groups are hydrophilic, while the rest part of C and H atoms are rather hydrophobic (Figure S7). This structure is similar to the surface with “correlation holes” in multivalence ions, which can provide sites for the adsorption of the incoming counterions.16 The interactions between the single polyelectrolyte chain and counterions are described as follows. First of all, the fixed charges in the backbone attract counterions to condense around it by electrostatic force and dispersion force. Then, with the increase of salt concentration, the counterions (K+) have more chance to contact the hydrophobic part of the chain. When the counterions with weak hydration approach to the hydrophobic part of C and H atoms, the hydrophobic force drives part of counterions adsorb on those atoms. With the effects of electrostatic force, dispersion force and hydrophobic force, the net charge is even larger than the original charge of the polyelectrolyte backbone in DI water, which is reflected by the F-E curves (Figure 6B): The single-chain enthalpic elasticity of PSSNa in equilibrium state II is larger than that in DI water. The three force curves, each corresponds to one of the three states of the single PSSNa chain in the full concentration range of KCl, are shown in Figure 8A.

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We have carried out force measurements with another salt, NaCl. Similar results can be observed (Figure S9), indicating that the reentrant variation of single-chain modulus of polyelectrolyte may be a common phenomenon for monovalent salts. Apart from SMFS, we have tried to measure the zeta potential of the PSSNa solution with different concentrations of KCl. It can be seen from Figure S8, as the KCl concentration increases, the value of zeta potential changes from negative to positive. This result suggests that the PSSNa chains become positively charged, when the concentration reached 3.5 M or higher. It is worth noting that zeta potential is mainly used to characterize colloid systems, but not a system of polymer solution. The value (and the change) of zeta potential is rather small, however, the tendency of the zeta potential is clear along with the increase of KCl concentration. To our best knowledge, there is no such an ensemble measurement method that reported to study the charge inversion of polyelectrolyte induced by monovalent ions. We will explore such a method to support the SMFS results in the future. CONCLUSIONS In this paper, we have measured the single-chain mechanics of a typical polyelectrolyte, PSSNa, by SMFS in KCl solutions over almost the whole range of concentrations, aiming at studying the interactions between a single polyelectrolyte chain and counterions. In a nonpolar organic solvent, a single PSSNa chain shows the same inherent elasticity to the uncharged polymer with the same C-C backbone (PS), even though the side chains are different. With the introduction of new monovalent counterions (K+) into the polyelectrolyte aqueous solution, the electrostatic force will be screened. At the same time, the dispersion force and hydrophobic force become more and more important. According to the single-chain enthalpic elasticity obtained from SMFS, we can infer that with the increase of the concentration of K+ (from zero to almost the saturation concentration), the single-chain modulus (K0) of PSSNa will present a reentrant variation: i) K0 = 35 000 pN (stiff or extended conformation, as observed in DI water), when [K+] ~ 0; ii) K0 = 29 700 pN (flexible or random-coil conformation), when [K+] is between 0.01 M to 3 M; iii) K0 = 50 000 pN (stiff or extended conformation), when [K+] ≥ 3.5 M.

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When [K+] is between 0.01 M to 3 M, the charges on the PSSNa backbone are almost completely screened, i.e., the PSSNa chain is virtually neutral in this case. Because K0 has a positive correlation with the net charge of the polymer chain, the increased K0 at very high KCl concentrations (≥ 3.5 M) indicates that the chain is charged again. Due to the negative charges on the backbone of PSSNa, only the positively charged counterions (K+) can be adsorbed on the chain. Thus, the PSSNa chain should be positively charged when KCl concentrations ≥ 3.5 M. That is, the charge inversion occurs in this case, which is induced by a monovalent salt. In summary, due to the condensation of counterions, the net charge of PSSNa chain goes from negative to virtually neutral, then goes to positive, when the KCl concentration changes from zero to almost the saturation concentration. It is anticipated that the current study of the interactions between simple polyelectrolytes and counterions is not only helpful to the applications of synthetic polyelectrolytes in the future, but also lays the foundation for the exploration of more complicated polyelectrolytes, such as DNA and protein. ASSOCIATED CONTENT Supporting Information Details of the QM-FRC model and supporting data. The Supporting Information is available free of charge on the ACS Publications website at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]; Phone/Fax +86-28-87600998 (S.C.) Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS 17



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This work was supported by the Natural Science Foundation of China (21574106) and the Sichuan Youth Science & Technology Foundation (2017JQ0009).

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TOC Graph 1000 Force / pN

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800

Equilibrium state II DI Water Equilibrium state I

+

+

SO3-

SO3-

+

+

+ +

600

+

+ SO3-

400

+

+

SO3-

[K+]

200 SO3-

0

SO3-


23


Reentrant Variation of Single-Chain Elasticity of Polyelectrolyte

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