Distinct Effects of Multivalent Macroion and Simple ... - ACS Publications

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Distinct Effects of Multivalent Macroion and Simple Ion on the Structure and Local Electric Environment of a Weak Polyelectrolyte in Aqueous Solution Chen Qu,† Benxin Jing,†,‡ Shengqin Wang,§ and Yingxi Zhu*,†,‡ †

Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556, United States Department of Chemical Engineering and Materials Science, Wayne State University, Detroit, Michigan 48202, United States § Institute of Materials Research and Engineering, Agency for Science, Technology and Research (A*Stat), 117602 Singapore ‡

S Supporting Information *

ABSTRACT: Adding ionic species can critically affect the structure of weak polyelectrolyte (PE) chains, whose charge density in aqueous solution can be greatly regulated by bathing solution conditions such as pH and added ions. Distinct from simple ions that can be treated as point charges, multivalent macroions of finite size, including many charged nanoparticles and biopolymers, could show strong electrostatic coupling with PEs and effectively modify the conformation and assembly of PEs in aqueous solution. In this work, we have compared the effects of hydrophilic multivalent macroion of finite size and simple divalent ion on the conformational transition of a model weak polybase, poly(2-vinylpyridine) (P2VP), in dilute aqueous solution. By using fluorescence correlation spectroscopy combined with photon counting histogram analysis, we have examined the swollen-to-collapsed conformational transition and local electric potential of a P2VP chain in ionic aqueous solution at a single-molecule level. Adding inorganic polytungstate ([W12]) macroion bearing eight negative charges per [W12] of ∼0.8 nm in diameter at increased concentration from 10−9 to 10−5 mM can lead to a shift of the critical conformational transition pH, pHcr, of P2VP to lower pH values, in an opposite trend to the previously reported effect of adding simple monovalent anion. Conversely, adding simple divalent sulfate anion can lead to a nonmonotonic change of pHcr when increasing its concentration from 0.03 to 15 mM. Additionally, at pH < pHcr where P2VP is highly protonated and adopts a swollen conformation, a monotonic decrease of P2VP size is observed with increased sulfate ionic concentration, exhibiting the typical ionic screening effect. In contrast, the size of the P2VP chain shows little change with increasing [W12] concentration before the precipitation of P2VP from water. To investigate the distinct effects of multivalent ion and macroion on the conformational transition of P2VP in aqueous solution, we have also measured the local proton concentration in the vicinity to a P2VP chain by an attached pH-sensitive fluorescence probe. In both cases, we have observed the monotonic reduction of the local electric potential of a swollen P2VP chain with increased ionic concentration, despite the increased protonation degree of P2VP. The results suggest that counterion condensation of multivalent ion and macroion can modify the effective net charge density of P2VP chains in dilute aqueous solution. However, possibly due to its high multivalency and finite size, multivalent [W12] macroion is much more effective in modifying the local electric environment and structure of P2VP chains at 3−7 orders of magnitude lower concentrations than simple sulfate counterion.

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like-charged microtubule and actin biopolymers,11,12 DNA condensation in the presence of multivalent cations,13 and PE coacervate complexation in salted solutions.14,15 The effect of simple ions on the interaction and conformational structure of strong PEs has been much studied in the past.16−21 Simple ions treated as point charges are weakly coupled with a strong PE chain bearing fixed charges. Their spatial distribution

INTRODUCTION Ions play a critical role in the structure and interaction of polyelectrolytes (PEs) in aqueous solution,1−7 which are polymers bearing completely or partially ionizable groups in their repeating units designated as strong (or quenched) and weak (or annealed) PEs, respectively.8−10 The presence of ions and macroions, the latter of which include charged nanoparticles, surfactant micelles, and charged polymers, could drastically modify the electrostatic interaction and resulting behaviors of PEs in aqueous solutions. Notable examples include multivalent ion- or macroion-mediated aggregation of © 2017 American Chemical Society

Received: June 2, 2017 Revised: July 21, 2017 Published: August 23, 2017 8829

DOI: 10.1021/acs.jpcb.7b05387 J. Phys. Chem. B 2017, 121, 8829−8837

Article

The Journal of Physical Chemistry B

stable charges,15,43,44 and to compare their impact on the conformational structure of weak PEs to that of simple multivalent ions. Specifically, we examine the conformational behavior of P2VP chains in dilute aqueous solutions of varied pH and added divalent sulfate anion or multivalent inorganic polytungstate macroion ([W12]). As a weak polybase, P2VP becomes highly protonated at pH lower than its pKa, and its protonation degree, α decreases with increasing pH. When electrostatic repulsion is weakened with decreased α and becomes insufficient to overcome hydrophobic attraction, the P2VP chain collapses in dilute aqueous solution. A sharp and abrupt transition from a highly charged, swollen conformation to a weakly charged, collapsed one is observed with P2VP in dilute salt-free aqueous solution.34,45 We also compare how the local electric potential coupled with the conformational structure, of P2VP chains can be modified by multivalent anionic [W12] and divalent sulfate counterions. Inorganic [W12] macroion belongs to the type of POM nanomaterials consisting of transition metal oxide clusters. [W12] is a strong heteropolyacid nanocluster of 0.8 nm in diameter and bears eight negative charges stoichiometrically distributed on its crystalline surface when it fully dissolves in water to form thermodynamically stable solution, which is distinct from a nanoparticle-formed suspension. We select the inorganic [W12] nanocluster as a model macroion because of its high hydrophilicity, stable multivalent surface charge, and robust nanocluster structure. In contrast to nanoparticles or polymer-based macroions, the selection of inorganic POM nanoclusters bearing a rigid framework as multivalent macroions also minimizes the complexity of the hydrophobic interaction between organic multivalent macroion and weak PE as well as any structural change of the macroion itself in this work. By using FCS, we determine the pH-dependent hydrodynamic sizes of P2VP chains in aqueous solutions with added SO42− and [W12] anions of varied concentration. By applying photon counting histogram (PCH) analysis with FCS, we measure the local proton concentration in the vicinity of a single P2VP chain to examine the coupling of the local electric environment and conformational structure of protonated P2VP chains in the presence of added multivalent anions.

near a strong PE surface can be modeled by linearized Debye− Hückel (DH) approximation or Gouy−Chapman (GC) theory.22,23 Recent theoretical and computer simulation studies have demonstrated that multivalent ions exhibit a stronger tendency than monovalent ions to induce the complexation of strong PEs due to counterion bridging and charge inversion.16−21 However, the effect of multivalent ions and macroion on the conformational structure of weak PEs is far more complicated than that on strong PEs due to multivalent ion/macroion-induced charge regulation and intra- and interchain bridging, giving rise to different length scales in the structure of weak PEs and PE−ion complexes.24,25 Theoretical and computer simulation prediction on the conformational behavior of weak PEs has been mostly limited to the case of monovalent ions,26−28 yet the details of the multivalent ionic effect on the local electric condition and conformational structure of weak PEs remain unclear. Experimentally, single-molecule study of weak PEs has been conducted to minimize PE aggregation upon chain collapse, which is often encountered by traditional polymer characterization methods such as titration, light scattering, and osmotic pressure measurements.29−32 For example, fluorescence correlation spectroscopy (FCS) has been employed to examine the coil-to-globule conformational transition of poly(2-vinylpyridine) (P2VP) in dilute aqueous solutions of varied pH and added monovalent salt at a single-molecule level.33,34 It has been reported that adding monovalent counterions to P2VP dilute solution could lead to a shift of the critical conformational transition pH, pHcr, to higher pH values than that in saltfree solution, resulting from increased ionization degree. Atomic force microscopy has been also employed to examine the conformation of single P2VP chains adsorbed on a mica substrate from saline solution with added counterions of different valency.35−37 It has been reported that adding multivalent counterions could cause further shrinkage of adsorbed P2VP at surface and lead to the formation of P2VP complexes at high ionic strength.35−37 Yet the effect of multivalent ions on the conformational structure of free, unbound weak PEs in dilute aqueous solution remains poorly understood. Different from simple multivalent ions, multivalent macroions of finite sizes cannot be treated as simple point charges and could show strong electrostatic coupling with PEs. The presence of finite-sized multivalent macroion, even at low concentrations, in PE aqueous solution could break the mean-field approximation for estimating the electrostatic interaction between PEs.23,38 In addition, much of the prior research on multivalent macroions has mainly focused on highly charged nanoparticles, dendrimers,39 and biopolymers,40−42 yet it is nearly impossible to locate accurately the charges on these macroions because the charges on their surfaces are often inhomogeneously distributed and can be largely altered by the local ionic environment, including the presence of other PEs and their own conformational change. Thus, it is difficult to precisely estimate the electrostatic interaction between PEs and macroions. To date, it remains a great challenge to solve the nonlinear Poisson−Boltzmann equation for the electrostatic interactions between macroions, while the DH and GC approximations become invalid for the macroion case.22 Also, the hydrophobic attraction resulting from the nonpolar groups of organic macroions could inevitably complicate the interaction of a multivalent macroion with a PE chain. To minimize these complications, in this work, we choose to investigate hydrophilic multivalent macroions, for instance, multivalent inorganic polyoxometalate (POM) nanoclusters of fixed and

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EXPERIMENTAL SECTION Materials and Sample Preparation. Amino terminalfunctionalized P2VP of Mn = 135 600 g/mol (polydispersity, PDI = 1.04) was purchased from Polymer Source (Quebec, Canada). The molecular weight was characterized by gel permeation chromatography (GPC) and reported by Polymer Source. P2VP was used directly without further purification and dissolved in dimethylformamide for fluorescence labeling. Fluorophore probes, Alexa Fluor 488 (Alexa488, λex = 488 nm) and pH-sensitive Oregon Green 488 (OG488, λex = 488 nm), were purchased from Invitrogen and used directly. Hydrochloric acid (HCl, ACS reagent), sodium sulfate anhydrous (Na2SO4), and ammonium polytungstate hydrate ((NH4)6H2W12O40·xH2O) ([W12]) were purchased from Sigma-Aldrich and used directly. A fluorophore probe, either Alexa488 or OG488, was attached to the amino terminal group of a P2VP chain by following a published protocol.46 After reaction with a fluorophore probe, P2VP in an aqueous solution of pH = 2.0 was incubated overnight to ensure chemical equilibrium of the fluorophore-tagged P2VP chain in aqueous solution. Subsequently, P2VP aqueous 8830


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The Journal of Physical Chemistry B solution was ultracentrifuged to remove excess fluorophore probes and redissolved in a HCl aqueous solution of varied pH values. The P2VP concentration at constant 10−9 M for this work is sufficiently low and equivalent to about one P2VP chain per FCS confocal volume of 1.5 × 10−16 L (corresponding to a confocal volume of ∼260 nm in width and ∼4 μm in height) to ensure single-chain resolution. The bulk pH of the P2VP aqueous solution, determined by an Oakon pH6 meter, was adjusted by the concentration of added HCl, instead of using buffer solutions, to minimize the effect of added acids on electrostatic screening.47−50 Na2SO4 or [W12] was added to the P2VP aqueous solution at a given pH with increased concentration under stirring for 1 h before characterization. Characterization Methods. The conformational dynamics of fluorophore-labeled P2VP chains in dilute aqueous solutions of varied pH and added ions was characterized by FCS.45,51,52 The FCS setup was based on an inverted microscope (Zeiss Axio A1) equipped with an oil-immersion objective lens (Plan Apochromat 100×, NA = 1.4). Briefly, the tiny fluctuation, I(t) in fluorescence intensity, due to the motion of fluorescent probes in and out of the laser excitation volume of an argon ion laser (Melles Griot, λex = 488 nm), was measured by two singlephoton counting modules (Hamamatsu) independently in a confocal detection geometry at a sampling frequency of 100 kHz in this work. The dimension of the excitation confocal volume was calibrated as ω̅ ≈ 260 nm in the lateral radius and z ≈ 4 μm in the vertical half-height by Alexa488 of known diffusion coefficient in dilute aqueous solution. The autocorrelation function, G(τ), of measured I(t) as G(τ ) = ⟨δI(t ) ·δI(t + τ )⟩/⟨I(t )⟩2

molecules within the confocal volume and the brightness in the unit of photon counts per second per molecule (CPSM) are obtained. We employed the PCH analysis34,45,47 with our FCS setup to measure the brightness of the pH-sensitive OG488 probe attached to the amino end-functional group of a P2VP chain in aqueous solution. The local proton concentration, or the local pH, near the P2VP was inferred by comparing the measured fluorescence brightness to the calibrated brightness of OG488 in a P2VP-free aqueous solution. It should be noted that the attachment of OG488 to a P2VP chain caused no change in the fluorescence properties of OG488 because no energy transfer occurred between OG488 and P2VP monomers according to distinction of the UV/vis adsorption band of P2VP typically below 300 nm from that of OG488 typically at around 500−600 nm.33,34

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RESULTS AND DISCUSSION We start with examining the pH-dependent conformational structure of the P2VP chain in a dilute aqueous solution with added [W12] of varied concentration by FCS. The gyration diameter of [W12] in deionized water is measured to be approximately 0.8 nm by small-angle X-ray scattering (SAXS) with Guinier fitting,54 as shown in Figure S1 of the Supporting Information. The measured autocorrelation functions, G(τ), of fluorescence-labeled P2VP in aqueous solutions of varied pH and added ions are shown in Figure S2 of the Supporting Information and fitted by eq 2 to obtain D and corresponding RH by eq 3. Without an added macroion, we have confirmed the sharp swollen-to-collapsed conformational transition of P2VP in deionized water based on the precipitous decrease of measured RH with increased pH. The onset pH to cause the abrupt collapse of P2VP chains, defined as pHcr, is thereby determined experimentally. The measured pHcr = 4.18 for P2VP of Mn = 135 600 g/mol in dilute salt-free aqueous solution agrees well with the previously reported values.34,45 As shown in Figure 1, the sharp swollen-to-collapsed conforma-

(1)

was thereby obtained by using a multichannel FCS data acquisition system (ISS) via cross-correlation analysis. The diffusion coefficient, D, and the probe concentration in the focal volume, [c] were obtained by fitting G(τ) with −0.5 −1 ⎛ 4Dτ ⎞ ⎛ 4Dτ ⎞ G(τ ) = ([c]π 2z 2ω̅ )−1⎜1 + 2 ⎟ ⎜1 + 2 ⎟ ⎝ (2) z ⎠ ω̅ ⎠ ⎝ by assuming three-dimensional Brownian motion. Therefore, the conformational structure, described by the hydrodynamic radius, RH, of a P2VP chain in aqueous solutions of varied pH and added ions, was obtained from the measured D according to the Stokes−Einstein equation

RH =

kBT 6πηD

(3)

where kB is the Boltzmann constant and η is the known viscosity of water. All of the measurements reported in this work were repeated at least three times for each sample at a given solution condition to obtain averaged values. All of the experiments were conducted at 20 °C. The PCH method was employed based on the same FCS setup to obtain the brightness of a single fluorophore probe attached to a P2VP chain as detailed elsewhere.45,47,52,53 Basically, PCH analyzes the distribution of fluorescence emission within the excitation confocal volume, for instance, the histogram of fluorescence photo counts. With the fluctuation of the number of fluorescence molecules in the optical detection volume due to the Brownian motion, the distribution of fluorescence photon counts, p(k), of detecting k photon counts at a given time can be fitted with a “super-Poisson” function. By analyzing p(k), the average number of fluorescent

Figure 1. Measured RH of P2VP against pH in a dilute aqueous solution in the absence of salt (squares) and added with [W12] at concentrations of 10−9 (circles), 10−8 (triangles), 10−7 (diamonds), 10−6 (stars), and 10−5 mM (hexagons).

tional transition against increased pH is preserved in aqueous solution with an added anionic [W12] macroion. However, adding [W12] to P2VP aqueous solution can effectively modify pHcr. At significantly low [W12] concentration from 10−9 to 10−5 mM, equivalent to one [W12] per 1000 P2VP chains to 0.1 P2VP chain, respectively, we observe a monotonic shift of pHcr from 4.18 to 3.29, as summarized in Figure 3. No effect of [W12] on pHcr is observed within experimental error when the 8831


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The Journal of Physical Chemistry B [W12] concentration is lower than 10−9 mM. Although classical electrostatic theories probably become inapplicable to aqueous solutions added with macroions of finite size like [W12], we expect that the screening effect resulting from added [W12] concentration could be negligible in that the [W12] concentration from 10−9 to 10−5 mM is about 5−8 orders of magnitude lower than that of HCl in aqueous solution of varied pH = 2.0−3.5. When the [W12] concentration exceeds 10−5 mM, precipitation is observed at pH = 2.0, suggesting strong interaction between [W12] anions and protonated P2VP and possibly [W12]-mediated P2VP aggregation.55 Considerably lowered pHcr indicates that an increased amount of protons is needed with increased [W12] concentration to maintain the electrostatic repulsion between P2VP segments for the swollen conformation of P2VP chains in aqueous solution. Thus, it suggests that adding [W12] could either lower the protonation degree of P2VP or weaken the electrostatic repulsion between protonated P2VP segments upon the binding of [W12] to P2VP chains. Yet the PCH results as detailed below have excluded the account of the decreased protonation degree for decreased pHcr. Other multivalent POM-based macroions, such as K5Na11[Ni9(OH)3(H2O)6(HPO4)2(PW9O34)3] ([Ni9]) of ∼1.9 nm in diameter and bearing 16 negative charges per macroion in aqueous solution, have been also examined to verify the generality of their effect on P2VP conformational dynamics. We have observed a similar reduction of pHcr with increased [Ni9] concentration in dilute P2VP aqueous solution, as shown in Figure S3 of the Supporting Information. In comparison to the case of the multivalent [W12] macroion, we have examined the effect of a simple divalent SO42− anion on the swollen-to-collapsed conformational transition of P2VP. As shown in Figure 2a, upon increasing the SO42−

concentration from 0.03 to 1 mM, pHcr appears to shift from 4.18 to 4.87, respectively. The shift of pHcr to higher pH values by adding SO42− at a concentration < 3 mM is similar to that of adding monovalent counterions on P2VP, as reported previously,34 but it clearly exhibits an opposite trend to that of adding multivalent [W12] macroions as compared in Figure 3.

Figure 3. Critical pH to induce the swollen-to-collapsed conformational transition, pHcr of P2VP against the ionic strength of added SO42− (circles) and [W12] (squares) in a dilute aqueous solution.

At the SO42− concentration range of 0.03−1 mM (equivalent to the change of the respective screening length from 32.1 to 5.6 nm), we expect that the screening effect is dominant and leads to the increased ionization degree of the P2VP chain due to screened electrostatic repulsion between P2VP and protons. Consequently, the pH region for the swollen P2VP conformation is broadened. However, further increasing the SO42− concentration leads to an opposite effect on pHcr, as shown in Figure 2b: the measured pHcr decreases from 4.87 down to 3.88 with increasing SO42− concentration from 1 to 10 mM, respectively, exhibiting a trend similar to that of multivalent [W12] macroion. Upon increasing the Na2SO4 concentration to 15 mM, the measured RH fluctuates at around 6−7 nm at varied pH, which is in close approximation to the size of the collapsed P2VP chain, indicating no apparent pH-induced conformational transition. Once the Na2SO4 concentration exceeds 15 mM, P2VP aggregation and precipitation are observed. When the screening length becomes comparable to the Bjerrum length (= 0.7 nm in aqueous solution), the counterion concentration of multivalent ions and “bridging” of PEs across multivalent ions occur.56−58 For the divalent SO42− anion, counterion condensation seems to occur at concentrations greater than 1 mM (corresponding to the screening length of 5.6 nm). An anionic [W12] macroion could be strongly attracted to protonated P2VP segments by electrostatic attraction in a similar fashion to the interaction between oppositely charged nanocolloids in aqueous media.59 Because of its −8 high multivalency, the coupling of [W12] with P2VP could occur at a much lower concentration than that of SO42−. Furthermore, the bridging of protonated P2VP chains by multivalent ions to cause the collapse of the P2VP chain could be much more facilitated by a [W12] macroion due to its finite size compared to the divalent SO42− anion as a point charge. As combined, adding a [W12] macroion could result in the reduction of pHcr at much lower concentrations than the simple SO42− counterion. We have scrutinized the measured RH of P2VP in aqueous solutions with varied added amounts of [W12] and SO42− anions at constant pH. Although classical electrostatic screening theories based on mean-field ion fluctuation for simple point

Figure 2. Measured hydrodynamic radius, RH of P2VP against pH in a dilute aqueous solution in the absence of salt (squares) and added with Na2SO4 (a) at the low concentrations of 0.03 (circles), 0.10 (triangles), 0.30 (diamonds), 0.60 (stars), and 1.00 mM (hexagons) and (b) at high concentrations of 1.0 (hexagons), 3.0 (open circles), 6.0 (open triangles), 10 (open diamonds), and 15 mM (open stars). 8832


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The Journal of Physical Chemistry B charges become inapplicable to macroions of finite size, we have compared the two multivalent ion cases in this work by using apparent ionic strength

and bulk proton concentration is dictated by the electrostatic repulsion strength between local protons and ionized P2VP monomers. Recently, we have probed the local electrostatic environment and P2VP protonation degree by examining the change of local pH near a P2VP chain with varied bulk pH by tagging a pH-sensitive fluorescence probe to the terminal functional group of the P2VP chain using FCS-PCH analysis.33,45,47,60 It should be noted that the deviation of measured local pH from the bulk pH by FCS-PCH has been also confirmed by independent quantum yield measurements with the same fluorophore-tagged P2VP in our recent work60 as well as other polymers by other researchers,47 which ensures the validity of the FCS-PCH experimental approach. In this work, we have examined how the local electrostatic environment near a P2VP chain can be modified by an added multivalent [W12] macroion and simple divalent SO42− counterion.

n

I=

1 ∑ cizi 2 2 1

(4)

where ci is the molar concentration of dissociated ions and zi is the valency of ion i. It should be noted that apparent ionic strength simply takes the multivalency and molar concentration of different ionic species into account and yet neglects the possible effect of multivalent ion size. Figure 4 shows the

Figure 4. Measured RH of P2VP against the ionic strength of added SO42− (circles) and [W12] (squares) in a dilute aqueous solution of constant pH = 3.0. The dashed line is the RH of P2VP in a salt-free aqueous solution at pH = 3.0.

comparison of measured RH at pH = 3.0, where P2VP is highly protonated and behaves similar to strong PEs. As expected, we have observed that the screening effect resulting from added SO42− counterions can significantly modify the RH of P2VP at I ≥ 0.09 mM (corresponding to a screening length of 32 nm or smaller). A monotonic decrease of RH of swollen P2VP chains is observed with increased SO42− ionic strength from I = 3.6 × 10−4 to 180 mM, which is consistent with that reported in recent computer simulation work.17−20 In sharp contrast, the measured RH of P2VP chains in [W12] added aqueous solution appears to be independent of [W12] concentration. One possibility is that the molar fraction of [W12] on P2VP monomer ranging from ∼10−6 to 10−2 [W12] per 2-vinylpyridine monomer is too low to cause any detectable modification of P2VP size. The other possibility suggests the formation of P2VP−[W12] complexes, in which the size reduction resulting from partial collapse of P2VP by added [W12] due to local attraction between anionic [W12] and protonated P2VP segments might be compensated by the excluded volume of a finite-sized [W12] macroion embedded in the P2VP network, resulting in nearly constant size of P2VP−[W12] complexes at varied [W12] concentration. Thus, it is worth investigating the formation of P2VP−[W12] complexes in aqueous solution in future experimental and computer simulation research. It has been reported that the conformational dynamics of weak PE is strongly coupled with its local electric environment.18,33,45 Only the local protons in the vicinity of a weak PE backbone contribute to the protonation−deprotonation equilibrium of ionizable monomers along the chain. In dilute P2VP aqueous solution, due to the repulsion between the protons on positively charged 2-vinylpyridine monomers, the local proton concentration in the vicinity of a P2VP chain is lower than the bulk proton concentration, or alternatively speaking, the local pH is higher than the bulk pH. The difference between local

Figure 5. (a) Measured fluorescence brightness, in units of photon CPSM, of OG488 in a P2VP-free K2HPO4 citric acid buffer solution (open squares) and P2VP-attached OG488 in a dilute aqueous solution without salt (solid squares) and added with Na2SO4 at concentrations of 0.03 (solid circles), 0.06 (solid triangles), 0.10 (solid diamonds), 0.30 (solid stars), and 3.00 mM (open circles). (b) Local pH near a P2VP chain against bulk solution pH in aqueous solutions of varied salt conditions with the same symbols corresponding to the concentrations stated in (a). Straight lines show the linear fitting with a simplified Boltzmann distribution function.

Figures 5a and 6a show the brightness profile of OG488 attached to the terminal group of P2VP in aqueous solutions with added SO42− and [W12] ions, respectively, in comparison to that in P2VP-free aqueous solution against bulk pH below their corresponding pHcr. In P2VP-free aqueous solutions, the calibrated brightness of OG488 shows a linear increase with solution pH over the range of pH = 4.0−6.5 due to the ionization equilibrium of OG488 in water.61 In contrast, the brightness of P2VP-attached OG488 increases with solution pH over a much lower pH range from pH = 2.0 to 4.1. In addition, at the same solution pH, the brightness of P2VP-attached OG488 appears to be much higher than that of free OG488. 8833


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between protons and charged P2VP backbones. Yet the difference between local and bulk pH is reduced monotonically with increasing the SO42− concentration from 0.03 to 3 mM, seemingly in contrast to the nonmonotonic change of pHcr. Surprisingly, we have observed similar behavior with increasing [W12] concentration from 10−9 to 10−5 mM. For both cases, the narrowed difference between local and bulk pH is observed with increasing ionic concentration, suggesting increased local proton concentration near P2VP. We have tentatively estimated the protonation degree, α, of P2VP in a solution of a given pH with different ions added, assuming that the pK0 (∼5.89) of the 2-ethylpyridine monomer remains constant at varied ionic strengths and species32 α pK 0 = pH local + lg (5) 1−α As shown in Figure 7a, the α of P2VP at a fix pH appears to increase with increasing concentration of SO42− and [W12],

Figure 6. (a) Measured fluorescence brightness, in units of CPSM, of OG488 in a P2VP-free K2HPO4 citric acid buffer solution (open squares) and P2VP-attached OG488 in a dilute aqueous solution without salt (solid squares) and added with [W12] at concentrations of 10−8 (solid circles) and 10−5 mM (solid triangles). Inset: blow-out of the squared region in the main panel. (b) Local pH near a P2VP chain against the bulk solution pH in aqueous solutions with the same symbols corresponding to the concentrations stated in (a). Straight lines show the linear fitting with a simplified Boltzmann distribution function.

For instance, the brightness of P2VP-attached OG488 in an aqueous solution of 0.03 mM SO42− concentration and solution pH = 4.0 is 2300 CPSM, which is equal to that of OG488 in a P2VP-free solution of pH = 5.7, yielding the local pH = 5.7 near P2VP corresponding to bulk solution at pH = 4.0. The local pH near the terminal group of the P2VP chain is thereby inferred from the corresponding pH to the same brightness calibrated by OG488 in polymer-free solution for the cases of added SO42− and [W12] ions. It should be noted that we have also conducted control experiments to exclude the possible artifact caused by the chemical linkage of OG488 to the P2VP chain by fluorescence spectroscopy. As shown in Figure S4 of the Supporting Information, steady fluorescence emission spectra of free OG488 at bulk pH = 5.5 and its attachment to a P2VP chain at bulk pH = 3.5 (corresponding to local pH = 5.5) appear to be identical without any anomalies or spectral distortion, indicating the negligible effect of P2VP attachment on the fluorescence characteristics of OG488 in aqueous solution.62 Upon P2VP chain collapse at pH > pHcr, OG488 could be trapped inside of the polymer chain with strengthened hydrophobic interaction, causing the decrease of measured fluorescence brightness. Therefore, in our analysis, we have determined the local pH at pH lower than the respective pHcr at varied ionic conditions, where the P2VP is highly charged and swollen in aqueous solution and the brightness of OG488 is exclusively determined by local pH. The local pH near P2VP in salt-free solution is higher than the bulk pH by 2−3 pH units, resulting from the repulsion

Figure 7. (a) Protonation degree at fixed pH = 3.0 and (b) local electric potential of P2VP against the ionic strength of added Na2SO4 (circles) and [W12] (squares) in a dilute aqueous solution. Right side y-coordinate axis of panel (b): normalized electric potential by ψo measured in a salt-free aqueous solution.

corresponding to the monotonic decrease of the local pH. To further analyze the local electric environment, we have applied the simplified Boltzmann equation to estimate the electric potential, ψ, of a charged P2VP chain by assuming the electric potential in the bulk solution to be zero as ⎛ eψ ⎞ [H+]local = [H+]bulk exp⎜ − ⎟ ⎝ kBT ⎠

(6)

where e is the unit charge, or alternatively eψ pH local = pH bulk + 0.43 kT

(7)

The yielded ψ of P2VP is plotted against the ionic strength of added SO42− and [W12] in Figure 7b. Apparently, the local 8834



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electric potential near a P2VP chain decreases considerably with increasing ionic concentration for both cases. For example, with the added SO42− counterion of I = 9 mM, the measured ψ is reduced to 26% of that in salt-free aqueous solution, which is significantly lower than the reported ψ of P2VP in solution with added monovalent counterion Cl− of I = 5 mM.34 With added [W12] of I = 3.6 × 10−4 mM, the measured ψ is reduced to 78% of that in the salt-free solution. The reduction in the measured electric potential of P2VP strongly suggests counterion condensation of multivalent SO42− and [W12] anions to cause the decrease of effective “net” charges of the protonated P2VP chain, despite the increased protonation degree of the P2VP chain with added SO42− and [W12]. Yet multivalent [W12] macroion, due to its higher valency, appears to be more effectively coupled with P2VP for charge regulation at much lower concentrations than divalent SO42− anions.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b05387. SAXS data of [W12] (Figure S1), autocorrelation function, G(τ) (Figure S2), effect of the [Ni9] macroion on the conformational transition of P2VP (Figure S3), and fluorescence characteristics of the OG488 fluorophore (Figure S4) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

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Benxin Jing: 0000-0002-8400-1937 Yingxi Zhu: 0000-0002-7968-1640

CONCLUSIONS In summary, the effect of simple divalent ion and multivalent macroion on the conformational structure and local electric potential of P2VP chains in dilute aqueous solutions is examined at a single-molecule level. Our results disclose distinct effects of a simple divalent counterion treated as a point change and a multivalent macroion of finite size on the pH-dependent conformational transition of P2VP chains. Adding simple divalent counterions at low concentrations exhibits the similar effect as adding monovalent ones to cause the shift of pHcr to higher pH values. In contrast, adding a divalent counterion at high concentration exhibits a similar effect as adding a multivalent inorganic macroion of finite size, where increasing the ionic concentration could shift pHcr in an opposite direction to considerably lower pH values. Possibly because of its high multivalency and finite size, multivalent [W12] macroion is much more effectively coupled with protonated P2VP to modify pHcr at 3−7 orders of magnitude lower concentrations than divalent SO42−. The local proton concentration, that is, the local pH, in the vicinity of an expanded P2VP chain is measured to further quantify the coupling between the local electrostatic environment and the P2VP chain conformation. The PCH analysis indicates that, accompanied by increased protonation degree, the local electric potential of P2VP decreases considerably with increasing the concentration of SO42− and [W12]. The results clearly suggest multivalent counterion condensation on P2PV chains, leading to the decrease of the effective net charges on a protonated P2VP chain, despite the increased ionization degree of the P2VP chain with added multivalent ions and macroions. Additionally, although it is intuitively expected that the macroion of finite size could facilitate the bridging of P2VP more than the multivalent point counterion, the size of swollen P2VP chains surprisingly shows little change with added [W12], in contrast to the monotonic shrinkage of P2VP chains with added SO42− ions due to the screening effect. A quantitative description of the electrostatic interaction between the multivalent macroion and PE in an aqueous medium demands sophisticated theoretical and computer simulation studies in the future. Nevertheless, the study of weak PE interaction with multivalent ions and macroions gives insight into electrostatic control of the structure of weak PEs in dilute aqueous solution with relevance to macroion complexation and many complex biomolecular processes.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS C.Q., B.J., and Y.Z. are grateful for financial support from the National Science Foundation (NSF CMMI-1129821 and DMR-1743041) for this work. C.Q. also acknowledges the Bayer Predoctoral Fellowship from the Center for Environmental Science and Technology (CEST) at the University of Notre Dame.

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