Distinct Effects of Multivalent Macroion and Simple Ion on the Structure

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Distinct Effects of Multivalent Macroion and Simple Ion on Structure and Local Electric Environment of Weak Polyelectrolyte in Aqueous Solution Chen Qu, Benxin Jing, Shengqin Wang, and Yingxi Zhu J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b05387 • Publication Date (Web): 23 Aug 2017 Downloaded from http://pubs.acs.org on August 24, 2017

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The Journal of Physical Chemistry

Distinct Effects of Multivalent Macroion and Simple Ion on Structure and Local Electric Environment of Weak Polyelectrolyte in Aqueous Solution Chen Qu,1 Benxin Jing,1,2 Shengqin Wang,3 Yingxi Zhu1,2,* 1

Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre

Dame, IN 46556 2

Department of Chemical Engineering and Materials Science, Wayne State University, Detroit,

MI 48202 3

Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology

and Research), 117602, Singapore *Email: [email protected]

ACS Paragon Plus Environment

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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-vinyl pyridine) (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 P2VP chain in ionic aqueous solution at a singlemolecule 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 the shift of 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 non-monotonic 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 P2VP chain shows little change with increasing [W12] concentration before the precipitation of P2VP from water. To investigate the distinct effect of multivalent ion and macroion on the conformational transition of P2VP in aqueous solution,


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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 observed the monotonic reduction of the local electric potential of a swollen P2VP chain with increased ionic concentration, despite increased protonation degree of P2VP. The results suggest that counterion condensation of multivalent ion and macroion can effectively modify the effective “net” charge density of P2VP chains in dilute aqueous solution. However, possibly due to high multivalence 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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INTRODUCTION Ions play a critical role in the structure and interaction of polyelectrolytes (PEs) in aqueous solution,

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which are polymers bearing completely or partially ionizable groups in their

repeating units designated as strong (or quenched) and weak (or annealed) PEs, respectively.810

The presence of ions and macroions, the latter of which includes 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 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 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 ion 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 inter-chain 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-


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yet the details of the multivalent ionic effect on 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-vinyl pyridine) (P2VP) in dilute aqueous solution 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 salt-free 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 valence.35-37 It has been also 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 in PE aqueous solution could break the meanfield approximation to estimate the electrostatic interaction between PEs even at low concentration.23, 38 In addition, much of prior research on multivalent macroions has mainly


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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 local ionic environment including the presence of PEs, or 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 non-linear 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 non-polar groups of organic macroions could inevitably complicate the interaction of 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 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, 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]


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and divalent sulfate counterion. Inorganic [W12] macroion belongs to the type of polyoxometalate (POM) nanomaterials consisting of transition metal oxide clusters. [W12] is a strong hetero-polyacid 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 nanoparticle-formed suspension. We select 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 rigid framework as multivalent macroions also minimizes the complexity of hydrophobic interaction between multivalent macroion and weak PE as well as any structural change of 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 counts histogram (PCH) analysis with FCS, we measure the local proton concentration in the vicinity of a single P2VP chain to examine the coupling of local electric environment and conformational structure of protonated P2VP chains in the presence of added multivalent anions.

EXPERIMENTAL

Materials and Sample Preparation. Amino terminal functionalized P2VP of Mn = 135,600 g/mol (polydispersity, PDI = 1.04) were purchased from Polymer Source (Quebec, Canada). The molecular weight was characterized by gel permeation chromatography (GPC) and


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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 the reaction with fluorophore probe, P2VP in aqueous solution of pH = 2.0 was incubated overnight to ensure chemical equilibrium of fluorophore-tagged P2VP chain in aqueous solution. Subsequently, P2VP aqueous solution was ultra-centrifuged to remove excessive fluorophore probes and redissolved in HCl aqueous solution of varied pH values. P2VP concentration at constant 10-9 M for this work is sufficiently low and equivalent to 1-2 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 the single chain resolution. The bulk pH of 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 P2VP aqueous solution at a given pH with increased concentration under stirring for 1 hr 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 FCS setup was based on an inverted microscope (Zeiss Axio A1) equipped with an


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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 single-photon 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 𝜔𝜔 �~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, 𝐺𝐺(𝜏𝜏) of measured I(t) as 𝐺𝐺(𝜏𝜏) = 〈𝛿𝛿𝛿𝛿(𝑡𝑡) ∙ 𝛿𝛿𝛿𝛿(𝑡𝑡 + 𝜏𝜏)〉/〈𝐼𝐼(𝑡𝑡)〉2 (Eq.1) was

thereby obtained by using a multichannel FCS data acquisition system (ISS) via crosscorrelation analysis. The diffusion coefficient, D and the probe concentration in the focal volume, [c] were obtained by fitting G( 𝜏𝜏 ) with G(τ) = ([𝑐𝑐]𝜋𝜋 2 𝑧𝑧 2 𝜔𝜔 �)−1 (1 + 4𝐷𝐷𝐷𝐷 −0.5 ) 𝑧𝑧 2

4𝐷𝐷𝐷𝐷 −1 ) (1 + �2 𝜔𝜔

(Eq.2) by assuming three-dimensional Brownian motion. Therefore, the

conformational structure, described by hydrodynamic radius, RH, of a P2VP chain in aqueous solutions of varied pH and added ions were obtained from the measured D according to the 𝑘𝑘 𝑇𝑇

𝐵𝐵 Stokes-Einstein equation, 𝑅𝑅𝐻𝐻 = 6𝜋𝜋𝜋𝜋𝜋𝜋 (Eq. 3), where kB is the Boltzmann constant, 𝜂𝜂 is the

known viscosity of water. All 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 the experiments were conducted at 20 °C. PCH method was employed based on the same FCS setup to obtain the brightness of 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


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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 “super-Poisson” function. By analyzing p(k), the average number of fluorescent 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 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 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 the distinction of the UV/Vis adsorption band of P2VP typically below 300 nm from that of OG488 typically around 500 – 600 nm.33, 34

RESULTS AND DISCUSSION

We start with examining the pH-dependent conformational structure of P2VP chain in dilute aqueous solution added with [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 fitting54 as shown in Figure S1 of Supporting Information. The measured auto-correlation functions, G(𝜏𝜏) of fluorescence-labeled P2VP in aqueous solutions of varied pH and added ions are shown in Figure S2 of Supporting Information and fitted by Eq. 2 to obtain D and corresponding RH by Eq. 3. Without added macroion, we have confirmed


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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.34,

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As shown in Figure 1, the sharp swollen-to-collapsed

conformational transition against increased pH is preserved in aqueous solution added with anionic [W12] macroion. However, adding [W12] to P2VP aqueous solution can effectively modify pHcr. At significantly low [W12] concentration from 10-9 mM to 10-5 mM, equivalent to one [W12] per 1000-0.1 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 [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 mM to 10-5 mM is about 5-8 orders of magnitude lower than that of HCl in aqueous solution of varied pH = 2.03.5. When [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


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[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 the similar reduction of pHcr with increased [Ni9] concentration in dilute P2VP aqueous solution as shown in Figure S3 of Supporting Information. In comparison to the case of multivalent [W12] macroion, we have examined the effect of simple divalent SO42- anion on the swollen-to-collapsed conformational transition of P2VP. As shown in Figure 2a, with increasing the SO42- concentration from 0.03 mM 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 the 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] macroion as compared in Figure 3. At the SO42- concentration range of 0.03 - 1 mM (equivalent to the change of respective screening length from 32.1 nm to 5.6 nm), we expect that the screening effect is dominant and leads to the increased ionization degree of P2VP chain due to screened electrostatic repulsion between P2VP and protons. Consequently, the pH region for swollen P2VP conformation is broadened. However, further increasing SO42concentration leads to an opposite effect on pHcr as shown in Figure 2b: measured pHcr decreases from 4.87 down to 3.88 as increasing SO42- concentration from 1 mM to 10 mM, respectively, exhibiting a trend similar to that of multivalent [W12] macroion. As increasing


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Na2SO4 concentration to 15 mM, the measured RH fluctuates around 6-7 nm at varied pH, which is in close approximation to the size of collapsed P2VP chain, indicating no apparent pH-induced conformational transition. Once 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), counterion concentration of multivalent ions and “bridging” of PEs across multivalent ions occur.56-58 For divalent SO42- anion, counterion condensation seems to occur at concentration greater than 1 mM (corresponding to the screening length of 5.6 nm). 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 media59. Because of its -8 high multivalence, the coupling of [W12] with P2VP could occur at a much lower concentration than that of SO42- counterion. Furthermore, the “bridging” of protonated P2VP chains by multivalent ions to cause the collapse of P2VP chain could be much more facilitated by [W12] macroion due to its finite size than divalent SO42- anion as a point charge. As combined, adding [W12] macroion could result in the reduction of pHcr at much lower concentrations than simple SO42- counterion. We have scrutinized the measured RH of P2VP in aqueous solutions added with varied amounts of [W12] and SO42- anions at constant pH. Although classical electrostatic screening theories based on mean-field ion fluctuation for simple point charges become inapplicable to macroions of finite size, we have compared the two multivalent ion cases in this work by using 1

apparent ionic strength, 𝐼𝐼 = 2 ∑𝑛𝑛1 𝑐𝑐𝑖𝑖 𝑧𝑧𝑖𝑖2 (Eq. 4), where ci is the molar concentration of

dissociated ions, zi is the valence of ion, i. It should be noted that apparent ionic strength simply


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takes the multivalence and molar concentration of different ionic species into account and yet neglects the possible effect of multivalent ion size. Figure 4 shows the 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 the 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 – 180 mM, which is consistent with the 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 ~10-6-10-2 [W12] per 2-vinyl pyridine 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 finite-sized [W12] macroion embedded in 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 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


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positively charged 2-vinyl pyridine monomers, the local proton concentration in the vicinity to 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 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 added multivalent [W12] macroion and simple divalent SO42counterion. Figure 5a and 6a show the brightness profile of OG488 attached to the terminal group of P2VP in aqueous solutions added with 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 - 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. For instance, the brightness of P2VP-attached OG488 in aqueous solution of 0.03 mM SO42-


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concentration and solution pH = 4.0 is 2300 CPSM, which is equal to that of OG488 in P2VPfree solution of pH = 5.7, yielding the local pH = 5.7 near P2VP corresponding to bulk solution pH = 4.0. The local pH near the terminal group of 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 P2VP chain by fluorescence spectroscopy. As shown in Figure S4 of 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 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 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 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 bulk pH by 2-3 pH units, resulting from the repulsion between protons and charged P2VP backbones. Yet the difference between local and bulk pH is reduced monotonically with increasing SO42- concentration from 0.03 mM to 3 mM, seemingly in contrast to the non-monotonic change of pHcr. Surprisingly, we have observed the similar behavior with increasing [W12] concentration from 10-9 mM to 10-5 mM. For both cases, the narrowed difference between local and bulk pH is observed with


16

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increasing ionic concentration, suggesting increased local proton concentration near P2VP. We have tentatively estimated the protonation degree, 𝛼𝛼 of P2VP in the solution of a given pH

added with different ions, assuming that the pK0(~5.89) of 2-ethylpyridine monomer remains 𝛼𝛼

constant at varied ionic strength and species:32 𝑝𝑝𝑝𝑝0 = 𝑝𝑝𝑝𝑝𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 + 𝑙𝑙𝑙𝑙 1−𝛼𝛼 (Eq.5). As shown in

Figure 7a, the 𝛼𝛼 of P2VP at a fix pH appears to increase with increasing the concentration of

SO42- and [W12] corresponding to the monotonic decrease of 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 eψ

solution to be zero as [H + ]local = [H + ]bulk exp �− 𝑘𝑘 T� (Eq. 6), where e is the unit charge, or eψ

𝐵𝐵

alternatively pHlocal = pHbulk + 0.43 kT (Eq. 7). The yielded ψ of P2VP is plotted against

ionic strength of added SO42- and [W12] in Figure 7b. Apparently, the local electric potential

near a P2VP chain decreases considerably with increasing ionic concentration for both cases. For example, with 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 added with monovalent counterion, Cl- of I = 5 mM.34 With added [W12] of I = 3.6×104

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 protonated P2VP chain, despite increased protonation degree of P2VP chain with added SO42- and [W12]. Yet multivalent [W12] macroion due to its higher valence appears to be more effectively coupled with P2VP for charge regulation at much lower concentrations than divalent SO42- anions.


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CONCLUSION

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 simple divalent counterion treated as point change and 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 divalent counterion at high concentration exhibit the similar effect as adding multivalent inorganic macroion of finite size, where increasing ionic concentration could shift the pHcr in an opposite direction to considerably lower pH values. Possibly because of high multivalence and finite size of macroion, multivalent [W12] macroion is much more effectively coupled with protonated P2VP to modify the pHcr at 3-7 orders of magnitude lower concentrations than divalent SO42-. Local proton concentration, aka local pH, in the vicinity to an expanded P2VP chain is measured to further quantify the coupling between local electrostatic environment and P2VP chain conformation. The PCH analysis indicates that accompanied with 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 effective “net” charges on a protonated P2VP chain, despite increased ionization degree of 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 multivalent point counterion, the size of swollen P2VP chains surprising shows little change with added [W12]


18

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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 multivalent macroion and PE in aqueous medium demands sophisticate theoretical and computer simulation studies in the future. Nevertheless, the study of weak PE interaction with multivalent ions and macroions gives insight to electrostatic control of the structure of weak PEs in dilute aqueous solution with relevance to macroion complexation and many complex biomolecular processes.

SUPPORTING INFORMAITON Supporting Information is available free of charge on the ACS Publications website at DOI: 10.102/acs.jpcc.xxxxxx. SAXS data of [W12] (Figure S1), auto-correlation function, G(τ) (Figure S2), effect of [Ni9] macroion on conformational transition of P2VP (Figure S3), and fluorescence characteristics of OG488 fluorophore (Figure S4) are available in the supporting information.

AUTHOR INFORMAITON *Email: [email protected];

Acknowledgement C. Q., B. J., and Y. Z. are grateful to the financial support from the National Science Foundation (NSF CMMI-1129821 and DMR-1743041) for this work. C.Q. also acknowledges the Bayer


19


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Predoctoral Fellowship from the Center for Environmental Science and Technology (CEST) at the University of Notre Dame.


20

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20 18

RH (nm)

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Page 28 of 35

16 14 12 10 8 3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

pH Figure 1. Measured RH of P2VP against pH in dilute aqueous solution in the absence of salt (squares) and added with [W12] at concentration of 10-9 mM (circles), 10-8 mM (triangles), 107

mM (diamonds), 10-6 mM (stars), and 10-5 mM (hexagons).


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

10

mM

(open

diamonds),

and


15

mM

(open

stars).

29


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


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12

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


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Figure 5. a) Measured fluorescence brightness, in the unit of photon counts per second per molecule (CPSM), of OG488 in P2VP-free K2HPO4 citric acid buffer solution (open squares) and P2VP-attached OG488 in dilute aqueous solution without salt (solid squares) and added with Na2 SO4 at the concentration of 0.03 mM (solid circles), 0.06 mM (solid triangles), 0.10

mM (solid diamonds), 0.30 mM (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 condition with the same symbols corresponding to the concentrations stated in (a). Straight lines show the linear fitting with simplified Boltzmann distribution function.


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(b)

Figure 6. a) Measured fluorescence brightness, in the unit of CPSM, of OG488 in P2VPfree K 2 HPO4 citric acid buffer solution (open squares) and P2VP-attached OG488 in dilute aqueous solution without salt (solid squares) and added with [W12] at concentration of 10-8 mM (solid circles) and 10-5 mM (solid triangles). Inset: the blow-out of the squared region in the main panel. b) Local pH near a P2VP chain against bulk solution pH in aqueous solutions with the same symbols corresponding to the concentrations stated in (a). Straight lines show the linear fitting with simplified Boltzmann distribution function.


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(a)

(b)

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


34

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TOC IMAGE

Divalent SO42- ion ain

Anionic [W12]8- macroion in


35

Distinct Effects of Multivalent Macroion and Simple Ion on the Structure

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