Counterion Cloud Expansion of a Polyelectrolyte by Dilution

1 hour ago - It has long been documented that the reduced viscosity of polyelectrolyte has an anomalous dependence on its concentration, i.e., the Fuo...
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Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

Counterion Cloud Expansion of a Polyelectrolyte by Dilution Kaikai Zheng, Kuo Chen, Weibin Ren, Jingfa Yang, and Jiang Zhao* Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China The University of Chinese Academy of Sciences, Beijing 100049, China S Supporting Information *

ABSTRACT: It has long been documented that the reduced viscosity of polyelectrolyte has an anomalous dependence on its concentration, i.e., the Fuoss law. To explore the molecular mechanism, the counterion distribution of sodium polystyrenesulfonate (NaPSS) as a function of concentration is investigated at the single-molecule level. By examination of the fluorescence resonance energy transfer (FRET) between a fluorescence donor on NaPSS chain and an acceptor in the counterions using single-molecule fluorescence spectroscopy, an increase of average counterion−chain distance is discovered upon dilution, indicating the expansion of counterion cloud. By photon counting histogram, an increase of effective charge of the NaPSS chain during dilution is exposed. The variation of these parameters agrees well with that of the reduced viscosity, helping to shed light on the molecular mechanism of the Fuoss law: the expansion of the counterion cloud increases hydrodynamic friction, and the increase of effective charges of NaPSS due to desorption of counterions brings about the stronger interchain coupling.

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paid to the charge density19 of the polyelectrolyte chains, especially for the salt-free polyelectrolyte solution. Because the rheological property is a macroscopic behavior involving multiple chains, interchain interaction is further emphasized.8 In addition, the interchain interaction is believed to affect the distribution of counterion and therefore the effective charge density of the main chain.20 Therefore, it is very important to explore the charges of a polyelectrolyte chain as a function of the concentration. It has long been a challenge to use suitable experimental techniques to study this issue. Recently, it has been proved that singlemolecule fluorescence microscopy and spectroscopy is very efficient in investigating polyelectrolytes at the single-molecule level, taking the advantage of their ultrahigh detection sensitivity. By fluorescence fluctuation spectroscopy, conformation transition and the counterion distribution have been effectively investigated, with synthetic polyelectrolyte as well as biomacromolecules.21−24 Driven by the question raised on the rheological behavior of polyelectrolytes and motivated by the effectiveness of singlemolecule fluorescence techniques, the charges and counterion distribution of polyelectrolytes as a function of its concentration are investigated in the current study. With an experimental system combining rheological, spectroscopic techniques, the charge state, and its evolution upon dilution of a typical strong polyelectrolyte system, sodium polystyrenesulfonate (NaPSS), have been investigated at the single-

INTRODUCTION The unique yet puzzling properties of charged macromolecules have been attracting tremendous research attention for decades.1−8 One of the interesting properties is the rheological behavior of polyelectrolyte solution, which appears to be anomalous compared with neutral polymers. For example, the reduced viscosity (η reduced) of polyelectrolyte solutions can be empirically expressed by the Fuoss law 1 as ηreduced = A /(1 + B c p ), where cp is the polymer concentration and A and B are constants related to the charge content and molecular weight.9−11 This empirical law indicates that the reduced viscosity of a polyelectrolyte solution increases upon dilution, in contrast with that of the neutral polymer solutions, which remains constant upon dilution. Later, the investigation within a bigger concentration range12 shows that upon dilution the reduced viscosity of polyelectrolyte solutions undergoes a further decrease after reaching a maximum value. The position of the maximum is found to depend on tempreature13 and valency of counterions.14 The origin of the maximum viscosity is further attributed to intrachain electrostatic repulsion, which causes the chain’s expansion from coil to rod upon dilution,3,15,16 as a result of the increasing dissociation of the ionizable groups so that a stronger friction between the charged chains is generated, leading to the increase of reduced viscosity. Further dilution cannot cause any chain expansion but reduces interchain interaction and therefore lowers the reduced viscosity. This argument was later challenged by studies using suspended polymer particles,17 whose dimension hardly changed upon dilution, and using the monofunctional telechelic ionomer18 with only one ionic end group. Attention is later © XXXX American Chemical Society

Received: January 12, 2018 Revised: March 27, 2018

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DOI: 10.1021/acs.macromol.8b00075 Macromolecules XXXX, XXX, XXX−XXX

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molecule level. By measuring the fluorescence resonance energy transfer (FRET) between the fluorescence donor tagged at the chain end of NaPSS and the fluorescence acceptor with opposite charge serving as counterions, the distribution of counterions around NaPSS chain as a function of concentration is investigated. By measuring the hydronium concentration around the NaPSS chain under different concentrations using the photon counting histogram (PCH) technique, the evolution of effective charge state of the charged chain with concentration is studied. The results clearly demonstrate what happens to the NaPSS molecule upon dilution, and the behavior shows excellent accordance with the variation of the reduced viscosity, helping to shed light on the possible mechanism of the unique rheological property of polyelectrolytes.

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Article

RESULTS AND DISCUSSION

As a demonstration of the concentration-dependent rheological property of NaPSS solution, the reduced viscosity of salt-free NaPSS solution with different concentrations were remeasured. For each concentration, the measured apparent viscosity does not show any dependence on the shear rate, indicating the absence of shear-thinning in the range of shear rate for all selected NaPSS concentrations (data provided in the Supporting Information, Figure S2). Therefore, the zero-shear rate viscosity (η0) of NaPSS solutions is extracted, and the reduced viscosity is calculated via ηreduced = (η0 − ηs)/ηscp, where ηs and cp denote the solvent viscosity and concentration of NaPSS solution, respectively. The variation of reduced viscosity with the concentration agrees with the reported results, and data are provided in Figure S2. Upon dilution, the ηreduced value of NaPSS solution increases and reaches a maximum at ∼0.005 mg/mL and undergoes a sharp decline upon further dilution. Under the same condition, fluorescence emission spectra of the mixed solution of NaPSS labeled with Alexa 488, the unlabeled NaPSS, and Atto 620 were measured. The concentration of NaPSS-Alexa 488 and Atto 620 is 4.2 × 10−9 and 1.0 × 10−7 M, respectively. The concentration of unlabeled NaPSS varies from 10−3 to 10−1 M. The typical data are displayed in Figure 1 while all data are provided in the Supporting Information.

EXPERIMENTAL SECTION

In general, the experiments were performed in the following way. The average distance between the counterions and NaPSS chain was determined by measuring FRET efficiency between Alexa 488 (donor) attached at the chain end of NaPSS and Atto 620 (acceptor) in the solution, which carries the opposite charge to the main chain and serves as counterions partially. On the other hand, the effective electric potential of single NaPSS chain is determined by measuring the difference in hydronium concentration at the chain end of NaPSS and that in the bulk solution because hydroniums also serve as counterions of the negatively charged PSS− chain. Materials. NaPSS was prepared through sulfonation of polystyrene (PS) (Mn = 120 × 103 g mol−1, Mn/Mw = 1.05), purchased from Polymer Source, Canada. The sulfonation was conducted according to a well-established protocol.25 NaPSS was later labeled at its chain end with fluorescent molecules such as Alexa Fluor 488 (Alexa 488) and Oregon Green 514 (OG 514). Special attention was paid to guarantee the complete purification of the labeled samples by polyacrylamide gel chromatography and ultrafiltration with a filter with cutoff molecular weight of 2K Da. The complete purification was demonstrated by the absence of fluorescence inside the residual fluent of the ultrafiltration, checked by single-molecule fluorescence measurements.21,22,26 OG 514 was adopted as the pH indicator to measure the local concentration of hydronium at the vicinity of NaPSS, i.e., to monitor the local pH value around the PSS− chain. In addition, FRET between Alexa 488 donor at the chain end and the counterion probe, Atto 620 (Invitrogen, USA), was measured to study the counterion distribution. Methods. Single-molecule fluorescence emission spectroscopy27 was adopted to measure the FRET efficiency between the fluorescence donor labeled at the chain end of NaPSS and the acceptor in counterions. The photon counting histogram was used to measure the fluorescence intensity from single pH-responsive fluorescence probe labeled at the NaPSS chain end.21−24,28−31 The details of these two methods are described in the Supporting Information. The rheological measurements of dilute NaPSS solutions were conducted on a commercial rheometer (MCR 302, Anton Par) equipped with air bearings and a double-gap measuring system, providing a large contact area between the sample and the surface of the measuring system so that testing with a high torque resolution and, in particular, measurement of liquids with low-viscosity such as water are enabled. The rheometer and spectroscopic apparatus are integrated together for the purpose of in situ measurements under shear, although the data reported in the current study are only from static measurements. The NaPSS solutions were kept in a liquid cell with its bottom window made of a 140 μm thick glass slide in order to match the working distance of the objective lens with the high numerical aperture. The top of the solution was covered with a thin layer of hexadecane so that the sample is isolated from the ambient atmosphere to prevent carbon dioxide dissolution.

Figure 1. Fluorescence emission spectra of the mixture of NaPSS− Alexa 488 and free Atto 620 under different concentrations of unlabeled NaPSS in aqueous solutions. The concentrations of NaPSS−Alexa 488 and Atto 620 are 4.2 × 10−9 and 100 × 10−9 M, respectively. The concentrations of unlabeled NaPSS are displayed by each data set. The data for donor only are also presented for the purpose of comparison. Inset: the apparent overall FRET efficiency (Ea) as a function of polymer concentration.

The spectra show two major features: one peak centered at 530 nm and another at 640 nm, corresponding to fluorescence emission from the donor (Alexa 488) and the acceptor (Atto 620), respectively. Control experiments proved the absence of emission from the solution of the acceptor only, Atto 620, because the excitation light (473 nm) is far away from its absorption band (demonstrated in Figure S5). Also, measurements of NaPSS−Alexa 488 only show no emission around 640 nm. The fluorescence emissions at both wavelengths are recorded only when NaPSS-Alexa 488 and Atto 620 are present B

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Macromolecules in the solution, due to the FRET process between the donor and acceptor. Data in Figure 1 show that the emission intensity of donor and acceptor is highly dependent on the concentration of the unlabeled NaPSS. The strongest FRET signal is observed at the concentration of 1.0 × 10−3 M, evidenced by the drastic decrease of the donor emission and the presence of the strong emission from acceptor. With the increase of NaPSS concentration, a huge increase of donor emission and a slight decrease of acceptor emission is recorded (Figure 1). The occurrence of FRET process between Alexa 488 fixed at NaPSS chain end and Atto 620 in the solution indicates their short mutual distance as a result of electrostatic attraction between the positively charged Atto 620 and the negatively charged NaPSS chain (Atto 620 serves as counterions of the PSS− chain, partially). A control experiment with the mixture of a polycation (quarternized poly-4-vinylpyridine) and Atto 620 does not show any FRET occurrence, as detailed in the Supporting Information. The FRET efficiency is exclusively dependent on the mutual distance between the donor and acceptor, expressed by the well-established Förster relation E = R06/(R06 + R6), where R is the distance between the donor and acceptor and R0 is the characteristic distance of 50% FRET efficiency, the so-called Förster distance. It is critical that the donor−acceptor distance should be less than 10 nm for a high enough FRET efficiency.32 Therefore, the occurrence of FRET shown in Figure 1 demonstrates the high concentration of fluorescent counterion probe (Atto 620) at the vicinity of the NaPSS chain due to the strong electrostatic attraction. Upon the increase of NaPSS concentration, an increase of donor emission and a decrease of acceptor emission are observed. Although such an observation appears to show a decrease of FRET efficiency, it indicates the opposite, i.e., an increase of FRET efficiency in the manner of one donor to one acceptor. Following the general definition of FRET efficiency, the apparent FRET efficiency (Ea) is defined as Ea = [I0 − I(cp)]/I0,32 where I0 is the intensity of donor in the absence of acceptor and I(cp) is the intensity of donor in the presence of acceptor under the polymer concentration of cp. The Ea value decreases with the increase of polymer concentration, shown in inset of Figure 1. (It is noted that the collected fluorescence passes the optical filters before guided into the spectrometer, and the recorded spectra of donor’s emission are not full because a portion is blocked by the optical filters. However, this does not affect the determination of Ea because the full spectra of donor’s emission is proportional to the spectra recorded, and this is further proved by control experiments.) Because the concentrations of the donor and acceptor are not identical (the concentration of NaPSS−Alexa 488 is 4.2 × 10−9 M and that of Atto 620 is 1.0 × 10−7 M), and also the acceptors will be petitioned to more and more unlabeled NaPSS chains, the apparent FRET efficient should be further normalized by concentration so that the real one-to-one FRET efficiency (Er) can be determined. This is performed by Er = Ea/(cAtto 620/cp), where cp and cAtto 620 are the concentrations of polymer and acceptor, respectively. Er is the average FRET efficiency within individual donor and acceptor pairs, which is inversely proportional to the sixth power of the average donor−acceptor distance, R̅ 6.32 After normalization, the value of real FRET efficiency is found to increase monotonically with the concentration of NaPSS while it is almost constant below cp of 0.005 mg/mL (Figure 2a).

Figure 2. (a) Value of real FRET efficiency, Er, and (b) average distance, R̅ , between individual NaPSS−Alexa 488 and Atto 620 as a function of the concentration of NaPSS. The data of reduced viscosity (ηreduced) are also displayed in parallel for comparison.

This indicates a change of the average distance between the donor (Alexa 488 at the chain end of NaPSS) and the acceptor (Atto 620) attracted at the vicinity of the NaPSS chain. The average distance is calculated by Förster relation, taking the value of Förster distance as 5.3 nm,33,34 and the data are displayed in Figure 2b. Apparently, the average distance increases generally with the decrease of NaPSS concentration: its value at 0.1 mg/mL is 7.4 nm and reaches the value of 9.5 nm at 0.005 mg/mL, below which the R̅ value is almost constant. The change of R̅ value with the concentration of NaPSS can serve as the evidence of the existence of the counterions cloud. It tells that the dimension of the counterion cloud is enlarged when the solution is diluted. The formation of the cloudlike structure of the counterions surrounding the charged chain is due to the balance between the electrostatic attraction and the maximization of the translational entropy of the counterions.22,35−37 The counterion cloud structure has been demonstrated in previous studies. For example, a difference of counterion concentration between the end and middle of NaPSS was discovered as a result of the difference of electrostatic attraction exerted on counterions from these two positions.21 A gradual decay of counterion concentration was revealed at farther distance from the NaPSS chain end, as a clear evidence of the counterion cloud structure.36,37 The dimension of the counterion cloud is therefore concentrationdependent as an entropic effectthe entropy reduction due to dilution makes the counterions stay further away from the charged chain because at lowered concentrations, a counterion will experience much higher entropic penalty to adsorb from the solution onto the charged polyelectrolyte chain.24,35,38 This induces an expansion of the counterion cloud. Although the above results show the situation near the chain ends, the overall expansion of the counterion cloud is certainly indicated due to the entropy-driven nature of the process. An important issue is to what extent the average distance between the donor and acceptor represents the dimension of counterions. Recent investigations by simulation and experiment have demonstrated the distribution profile of the counterions as described by an inverse-quadratic 36 or exponential37 dependence on distancea much more gradual dependence than that of FRET efficiency. However, because C

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Macromolecules the dimension of the counterions is in the order of a few nanometers,22,36,37 well within the sensitive detection range of FRET measurements, the R̅ value can certainly be a measurement showing the dimension of the counterion cloud. Also, being a relatively big organic molecule, Atto 620 has a much lower charge density compared with hydronium and sodium ions. This brings about its weaker interaction with the PSS− chain and makes its distribution much looser than hydronium and sodium ions. The acceptor is very mobile, and it can average all possible positions within the counterion cloud, making its average distance to the donor at the PSS− chain end meaningful for describing the dimensions of the portion of counterion cloud constituted by Atto 620. Another subtle point is whether the saturation of the increase of average distance is because of the detection limit brought by low efficiency at large donor−acceptor distance. This possibility is excluded by the agreement of the results of FRET measurements to that of the single chain electric potential determined by PCH measurement, which is never a length-scale-limited method. Please refer to the latter text. An interesting feature is discovered when the data of R̅ are compared with the reduced viscosity under different NaPSS concentration. As demonstrated in Figure 2b, the changes of R̅ exhibit a similar feature with the variation of reduced viscosity for concentration above 0.005 mg/mLthe R̅ value increases in parallel with ηreduced values upon dilution of the solution. Around the concentration of 0.005 mg/mL, both them reach their maximum, and below this concentration, the R̅ value remains almost constant while ηreduced drops sharply. These data have shown that the increase of reduced viscosity of NaPSS due to dilution is in accordance with the expansion of counterions cloud around NaPSS chain. This can be understood as that with the expansion of counterion cloud; a polyelectrolyte chain should have a bigger hydrodynamic radius, and therefore a much higher friction is generated from its interaction with the surrounding solvent.22 Under such a circumstance, individual polyelectrolyte chains experience higher friction with the surroundings and should generate a bigger contribution to the viscosity of the solution. The expansion of counterion cloud should affect the effective charges on the NaPSS due to less counterions are adsorbed to neutralize the original charges on the main chain. This is verified by PCH measurements of the local hydronium concentration in the vicinity of the NaPSS chain. Being a part of the counterions, hydroniums are attracted around the negatively charged PSS− chain, resulting in much higher hydronium concentration locally at the chain and therefore a much lower local pH value. A number of previous studies have shown the concentrated hydronium near polyanions and the depleted hydronium near the polycations.21−24,37 Taking the similar strategy, the local hydronium concentration (the local pH value) is measured by PCH measurement of the molecular brightness of single pH-responsive fluorescent probe (OG 514) chemically attached to the end of PSS− chain. Figure 3a shows the molecular brightness (ε) of OG 514 as a function of pH value when it is freely dissolved in aqueous solution, and Figure 3b is the ε value of OG 514 attached to the chain end of NaPSS as a function of concentration of NaPSS. (The concentration is mainly determined by that of unlabeled NaPSS because it is orders of magnitude higher than the labeled ones.) Both solutions are free of external salt addition except those for pH adjustment. In the experiment, the pH value is tuned by addition of HCl (pH = 2) and NaOH (pH =

Figure 3. (a) Molecular brightness of free OG 514 as a function of pH value, serving as the master curve for local pH determination. (b) Molecular brightness of OG 514 attached to the chain end of NaPSS as a function of concentration of unlabeled NaPSS. The concentration of NaPSS−OG 514 is 4.2 × 10−9 M.

12) solution dropwise, and no buffer solution is used. In this way, the possible salt effect can be minimized, as proved and demonstrated in detail in a few previous reports.21−24 The pH response of OG 514 is clearly demonstrated by its monotonous increase of brightness with the increase of pH value (Figure 3a), and this data set serves as the master curve for pH determination of the location wherever the probe is positioned. Figure 3b displays the molecular brightness of OG 514 attached to the chain end of NaPSS as a function of the concentration of unlabeled NaPSS. Apparently, its value increases with the concentration of NaPSS, indicating that the local pH at the vicinity of NaPSS is increasing under higher NaPSS concentration. According to the chemical structure of the attachment, the OG 514 probe is approximately 1.0 nm away from the main chain of NaPSS. Therefore, the data in Figure 3b demonstrate the decrease of hydronium concentration at that distance from the chain (at the chain end region) when NaPSS concentration increases. This result is further confirmed by a separate SMS experiment (detailed in Figure S7). As expected to be the result of expansion of the counterion cloud, there should be a change of the difference between the local hydronium concentration (pH value) of the NaPSS and the bulk solution (at the infinite distance from the NaPSS chain). The data are provided in Figure 4a, in which both the bulk pH and local pH value increase with the NaPSS concentration but the latter increases much faster than the former, leading to a smaller difference between them. The bulk pH increases with the polymer concentration, indicating a limited number of hydroniums are distributed to more PSS− chains, leaving a smaller amount of hydroniums in the bulk solution. (The limited dissociation constant of water cannot maintain a constant pH value. Insulation of the sample to ambient air prevents dissolution of CO2.) The local pH at the vicinity of PSS− chain increases much faster than the bulk pH, further demonstrating the fact that the limited hydronium ions are forced to be shared with multiple negatively charged chains, leading to a situation that each PSS− chain loses prepossessed hydroniums. D

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and pHbulk denote the local pH value in the vicinity of PSS− chain and that in the bulk solution, respectively.21 The amplitude of electric potential (|ψ|) of PSS− chain under different concentrations is shown in Figure 4b. The |ψ| value increases when the NaPSS concentration decreases, and it saturates around the NaPSS concentration of 0.005 mg/mL, below which the |ψ| value becomes constant. This is a very similar behavior as the average donor−acceptor distance in the FRET experiments, the counterion cloud expansion. Again, a clear coincidence of the concentration is discovered at 0.005 mg/mL, at which the |ψ| value almost reaches its maximum and the reduced viscosity reaches its peak value. Apparently, both counterion cloud expansion and increase of the electric potential upon dilution coincide with the increase of the reduced viscosity, giving a strong hint that the counterion redistribution can be one of the major origin of the concentration dependence of rheological behavior of the polyelectrolyte solution. Upon dilution, the maximization of translation entropy of the counterions makes the counterion cloud of NaPSS chain expand, together with desorption of preadsorbed counterions on the PSS− main chain, increasing the effective charges of the chain. Such a process continues until the concentration reaches a very low level, 0.005 mg/mL, corresponding to 2.1 × 10−8 M. At this concentration, the counterion cloud expansion and the increase of effective charge starts to saturate, and at even lower concentration, it retains almost a constant value. This is because of the increase of entropic free energy barrier, which is inversely proportional to concentration, i.e., ∂U/∂cp ∝ T ∂ ln cp/∂cp ∝ 1/ cp, in which U and cp denotes free energy and polymer concentration (concentration of NaPSS in the current case), respectively. This leads to a dependence of counterion concentration change on polymer concentration, proportional to c p −1 e −U , which saturates severely at low polymer concentration. Therefore, as dilution proceeds to low enough concentration, the expansion of the counterion cloud slows down and makes very small changes in response to the variation of polymer concentration. Under such a condition, the PSS− chain has its almost biggest dimension of counterion cloud and almost the highest amount of effective charge. It is under such a condition that the PSS− chain reaches almost its biggest hydrodynamic dimension and therefore experiences the highest friction from the solvent. Meanwhile, the high effective charge of the PSS− chain brings about possibly the strongest mutual chain−chain interaction so that their motions are coupled the strongest. All these facts can explain why the reduced viscosity keeps on increasing when polymer concentration decreases. Along the way of dilution, another process emerges to bring about the reduction of the reduced viscositythe increase of interchain distance, which leads to a weakened interchain electrostatic interaction and the mutual coupling of the motions of different chains. At the concentration of the maximum reduced viscosity (0.005 mg/ mL and 2.1 × 10−8 M), corresponding to the interchain distance of 430 nm, being close to the Debye length of an ordinary salt-free aqueous solution. Therefore, further dilution results in the increase of interchain distance and brings about a weakened interchain electrostatic interaction and therefore a downshift of the reduced viscosity. The possible mechanism of chain−chain overlapping at the maximum viscosity is excluded. Assuming that the NaPSS chains take the rod-like conformation as they do in the condition of extreme dilution,22 the calculated radius of

Figure 4. (a) Bulk pH value and local pH value at the vicinity of PSS− chain as a function of the concentration of NaPSS. The concentration is adjusted by the amount of unlabeled NaPSS in the solution. (b) Amplitude of electric potential of PSS− as a function of NaPSS concentration, as calculated from the data in (a).

What is emphasized is the bigger and bigger difference between the bulk and local pH value along the direction of dilution. This is a clear indication of the increase of effective charges on the PSS− chain upon dilutionan identical process of the expansion of counterion cloud. The chemical connection of OG 514 to PSS− chain positions the probe at a certain distance (approximately 1.0 nm) away from the chain end, letting it probe the hydronium concentration at that distance to the chain. Because of the dilution, the maximization of translational entropy of counterions makes counterions stay further away from the charged chain. Therefore, a certain number of counterions previously residing closer to the chain than the probe move out, leaving a higher amount of effect net charge behind. Another process is accompanying the counterion cloud expansion: the desorption of some of the counterions previously adsorbed on the PSS − chain. As proved previously,20,35 the interaction of the counterions with the polyelectrolyte chain is under dynamical exchange of the adsorbed and unadsorbed ones, a process depending on the concentration of polyelectrolytes. Dilution depromotes adsorption of the counterions, leading to the desorption of them. Therefore, during the expansion of the counterion cloud, the degree of ionization (the effective charge amount) also increases. The desorbed counterions will join the cloud, attracted by the PSS− chain, moving together with charged chain as a part of the expanded counterion cloud. As dilution proceeds, some of the counterions will leave the cloud and can possibly reduce the size of the counterion cloud.20 However, the observed expansion demonstrates the overwhelming effect of the strong electrostatic attraction. The electric potential at the end of the PSS− chain is determined by analyzing the distribution of hydroniums by the universal Boltzmann distribution function: [H+]local = [H+]bulk exp(−eψ/kBT), where [H+]local and [H+]bulk denote the local concentration of hydronium in the vicinity of PSS− chain and that in the bulk solution, respectively, e the element charge, ψ the electric potential, kB the Boltzmann constant, and T the room temperature. This relation is further converted in terms of pH values as pHlocal = pHbulk + 0.43eψ/kBT, where pHlocal E

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Macromolecules gyration is about 86 nm, leading to a value of overlap concentration as 6.2 × 10−7 M (0.146 mg/mL). Actually, the rod-like conformation may not retain at elevated concentrations43,44 and the overlap concentration can be even higher. Therefore, the overlap concentration should be at least 1 order of magnitude higher than the concentration of maximum viscosity. These experimental evidences have demonstrated two major contributions to the anomalous rheological behavior of polyelectrolyte solution: (1) The increase of effective charges and the expansion of its counterion cloud. This factor increases the interchain electrostatic interaction and the hydrodynamic friction of individual chains. (2) The increase of interchain distance, which weakens the chain−chain interaction and their mutual motion coupling. This lowers the reduced viscosity. Molecular conformation should be another important factor related. While this is still a challenge for experimental characterization of polyelectrolytes under strong electrostatic interaction,39−42 a recent study by computer simulation has shown that the dimension of the charged chain also expands upon dilution.36 From the experimental point of view, it is demonstrated that the polyelectrolyte chain takes a rod-like conformation at extreme dilution22 while it takes coil conformation at high concentration.22,43 Because of the longrange electrostatic interaction and the entropy effect of the multiple counterions, the charge state of polyelectrolytes is concentration-dependent. The findings of the current study have a number of agreements with the results of computer simulations, including the counterion cloud dimension, effective charge density, and molecular conformation,36,44 as well as with a previous experimental measurement on the petitioning fluorescent counterion probe as a function of polymer concentration.20 The current experimental investigation by single-molecule fluorescence techniques has provided evidence to help to understand the unique concentration-dependent rheological properties of polyelectrolytes. More efforts to look deeper into this question should be highly desirable.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (J.Z.). ORCID

Jiang Zhao: 0000-0001-7788-2708 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support by the National Natural Science Foundation of China (51573197) and the National Basic Research Program of China (2014CB643601) is appreciated.

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CONCLUSION Both FRET and PCH measurements demonstrate that upon dilution there happens the expansion of the counterion cloud of NaPSS chain and desorption of counterions from the main chains. The average counterion−chain distance as well as the effective charge amount increases during the dilution process and reaches their saturation at the concentration of 0.005 mg/ mL, which coincides with the point of maximum value of the reduced viscosity. The expansion of counterion cloud brings about enlarged hydrodynamic friction and desorption of preadsorbed counterions enhanced chain−chain interaction and motion coupling, contributing to the increase of reduced viscosity. Further dilution does not change the effective charge but increases the interchain distance and therefore reduces the chain−chain interaction and coupling, resulting in a reduction of viscosity.

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Alexa 488 in pure water (Figure S1); shear rate dependence of apparent viscosity and polymer concentration dependence of reduced viscosity for selected NaPSS solutions with no added salt (Figure S2); singlemolecule FRET spectra between end-labeled NaPSS− Alexa 488 and free Atto 620 under different Atto 620 concentrations in aqueous solutions and apparent overall FRET efficiency as a function of the concentration of Atto 620 (Figure S3); single-molecule FRET spectra between end-labeled NaPSS−Alexa 488 and free Atto 620 under different NaPSS concentrations in aqueous solutions and apparent overall FRET efficiency as a function of the concentration of NaPSS (Figure S4); excitation and emission fluorescence spectroscopy of free Atto 620 in aqueous solution (Figure S5); singlemolecule fluorescence emission spectra of QP4VP− Alexa 488 only and mixed solution of QP4VP−Alexa 488 and free Atto 620 (Figure S6); SMS of free OG 514 under different pH values and end-labeled NaPSS−OG 514 under different NaPSS concentrations (Figure S7); and typical data of photon counts of free OG 514 under different pH values and NaPSS−OG 514 under different polymer concentrations (Figure S8) (PDF)

REFERENCES

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b00075. Detailed information on normalized autocorrelation function curves for PSS− labeled with OG 514 and F

DOI: 10.1021/acs.macromol.8b00075 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.8b00075 Macromolecules XXXX, XXX, XXX−XXX