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Modulation of the Electrochemical Reactivity of Solubilized Redox Active Polymers via Polyelectrolyte Dynamics Mark Burgess, Kenneth Hernandez-Burgos, Jonathon K. Schuh, Jasmine Davila, Elena C. Montoto, Randy H. Ewoldt, and Joaquin Rodriguez-Lopez J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.7b08353 • Publication Date (Web): 25 Jan 2018 Downloaded from http://pubs.acs.org on January 25, 2018

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Journal of the American Chemical Society

Modulation of the Electrochemical Reactivity of Solubilized Redox Active Polymers via Polyelectrolyte Dynamics Mark Burgess,&,‡,£ Kenneth Hernández-Burgos,&,‡,†,£ Jonathon K. Schuh,‡,◊ Jasmine Davila,& Elena C. Montoto,&,‡ Randy H. Ewoldt, †,‡,◊ and Joaquín Rodríguez-López&,‡,†,* &

Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews

Avenue, Urbana, IL 61801 ‡

Joint Center for Energy Storage Research

†

Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-

Champaign ◊

Department of Mechanical Science and Engineering, University of Illinois at Urbana-

Champaign, Urbana, IL 61801, USA. £

These authors contributed equally

*

Corresponding Author

1 ACS Paragon Plus Environment

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Abstract Redox active polymers (RAPs) are electrochemically versatile materials that find key applications in energy storage, sensing, and surface modification. In spite of the ubiquity of RAPmodified electrodes, a critical knowledge gap exists in the understanding of the electrochemistry of soluble RAPs and their relation to polyelectrolyte dynamics. Here, we explore for the first time the intersection between polyelectrolyte behavior and the electrochemical response that highly soluble and highly substituted RAPs with viologen, ferrocene, and nitrostyrene moieties elicit at electrodes. This comprehensive study of RAP electrolytes over several orders of magnitude in concentration and ionic strength reveals distinct signatures consistent with surface confined, colloidal, and bulk-like electrochemical behavior. These differences emerge across polyelectrolyte packing regimes and are strongly modulated by changes in RAP coil size and electrostatic interactions with the electrode. We found that, unlike monomer motifs, simple changes in the ionic strength caused variations over one order of magnitude in the current measured at the electrode. In addition, the thermodynamics of adsorbed RAP films were also affected, giving rise to standard reduction potential shifts leading to redox kinetic effects as a result of the mediating nature of the RAP film in equilibrium with the solution. Full electrochemical characterization via transient and steady-state techniques, including the use of ultramicroelectrodes and the rotating disk electrode, were correlated to dynamic light scattering, ellipsometry, and viscometric analysis. These methods helped elucidate the relationship between electrochemical behavior and RAP coil size, film thickness, and polyelectrolyte packing regime. This study underscores the role of electrostatics in modulating the reactivity of redox polyelectrolytes.


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1- Introduction Electrostatic

interactions

arising

from

electrified

interfaces,

ions,

and

polyelectrolytes play a central role in the emergence of structure-property relationships in chemical and biological systems. The formation of an electrical double layer and ionic atmospheres modifies the thermodynamics and kinetics of electron transfer at electrodes and within molecules undergoing redox exchange.1,2,3,4 The rise of nano-confined electrochemical systems and of nanomaterials commensurate with the Debye length, has sparked interest in elucidating the role of electrostatic effects on redox activity. This is evidenced by recent works on nano-particle dynamics,5,6 redox cycling in constrained geometries,7,8-10,56 and the evaluation of electron transfer rates using nanoelectrodes,11,12,13 to only name a few. Our laboratories recently introduced highly dispersible redox active polymers (RAPs) as a new class of flowable energy storage material that incorporate a large number of redox units within a macromolecular architecture.14,15 Because these RAPs exhibit polyelectrolyte characteristics as they undergo redox reactions, they enable new insights relating reactivity with molecular size, structure, and specific chemical interactions. While RAPs have been studied since at least the 1960’s,15, 16, the bulk of this work has centered on studying them only in the form of polymer modified electrode surfaces or in oligomeric forms. Despite this historical precedent, there is yet no systematic study on the effects of polyelectrolyte dynamics in the electrochemical responses of soluble RAPs.15,16 As there is the possibility for modulation of polymer conformations in solution, soluble RAPs present a timely opportunity for studying polyelectrolyte dynamics in redox nanomaterials. Here, we present the first comprehensive study linking electrostatic effects and polyelectrolyte behavior to the electrochemical response of solution-phase RAPs.



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Polyelectrolytes are polymer chains that bear ionic functional groups, which electrostatically interact with one another and with ions in solution. Since at least the 1950’s there have been considerable efforts to detail the solution dynamics of polyelectrolytes.17,18,19 These theories predict that polyelectrolyte coil conformations are strongly correlated to the electrostatics of the solution, which can be adjusted by tuning the amount of added salt. As depicted in Figure 1, the charged polyelectrolyte chains are separated by distances small enough that it is possible to have overlapping electrical double layers. The thickness of these layers is described by a Debye length, , which scales inversely proportional to the ionic strength. In low added salt regimes, when the Debye lengths are the longest, the pendants of polyelectrolytes are electrostatically repelled by one another, which influences the expansion of the polymer coil to minimize their electrostatic repulsions. Conversely, in high salt solutions, polyelectrolytes tend to shrink in size as their electrostatic repulsive forces are screened by the supporting electrolyte,20 and attractive interactions arising from Van der Waals forces from the organic backbone dominate. 4 ACS Paragon Plus Environment

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Finally, the amount of salt in solution has strong influences on the adsorption of polyelectrolytes to surfaces.21,22, 23 One source of polyelectrolyte adsorption comes from the well-understood “salting out” effect,24 which can drive charged objects in solution to eventually crash out when sufficient salt is added. In unconjugated RAPs, charge transfer through the chain and their dispersions is mediated by inter-pendant electron exchange, facilitated by charge hopping.15,25,26 Modulating the pendant-to-pendant distance (δ), the concentration of redox pendants (C), or the magnitude of electron self-exchange (kEX), has an impact on the intra-chain charge transport diffusion coefficient, DE. The physical diffusion coefficient, DP, can be expressed through the Stokes-Einstein equation where kB is the Boltzmann constant, T the temperature, ηS the solvent viscosity and the hydrodynamic radius, rH, is used to describe the particle size. Together DE and DP constitute the total diffusion coefficient in the threedimensional Dahms-Ruff model, Equation 1:27,28,59

= + = +

C

(1)

Changes in coil packing and size as both polymer and electrolyte concentration are varied will impact D, and are likely to elicit diverse electrode responses. Charge transfer at the electrode and the use of permanent ionic substituents on polymer coils create conditions for polyelectrolyte dynamics and interactions with a poised electrode surface to strongly impact the kinetics and potentials of electron transfer at RAPs.17,29,30,31,32,33,34,35 In this study, we explore the role of electrostatics and polyelectrolyte dynamics in electrochemical analysis via modulating the ionic strength for three soluble RAPs with different states of charge and redox potentials, poly (amino ferrocene) (PAF), poly (benzyl ethyl viologen) (VioRAP), and poly (para-nitrostyrene) (PNS). The structures and properties for these 5 ACS Paragon Plus Environment


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RAPs are shown in Scheme 1. This first study into the role of polyelectrolyte dynamics on solubilized RAP electrochemistry reveals that the choice in solution ionic strength is not a trivial experimental parameter. We clearly demonstrate that the careful selection of electrolyte concentration is crucial for extracting thermodynamic, rate, and charge accessibility parameters from electroanalytical methods. Here, we show that soluble RAPs behave much differently than their monomer constituents and special considerations need to be taken into account that optimize different aspects of their reactivity for unleashing their full potential and performance for applications such as energy storage, catalysis, and sensing.

Scheme 1. 1 = ethyl viologen dihexafluorophosphate (Vio). 2 = poly (benzyl ethyl viologen) (VioRAP) with a Mn of 318 kDa and 537 pendants per chain on average. Vio and VioRAP undergo two reversible electrochemical reductions, changing the oxidation state of the pendant from 2+/1+ and 1+/0, respectively. 3 = poly (amino ferrocene) (PAF) with a Mn of 271 kDa and 537 pendants per chain on average. PAF is reversibly oxidized at the iron center to change the oxidation state of each pendant from 1+/2+. 4 = poly (nitrostyrene) (PNS) with a Mn of 50 kDa and 335 monomers per chain on average. PNS undergoes reversible reduction which changes the oxidation state of each pendant from 0/1–.

2- Results and Discussion 2-1 Ionic Strength and Polymer Concentration Modulate Steady-State Electrochemical Responses We tested the modulation of electrochemical reactivity by polyelectrolyte dynamics: first, as a function of ionic strength, which determines chain conformation, and second, as a function of RAP concentration, which impacts inter-chain charge transfer. The large concentration range accessible through soluble VioRAPs allowed us to probe a broad range 6 ACS Paragon Plus Environment

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of polymer and electrolyte concentrations to explore these effects. In all cases for VioRAP and for Vio, we accessed the 2+/1+ redox state. We first approached the characterization of RAPs using ultramicroelectrode (UME) steady state electrochemistry to evaluate the sustained rate of charge transfer at the electrode. Steady state measurements suppress the contribution from transient redox processes caused by an adsorbed RAP layer, which is always present on the electrode surface. In addition to providing a convenient dynamic range for measurements across several orders of magnitude of polymer and electrolyte compositions, UME’s allow probing solution reactivity in the limit of no added salt because of their minimal i-R drop.36 As a first control experiment, UME voltammetry (Figure 2A) and chronoamperometric steps (Figure S16) of Vio were evaluated. In Figure 2A, all the voltammetric waves of Vio in a series of solutions varying in ionic strength are consistent with the sigmoid shape expected for facile charge transfer at the UME electrode, and readily attain a plateauing current. The UME voltammetric behavior of RAP solutions is in stark contrast with that of Vio. The reactivity of the VioRAP (Figure 2B) is strongly impacted by changes in salt concentration. Under conditions of no added salt, the voltammetric wave shape of the VioRAP solution is completely dominated by a process relatable to the response of a surface confined species, as indicated by a symmetrical redox wave and a barely discernable steady-state current. The absence of supporting electrolyte accentuates the proclivity for adsorption of VioRAP onto the electrode surface due to the electrostatic attraction of a cationic polymer and a negatively poised electrode surface. In the absence of excess salt, repulsive electrostatic interactions will dominate the behavior of



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polyelectrolytes because the Debye length, , under these conditions is quite large ( > 3nm).

Figure 2. UME analysis of Vio and VioRAP. (A) UME cyclic voltammetry at 20 mV/s of 0.5 mM of Vio in acetonitrile at different ionic strengths of TBAPF6 salts. (B) UME cyclic voltammetry at 20 mV/s of 5 mM VioRAP in acetonitrile at different ionic strengths. (C) Chronoamperometric steps at a UME held at -0.9 V in a 5 mM VioRAP in acetonitrile in different ionic strengths. (D) UME cyclic voltammetry at 20 mV/s of 500 mM VioRAP in acetonitrile at different ionic strengths. (E) Current function across various electrolyte and VioRAP concentrations. Data points come from the viscosity corrected limiting currents following a chronoamperometric step at -0.9 V vs. Ag/Ag+ after 60 s. All done at varying TBAPF6 concentrations in acetonitrile and at 20mV/s.

Although the condition of zero excess salt presents itself as an interesting case relative to Vio, electrochemical measurements without excess supporting electrolyte are rarely performed due to uncertainties in migrational transport. A general rule of thumb for electroanalytical experiments is to have at least a 10:1 ratio of supporting electrolyte to active species in order to observe reactivity under diffusion control.36 However, it is clear that this rule is not sufficient to describe RAPs. Surprising results were still observed when


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excess electrolyte was added to the solution. Under conditions of excess, but moderate concentrations of supporting electrolyte (10 mM, 100 mM), the UME voltammetry in Figure 2B of the VioRAP begins to resemble the sigmoidal wave shapes observed with Vio. When additional salt was added (500 mM, 1000 mM) we observed new deviations from this shape. Although there is a steady state current achieved in the forward sweep, scan reversal creates a large stripping peak that results from the adsorption of the reduced RAP. We now turn to evaluate the steady-state response obtained under mass transfer limited conditions. UME chonoamperometry with the VioRAP, plotted for a representative system in Figure 2C, shows that unlike Vio (Figure S16), the steady state currents are also strongly affected by changes in the electrolyte concentration. We rigorously tested the observed trends by changing the concentration of the VioRAP over four orders of magnitude, and by changing the identity of the salt by probing in both in LiBF4 and TBAPF6 electrolytes (Figures S1-S12). These results are summarized in Figure 2E, where the steady state currents under all of the different RAP and supporting electrolyte concentration conditions are divided by nFa, where n is the number of electrons (1 for viologen), F is Faraday’s constant (96,485 C/mol), and a is the electrode radius (12.5 µm) to display the response in terms of an effective current function in mol/(cm*s). The current function data points have been corrected for viscosity, Table S1, via use of Walden’s rule, multiplying the current function by the ratio of the solvent viscosity at the desired supporting electrolyte concentration to that of the base solvent.14 An equivalent plot for PAF, and one for VioRAP in LiBF4 salt, are shown in the Supporting Information, Figure S23.



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As seen in Figure 2E, when the VioRAP solutions are relatively dilute (< 50 mM) there are strong dependencies of the current function on the ionic strength that are not seen with Vio. Independent of the identity of the supporting electrolyte, the current function changes almost an order of magnitude going from low to high ionic strength despite the equimolar viologen concentration in solution. Above 50 mM concentration of VioRAP, the dependency of the current function on the ionic strength is smaller, but still larger than for Vio. We hypothesize this transition of behavior is due to a changeover in the regimes of polymer dynamics as a function of RAP concentration. Above a critical concentration, termed the overlap concentration, polymer coils are no longer considered independent and will interact with one another.37 In this case, steady-state UME measurements suggest that when individual coils interact with the electrode, as would be expected at low polymer concentration and low to intermediate ionic strength, charge transfer to RAPs is most sensitive. This is further evidenced by CVs performed at high RAP concentration shown in Figure 2D. At low RAP concentrations, both limiting currents and voltammetric shapes are strongly affected by changes in ionic strength, whereas at high RAP concentrations the shape of the CV is less sensitive. A surprising finding is that there is almost always an optimum in the reactivity at 100 mM of supporting electrolyte, suggesting a maximum in charge accessibility under these conditions. A lower molecular weight analogue of this RAP (22 kDa) exhibited a similar response, whereby the ionic strength modulated the reactivity (Fig. S24). Altogether, these observations point to the occurrence of several phenomena that are unique to the reactivity of RAP solutions on electrodes. The following sections will explore the link between electrolyte-induced changes in RAP structure, adsorption onto surfaces, and reactivity.


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2-2 Linking Electrochemical Response to Polyelectrolyte Dynamics To this point, we have clearly demonstrated that changing the salt concentration has dramatic effects on the electrochemical measurements of RAPs. A critical link between the electrochemical response and RAP structure is that size in terms of hydrodynamic radii, rH, is related to the ionic strength. To measure rH for the RAPs at different ionic strengths, two different techniques were utilized for comparison. First, rH was estimated via an intrinsic viscosity,, analysis via the Einstein-Simha relation.38 Second, rH was measured by dynamic light scattering (DLS) via fitting of the cumulants of an autocorrelation function. Since DLS determination of rH requires a priori knowledge of the solution viscosity, it makes sense to discuss viscometric results first. Viscosity measurements for solutions of VioRAP at different concentrations and ionic strengths were performed on a microfluidic device (mVROC, RheoSense Inc), where the viscosity was obtained from pressure drop and flow rate measurements across the microfluidic chip. All the VioRAP samples tested behaved as Newtonian fluids (constant viscosity to within 4%) over a shear rate range of 3,000-30,000 1/s. The average viscosities over the tested shear rate range for each sample are plotted in Figure 3A. For the range of compositions tested, viscosity varies from 0.3 mPa*s to 12 mPa*s. Viscosity generally increases with both VioRAP concentration and supporting electrolyte concentration. A notable exception is at 1000 mM supporting electrolyte, where the viscosity appears to plateau at the highest VioRAP concentrations. We attribute this to the VioRAP reaching its solubility limit and excess polymer precipitating out of solution.



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The initial increase in viscosity with VioRAP concentration can be used to estimate the size of the polymer coils, through the intrinsic viscosity [η]. Huggins39 showed that the viscosity, η, of polymeric solutions should increase with the polymer concentration as

(

η = η s 1 + [η ] C + k H [η ] C 2 + O ( C 3 ) 2

)

(2)

where ηs is the solvent viscosity (mPa*s), [η] is the intrinsic viscosity (L/mol), C is the concentration of the polymer (mol/L), O(C3) represents higher order dependence on concentration, and kH is the Huggins parameter that describes the quality of the solvent for the given polymer, with good solvents having kH < 0.5. For our system, ηs is the viscosity of the solution of the base solvent (acetonitrile) at the corresponding concentration of supporting electrolyte (nominal viscosity without electrolyte η=0.334 mPa*s)40. Equation 2 can be rearranged as

η −1 ηs C

2

= [η ] + k H [η ] C

(3)

so that the intrinsic viscosity can be interpreted as an intercept in the limit that C goes to 0. Figure 3B shows the data of Figure 3A plotted in the form of Equation 3, along with the fit of Equation 3. For solutions with salt concentrations of 1000 mM, only the constant value of [η] was fit to the data. The values of kH and the overlap concentration C*=1/[η] obtained for each sample are given in Table 1. The fit parameters were then substituted into Equation 2, which is plotted against the experimental data in Figure 3A. Good agreement was seen between the experimental data and the fits. Unfortunately, we were unable to perform this same viscometric analysis with PAF, since this polymer was not sufficiently soluble to provide meaningful differences.


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The intrinsic viscosities of the VioRAP solutions at different ionic strengths provide a way to calculate the hydrodynamic radius rH of the VioRAP coils using a rearrangement of the Einstein-Simha relation

η − 1 = νϕ , where ν is the Simha coefficient (that depends on the ηs

asymmetry of the molecules) and φ is the volume fraction.41 If we assume that the polymers can be modeled as hard spheres,42 then ν =

[η ] C =

5 . For Equation 2 to match Einstein’s predictions, 2

5 4  ϕ . The volume fraction is related to the polymer concentration by ϕ = C  π rH 3  N A , 2 3 

where NA is Avogadro’s number. Substituting this into the Einstein prediction and rearranging gives a method for estimating the effective hydrodynamic radius rH from the obtained values of

[η ] as 1/3

    [η ]  . rH =    5  4 π  N    2  3  A      

(4)

However, proper analysis of the rH for VioRAP coils with no added salt to the solution requires special considerations. For simple polymer solutions, Huggins39 predicted that the reduced viscosity, defined as

ηred ≡

η −1 ηs C

(5)

approaches a constant value in the limit C→0, and this constant is defined as the intrinsic viscosity

[η ] .

Polyelectrolyte solutions (without a background electrolyte), however, do not show this



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expected trend. Kulicke and Clasen43 show that ηred actually increases in the limit of C→0. At low polyelectrolyte concentrations, the Coulombic repulsion forces between the ionic groups on the polymer chain increase, which causes the polymer coil to expand, leading to the increase in ηred . This increase in ηred means that [η ] , defined in the manner of Huggins, cannot be obtained for polyelectrolyte solutions without a background electrolyte. An estimate for [η ] , and subsequently an estimate for the size of the polymer, can be obtained by determining the concentration where

η = 2 , and denoting this concentration as C*. ηs

The estimate for the intrinsic viscosity is then [η ] =

1 , which can be substituted into the EinsteinC*

Simha equation to obtain an estimate for the size of the polymer. The estimated size of the VioRAP without any supporting electrolyte is given in Table 1. We also estimate how the size of the polymer changes as a function of concentration by fitting a power law to ηred when the concentration of the polymer is less than C*. Fuoss proposed that in this region, ηred ~ C −1/2 ,37 which suggest that

[η ] =

A . C

(6)

The values for [η ] at different concentrations can be used with the Einstein-Simha equation to again estimate the size of VioRAPs at different concentrations, shown in Table S4. The size of the polymer increases as the RAP concentration decreases, which is consistent with results predicted by Kulicke and Clasen.43


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Table 1. Evaluated parameters for VioRap solutions, using TBAPF6 as supporting electrolyte in acetonitrile. (We calculated the uncertainty in rH based on error propagation through Equation 4 due to uncertainty of the fit to the intrinsic viscosity). Electrolyte Concentration (mM)

rH from Viscometry kH (nm) (Huggins Parameter)

Overlap Concentration C*= 1/ (mol/L)

0

24.3 ± 1.6

N/A

11 x 10-3

10

19.4 ± 1.3

0.046

227 x 10-3

100

15.5 ± 1.0

0.215

42 x 10-3

500

14.9 ± 1.0

0.241

48 x10-3

1000

13.9 ± 0.9

N/A

59 x10-3

Figure 3. Viscometric analysis of VioRAP. (A) Measured viscosity of VioRAP solutions at different concentrations of RAP and supporting electrolyte. Data points are shown as symbols and the model fits (Equation 2) are shown as solid lines. (B) Rearrangement of the data in (A) allows for identification of intrinsic viscosity as the y-intercept. All systems use TBAPF6 as supporting electrolyte in acetonitrile

To check that our viscosity measurements of VioRAP are consistent with previously reported scaling laws of polyelectrolytes, we analyzed the specific viscosity, η/ηs-1, versus VioRAP concentration under the condition of no added salt, shown in Figure 4A. As understood from Fuoss’s Law,17,37 the specific viscosity of a polyelectrolyte should increase in a square root relationship with its concentration, provided no excess salt is added to the solution. Our VioRAP viscosity measurements closely follow this predicted trend, as shown by the red line in Figure 4A. We note that this constant increase in specific viscosity 15 ACS Paragon Plus Environment


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continues even beyond the calculated overlap concentration (C*). For polyelectrolytes, it is known that the overlap concentration and the concentration at which polymer coils become entangled (Ce) can be different,37 with the latter occurring at higher polymer concentration. We estimate that the critical concentration for entanglement and the beginning of reptation dynamics46,47 for VioRAP to be ~100 mM. This was determined via the large increase in slope in the specific viscosity plot beginning at ~100 mM of VioRAP. It is has been previously reported that entangled polyelectrolyte solutions will have an increase in their specific viscosities as a function of polyelectrolyte concentration with a slope of 1.5,37 which our experimental results closely follow, as shown by the blue line in Figure 4A. The calculated values of rH for the VioRAP samples at different ionic strengths are shown in Table 1. When the ionic strength of the solution is increased, the effective rH for VioRAP decreases from 24.3 nm to 13.9 nm. Dobrynin et al. hypothesized that in the dilute polymer regime, [η] ∝ Cs-3/5,37 where Cs is the electrolyte concentration. Substituting this expression into Equation 4 suggests that rH ∝ Cs-1/5. Analysis of Table 1 for VioRAP and Table S5 for PAF, show best fits for a power law of -0.07 and -0.37 respectively (Figure S67). We hypothesize that the π-π interactions between viologen groups44 could make the VioRAP chain more rigid than expected. This would increase the value of a in a Mark-Houwink relation beyond that of a perfectly flexible chain45 and provide fewer degrees of motional freedom to shrink when the ionic strength is increased. In the case of PAF, the strength of electronic interactions between ferrocene pendants are weaker, leading to larger values in the power law.


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Figure 4. RAP sizing and electrochemical correlations. (A) Specific viscosity (/ − 1) of VioRAP solutions at different concentration of RAP in the absence of any added salt to the solution. Theoretical slopes of 0.5 (red) and 1.5 (blue) denote the expected magnitude of viscosity increase for dilute and concentrated polymer solutions, respectively. We used agreement with this scaling to identify the different regimes. Uncertainty bars in the plot (A) are smaller than, or comparable to, the symbol size. Panels B-C show comparison between experimental and model predictions for the limiting current function as determined by rH measurements. “High accessibility” for all model predictions was recreated using kEX=1x108 m3/mol*s. (B) DLS measurements for PAF as experimental input, “medium accessibility” recreated using kEX=3x106 m3/mol*s, and “low accessibility” recreated using kEX=2x105 m3/mol*s. (C) Viscometric measurements for VioRAP, “medium accessibility” recreated using kEX=1.5x107 m3/mol*s. Number labels indicate rH for each data point. δ value for all model predictions was 0.9 nm.

With polymer dynamics in hand, it is possible to establish relationships to the reactivity of RAP solutions. Figure 4A helps elucidate the observation of two regimes in 17 ACS Paragon Plus Environment


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the current functions shown in Figure 2E. In dilute RAP solutions it is possible to modulate the rH of the RAP coils by changing the ionic strength in a way that modifies the charge accessibility (DE) and physical diffusion of the polymer chains (DP). However, above C*, and certainly when above Ce, describing RAPs with an effective rH becomes less meaningful. In these types of solutions, the polymer dynamics are more correlated and should be described in terms of entangled polymer concepts. As such, when the entire solution of polymers is entangled, it approaches the absolute limit in packing density that is possible in solution phase. Although changing the ionic strength could modify the effective size of individual RAP chains, this effect matters less, and thus electrochemical measurements in entangled solutions will be dominated by a bulk-like behavior, and not from modifications to individual chains. This is evident when comparing the UME voltammetry of VioRAP in the dilute (Figure 2B) and entangled (Figure 2D) regimes. The latter shows essentially the same CV waveform, with the current response only modified by changes in the electrolyte viscosity as the supporting electrolyte is increased. In order to explain the larger modulation in current intensity observed for the dilute regime, we now evaluate the impact of a changing rH on the response elicited by the polymer coils at the electrode. Because collision of polymer coils with the electrode precedes charge transfer, we assumed the limiting current will depend on DP for the polymer, evaluated as a hard sphere, multiplied by an accessibility function, A(rH). This function describes the efficiency of electrolysis in terms of DE. Introducing these terms into the limiting current expression for a UME yields: !

= 4#$%&'()*+, -./ )0-./ )

(7)


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Where F is Faraday’s constant, a is the radius of the microdisk, Cpolymer is the concentration of polymer coils in solution, and n corresponds to the number of redox sites per polymer coil. If each redox site exchanges one electron, the product nCpolymer is more conveniently expressed as the concentration of redox pendants in solution. Equation 7 emphasizes that Dp and A are functions of rH, and therefore will correspond to properties related to the polymer coils. Dp(rH) can be expressed per the Stokes-Einstein equation, while A(rH) is obtained by proposing Equation 9, where npolymer represents the moles of redox active species per polymer coil: -./ ) =

0-./ ) = 1 (./ ) =

&(./ ) =

(8)

1

(9)

2 3 1

∗

56789:;< =

> >

=

56789:;< ? >

(10)

Substituting these expressions in Equation 7 for iL gives us a simple model for probing the potential impact of several variables on the steady-state response. Scheme 2 depicts two limiting cases. At low ionic strength, the polymer coils are more extended (larger rH) resulting in both the local decrease in pendant concentration, lowering DE, and decreasing the value of DP. At high ionic strength, DE should become larger as the local concentration increases. However, now there is a competing effect on DP due to the decrease in rH but the increase in ηS. The predicted decrease in iL at low ionic strength combined with this competition gives rise to the possibility of observing a maxima, as observed in Figure 2E. Indeed, comparison between the experimental results for VioRAP and PAF and the model predictions using data from DLS and viscometry (only VioRAP) as input for rH show this trend, Figure 4B-C. What this analysis shows, is that the hard-sphere model is not sufficient



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to explain the large changes in current observed at low ionic strength. This hard-sphere model is introduced as the “high accessibility” case in Figure 4B-C, where A(rH) =1 for all modeled points by using a larger value for kEX. In contrast, using a lower value for kEX that is consistent with that calculated previously,48,49 the large changes observed in this region are better recreated. Likewise, at high ionic strength for PAF (Figure 4B), a lower accessibility value is necessary to reproduce the predicted iL because the >1M intra-coil redox species concentration predicted for the small rH likely leads to crowding effects upon electrolysis.25 Although the results for VioRAP (Figures 4C) show the same trends predicted by our model, quantitative agreement was not possible. We believe this is in part a reflection of the same difficulties observed in the rheological characterization of VioRAP. However, our model is currently limited by several factors: we have not considered migrational effects on the limiting current, modulations of η or its impacts on electron transfer, or the possibility of structural re-arrangements such as those predicted by counterion condensation theories.50,51 The model also assumes that rH is a suitable descriptor of the particle size for electrolysis purposes. While our groups are actively working on elucidating all these aspects, our simple model captures for the first time the main aspects of the modulation of iL on dilute RAPs as a function of ionic strength.

2-3 Macrodisk Voltammetry, Rotating Disk Electrode, and Adsorbed RAP Layer Studies


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Macrodisk CV experiments confirm the unique reactive features of RAPs observed with UME’s and provide additional information regarding the impact of the adsorbed polymer layer. Figure 5A shows a representative example of macroelectrode CV at 0.5 mM concentration of the VioRAP at a series of supporting electrolyte concentrations. Potential shifts and the emergence of multiple peaks show the strong influence that ionic strength has on the reaction mechanisms under transient conditions.

Figure 5. Macrodisk and RDE characterization of RAPs. (A) Cyclic Voltammograms at 10 mV/s for VioRAP (0.5 mM) as a function of electrolyte concentration (TBAPF6). (B) Linear sweep voltammograms of VioRAP (5 mM) in acetonitrile as a function of rotation rate at 100 mM of electrolyte concentration (TBAPF6). VioRAP film voltammetry. (C) Cyclic Voltammograms at 10 mV/s for VioRAP films deposited at different electrolyte concentration (as indicated in the legend), but measured at 100 mM TBAPF6. Film was deposited by cycling 10 times accessing the redox process (Figures S14-S15). (D) Cyclic Voltammograms at 10 mV/s for VioRAP film deposited at a 100 mM TBAPF6 as a function of electrolyte concentration. All done at varying TBAPF6 concentrations in acetonitrile.

At low electrolyte concentrations (10 mM) and for 0.5 mM VioRAP a peak is observed approximately 100 mV more positive than the diffusive wave at ca. -0.68 V vs. Ag/Ag+, strongly suggesting a pre-adsorption equilibrium favoring the reduced product. At intermediate electrolyte concentrations, e.g. 100 mM, we obtained a reversible wave that is consistent with a diffusion-controlled process, mirroring the mass transfer behavior observed in UME voltammetry at this salt concentration. Finally, in concentrated 21 ACS Paragon Plus Environment


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supporting electrolyte an asymmetric voltammogram featuring a pre-peak at approximately 30 mV observed before the main oxidation wave upon reversal. This shape is typical of an adsorption/desorption process, although its observation only upon reversal implies that it is the consequence of processes triggered by the accumulation of the reduced form. However, its appearance is not unexpected as high ionic strength promotes polymer adsorption due to electrostatic screening between the polymer and electrode. Macrodisk volammetry with other concentrations of RAP and ionic strengths are shown in the Supporting Information Figures S1-S21. Rotating disk electrode voltammetry (RDE) experiments were performed to study the effects of ionic strength on the kinetics of electron transfer to RAPs (Figure 5B, S30S46) on 5 mM VioRAP. Consistent with the charge transfer limitations observed in Figure 2 for UME voltammetry at low supporting electrolyte, no rotation rate dependence was observed in these conditions for either PAF or VioRAP (Figures S30 and S33). This implies that a kinetic bottleneck was reached even at the lowest rotation rates explored. However, for the cases in which 100 mM (Figure 5B) or 500 mM supporting electrolyte was used, the RDE responses did have rotation rate dependencies. These experiments support the results obtained through UME (Figure 2), where a larger current function was observed near 100 mM (Figure S40). The extrapolated values of kf and k0 (Table S3) from a Koutecky-Levich36 (Figures S34-S36) under these conditions did not show any strong dependence on the electrolyte concentration and the values agreed well with those for VioRAP and PAF that we have previously reported.48 Although more subtle at 100 mM electrolyte, at 500 mM supporting electrolyte there is clear evidence for the adsorption of the VioRAP onto the electrode surface as evidenced by a voltammetric peak before


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attaining steady state (Figure S43). Lastly, we designed an experiment to show that viscosity effects are not the primary source of observed changes in RAP reactivity when the ionic strength is increased. RDE studies were performed in dimethylformamide (DMF) and propylene carbonate (PC). The viscosity of DMF is 0.92 mPa*s and the viscosity of PC is 2.5 mPa*s, which is 2.8 and 7.5 times the viscosity of acetonitrile, respectively.40 Consistent with behavior in acetonitrile, the amount of adsorption was linked to the ionic strength and optimum reactivity was still observed at 100 mM supporting electrolyte (Figure S40 and S37-S44). These experiments underscore the role of electrostatics, regardless of the solvent chosen. A feature observed in all voltammetric results so far, is that there is a dependence on wave position as a function of electrolyte concentration, a phenomena previously studied by Tagliazucchi et al.57 for osmium pyridine-bipyridine based polymers. Therefore, we turned to evaluating the mediating role of the adsorbed RAP layer on the reactivity of the dissolved RAPs. To study the RAP film’s electrochemical properties we performed two different experiments. First, we electrochemically generated a series of RAP films in solutions with different ionic strengths. Afterwards, we rinsed these filmed electrodes and placed them in 100 mM blank supporting electrolyte solution for chronoamperometric and voltammetric testing. Second, we studied a RAP film that was generated in a solution containing 100 mM supporting electrolyte and subsequently tested in a series of solutions of varying ionic strength. Figure 5C shows the resulting electrochemical tests of the films grown at different ionic strengths. In all experiments, we observed a surface confined redox process, with a peak current magnitude that was proportionally related to the ionic strength used to generate the film. As the supporting electrolyte concentration increased, a larger



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amount of polymer was electrochemically accessed, either by an increase in the film accessibility or an increase in the amount of polymer deposited. This was confirmed by spectroscopic ellipsometry, via a process described and discussed further in the Supporting Information (Table 2 and S2, Figures S49-S57) where the thicknesses of the adsorbed RAP films were obtained.

Figure 6. Cyclic Voltammograms at 10 mV/s for a modified VioRAP film, a 1 mM Viologen monomer solution and a modified VioRAP film in a 1 mM Viologen monomer solution at (A) 10 mM, (B) 100 mM, (C) 500 mM and (D) 1000 mM TBAPF6 electrolyte. All done at varying TBAPF6 concentrations in acetonitrile and at 20mV/s.

Interestingly, the film’s electrochemical properties were significantly altered when a film that was formed in 100 mM supporting electrolyte was then measured in different ionic strength solutions, Figure 5D. The most immediate difference was a shift in the formal potential,57 resulting in more negative values with increasing ionic strength. These displacements are not the result of artifacts such as reference electrode potential drift (Figure S27), and thus we attribute the observed potential shift to altered thermodynamic 24 ACS Paragon Plus Environment

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properties of the adsorbed RAP. In Figure S25 we explored the use of electrochemical simulation software for reproducing the observed potential shifts. While our results suggest that these shifts are plausibly obtained by varying interaction the parameters between the electrode and the reduced and oxidized species,52, 57 it is also possible that interactions interand intra- chain interactions between the redox pendants drive the observed thermodynamic changes.25 Interestingly, the same experiment with PAF films showed no potential shifts or change in voltammogram shape (Figure S19). The importance of systematically characterizing the potential shifts in RAP layers is that these films mediate all charge transfer to solution species. Matching the redox potential of the adsorbed RAP film and solution species is important for achieving efficient charge mediation. As observed in Figures 6 and S28, when VioRAP modified platinum electrodes were used to electrochemically reduce Vio in solution, we observed profound changes in the voltammetric features. The negative potential shift of the VioRAP films in high ionic strength causes the reduction of Vio to also shift negatively, and deviate significantly from the Nernstian wave otherwise observed at a bare electrode (Figure 6D). When the mediation process of the VioRAP film and Vio in solution were studied as a function of solution ionic strength, we determined through simulations a 3-fold change in redox kinetics between the 10 mM and 1000 mM electrolyte solution (Figure S29). As presented in Figure 5C-5D, a seemingly small negative potential shift of 40 mV for the onset of reduction of adsorbed VioRAP can have pronounced kinetic effects for the reduction of solution species. Referencing back to Figures 2 and 5, it is now clear that the distortions and potential shifts observed during steady-state voltammetry are partially



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ascribed to the mediation effects through the adsorbed layer being modified by the ionic strength. Table 2: Evaluated Parameters for VioRAP Films Electrolyte Concentration (mM)

Thickness (nm)

Charge (mC)

10

80.6 ± 13.4

0.592

100

164.8 ± 11.1

0.589

500

311.9 ± 34.7

0.755

1000

342.4 ± 48

0.749

2-4. Impact of the RAP Charge on the Electrochemical Response The observations made regarding differences in reactivity between PAF and VioRAP led us to further explore the impact of backbone charge. PNS is a neutral RAP in its oxidized state and undergoes reduction to form a radical anion at potentials negative of the potential of zero charge for a platinum electrode in acetonitrile. PNS is highly soluble in dimethylformamide,29 so we proceeded to determine its rH through DLS as a function of electrolyte concentration. Figure 7A shows that for this polymer there is no observable modulation of the coil size, ca. 7.4 nm. Further analysis of PNS solutions at the limit of low RAP concentration show that its voltammetric response as a function of ionic strength at a macrodisk electrode (Figure 7B) and a UME (Figure 7C) are considerably less affected than those for VioRAP and PAF. Macrodisk CVs showed a near-Nernstian response, while UME CVs displayed the characteristic sigmoid, indicative of a facile electrode response. No shift in the wave potentials were observed when the electrolyte concentration was screened. We ascribe the different behavior with respect to other RAPs to the null changes


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in coil size and the decreased electrostatic interaction between the electrode and the neutral oxidized form of PNS.

Figure 7. Sizing and electrochemical analysis of PNS. (A) Intensity distribution of DLS scattering events of solutions of PNS at 5 mM concentration in acetonitrile at different ionic strengths as function of coil size in solution. (B) Macroelectrode and (C) UME cyclic voltammetry for PNS as function of supporting electrolyte concentration in DMF.

2-5. Summary of RAP Electrochemistry In summary, polyelectrolyte dynamics greatly impact the reactivity of RAPs that bear ionic pendants. From the presented electrochemical analysis and materials characterization it is clear that the concentration of both the polyelectrolyte itself and the



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background supporting electrolyte are significant factors to consider in order to tune their reactivity. Figure 8 presents a visual reference of the broad experimental space probed here, as well as its associated electrochemical responses for solubilized and filmed RAPs. To the best of our knowledge, this is the first report of the generalized behavior of redox active polyelectrolytes and their electrochemical performance as a function of ionic strength.

Figure 8. Depiction of the generalized electrochemical responses, polyelectrolyte coil conformations, and deposited film layers when either the supporting electrolyte or polyelectrolyte concentration is changed. Careful selection of polyelectrolyte and supporting electrolyte conditions are needed in order to observe different regimes of RAP reactivity.

3- Conclusions For the first time, highly soluble RAPs allowed to probe a wide range of electrolyte conditions for establishing firm links between solution-phase RAP structure and their electrochemical response. This comprehensive study into the role of polyelectrolyte dynamics in charge transfer processes on soluble RAPs shows that the ionic strength of the 28 ACS Paragon Plus Environment

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solution is a critical experimental parameter. Dynamic light scattering and viscometric characterization of RAP electrolytes shed light on the complex electrochemical responses observed in both transient and steady-state experiments. When dilute, permanently charged RAPs exhibit a modulation in their hydrodynamic radius as a function of ionic strength. In turn, these changes modify the rate of charge accessibility to the species in solution, causing differences of up to one order of magnitude in the steady state current observed at electrodes. An early model based on the impact of coil size on polymer diffusion and charge accessibility effectively captured the main trends observed electrochemically under masstransfer limited conditions. Further development of this model is ongoing. The impact of electrostatic effects is more pronounced when the RAP exhibits a permanent charge that is opposite to that of the electrode. The reactivity of VioRAP, a doubly-charged positive species reduced at a negatively charged electrode, exhibits more dramatic effects than that of PAF, a singly charged positive species oxidized at a positively charged electrode, and PNS, a neutral polymer. UME CV experiments showed that VioRAP solutions beyond the entanglement concentration displayed a bulk-like electrolysis behavior that was distinct from the sigmoid CVs resulting from reduction of isolated polymer coils. Furthermore, transient and steady-state analysis showed unexpectedly that optimal electrochemical reactivity is attained at an intermediate electrolyte concentration (100 mM). Beyond resistive drop effects, having too little electrolyte causes a significant decrease in charge accessibility, while having too much supporting electrolyte causes deleterious precipitation of the RAP on the electrode and consequently charge mediation bottlenecks. This behavior is unique to RAPs, and such limitations were not observed for the monomer species.



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Adsorbed RAP film reactivity was characterized by cyclic voltammetry and simulation analysis, surprisingly showing that the standard reduction potential of the RAP film is also modified by the ionic strength. A monotonic potential shift of over -40 mV was observed when going from 10 mM to 1 M supporting electrolyte, highlighting the role of electrostatics not only in determining film thickness, but also in its mediating power. Indeed, thermodynamic shifts led to changes in the kinetics of electron transfer to solution species, strongly suggesting that differences in the shape and onset of solution RAP voltammetry are due to changes in the electron transfer mediation of the RAP film. Furthermore, spectroscopic ellipsometry measurements lead us to conclude that as the salt concentration in the cell is increased not only does this result in thicker deposited RAP films, but these films are also less electrochemically addressable. Altogether, these observations point to the crucial role that electrostatics have on the electrochemical responses of RAPs undergoing charge transfer, in both solution-phase and adsorbed film formats. We speculate that these effects have a large impact in the performance of devices consisting of polymer modified electrodes.53 However, up to now there has been no systematic study into these effects. Furthermore, this work shows that soluble RAPs behave much differently than their monomer constituents and special considerations need to be taken into account that balance solution conductivity with electrostatic effects in order to unleash their full performance. 4- Experimental 4-1. Chemicals All reagents were used as received without any further purification. Acetonitrile (99.8% anhydrous), dimethylformamide (99.8% anhydrous), propylene carbonate (99.7% 30 ACS Paragon Plus Environment

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anhydrous), tetrabutylammonium hexafluorophosphate (99% electrochemical grade), lithium tetrafluoroborate (anhydrous powder 99.99% trace metal analysis), ethyl viologen diperchlorate (98%), ferrocene (98%) were all purchased from Sigma-Aldrich (St. Louis, MO). Unsubstituted polymer backbone, Poly(vinylbenzyl chloride) (82 kDa), was purchased from Polymer source. 4-2. Electrochemical Measurements All electrochemical measurements were performed with a CH Instruments (Austin, TX) 760E bipotentiostat inside of a glovebox from VTI Technologies (Gloucester, MA). The glovebox maintained a consistent inert atmosphere to have less than 0.1 ppm water and oxygen content. All rotating disk electrode voltammetry experiments were done with a Pine rotator. All voltammetry was measured versus a 0.1 M Ag/Ag+ reference electrode (CH instruments) and utilized a Pt wire counter electrode. Macrodisk working electrodes for voltammetry were a 1.5 mm radius Pt disk electrode from CH Instruments. Additional gold coated Si substrates were fabricated via electron beam evaporation for measuring electrochemistry of polymer films and to produce samples to be analyzed by spectroscopic ellipsometry. Electron beam evaporator (Temescal Systems) was used to deposit 46 nm thick gold layer on Si wafer (Monsanto) with 5 nm Ti as adhesion layer. Thickness of both the gold and titanium layers was verified via spectroscopic ellipsometry. Pt ultramicroelectrodes (UME) with a radius of 12.5 µm were fabricated via a previously reported procedure.48 4-3. RAP Characterization For a detailed description of the synthetic details of the ferrocene (271 kDa), viologen (318 kDa), and nitrostyrene (50 kDa) based RAPs, see the Supporting Information section 1.0. 31 ACS Paragon Plus Environment


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Hydrodynamic radii of the RAPs in acetonitrile at a series of supporting electrolyte concentrations was evaluated spectroscopically via dynamic light scattering (DLS) using a Malvern Zetasizer Nano. Calculated hydrodynamic radii are presented as Z-averages arising from fits of the cumulants of the autocorrelation function. All samples were measured in quartz capped cuvettes (Starna cells) to prevent evaporation or dust contamination. Samples were passed through a 0.2 µm syringe filter (Cole Parmer) to remove dust contaminants and aggregates.

Further

characterization of solution phase RAP coil sizes in acetonitrile utilized intrinsic viscosity measurements. Viscosity of RAP solutions at different shear rates were measured from pressuredriven flow through a microfluidic chip (small sample viscometer, m-VROC, Rheosense, Inc.). Here the internal flow device is preferred over standard rotational rheometers because it requires smaller sample volumes (typically down to 300 µL) and the internal flow configuration eliminates free surface effects such as surface tension forces54,55 and time-dependent viscosity due to exposure to uncontrolled relative humidity. Pressure sensors measure the pressure drop along the flow path within the device, and a syringe pump sets the flow rate. From the pressure drop ∆ P and flow rate Q, the shear stress (τ ) and shear rate ( γ& ) are calculated as ∆P  wh    L  2 w + 2h 

(12)

6Q wh2

(13)

d ln ( γ&app )  2+  3  d ln (τ )   

(14)

τ =−

and

γ&app =

γ& =

γ&app 


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where w is the width of the channel (2 mm), h is the height of the channel (51.1 µm), and L is the length over which ∆ P is measured (1.5 cm). The viscosity is then calculated from the definition

τ η= . γ&

(15)

RAP film thickness on electrode surfaces was characterized ex-situ via spectroscopic ellipsometry using a Woolam VASE ellipsometer and a commercial software package (J.A. Woolam Co.). UV-vis measurements of reduced VioRAPs were taken in quartz cuvettes using a SEC2000 spectrometer from ALS Co. 4-3. RAP Electrochemical Deposition In order to study the adsorbed RAP film properties we utilized a means of reproducibly creating RAP films between experiments. Here, RAP films were electrochemically deposited at different supporting electrolyte concentrations by cycling 10 times through the second reduction of the VioRAP, or the oxidation in the case of PAF, at 50 mV/s. Using the same deposition method between films allowed us to compare the different experimental conditions for either ionic strength or RAP concentration. Figures S14-S15 show the different deposition CVs as a function of supporting electrolyte concentration. A surface process is verified during electrochemical deposition by the almost zero peak splitting of the reduction and oxidation processes. Interestingly, fundamental differences in the CVs were obtained at different conditions. First, the potential of the first reduction for VioRAP shifts positively when low amounts of supporting electrolyte were used. Additionally, the CVs of high (50 mM) versus low (0.5 mM) concentration of RAP show different behaviors in the accessible charge, possibly related to differences in the amount of polymer deposited per cycle. At 0.5 mM RAP concentration we can see that the



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peak current magnitude for both the first and second reduction of VioRAP at the final cycle becomes larger with increasing ionic strength, suggesting the formation of thicker layers. However, with a larger RAP concentration (50 mM) a maximum level of current is seen after only 2 cycles and a larger resistance to current flow is observed as the film thickness increases, thus suggesting a quick saturation of the surface with RAP material.

5- Acknowledgements The authors would like to thank the Joint Center for Energy Storage Research (JCESR), an Energy Innovation Hub funded by the Department of Energy, Office of Science, Basic Energy Sciences for funding. M.B. acknowledges additional support from the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-114425. Materials characterization was carried out in part in the Frederick Seitz Materials Research Laboratory Central Research Facilities at the University of Illinois at Urbana-Champaign. K.H.B. gratefully acknowledges the Beckman Institute Postdoctoral Fellowship at the University of Illinois at Urbana-Champaign, with funding provided by the Arnold and Mabel Beckman Foundation. E.C.M. acknowledges support by the Ford Foundation Fellowship Program. J.R.L acknowledges additional support from a Sloan Research Fellowship. We thank Dr. Yu Cao and Prof. Jeffrey S. Moore for helping in synthesis of PNS samples. We thank Professor Christian Amatore for helpful discussions. 6- Supporting Information Synthetic details, additional electrochemical and optical characterization experiments, ellipsometry, and rheology experiments are supplied in the Supporting Information text document.


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