Anodic Electrodeposition of a Cationic Polyelectrolyte in the Presence

Jul 15, 2016 - The electrochemical quartz crystal microbalance (QCM) was used to investigate the deposition of poly(allylamine hydrochloride) (PAH) wi...
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Anodic Electrodeposition of a Cationic Polyelectrolyte in the Presence of Multivalent Anions Elizabeth J. Martin, Kazi Sadman, and Kenneth R. Shull* Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States

ABSTRACT: The electrochemical quartz crystal microbalance (QCM) was used to investigate the deposition of poly(allylamine hydrochloride) (PAH) with molybdate anions under anodic conditions. The PAH−molybdate complex was used as a model system to understand possible deposition criteria which may be relevant to the formation of proteinaceous films on CoCrMo hip implants. Data indicate that PAH deposition will occur above ∼0.60 V vs SCE if molybdate anions are present in the electrolyte above a critical concentration, and if the polymer concentration remains below a critical value. Numerical modeling and dynamic light scattering (DLS) studies were performed to understand the conditions that enable deposition to occur at these potentials. The results indicate that PAH−molybdate complexes form most efficiently when the polyvalent positive charge and polyvalent negative charge in the system are in an optimum range with respect to each other.

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INTRODUCTION Polymer electrodeposition has been studied extensively as a method to produce functional coatings for applications in medicine, electronics, and biosensing.1−6 Two common routes of polymer electrodeposition include the electropolymerization of conducting polymers, such as polypyrrole, polyaniline, and polythiophene, and deposition based on the generation of a pH gradient at the electrode surface.7 In the latter case, the deposited polymer is typically a polyelectrolyte that is neutralized at the electrode surface, causing it to precipitate out of solution and onto the electrode. For example, electrodeposited paints that contain carboxylate groups ( COO−) protonate at anodic surfaces and precipitate as carboxylic acid (COOH).7 This technique is advantageous because it enables spatiotemporal control of the deposition process and facilitates the homogeneous coating of complex shapes. Poly(allylamine hydrochloride) (PAH) is a weak, cationic polyelectrolyte that has been studied extensively in the context of layer-by-layer assembly5,8 and polyelectrolyte complexation.9,10 Cathodic electrodeposition of PAH and other similar amine side chain containing polyelectrolytes such as polylysine and chitosan, have been explored for producing composite films2,3 and biocompatible coatings.11 The local basic environment at the cathode deprotonates the amine groups, reducing their solubility and causing them to precipitate at the electrode, providing a facile approach for achieving conformal coatings. The deposited coating is stable in basic to neutral environ© XXXX American Chemical Society

ments, while acidic conditions lead to reprotonation of the amines followed by dissolution. Anodic electrodeposition of cationic polyelectrolytes is rare due to the challenge of overcoming strong electrostatic repulsions, but has been observed in specific cases. For example, Ngankam et al. demonstrated that poly(L-lysine) could be continuously adsorbed onto anodic ITO surfaces due to modulation of the surface charge density12 and Gray et al. showed that chitosan could be anodically electrodeposited by the formation of covalent cross-links in the system.7 Under physiological conditions proteins may deposit onto implanted surfaces and form biofilms through mechanisms analogous to those discussed above. In the case of metallic implants, corrosion products released from the surface under anodic conditions may play a key role in the formation and stability of the films. In our previous work, we showed that protein films can deposit at CoCrMo or Mo surfaces under anodic conditions if molybdate anions are present in the proteinaceous electrolyte.13,14 These protein films are similar to carbonaceous layers that form naturally at the articulating surfaces of CoCrMo metal-on-metal hip implants.15 The in vivo performance of CoCrMo implants are affected through the formation of protein-metal complexes under the physiologically corrosive environment, with work by Liao et al. suggesting that Received: April 25, 2016 Revised: June 23, 2016

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Figure 1. Schematic of the PAH−molybdate film deposition process.

the biofilm is actually beneficial due to its anticorrosive and lubricating properties.16 An improved understanding of the mechanisms by which these films form is therefore desirable. We previously demonstrated that molybdate anions play a critical role in the formation of protein films at the surface of CoCrMo alloys.13 In the present work, we investigate the mechanistic criterion for film formation at a corroding electrode by studying a simpler model where the CoCrMo alloy is replaced by chromium and where the protein is replaced by poly(allylamine hydrochloride) (PAH). The absence of secondary and tertiary structure and the high concentration of amine groups a makes PAH an attractive candidate to study deposition criteria. In contrast to the cathodic deposition of PAH investigated by other authors,2,3,6 the anodic conditions in these experiments will cause the pH at the electrode to decrease, further protonating the PAH. The increased chain repulsion due to the pH-induced increase in the degree of ionization will preclude deposition on a positively charged surface, but we speculated that a polymer film could form through ion complexation as illustrated in Figure 1, provided that molybdate anions are also present in solution. While we are interested specifically in the role of molybdates in the formation of complexes with a cationic polymer, the process is general has been studied in other contexts as well.17 In the present study, electrochemical quartz crystal microbalance (QCM) experiments were conducted to determine the experimental conditions that enable film formation, and dynamic light scattering was used to investigate the conditions under which complexes were formed in solution. Numerical modeling of the chemical species transport at the electrode surface was conducted to extract local properties at the electrode−electrolye interface at the onset of deposition. As we describe in the following sections, film formation was quantified through the mass change occurring at the working electrode of the QCM during potentiodynamic scans, and the local concentrations of polyvalent species at the onset of film formation were used to calculate the ratio f−, which appears to be an important metric for complexation in the Cr−PAH− molybdate system: f− ≡

[−charge] [−charge] + [+charge]

We refer to our previous work for a complete treatment of the QCM in characterizing soft matter.14 When a material is applied at the surface of a quartz crystal, the resonant frequency of the crystal and its energy dissipation values shift relative to the bare crystal, measured as Δf n and ΔΓn respectively. ΔΓn is small for sufficiently rigid films, while it is ≫0 for films possessing viscoelastic character, as is the case in the studies here. To a first approximation, the frequency shift is proportional to the areal mass of the film (ΔMQCM ) through A the well-known Sauerbrey relation for thin rigid films:18−20 Δfsn =

−2nf12 Zq

ΔM AQCM

(2)

where f1 is the resonance frequency of quartz (5 MHz), n is the order of the measured harmonic (1 or 3 in our experimients), and Zq is the acoustic impedance of quartz (8.84 × 106 kg· m−2s−1). In our experiments, we reference Δf n to the resonance frequency of the bare crystal submerged in solution and approximate the mass of the deposited film with eq 2. In an electrochemical QCM measurement, the QCM electrode in contact with the aqueous medium serves as the working electrode in a three-electrode corrosion cell. The current or potential can be controlled and measured by a potentiostat, while the QCM simultaneously measures changes in mass at the electrode surface due to electrochemical processes. The technique provides a “mass per charge” (m/q) ratio of the corroding electrode, obtained by dividing the Sauerbrey mass by the total corrosion charge, Q, obtained in turn by integration of the corrosion current. If we assume that the electrode continues to corrode while the PAH film deposits at the surface, then we can estimate the total areal mass of the film (ΔMfilm A ) with the relation: ⎛Q m⎞ ΔMAfilm = ΔM AQCM + ⎜ × ⎟ q⎠ ⎝ AF

(3)

ΔMQCM A

where is the mass measured directly with the QCM according to eq 2, A is the electrode area, and F is Faraday’s constant (96 500 C/mol).14

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FINITE ELEMENT MODELING Finite element modeling (FEM) was used to quantify the pH and ion concentration gradients established during the electrochemical QCM tests in order to understand the electrode−electrolyte interface conditions at the onset of deposition. Chemical components modeled included corrosion products as well as salts present in the electrolyte. To calculate concentration gradients at an electrode interface due to electrochemical reactions, FEM was used to solve a system of equations relating component fluxes to the corrosion current.

(1)

Because the QCM and numerical modeling techniques are essential to our investigations, we provide a brief overview of these approaches in the following sections.

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ELECTROCHEMICAL QUARTZ CRYSTAL MICROBALANCE The QCM enables in situ quantification of mass changes at an electrode surface accompanying electrochemical processes.13,18 B

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Langmuir The flux of a component i (Ni) at the corroding electrode is related to its contribution to the current, ji, by Faraday’s Law, written in the notation as follows:21

Ni =

of 0.25 mV/s. Tests were conducted in nine different poly(allylamine HCl) (PAH) solutions (Polysciences, Inc., MW: 60 000) with varying concentrations of sodium molybdate (Sigma-Aldrich, St. Louis, MO). Each solution also contained 85 mM NaCl as the supporting electrolyte. In our sample naming system, the number following “P” indicates the PAH concentration in g/L. The number following the “M” indicates the Na2MoO4 concentration in mM. For example, the solution termed P05M1 contained 0.5 g/L PAH and 1 mM Na2MoO4. All solutions were adjusted to pH 7.6 with NaOH and HCl. Prior to each electrochemical experiment, the open circuit potential (OCP) of the working electrode was measured for 3 min. Next, the specimen was held at a cathodic potential of −0.9 V for 10 min to clean the surface and remove any oxide that may have formed in air. The OCP was then measured again as the system was allowed to stabilize for 1 h. Subsequently, potentiodynamic tests were conducted while the QCM measured shifts in frequency (Δf n) at the first, and third harmonics (n = 1, 5 MHz and n = 3, 15 MHz). All tests were conducted at room temperature. The change in mass at the Cr surface, ΔMA, was determined by the Sauerbrey relation (eq 2), with Δf n referenced to the frequency at the outset of the potentiometric scan. Here, we only report ΔMA measured at the third harmonic for clarity, but the Sauerbrey relation showed close agreement at both harmonics. Titration of Poly(allylamine) HCl. Titrations were conduced in 100 mL solutions. After bringing the pH of the solutions to alkaline conditions with NaOH, HCl was added in increments while a pH meter simultaneously measured the solution pH. ’Solvent’ solutions were prepared with 85 mM NaCl, while the ’PAH’ solutions were prepared with either 0.5, 5.0, or 30 g/L PAH. No solutions contained Na2MoO4. Dynamic Light Scattering. Dynamic light scattering (DLS) was conducted on 0.5 g/L PAH solutions with 85 mM NaCl at varying pH levels and Na2MoO4 concentrations. Measurements were taken at 25 °C with a Malvern Zetasizer Nano S (Worcestershire, U.K.) system, using a 173° backscatter angle. The light source was a 633 nm He−Ne laser. The refractive index (1.330) and viscosity (0.8872 cP) of water at 25 °C were used as the dispersant properties; the refractive index and absorption of the polymer were estimated at 1.45 and 0.001, respectively. The Z-average radius, as determined by the Zetasizer software, is reported here to compare polymer sizes under each test condition. We report the average ± one standard deviation of three measurements at each condition. Numerical Modeling. Comsol Multiphysics 5.2 software with a Corrosion Module extension was used to model pH and ion concentration gradients at the electrode−electrolyte interface during electrochemical QCM tests on Cr electrodes. A reduced 1-D, time-dependent, tertiary current distribution study format was employed. Models were modified from the electrochemical models described by Walton et al., 22 Abdulsalam et al.,23 and Brackman et al.24 The diffusion coefficient inputs of the species are listed in Table 1.25 The initial concentration of each species was set as enumerated in Table 2. Current and potential at the electrode surface were defined as functions of time using the measured values from each electrochemical QCM test. The total length of the 1-D interval over which the simulations was performed was specified as 6 DH tf , where DH is the diffusion coefficient of a proton and tf was the final simulation time, chosen to exceed the relevant time scales for an experiment. The 1-D interval

νiji niF

(4)

where νi is the stoichiometric coefficient of the component, ni is the number of electrons involved in the reaction, and F is Faraday’s constant. Component fluxes are driven by three forces, diffusion, electromigration, and convection, according to the Nernst−Planck equation:21 Ni = −Di ▽ci − zium , iFci ▽ϕl + ci u

(5)

where ci is the concentration of component i, Di is its diffusion coefficient, zi is its charge, um,i is its mobility, ϕl is the electrolyte potential, and u is the velocity vector driving convection. The three terms on the right-hand side of eq 5 correspond, from left to right, to diffusion, electromigration, and convection. Convection is neglected in our case (u = 0). Ionic mobility is related to the diffusion coefficient through the Nernst−Einstein relation:21 um , i =

Di RT

(6)

where R is the molar gas constant and T is temperature. The degree of ionization of a weak polyelectrolyte is a function of the local pH. Therefore, zi in eq 5 must be modified to take into account this behavior. As such, the quantity zi for the poly(allylamine) units was redefined in the following way: zi = Pnα

(7)

where Pn is the degree of polymerization of PAH and α is its degree of ionization. Therefore, the product Pnα gives the average number of charged monomer units on a given polymer molecule as a function of pH. The experimental determination of α throughout the pH range from titration curves is discussed in the following sections. The total transport rate of component i through the electrolyte, Ri,tot, is given by the mass balance equation:21 ∂ci + ▽Ni = R i ,tot ∂t

(8)

where eq 8 can be solved numerically for the concentrations of the i components as a function of time. The experimental parameters used in the simulation to determine concentration gradients during electrodeposition are described in the Materials and Methods section below.

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MATERIALS AND METHODS Electrochemical Quartz Crystal Microbalance. An electrochemical quartz crystal microbalance (QCM) was used as previously described.13 Briefly, a QCM holder (Inficon, East Syracuse, NY) was connected to both a N2PK vector network analyzer (Thornhill, ON, Canada) and a potentiostat (BioLogic SP-150, France). Electrochemical tests were conducted in a custom three-electrode corrosion cell with a saturated calomel reference electrode (SCE) and graphite counter electrode. All potentials reported in this paper are referenced to the SCE. ATcut, 5 MHz quartz crystals with Cr electrodes (Inficon, East Syracuse, NY) were used as manufactured for the working electrode, with an exposed Cr area of 1.27 cm2. Potentiodynamic scans were conducted from −0.8 to 1.0 V at a scan rate C

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polymer concentration. The degree of ionization is an important parameter for quantifying complex formation, especially in the context of eq 1, where the concentration of protonated amine groups (referred to here as PAH+) is required to calculate f−. Itano et al. and Petrov et al. demonstrated that the pKa of poly(allylamine) can differ based on the ionic strength of the solution and the local environment of the chain.26,27 Therefore, acid−base titrations were conducted to determine Keq of dissociation for PAH experimentally. Figure 2 displays the titration curves for PAH at different concentrations that were used to calculate α as a function of pH using the following relationship:

Table 1. Components Defined as Dependent Variables in FEM and Their Diffusion Coefficientsa diffusion coefficient (m2/ s)25

component +

H OH− Na+ Cl− CrO2− 4 MoO2− 4 HMoO−4 H2MoO4 PAH (5 g/L) PAH (30 g/L)

9.3 5.3 1.3 2.0 1.1 2.0 1.0 1.0 7.8 2.8

× × × × × × × × × ×

10−9 10−9 10−9 10−9 10−9 10−9 10−9 10−9 10−12 10−12

α=

a Diffusion coefficients for PAH were determined using dynamic light scattering.

10−pHs − 10−pHp [PAH]tot

(9)

where pHs and pHp are the pH values in the solutions without and with PAH, respectively. [PAH]tot is the total molar concentration of amine groups in the PAH solution, determined from the concentration of polymer dissolved in the solvent. Next, the equilibrium constant of the dissociation reaction (eq 17) was determined as a function of pH by the following:

consisted of the electrode boundary at one end and the electrolyte boundary on the other. Four boundary conditions were employed in the model: 1. A no flux condition was set at the electrode boundary. 2. The potential at the electrode boundary was defined as a function of time from the experimental data. 3. The electrolyte potential at the electrolyte boundary was set to the open circuit potential of the solution. − 2− 4. The concentrations of H+, CrO2− 4 , Cl , MoO4 , and + protonated poly(allylamine) (PAH ) were set as their bulk concentrations at the electrolyte boundary.

Keq =

10−pHp(1 − α) α

(10)

Figure 3 shows the calculated α and Keq at each polymer concentration as a function of pH. According to Figure 3a, the pKa value of PAH in the dilute regime of 0.5 g/L was observed to be approximately 9.2 and it become fully protonated by a pH of 7, in good agreement with previously reported numbers by Petrov et al.27 For higher concentrations, we observed the pKa shift to about 8.8, and that α varied more smoothly− an effect we attribute to the higher ionic strength of the solution. Note that the data in Figure 3a now allows calculating [PAH+]at any pH when the initial molar concentration of PAH is known. The pH and concentration dependent values of Keq for PAH were used in the numerical modeling studies. Electrochemical QCM. Potentiodynamic scans were conducted on Cr QCM electrodes in each of the polymer solutions described in Table 2 to determine the conditions for which PAH will deposit at the Cr surface. Cr has a molar mass of 52 g/mol, therefore oxidation of Cr to Cr6+ to form CrO2− 4 will give a m/q = 8.7 g/equiv. Competing side reactions, such as the oxidation of water, will lead to lower observed value of m/q. For simplicity, we pick the solution P05M2 for the proceeding arguments, but an analogous discussion is valid for all the solutions listed in Table 2 where film deposition was observed.

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RESULTS AND DISCUSSION We previously demonstrated that protein films may form at corroding electrodes if molybdates were also present in solution.14 The focus of the present work is to determine the conditions that facilitate polymer film formation at corroding surfaces. Our hypothesis is that deposition will occur if the local concentration of multivalent anions at an electrode are in an appropriate stoichiometric range with respect to the cationic charge on the polyelectrolyte, as quantified by f− (eq 1). We explore this hypothesis by studying the simple system of Cr− PAH−molybdate where corrosion of a Cr electrode under anodic potentials shifts the value of f− in the vicinity of the electrode. In the subsequent sections, we present data from electrochemical QCM tests, numerical modeling and DLS that shows the effect of f− on determining film formation. Titration of Poly(allylamine) HCl. PAH is a weak polyelectrolyte, and therefore its degree of ionization (α) is contingent on the solution pH, ionic strength, and overall

Table 2. Poly(allylamine HCl) Solutions Used in Electrochemical QCM Testsa solution number

[PAH] (g/L)

[PAH] (mM)

[Na2MoO4] (mM)

[Na2MoO4]/[PAH]

2 ΔMfilm A (mg/m )

f−s

P05M0 P05M1 P05M2 P05M3 P05M4 P05M5 P05M8 P5M8 P30M8

0.5 0.5 0.5 0.5 0.5 0.5 0.5 5.0 30

5.34 5.34 5.34 5.34 5.34 5.34 5.34 53.4 320

0 1 2 3 4 5 8 8 8

0 0.187 0.375 0.562 0.749 0.94 1.50 0.15 0.025

0 5 270 415 350 200 100 0 0

0 0.30→0.26 0.46→0.41 0.57→0.49 0.63→0.56 0.68→0.61 0.77→0.74 0.30→0.24 0.05

− Values of ΔMfilm A correspond to the maximum film mass measured during the test, as determined by eq 3. The quantity fs corresponds to the value − of f at the electrode-electrolyte interface during the tests, with the provided ranges determined by the numerical modeling methods. a

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Figure 2. Acid titrations of PAH and solvent solutions with (a) 0.5 g/L PAH, (b) 5.0 g/L PAH, and (c) 30 g/L PAH. 85 mM NaCl was used as the electrolyte in each solution, with the blank “solvent” titrations containing no PAH.

Figure 3. (a) Fraction of protonated amine groups in PAH solution, determined from data in Figure 2. (b) Keq determined from data in (a) as a function of pH in the polymer solution. Points marked with a “+” in (a) represent the value of α at a pH of 7.6, which is the initial solution pH in all experiments performed.

Figure 4. (a) Frequency and (b) dissipation shifts at 5 and 15 MHz from the QCM during a potentiodynamic scan from −0.8 to 1.0 V (scan rate 0.25 mV/s) in the P05M2 solution, plotted along with the current density. Note that significant change in the Δf and ΔΓ does not occur until the transpassive region marked by a large increase in the corrosion current density corresponding to the breakdown of the protective oxide scale.

test using eq 2 against the charge, q, where the slope corresponds to a m/q = 5.8 g/equiv. These results are similar to our previous electrochemical QCM studies on Cr electrodes in protein solutions, during which the electrode corroded above 0.56 V with m/q ≈ 6 g/equiv.14 We use eq 3 with this value of m/q to estimate the total mass of the deposited polymer film. For the P05M2 solution this film mass stabilizes at ∼300 mg/ m2, as shown in Figure 5b.

Typical results for a polymer deposition experiment are shown in Figure 4, where Δf and ΔΓ are plotted as a function of time and electrode potential for solution P05M2. Some polymer deposition is observed at the beginning of the potentiodynamic scan, but a much more significant and rapid deposition of polymer is observed for potentials above ∼0.63 V. For potentials above ∼0.75 V, an overall mass decrease is observed, as the rate of electrode corrosion exceeded the rate of polymer deposition. Figure 5a plots the Sauerbrey mass from the same E

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Figure 5. (a) Changes in mass as a function of charge during the potentiodynamic scan from −0.8 to 1.0 V (scan rate 0.25 mV/s) in the P05M2 solution at 5 and 15 MHz. The slope of this curve represents the mass/charge ratio of the corroding electrode. (b) The total film mass, as determined by eq 3, during the same test, plotted along with the current density.

The maximum total film mass obtained during the potentiodynamic scans in each solution is listed in Table 2. It must be noted at this point that the ΔΓ values observed in Figure 4b indicate that the deposited film is viscoelastic in nature. Viscoelastic films require a correction to the Sauerbrey limit of eq 2, however, we previously demonstrated that this correction is less than 10% for the conditions of these experiments.14 Furthermore, the large change in Δf and ΔΓ are observed in the transpassive region (E > 0.6 V), where the current increases dramatically due to breakdown of the protective oxide layer at highly oxidative potentials. This suggests that the corrosion process itself is integral to the onset of film deposition. We address this corrosion process in detail in the following Numerical Modeling section. Data from the QCM tests enumerated in Table 2 indicate that deposition does not occur if the PAH concentration exceeds a critical level or if the molybdate concentration is too low. Deposition proceeds as the PAH becomes increasingly protonated due to the drop in pH at the Cr surface throughout the potentiodynamic scan, enabling the polymer to complex with negatively charged molybdate ions in solution. We hypothesize that electrodeposition occurs when the protonated amine groups are present at an appropriate stoichiometric balance with multivalent MoO2− 4 ions. We express the relative − amount of PAH+ and MoO2− 4 as f , the fraction of overall polyvalent charge that is negative. While molybdate ions represent the dominant polyvalent anion in the system, we include chromates evolved during corrosion as well in the definition of f−: f− ≡

conditions by accounting for the transport of all chemical species and corrosion products. Current densities from the electrochemical tests were used in the numerical models to determine the ion release rate due to Cr oxidation and water oxidation according to eqs 12 and 13. Modeling was not performed at times beyond the initial time of rapid polymer deposition as detected by the QCM because the deposited film changes the diffusion rates in a manner that is difficult to quantify. The aim of the simulation was to determine the criterion (f−) for film formation at the corroding electrode surface at the onset of film formation. Two electrochemical reactions were assumed to proceed at the electrode boundary: (12)

2H 2O ↔ 4H+ + O2 + 4e−

(13)

All of the current measured below 0.54 V vs SCE was attributed to the Cr oxidation reaction (eq 12). At higher potentials contributions to the current from the oxidation of water need to be taken into account.28 Therefore, above 0.54 V, 75% of the current was attributed to Cr oxidation and the remaining 25% was attributed to eq 13. This ratio was chosen because it is consistent with the mass and charge data collected during the electrochemical QCM data. In other words, we assume that the processes represented by eqs 12 and 13 occur at relative rates consistent with the measured values of m/q. Four equilibrium reactions were also assumed to proceed in the electrolyte. The first was the self-ionization of water, given by

2[MoO24 −] + 2[CrO24 −] 2[MoO24 −] + 2[CrO24 −] + [PAH+]

Cr + 4H 2O ↔ CrO24 − + 8H+ + 6e−

H 2O ↔ H+ + OH−, (11)

Keq = 10−14

(14)

The next two reactions were the protonation of the molybdate ion to molybdic acid, which proceed as follows:29

Numerical modeling was conducted to calculate changes in the local pH, concentration of PAH+ ions, and concentration of MoO2− 4 ions at the electrode surface during potentiodynamic scans. Additionally, dynamic light scattering was conducted on polymer solutions with and without molybdate ions as a function of pH to determine the range of f− values for which complexation is observed. In the following sections, we present the results of these investigations and use the quantities f−s and f−e to refer to simulated and experimental ratios respectively, and use f− when referring to the charge ratio generally. Numerical Modeling. Numerical simulations were performed to elucidate the electrode−electrolyte interface

MoO24 − + H+ ↔ HMoO−4 ,

Keq = 10−4.08

(15)

Keq = 10−3.6

(16)

and HMoO−4 + H+ ↔ H 2MoO4 ,

Finally, the ionization of PAH was included: PAH+ ↔ PA + H+

(17)

where PAH+ represents the protonated form of the amine groups present on the polymer, and PA represents the F

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Figure 6. Results from numerical modeling of potentiodynamic scans on Cr in the test solutions P05M1, P05M2, and P5M8. The experimentally measured mass change at the working electrode is presented in the top set (red dashed lines) and the species concentrations as determined from FEM simulation are presented in the lower 4 sets (blue symbols). Here, all species concentrations are reported for the electrode−electrolyte interface (i.e., at a distance x = 0 from the working electrode). Note that the simulation was only performed up until the time of rapid mass change, occurring approximately at 100 min and that f−s refers to values of f− calculated using surface concentrations of the quantities appearing in eq 11 obtained from numerical modeling.

Na2MoO4 that were an order of magnitude higher than the concentrations of interest in this investigation. In our dilute limit (Na2MoO4 ≤ 8 mM) with relatively high pH (>4), Sonnemans and Mars reported that molybdate anions do not form oxometalate clusters.31 On the basis of these studies, we assume that oxomolybdate clustering does not occur significantly in our system, and subsequently only consider eq 15 and 16 to be the molybdate equilibrium reactions. During the tests that did not show deposition (P05M1, P5M8 and P30M8), the pH also dropped to between 4 and 5 and the [PAH+] exceeded its bulk valuea phenomenon also observed in cases where deposition did occur. These results indicate that a deposition criterion is not entirely determined by the pH or by [PAH+], and that the relative fraction of multivalent cations and anions, expressed for example by the ratio f− (eq 11) is a more appropriate control parameter. The range of values of f− from the beginning of the experiment to the point where deposition is observed are listed in Table 2.

deprotonated form. The equilibrium constant of the PAH reaction was determined experimentally as described above. Representative simulation results from three tests are plotted in Figure 6 as a function of time and are correlated with mass changes at the electrode surface as measured with the QCM. During the potentiodynamic scans in solutions containing 0.5 g/L PAH and between 2−5 mM Na2MoO4, the pH at the electrode surface dropped from 7.6 to between 4 and 5 by the time of rapid polymer deposition, while the PAH+ concentration climbed to 5.34 mM for the 0.5 g/L PAH solutions and 48 mM for the 5 g/L solution. It is necessary at this juncture to comment on rich polyoxomolybdate clusters that may self-assemble under acidic conditions. The propensity to form clusters increases with increasing molybdate concentration and decreasing pH. Krishnan et al. reported that MoO2− 4 ions in solution remain as isolated dianions in the pH range of 7−12, and form Mo7O6− 24 4− and Mo8O26 in the pH range of 3−5 and below 2, respectively.30 However, these authors used concentrations of G

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Langmuir Deposition was only observed when f−s was in the range of 0.40−0.75. Dynamic Light Scattering. Dynamic light scattering provides an additional probe of the conditions for which molecular complexes are formed in our system. Four sets of measurements were performed, with the results summarized in Table 3. In the first set of measurements, the hydrodynamic

was set to values ranging from 7.6 to 5.5. At pH 7.6, the hydrodynamic radius was an order of magnitude larger than was measured at this pH with only 2 mM Na2MoO4, indicating the formation of a polymer−molybdate complex. As the pH was decreased, the size of the complex continued to increase. In the final set of DLS measurements, the PAH size was measured at pH 5.5 with increasing amounts of Na2MoO4. The size increased dramatically when the Na2MoO4 concentration reached 5 mM, suggesting the formation of a polymer− molybdate complex. These data lead to the conclusion that complexes form when Na2MoO4 is between 5 and 8 mM and the pH is between 5.5 and 7.6. In Figure 7, we plot the complex size as measured by DLS and the maximum film mass obtained from the QCM, both as a function of f−. The light scattering data indicate that poly(allylamine) will form a complex with molybdate ions when f− reaches a value close to 0.7, while numerical simulation suggests that the range is 0.4−0.75. The detailed behavior at higher concentrations differs for the two types of experiment, but it is clear in both cases that complex formation is not favored for values of f− that are too low or too high. Our results overall lead to a similar conclusion as obtained by Chollakup et al., who studied the phase behavior of poly(allylamine) complexes with poly(acrylic acid). These authors showed that polyelectrolyte complexes will form when the relative amounts of positively and negatively charged ions on the polymers are in a critical range,9 although they did not consider the charge state of both ions in the same way that we have done here. The overall picture that emerges from this work is that complex formation between positively charged poly(allylamine) and negatively charged molybdate dianions occur when the multivalent anionic charge fraction expressed by f− is in the vicinity of 0.5, and that the complex forms a stable film on the electrode for potentials above ∼0.6 V vs SCE. The existence of an optimum value for f− is also seen in the dynamic light scattering experiments, although the largest complexes are seen for slightly higher values of f−, as demonstrated in Figure 7. The magnitude of f− depends on the local pH of the solution, which cannot be measured directly for the interfacial deposition experiments, but can be estimated from numerical simulation of the appropriate transport and equilibrium equations. This simulation accounts for diffusion and electromigration of the different solution components, interfacial generation of protons as obtained from the measured corrosion current, and the

Table 3. Hydrodynamic Radii of 0.5 g/L PAH with Varying pH and Na2MoO4 Concentration. f−e Calculated by eq 11a [Na2MoO4] (mM)

pH

f−e

0 0 0 2 2 2 2 2 2 2 2 8 8 8 3 4 5

5.5 6.6 7.6 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.6 5.5 6.6 7.6 5.5 5.5 5.5

0 0 0 0.25 0.35 0.40 0.41 0.42 0.42 0.43 0.45 0.74 0.75 0.77 0.52 0.59 0.64

radius (nm) 32.8 41.3 45.1 24.7 24.7 23.5 23.2 25.1 33.6 37.4 46.1 3925.8 2529.3 335.6 45.9 56.1 13823.3

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

3.3 2.3 7.3 0.2 0.1 0.7 0.1 0.2 2.3 5.6 4.8 1513.9 684.7 21.9 0.9 0.5 4163.0

a Using the degree of ionization of PAH according to Figure 3a, and accounting for the fact that MoO2− 4 is a weak base as outlined by eq 15.

radii of PAH molecules in the dilute regime were measured in the absence of added Na2MoO4 as the solution pH was decreased from 7.6 to 5.5. The hydrodynamic radius changed very little with pH, although there was a slight size decrease when the pH was dropped to 5.5. In the second set of measurements, the size of the PAH was measured with 2 mM Na2MoO4 while the pH was decreased from 7.6 to 4.0. Again, there was little change in size with pH, although the addition of the Na2MoO4 decreased the hydrodynamic radius, an effect that we attribute to charge screening and decreased intramolecular charge repulsion. In the third set of DLS measurements, the Na2MoO4 concentration was increased further to 8 mM and the pH

Figure 7. (a) Hydrodynamic radii of poly(allylamine) chains in solutions as obtained from the dynamic light scattering measurements. (b) Maximum film areal mass measured during potentiodynamic scans in each of the nine PAH solutions. Both quantities are plotted as a function of the experimental ( f−e ) or simulated ( f−s ) charge ratio (eq 11). H

DOI: 10.1021/acs.langmuir.6b01536 Langmuir XXXX, XXX, XXX−XXX

Article

Langmuir

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charge state of the different molecular species. The degree of ionization of the poly(allyamine) is particularly complex, and depends on pH in a way that is described by a concentrationdependent equilibrium constant between protonated and neutral amine groups on the polymer. Because the transport equations are affected by the deposited layer itself, the simulation approach is best suited for determining local pH and component concentrations up until the onset of mass deposition. This onset is pinpointed quite accurately by the mass sensing capability of the quartz crystal microbalance that is used as the working electrode.

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CONCLUSIONS The corrosion triggered electrodeposition of cationic a polyelectrolyte was investigated through a multipronged approach using the quartz crystal microbalance, numerical simulation, and dynamic light scattering. We demonstrated that the strong electrostatic repulsions of cationic polyelectrolytes at anodic surfaces can be mediated by the presence of multivalent anions, molybdates in this case. However, this mediation is optimized only when the ionically cross-linking polyanions are present in an appropriate range of ratios with respect to the degree of ionization of the polyelectrolyte, as quantified by the ratio f− (eq 11). The range of f− for which film deposition is observed serves as the criterion for film formation. The simplified model system of Cr−PAH−molybdate studied in the work presented here may offer mechanistic insights into the onset of protein film formation at corroding CoCrMo hip implant surfaces. The combined experimental and modeling approach used in this work is quite powerful, and can be utilized to design deposition schemes for a variety electrochemically driven processes where the pH plays an important role.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (K.R.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This work was supported by the Polymers Program of the National Science Foundation under grant DMR-1410968.

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DOI: 10.1021/acs.langmuir.6b01536 Langmuir XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.langmuir.6b01536 Langmuir XXXX, XXX, XXX−XXX