Electron Transfer Processes in Ferrocene-Modified Poly(ethylene glycol) Monolayers on Electrodes.

Electrochemistry is a powerful tool to study self-assembled monolayers. Here, we modified cystamine-functionalized electrodes with different lengths of linear poly(ethylene glycol) (PEG) polymers end-functionalized with a redox-active ferrocene (Fc) group. The electron transport properties of the Fc probes were studied using cyclic voltammetry. The Fc moiety attached to the shortest PEG (Mn = 250 Da) behaved as a surface-confined species, and the homogeneous electron transfer rate constants were determined. The electron transfer of the ferrocene group on the longer PEGs (Mn = 3.4, 5, and 10 kDa) was shown to be driven by diffusion. For low surface densities, where the polymer exists in the mushroom conformation, the diffusion coefficients (D) and rate constants were increasing with polymer length. In the loose brush conformation, where the polymers are close enough to interact with each other, the thickness of the layers (e) was unknown and a parameter D1/2/e was determined. This parameter showed no dependence on surface density and an increase with polymer length.

Introduction

Understanding conformations of (bio)polymers at surfaces is important since such layers are widely used for electrochemical detection methods, for example, for DNA sensing.[1−7] The mechanism of so-called E-DNA sensors relies on changes in conformation upon binding with the analyte, and this conformational change results in a change in signal.[3] As such, the flexibility of the linker plays an important role in the signal output.

The configuration of end-tethered polymers on surfaces is dictated by the surface density and the length of the polymers.[8,9] The transition between the mushroom and brush conformation, where the polymers begin to overlap, has been modeled[10,11] and observed experimentally[12,13] with different results for the onset of the brush formation. If the molecules are tethered with an electrochemical probe, the behavior of the end-group can be studied using electrochemical methods. Several studies have been performed with poly(ethylene glycol) (PEG) layers end-tethered with ferrocene, both with an atomic force/scanning electrochemical microscope setup[14] and on single electrodes.[15,16] The polymer behavior in the mushroom configuration, where the polymer chains exist as isolated entities, has been modeled.[17] These studies have shown that the electrochemical response of the end-group involves diffusion to the surface. As the surface density is increased, which brings about conformational changes, changes in bound diffusion and kinetics can be expected, as have indeed been observed for DNA and PNA layers.[18] A detailed experimental study on a well-defined model system in which the length and density of surface-attached PEG chains are varied is however currently lacking.

Herein we study the effect of polymer length and surface density of end-tethered PEG layers immobilized on electrodes, in order to study the electron transfer behavior of the end-group. The surface densities are varied to achieve the mushroom and loose brush conformations, and the influence of the varying surface density on the electrochemical properties of the ferrocene group is established using cyclic voltammetry.

Results and Discussion

PEG chains bearing on one end a ferrocene (Fc) moiety, used for electrochemical detection, and on the other end a reactive succinimide (NHS) group, used for surface attachment, were synthesized according to known procedures.[15,19] Fc-PEG-NHS derivatives of four molecular weights (Mn = 0.25, 3.4, 5, and 10 kDa, i.e., Fc-PEG250-NHS, Fc-PEG3k-NHS, Fc-PEG5k-NHS, and Fc-PEG10k-NHS, respectively) were separately grafted onto gold electrodes that were pretreated with cystamine.[15,16] The PEGs (with the exception of PEG250) used here were reported to have a polydispersity index of 1.08, and their average molecular weights correspond to fully extended lengths of L = 2.1, 27, 40, and 79 nm (Table ) for PEG250, PEG3k, PEG5k, and PEG10k, respectively. The conformation of the polymers is dictated by the surface density (Figure a). If the density is sufficiently low (Table ), the polymers exhibit a mushroom conformation. As the surface density increases and the chains start to interact, the polymers extend outward into the solution and form a loose brush.

Table 1

Overview of the Used Polymers, Their Molecular Weights and Standard Deviations Calculated from the Reported Polydispersity (1.08), Calculated Flory Radius, Rf, Fully Extended Chain Length (L), and the Calculated Surface Density at Which the Chains Start to Interact and Move into a Loose Brush Regimea

Mn (kDa)	Rf (nm)	L (nm)	mushroom to brush transition density (mol/cm2)
0.25b	1.0	2.1	1.6 × 10–10
3.4 ± 1.0	4.7	27	7.4 × 10–12
5.0 ± 1.4	6.0	40	4.6 × 10–12
10 ± 2.8	9.1	79	2.0 × 10–12

For the calculations of these densities, see the Experimental Section).

Polydispersity not reported.

Figure 1

(a) Surface density effect on polymer conformation. If the surface density is sufficiently low, i.e., when the Flory radius (Rf) is smaller than the distance between the grafting points (s), the polymers are in the mushroom conformation (left). When the surface density is increased, the polymers start to overlap, and a loose brush is formed (right). (b) Gaussian fully extended chain length distribution for the PEG3k, PEG5k, and PEG10k used here (represented by the colors red, blue, and black, respectively).

Cleaned gold electrodes were modified with cystamine, resulting in a monolayer with free amine groups onto which the Fc-PEG-NHS polymers were grafted via their succinimide groups. Cyclic voltammetry measurements of the modified electrodes were performed in a 1 M NaClO4 solution. The results (see Figure a for a cyclic voltammogram of a the Fc-PEG250 layer) were typical for surface-attached species, with a small peak separation (<59 mV) and a peak current that was linearly dependent on the scan rate, indicating that all the redox couples have sufficient time to contribute to the electron transfer. In this regime, the charge determined from the peak area remains constant independent of scan rate, and the surface density (Γ) of the PEG molecules can be determined according to eq .

Figure 2

(a) Cyclic voltammogram of a Fc-PEG250 monolayer, obtained upon a reaction time of 5 min, recorded in 1 M NaClO4 at 2 V/s vs a Hg/Hg2SO4 reference electrode. (b) Trumpet plot of the peak separation, η, versus the logarithm of the scan rate, ν.

In eq , Q is the charge of the integrated peak area, A the microscopic surface area as determined from sulfuric acid cleaning scans, F the Faraday constant, and n the number of electrons involved (n = 1 for ferrocene). At scan rates above 200 V/s a significant peak separation became apparent for Fc-PEG250, resulting in a characteristic trumpet plot (Figure b) when plotting the peak separation, η, versus the logarithm of the scan rate, ν.

When the peak separation increased past 200 mV and the electron transfer became electrochemically irreversible, the peak potentials changed linearly with the logarithm of the scan rate. In that case, a standard rate constant, k, can be determined using Laviron’s formulation (eq ).[20]

In eq , α is the transfer coefficient, taken as 0.5, and R and T are the ideal gas constant and the temperature, respectively, while νc and νa are the cathodic and anodic scan rates, respectively. From this treatment, rate constants k of 2.4 × 103 s–1 and 1.7 × 103 s–1 were found for the anodic and cathodic processes, respectively. These values are significantly larger than the standard rate constants determined for ferrocene moieties on well packed alkane monolayers of similar length,[21] thus indicating a loosely packed layer in the case of PEG layers. This is confirmed by the measured surface densities, for which values between 2 and 3 × 10–10 mol/cm2 were obtained when using a surface functionalization time of 5 min.

The peak separation for the longer PEGs was less pronounced and was mostly caused by a shift of the cathodic peak and a smaller shift of the anodic peak combined with significant peak broadening (Figure a and d). At increased scan rates, the current became linear with the square root of the scan rate (Figure c) following the Randles-Sevcik equation,[22] indicating an additional dependence of the electron transfer rate on the diffusion of the ferrocene head groups to and from the surface. Since the effect of diffusion on the electron transfer excludes the use of the Laviron method for the determination of rate constants, these were determined using the Nicholson method for diffusing species adjusted for surface-confined species.[18,23,24] In order to do this, the diffusion constants of ferrocene and oxidized ferrocenium species (DFc and DFc, respectively) were determined from the anodic and cathodic peak currents using the Randles-Sevcik equation (eq ).

Figure 3

(a) Cyclic voltammogram of a 1.5 × 10–11 mol/cm2 monolayer of Fc-PEG10k (obtained from a reaction time of 90 min) in 1 M NaClO4 at 10 V/s. (b) Anodic peak current, ia, plotted versus the square root of the scan rate ν; the line is a linear fit to the data. (c) Anodic peak current density (ja = ia/A), normalized to the square root of the scan rate, vs the logarithm of the scan rate. (d) Peak separation vs the logarithm of the scan rate.

In eq , the concentration, C, can be replaced by Γ/e, with e being the layer thickness. Normalizing the anodic peak current densities (ja = ia/A) to ν1/2 showed that at higher scan rates ja/ν1/2 became independent of the scan rate, thus reaching a plateau (Figure c). From the height of this plateau the diffusion coefficients DFc and DFc were determined using the Randles-Sevcik equation for the polymers in the mushroom conformation. When the surface density is sufficiently low so that the polymers on the surface can be assumed to exist in the mushroom conformation (see Table ) and do not interact with each other, the average thickness of the polymer layer, e, can be taken as the Flory radius.

As can be seen in Table , the determined diffusion coefficients show that the bound ferrocenium cation diffuses faster (2.5–4 times) than the reduced ferrocene, which is also visible from the peak asymmetry (Figure a), the cathodic peak being sharper than the anodic peak.[15] This effect is not present for ferrocene species in solution[25,26] but has been noted before for surface-bound Fc-PEG, and has been attributed to the positively charged Fc+ being “propelled away” from the surface, caused by electrostatic repulsion between the surface and the Fc+ moiety directly after the oxidation step.[15]

Table 2

Diffusion Coefficients and Homogeneous Electron Transfer Rate Constants Determined for Fc-PEG3k, Fc-PEG5k, and Fc-PEG10k in the Mushroom Regime

polymer	DFc (×10–12 cm2/s)	DFc+ (×10–12 cm2/s)	k0 (s–1)
Fc-PEG3k	1.4 ± 1.0	6.0 ± 1.3	88 ± 23
Fc-PEG5k	1.9 ± 0.4	6.2 ± 0.4	114 ± 104
Fc-PEG10k	9.1 ± 6.3	29.8 ± 9.7	228 ± 54

The diffusion coefficients increased with increasing polymer length, which is counterintuitive. For the mushroom configuration, the concentration of ferrocene can be represented by a Gaussian distribution with the highest concentration close to the surface. The longer molecules have a higher local density due to the amount of polymer surrounding the ferrocene head, which is expected to slow down diffusion. Indeed, the opposite trend has been observed for different lengths of Fc-modified PNA strands tethered on electrodes, with the diffusion coefficients decreasing and the system becoming more surface confined as the strand length decreased.[18] On the other hand, it has been shown that the diffusion coefficient for tethered PEG3k is higher than for PEG600 in dichloromethane, even with the PEG3k being in a loose brush conformation and the PEG6k in a mushroom conformation, which has been attributed to an increased influence of the spring constant on the diffusion coefficient.[15]

As mentioned above, using the diffusion coefficients, the homogeneous electron transfer rate constants could be determined using the Nicholson method for diffusing species when the peak separation is between 61 and 212 mV. In short, the peak separation is related by a kinetic parameter ψ, from which the rate constant can be calculated.[23] As can be seen in Table , the determined rate constants are lower than the value (approximately 2 × 103 s–1) determined for PEG250, in which case the electron transfer is not affected by diffusion. Furthermore, the rate constants increased with increasing polymer length, which could indicate that for the longer molecules the ferrocene end groups are on average closer to the surface.[18]

As the surface density was increased by employing longer reaction times of Fc-PEG-NHS on the cystamine surfaces (Figure a), the average distance between the anchoring points became smaller than the Flory radius, and consequently the polymer conformation moved from a mushroom into a loose brush regime. In the brush regime, the polymer chains stretch outward into the solution; therefore, the layer thickness (e) is no longer related to the Flory radius, but instead becomes proportional to the average number, N, of monomers per chain, by e ∼ pNaσ1/3,[8] where a is the monomer size, σ the graft density, and p a proportionality coefficient. Since the actual layer thickness is unknown in this case, the diffusion and rate constants cannot be directly determined.

Figure 4

(a) Obtained surface densities as a function of the reaction time, t. (b,c) Anodic (ja) and cathodic (jc) peak current densities normalized to the square root of the scan rate, vs surface density, for Fc-PEG3k (red), Fc-PEG5k (blue), and Fc-PEG10k (black). Standard deviations of the values were determined using the least-squares method and fall within a range of 15%.

The anodic and cathodic peak current densities normalized to the square root of ν, jc/ν1/2, showed a linear increase upon increasing surface density (Figure b and c). Since the slope of this line is now solely dependent on the parameter DFc1/2/e (see eq ), this parameter was determined for all three PEG lengths in the brush conformation. The values for DFc1/2/e were found to be 10.6 ± 1.7, 9.2 ± 0.6, and 9.1 ± 0.8 s–1/2 for Fc-PEG3k, Fc-PEG5k, and Fc-PEG10k, respectively, when using the cathodic peak current densities. The DFc1/2/e values, determined from the anodic peak current densities, were again lower, 4.5 ± 1.4, 6.6 ± 0.7, and 6.1 ± 1.5 s–1/2. The similarity between the PEGs can partly be attributed to the broad size distributions, which show that a large proportion of the size distributions overlap (Figure b), despite the difference in Mn and a relatively small polydispersity of 1.08. The fact that the D1/2/e values remain constant implies that, as the layer thickness increases, the diffusion constants must increase as well. An increase of the diffusion constant with increased surface density can be explained with an increased proximity of the redox centers to the surface.[27] For a surface density of 1.5 × 10–12 mol/cm2, and a layer thickness of 40 nm (half of the fully extended length of PEG10k), the ferrocene concentration inside that layer can be calculated to be 3.8 mM, which is of the same order of magnitude as electrochemical mediators in solution.[28] This cannot be the sole contribution to the diffusion process, since the diffusion constant is greater for PEG10k, which must mean that the local ferrocene concentration is lower than for shorter PEGs, as the layer thickness is larger.

Conclusions

Surfaces were modified with different lengths of poly(ethylene glycol) (PEG) end-tethered with a ferrocene moiety and studied using cyclic voltammetry. The shortest Fc-PEG, Fc-PEG250, behaved as a surface-confined layer for which homogeneous rate constants could be determined using the Laviron method. These results suggest that a loosely packed layer was formed. For longer Fc-PEGs, diffusion coefficients and homogeneous electron transfer rate constants could be determined when the layers were present in the mushroom conformation, both of which increased with the polymer length. As the surface density was increased, and the polymer layers entered the loose brush regime, the determination of these parameters was not possible due to the unknown layer thickness. Instead, D1/2/e values were determined for both ferrocene and ferrocenium, and were shown to be constant for increasing surface densities, implying an increase in diffusion coefficient with surface density. This increase is attributed to an increased chance of electron hopping as the local ferrocene concentration increases. However, the diffusion coefficient also appears to become larger for longer PEGs, while these form a thicker layer and thus a lower Fc concentration. More information is needed to fully explain this increase. Overall, the data presented here highlight that redox-modified polymers attached to an electrode surface show a rich and complex electrochemical behavior, that leads to currents that depend on a multitude of parameters. Unraveling these dependencies will assist in the development of electrochemical sensors that rely on redox behavior of surface-tethered probe molecules.

Experimental Section

Materials

Reagents and solvents were purchased from Sigma-Aldrich, high-purity water (Milli-Q) was used (Millipore, R = 18.2 Ω). All bis-NHS-functionalized PEGs were purchased from Nanocs and have a reported dispersity of 1.08. The Fc-PEG-NHS molecules were synthesized according to known procedures.[15] Fc-PEG250-NHS was further purified by column chromatography with dichloromethane as eluent. After the first fraction was removed, the eluent was changed to DCM/EtOH (95:5). Fc-PEG3k-NHS, Fc-PEG5k-NHS, and Fc-PEG10k-NHS were further purified by size exclusion chromatography (Biobeads SX-1) with DCM as eluent.

2-Ferrocene-Ethylamine

2-Ferrocene-ethylamine was synthesized by the reduction of ferrocene acetonitrile by LiAlH4 as described in the literature,[19] with some modifications. An amount of 0.25 g (6.5 mmol) LiAlH4 and 0.6 g (4.5 mmol) AlCl3 were carefully added to 10 mL dry THF while stirring in an ice bath. Ferrocene acetonitrile (0.5 g, 2.25 mmol) was dissolved in 5 mL dry THF and subsequently added to the cooled mixture and refluxed overnight under an argon atmosphere. After cooling, water was added dropwise to decompose the excess LiAlH4. A volume of 0.25 mL of concentrated NaOH was added to destroy the formed AlCl3/2-ferrocene-ethylamine complex. The aqueous phase was extracted three times with diethyl ether. The combined organic phases were dried with MgSO4 and filtered, and the solvent was removed by rotary evaporation. The product was purified by column chromatography with dichloromethane as the eluent. After drying in vacuo, a brown solid was obtained (0.13 g; 26%). 1H NMR (300 MHz, CDCl3): δ (ppm) 4.2 (m, 9H, Fc), 2.82 (t, 2H, CH2-Fc), 2.48 (t, 2H, CH2-N).

PEG250-(NHS)2

The bis-NHS ester of the PEG250 diacid was prepared according to a procedure described earlier.[15] An amount of 0.44 g (3.8 mmol) of N-hydroxysuccinimide (NHS) and 0.78 g (3.8 mmol) dicyclohexylcarbodiimide (DCC) were added to a stirred solution of 0.4 g (1.6 mmol) poly(ethylene glycol) bis(carboxymethyl) ether in 30 mL 1,4-dioxane. After stirring overnight at room temperature under an argon atmosphere, the mixture was filtered to remove the 1,3-dicyclohexylurea precipitate. The solvent was removed by rotary evaporation and the residue was further dried under vacuum. 1H NMR (300 MHz, CDCl3): δ (ppm) = 4.56 (s, 4H, CH2C=O), 366 (s, 12H, C2H4-O), 2.81 (s, 8H, NHS).

Surface Functionalization and Electrochemistry

All electrochemical measurements were performed on a CH Instruments bipotentiostat 760D. Cyclic voltammetry measurements were performed in a three-electrode setup using 2-mm-diameter (CH Instruments) or 1.6-mm-diameter (BASi) gold disk electrodes, a platinum wire as the counter electrode, and a Ag/AgCl reference electrode in aqueous 1 M NaClO4.

Before modification the electrodes were polished using 50 nm alumina particles (CH Instruments), followed by extensive rinsing with ethanol and 5 min of ultrasonic treatment in ethanol and 5 min in Milli-Q water. Subsequently, the electrodes were cleaned electrochemically in 0.5 M H2SO4 by applying an oxidizing potential of 2 V for 5 s followed by a reducing potential of −0.35 V for 10 s. Then, the electrode potential was scanned from −0.25 to 1.55 V and back for 40 cycles at a scan rate of 100 mV/s, the surface area of the electrodes was determined from the Au–O reduction peak, using a value of 386 μC/cm2 to convert the charge into surface area.[29,30] The determined surface areas are typically between 1.5 and 2 times the geometrical surface area.

Following a procedure published before,[15,16] the cleaned electrodes were rinsed with Milli-Q water and ethanol and dried under a flow of N2 and placed immediately in a 2 mM cystamine solution and left overnight. Subsequently, the electrodes were rinsed with Milli-Q water and dried under a flow of N2 and placed in a 0.2 mM Fc-PEG-NHS solution. The surface densities were varied by changing the reaction time between 5 and 120 min. The prepared electrodes were copiously rinsed with Milli-Q water and subsequently cycled electrochemically at 100 mV/s in 1 M NaClO4 until a stable signal was obtained. Surface densities were determined from the average charges of at least 3 cyclic voltammograms recorded at scan rates below 500 mV/s, the surface densities have an error margin of <10%. The slope of the currents vs ν1/2 were determined over a range of at least 15 different scan rates, standard deviations were determined using the least-squares method and all determined standard deviations are smaller than 15%. The iR compensation function of the bipotentiostat was used to check the effect of solution resistance and double layer capacitance on the peak currents and peak separations at high scan rates, and there was shown to be no difference in the used scan rate regime.

Calculations

The Flory radii (Rf) in Table were calculated with Rf = aN3/5 where a is the size of the individual ethylene glycol monomer (a = 0.35 nm[31]) and N the degree of polymerization (N = 6, 77, 114, and 227 for PEG250, PEG3k, PEG5k, and PEG10k, respectively). When the distance between the grafting points (s) of the PEG molecules approaches the Rf, the chains start to overlap and form a polymer brush at the critical dimensionless coverage σcritical = (a/Rf)2 = (NaΓ)a2, where Na is Avogadro’s constant. From this the critical surface densities as shown in Table can be determined.[14]