Atomistic simulations of dopamine diffusion dynamics on a pristine graphene surface

Abstract

Carbon microelectrodes enable in vivo detection of neurotransmitters, and new electrodes aim to optimize the carbon surface. However, atomistic detail on the diffusion and orientation of neurotransmitters near these surfaces is lacking. Here, we employ molecular dynamics simulations to investigate the surface diffusion of dopamine (DA), its oxidation product dopamine-o-quinone (DOQ), and their protonated forms on the pristine basal plane of flat graphene. We find that all DA species rapidly adsorb to the surface and remain adsorbed, even without a holding potential or graphene surface defects. We also find that the diffusivities of the adsorbed and the fully solvated DA are similar and that the protonated species diffuse more slowly on the surface than their corresponding neutral forms, while the oxidized species diffuse more rapidly. Structurally, we find that the underlying graphene lattice has little influence over the molecular adsorbate’s lateral position, and the vertical placement of the amine group on dopamine is highly dependent upon its charge. Finally, we find that solvation has a large effect on surface diffusivities. These first results from molecular dynamics simulations of dopamine at the aqueous-graphene interface show that dopamine diffuses rapidly on the surface, even without an applied potential, and provide a basis for future simulations of neurotransmitter structure and dynamics on advanced carbon materials electrodes.

2. Introduction

In vivo electrochemistry is a powerful quantitative analytical technique that can measure the oxidation or reduction of target compounds within living organisms [1, 2, 3]. In these experiments, a biocompatible carbon electrode is inserted into live tissue to observe transient changes of key biochemical species, such as neurotransmitters [4], signaling molecules [5], and physiological metabolites [1, 6, 7, 8, 9] – species whose biological activities depend on the timing and location of their release. One such species, dopamine (3,4-dihydroxyphenethylamine, DA), is a critical neurotransmitter in the central nervous system and controls reward-motivated behaviors [10, 11, 12]. DA is a common target for in vivo electroanalytical detection and rapid electrochemical studies of dopamine have improved our understanding of its role underlying positive reinforcement, decision making, and addiction [13, 14, 15, 16, 17, 18]. The oxidative product of DA is dopamine-o-quinone (4-(2-Aminoethyl)-3,5-cyclohexadiene-1,2-dione, DOQ), which is an important intermediate product in DA metabolism [19]. Carbon-based microelectrodes are widely used for the in vivo electrochemical detection of DA [20, 13, 14, 18] and similar species due to their fast electron transfer rates, biocompatibility, and low costs [21, 22, 13, 23]. Coupled with fast-scan cyclic voltammetry (FSCV), which uses rapid potential sweeps to repeatedly oxidize and reduce analytes of interest, carbon microelectrodes have been able to measure neurotransmitters in vivo with millisecond temporal resolution [18, 14, 24].

The first generation carbon microelectrodes consisted primarily of carbon fibers of disordered graphite [25, 21, 15, 13, 26], often treated to enhance electrochemical activity. Beveling or physically polishing a graphite disk increases the ratio of edge to basal planes, while electrochemical pre-treatments increase the frequency of electrochemically active defects and graphite oxide moieties on the surface [27]. Such carbon surface features enhance the adsorption of catecholamines and facilitate the subsequent oxidation and reduction during electrodetection [28, 29, 13, 30, 31, 32, 33].

At the same time, recent local electrochemical imaging studies by Unwin and coworkers have emphasized that even the basal planes of pristine highly-ordered pyrolytic graphite (HOPG) and carbon nanotubes (CNTs) display significant electrochemical activity towards catecholamines [34]. Indeed, even early work on freshly fractured glassy carbon microelectrodes showed that pristine basal plane graphene sheets exhibited significant DA adsorption and activity, although electrochemical activity could still be enhanced after certain pre-treatments [31].

In more recent years, a wide variety of advanced carbon electrodes have been developed, including graphene oxide nanoribbons [35], CNT yarn microelectrodes (CNTYMEs) [36], carbon nanospikes [37], cavity carbon nanopipettes [38, 39], laser activated CNTYMEs [15], and microelectrodes coated with carbon nanohorns or nanodiamonds [40, 41, 42, 43]. These novel microelectrodes have improved sensitivity, temporal resolution, and analyte specificity.

Although investigations of these novel carbon microelectrodes have led to reliable general principles governing the relationship between electrode structure and its function [37], details are still lacking on the underlying molecular-scale determinants of analyte adsorption and desorption, oxidation and reduction catalysis, and analyte dynamics in solution and on the electrode surface. Indeed, even the simplest questions regarding the diffusivity of catecholamines on the pristine basal plane of graphene have not yet been comprehensively studied.

While catecholamine adsorption and desorption occurs on the μs to s timescale [44, 45], diffusion of solvated catecholamines to the surface is more rapid [30] with flow injection experiments suggesting a solvated diffusion constant of D = 0.6×10⁻⁵ cm²/s [46]. Diffusion constants for catecholamines adsorbed on carbon microlectrode surfaces have not been characterized, although evidence suggests that these could also be much faster than the adsorption/desorption times. An MD study of DA on a TiO₂ surface reported that, at a surface coverage close to the saturation limit, the DA distribution over surface facets of 70 nm² had equilibrated by 2 ns [47]. Since very local surface features can influence nearby electrochemical activity [13, 37], and DA dwell time on the surface has been estimated to be more than 0.2 seconds [44], characterizing the surface dynamics of adsorbed analytes is essential for understanding microelectrode function. Indeed, recent work postulated the existence of electroactive surface domains separated by inactive domains and showed that the dependence of oxidation wave peak current intensities on FSCV scan rate could be explained by the time it takes for adsorbed DA to move between them during the scan window [48]. Although previous computational studies investigated the strength of the energetic interactions between graphene and DA in different orientations [49] as well as the behavior of atomic adsorbates [50, 51] and C₆₀ molecules [52, 53] on graphene surfaces, the diffusion of DA and DOQ on graphene has not been previously simulated.

In this paper, we use molecular dynamics (MD) to investigate the surface dynamics of various DA species on the basal plane of pristine graphene. In Section 2, we describe our modeling approach for simulating DA, its oxidized form dopamine-o-quinone (DOQ), and their protonated counterparts on a pristine flat graphene surface. In Section 3, we quantify the differences in diffusion between the DA species and the lateral and vertical distributions of their constituent moieties on the surface, comparing our results to those of a structureless adatom of the same mass. Finally, we discuss our findings and their implications in Section 4 and conclude in Section 5. These studies show how dopamine diffuses on a pristine graphene surface, which is crucial for understanding dopamine-electrode interactions and designing better materials for electrodes.

3. Methods

We employed atomistic MD simulations on 3D periodic systems that contained a single adsorbate, a flat graphene surface, and TIP3P water molecules.

Dopamine and Adatom Adsorbates.

In our modeling, we represented DA, DOQ, and their singly protonated species atomistically (see Fig. 1a) and assigned optimized charge distributions for each species (see SI for additional details). pH is well regulated in the human body, with an arterial pH between 7.36 and 7.44 and an intracellular pH of approximately 7.2 [54]. The three pK_a’s of DA are estimated to be pK_a,1 = 8.71, pK_a,2 = 10.90, and pK_a,3 = 13.68 [55]. As a result, at physiological pH, DA and DOQ primarily exist in their singly protonated states, as DAH⁺ and DOQH⁺ [56]. Counter-charges for the protonated species were added in the form of Cl⁻ ions. DA is a catecholamine containing three key moieties: the side-chain amine, the aromatic ring, and two ortho-hydroxyl groups [19]. We refer to these moieties as “amine,” “ring,” and “diol” or “quinone,” the last depending on whether it is DA or DOQ. In addition to the DA species, we also model a charge-neutral atomic adsorbate with the same molar mass as dopamine (153.18 a.u.) for comparison purposes, which we refer to as “adatom(DA).”

Figure 1: DA species and graphene.

(a) Various dopamine (DA) species: DOQ is the oxidized product of DA, and DAH⁺ and DOQH⁺ are the protonated species of DA and DOQ, respectively. (b) An atomistic representation of DA is shown adsorbed onto the flat graphene surface. (c, d) One configuration of DA on flat graphene surface is shown from two directions.

Flat Graphene Surface.

A single-layered pristine flat graphene surface was used in our simulations to represent a conventional carbon fiber microelectrode surface. Fig.1(b–d) illustrates the simulated graphene system. The decision to model just a single layer of graphene was made after comparisons between the surface diffusion dynamics on single- and triple-layered graphene in the solvated systems displayed no significant differences (see SI for more details). The graphene carbon atoms were kept fixed in order to mimic a stationary bulk phase carbon electrode while minimizing complications that could be introduced by other approaches to keep graphene stationary. This choice is discussed further in the SI. The simulation box extended both 15 Å above and 15 Å below the carbon surface in the z-direction. Finally, after simulating a series of different dimensions for the flat graphene surface to test the influence of the system size on the resulting DA diffusion constants, we chose the largest simulation size, with graphene surface dimensions of 98.2×97.8 Ų, to minimize the finite system-size effects. A full discussion of the finite system size effect can be found in the SI, and estimates of the infinite system size diffusion constant, D_∞, are made there for DA and adatom(DA) by fitting the results from five different system sizes and extrapolating to the infinite case. This extrapolation can be seen in Figure S1, and the resulting D_∞ values are reported in Table S2.

Simulation Details.

Atomistic MD simulations were performed in the canonical ensemble at 300K for 5 ns using a Nosé-Hoover thermostat. The equations of motion were integrated using a standard velocity-Verlet algorithm with a time step of 1 fs. The cutoff distance for the Lennard-Jones (LJ) interaction was set to 10 Å, the cutoff distance for the short-range component of the electrostatic interaction was also set to 10 Å, and the long-range component of the electrostatic interaction beyond that cutoff distance was computed in reciprocal space using Ewald summation. Ten independent MD simulations were performed for all results presented below, using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [57]. Additional simulation details can be found in the SI.

The interactions between the adsorbates and the flat graphene surface were modeled using the classical OPLS-AA force field [58], which has been validated for similar systems in prior studies. In Lazar et al., the enthalpies of a series of small organic molecules adsorbing onto the graphene surface were calculated using OPLS-AA, and the results correlated well to the experimentally determined adsorption enthalpies, although they underestimated the experimental values by about 1.9 kcal/mol [59]. In Björk et al., the accuracy of various computational approaches in calculating binding energies per carbon atom was assessed for a series of π-conjugated systems adsorbed on the graphene surface, and OPLS-AA was again able to reproduce the experimentally observed trend [60].

For simplicity and clarity, no external voltage was applied in the MD simulation results presented in this paper. Although the applied potential exerts significant influence over adsorbed DA, the potential typically scans rapidly from −0.4 V to 1.3 V (vs. an Ag/AgCl reference) and back, with the limits of that scan chosen strategically to maximize DA adsorption at the holding potential of −0.4 V, cover the full range of the oxidation and reduction peaks, and optimize electrode performance via a surface activation at the potentials > 1.0 V [24]. Moreover, the location of the peaks actually shift with FSCV scan rate [24]. Thus, a comprehensive assessment of the influence of the applied voltage on DA dynamics is complex and lies outside the scope of this first investigation of DA dynamics on the graphene surface.

A small number of simulations were also run without solvent, in order to isolate the influence of the surface on adsorbate diffusion. In these cases, only neutral DA and DOQ were modeled and simulations were run within the NVE ensemble.

4. Results

4.1. DA species adsorb rapidly and remain on the pristine graphene surface.

All simulations were initially set up with the analyte fully dissolved some distance above the graphene surface. Adsorption and desorption timescales were estimated for the DA and DOQ concentrations within our simulations, using the kinetic model proposed by Bath et al. [61, 36]. Desorption events, for both DA and DOQ, were estimated to take place on the timescale of seconds, while adsorption events were estimated to take place several orders of magnitude more rapidly (see SI for details). Desorption events are thus not expected to occur on the timescales accessible in our equilibrium MD simulations. Indeed, in all simulations, the DA species adsorbed to the surface within the first 0.2 ns of the initial NPT equilibration run and remained there for the remaining 0.8 ns of the NPT set-up run as well as the full 7 ns of the subsequent NV T run.

4.2. DA species have varying diffusivities on graphene.

From these simulations, we calculated the diffusion constants of adatom(DA), DA, DAH⁺, DOQ, and DOQH⁺ on flat graphene. Figure 2 plots the directional mean squared displacements (MSDs) and velocity auto-correlation functions (VACFs) of these adsorbates, where the x and y directions lie along the graphene plane, and the z direction extends out from the surface. The linear region of the MSD plots were then used to calculate the directional diffusion coefficients reported in Table 1. As discussed in the Methods, it should be noted that the reported values of D in Table 1 will be an overestimate of the D_∞ values due to the finite size of the simulation box. The magnitude of the correction can be estimated by comparing the last two rows in Table S2, which indicates a value of 1.92 × 10⁻⁵ cm²/s for D_Graphene100, while D_∞ is estimated to be 1.24 × 10⁻⁵ cm²/s. All D values reported in the main text are those obtained directly from this largest simulation size, “Graphene100,” which has graphene surface dimensions of 98.2 × 97.8 Ų. A more detailed discussion can be found in the SI.

Figure 2: Mean squared displacements and velocity auto-correlations of DA species on graphene.

Mean squared displacements (MSD, left column) and velocity auto-correlation functions, VACFs (C_v, right column) are shown as a function of time along three directions: x and y lie on the graphene plane (as shown in the schematic on the left), while z is normal to the plane. The inset plots show the enlarged MSD curves in the 0–0.5 ps and 0–0.25 Ų range. MSDs and VACFs were collected from ten 5 ps NVT trajectories at 300K at a recording interval of 0.01 ps. Plots showing the comparison of the MSDs for all ten trials of each DA species are shown in Figure S2.

Table 1:

Diffusivities of DA species on graphene.

Adsorbates	Dx (×10−5 cm2/s)	Dy (×10−5 cm2/s)	Dz (×10−5 cm2/s)(a)	D (×10−5 cm2/s)(b)
Adatom(DA)	4.59 ± 0.32(c)	4.71 ± 0.31	0.00 ± 0.01	4.65 ± 0.29
DA	1.92 ± 0.12	1.92 ± 0.13	0.00 ± 0.00	1.92 ± 0.07
DAH+	1.73 ± 0.13	1.74 ± 0.15	0.00 ± 0.00	1.74 ± 0.07
DOQ	2.34 ± 0.22	2.23 ± 0.17	0.00 ± 0.00	2.29 ± 0.16
DOQH+	1.96 ± 0.24	1.94 ± 0.15	0.00 ± 0.00	1.95 ± 0.14
DA-in-water(d)	1.51 ± 0.11	1.60 ± 0.12	1.47 ± 0.11	1.53 ± 0.06(e)

^(a)Directional diffusion coefficients, D_x, D_y, and D_z, were computed by linearly fitting the MSD curves in Fig. 2 using the Einstein relation from 4–10 ps.

^(b)The 2D diffusion coefficient, D, was computed from the arithmetic mean of D_x and D_y.

^(c)All standard deviations are reported across ten independent 5 ns NVT trajectories at 300K.

^(d)The last row is the directional diffusion coefficients of DA in a cubic (100 Å)³ simulation box consisting only of water.

^(e)For “DA-in-water,” D is the 3D diffusion coefficient.

For all species, both the displacement and velocity autocorrelations in the z direction show evidence of the species’ adsorption on the surface, with extremely limited displacements in the MSD_z and evidence of a region of anti-correlation in the corresponding VACF, C_vz, which together reflect the constrained motion in the z-direction. In contrast, the MSD_x and MSD_y plots show evidence of the initial inertial regime followed by diffusive behavior for all species with no significant regions of anti-correlation observed in either C_vx or C_vy.

In order to evaluate the accuracy of DA dynamics within these MD simulations, it is helpful to first benchmark the diffusion constant obtained from our simulations of a fully solvated DA, D = 1.53 × 10⁻⁵ cm²/s (see Table 1, last row), with that obtained from flow injection analysis experiments, D = 0.6 × 10⁻⁵ cm²/s [46]. The correspondence between these two values is impressive given the different ways they were obtained. We can then compare our simulation-derived diffusion coefficient for DA on the 98.2 Å by 97.8 Å graphene surface, 1.92 × 10⁻⁵ cm²/s, to that obtained for fully solvated DA in a cubic (100 Å)² box, 1.53 × 10⁻⁵ cm²/s, which indicates that the overall diffusivity of adsorbed and solvated DA are quite similar, albeit the former is only free to diffuse on the two-dimensional surface.

The results in Figure 2 and Table 1 also showed that the structureless adatom adsorbate diffuses more rapidly than the molecular adsorbates. DA is significantly larger than the atomic adsorbate modeled here and asymmetric in both shape and charge distribution. For comparison, the adatoms are 2.64 Å in diameter, which is slightly smaller than the dimension of the hexagonal lattice spacing of graphene, 2.84 Å across. Although the aromatic ring of DA is the same size as the lattice spacing, the diol and amine groups extend out from the ring in opposite directions, making its molecular structure larger than the lattice spacing. The larger and more extended structure also means that the molecular adsorbate will have additional collisions with the solvating water molecules, which we would expect to result in a more rapid velocity decorrelation, as is evident in C_vx and C_vy in Figure 2.

Among the DA-derived molecular species, small, but consistent, shifts are apparent in comparing the calculated diffusion constants for the protonated vs. deprotonated as well as the oxidized vs. reduced species. The protonated species have smaller diffusion constants: 1.74 vs. 1.92 (×10⁻⁵ cm²/s) for DAH⁺ vs. DA; and 1.95 vs. 2.29 (×10⁻⁵ cm²/s) for DOQH⁺ vs. DOQ. A slightly larger shift can be seen in comparing the diffusion constants of the reduced vs. the oxidized species as well: 1.92 vs. 2.29 (×10⁻⁵ cm²/s) for DA vs. DOQ; and 1.74 vs. 1.95 (×10⁻⁵ cm²/s) for DAH⁺ vs. DOQH⁺. These shifts hold between different DA species, and their consistency across different simulation runs can be seen clearly in Figure S2. We further investigate and discuss the origins of these shifts below.

4.3. Molecular adsorbates show only slight preferences for different lateral positions on the graphene surface.

Previous computational work has shown that the atomic-level structuring of graphene and its chirality in CNTs can influence the surface dynamics of an atomic adatom [50]. In this section we compare the lateral distributions of adatom(DA), the center of mass (COM) of the molecular DA species, and the COM of their constituent chemical moieties. Figures 3 & 4 display lateral distributions of the adsorbed species projected onto the graphene surface, for the COM of each species (Fig. 3) as well as the COM of various chemical groups within DA and DOQ (Fig. 4).

Figure 3: Lateral COM distributions of adatom(DA) and the molecular DA species on flat graphene.

From left to right, the five subplots show results for adatom(DA), DA, DOQ, DAH⁺, and DOQH⁺, respectively. The projected COM coordinates on the surface were wrapped into 4 unit cells, which are separated by dashed lines. The dot-dashed lines represent the carbon-carbon bonds. Results were collected from ten 5 ns NVT trajectories at 300K at a recording interval of 0.01 ps, and the colormaps show the distribution density on the carbon surface with a spatial resolution of 0.1 × 0.1 Ų.

Figure 4: Lateral distributions of three functional groups of (a) DA, (b) DAH⁺, (c) DOQ, and (d) DOQH⁺, all on flat graphene.

From left to right, the three plots show results for the phenyl ring, diol/quinone group, and amine group, respectively. The projected COM coordinates for each moiety on the surface were wrapped into 4 unit cells, which are separated by dashed lines. The dot-dashed lines represent the carbon-carbon bonds. Results were collected from ten 5 ns NVT trajectories at 300K at a recording interval of 0.01 ps, and the colormaps show the distribution density on the carbon surface with a spatial resolution of 0.1 × 0.1 Ų.

In Figure 3, the 2D COM distributions of adatom(DA) show a clear preference for the adatom to be located at the center of each hexagonal ring. However, no such preference is seen for the COM of the molecular DA species. Indeed, in Figure 4, only slight preferences can be seen for the phenyl ring and diol/quinone COM placements that correspond to a favorable slipped ring stacking configuration [62, 63], and no lateral patterning is apparent for the location of the amine’s COM.

4.4. Vertical distributions of the amine groups depend on protonation.

Vertical distributions shown in Figure 5 characterize the spatial distribution of the adsorbate along the direction normal to the graphene surface, where the distance, d, is computed between the COM of a molecule or a chemical group and the closest point on the carbon surface.

Figure 5: Vertical distributions of the center-of-mass (COM) and different moieties of DA and DOQ on the graphene surface.

From left to right, the four plots show the vertical distributions of the adsorbate COM, its aromatic ring, its diol/quinone moiety, and its amine group, respectively. Colored curves within each subfigure indicate different adsorbates. d is the distance to the surface, and p(d) is its probability. Data for each distribution were collected from ten 5 ns NVT trajectories at 300K at a recording interval of 0.01 ps.

The vertical distributions of the phenyl ring and diol/quinone moieties are relatively narrow, located just above the graphene surface at about 3 Å, and remain nearly identical across all DA species. In contrast, the vertical distributions of the amine group are much broader, peak at about 6 Å above the graphene surface, and display a significant dependence upon the amine protonation state (see Figure 5, right-most panel). For the protonated species, the vertical distributions of the amine group shift further from the surface for both the oxidized and reduced species.

To better understand this shift, in Fig. 6 we focus on the peaks within these vertical amine distributions and show a series of representative DA and DAH⁺ configurations at those distances. In Fig. 6a, the amine distance distributions of the charge-neutral species, DA and DOQ, are remarkably similar, as are those of the protonated species, DAH⁺ and DOQH⁺. For both neutral species, there is a smaller peak at about 3.7 Å (i), a shoulder at about 5.0 Å (ii), and a larger peak at 5.9 Å (iii). For both protonated species, however, there is no peak at 3.7 Å, the shoulder at ~ 5.0 Å is greatly reduced (iv), and the last peak is even larger and further shifted from the surface at 6.1 Å (v). As can be seen in the corresponding configurations in Fig. 6c, the peak closest to the surface corresponds to a configuration where the amine group is approximately the same distance from the surface as the phenyl ring. The shoulders in (ii) and (iv) correspond to configurations where one bond in the carbon linker between the phenyl ring and the amine group has rotated away from the surface. Finally, the largest peaks at (iii) and (v) represent configurations with the linker fully rotated out away from the surface into the solvating water layer. This last configuration is the most probable one for all four species, and the dominant configuration for the protonated DA species. In this configuration, the amine group extends into the bulk water where it can more readily form hydrogen bonds and, when protonated, its positive charge can interact more directly with the polar solvent.

Figure 6: Amine group distributions and configurations.

(a) Vertical distributions of the amine groups from Fig. 5 are shown here in more detail for DA, DOQ, DAH⁺, and DOQH⁺. Peaks in these distributions are labeled and correspond to the vertical distances and conformations shown in (b) and (c). In (b), the positions are listed for the peaks of the vertical distance distributions, which were obtained from curve-fitting using Gaussian functions. In (c), representative configurations of the adsorbate and the amine-solvating waters (within 5 Å of the amine N) are shown for each identified distance position for DA (i-iii) and DAH⁺ (iv, v).

4.5. Differences in D between DA species reflect differences in their solvent interactions.

To understand the differences we observed in D across various DA species adsorbed at the graphene-water interface, it is helpful to separately consider the influence of the graphene surface and the aqueous solvent.

Lateral distributions of the adsorbates and their chemical groups in Figures 3 & 4 show only a slight dependence on the underlying graphene structure. In addition, the trends that are present do not explain the observed trends in D values. The lateral COM distributions reveal significant energetic barriers only for the adatom(DA), however, this species diffuses the most rapidly of all those simulated. Moreover, if the energetic barriers of the graphene surface were the dominant factor, DA might be expected to diffuse the most rapidly of the molecular adsorbates and DOQH⁺ the most slowly, based upon the degree of ordering displayed in the four panels in Figure 4. Instead, these two species have similar D values, while DOQ diffusion is the most rapid and DAH⁺ is the slowest. Taken together, these observations make it clear that the differences in diffusion constants observed in our simulations cannot be attributed to the observed differences in interactions with the pristine graphene surface, leading us to consider in more detail the influence of the aqueous solvent.

To test the hypothesis that it is the solvent interactions that give rise to the observed differences in diffusivity, we simulated the diffusion of the neutral species, DA and DOQ, on a pristine graphene surface with no solvent. The results are shown in Figure 7 – the differences between the MSDs of DA and DOQ at the graphene-aqueous (“solvated”) and graphene-vacuum (“vacuum”) interfaces are shown in Figure 7a for ten trials for each case, and a better view of the MSDs of the two species at the graphene-vacuum interface is shown in Figure 7b for all forty trials of each species. As expected, the curves show that inertial dynamics dominates the motion of the DA species at the graphene-vacuum interface over a much longer time window than in the solvated case, which precludes the calculation of a diffusion constant in this time window. Moreover, considering the artificial lack of thermal fluctuations on the simulated graphene surface itself, the observed MSD curves cannot be taken as indicative of the realistic graphene-vacuum dynamics of these species. Nonetheless, this approach allows us to directly remove the influence of water within these simulations and enables us to observe two key differences between the dynamics of the adsorbates at the solvated and vacuum interfaces. First, the solvent is clearly responsible for a dramatic slow down in the diffusion of the adsorbed species. Second, the differences between DA and DOQ, which can be reliably seen in the segregation of the ten pink and ten blue traces for the solvated species in Figure 7a, are not apparent in the species on the graphene-vacuum interface in Figure 7b, where no similar segregation can be seen among the forty blue DA and forty pink DOQ traces. We therefore conclude that the difference between the D values observed in our simulations of DA and DOQ arise from their interactions with the solvating water molecules.

Figure 7: In-plane mean squared displacements of DA and DOQ at the aqueous-graphene and vacuum-graphene interfaces.

(a) The comparison between DA (blue) and DOQ (pink) at the two interfaces is shown for ten independent 5 ps NVE vacuum simulations (lighter colors), and ten independent 5 ps NVT solvated simulations at 300K (darker colors), both at a recording interval of 0.01 ps. (b) The MSDs for DA (blue) and DOQ (pink) are shown from forty independent trajectories each for the NVE vacuum simulations. Please note the different scales of the MSD axes in the two plots.

The Stokes-Einstein equation [64, 65, 66, 67] describes how the diffusion constant, D, of a fully solvated spherical particle in non-turbulent flow depends on various properties of both the solvent and the diffusing particle:

$$D=\frac{k_{\text{B}}T}{c\pi \eta R_{\text{H}}},$$ (1)

where c is a numerical constant depending on boundary conditions at the solvent-particle interface, k_B is the Boltzmann constant, T is the temperature, η is the solvent viscosity, and R_H is the hydrodynamic radius of the diffusing particle [68, 69, 64].

The direct applicability of the Stokes-Einstein (SE) equation is limited in this case since the adsorbates are not fully solvated. In addition, DA is not spherical and only moderately larger than the solvating water molecules – both of which can give rise to deviations from the SE-described behavior [70, 71, 72]. Finally, significant interactions between the solvent and the solute are expected to yield an effective hydrodynamic radius larger than the actual particle radius, the size of which depends on the strength of those interactions [68]. Since changes in asphericity and size are negligible between the different DA species, we focus here on these expected variations in the effective R_H to determine if they can explain the differences in diffusivity observed in the simulations between the neutral and protonated species and between the oxidized and reduced species.

First we consider the observation that the charged species, DAH⁺ and DOQH⁺, both display a lower D value in our simulations than their uncharged counterparts, DA and DOQ (see Table 1). The positively-charged DAH⁺ and DOQH⁺ have stronger electrostatic interactions with water than the neutral DA and DOQ species, which will increase their effective hydrodynamic radii and correspondingly decrease their diffusivities, D. Indeed, simulations have shown that the effective hydrodynamic radius of a small nanoparticle directly depends upon its charge [65]. In addition, the shift in the amine position towards the solvent in the protonated species (see Figure 6) clearly reflects its increased attractive interactions with the solvent. Moreover, this amine shift enhances the effect of its additional charge on the effective hydrodynamic radius by enabling it to interact with the solvent in a manner more closely mimicking that of a fully solvated molecule. We therefore conclude that the observed decrease in the diffusivities of DA and DOQ upon protonation results from increased interactions with the solvent, due to both the additional electrostatic interactions between the polar solvent and the charged species as well as the corresponding shift towards more solvated configurations for the protonated amine.

Second, we consider the observed trend that the oxidized species, DOQ and DOQH⁺, both display a larger D value in our simulations than their reduced counterparts, DA and DAH⁺ (see Table 1). The difference between these species lies in the oxidation of the two alcohol groups to form a quinone group. Experimental studies have shown that the diffusion of a water molecule is significantly slowed when it moves through a solvent capable of forming hydrogen-bonds [73]. Importantly, the alcohols in DA and DAH⁺ are able to participate in hydrogen bonding with the solvating water molecules as both hydrogen bond donors and hydrogen bond acceptors, while the ketones that constitute the quinone moiety in DOQ and DOQH⁺ are only able to act as hydrogen bond acceptors and can thus form fewer hydrogen bonds with the solvent. Despite this difference, the position of the diol/quinone moiety does not shift vertically upon oxidation, which reflects the strength of the favorable attractions between the phenyl ring and the graphene surface. However, the diol/quinone moieties still interact with solvating water molecules, and the additional hydrogen bonding possible for the alcohol groups in the DA and DAH⁺ species should increase their effective hydrodynamic radii, in comparison to those of DOQ and DOQH⁺, and thereby reduce their D values, which is precisely the trend observed in the simulations.

To summarize, given the complexities of the aqueous-graphene interface and the solute-solvent interactions, the Stokes-Einstein equation cannot be used to predict the precise diffusion constants for these molecular DA species. However, the SE relation between diffusivity and the effective hydrodynamic radius explains both the observed trends in D, demonstrating the importance of the solvent in determining the dynamics of these DA species on the microelectrode surface.

5. Discussion

The simulations in this study provide novel atomistic-level detail on the structure and dynamics of various dopamine species adsorbed onto a pristine graphene microelectrode surface. These details yield unique insight regarding the necessary components for dopamine adsorption to the microelectrode surface, details on diffusion timescales and determinants, and implications for various experimental conditions. The main conclusion is that dopamine and its oxidation product DOQ have fast diffusion on a graphene surface, and thus they should be able to sample many domains on a microelectrode surface.

Adsorbed dopamine stability and structure.

First, we find that DA, DOQ, and their protonated counterparts all readily adsorb from the aqueous phase onto a pristine, flat graphene surface. For all species, adsorption occurred rapidly, and not a single desorption event was observed over the ns timescale of our equilibrium MD simulations. Moreover, since the OPLS-AA force field employed in this work is expected to slightly underestimate the attractions acting between the adsorbate and the graphene surface [59], adsorption is expected to be even more robust in the physical system. Although the standard FSCV holding potential of −0.4 V was designed to maximize DA adsorption [24] and surface oxidation is known to enhance adsorption [31, 30], it is important to note that we find neither an applied potential nor surface oxidation necessary for a single DA to adsorb to and remain on the basal plane of pristine graphene. This conclusion is supported by various experimental studies that point to DA’s ability to adsorb directly to pristine graphene surfaces, from early studies on freshly fractured graphene [31] to more recent work on HOPG surfaces [34].

Second, the vertical distributions shown in Figure 6a and Figure 6c(v), indicate that the protonated amines in our simulations (which have no applied potential) extend out into the solvent at nearly all times and therefore cannot be a primary contributor to the favorable energetic interactions driving the robust surface adsorption we observed for DAH⁺ and DOQH⁺. While early experimental work appeared to show that amine groups were necessary for adsorption [25], our conclusions here are supported by later work by Allred and coworkers demonstrating the ready adsorption of catechols, even those lacking an amine group, to freshly fractured glassy carbon surfaces [31]. We note, however, that the same study still observed an increase in the adsorption of DAH⁺, with its positively-charged amine, to oxidized carbon microelectrode surfaces [31], as have subsequent experiments [30, 74, 75]. Interestingly, the sensitivity of the amine configuration to its charge state, as observed in these simulations, suggests that DA’s interactions with the graphene surface and the solvating waters will shift significantly during a CV experiment as the applied potential scans over a range of voltages; differences in DA’s configuration at each voltage will play an important role in determining the shifting equilibrium constant between adsorbed and desorbed DA species during a cyclic scan.

Dopamine diffusion dynamics.

We have also gained new insight into the dynamics of these dopamine species in bulk solvent as well as on the pristine graphene surface, both at the aqueous and vacuum interfaces. To start, we note again the similarity between the diffusion constants we calculate here for DA in bulk water (1.53 × 10⁻⁵ cm²/s) and on the graphene surface (1.92 × 10⁻⁵ cm²/s). Given the experimentally-observed adsorption-related lag time for DA signal detection [30, 44], this similarity suggests that adsorption and desorption are occurring at a slower rate than diffusion on the electrode surface.

Importantly, simulations were performed both in the presence of explicit solvating waters as well as in a vacuum for comparison purposes, enabling us to determine the effect of the aqueous interface on analyte dynamics. First, we note that the diffusion of DA and DOQ at the graphene-vacuum interface is far faster than at the graphene-water interface (Fig. 7a), and the difference between DA and DOQ diffusion at the graphene-water interface disappears at the graphene-vacuum interface (Fig. 7b). These results demonstrate the essential role that solvating waters play in determining the adsorbate’s motion on pristine graphene. Indeed, the differences in diffusivities between the protonated and deprotonated and the oxidized and reduced species at the graphene-water interface can be fully explained by differences in their effective hydrodynamic radii in the solvating water phase.

These observations lead us to three conclusions regarding the determinants of analyte motion on the graphene microelectrode surface. First, small changes in an analyte’s chemical composition can easily influence its surface diffusivity by altering its effective hydrodynamic radius in the solvating phase – even if the changes do not appreciably influence its interactions with the graphene surface itself. Second, slight changes to the internal structure of a diffusing analyte – for instance, when an applied potential pulls particular moieties closer to the electrode surface during a portion of a cyclic scan – may also influence its surface diffusivity, either solely through changes in analyte-solvent interactions or more directly through shifts in the analyte-electrode interactions. In the case of dopamine, the protonated amines we simulated preferred to extend out towards bulk water and thereby interact with more solvating water molecules. However, under a negative holding potential, the protonated amine would be attracted to the surface and thus unable to participate in some portion of these water interactions. As a result, the holding potential could either increase or decrease DAH⁺’s surface diffusivity, depending on the relative balance between an increase in the diffusion rate, from the expected decrease in the effective hydrodynamic radius, and a decrease in the diffusion rate rate, from the expected increase in the analyte-surface interactions. Third, we conclude that analyte surface dynamics will be sensitive to changes in the dynamics of the solvating water. Results from multiple studies suggest that the mobility of water under nanoscale confinement depends sensitively on the geometry of the confining regions and the geometry-dependent energy landscape experienced by water at the surface [76, 77, 78, 79, 80]. Recent innovations in carbon microelectrode architecture that involve the introduction of nanoscale patterning or pores will clearly influence the dynamics of the solvating water. It is already recognized that the diffusion dynamics of the analyte towards and away from the electrode will be influenced by these geometric constraints, and this has been seen in the thin layer effects observed for electrode surfaces with micron scale roughness [37, 15, 39, 38].

Many microelectrodes have more defects or functional groups, but an investigation of the influence of additional functional groups or other defects on the graphene surface lies outside the scope of this initial work. However, we note that any site-specific surface interactions with the analyte, for instance between a positively charged amine group on DA and a graphitic oxide species, is expected to significantly impact its surface dynamics or even arrest its motion for lengths of time. The presence of multiple adsorbates – of the analyte, its oxidized derivative, or other contaminating organic material – may also significantly complicate and alter diffusion dynamics. Future studies will be needed to address these questions.

Implications for Experimental Timescales.

The simulation-derived diffusivities of various DA species at the pristine graphene-water interface provide the information needed to translate observed FSCV scan-rate dependencies to length-scales over which a DA analyte can be expected to diffuse during a single scan. Evidence has long suggested that certain domains on carbon fiber electrode surfaces have an increased electrochemical activity [48, 81]. Even pristine graphene surfaces have recently been shown to display spatially heterogeneous electrode activity [82]. In one particularly interesting study, Oleinick and coworkers identified ranges of scan rates between which DA detection varies considerably [48]. They concluded that at the lowest scan rates (≤ 100 V/s), all adsorbed DA are able to diffuse to electrochemically active domains for oxidation, while at the highest scan rates (≥ 1000 V/s), only adsorbed DA within an active domain would be oxidized and detected. If we take the value of D = 1.73 × 10⁻⁵ cm²/s for DAH⁺ on pristine graphene, as calculated in our simulations, and use it to estimate the root mean squared distance traveled by DAH⁺ during a single oxidation scan of FSCV, these timescales map to estimated diffusion distances of ≤ 3.4 μm for the fastest scans and ≥ 10.8 μm for the slower scans. For a typical scan rate of 400 V/s, this distance corresponds to 5.4 μm. Notably, for slower scans, the diffusion distance is on the order of the diameter of a typical carbon-fiber electrode. Of course, this estimate assumes that diffusion is occurring across a pristine and homogeneous graphene surface, which neglects entirely the differences in diffusivities that would be expected between the regions of differing electrochemical activities. Nonetheless, it provides a baseline estimate for how far we might expect DAH⁺ to diffuse during an experiment, as well as the magnitude of the difference expected between diffusion during a fast and a slow scan.

These experiments are the first to look directly at the diffusion of dopamine, DOQ, and their protonated species on pristine graphene. The results show extremely fast diffusion on the surface, on the order of solution diffusion rates. Thus, DAH+ and DOQH+ will sample much of the surface as they diffuse on a graphene that is the size of a typical microelectrode. This insight is the first step in understanding dopamine-carbon interactions at electrodes, which will enable the development of better electrode surfaces. Future studies will look at the effects of surface functional groups and applied voltage, and atomistic simulations will prove to be an important tool to predict surface behavior and thus electrochemistry at electrodes.

6. Conclusions

Carbon microelectrode surface structure can dramatically influence the timeresolution and signal-to-noise ratio of electroanalytical measurements, as well as impact their sensitivity and specificity [15, 36]. However, atomistic simulations have not yet been employed to probe how the transport of molecular neurotransmitters on these carbon surfaces depends upon their structural features. In this work, we simulated the diffusion of DA, DOQ, and their protonated counterparts on the simplest of these surfaces – the pristine basal plane of graphene. We found that adsorption on this defect-free surface was rapid and did not require a holding potential. In addition, the molecular adsorbate’s lateral position is not significantly influenced by the underlying graphene lattice, while the charge on the amine group does significantly impact its distance from the surface. We also found that adsorbate diffusion on the surface was relatively rapid and highly dependent upon interactions between the adsorbates and the solvating liquid water, giving rise to differences in the diffusivities between the protonated and deprotonated and between the oxidized and reduced species. This investigation has advanced our understanding of the diffusion-controlled surface transport for dopamine on the pristine graphene surface and has laid the groundwork for future investigations to determine the influence of more complex microelectrode surface structures on analyte dynamics. Such studies will be essential for using atomistic simulations to predict dopamine surface diffusivity and how it influences electrochemistry.