# Structure and Dynamics of Adsorbed Dopamine on Solvated Carbon Nanotubes and in a CNT Groove

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modeling

#### 2.1. Flat and Curved Pristine Carbon Surfaces

**Flat graphene.**We modeled a single layer of pristine flat graphene with a lateral box size of $98.2419\times 97.8420$ Å${}^{2}$, using 3D periodic boundary conditions. A single layer of graphene was used as no differences were observed between adsorbate dynamics on a single and a triple layered fixed carbon surface [18].

**Single-walled CNTs.**To look at analyte motion on various CNT surfaces, we modeled single-walled CNTs of three diameters and two helicities: armchair and zigzag. Armchair CNTs included $(15,15)$-CNT, $(22,22)$-CNT, and $(29,29)$-CNT, while the zigzag CNTs included $(0,26)$-CNT, $(0,38)$-CNT, $(0,51)$-CNT. Within each set, the radii are approximately 10, 15, and 20 Å, respectively. Details on the CNT diameters, lengths, and helicities are listed in Table S1. In addition, images of the CNTs can been seen in Figure 1. CNTs larger than 20 Å in diameter were chosen to avoid complications arising from significant confinement effects, which are more prominent in CNTs under 15 Å [26,27]. CNTs of of various lengths—ranging from 25 Å to 100 Å—were simulated in order to correct for finite size issues arising from the periodic boundary conditions, as discussed in the SI [18,37,38,39,40]. Results are generally presented from 100 Å-long CNTs; however, extrapolations to the infinitely sized systems are included for key cases.

**CNT groove.**We also placed two $(15,15)$-CNTs in a parallel alignment along the z-direction to construct a one-dimensional CNT groove. The CNTs are both 100.7 Å long and separated by $3.4$ Å, corresponding to the sum of the van der Waals (vdW) radii of the closest carbon atoms on the different CNTs [41].

#### 2.2. DA and DOQ Adsorbates

## 3. Results and Discussion

#### 3.1. Solvated Adsorbate Diffusivities Depend on Surface Curvature

**Curvature dependence is observed for DA, DAH${}^{+}$, DOQ, and DOQH${}^{+}$.**Table 2 presents the diffusion constants obtained for these four species on both the interior and exterior surfaces of $(15,15)$-CNT, along with the flat graphene results. From these measurements, we find that the curvature-dependence is similar across all four species.

#### 3.2. Dependence Does Not Arise from Curvature-Induced Shifts in Surface Roughness

**Lateral distributions of molecular adsorbates are similar across curvatures.**In Figure 4, we plot the lateral distributions for the adatom(DA), DA, and its moieties on three differently curved surfaces: the exterior of a $(15,15)$-CNT nanotube, flat graphene, and the interior of a $(15,15)$-CNT nanotube. By comparing these distributions to the underlying hexagonal aromatic ring pattern of the carbon surfaces, we can observe how curvature-induced differences in the energy surface roughness influence the placement of these atomic and molecular adsorbates.

**Diffusion coefficients for zigzag and armchair CNTs are indistinguishable.**Helicity-dependent diffusion of atomic adsorbates on CNT surfaces has been previously observed in simulations, where different diffusive pathways were observed on armchair and zigzag CNT surfaces due to the surface energy landscapes that emerged upon curving graphene in different directions [23,48]. To probe this effect for our solvated system, we simulated the diffusion of both DA and adatom(DA) on the interior and exterior surfaces of highly curved armchair and zigzag CNTs. Figure 5 shows the two CNT structures with 10 Å radii ($(15,15)$-CNT and $(0,26)$-CNT) as well as the ${D}_{\perp}$, ${D}_{\Vert}$, and 2D D values obtained from these simulations. The corresponding results on flat graphene are also shown in each case for comparison.

**Curvature dependence of D disappears in the absence of solvent.**The negligible influence of the carbon surface’s hexagonal patterning on DA’s lateral distributions in Figure 4 suggests that the differences in D between the CNT surfaces of various curvature in Figure 3 and Table 1 do not actually arise from curvature-mediated changes to the energetic interactions between the adsorbate and the surface. The lack of dependence of DA diffusion on CNT helicity in Figure 5 supports this conclusion.

#### 3.3. Adsorbate Structure Depends on Curvature, Charge, and Solvation

**The distance of the adsorbate above the surface depends on curvature, charge, and solvation.**The vertical distance, d, is defined as the distance between the COM of a moiety and its closest point on the carbon surface. Figure 7 displays the vertical distributions for the aromatic ring (left column), the diol/quinone (middle column), and the amine group (right column) on the three surfaces. DA and DOQ distributions are shown at both the carbon:water and carbon:vacuum interfaces, while DAH${}^{+}$ and DOQH${}^{+}$ distributions are only shown at the carbon:water interface.

**Amine configurations are highly variable and display significant curvature dependence.**Given the complex variation observed in the amine vertical distributions, in Figure 8, we investigate in more detail these distributions for DA at the carbon:water interface. The three peaks for the CNT${}_{\mathrm{ext}}$, flat graphene, and CNT${}_{\mathrm{int}}$ distributions have been marked with letters in Figure 8a, their positions are listed in the table shown in Figure 8b, and a sample configuration at the characteristic distance within each peak is shown in Figure 8c.

**The aromatic ring’s tilt angle above the surface depends on curvature, charge, and solvation.**The distributions of the tilt angle between the aromatic ring and the surface are shown in Figure 9 for DA on differently curved carbon surfaces at both the carbon:water (Figure 9c) and carbon:vacuum (Figure 9d) interfaces. In addition, the tilt distributions of DA, DOQ, and their protonated species are shown for flat graphene at the aqueous interface in Figure 9e.

**Adsorbate alignment with CNT axis also depends on curvature and solvation.**In Figure 10, the orientational alignment of DA with the axis of the CNT, as defined by $\theta $ in Figure 10a,b, is shown on differently curved carbon surfaces at the carbon:water interface (Figure 10c) and at the carbon:vacuum interface (Figure 10d). The $\theta $ distributions of DA, DOQ, and their protonated species are also shown for flat graphene at the aqueous interface in Figure 10e.

**Adsorbate solvation shell depends on curvature and influences ${\mathit{R}}_{{H}}$.**According to the Stokes–Einstein equation, the diffusion constant, $D\propto (1/{R}_{\mathrm{H}})$, where ${R}_{\mathrm{H}}$ is the effective hydrodynamic radius, which depends on the magnitude of attractions between the diffusing particle and the nearby solvent molecules. In the case of a particle adsorbed to a surface, solvation is necessarily limited by the presence and geometry of that surface. Although the Stokes–Einstein relation cannot be directly applied in that situation, it does provide a way to think about the influence of the degree of solvation on diffusion, as the magnitude of any favorable interactions between the particle and nearby solvent will influence the particle’s effective hydrodynamic radius, ${R}_{\mathrm{H}}$. To investigate this effect, we calculated the number of solvating water molecules within the first water shell around the DA or DOQ atoms for each surface architecture. A distance of 5 Å was chosen as the cutoff of that first water shell based on the distribution shown in Figure S5. The results are shown in Figure 11a and display a clear trend from fewest solvating waters on the smallest CNT’s interior to the most solvating waters on the smallest CNT’s exterior—as expected given the geometric constraints of the surface. This trend matches that seen in the diffusion constants on different surface curvatures, as seen in Figure 3c. To determine how well this solvation effect can explain the trend in diffusivities, we plotted in Figure 11b the diffusivities from Figure 3c vs. ${\left({N}_{\mathrm{water}}\right)}^{-1/3}$, where ${N}_{\mathrm{water}}$ is the number of waters within 5 Å of a DA atom, since $D\propto (1/{R}_{\mathrm{H}})$, and ${R}_{\mathrm{H}}$ is roughly $\propto {\left({N}_{\mathrm{water}}\right)}^{1/3}$. The correspondence is quite strong, and this effect is even able to explain the overlapping values seen in the diffusivities even as curvature steadily changes for the CNT exteriors and for the $(22,22)$-CNT${}_{\mathrm{int}}$ and $(29,29)$-CNT${}_{\mathrm{int}}$ cases. Since there is a clear geometric trend across these different diameter CNTs, the fact that the number of solvating waters is the same implies that a change in the adsorbate structures, as documented above, must compensate for that change in a way that maintains a similar degree of solvation.

#### 3.4. DA Localizes and Diffuses within a CNT Groove

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Sample Availability

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**Figure 1.**Simulated CNT and graphene surfaces. DA is shown on (

**a**) the exterior surfaces of CNTs of varying curvatures, (

**b**) flat graphene, and (

**c**) the corresponding CNT interiors. In (

**d**), DA diffuses along the exterior groove formed by two parallel $(15,15)$-CNT nanotubes. The dimensions of the CNTs are listed in Table S1, and the solvating water molecules were omitted here for visual clarity.

**Figure 2.**DA and DOQ. The adsorbate structures of DA and DOQ are shown here. The corresponding protonated species, DAH${}^{+}$ and DOQH${}^{+}$, have an additional hydrogen in their positively charged amine groups. The C2–C7 vectors (red arrows) are used to define the orientation and tilt of the adsorbates above the carbon surface.

**Figure 3.**DA diffusion on differently curved carbon surfaces. Results are shown here for the diffusion of DA on the interior (int) and exterior (ext) surfaces of armchair CNTs of varying diameters and flat graphene. (

**a**) The armchair designation [45] refers to the edge morphology of the CNT along the perpendicular direction. Diffusion on the surface in the same direction as the CNT axis is referred to as parallel (‖), while that around the circumference of the CNT is denoted as perpendicular (⊥). All CNTs presented in this table are 100.698 Å along the periodic ‖ direction, and the graphene sheet is $98.2419\times 97.8420$ Å${}^{2}$ in size and periodic in two directions along the surface. (

**b**) The MSDs as a function of time are shown in both surface directions: ⊥ (top panel) and ‖ (bottom panel). (

**c**) The diffusion constants ${D}_{\perp}$, ${D}_{\Vert}$, and the overall 2D D values are computed from linearly fitting the MSD curves in (

**b**) using the Einstein relation, Equation (S4), over the 4–10 ps range. In both (

**a**,

**b**), the carbon surface results are organized from most concave to the most convex.

**Figure 4.**Lateral distributions of adatom(DA) and DA above the CNT and graphene surfaces. The plots show the distribution densities of the adsorbates above the carbon surface. From left to right, the columns show the distributions on the exterior surface of $(15,15)$-CNT, on flat graphene, and on the interior surface of $(15,15)$-CNT, as indicated with the cartoon images above each column. From top to bottom, the rows show the results for adatom(DA) (an atomic adatom with the mass of DA), the COM of DA, and the three COMs of the red-circled DA moieties. The projected COM coordinates are binned with a spatial resolution of $0.1\times 0.1$ Å${}^{2}$ and wrapped into 4 unit cells, which are separated by the dashed lines.

**Figure 5.**Diffusion coefficients of DA and adatom(DA) on armchair and zigzag CNTs. Armchair and zigzag CNTs are two conformations which describe the carbon atom arrangements along the perpendicular direction. The values of the diffusion constants ${D}_{\perp}$, ${D}_{\Vert}$ and the overall 2D D were calculated from the MSDs of the adsorbates on the different surfaces. The 1D diffusion constants on the flat graphene surface along the direction with the same chirality as each CNT direction were chosen for the comparison. Finite system size results are shown here as calculated within the 100 Å long systems.

**Figure 6.**MSDs of DA and DOQ on differently curved carbon:vacuum surfaces. The top and bottom panels show the MSDs as a function of time along two surface directions, ‖ and ⊥, on graphene and on the interior and exterior of the $(15,15)$-CNT. The left and right panels display the results for adsorbates DA and DOQ, respectively. The lines show the average MSD values, while the shaded regions show the standard deviation in that value across ten trials, with red shading for $(15,15)$-CNT${}_{\mathrm{int}}$, green shading for flat graphene, and blue shading for $(15,15)$-CNT${}_{\mathrm{ext}}$.

**Figure 7.**Vertical distributions of DA and DOQ moieties at the carbon:water and carbon:vacuum interfaces. From left to right, three columns show the vertical distributions of the aromatic ring, the diol/quinone moiety, and the amine group, respectively, with d representing the distance between that moiety’s COM and the closest point on the surface. From top to bottom, the six rows correspond to DA, DA in vacuum, DOQ, DOQ in vacuum, DAH${}^{+}$, and DOQH${}^{+}$. Colored curves within each subplot indicate the distributions at the flat graphene or the interior and exterior $(15,15)$-CNT surfaces.

**Figure 8.**Vertical distributions and configurations of DA at the carbon:water interface. Panel (

**a**) shows the vertical distributions of the amine group of DA on flat graphene and on the exterior and interior of a $(15,15)$-CNT. The three peaks in each distribution are labeled and correspond to the distances shown in panel (

**b**) and the sample conformations shown in panel (

**c**). Peak positions in (

**b**) were obtained from curve-fitting using Gaussian functions. In panel (

**c**), only water molecules within 3 Å radius of the nitrogen in the amine group are displayed.

**Figure 9.**Tilt angle distributions of DA and other adsorbates on differently curved and solvated CNT and graphene surfaces. The tilt angle $\varphi $ is defined as shown in (

**a**,

**b**) between the C2–C7 vector (blue arrows) and a vector tangent to the surface at the midpoint of the C2–C7 vector (red arrows). $\varphi $ distributions for DA on differently curved surfaces, plotted as histograms with a binwidth of 0.36${}^{\circ}$, are shown in (

**c**) at the carbon:water interface and in (

**d**) at the carbon:vacuum interface. The results for DA, DOQ, and their protonated counterparts are shown in (

**e**) on solvated flat graphene.

**Figure 10.**Orientational alignment of DA and other adsorbates with the CNT axis direction on differently curved and solvated CNT and graphene surfaces. The orientational angle, $\theta $, is defined as the angle between the C2–C7 vector (blue arrows) and the CNT axis direction (red arrows), as shown in (

**a**,

**b**). $\theta $ distributions of DA on differently curved surfaces, plotted as histograms with a binwidth of 3.6${}^{\circ}$, are shown in (

**c**) for the carbon:water interface and in (

**d**) for the carbon:vacuum interface. The same results for DA, DOQ, and their protonated counterparts are shown in (

**e**) on solvated flat graphene. $\theta $ has a range of $[0,{180}^{\circ}]$; however, the results are wrapped so that $p\left(\theta \right)=p({180}^{\circ}-\theta )$, for all $\theta >{90}^{\circ}$, due to the symmetry of the system.

**Figure 11.**Correspondence between CNT surface, solvating waters, and D. (

**a**) The number of waters in the first solvation shell around DA are calculated across the different surfaces. For a given water molecule, its distance to DA is the shortest distance between its oxygen atom and any the atoms of DA. Only the water molecules that are on the same side of the surface as DA are counted. ${N}_{\mathrm{water}}$ and its statistical errors were computed from 10 trajectories. (

**b**) The diffusion constants, D, from Figure 3c are plotted vs. ${N}_{\mathrm{water}}^{-1/3}$ for DA on a range of differently curved surfaces. A linear fit line is shown here along with the coefficient of determination, ${R}^{2}$.

**Figure 12.**Spatial distributions of DA in a solvated CNT groove. The COM coordinates of DA within a solvated CNT groove formed by two parallel CNT, as seen in a typical configuration shown in (

**a**), are plotted here in both (

**b**) 2D and (

**c**) 3D. The CNT groove is constructed of two parallel, 100 Å $(15,15)$-CNTs. In the 2D distribution plot in (

**b**), locations along the axial direction were wrapped into two unit cells. The gray dashed circles represent the location of the surface carbon atoms, and the black dashed line in the middle at $\perp =0$ Å represents the location on the CNT circumference where the distance between the two CNTs is smallest. The distribution density in region to the left of that dashed line results from configurations where the adsorbate is closest to the CNT on the left, while the density to the right results from configurations where the adsorbate is closest to the CNT on the right. In the 3D distribution in (

**c**), the COM coordinates along the axial direction were wrapped into ten unit cells for plotting.

**Figure 13.**Diffusion coefficients of DA within a CNT groove. The CNT groove is constructed of two 100 Å long, aligned, $(15,15)$-CNTs. (

**a**) Diffusion constants for the solvated CNT groove and a solvated $(15,15)$-CNT${}_{\mathrm{ext}}$ surface are shown here, both from the 100 Å simulation directly (top rows) and from the infinite-system size extrapolation (bottom rows). ${D}_{\Vert}$ is the 1D diffusion coefficient for motion along the CNT groove and axis, and ${D}_{\perp}$ is the 1D diffusion coefficient around the CNT circumference. (

**b**) The axial mean squared displacement of DA is plotted for various surfaces at the carbon:vacuum interface. These MSD results are taken directly from simulations done in the vacuum on 100 Å CNTs and $100\times 100$ Å${}^{2}$ graphene.

**Table 1.**Diffusion coefficients extrapolated to the infinite system sizes. For a subset of the carbon surfaces, diffusion constants for the infinite system sizes, ${D}_{\infty}$, were extrapolated from a series of differently sized finite simulations. The extrapolation was done to correct for unphysical effects that arise from the necessarily finite simulation sizes, and the ${D}_{\infty}$ values thus represent the actual diffusivities expected within the larger physical systems. See SI and Figure S4 for details.

Adsorbate | Carbon Surfaces | ${\mathit{D}}_{\mathit{\infty},\perp}$ ($\times {10}^{-5}$ cm${}^{2}$/s) | ${\mathit{D}}_{\mathit{\infty},\Vert}$ ($\times {10}^{-5}$ cm${}^{2}$/s) | ${\mathit{D}}_{\mathit{\infty}}$ ($\times {10}^{-5}$ cm${}^{2}$/s) |
---|---|---|---|---|

DA | $(15,15)$-CNT${}_{\mathrm{int}}$ | $3.50\pm 0.15$ | $1.41\pm 0.19$ | $2.45\pm 0.13$ |

Flat Graphene | $1.27\pm 0.07$ | $1.22\pm 0.10$ | $1.24\pm 0.06$ | |

$(15,15)$-CNT${}_{\mathrm{ext}}$ | $1.17\pm 0.02$ | $1.06\pm 0.05$ | $1.12\pm 0.03$ |

**Table 2.**2D diffusion coefficients of DA, DOQ, and their protonated counterparts. The values of the overall 2D diffusion constant, D, were calculated from the MSDs of the adsorbates on the interior of the armchair $(15,15)$-CNT, flat graphene, and the exterior of the armchair $(15,15)$-CNT. Finite system size results are shown here as calculated within the ≈100 Å long systems.

D ($\times {10}^{-5}$ cm${}^{2}$/s) | ||||
---|---|---|---|---|

DA | DAH${}^{+}$ | DOQ | DOQH${}^{+}$ | |

(15,15)-CNT_{int} | $3.34\pm 0.26$ | $3.24\pm 0.21$ | $3.72\pm 0.29$ | $3.65\pm 0.35$ |

Graphene | $1.92\pm 0.07$ | $1.74\pm 0.07$ | $2.29\pm 0.16$ | $1.95\pm 0.14$ |

(15,15)-CNT_{ext} | $1.30\pm 0.04$ | $1.20\pm 0.06$ | $1.53\pm 0.10$ | $1.37\pm 0.05$ |

**Table 3.**Diffusion coefficients of DA, DOQ, DAH${}^{+}$, and DOQH${}^{+}$ in a solvated CNT groove. The CNT groove results shown here are reported directly from the finite 100 Å-long CNT simulations.

Adsorbate | ${\mathit{D}}_{\Vert}$ ($\times {10}^{-5}$ cm${}^{2}$/s) | ${\mathit{D}}_{\perp}$ ($\times {10}^{-5}$ cm${}^{2}$/s) |
---|---|---|

DA | $1.82\pm 0.09$ | $0.02\pm 0.01$ |

DOQ | $1.98\pm 0.17$ | $0.04\pm 0.03$ |

DAH${}^{+}$ | $1.60\pm 0.10$ | $0.02\pm 0.01$ |

DOQH${}^{+}$ | $1.63\pm 0.05$ | $0.02\pm 0.00$ |

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**MDPI and ACS Style**

Jia, Q.; Venton, B.J.; DuBay, K.H.
Structure and Dynamics of Adsorbed Dopamine on Solvated Carbon Nanotubes and in a CNT Groove. *Molecules* **2022**, *27*, 3768.
https://doi.org/10.3390/molecules27123768

**AMA Style**

Jia Q, Venton BJ, DuBay KH.
Structure and Dynamics of Adsorbed Dopamine on Solvated Carbon Nanotubes and in a CNT Groove. *Molecules*. 2022; 27(12):3768.
https://doi.org/10.3390/molecules27123768

**Chicago/Turabian Style**

Jia, Qizhang, B. Jill Venton, and Kateri H. DuBay.
2022. "Structure and Dynamics of Adsorbed Dopamine on Solvated Carbon Nanotubes and in a CNT Groove" *Molecules* 27, no. 12: 3768.
https://doi.org/10.3390/molecules27123768