Confinement and Diffusion of Small Molecules in a Molecular-Scale Tunnel

Multi-step reaction cascades can be designed to include channeling mechanisms, which provide electrostatic or steric control over intermediate transport such that intermediates do not escape to the bulk between active sites. Physical con ﬁ nement of the intermediate pathway between sites retains intermediate from bulk access and thus provides high transport ef ﬁ ciency. In this work, we use molecular dynamics to study the transport of intermediates (charged oxalate and neutral ethanol) inside a nanochannel represented by a single-walled carbon nanotube (SWCNT). This approach reveals that solvent orientation highly impacts intermediate transport. At small nanochannel diameter near 1 nm, highly structured solvent water and Knudsen diffusion decreases effective intermediate diffusivity. Finally, modi ﬁ ed SWCNT termini with electrostatically-charged carboxylate groups are shown to increase intermediate retention for both charged and uncharged intermediates by up to ﬁ ve-fold. When catalyst sites are located within the nanochannel, decreased diffusion rate and increased retention time will enhance cascade ef ﬁ ciency. an the terms of the (CC of the in any medium, the original work is

The integration of multi-step reaction cascades within a single catalytic platform is an efficient way to control yield and selectivity. 1 Such a design seeks to prevent diffusional loss of reaction intermediates by controlling transport between reaction steps. 1 Mechanisms that achieve such transport control are collectively known as substrate channeling. 2 Various substrate channeling mechanisms have been studied, including confinement of intermediate inside molecular tunnels, 1,3 electrostatic interactions between intermediate and catalyst surfaces [4][5][6][7][8][9] and chemical swing arms. [10][11][12][13][14] As a naturally-occurring example, the nano-scaled molecular tunnel present in tryptophan synthase (TS), a bifunctional enzyme, transfers an intermediate, indole, between two active sites with high diffusion rate (⩾1000 s −1 ), comparable to conversion rates. 10,15 This manuscript represents the first steps toward understanding the molecular-scale kinetics and transport in such a channeling system.
Our previous model of nano-scaled confinement using continuum, finite element methods demonstrated that confinement enhances the yield of a two-step reaction system compared to a nonconfined system. 16 This nano-scale model treated reaction and diffusion inside a single-walled carbon nanotube (SWCNT) and considered a range of geometric, transport and kinetic parameters. However, nano-scale molecular interactions were not considered and can significantly affect the transport properties of the system.
The solvent structure inside a SWCNT plays a critical role in transport through that region. Carbon nanotubes have been studied extensively for water confinement. Both experimental 17,18 as well as simulation [19][20][21][22][23][24] studies show that, even though CNT surfaces are hydrophobic in nature, water can easily fill the CNT interior through open ends. However, water molecules confined inside SWCNTs of diameter approaching molecular scales exhibit different behavior than in the bulk. 19 For diameters less than 1 nm, water molecules experience the hydrophobicity of the SWCNT wall, resulting in a single-file hydrogen bonding pattern. 25 As SWCNT diameter increases, a transition from tubular to bulk pattern is observed, accompanied by increased water density. 25,26 In this work, transport of the intermediates inside the nanochannel is studied by using molecular dynamics (MD). We represent the molecular tunnel with single-walled carbon nanotube (SWCNT) and consider negatively charged, oxalate that is found in abundance in biological reaction cascades. [27][28][29] In contrast, ethanol is considered as an uncharged intermediate species, because its size is comparable with oxalate. We observe the variation in the diffusivity of intermediate within the nanochannel and study the structure of aqueous solvent surrounded to the intermediate in this region. Finally, we modified the nanotube ends using electrostatic charges in order to further retain charged and polar intermediates.

Methods
A carbon-ended, armchair, single-walled carbon nanotube (SWCNT) was used as a nanoscale confined tunnel (Fig. 1). Armchair carbon nanotubes have lower local charge magnitudes than zigzag SWCNT. 19 This provides more control to study intermediate charge effects. Therefore, armchair SWCNT was used in this study. Transport of a negatively charged small molecule (oxalate, C 2 H 4 − ) and a neutral molecule (ethanol, C 2 H 5 OH) were studied within this tunnel. Specifically, molecular dynamics (MD) studies were performed to track the motion of intermediate molecule inside the SWCNT for 5-30 ns. We performed these studies for four different SWCNT diameters: 1.08 (8,8), 1.35 (10, 10), 2.06 (15,15) and 3.02 nm (22,22). The effect of length: diameter ratio on retention time was studied with SWCNT diameters 1.35, 2.06 and 3.02 nm by varying this ratio from 1:1 to 10:1.
In our previous work, an FEM continuum model demonstrated higher yield with increased distance between active sites and the tube ends. 16  boundary conditions (PBC) were applied to all MD simulations. The carbon nanotube/intermediate couple was first solvated with SPCE water molecules in a cubic box. Initial box size was determined by keeping a 1.5 nm minimum distance between the periodic boundary and SWCNT (initial box volume ∼1000 to 3000 nm, 3 depending on SWCNT diameter). System energy was minimized before equilibration using the steepest descent method, followed by NVT (0.1 ns) and NPT (1.0 ns) equilibration with position restraints for both the SWCNT and intermediate. Finally, the MD simulation was performed under NPT ensembles for 5-20 ns (2 fs timestep), repeating 30 times for each system. During the MD simulation, four carbon atoms were position-restrained, two at each end of the SWCNT, in order to fix the SWCNT in place. The system temperature was coupled at 300 K by a velocity rescale thermostat 36 and the pressure was kept constant at 1 bar using the Parrinello-Rahman scheme. 37 A neighbor searching algorithm used a 1 nm cutoff value for both short-range electrostatic and Van der Waals interactions. Long-range electrostatic interactions were calculated using the Particle-mesh Ewald method (PME). 38 For non-homogeneous systems, the PME method can generate unwanted artifacts in systems with net charge. 39 Therefore, in order to neutralize negative charges of oxalate or/and carboxylates, fully dissociated Na + ions were added outside the SWCNT. 40,41 With this approach, ionic strengths ranging from 10 to 23 mM and debye lengths from 86 nm to 64 nm were obtained. A Verlet cutoff scheme was used to calculate non-bonded interactions on a GPU accelerator. 42 Data analysis.-Time-coordinate data from MD trajectories was analyzed using the python packages MDAnalysis 43,44 and GromacsWrapper. 45 This data was used to determine the simulation time at which the intermediate escapes the SWCNT, i.e. retention time, and to calculate diffusivity from mean-square displacement.
During MD simulation, the intermediate's initial position was chosen as the geometric center of the SWCNT, allowing the intermediate to diffuse equal lengths in either direction towards the SWCNT terminus. The mean-square displacement (MSD) was calculated as a function of lag time, τ. Three-dimensional displacement (axial and radial) of the intermediate was considered to understand the interaction between the wall and intermediate. For a three-dimensional system, the diffusion coefficient, D, can be calculated using Einstein's equation 46 : where τ is the lag time over which displacement occurs. Neglecting a brief induction period of ∼10 ps simulation time, mean-square displacement (MSD) was calculated over the total simulation time for varying lag times. The MSD varies linearly for 0 < t < 100 ps; at larger lag times, uncertainty grows due to reduced sampling. 47 Therefore, a straight line was fitted to the MSD plot over the 0-100 ps range of lag time, and diffusivity calculated from the slope of this line according to Eq.
The radial density function (RDF, ( ) g r ) provides information about the probability of finding the molecule at a distance, r, from a reference position. 50 In this work, RDFs were calculated between the center of the SWCNT and the water molecules inside the SWCNT, as well as between the center of the SWCNT and carboxylate groups at the SWCNT termini, and normalized with the maximum density. The RDF is calculated as follows: where, ( ) r r is the local particle density and r the overall particle density.  Carboxylate groups (COO − ) was attached to SWCNT termini by replacing one or more terminal hydrogen atoms. Carboxylate carries −1 net charge for pH above 3.75. Partial negative charge is present on the oxygen atoms of carboxylate due to high electronegativity, making carboxylate a slightly polar molecule. 51 Dissolved, positively-charged sodium atoms were added outside the SWCNT in equal number to carboxylate and oxalate to maintain overall electroneutrality. This led to increasing ionic strength in the system as the number of carboxylate groups increased. Therefore, the ionic strength of the system ranged from 10.84 mM with no carboxylate end-groups to 23.02 mM with 8 COOper terminus. For a nano-scale confined system, the mean free path (MFP) of molecules in the liquid phase is comparable to the length scale of the system. In such a system, particles are more likely to be influenced by Knudsen diffusion. 52,53 The diffusion coefficient can therefore quantify the effect of geometry on solute transport. Figure 3 shows the average diffusion coefficient, D CNT , as determined by MD simulations for intermediates (oxalate, Fig. 3a and ethanol, Fig. 3b) inside SWCNTs of varying diameter, d. As SWCNT diameter increases from 1.08 nm to 3.02 nm, the diffusion coefficient generally increases towards the bulk diffusivity. The calculated diffusivity of oxalate compares well with the estimated effective diffusivity, D eff , suggesting that interactions with the nanotube wall influence transport over a broad range of d. In comparison, the diffusivity of ethanol shows a stronger dependence on d, and achieves bulk values at large nanotube diameters. This trend is further explored in the next section.

Results and Discussion
Density inside the CNT.-MD simulations were analyzed to determine water density and radial distribution inside the SWCNT. Figures 4a and 4c depicts water molecules inside SWCNT at diameters 1.08 nm, 1.35 nm, and 2.06 nm. This is an axial view of the nanotube, in which carbons in the SWCNT wall are blue, atoms  As diameter increases further, water orientation transitions to a mixture of organized and unorganized (bulk-like) structure within the 1.35 nm nanotube, and unorganized, bulk-like water structure orientation at 2.06 nm. The minimum distance between interior waters and the CNT surface is fairly constant at ∼3.85 Å ± 1.19 Å for all nanotube sizes (Fig S1 is available online at stacks.iop.org/ JES/167/023505/mmedia). This value is same as Lennard-Jones parameters defined for water-carbon hydrophobic interactions and reflects the hydrophobicity of the SWCNT surface. 54 The structural transition of water observed here is describe extensively in the literature. Computational studies have indicated the presence of polygonal (n = 4 to 8) layers inside the SWCNT, referred to as shell-water, for varying Lennard-Jones parameters, temperature and water models. 19,50,55,56 However, experimental NMR and IR studies could only prove the presence of ordered water structure but not the shape. [57][58][59][60] In Fig. 4b, shell-water with a water chain at the SWCNT centerline is observed for d = 1.35 nm. This type of structure can form due to the change in hydrogen bonding of shell water and thus affects the water molecules at the center. 50,60,61 Figures 4d and 4f shows the probability of finding water molecules and oxalate inside the SWCNT along the radius at diameters 1.08 nm, 1.35 nm and 2.06 nm. For all diameters, the probability of finding oxlate at the radial center is higher than close to the SWCNT wall, and shell water predominates at higher radii than oxalate. Since the SWCNT cannot provide hydrogen bonding to the oxalate, oxalate prefers to be at the radial center where hydrogen bonding can be satisfied by chain water (i.e. non-shell water molecules). This indicates that shell-water might act as a solidwall type of barrier for intermediate diffusion.
Water density inside the SWCNT was analyzed with both rigid (SPCE) and non-rigid (TIP3P) water models to eliminate error due to water models. Due to the varying rigidity of water in each model, it is possible that water inside SWCNT can show different structural configuration. Alexiadis et al. observed different water configurations for SPCE and TIP3P models for SWCNT of 0.89 nm. 19 In this study, we calculated the normalized radial distribution function between the center of carbon nanotube and water molecules present inside the SWCNT for both the models. It is found that for SWCNT of diameter 1.084 nm and above, SPCE and TIP3P models showed similar results (Fig. S2).
The configuration of water within the nanotube suggests that the intermediate does not experience a bulk-like liquid environment for SWCNT diameters below 2.06 nm. Water density inside the SWCNT was calculated from MD simulations and compared with literature results in Fig. 5, where fair agreement is observed. 25 Retention time.-In order to maximize the probability that a reaction would occur at a catalytic site inside the nanotube, the time over which the intermediate is retained within the nanotube should be maximized. Retention time was studied by varying the diameter of unmodified SWCNT (i.e. no charged at the SWCNT termini) while holding the length:diameter ratio constant at 5 (Fig. 6a). It is found that the retention time of both the intermediates, oxalate and ethanol, is less than 5 ns and independent of SWCNT diameter for constant length:diameter ratio.
We further studied the effect of length:diameter ratio on retention time for varying SWCNT diameter (Fig. 6b). At a constant diameter, retention time increased with increase in length. For the smaller diameters, and for the 3.0 nm tubes below a length:diameter ratio of 5, there is no significant effect of diameter given the range of error observed. For the 3.0 nm diameter at length:diameter ratio above 5, retention time increased significantly with increasing length and diameter. These results are consistent with retention time being proportional to diffusion time ∼L 2 /D eff , where L is the diffusion length and D eff is effective diffusivity. The diameter only weakly affects D eff via Knudsen diffusion. Hence, retention time increases primarily due to increase in length. The appearance of more bulklike solvent in the large 3.0 diameter nanotubes may increase retention due to the enhanced three-dimensional mobility of the intermediate. For the remainder of this study the length:diameter ratio is fixed at 5:1.
One way to ensure longer intermediate retention time is to close off the SWCNT termini, to mimic tryptophan synthase's closed confirmation. 15 As a proxy for this functionality, we introduced a   Figure 7 shows the effect of the presence of charged termini on the retention time of intermediates at constant SWCNT diameter of 1.35 nm. The retention time of oxalate increases from 1 to 5 ns when total terminal charge was changed from 0 to −8. This suggests that whenever oxalate attempts to exit the SWCNT, it is electrostatically repelled by the terminal carboxylates. Unexpectedly, ethanol displays significantly higher retention time in the presence of charged termini (Fig. 7), particularly for a small amount of terminal charge, above which the retention time stays approximately constant. In the presence of terminal charges, the retention time of ethanol increased from 3.7 ns to 16.7 ns, a significantly higher sensitivity compared to oxalate. The effect of terminal charge on the retention time was further studied using probability density calculations to observe the predominant axial locations of intermediates within the SWCNT.
The probability density of oxalate along the length of SWCNT (Fig. 8a) shows that as terminal charge increases, the probability of finding oxalate at the center is higher than at the termini, presumably due to increasing electrostatic repulsion from the termini. Ethanol is a non-charged but polar molecule, and hence can be attracted to the negatively charged terminal groups. The probability of finding ethanol at the tube ends is higher than at the center and increases with increasing terminal charge, providing evidence of such attraction (Fig. 8b). For unmodified SWCNT, a different PDF trend was observed due to the difference in hydrogen bonding of ethanol (two hydrogen bonds) and oxalate (eight hydrogen bonds).
Electrostatically modified SWCNTs did show significant improvement in the retention time. However, the terminal carboxylate groups experienced electrostatic repulsion among themselves as the number of carboxylates increased. This resulted in a change of orientation of carboxylate such that negatively charged oxygen atom is pointed outside the SWCNT (Fig. 2). Thus, dilution of negative charge reduced the magnitude of electrostatic forces at the tube ends. It is also important to consider the increase in ionic strength with increasing terminal charge, which affects the strength of potential fields. One possible way to address this reduction of charge density is to modify SWCNT termini with more rigid negative charges, for example by esterifying carbon-nanotube ends. 62 Consideration of reaction processes is a natural next-step based on the present results. First, the effect of incorporated catalyst inside the SWCNT would necessarily affect the transport results obtained here, as would the introduction of defects in the nanotube. Both of these modifications could be modeled using classical MD approaches to account for specific molecular interactions. On the other hand, the time scale of reaction processes, typically greater than 1 ms, makes it difficult to study the kinetics of the present system using molecular dynamics. Kinetic Monte Carlo (KMC) simulation, on the other hand, can be parameterized using MD and used to study kinetics. 9,63 This approach can fill the gap between atomistic simulation and continuum modeling by considering the state to state transition of a molecule rather than following a trajectory of the molecule. 64 The results presented here can facilitate a KMC simulation in which a catalytic site is introduced within the SWCNT. Diffusion coefficients obtained via MD simulation, for example, can be applied in such a KMC model to study the time evolution of reaction and intermediate transport.

Conclusions
Intermediate transport inside a water-filled nanochannel was studied using single-walled carbon nanotube as a model structure. MD simulations reveal that intermediate inside the nanochannel follows a diffusion mode that combines molecular and Knudsen diffusion. A length:diameter ratio above 5 can also retain molecule significantly. The unusual structure of water molecules inside the SWCNT plays a critical role in intermediate transport at smaller SWCNT diameters, where water showed ice-like ordered structure that restricts intermediate transport to the nanotube center. However, retention time can be increased by functionalizing the SWNT termini with an electrostatic charge, even if the intermediate is uncharged.  Journal of The Electrochemical Society, 2020 167 023505