The study of boron-nitride nanotube behavior as an atomic nano-pump for biomedicine applications

Complex physical and chemical interactions take place in drug delivery using nanotube structures. Various descriptions of the ultrastructural arrangement to various nanotube design features ranging from geometries to surface modifications on the nano levels have been put forward. In this work, molecular dynamics simulations were applied to understand the boron nitride nanotube (BNNT) performance for drug delivery applications. Here, we have carried out the molecular dynamic (MD) simulation using the Tersoff force field to obtaining optimum performance of BNNT and fullerene molecules for the first time. The result of the equilibrated system accomplished excellent stability of BNNT during MD simulation, which proves the appropriateness of chosen force field. Furthermore, to describe the BNNT nano pumping process, we have calculated the fullerene molecule’s velocity and translational/rotational kinetic energy. Numerically, by increasing simulated structures’ temperature from 275 to 350 K, the nano pumping time varies from 9.31 to 8.55 ps. Moreover, the outcoming results indicate that atomic wave production in BNNT is an essential parameter for the nano pumping process. Therefore, with the help of the simulation result, we succeed in decreasing the nano pumping time to 7.79 ps by adjusting the nano pumping process parameters. Our study revealed the molecular-level dispersion mechanism of BNNT as a drug delivery tool. Concerning the medical applications of fullerenes as drug molecules, including antiviral activity, antioxidant activity, and drug delivery use, the current study can shed light on the understanding of the dispersion of nanotubes to optimize the process for several biomedical applications.


Nomenclature
F ij Interatomic force between atoms i and j (eV/Å) E Interaction energy (eV) V ij Interatomic potential (eV) f R Two-body term of Tersoff potential (eV) f A Three-body term of Tersoff potential (eV) R Distance parameter in Tersoff potential (Å) D Distance parameter in Tersoff potential (Å) A Energy parameter in Tersoff potential (eV) B Energy parameter in Tersoff potential (eV) m Atomic mass (u) r ij Atomic distance between atoms i and j (Å) t Simulation time (ps) v Atomic velocity (Å/ps) a Atomic acceleration (Å/ps 2 ) f Frequency of atomic oscillation (1/ps) A 0 The amplitude of atomic oscillation (Å

Introduction
Nanotechnology is the manipulation of structures on a nanometric scale. The first widespread definition of this technology referred to the particular practical goal of optimizing atoms to produce macro-scale applications [1,2]. Boronnitride nanotube (BNNT) is one of the promising materials for various nanotechnology aims [3,4]. These nanostructures are a polymorph of boron nitride mixture. The existence of BNNT was theorized by Marvin Cohen (UC Berkeley) in 1994 [4]. The first synthesized BNNT using the arc discharge/arc-jet plasma method in the following year [5]. The BNNT structures are similar to common carbon nanotubes (CNTs), with cylindrical atomic shapes in nanometric size, except that C atoms in CNTs are replaced by N and B atoms in BNNT [6][7][8].
Although the physical behavior of BNNY is different comparing with CNTs, both structures have promising mechanical properties and providing a wide range of applications [9]. Like CNTs, the BNNT mechanical properties are 100 times stronger than steel [10], making them excellent nanostructured buildings appropriate for various applications. Recently, toxicological research on BNNT shows their biocompatibility and enhanced chemical inertia. Therefore, they seem to be good candidates in medical applications such as drug delivery [11][12][13][14]. The potential of the BNNT was investigated by Dehghani et al. as an active and stable nanostructured catalyst by using transmission electron microscopy, scanning transmission electron microscopy, energy-dispersive X-ray spectroscopy, and X-ray photoelectron spectroscopy methods [15]. Also, the BNNT for the drug delivery applicants formed the basis of the new branch in situ human organ pressure detection [16,17]. Xu et al.
[18] studied the atomic interactions between BNNT surface and drugs to reveal the binding mechanism of these structures during the drug delivery process. As a result, the drugs can then be delivered directly into the cells for cancer treatment. Shayan et al. [19] described that the physical properties of the armchair BNNT interacted with the 5-FU as an anticancer drug at the B3LYP/6-31G (d,p) level of theory. His study shows that the encapsulation and adsorption of 5-FU molecules on the BNNT surface are favorable processes. Khatti et al.
[20] investigated a drug delivery system based on BNNT to carry platinum-based anticancer drugs.
The nanopump, which relies on the van der Waals interaction between external atoms and nanotube structure, is one of the common ways to drug delivery procedures. In this nanoscale mechanism, the inserted particles to BNNT would prefer to stay in a symmetrical position inside this nanotube [21][22][23][24]. However, the existence of the energy barrier produced in the pumping procedure prevents the encapsulation of inserted atoms inside an atomic structure of the nanotube [25]. Understanding the drug delivery using nanotubes under experimental conditions is rapidly evolving due to the introduction of these novel techniques. Nevertheless, the current understanding of the interface zone of target drugs and tubes is still hampered by the shortcomings of theoretical explanations for resolving the finer details of the method. The MD simulation is a powerful approach to analyzing molecular systems' behavior in time and space for various nanostructures behavior [26][27][28][29]. The MD is considered proficient in resolving structural, dynamic, and functional properties of complex biomolecular systems at the nanoscale level, for instance, pumping of fluids at the nanoscale and drug delivery. Dehghani et al. [30] verified the self-insertion process of the protein SmtA, metallothionein, into the BNNT with the MD approach. Their results indicated that the protein was self-inserted into the BNNT through the protein-BNNT van der Waals interaction, which descended and reached the average value of −189.63 kcal/mol at t=15 ns. The MD computational method is also a commonly used method for the study of the nano pumping process in CNT-based structures [31,32]. However, the potential of the MD method is not used for other nanotube structures such as BNNT.
In this work, we used Md simulation to study the nano pumping of BNNT for the first time. We propose to actuate wave propagation in a BNNT using copper (Cu) oscillating tips. We demonstrate the nano pumping process of a fullerene molecule via an ideal BNNT. The results are helpful for researchers working to implement optimal frequency of tips and trajectories delivery systems. Also, optimal time crossing and the criteria for proper delivery are studied. Considering the wide range of applications of Fullerenes as nanomolecular carbon cages that can serve as platforms for the delivery of drugs and imaging agents [33], our findings can pave the way towards efficient energy conversion, pumping at the nanoscale, and optimizing the drug delivery process.

Computational methods
Comprehensive results of the MD simulation for the BNNT nano pumping device are reported, demonstrating the influence of the pumping process parameters on the properties of drugs delivery. A simulation box with geometries of 200 ×100 ×100 Å length in x-, y-, and z-directions was made in LAMMPS. The C 20 molecule and BNNT with 1.955 Å and 5.205 Å diameters have been simulated using LAMMPS molecular dynamics simulation package [34, 35] (Fig. 1). The cubic Cu tips structure with dimensions of 8×8×8Å have been simulated at the entrance of the nanotube. The atomic arrangement (atomic model) was initially prepared in Avogadro and Packmol free source software and later has been visualized using Ovito software [36-38] with transferring provided files. The periodic boundary conditions are implemented in the x-direction and fixed boundary used for y-and z-directions [39]. Subsequently, the Nose-Hoover thermostat is used for temperature equilibration of the simulated system [40, 41].
The computational thermostat equilibrates the BNNT and C 20 temperature at 300 K with a 0.1 damping rate.
Interatomic force-field is a significant parameter in MD simulations. To simulate the atomic structures in our computational study, we used the Tersoff force-field [42, 43], which is defined by the following equations [43]: where f R is a two-body term, and f A includes three-body interactions. The summations in equation (2) are overall neighbors j and k of an atom i within a cutoff distance. Computationally, f C , f R , and f A constants can be expressed as below equations: While R and D reflect the distance dimension, A and B have the energy dimension, and λ 1 and λ 2 show the 1 distance dimension. Other constant values of MD simulations are demonstrated in Table 1.
The tips made from Cu atoms interaction are described by embedded atom model (EAM), which is defined as below [44, 45]: where F is the embedding energy, and it is a function of the atomic electron density ρ, φ for calculating potential pair interaction. The α and β are the element types of atoms i and j. Finally, the atomic interaction between defined structures is described with the Lennard Jones functions using DREAD-ING information for various elements [46].
Newton's law explains the atoms' time evolution in the simulation box for the gradient of force-field function [47]: The integrated form of Newton law is done by the Velocity-Verlet algorithm in equations (7) and (8)  where r(t+Δt) and v(t+Δt) is the atomic position and velocity in (t+Δt), respectively. Finally, according to the reported descriptions, MD simulations in this computational study were carried out in two main steps: Primarily, BNNT, C 20 and Cu tips were simulated with Tersoff and EAM interatomic force fields. The atomic structures were equilibrated using the Nose-Hoover thermostat for ten ns simulation time. The MD simulation temperature was set at 300 K, and the atomic performance of the arrangement was observed to check the stability of the structure.
Later, the BNNT nano pumping process is modeled to hypothesize the nano pumping process using relevant physical  parameters such as velocity, transitional, and rotational component of kinetic energy. Finally, the effect of temperature, amplitude, and frequency variation of Cu tips on the pumping performance of BNNT has been assessed to indicate the optimized parameters of pumping.

Results and discussion
Equilibration process of atomic structures Initially, the system, including BNNT, C 20 , and Cu tips, was equilibrated at temperatures of (T=275 K, 300 K, 325 K, and 350 K) and stabilized for the defined force fields, considering the temperature and potential energy of the system. The temperature variation as a function of simulation time is plotted in Fig. 2. The atomic equilibrium arises from atomic oscillation reducing over MD simulation time. Figure 3 shows the potential energy of arrangement as a function of MD simulation time. The results show the potential energy converged to −9224 eV after 10000000-time steps at T=275 K. The system's stability slightly decreases by temperature changes from T=300 to T=350 K. Subsequently, the mean distance between various atoms increases, and thus the atomic stability decreases.

Nano pumping process in BNNT structure
The pumping arrangement has been designed using two Cu made tips, with up and down movements (in the y-direction), to produce the oscillation for the nano pumping process. Thus, the nano pumping process is including the deviations of velocity and kinetic energy of the C 20 molecule. Figure 4 reveals the time evolution of the nano pumping process. The Cu tips oscillate with 1.75 Å magnitude and 0.50 THz frequency using the following equations: As shown in Fig. 4, the fullerene molecule is inserted into the nanotube next to the atomic Cu tips. As tips oscillate, the structure actuated wave and push the fullerene molecule to move in z-direction due to the repulsive interaction between the C 20 and BNNT atoms. As a result, the position of C 20 molecule varies from 0 to 100 Å in z-direction after 8.99 ps. The results here are comparable with previous theoretical works for similar structures [50,51].
From the calculated time of C 20 molecule transferring inside BNNT, we conclude that MD simulation time is long enough for the nano pumping process. The fullerene's velocity and kinetic energy are plotted in Figs. 5 and 7, respectively. The calculated time of C 20 molecules traveling to the right end of BNNT appeared to be 8.99 ps. With another 0.31 ps to overcome the barrier energy of the BNNT end, the total pumping time is 9.3 ps. Here, the nano pumping process can be theorized with two main steps. The first step is increasing in velocity phase, which can be described by calculating the C 20 molecule velocity as a function of MD simulation time and temperature, as depicted in Fig. 5. Our calculations at T=275 K conclude that the maximum value of C 20 acceleration occurs in the 0 to 734-time steps, and this molecule velocity reaches 1211 m/s. Next, the C 20 molecule accelerates at a lower value for the 4200-time steps, and the velocity reaches 1682 m/s. The second step is decreasing the velocity phase. The fullerene velocity is gradually reduced to 1375 m/s at the end of the BNNT, prior to ejecting out of the nanotube. Despite the C 20 translation rate decreasing in the second phase, the provided energy of the BNNT structure is providing sufficient kinetic energy to overcome the energy barrier of the atomic nanotube end. Therefore, the fullerene molecule speed after the ejection process reaches 448 m/s. The calculated ejection speed of C 20 needs to be taken to account for the related biomedical applications.
Further analysis was conducted to estimate the C 20 molecules rotational motion during the nano pumping process. The obtained results in Fig. 6 confirm a simultaneous rotation occurred as C 20 molecules translate in the z-direction. So, through the interaction between carbon atoms and BNNT, the nanotube wave transfers the energy into the fullerene in translational/rotational components, as depicted in Fig. 7 (T = 275 K). In conclusion, the fullerene rotation with high velocity leads to disruption in translational motion along the z-direction, followed by translational velocity decreasing. Thus, it is crucial to minimize the rotational energy (rotational velocity) of the target material to increase translational energy and increase nano pumping efficiency.
As shown in Fig. 8, the temperature of simulated structures is an essential parameter in the nano pumping process. The initial temperature of systems was set to T=275 K, T=300 K, T=325 K, and T=350 K. It is revealed that temperature rise produces higher translational velocity, consequently reducing pumping efficiency. Furthermore, a failure occurs as the temperature rises to 400 K, and the process ends unsuccessful (see Fig. 8). Thus, we conclude that the nano pumping process is delayed with temperature increasing. The numerical results are reported in Table 2. The efficiency of nano pumping can be manipulated with Cu tips oscillation, amplitude, and frequency. Therefore, we performed a simulation setup for various Cu tips amplitude and frequencies stated in Fig. 9. The results show that the 1.75 Å amplitude of oscillation for BNNT is appropriate in the nano pumping process. The Cu tips oscillation amplitude larger than 2.75 Å causes the upper and lower regions of the BNNT to form a bond, and the Cu tips oscillation leading to the breakdown of actuation. Accordingly, the optimized value for Cu tips oscillation frequency was considered 0.75 THz. Our results also confirm that if the Cu tips oscillation frequency gets lower than 0.50 THz, the C 20 molecule exhibits significant rotational energy, and the nano pumping process ends unproductively. For frequency higher than 2.25 THz, no effective atomic wave can be detected in the BNNT, and it takes a long time to complete the nano pumping process. Finally, the MD results show that the Cu tips oscillation with A=1.75 Å amplitude and f=0.75 THz frequency are optimum values with a minimum pumping time of 7.79 ps (Fig. 9). The correlated translational and rotational energies for this optimum condition have been depicted in Fig. 10.
In addition to all calculated factors, the size of Cu tips and fullerene molecule (as a target structure) is another critical parameter in the nano pumping. We found the current size of tips optimum to initiate proper oscillation; however, we found that the change in the size of atomic tips will lead to changes in the amplitude and frequency, which is out of the scope of this work. Further investigation needs to be done on fullerene molecule enlarging for effective nano pumping process detecting.

Conclusions
The BNNT-based target-specific delivery of drugs has emerged as one of the most potential biomedical Fig. 7 Comparison of (a) translational and (b) rotational component of C 20 kinetic energy in successful pumping process for various initial temperatures  applications of nanotechnology. However, to achieve an efficient nano-drug delivery system, the interactions between the drug (the fullerenes molecule (C 20 )), BNNT need to be adequately optimized. The BNNT-drug interactions and nano pumping method can be optimized by adjusting several process parameters of BNNT to achieve effective drug delivery. Recent developments in computer modeling methods such as molecular design tools, particularly MD simulation studies, offer a practical approach for such optimization. The detailed analysis of the MD approach discussed in this paper will be useful to build new strategies to develop the necessary computational setup for designing a drug delivery system using BNNT. The molecular dynamics simulations indicated distinct behaviors for the nano pumping process of fullerenes molecule  Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.