Size effect in determining the water diffusion rate in carbon nanotubes

In this paper, we address lattice heat transport in single-walled carbon nanotubes (CNTs) by a quantum mechanical calculation of three-phonon scattering rates in the framework of the Boltzmann transport equation (BTE) and classical molecular dynamics (MD) simulation. Under a consistent choice of an empirical, realistic atomic interaction potential, we compare the tube-length dependence of the lattice thermal conductivity (TC) at room temperature determined from an iterative solution of the BTE and from a nonequilibrium MD (NEMD) approach. Qualitatively similar trends are found in the limit of short tubes, where an extensive regime of ballistic heat transport prevailing in CNTs of lengths $L\ensuremath{\lesssim}1\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ is independently confirmed. In the limit of long tubes, the BTE approach suggests a saturation of TC with tube length, whereas direct NEMD simulations of tubes extending up to $L=10\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{m}$ are demonstrated to be insufficient to settle the question of whether a fully diffusive heat transport regime and an intrinsic value of TC exist for CNTs. Noting that acoustic phonon lifetimes lie at the heart of a saturation of TC with tube length as per the BTE framework, we complement the quantum mechanical prediction of acoustic phonon lifetimes with an analysis of phonon modes in the framework of equilibrium MD. A normal mode analysis with an emphasis on long-wavelength acoustic modes corroborates the BTE prediction that heat transport in CNTs in the long tube limit is governed by the low attenuation rates of longitudinal and twisting phonons.

There has been a lot of debate on whether non-Fourier thermal conduction can be observed in quasi-one-dimensional materials such as carbon nanotubes (CNTs) and, additionally, whether the phenomenon can be found by equilibrium or nonequilibrium molecular dynamics (EMD or NEMD) simulations. In fact, so far EMD and NEMD simulations have revealed disparities of thermal transport in CNTs, ranging from purely diffusive behavior, to diffusive-ballistic transition, and to non-Fourier thermal conduction. By carefully examining the roles of interfacial thermal resistances and applied temperature differences in NEMD simulations, we show that the two effects often yield spurious results. After removing the unwanted effects that have been overlooked by previous works, we find that most EMD and NEMD simulations on CNTs consistently display diffusive thermal conduction for length (L) g 200 nm. The finding is further supported by the disappearance of nonlocal thermal conduction for L g 200 nm. Our results clarify many discrepancies of previous works and point out that nonideal thermostats commonly used in EMD and NEMD simulations would give an effective contact thermal resistance that misleads data interpretations. Overall, we find EMD and NEMD simulations conducted so far disagree with the current experimental results of nondiffusive thermal conduction in CNTs.

Equilibrium molecular dynamics (EMD) simulations with the Green-Kubo formula and nonequilibrium molecular dynamics (NEMD) simulations with the Fourier's Law are two widely used methods for calculating thermal conductivities of materials. It is well known that both methods suffer from domain size effects, especially for NEMD. But the underlying mechanisms and their comparison have not been much quantitatively studied before. In this paper, we investigate their domain size effects by using crystalline silicon at 1000 K, graphene at 300 K, and silicene at 300 K as model material systems. The thermal conductivity of silicon from EMD simulations increases normally with the increasing domain size and converges at a size of around 4×4×4 nm3. The converging trend agrees well with the wavelength-accumulated thermal conductivity. The thermal conductivities of graphene and silicene from EMD simulations decrease abnormally with the increasing domain size and converge at a size of around 10×10 nm2. We ascribe the anomalous size effect to the fact that as the domain size increases, the effect of more phonon scattering processes (particularly the flexural phonons) dominates over the effect of more phonon modes contributing to the thermal conductivity. The thermal conductivities of the three material systems from NEMD simulations all show normal domain size effects, although their dependences on the domain size differ. The converging trends agree with the mean free path accumulation of thermal conductivity. This study provides new insights that other than some exceptions, the domain size effects of EMD and NEMD are generally associated with wavelength and mean free path accumulations of thermal conductivity, respectively. Since phonon wavelength spans over a much narrower range than mean free path, EMD usually has less significant domain size effect than NEMD.

Data for the flow rate of water in carbon nanopores is widely scattered, both in experiments and simulations. In this work, we aim at precisely quantifying the characteristic large slip length and flow rate of water flowing in a planar graphene nanochannel. First, we quantify the slip length using the intrinsic interfacial friction coefficient between water and graphene, which is found from equilibrium molecular dynamics (EMD) simulations. We then calculate the flow rate and the slip length from the streaming velocity profiles obtained using non-equilibrium molecular dynamics (NEMD) simulations and compare with the predictions from the EMD simulations. The slip length calculated from NEMD simulations is found to be extremely sensitive to the curvature of the velocity profile and it possesses large statistical errors. We therefore pose the question: Can a micrometer range slip length be reliably determined using velocity profiles obtained from NEMD simulations? Our answer is "not practical, if not impossible" based on the analysis given as the results. In the case of high slip systems such as water in carbon nanochannels, the EMD method results are more reliable, accurate, and computationally more efficient compared to the direct NEMD method for predicting the nanofluidic flow rate and hydrodynamic boundary condition.

The hydrodynamic boundary condition is now a subject of greater interest than ever before, even though the problem of formulating the correct boundary condition has existed from the beginning of the 19th century. Since then, many researchers have attempted to formulate a general boundary condition for fluid-solid interfaces. The 21st century has seen revolutionary advancement in nanoscale science and technology, which in turn, poses many fundamental questions about the nature of fluid flow in nanometric pores such as carbon nanotubes (CNTs) and aquaporins. Among them, one of the most important is the boundary condition. In this work, based on a statistical mechanics approach, we present a method to calculate the intrinsic interfacial friction coefficient between a fluid and solid at a planar and cylindrical interface, which determines the slip and boundary condition. We apply the method in conjunction with equilibrium molecular dynamics (EMD) simulation technique to fluids such as argon, methane and water flowing in planar graphene nanoslit pores and CNTs. We compare our model predictions against direct non-equilibrium molecular dynamics (NEMD) simulations and find excellent agreement. We identify several limitations of generally used NEMD methods to predict the slip and boundary condition and show that great care needs to be taken in analyzing the results of NEMD slip data for high-slip systems. We suggest some procedures to increase the reliability of the slip estimates. We also study the shear rate and external field dependent behavior of slip in Couette and Hagen-Poiseuille type flows. The slip length remains constant (indicating a linear response of the fluid to the external perturbation) only for low shear rates/external fields and as the field increases, the slip length increases rapidly. At these high fields the Navier-slip model breaks down. We attempt to resolve the highly debated issue of flow rates of water in carbon nanotubes, the values of which are scattered over 1 to 5 orders of magnitude in literature. We accurately predict these flow rates using both the CNT diameter dependent interfacial friction coefficient between water-CNTs and NEMD simulations streaming velocity profiles. Very narrow tubes show higher flow rate enhancements and as the tube diameter increases, the flow rates approach classical Navier-Stokes predictions with the no slip boundary condition. As the diameter of the tube increases, the slip length decreases monotonically and asymptotically approaches a constant value, which is equal to the slip length on a planar graphene surface. Our model gives the linear regime slip length which corresponds to experimental condition flow rates, which is otherwise cumbersome to find using NEMD simulation techniques. The proposed method is robust, general and can be used to find the slip and boundary condition accurately at any fluid-solid interface.

Background: Engineered carbon nanotubes (CNTs) are expected to be increasingly released into the environment with the rapid increase in their production and use. The discharged CNTs may interact with coexisting contaminants and subsequently change environmental behaviors and ecological effects of both the CNTs themselves and the contaminants. Dissolved organic matter (DOM) plays a critical role in the transport of CNTs in the aquatic environment, affecting both CNT's surface properties through adsorption, and its colloidal stability in solution. Therefore, CNT-bound DOM complexes may interact with coexisting contaminants, thus affecting their environmental fate. With increasing production and use of CNTs, there is an increasing risk that humans could be exposed to CNTs mainly through ingestion and inhalation. Since CNTs can be carriers of contaminants due to their high adsorption affinity and capacity, the distribution of these nanoparticles in the environment holds a potential environmental and health risk. Project objectives: The overall goal of this project was to gain a better understanding of the environmental behavior of engineered nanoparticles with DOM and organic pollutant in aqueous systems. The scope of this study includes: characterizing various types of engineered nanoparticles and their interaction with DOM; binding studies of organic contaminants by nanoparticles and DOM-nanoparticle complexes; and examining interactions in DOM-nanoparticles-contaminant systems. Major conclusions, solutions and achievements: DOM has a pronounced effect on colloidal stability of CNTs in solution and on their surface chemistry and reactivity toward associated contaminants. The structure and chemical makeup of both CNTs and DOM determine their interactions and nature of formed complexes. CNTs, contaminants and DOM can co-occur in the aquatic environment. The occurrence of co-contaminants, as well as of co-introduction of DOM, was found to suppress the adsorption of organic contaminants to CNTs through both competition over adsorption sites and direct interactions in solution. Furthermore, the release of residual contaminants from CNTs could be enhanced by biomolecules found in the digestive as well as the respiratory tracts, thus increasing the bioaccessibility of adsorbed contaminants and possibly the overall toxicity of contaminant-associated CNTs. Contaminant desorption could be promoted by both solubilization and sorptive competition by biological surfactants. Scientific and agricultural implications: The information gained in the current project may assist in predicting the transport and fate of both CNTs and associated contaminants in the natural environment. Furthermore, the results imply a serious health risk from contaminant-associated CNTs.

Dissolved organic matter (DOM) has been reported to stabilize carbon nanotube (CNT) suspensions, which increases concern over the subsequent transport and behavior of CNTs. However, it is unknown exactly which compounds or functional groups cause the stabilization of CNTs in natural environments. Naturally occurring tannic acid (TA), which has a large number of aromatic functional groups, was used as a surrogate of DOM to investigate its interaction with CNTs. CNT suspendability in TA solution increased with increasing CNT diameter without the aid of sonication. Sorption affinity of CNTs for TA increased with decreasing CNT diameter, positively related to their surface area. A two-stage sorption model was proposed to illustrate the interaction between CNTs and TA. TA molecules may be adsorbed first onto CNTs with aromatic rings binding to the surface carbon rings via pi-pi interactions, until forming a monolayer; the TA monolayer then further sorbed the dissolved TA by hydrogen bonds and other polar interactions. The sorbed TA increased the steric repulsion between individual CNTs, which might disperse the relatively loose CNT aggregates and result in the stabilization of large-diameter CNTs in TA solution. The sorption and suspending processwere also examined bytransmission electron microscopy, providing further evidence for the above proposed CNT-TA interactions. This study implies that widely distributed TA may promote the mobility and transport of CNTs in natural aqueous environments.

Carbon nanotubes (CNTs) are widely manufactured nanoparticles, which are being utilized in a number of consumer products, such as sporting goods, electronics and biomedical applications. Due to their accelerating production and use, CNTs constitute a potential environmental risk if they are released to soil and groundwater systems. It is therefore essential to improve the current understanding of environmental fate and transport of CNTs. The transport and retention of CNTs in both natural and artificial media have been reported in literature, but the findings widely vary and are thus not conclusive. There are a number of physical and chemical parameters responsible for variation in retention and transport. In this study, a complete procedure of selected multiwalled carbon nanotubes (MWCNTs) is presented starting from their surface modification to a complete set of laboratory column experiments at critical physical and chemical scenarios. Results indicate that the stability of the commercially available MWCNTs are critical with their attached surface functional group which can also influence the transport and retention of MWCNT through the surrounding medium.

Carbon nanotubes (CNTs) are widely manufactured nanoparticles, which are being utilized in a number of consumer products, such as sporting goods, electronics and biomedical applications. Due to their accelerating production and use, CNTs constitute a potential environmental risk if they are released to soil and groundwater systems. It is therefore essential to improve the current understanding of environmental fate and transport of CNTs. The transport and retention of CNTs in both natural and artificial media have been reported in literature, but the findings widely vary and are thus not conclusive. There are a number of physical and chemical parameters responsible for variation in retention and transport. In this study, a complete procedure of selected multiwalled carbon nanotubes (MWCNTs) is presented starting from their surface modification to a complete set of laboratory column experiments at critical physical and chemical scenarios. Results indicate that the stability of the commercially available MWCNTs are critical with their attached surface functional group which can also influence the transport and retention of MWCNT through the surrounding medium.

Nonequilibrium molecular dynamics (NEMD) simulations are used to investigate pressure-driven water flow passing through carbon nanotube (CNT) membranes at low pressures (5.0 MPa) typical of real nanofiltration (NF) systems. The CNT membrane is modeled as a simplified NF membrane with smooth surfaces, and uniform straight pores of typical NF pore sizes. A NEMD simulation system is constructed to study the effects of the membrane structure (pores size and membrane thickness) on the pure water transport properties. All simulations are run under operating conditions (temperature and pressure difference) similar to a real NF processes. Simulation results are analyzed to obtain water flux, density, and velocity distributions along both the flow and radial directions. Results show that water flow through a CNT membrane under a pressure difference has the unique transport properties of very fast flow and a non-parabolic radial distribution of velocities which cannot be represented by the Hagen-Poiseuille or Navier-Stokes equations. Density distributions along radial and flow directions show that water molecules in the CNT form layers with an oscillatory density profile, and have a lower average density than in the bulk flow. The NEMD simulations provide direct access to dynamic aspects of water flow through a CNT membrane and give a view of the pressure-driven transport phenomena on a molecular scale.

Effects of modification groups and defects on the desalination performance of multi-walled carbon nanotube (MWNT) membranes

Nonequilibrium molecular dynamics (NEMD) simulations are presented to investigate the effect of water-membrane interactions on the transport properties of pressure-driven water flow passing through carbon nanotube (CNT) membranes. The CNT membrane is modified with different physical properties to alter the van der Waals interactions or the electrostatic interactions between water molecules and the CNT membranes. The unmodified and modified CNT membranes are models of simplified nanofiltration (NF) membranes at operating conditions consistent with real NF systems. All NEMD simulations are run with constant pressure difference (8.0 MPa) temperature (300 K), constant pore size (0.643 nm radius for CNT (12, 12)), and membrane thickness (6.0 nm). The water flow rate, density, and velocity (in flow direction) distributions are obtained by analyzing the NEMD simulation results to compare transport through the modified and unmodified CNT membranes. The pressure-driven water flow through CNT membranes is from 11 to 21 times faster than predicted by the Navier-Stokes equations. For water passing through the modified membrane with stronger van der Waals or electrostatic interactions, the fast flow is reduced giving lower flow rates and velocities. These investigations show the effect of water-CNT membrane interactions on water transport under NF operating conditions. This work can help provide and improve the understanding of how these membrane characteristics affect membrane performance for real NF processes.

We introduce an analytical method to predict the slip length (Ls) in cylindrical nanopores using equilibrium molecular dynamics (EMD) simulations, following the approach proposed by Sokhan and Quirke for planar channels []. Using this approach, we determined the slip length of water in carbon nanotubes (CNTs) of various diameters. The slip length predicted from our method shows excellent agreement with the results obtained from nonequilibrium molecular dynamics (NEMD) simulations. The data show a monotonically decreasing slip length with an increasing nanotube diameter. The proposed EMD method can be used to precisely estimate slip length in high slip cylindrical systems, whereas, Ls calculated from NEMD is highly sensitive to the velocity profile and may cause large statistical errors due to large velocity slip at the channel surface. We also demonstrated the validity of the EMD method in a BNNT-water system, where the slip length is very small compared to that in a CNT pore of similar diameter. The developed method enables us to calculate the interfacial friction coefficient directly from EMD simulations, while friction can be estimated using NEMD by performing simulations at various external driving forces, thereby increasing the overall computational time. The EMD analysis revealed a curvature dependence in the friction coefficient, which induces the slip length dependency on the tube diameter. Conversely, in flat graphene nanopores, both Ls and friction coefficient show no strong dependency on the channel width.

Phase change materials such as n-alkanes that exhibit desirable characteristics such as high latent heat, chemical stability, and negligible supercooling are widely used in thermal energy storage applications. However, n-alkanes have the drawback of low thermal conductivity values. The low thermal conductivity of n-alkanes is linked to formation of randomly oriented nano-domains of molecules in their solid structure that is responsible for excessive phonon scattering at the grain boundaries. Thus, understanding the thermal boundary conductance at the grain boundaries can be crucial for improving the effectiveness of thermal storage systems. The concept of the ideal crystal is proposed in this paper, which describes a simplified model such that all the nano-domains of long-chain n-alkanes are artificially aligned perfectly in one direction. In order to study thermal transport of the ideal crystal of long-chain n-alkanes, four (4) systems (C20H42, C24H50, C26H54, and C30H62) are investigated by the molecular dynamics simulations. Thermal boundary conductance between the layers of ideal crystals is determined using both non-equilibrium molecular dynamics (NEMD) and equilibrium molecular dynamics (EMD) simulations. Both NEMD and EMD simulations exhibit no significant change in thermal conductance with the molecular length. However, the values obtained from the EMD simulations are less than the values from NEMD simulations with the ratio being nearly three (3) in most cases. This difference is due to the nature of EMD simulations where all the phonons are assumed to be in equilibrium at the interface. Thermal conductivity of the n-alkanes in three structures including liquid, solid, and ideal crystal is investigated utilizing NEMD simulations. Our results exhibit a very slight rise in thermal conductivity values as the number of carbon atoms of the chain increases. The key understanding is that thermal transport can be significantly altered by how the molecules and the nano-domains are oriented in the structure rather than by the length of the n-alkane molecules.

Modulation of water transport in carbon nanotubes by local charges