Slip flow in graphene nanochannels

We investigate the hydrodynamic boundary condition for simple nanofluidic systems such as argon and methane flowing in graphene nanochannels using equilibrium molecular dynamics simulations (EMD) in conjunction with our recently proposed method [J. S. Hansen, B. D. Todd, and P. J. Daivis, Phys. Rev. E 84, 016313 (2011)]. We first calculate the fluid-graphene interfacial friction coefficient, from which we can predict the slip length and the average velocity of the first fluid layer close to the wall (referred to as the slip velocity). Using direct nonequilibrium molecular dynamics simulations (NEMD) we then calculate the slip length and slip velocity from the streaming velocity profiles in Poiseuille and Couette flows. The slip lengths and slip velocities from the NEMD simulations are found to be in excellent agreement with our EMD predictions. Our EMD method therefore enables one to directly calculate this intrinsic friction coefficient between fluid and solid and the slip length for a given fluid and solid, which is otherwise tedious to calculate using direct NEMD simulations at low pressure gradients or shear rates. The advantages of the EMD method over the NEMD method to calculate the slip lengths/flow rates for nanofluidic systems are discussed, and we finally examine the dynamic behaviour of slip due to an externally applied field and shear rate.     

Equilibrium and nonequilibrium molecular dynamics simulations of the thermal conductivity of molten alkali halides

The thermal conductivity of molten NaCl and KCl was calculated through the Evans-Gillan nonequilibrium molecular dynamics (NEMD) algorithm and Green-Kubo equilibrium molecular dynamics (EMD) simulations. The EMD simulations were performed for a "binary" ionic mixture and the NEMD simulations assumed a pure system for reasons discussed in this work. The cross thermoelectric coefficient obtained from Green-Kubo EMD simulations is discussed in terms of the homogeneous thermoelectric power or Seebeck coefficient of these materials. The thermal conductivity obtained from NEMD simulations is found to be in very good agreement with that obtained through Green-Kubo EMD simulations for a binary ionic mixture. This result points to a possible cancellation between the neglected "partial enthalpy" contribution to the heat flux associated with the interdiffusion of one species through the other and that part of the thermal conductivity related to the coupled fluxes of charge and heat in "binary" ionic mixtures.     

Nonequilibrium molecular dynamics simulation of water transport through carbon nanotube membranes at low pressure

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.     

Molecular diffusion and slip boundary conditions at smooth surfaces with periodic and random nanoscale textures

The influence of periodic and random surface textures on the flow structure and effective slip length in Newtonian fluids is investigated by molecular dynamics (MD) simulations. We consider a situation where the typical pattern size is smaller than the channel height and the local boundary conditions at wetting and nonwetting regions are characterized by finite slip lengths. In the case of anisotropic patterns, transverse flow profiles are reported for flows over alternating stripes of different wettability when the shear flow direction is misaligned with respect to the stripe orientation. The angular dependence of the effective slip length obtained from MD simulations is in good agreement with hydrodynamic predictions provided that the stripe width is larger than several molecular diameters. We found that the longitudinal component of the slip velocity along the shear flow direction is proportional to the interfacial diffusion coefficient of fluid monomers in that direction at equilibrium. In case of random textures, the effective slip length and the diffusion coefficient of fluid monomers in the first layer near the heterogeneous surface depend sensitively on the total area of wetting regions.     

Transient molecular dynamics simulations of viscosity for simple fluids

A transient molecular dynamics (TMD) method has been developed for simulation of fluid viscosity. In this method a sinusoidal velocity profile is instantaneously overlaid onto equilibrated molecular velocities, and the subsequent decay of that velocity profile is observed. The viscosity is obtained by matching in a least-squares sense the analytical solution of the corresponding momentum transport boundary-value problem to the simulated decay of the initial velocity profile. The method was benchmarked by comparing results obtained from the TMD method for a Lennard-Jones fluid with those previously obtained using equilibrium molecular dynamics (EMD) simulations. Two different constitutive models were used in the macroscopic equations to relate the shear rate to the stress. Results using a Newtonian fluid model agree with EMD results at moderate densities but exhibit an increasingly positive error with increasing density at high densities. With the initial velocity profiles used in this study, simulated transient velocities displayed clear viscoelastic behavior at dimensionless densities above 0.7. However, the use of a linear viscoelastic model reproduces the simulated transient velocity behavior well and removes the high-density bias observed in the results obtained under the assumption of Newtonian behavior. The viscosity values obtained using the viscoelastic model are in excellent agreement with the EMD results over virtually the entire fluid domain. For simplicity, the Newtonian fluid model can be used at lower densities and the viscoelastic model at higher densities; the two models give equivalent results at intermediate densities.     

A simple and effective boundary model in nonequilibrium molecular dynamics method

We propose a simple and effective boundary model in a nonequilibrium molecular dynamics (NEMD) simulation to study the out-of-equilibrium dynamics of polymer fluids. The present boundary model can effectively weaken the depletion effect and the slip effect near the boundary, and remove the unwanted heat instantly. The validity of the boundary model is checked by investigating the flow behavior of dilute polymer solution driven by an external force. Reasonable density distributions of both polymer and solvent particles, velocity profiles of the solvent and temperature profiles of the system are obtained. Furthermore, the studied polymer chain shows a cross-streaming migration towards center of the tube, which is consistent with that predicted in previous literatures. These numerical results give powerful evidences for the validity of the present boundary model. Besides, the boundary model can also be used in other flows in addition to the Poiseuille flow.     

Shear viscosity of molten alkali halides from equilibrium and nonequilibrium molecular-dynamics simulations

The shear viscosity of molten NaCl and KCl was calculated through equilibrium (EMD) and nonequilibrium molecular-dynamics (NEMD) simulations in the canonical (N,V,T) ensemble. Two rigid-ion potentials were investigated, namely, the Born-Mayer-Huggins-Tosi-Fumi potential and the Michielsen-Woerlee-Graaf-Ketelaar potential with the parameters proposed by Ladd. The NEMD simulations were performed using the SLLOD equations of motion [D. J. Evans and G. P. Morriss, Phys. Rev. A 30, 1528 (1984)] with a Gaussian isokinetic thermostat and the results are compared with those obtained from Green-Kubo EMD (N,V,T) simulations and experimental shear viscosity data. The NEMD zero strain rate shear viscosity, eta(0), was obtained by fitting a simplified Carreau-type equation and by application of mode-coupling theory, i.e., a eta-gamma(1/2) linear relationship. The values obtained from the first method are found to be significantly lower than those predicted by the second. The agreement between the EMD and NEMD results with experimental data is satisfactory for the two potentials investigated. The ion-ion radial distribution functions obtained with the two rigid-ion potentials for both molten salts are discussed in terms of the differences between the two models.     

Transient molecular dynamics simulations of liquid viscosity for nonpolar and polar fluids

A transient molecular dynamics (TMD) method for obtaining fluid viscosity is extended to multisite, force-field models of both nonpolar and polar liquids. The method overlays a sinusoidal velocity profile over the peculiar particle velocities and then records the transient decay of the velocity profile. The viscosity is obtained by regression of the solution of the momentum equation with an appropriate constitutive equation and initial and boundary conditions corresponding to those used in the simulation. The transient velocity decays observed appeared to include both relaxation and retardation effects. The Jeffreys viscoelastic model was found to model accurately the transient responses obtained for multisite models for n-butane, isobutane, n-hexane, water, methanol, and 1-hexanol. TMD viscosities obtained for saturated liquids over a wide range of densities agreed well for the polar fluids, both with nonequilibrium molecular dynamics (NEMD) results using the same force-field models and with correlations based on experimental data. Viscosities obtained for the nonpolar fluids agreed well with the experimental and NEMD results at low to moderate densities, but underpredicted experimental values at higher densities where shear-thinning effects and viscous heating may impact the TMD simulations.     

Transient-time correlation function applied to mixed shear and elongational flows

The transient-time correlation function (TTCF) method is used to calculate the nonlinear response of a homogeneous atomic fluid close to equilibrium. The TTCF response of the pressure tensor subjected to a time-independent planar mixed flow of shear and elongation is compared to directly averaged non-equilibrium molecular dynamics (NEMD) simulations. We discuss the consequence of noise in simulations with a small rate of deformation. The generalized viscosity for planar mixed flow is also calculated with TTCF. We find that for small rates of deformation, TTCF is far more efficient than direct averages of NEMD simulations. Therefore, TTCF can be applied to fluids with deformation rates which are much smaller than those commonly used in NEMD simulations. Ultimately, TTCF applied to molecular systems is amenable to direct comparison between NEMD simulations and experiments and so in principle can be used to study the rheology of polymer melts in industrial processes.     

分子动力学模拟纳米尺寸限制体系下氩溶液中I2的振动能量弛豫

利用平衡态分子动力学方法(EMD)模拟了纳米尺寸限制球壳内I2在Ar溶液中的振动能量转移. 计算并讨论了I2振动能量弛豫时间T1随球壳半径、溶剂密度的变化规律. 通过分子间相互作用分析, 在原子、分子水平上, 揭示了随着球壳半径的减小, T1呈逐渐增大趋势的原因. 结果表明, 球壳的几何限制效应和表面作用对受限溶液密度分布的影响较大, 从而导致溶质振动弛豫的显著变化. 此外, 非限制体系模拟显示, 非平衡态分子动力学(NEMD)方法可以得到与平衡态分子动力学方法较一致的振动能量弛豫时间T1.     

Investigation of entrance and exit effects on liquid transport through a cylindrical nanopore

The entrance and exit effects on liquid transport through a nano-sized cylindrical pore under different solid wall-liquid interactions were studied by comparing molecular dynamics (MD) results of a finite length nanopore in a membrane with those of an infinite length one. The liquid transport through a finite length nanopore in a membrane was carried out by using a pressure-driven non-equilibrium molecular dynamics (NEMD) method proposed by Huang et al. [C. Huang, K. Nandakumar, P. Choi and L. W. Kostiuk, J. Chem. Phys., 2006, 124, 234701]. The fluid motion through an infinite length nanopore, which had the same cross-stream dimension as the finite length channel in the membrane, but with periodic boundary conditions in the stream-wise direction, was carried out by using the external-field driven NEMD approach [J. Koplik, J. R. Bavanar and J. F. Willemsen, Phys. Rev. Lett., 1988, 60, 1282]. The NEMD results show that the pressure and density distributions averaged over the channel in the radial direction in both finite and infinite length channels are similar, but the radial distributions of the stream-wise velocity were significantly different when the solid wall was repulsive. The entrance and exit effects lead to a decrease in flow rate at about 39% for the repulsive wall and 6% for the neutral-like wall.     

Determining the Local Shear Viscosity of a Lipid Bilayer System by Reverse Non‐Equilibrium Molecular Dynamics Simulations

The parallel shear viscosity of a dipalmitoylphosphatidylcholine (DPPC) bilayer system is studied by reverse non‐equilibrium molecular dynamics simulations (RNEMD) with two different united‐atom force fields. The results are related to diffusion coefficients and structural distributions obtained by equilibrium molecular simulations. We investigate technical issues of the algorithm in the bilayer setup, namely, the dependence of the velocity profiles on the imposed flux and the influence of the thermostat on the calculated shear viscosity. We introduce the concept of local shear viscosity and investigate its dependence on the slip velocity of the monolayers and the particle density at the headgroup–water interface and the tail–tail interface. With this we demonstrate that the lipid bilayer is more viscous than the surrounding water phase, and that slip takes place near the headgroup region and in the centre of the bilayer where the alkyl tails meet. We also quantify the apparent increase in viscosity of the water molecules entangled at the water–headgroup interface.     

Mass accommodation mechanism of water through monolayer films at water∕vapor interface

The mass transfer dynamics at water∕vapor interface through monolayer films was theoretically investigated by a combination of molecular dynamics and Langevin dynamics simulations. The rare events of mass accommodation are sampled by the Langevin simulation with sufficient statistical accuracy, on the basis of the free energy and friction profiles obtained by the molecular dynamics simulation. The free energy profiles exhibit a barrier in the long-chain monolayers, and the mechanism of the barrier is elucidated in relation to the "water finger" formation. The present Langevin simulation well described the remarkable dependence of the mass accommodation coefficient on the chain length and surface density. The transition state theory for the barrier passage remarkably overestimates the mass accommodation coefficient, and the Kramers or Grote-Hynes theory may not be appropriate, due to large variation of the friction in the entrance channel and∕or broad barrier.     

On the Origin of Water Flow through Carbon Nanotubes

The transport of water molecules through carbon nanotubes (CNTs) is of primary importance for understanding water‐mediated biological activities as well as for the design of novel nanoporous materials. Herein, we analyze the water flow through CNTs by using molecular dynamics simulations with the hope of finding basic parameters determining the flow value. Of particular interest is that a simple equation as a function of water diffusion, occupancy and CNT size, can well describe the water flow through CNTs with different sizes. Specifically, both the simulation and equation flow exhibit power law relations with the CNT diameter and length, where the two exponents are close to each other. The water occupancy and translocation time also demonstrate interesting relations with the CNT size. The water dipole orientations and density profiles are also sensitive to the change of CNT size. These results greatly enhance our knowledge on the nature of water flow through CNTs and are helpful in predicting the water flow of CNTs up to the experimental length scale.     

Static and dynamic properties of the interface between a polymer brush and a melt of identical chains

Molecular-dynamics simulations of a short-chain polymer melt between two brush-covered surfaces under shear have been performed. The end-grafted polymers which constitute the brush have the same chemical properties as the free chains in the melt and provide a soft deformable substrate. Polymer chains are described by a coarse-grained bead-spring model, which includes excluded volume and backbone connectivity of the chains. The grafting density of the brush layer offers a way of controlling the behavior of the surface without altering the molecular interactions. We perform equilibrium and nonequilibrium molecular-dynamics simulations at constant temperature and volume using the dissipative particle dynamics thermostat. The equilibrium density profiles and the behavior under shear are studied as well as the interdigitation of the melt into the brush, the orientation on different length scales (bond vectors, radius of gyration, and end-to-end vector) of free and grafted chains, and velocity profiles. The obtained boundary conditions and slip length show a rich behavior as a function of grafting density and shear velocity.     

Molecular dynamics simulation of a pressure-driven liquid transport process in a cylindrical nanopore using two self-adjusting plates

Fluid transport through a nanopore in a membrane was investigated by using a novel molecular dynamics approach proposed in this study. The advantages of this method, relative to dual-control-volume grand-canonical molecular dynamics method, are that it eliminates disruptions to the system dynamics that are normally created by inserting or deleting particles from control volumes, and that it functions well for dense systems due to the number of particles being fixed in the system. Using the proposed method, we examined liquid argon transport through a nanopore by performing nonequilibrium molecular dynamics (NEMD) simulations under different back pressures. Validation of the code was performed by comparing simulation results to published experimental data obtained under equilibrium conditions. NEMD results show that constant pressure difference across the membrane was readily achieved.     

Designing carbon nanotube membranes for efficient water desalination

The transport of water and ions through membranes formed from carbon nanotubes ranging in diameter from 6 to 11 A is studied using molecular dynamics simulations under hydrostatic pressure and equilibrium conditions. Membranes incorporating carbon nanotubes are found to be promising candidates for water desalination using reverse osmosis, and the size and uniformity of tubes that is required to achieve a desired salt rejection is determined. By calculating the potential of mean force for ion and water translocation, we show that ions face a large energy barrier and will not pass through the narrower tubes studied ((5,5) and (6,6) "armchair" type tubes) but can pass through the wider (7,7) and (8,8) nanotubes. Water, however, faces no such impediment due to the formation of stable hydrogen bonds and crosses all of the tubes studied at very large rates. By measuring this conduction rate under a hydrostatic pressure difference, we show that membranes incorporating carbon nanotubes can, in principle, achieve a high degree of desalination at flow rates far in excess of existing membranes.     

Understanding flow enhancement in graphene‐coated nanochannels

In this work, we investigate pressure‐driven water flows in graphene‐coated copper nanochannels through molecular dynamics simulations. It is found that the flow rate in bare copper nanochannel can be significantly enhanced by a factor of 45 when the nanochannel is coated with monolayer graphene. The enhancement factor for the flow rate reaches about 90 when the nanochannel is modified with 3 or more graphene layers. The dipole relaxation time and the hydrogen bond lifetime of interfacial water molecules show that the graphene coating promotes the mobility of water molecules at the interface. The distribution of the potential of mean force and the free energy barriers also confirm that graphene coating reduces the flow resistance and 3 layers of graphene can fully screen the surface effects. The results in this work provide important information for the design of graphene‐based nanofluidic systems for flow enhancement.     

Investigation of nanocomposite PNIPAm-g-graphene with pre-lower critical solution temperature rapid thermal response function for chip adaptive cooling: A molecular dynamics and computational fluid dynamics simulations

Temperature-sensitive hydrogels have been widely used for rapid adaptive cooling in electronic device thermal management with promising applications. However, existing temperature-sensitive hydrogels can only regulate the flow in the chip cooling system after the ambient temperature reaches their lower critical solution temperature (LCST). Before reaching LCST, effective rapid heat dissipation for electronic chips is not achievable. This study aims to develop a temperature-sensitive hydrogel that can provide assisted adaptive cooling for electronic chips before reaching its LCST. This requires the hydrogel to have a thermal conductivity far surpassing existing hydrogel materials. Using the temperature-sensitive hydrogel PNIPAm and graphene molecules as base materials, this research utilized molecular dynamics simulations to graft graphene molecules onto PNIPAm molecules in different ways, resulting in the temperature-sensitive hydrogel material PNIPAm-g-graphene. Non-equilibrium molecular dynamics (NEMD) was employed to calculate the thermal conductivity of this material under different temperature conditions. The results indicate that the thermal conductivity of PNIPAm-g-graphene can reach up to 1.95474 W/m K (graphene grafted at  CH₃ functional group, temperature at 280 K). Compared to the thermal conductivity of PNIPAm under the same conditions (0.45 W/m K), the increase in thermal conductivity is significant, demonstrating excellent thermal conductivity compared to PNIPAm. Subsequently, this study analyzed the underlying mechanisms of different thermal conductivities in materials obtained by grafting graphene molecules at different points using the method of overlap in Phonon Density of States Curves (PDOS) from the perspective of interfacial thermal conduction. Finally, through computational fluid dynamics (CFD) simulations, this study investigates the chip's adaptive cooling performance with PNIPAm-g-graphene material. The results show that, compared to traditional temperature-sensitive hydrogels, PNIPAm-g-graphene can achieve efficient adaptive cooling of chip hotspots before the cooling fluid temperature reaches its LCST value. This finding is significant for the field of chip cooling. The study proposes a new method for rapid, adaptive cooling of chip hotspots and explores its feasibility from the perspectives of molecular dynamics and CFD simulation. It holds importance in the thermal management of electronic devices and the rapid adaptive cooling of electronic chips.