A lattice dynamical treatment for the total potential energy of single-walled carbon nanotubes and its applications: relaxed equilibrium structure, elastic properties, and vibrational modes of ultra-narrow tubes

In this paper, we propose a lattice dynamic treatment for the total potential energy of single-walled carbon nanotubes (SWCNTs) which is, apart from a parameter for the nonlinear effects, extracted from the vibrational energy of the planar graphene sheet. The energetics, elasticity and lattice dynamics are treated in terms of the same set of force constants, independently of the tube structures. Based upon this proposal, we have investigated systematically the relaxed lattice configuration for narrow SWCNTs, the strain energy, the Young's modulus and Poisson ratio, and the lattice vibrational properties with respect to the relaxed equilibrium tubule structure. Our calculated results for various physical quantities are nicely in consistency with existing experimental measurements. In particular, we verified that the relaxation effect makes the bond length longer and the frequencies of various optical vibrational modes softer. Our calculation provides evidence that the Young's modulus of an armchair tube exceeds that of the planar graphene sheet, and that the large diameter limits of the Young's modulus and Poisson ratio are in agreement with the experimental values of graphite; the calculated radial breathing modes for ultra-narrow tubes with diameters ranging between 2 and 5 angstrom coincide with the experimental results and the existing ab initio calculations with satisfaction. For narrow tubes with a diameter of 20 angstrom, the calculated frequencies of optical modes in the tubule's tangential plane, as well as those of radial breathing modes, are also in good agreement with the experimental measurements. In addition, our calculation shows that various physical quantities of relaxed SWCNTs can actually be expanded in terms of the chiral angle defined for the corresponding ideal SWCNTs.

What has brought on the effects of number-average molecular weight on the spinodals in polymer mixtures?

On the basis of the thermodynamics of Gibbs, the spinodal for the quasibinary system was derived in the framework of the Sanchez-Lacombe lattice fluid theory. All of the spinodals were calculated based on a model polydisperse polymer mixture, where each polymer contains three different molecular weight subcomponents. According to our calculations, the spinodal depends on both weight-average ((M) over bar (w)) and number-average ((M) over bar (n)) molecular weights, whereas that of the z-average molecular weight is invisible. Moreover, the extreme of the spinodal decreases when the polydispersity index (eta = (M) over bar (w)/(M) over bar (n)) of the polymer increases. The effect of polydispersity on the spinodal decreases when the molecular weight gets larger and can be negligible at a certain large molecular weight. It is well-known that the influence of polydispersity on the phase equilibrium (coexisting curve, cloud point curves) is much more pronounced than on the spinodal. The effect of M, on the spinodal is discussed as it results from the infuluence of composition temperatures, molecular weight, and the latter's distribution on free volume. An approximate expression, which is in the assumptions of v* v(1)* = v(2)* and 1/r --> 0 for both of the polymers, was also derived for simplification. It can be used in high molecular weight, although it failed to make visible the effect of number-average molecular weight on the spinodal.

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMER MIXTURES

A statistical thermodynamics theory of polydisperse polymer blends based on a lattice model description of a fluid is formulated. Characterization of a binary polydisperse polymer mixture requires a knowledge of the pure polymer system and the interaction energy. It is assumed that the intrinsic and interactive properties of polymer (for example, T*, P*, rho*, and epsilon(ij)*) are independent of molecular size. Thermodynamic properties of ternary and higher order mixtures are completely defined in terms of the pure fluid polymer parameters and the binary interaction energies. Thermodynamic stability criteria for the phase transitions of a binary mixture are shown. The binodal and spinodal of general binary systems and of special binary systems are discussed.

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMER BLENDS WITH STRONG INTERACTION

A statistical thermodynamics theory of polydisperse polymer mixtures with strong interaction between dissimilar components based on a lattice fluid model is formulated. Expressions for the free energy, equation of state, phase stability and spinodal for a polydisperse, binary polymer mixture with strong interaction are derived.

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMERS

A statistical thermodynamics theory of polydisperse polymers based on a lattice model of fluids is formulated. Pure polydisperse polymer can be completely characterized by three scale factors and the molecular weight distribution of the system. The equation of state does not satisfy a simple corresponding-states principle, except for a polymer fluid of sufficiently high molecular weight. The relationships between thermal expansion coefficient alpha and isothermal compressibility beta with reduced variables are also predicted.

Statistical thermodynamics of polydisperse polymer systems in the framework of lattice fluid model: Effect of molecular weight and its distribution on the spinodal in polymer solution

With the aid of thermodynamics of Gibbs, the expression of the spinodal was derived for the polydisperse polymer-solvent system in the framework of Sanchez-Lacombe Lattice Fluid Theory (SLLFT). For convenience, we considered that a model polydisperse polymer contains three sub-components. According to our calculation, the spinodal depends on both weight-average ((M) over bar (w)) and number-average ((M) over bar (n)) molecular weights of the polydisperse polymer, but the z-average molecular weight ((M) over bar (z)) dependence on the spinodal is invisible. The dependence of free volume on composition, temperature, molecular weight, and its distribution results in the effect of (M) over bar (n) on the spinodal. Moreover, it has been found that the effect of changing (M) over bar (w) on the spinodal is much bigger than that of changing (M) over bar (n) and the extrema of the spinodal increases with the rise of the weight-average molecular weight of the polymer in the solutions with upper critical solution temperature (UCST). However, the effect of polydispersity on the spinodal can be neglected for the polymer with a considerably high weight-average molecular weight. A more simple expression of the spinodal for the polydisperse polymer solution in the framework of SLLFT was also derived under the assumption of upsilon(*)=upsilon(1)(*)=upsilon(2)(*) and (1/r(1)(0))-(1/r(2i)(0))-->(1/r(1)(0)).

The enhancement of TiO2 photocatalytic activity by hydrogen thermal treatment

In this study, conventional TiO2 powder was heated in hydrogen (H-2) gas at a high temperature as pretreatment. The photoactivity of the treated TiO2 samples was evaluated in the photodegradation of sulfosalicylic acid (SSA) in aqueous suspension. The experimental results demonstrated that the photodegradation rates of SSA were significantly enhanced by using the H-2-treated TiO2 catalysts and an optimum temperature for the H-2 treatment was found to be of 500-600 degreesC. The in situ electron paramagnetic resonance (EPR) signal intensity of oxygen vacancies (OV) and trivalent titanium (Ti3+) associated with the photocatalytic activity was studied. The results proved the presence of OV and Ti3+ in the lattice of the H2-treated TiO2 and indicated that both were contributed to the enhancement of photocatalytic activity. Moreover, the experimental results presented that the EPR signal intensity of OV and Ti3+ in the H-2-treated TiO2 samples after 10 months storage was still significant higher than that in the untreated TiO2 catalyst. The experiment also demonstrated that the significant enhancement occurred in the photodegradation of phenol using the H-2-treated TiO2. (C) 2002 Elsevier Science Ltd. All rights reserved.

Lattice Boltzmann study of hydrodynamic effects in lamellar ordering process of two-dimensional quenched block copolymers

By incorporating self-consistent field theory with lattice Boltzmann method, a model for polymer melts is proposed. Compared with models based on Ginzburg-Landau free energy, our model does not employ phenomenological free energies to describe systems and can consider the chain topological details of polymers. We use this model to study the effects of hydrodynamic interactions on the dynamics of microphase separation for block copolymers. In the early stage of phase separation, an exponential growth predicted by Cahn-Hilliard treatment is found. Simulation results also show that the effect of hydrodynamic interactions can be neglected in the early stage.

An extension of the Quasicontinuum Treatment of Multiscale Solid Systems to Nonzero Temperature

Covering the solid lattice with a finite-element mesh produces a coarse-grained system of mesh nodes as pseudoatoms interacting through an effective potential energy that depends implicitly on the thermodynamic state. Use of the pseudoatomic Hamiltonian in a Monte Carlo simulation of the two-dimensional Lennard-Jones crystal yields equilibrium thermomechanical properties (e.g., isotropic stress) in excellent agreement with ``exact'' fully atomistic results.

Thermophoretic deposition of particles in gas flowing over cold surfaces

Some of the calculated parameters show a maximum value for specimens heat-treated at about 100°C. The tensile strength is, for instance, substantially higher for specimens shock-heated at 100°C than for non-heated ones. Another striking feature is the initial decrease of the diameter observed in specimens heat-treated at 600°C when loaded in uniaxial compression. Both optical microscopy and DSA experiments reveal a large increase in microcracking when the heat-treatment temperature exceeds 300°C.

Information preservation (IP) method in simulation of internal rarefied gas flows in MEMS

This paper reviews firstly methods for treating low speed rarefied gas flows: the linearised Boltzmann equation, the Lattice Boltzmann method (LBM), the Navier-Stokes equation plus slip boundary conditions and the DSMC method, and discusses the difficulties in simulating low speed transitional MEMS flows, especially the internal flows. In particular, the present version of the LBM is shown unfeasible for simulation of MEMS flow in transitional regime. The information preservation (IP) method overcomes the difficulty of the statistical simulation caused by the small information to noise ratio for low speed flows by preserving the average information of the enormous number of molecules a simulated molecule represents. A kind of validation of the method is given in this paper. The specificities of the internal flows in MEMS, i.e. the low speed and the large length to width ratio, result in the problem of elliptic nature of the necessity to regulate the inlet and outlet boundary conditions that influence each other. Through the example of the IP calculation of the microchannel (thousands m ? long) flow it is shown that the adoption of the conservative scheme of the mass conservation equation and the super relaxation method resolves this problem successfully. With employment of the same measures the IP method solves the thin film air bearing problem in transitional regime for authentic hard disc write/read head length ( 1000 L m ? = ) and provides pressure distribution in full agreement with the generalized Reynolds equation, while before this the DSMC check of the validity of the Reynolds equation was done only for short ( 5 L m ? = ) drive head. The author suggests degenerate the Reynolds equation to solve the microchannel flow problem in transitional regime, thus provides a means with merit of strict kinetic theory for testing various methods intending to treat the internal MEMS flows.

Monte Carlo Modeling of Micro Scale Gas Flows

An information preservation (IP) method has been used to simulate many micro scale gas flows. It may efficiently reduce the statistical scatter inherent in conventional particle approaches such as the direct simulation Monte Carlo (DSMC) method. This paper reviews applications of IP to some benchmark problems. Comparison of the IP results with those given by experiment, DSMC, and the linearized Boltzmann equation, as well as the Navier-Stokes equations with a slip boundary condition, and the lattice Boltzmann equation, shows that the IP method is applicable to micro scale gas flows over the entire flow regime from continuum to free molecular.