Wetting of Alkanes on Water from a Cahn-Type Theory: Effects of Long-Range Forces

We apply the phenomenological wetting theory of Cahn to fluids with van der Waals forces, and in particular to the wetting of pentane on water. Taking into account explicitly the long-range substrate–adsorbate interaction allows us to reproduce the experimentally observed critical wetting transition, which arises from the vanishing of the Hamaker constant at T53°C. This transition is preceded by a first-order transition between a thin and a thick film at a (much) lower temperature. If long-range forces are neglected, this thin–thick transition is the only wetting transition and critical wetting is missed. Our study focuses on the development of useful theoretical tools, such as phase portraits and interface potentials adapted to systems with van der Waals forces.     

Cross-Over Between First-Order and Critical Wetting at the Liquid-Vapour Interface of n-Alkane/Methanol Mixtures: Tricritical Wetting and Critical Prewetting

A simple mean-field theory is presented which describes the basic observations of recent experiments revealing rich wetting behaviour of n-alkane/methanol mixtures at the liquid-vapour interface. The theory, qualitative and in part heuristic, is based on a microscopic lattice-gas model from which a Cahn–Landau approach is distilled. Besides the physics associated with the short-range components of the intermolecular interactions, effects of the long-range tails of the net van der Waals forces between interfaces are also taken into account. Further, gravitational thinning of the wetting phase is incorporated. The calculation of the spreading coefficient S is extended to the experimentally relevant situation in which the bulk adsorbate is slightly away from two-phase coexistence due to gravity. Analysis of this novel approximation to S for systems with short-range forces leads to the conclusion that the surface specific heat exponents _s =1,1/2, and 0, for first-order wetting, tricritical wetting and critical wetting, respectively, are robust with respect to (weak) gravitational thinning, consistently with experiment. For three different systems the adsorption is calculated as a function of temperature and compared with the experimentally measured ellipticity. Including weak long-range forces which favour wetting in the theory does not visibly alter the critical wetting transition for the nonane/methanol mixture, in contrast with the generic expectation of first-order wetting for such systems, but in good agreement with experiment. For decane/methanol weak long-range forces bring the transition very close to the prewetting critical point, leading to an adsorption behaviour closely reminiscent of short-range tricritical wetting, observed experimentally for alkane chain length between 9.6 and 10. Finally, for undecane/methanol the transition is clearly of first order. First-order wetting is also seen in the experiment.     

What controls the thickness of wetting layers near bulk criticality?

We study the thickness of wetting layers in the binary-liquid mixture cyclohexane methanol. Far from the bulk critical point, the wetting layer thickness is independent of temperature, resulting from the competition between van der Waals and gravitational forces. Upon approaching the bulk critical temperature [t=(T(c)-T)/T(c)-->0], we observe that the wetting layer thickness diverges as t(-beta) with effective critical exponent beta=0.23+/-0.06. This is characteristic of a broad, intermediate scaling regime for the crossover from van der Waals wetting to critical scaling. We predict beta=beta/3 approximately 0.11, with beta the usual bulk-order parameter critical exponent, showing a small but significant difference with experiment.     

热力耦合作用下双层碳纳米管的扭转屈曲

考虑碳纳米管周边弹性介质和层间范德瓦耳斯力的作用,利用连续介质力学的壳体理论,建立了热力耦合作用下碳纳米管屈曲问题的控制方程,给出了相应的临界屈曲扭矩的解析解.数值模拟结果表明,在低温和室温环境下,碳纳米管的临界屈曲载荷随着温度变化量的增加而提高;在高温环境下,碳纳米管的临界屈曲载荷随着温度变化量的增加而降低. 关键词： 碳纳米管 屈曲 热力耦合     

A new approach to the evaluation of Casimir and van der Waals forces in the transition region

This paper studies the incorporation of Casimir and van der Waals forces applied to a nanostructure with parallel configuration. The focus of this study is in a transition region in which Casimir force gradually transforms into van der Waals force. It is proposed that in the transition region, a proportion of both Casimir and van der Waals forces, as the interacting nanoscale forces, can be considered based on the separation distance between upper structure and substrate during deflection. Moreover, as the separation distance descends during deflection, the nanoscale forces could transform from Casimir to a proportion of both Casimir and van der Waals forces and so as to van der Waals. This is also extended to the entire surface of the nanostructure in such a way that any point of the structure may be subjected to Casimir, van der Waals or a proportion of both of them about its separation distance from the substrate. Therefore, a mathematical model is presented which calculate the incorporation of Casimir and van der Waals forces considering transition region and their own domination area. The mechanical behavior of a circular nano-plate has been investigated as a case study to illustrate how different approaches to nanoscale forces lead to different results. For this purpose, the pull-in phenomena and frequency response in terms of magnitude have been studied based on Eringen nonlocal elasticity theory. The results are presented using different values of the nonlocal parameter and indicated in comparison with those of the classical theory. These results also amplify the idea of studying the mechanical behavior of nanostructures using the nonlocal elasticity theory.     

Thermodynamics of superspreading

A simple model for calculation of the spreading coefficient of an aqueous surfactant solution on an apolar solid is proposed. The spreading coefficient is predicted to have two components: i) the van der Waals component, which is similar to the spreading coefficient of the alkane, making up the surfactant tail; and ii) the monolayer frustration component, dependent on the bending moduli and the spontaneous curvature of the surfactant. The frustration term is minimized at a negative spontaneous curvature. In order for a solution to spread, the van der Waals component of the spreading coefficient must be positive and larger than the monolayer frustration term. The spreading is facilitated by surfactants having very short and branched alkyl tails. Received 19 May 1999 and Received in final form 29 October 1999     

Coulombic Phase Transitions in Dense Plasmas

We give a survey on the predictions of Coulombic phase transitions in dense plasmas (PPT) and derive several new results on the properties of these transitions. In particular we discuss several types of the critical point and the spinodal curves of quantum Coulombic systems. We construct a simple theoretical model which shows (in dependence on the parameter values) either one alkali-type transition (Coulombic and van der Waals forces determine the critical point) or one Coulombic transition and another van der Waals transition. We investigate the conditions to find separate Van der Waals and Coulomb transitions in one system (typical for hydrogen and noble gas-type plasmas). The separated Coulombic transitions which are strongly influenced by quantum effects are the hypothetical PPT, they are in full analogy to the known Coulombic transitions in classical ionic systems. Finally we give a discussion of several numerical and experimental results referring to the PPT in high pressure plasmas.     

Effect of temperature and geometrical nonlinearity on wave propagation characteristics of carbon nanotubes

Considering the effect of temperature and geometrical nonlinearity in the constitutive relation, the equation of motion for a carbon nanotube is obtained based on the Euler–Bernouli beam model. Also, the effect of van der Waals forces is taken into account in the formulation. The carbon nanotube is assumed to be under the application of a constant distributed external load. At any temperature, the equilibrium solutions of the governing equations for a single-walled carbon nanotube (SWCNT) and a double-walled carbon nanotube (DWCNT) are obtained. A small perturbation is assumed around the equilibrium solution. Using this perturbation, the nonlinear equations of motion are linearized. Using the linearized form of the equations of motion, the characteristic equations and dispersion relations are obtained. It is shown that in the linear case and for the case of high temperature there exists a temperature beyond which the phase velocity does not exist. It is shown that in the case of room or low temperature there is no critical value for temperature. Based on the dispersion equation, a relation for the critical value of temperature is obtained. It is found that when the large deformation effect is taken into account, the critical value for temperature does not exist. Also, the effect of large deformations on phase velocities and lateral deformations of single-walled and double-walled carbon nanotube beams are studied. It is found that unlike the linear theory, the nonlinear theory predicts a non-zero phase velocity at the temperature corresponding to linear critical temperature.     

Contribution of macroscopic van der Waals interactions to friction forces

Using an approximation linear in velocities, an expression is obtained for friction forces due to nonretarded macroscopic van der Waals interactions. These forces are generated when field drag effects by a moving medium are taken into account.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 102–107, November, 1976.The author is grateful to Yu. S. Barash for critical remarks and discussions.     

A theory of monolayer phase transitions

We present the exact calculation of the equation of state for a simple model describing the phase transitions occurring in lipid monolayers. The model is of the van der Waals type, but with the density dependent attraction replaced by a long range interaction of another kind. For the size of the molecular hard cores we choose a function which increases with the internal energy of the p possible states of the molecule. As a result of this choice we find p - 1 first order phase transitions between the liquid and the solid state of the monolayer.     

Liquid-liquid critical point: an analytical approach

Theoretical simulations and experimental studies have showed that many systems (like liquid metals) can exhibit two phase transitions: gas-liquid and liquid-liquid. Consequently the fluid phase of these systems presents two critical points, namely the usual gas-liquid (G-L) critical point and the liquid-liquid critical point that results from a phase transition between two liquids of different densities: a low density liquid (LDL) and a high density liquid (HDL). The van der Waals theory for simple fluids [Phys. Rev. E 50, 2913 (1994)] is based on taking a system with purely repulsive forces as a reference, is able to describe two stable first-order phase transitions between fluids of different densities. The particles in our system interact via a total pair potential, which splits into a repulsive V_R and a density-dependent attractive V_A part.     

Triple-point wetting on rough substrates

The influence of substrate roughness on the wetting scenario of adsorbed van der Waals films is investigated by theory and experiment. Calculating the bending free energy penalty of a solid sheet picking up the substrate roughness, we show that a finite roughness always leads to triple-point wetting reducing the widths of the adsorbed solid films considerably as compared to that of smooth substrates. Testing the theory against our experimental data for molecular hydrogen adsorbed on gold, we find quantitative agreement.     

Molecular forces caused by the confinement of thermal noise

We have investigated spontaneous surface instabilities of very thin polymer films. Film stability and the wavelength of the dominating unstable mode were found to depend sensitively on the media adjacent to the film. Our experimental results cannot be explained by van der Waals interactions alone. To account for the presence of an additional destabilizing force, we propose that the geometrical confinement of thermally excited acoustic waves gives rise to a force that is strong enough to destabilize thin films. This thermoacoustic effect is of similar magnitude as van der Waals forces.     

A self-consistent approach for modelling the interfacial properties and phase diagrams of Yukawa,Lennard-Jones and square-well fluids

A self-consistent density-functional approach is presented for describing the phase behaviour and interfacial tensions of van der Waals fluids represented by the hard-core Yukawa (HCY), Lennard-Jones (LJ) and square-well (SW) potentials. The excess Helmholtz energy functional is formulated in terms of a modified fundamental measure theory (MFMT) for the short-ranged repulsion and a density-gradient expansion for the van der Waals attractions. Analytical expressions for the direct correlation functions of uniform fluids are utilized to take into account the effect of van der Waals’ attraction on intermolecular correlations. For bulk phases, the density functional theory is reduced to an equation of state (EOS) that provides accurate saturation pressures and vapour–liquid phase diagrams. Near the critical region, the long-range fluctuations can be corrected by using the renormalization group (RG) theory. With the same set of molecular parameters, the theory also yields satisfactory surface tensions and interfacial density profiles at all relevant temperatures.     

Effect of long-range forces on surface freezing

We examine the effect of long-range van der Waals interactions on surface freezing (SF) in linear hydrocarbon chain molecules, and the wetting criteria of the bulk liquid by the crystalline surface phase. We find that although the effect of van der Waals interactions is small for SF of normal alkanes, it is important for SF of dry and hydrated alcohols. We also find that the long-range interactions should not be ignored in the interpretation of wetting phenomena in recent experimental results. The results are in good agreement with recent experiments.     

Dynamic behavior of triple-walled carbon nanotubes conveying fluid

In this study, the instability of triple-walled carbon nanotubes (TWCNTs) conveying fluid is studied based on an Euler–Bernoulli beam model. The van der Waals (vdW) interactions between different carbon nanotubes (CNTs) are taken into account in the analysis, and the Galerkin discretization approach is used to solve the coupled equations of the motions. Numerical simulations show that the interlayer vdW interactions play a significant role in the natural frequencies and the stability of TWCNTs. The critical flow velocities—associated with divergence, restabilization and flutter—are determined. The effects of different inner radius and the value of mode N used in Galerkin discretization on the dynamical behaviors of the fluid-conveyed TWCNTs are also examined in detail. Results reveal that the internal moving fluid plays an important role in the instability of TWCNTs.     

Double-walled carbon nanotube with surrounding elastic medium under axial pressure

In this paper, the buckling behavior and critical axial pressure of double-walled carbon nanotubes (DWCNTs) with surrounding elastic medium are investigated. A double-shell (circular cylindrical shell) model is presented and the effects of surrounding elastic medium on the outer tube and the van der Waals forces between two adjacent tubes are taken into account. The analysis and the numerical solution method are based on the classical theory of plates and shells and the Galerkin method. Equations are derived for the critical axial forces and pressures of DWCNTs; the critical axial forces and pressures are calculated for different axial half sine wavenumbers and circumferential sine wavenumbers and compared with those for single-walled carbon nanotubes (SWCNTs).Results indicate that the critical axial force of a DWCNT is higher than that of an SWCNT, but the critical axial pressure of a DWCNT is lower than the critical axial pressure of a SWCNT. Although the critical axial force of a DWCNT decreases as the axial half sine wavenumbers increase, it rises as the circumferential sine wavenumbers increase.     

Lattice Boltzmann Simulation of van der Waals Phase Transition with Chemical Potential

In this paper phase transition of van der Waals gas is simulated by the Boltzmann lattice method. Thermodynamics and chemical potentials have been taken into account.     

论范德瓦尔斯a和b参数与温度的关系

范德瓦尔斯方程中a、b参数是否与温度相关,不但不同文献中的说法互不相同,而且有同一文献前后的结论相互矛盾.本文分析了这个令人迷惑的问题.在热力学中a和b参量被处理为与温度无关,它仅仅在临界点附近有效并可以把范德瓦尔斯方程表述为对应态定律;在更加广泛的温度区间a、b参量和温度有关,但是范德瓦尔斯方程却丧失了其独特性.统计物理文献把a和b参量处理成为位力展开的一种拟合方程,发现一般情况下两个参数都依赖于温度,仅仅在特殊情况下和温度无关,以说明对应态定律成立的条件.热力学和统计物理关于a和b参量是否依赖于温度相互矛盾的表述,源于这两个理论中范德瓦尔斯状态方程适用范围不同.