Nanodrop on a nanorough hydrophilic solid surface: contact angle dependence on the size, arrangement, and composition of the pillars

A two-dimensional nanodrop on a hydrophilic solid surface decorated with nanopillars is examined using a nonlocal density functional theory. It is shown that, in contrast to the commonly used Wenzel formula, even an extremely small roughness can considerably increase the contact angle. The contact angle depends on the distance between pillars, their height and width, as well as their composition. It was found that for all selected pillar heights and compositions, the largest contact angle is obtained when the distance between pillars acquires a size at which the liquid molecules can no longer penetrate between them. The further decrease in the interpillar distance decreases the contact angle, in qualitative agreement with the Cassie-Baxter formula. Considering pillars of various compositions, the role of the gradient of the fluid-solid interaction potential is examined. The presence of such a gradient does not allow the formation of a stable nanodrop on the surface. However, asymmetrical metastable nanodrops can be formed.     

Effect of fluid-solid interactions on symmetry breaking in closed nanoslits

The possibility of symmetry breaking of the fluid (argon) density distribution across a long closed slit with identical walls composed of solid carbon dioxide was noted in previous papers by the authors. The main conclusion was that there is a range of average densities in which symmetry breaking occurs and that outside that range the fluid density profile is symmetrical. A critical temperature T(sb) was also identified below which symmetry breaking can occur. In this paper, symmetry breaking is examined for walls made of other materials and it is shown that it occurs only when the energy parameter epsilon(fw) of the fluid-wall interaction in the Lennard-Jones potential satisfies the inequalities epsilon(fw1) < or = epsilon(fw) < or = epsilon(fw2), where epsilon(fw1) and epsilon(fw2) are temperature-dependent critical values of epsilon(fw). The value of epsilon(fw1) increases and that of epsilon(fw2) decreases with increasing temperature. The comparison of the theory with Monte Carlo simulations confirms the existence of symmetry breaking across the slit. The possibility of symmetry breaking along the slit is also noted.     

Fluid density profile transitions and symmetry breaking in a closed nanoslit

The density profiles in a fluid interacting with the two identical solid walls of a closed long slit were calculated for wide ranges of the number of fluid molecules in the slit and temperature by employing density functional theory in the local density approximation. Two potentials, the van der Waals and the Lennard-Jones, were considered for the fluid-fluid and the fluid-walls interactions. It was shown that the density profile corresponding to the stable state of the fluid considerably changes its shape with increasing average density (rhoav) of the fluid inside the slit, the details of changes being dependent on the selected potential. For the van der Waals potential, a single temperature-dependent critical value rhosb of rhoav was identified, such that for rhoav < rhosb the stable state of the system is described by a symmetric density profile, whereas for rhoav >/= rhosb it is described by an asymmetric one. This transition constitutes a spontaneous symmetry breaking of the fluid density distribution in a closed slit with identical walls. For rhoav >/= rhosb, a metastable state, described by a symmetric density profile, was present in addition to the stable asymmetric one. The shape of the symmetric profile changed suddenly at a value rhoc-h > rhosb of the average density, the density rhoc-h being almost independent of temperature. Because of the shapes of the profiles before and after the transformation, this transition was named cup-hill transformation. At the transition point, the density of the fluid near the walls decreased suddenly from a liquid-like value becoming comparable with the density of a gaseous phase, and the density in the middle of the slit increased suddenly from a gaseous-like value becoming on the order of the density of a liquid phase. For the Lennard-Jones potential, there are two temperature-dependent critical densities, rhosb1 and rhosb2, such that the stable density profile is asymmetric (symmetry breaking occurs) for rhosb1 相似文献   

Calculation of Total Cross Section for γγ→γZ Scattering at High Energy

The total cross sections of γγ→γZ process for γγ c.m.s. energy 91.2—2000GeV are presented. W loop contribution is dominating when γγ c.m.s. energy is larger than 140GeV. The total cross section has a maximum, 220 fb(|cosθ|33cm^－2·s^－1 in which case more than 6000 events for γγ→γZ would be observable. In principle this process provides a test of the non-abelian nature of the standard model, especially the anomalous triple and quartic W-boson vertices.     

γγ→γZ过程高能总截面的数值计算

给出了γγ→γZ过程,质心系总能量在91.2—2000GeV的总截面.结果表明在总能量大于140GeV时,W玻色子图的贡献比起费米子图的贡献要大,当总能量在750GeV左右,截面达到极大值220fb(|cosθ|33cm^－2·sec^－1,每年在总能量750GeV处可观察到6000多个γγ→γZ事例,用它可以进一步验证标准模型,特别是其中规范粒子的三顶角和四顶角相互作用.     

Microscopic interpretation of the dependence of the contact angle on roughness

The macroscopic contact angle theta(m) of a liquid drop on a rough solid surface in the presence of a gas is calculated microscopically on the basis of a variational minimization of the total potential energy of the drop. Two limiting cases are considered: the liquid penetrates into the space between asperities (Wenzel regime) and the liquid resides on the top of asperities (Cassie-Baxter regime). Long-range as well as short-range interactions between the molecules of liquid, solid, and gas are taken into account. It was also assumed that small portions of insoluble gas are accumulated near the edges of the asperities during the formation of the droplet. The contact angle depends on several parameters involved in the microscopic interactions as well as on the fractions of solid surface between asperities, and of the surface of the asperities themselves, that are in contact with the liquid. It is shown that the theory can explain the nonlinear dependence of cos theta(m) on roughness observed by Krupenkin et al. [Krupenkin, T. N.; Taylor, J. A.; Schneider, T. M.; Yang, S. Langmuir 2004, 20, 3824].(1).     

Microscopic treatment of a barrel drop on fibers and nanofibers

The microscopic approach of Berim and Ruckenstein (J. Phys. Chem. B 108 (2004) 19330, 19339) regarding the shape and stability of a liquid drop on a planar bare solid surface is extended to a liquid barrel drop on the bare surface of a solid cylinder (fiber) of arbitrary radius. Assuming the interaction potentials of the liquid molecules between themselves and with the molecules of the solid of the London-van der Waals form, the potential energy of a liquid molecule with an infinitely long fiber was calculated analytically. A differential equation for the drop profile was derived by the variational minimization of the total potential energy of the drop by taking into account the structuring of the liquid near the fiber. This equation was solved in quadrature and the shape and stability of the barrel drop were analyzed as functions of the radius of the fiber and the microscopic contact angle theta(0) which the drop profile makes with the surface of the fiber. The latter angle is dependent on the fiber radius and on the microscopic parameters of the model (strength of the intermolecular interactions, densities of the liquid and solid phases, hard core radii, etc.). Expressions for the evaluation of the microcontact angle from experimentally measurable characteristics of the drop profile (height, length, volume, location of inflection point) are obtained. All drop characteristics, such as stability, shape, are functions of theta(0) and a certain parameter a which depends on the model parameters. In particular, the range of drop stability consists of three domains in the plane theta(0)-a, separated by two critical curves a=a(c)(theta(0)) and a=a(c1)(theta(0)) [a(c)(theta(0))h(m1) cannot exist, whereas in the third domain (between those curves) the drop can have values of h(m) either smaller than h(m1) or larger than h(m2), where h(m2)>h(m1) is a second critical height. For sufficiently large fiber radii, R(f)1 >/= microm, the critical curves almost coincide and only two domains, the first and the second, remain. The smaller the radius, the larger is the difference between the critical curves and the larger is the second domain of drop stability. The shape of the drop depends on whether the point (theta(0),a) on the theta(0)-a plane is far from the critical curve or near it. In the first case the drop profile has generally a large circular part, while in the second case the shape is either almost planar or contains a long manchon that is similar to a film on the fiber.     

局域模(实的及虚的)的一种新表述

本文给出了一种新的表述局域模(实的及虚的)的方法。我们引入了变形豫解式的迹P(z).它仅在z平面的实轴上有奇异性,孤立极点对应于实局域模。将P(E+iη)向下解析延拓至第二黎曼面,则其复极点对应于虚的(或不稳定的)局域模。复极点的实部是不稳定局域模的能量,虚部是它寿命的倒数,自然地得到了寿命为正的限制。此能量与寿命符合于相应共振散射的能量与宽度。本文还讨论了实局域模与虚局域模之间的关系。最后,比较了P(z)的奇异性与态密度的变化,并进一步阐明了寿命为正的及负的解之间的差别。指出,一般说来,只有寿命为正的解当作用强度增加时会变成实的局域模,负寿命的解是不会的。