Interface length scale

In order to describe the second-order nonlinear response from the interface of two centrosynnnetric media, the material system may be divided into tlnee regions the interface and the two bulk media. The interface is defined to be the transitional zone where the material properties—such as the electronic structure or molecular orientation of adsorbates—or the electromagnetic fields differ appreciably from the two bulk media. For most systems, this region occurs over a length scale of only a few Angstroms. With respect to the optical radiation, we can thus treat the nonlinearity of the interface as localized to a sheet of polarization. Fonnally, we can describe this sheet by a nonlinear dipole moment per unit area, -P ", which is related to a second-order bulk polarization by hy P - lx, y,r) = y. Flere z is the surface nonnal direction, and the... 

On short length scales the coarse-grained description breaks down, because the fluctuations which build up the (smooth) intrinsic profile and the fluctuations of the local interface position are strongly coupled and camiot be distinguished. The effective interface Flamiltonian can describe the properties only on length scales large compared with the width w of the intrinsic profile. The absolute value of the cut-off is difficult... 

These chain models are well suited to investigate the dependence of tire phase behaviour on the molecular architecture and to explore the local properties (e.g., enriclnnent of amphiphiles at interfaces, molecular confonnations at interfaces). In order to investigate the effect of fluctuations on large length scales or the shapes of vesicles, more coarse-grained descriptions have to be explored. 

The surface dividing the components of the mixture formed by a layer of surfactant characterizes the structure of the mixture on a mesoscopic length scale. This interface is described by its global properties such as the surface area, the Euler characteristic or genus, distribution of normal vectors, or in more detail by its local properties such as the mean and Gaussian curvatures. 

These apparent restrictions in size and length of simulation time of the fully quantum-mechanical methods or molecular-dynamics methods with continuous degrees of freedom in real space are the basic reason why the direct simulation of lattice models of the Ising type or of solid-on-solid type is still the most popular technique to simulate crystal growth processes. Consequently, a substantial part of this article will deal with scientific problems on those time and length scales which are simultaneously accessible by the experimental STM methods on one hand and by Monte Carlo lattice simulations on the other hand. Even these methods, however, are too microscopic to incorporate the boundary conditions from the laboratory set-up into the models in a reahstic way. Therefore one uses phenomenological models of the phase-field or sharp-interface type, and finally even finite-element methods, to treat the diffusion transport and hydrodynamic convections which control a reahstic crystal growth process from the melt on an industrial scale. 

Consider a planar premixed flame front, such as that sketched in Figure 5.1.1. For the moment, we will be interested only in long length scales and we will treat the flame as an infinitely thin interface that transforms cold reactive gas, at temperature and density T p, into hot burnt gas at temperature and density T, A.-The flame front propagates at speed Sl into the xmbumt gas. We place ourselves in the reference frame of the front, so cold gas enters the front at speed = Su and because of thermal expansion, the hot gases leave the front at velocity 14 = Sl(Po/a)- The density ratio, Po/Pb, is roughly equal to the... 

Classical surface and colloid chemistry generally treats systems experimentally in a statistical fashion, with phenomenological theories that are applicable only to building simplified microstructural models. In recent years scientists have learned not only to observe individual atoms or molecules but also to manipulate them with subangstrom precision. The characterization of surfaces and interfaces on nanoscopic and mesoscopic length scales is important both for a basic understanding of colloidal phenomena and for the creation and mastery of a multitude of industrial applications. 

Recent developments of materials and devices with structures in nanometer length scales have created new opportunities and challenges in the science of thermal transport. Interfaces play a particularly important role in the properties of nanoscale structures and nanostructured materials [97-98], This is why a renewed interest for contact resistance arose in recent years with studies of nanocomposite, semicrystalline and polycrystalline materials where contact resistances has a controlling role to determine the bulk thermal conductivity of the material [99-100],... 

Several recent molecular dynamics simulations (e.g. [10] and references therein) have focussed on the wetting of interfaces (Section 6.1) and, for example, the behaviour of very small droplets at the nanoscale. Such simulations are able to relate the atomistic behaviour directly to relevant macroscopic parameters such as the contact angle and are able to show the dramatic effects at this length scale of addition of surfactant molecules or roughening of the surface. 

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