Molecular structures spatial scaling

A reevaluation of molecular structure of humic substances based on data obtained primarily from nuclear magnetic resonance spectroscopy, X-ray absorption near-edge structure spectroscopy, electrospray ionization-mass spectrometry, and pyrolysis studies was presented by Sutton and Sposito (2005). The authors consider that humic substances are collections of diverse, relatively low molecular mass components forming dynamic associations stabilized by hydrophobic interactions and hydrogen bonds. These associations are capable of organizing into micellar structures in suitable aqueous environments. Humic components display contrasting molecular motional behavior and may be spatially segregated on a scale of nanometers. Within this new structural context, these components comprise any molecules... 

While molecular diffusivity is commonly independent of direction (isotropic, to use the correct expression), turbulent diffusivity in the horizontal direction is usually much larger than vertical diffusion. One reason is the involved spatial scales. In the troposphere (the lower part of the atmosphere) and in surface waters, the vertical distances that are available for the development of turbulent structures, that is, of eddies, are generally smaller than the horizontal distances. Thus, for pure geometrical reasons the eddies are like flat pancakes. Needless to say, they are more effective in turbulent mixing along their larger axes than along their smaller vertical extension. 

Figure 2 illustrates major modeling methods, i.e., ab initio molecular dynamic (AIMD), molecular dynamic (MD), kinetic Monte Carlo (KMC), and continuum methods in terms of their spatial and temporal scales. Models for microscopic and macroscopic components of a PEFC are placed in the figure in terms of their characteristic dimensions for comparison. While continuum models are successful in rationalizing the macroscopic behaviors based on a few assumptions and the average properties of the materials, molecular or atomistic modeling can evaluate the nanostructures or molecular structures and microscopic properties. In computational... 

As discussed in a recent review on allostery, the key challenge for understanding a specific system is to provide a molecular level description regarding how events of different spatial scales (domain vs. sidechain) and physicochemical nature (hydrolysis vs. structural isomerization) are tightly coupled to achieve the desired... 

Chiral liquid crystals belong to a wide class of soft condensed phases. The director field in the ground state of chiral phases is nonuniform because molecular interactions lack inversion symmetry. Among the broad variety of spatially distorted structures the simplest one is the cholesteric phase in which the director n is twisted into a helix. The spatial scale of background deformations, e.g., the pitch p of the helix, is normally much larger than the molecular size ( > 0.1 pm) since the interactions that break the inversion symmetry are weak. 

The theory of fluid flow, together with the theory of elasticity, makes up the field of continuum mechanics, which is the study of the mechanics of continuously distributed materials. Such materials may be either soKd or fluid, or may have intermediate viscoelastic properties. Since the concept of a continuous medium, or continuum, does not take into consideration the molecular structure of matter, it is inherently an idealization. However, as long as the smallest length scale in any problem under consideration is very much larger than the size of the molecules making up the medium and the mean free path within the medium, for mechanical purposes all mass may safely be assumed to be continuously distributed in space. As a result, the density of materials can be considered to be a continuous function of spatial position and time. 

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