Length-scale domain

Shulha, H., Foo, C.W.P., Kaplan, D.L., and Tsukruk, V.V. "Unfolding the multi-length scale domain structure of silk fibroin protein"Polymer 47(16), 5821-5830 (2006). 

The most important property of the self-organized critical state is the presence of locally connected domains of all sizes. Since a given perturbation of the state 77 can lead to anything from a trivial one-site shift to a lattice-wide avalanche, there are no characteristic length scales in the system. Bak, et al. [bak87] have, in fact, found that the distribution function D s) of domains of size s obeys the power law... 

There are a number of industrial and technological areas in which nanoscale adhesion is important. One of the earliest fields concerned with adhesion on this scale was colloid science. Colloid particles lie in the intermediate region between macro and nano, with dimensions typically of the order of hundreds of nanometers up to a few microns. This means that their true contact areas he well within the nano-domain and are influenced by interactions on this length scale. Adhesion between such particles is important, due to its influence on mineral separation processes and on the aggregation of powders, for example, on the walls of machinery or in the forming of medical tablets. In an extraterrestrial context, such... 

Other key features in the analysis of pore structure are the length scales associated with the various micro- (nano)-scale obstacles and pores, the possible larger-scale variations in structure, and the averaging domain over which information is needed [6,341,436], The hterature refers to analysis of homogeneous and heterogeneous porous media, where homogeneous refers to media with no variation in physical properties (e.g., porosity, diffu-... 

Figure 1.8. Relevant length scales in catalysis range from the subnanometre domain of the atomic and molecular level to the macroscopic domain of an industrial reactor.

Kn is the ratio of two length scales, the mean free path of the gas molecules A and a characteristic length scale of the flow domain L, for example the channel diameter. For molecules interacting as hard spheres of diameter d, the mean free path is given as (see, e.g., [4])... 

In choosing a model, the user can optimize fate assessment efforts by delineating first, the source release patterns and second, the dominant dynamical processes. Taking the intramedia processes first, one can address model criteria by considering the ratio of characteristic times. The advection time is the principal length scale of the domain L divided by the average flow speed u i.e. 

The ESRI experiments described in our publications and summarized in this chapter led to spatially resolved information on the effect of treatment conditions, amount of stabilizer, and polymer composition on the degradation rate. In the heterophasic systems studied in our laboratory, ESRI has identified specific morphological domains where chemical processes are accelerated. The combination of ID and 2D spectral-spatial ESRI experiments led to mapping of the stabilizer consumption on two length scales within the sample depth on the scale of a few mm, and within morphological domains on the scale of a few gm. 

The electrodeposited TiAl3 described above displays crystallographic features of distinctly different length scales. The deposit grain size is on the order of 0.1 to 0.5 pm while the Ll2 domain size is on the order of 5-10 nm. The domains appear to have grown through a first order nucleation and growth process that is independent... 

In the LEM, turbulence is modeled by a random rearrangement process that compresses the scalar field locally to simulate the reduction in length scales that results from turbulent mixing. For example, with the triplet map, defined schematically in Fig. 4.2, a random length scale / is selected at a random point in the computational domain, and the scalar field is then compressed by a factor of three.14 The PDF for /,... 

According to the U.S. National Nanotechnology Institute, nanotechnology encompasses research and development to synthesize, control, and manipulate stmctures, devices, and systems of novel properties and functions because of their size at the atomic, molecular, or macromolecular levels in the length scale ranging from approximately 1 to 100 nanometers. Indeed, this length scale is of particular relevance to heterogeneous catalysis, where the active sites are small crystallites or domains of the active phase. The reaction typically involves atom-molecule interactions, and the active sites are placed in or on an extended solid where the access paths to the active sites are tens to hundreds of nanometers. The issue of access path is a familiar territory in... 

Pulsed field gradient (PFG)-NMR experiments have been employed in the groups of Zawodzinski and Kreuer to measure the self-diffusivity of water in the membrane as a function of the water content. From QENS, the typical time and length scales of the molecular motions can be evaluated. It was observed that water mobility increases with water content up to almost bulk-like values above T 10, where the water content A = nn o/ nsojH is defined as the ratio of the number of moles of water molecules per moles of acid head groups (-SO3H). In Perrin et al., QENS data for hydrated Nation were analyzed with a Gaussian model for localized translational diffusion. Typical sizes of confining domains and diffusion coefficients, as well as characteristic times for the elementary jump processes, were obtained as functions of A the results were discussed with respect to membrane structure and sorption characteristics. ... 

The reduction of the long-range diffusivity, Di by a factor of four with respect to bulk water can be attributed to the random morphology of the nanoporous network (i.e., effects of connectivity and tortuosity of nanopores). For comparison, the water self-diffusion coefficient in Nafion measured by PFG-NMR is = 0.58 x 10 cm s at T = 15. Notice that PFG-NMR probes mobilities over length scales > 0.1 /rm. Comparison of QENS and PFG-NMR studies thus reveals that the local mobility of water in Nafion is almost bulk-like within the confined domains at the nanometer scale and that the effective water diffusivity decreases due to the channeling of water molecules through the network of randomly interconnected and tortuous water-filled domains. ... 

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