Conformal diffusion

The interfacial zone is by definition the region between the crystallite basal surface and the beginning of isotropy. Due to the conformationally diffuse nature of this region, quantitative contents of the interphase are most often determined by indirect measures. For example, they have been computed as a balance from one of the sum of the fractional contents of pure crystalline and amorphous regions. The analysis of the internal modes region of the Raman spectrum of polyethylene, as detailed in the previous section of this chapter, was used to quantify the content of the interphase region (ab). 

I. Goychuk and P. Hanggi, The role of conformational diffusion in ion channel gating. PhysicaA, 325 9-18 (2003). 

For pores smaller than 10 m, a molecular sieving effect can be present and the movement of one or more species inside the porous solid occurs due to the molecular interactions between the species and the network of the porous body here, for the description of species displacement, the theory of molecular dynamics is frequently used. The affinity between the network and the species is the force that controls the molecular motion at the same time, the affinity particularities, which appear when two or more species are in motion inside the porous structure, explain the separation capacity of those solids. We can use a diffusive characterisation of species motion inside a porous solid by using the notion of conformational diffusion. 

Reed, W.F. Light Scattering Results on Polyelectrolyte Conformations, Diffusion and Interparticle Interactions and Correlations, invited entry for ACS Symposium Series 548, Macroion Characterization. Schmitz, K. Ed., ACS, 1994, pp. 297-314. 

A subtle refutation of the simple spontaneous curvature model without the bilayer aspect follows from the observation of vesicles of non-spherical topology, i.e. vesicles with holes (like anchor rings) or with handles. For vesicles with at least two holes or handles, the shape of lowest total energy is not unique but rather one fold continuously degenerate due to conformal invariance. This theoretical finding led to the prediction that such vesicles should permanently change their shape, a phenomenon termed conformal diffusion [21], This was indeed verified experimentally somewhat later [22]. Apart from the esthetic pleasure when visualizing conformal transformations under the microscope, this observation also shows the spontaneous curvature model to be incomplete with out the additional term. 

Piela L, Kostrowicki J and Scheraga H A 1989 The multiple-minima problem in the conformational analysis of molecules. Deformation of the potential energy hypersurface by the diffusion equation method J. Phys. Chem. 93 3339... 

Fig. 9. Uptake curves for N2 in two samples of carbon molecular sieve showing conformity with diffusion model (eq. 24) for sample 1 (A), and with surface resistance model (eq. 26) for example 2 (0)j LDF = linear driving force. Data from ref. 18.

Diffusion-controlled mass transfer is assumed when the vapor or liquid flow conforms to Tick s second law of diffusion. This is stated in the unsteady-state-diffusion equation using mass-transfer notation as... 

Consider a diffusion process in which a molecule is initially in a conformation defined by the coordinates rj,. A transition probability can be constructed using a product of joint probabilities /5(r(,+i rj,) for moving between intermediate positions rj, and rj,+ i integrated over all intennediate states,... 

Depending on experimental parameters, NOE intensities will be affected by spin diffusion (Eig. 8). Magnetization can be transferred between two protons via third protons such that the NOE between the two protons is increased and may be observed even when the distance between the two protons is above the usual experimental limit. This is a consequence of the distance dependence of the NOE. Depending on the conformation, it can be more efficient to move magnetization over intennediate protons than directly. The treatment of spin diffusion during structure refinement is reviewed in more detail in Refs. 31, and 71-73. 

Although the diffusion mechanism can be seen as mechanical but occurring at molecular dimensions, van der Waals intermolecular interactions and conformational entropic energy provide an additional mechanism that increases adhesion [62]. It is interesting to note the analogy that exists between this mechanism at the molecular level with the adherence, adhesion and viscoelastic deformations concept applied for a macroscopic adhesive. 

For dynamical studies of diffusion, conformational and transport behavior under shear stress, or kinetics of relaxation, one resorts to dynamic models [54,58,65] in which the topological connectivity of the chains is maintained during the simulation. 

The reduced oxidation near sample corners is related to these stress effects, either by retarded diffusion or modified interfacial reactionsManning described these stresses in terms of the conformational strain and distinguished between anion and cation diffusion, and concave and convex surfaces. He defined a radial vector M, describing the direction and extent of displacement of the oxide layer in order to remain in contact with the retreating metal surface, where ... 

A very similar effect of the surface concentration on the conformation of adsorbed macromolecules was observed by Cohen Stuart et al. [25] who studied the diffusion of the polystyrene latex particles in aqueous solutions of PEO by photon-correlation spectroscopy. The thickness of the hydrodynamic layer 8 (nm) calculated from the loss of the particle diffusivity was low at low coverage but showed a steep increase as the adsorbed amount exceeded a certain threshold. Concretely, 8 increased from 40 to 170 nm when the surface concentration of PEO rose from 1.0 to 1.5 mg/m2. This character of the dependence is consistent with the calculations made by the authors [25] according to the theory developed by Scheutjens and Fleer [10,12] which predicts a similar variation of the hydrodynamic layer thickness of adsorbed polymer with coverage. The dominant contribution to this thickness comes from long tails which extend far into the solution. 

The most possible reason may be in the higher free energy of the protein adsorption on PolyPROPYL A materials. Chemisorbed neutral poly(succinimide) of molecular weight 13000 apparently forms a diffuse interface as predicted by theory (see Sect. 2.2). Controversially, a short polyethyleneimine exists on a surface in a more flat conformation exhibiting almost no excluded volume and producing... 

Alzheimer s Disease. Figure 1 A(3 monomers can self-associate to form dimers, trimers and higher oligomers. Globular structures of synthetic A(342 are known as A(3-derived diffusible ligands (ADDLs) (3-12-mers of A(3). These structures are similar to the smallest protofibrils and represent the earliest macromolecular assembly of synthetic A(3. The characteristic amyloid fiber exhibits a high beta-sheet content and is derived in vitro by a nucleation-dependent self-association and an associated conformational transition from random to beta-sheet conformation of the A(3 molecule. Intermediate protofibrils in turn self-associate to form mature fibers. 

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