Motion of Crystalline Interfaces

When particles or large molecules make contact with water or an aqueous solution, the polarity of the solvent promotes the formation of an electrically charged interface. The accumulation of charge can result from at least three mechanisms (a) ionization of acid and/or base groups on the particle s surface (b) the adsorption of anions, cations, ampholytes, and/or protons and (c) dissolution of ion-pairs that are discrete subunits of the crystalline particle, such as calcium-oxalate and calcium-phosphate complexes that are building blocks of kidney stone and bone crystal, respectively. The electric charging of the surface also influences how other solutes, ions, and water molecules are attracted to that surface. These interactions and the random thermal motion of ionic and polar solvent molecules establishes a diffuse part of what is termed the electric double layer, with the surface being the other part of this double layer. 

J.W. Cahn. Theory of crystal interface motion in crystalline materials. Acta Metall., 8(8) 554—562, 1960. 

Analysis is simplified if 7 is isotropic—i.e., independent of geometrical attributes such as interfacial inclination n and, for internal interfaces in crystalline materials, the crystallographic misorientation across the interface. All interfacial energy reduction then results from a reduction of interfacial area through interface motion. The rate of interfacial area reduction per volume transferred across the interface is the local geometric mean curvature. Thus, local driving forces derived from variations in mean curvature allow tractable models for the capillarity-induced morphological evolution of isotropic interfaces. 

In spin-diffusion studies it is possible to detect not only two but three domain sizes. The third domain can be considered the interface (i) between the other two domains, which can be different chemical species in a polymer blend or rigid crystalline (r) and mobile amorphous (m) material in a semicrystalline polymer. To illustrate this point, a mobility timescale is depicted in Fig. 7.2.25(a) and the simplified ID domain structure of PE underneath in (b). Rigid crystalline and mobile amorphous materials exhibit motion of chain segments with different correlation times Tc. The chains at the interface between both domains exhibit intermediate mobility. The exact ranges of correlation times in the individual domains depend on the particular choice of filters. Therefore, the values of domain sizes derived through spin-diffusion NMR also depend on the type of filters used. In particular, the interface is defined solely by the NMR experiment and can only be detected if the filters are properly chosen. 

The model is divided into four parts (1) the definition of the surface to be interfaced with blood, (2) the mode of the plasma protein(s) and/or electrolyte adsorption, (3) relaxation motion of the blood interfacing side chain groups, and (4) protein denaturation and/or liquid crystalline order. 

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