Heterogeneity length

Figure 5. Dynamic heterogeneity length scale plotted as a function of Tg for tridecamer, PAMS19k, PAMSIOOk, the blends shown in Figure 1, as well as for the pure pentamer, PAMSlOSk, and other blends previously studied [17]. The name of the materials has been shown in Table 1. Red and blue symbols represent pure components and blends, respectively. Open symbols are analyzed from data [17].

The flux is related both to an equiUbrium quantity, ie, the chemical activity, through the solubiUty and to a nonequilihrium coefficient D. In contrast, for an ideal membrane emphasizes the path length and the diffusion constant. Binding and heterogeneity of the membrane may compHcate these simple relationships. 

Heterogeneous reactions of industrial significance occur between all combinations of gas, liquid, and solid phases. The solids may be inert or reac tive or catalysts in granular form. Some noncatalytic examples are listed in Table 7-11, and processes with solid catalysts are listed under Catalysis in Sec. 23. Equipment and operating conditions of heterogeneous processes are covered at some length in Sec. 23 only some highlights will be pointed out here. 

Bulk polymerisation is heterogeneous since the polymer is insoluble in the monomer. The reaction is autocatalysed by the presence of solid polymer whilst the concentration of initiator has little effect on the molecular weight. This is believed to be due to the overriding effect of monomer transfer reactions on the chain length. As in all vinyl chloride polymerisation oxygen has a profound inhibiting effect. 

An important issue in the thermodynamics of confined fluids concerns their symmetry which is lower than that of a corresponding homogeneous bulk phase because of the presence of the substrate and its inherent atomic structure [52]. The substrate may also be nonplanar (see Sec. IV C) or may consist of more than one chemical species so that it is heterogeneous on a nanoscopic length scale (see Sec. VB 3). The reduced symmetry of the confined phase led us to replace the usual compressional-work term —Pbuik F in the bulk analogue of Eq. (2) by individual stresses and strains. The appearance of shear contributions also reflects the reduced symmetry of confined phases. 

FIG. 1 Profiles of the heterogeneous surface generated by the procedure of Bakaev and Steele [81]. Each profile (except the upper one) is shifted downward with respect to the previous one by the unit of length. (Reprinted with permission from Langmuir 5 148-154, August 1992. 1992, American Chemical Society.)... 

It is basically a fractionation process that depends not only on molecular size, but also on chemical composition, stereo-configuration, branching, and crosslinking. For multicomponent systems, fractionation with different ion polymolecularity, chemical heterogeneity and sequence length distribution, solubility or elution fractionation is of primary importance. Therefore, gel permeation chromatography or size exclusion chromatography is used as an important tool for the characterization of PBAs. 

Objective Evaluation of Color. In recent years a method has been devised and internationally adopted (International Commission on Illumination, I.C.I.) that makes possible objective specification of color in terms of equivalent stimuli. It provides a common language for description of the color of an object illuminated by a standard illuminant and viewed by a standard observer (H). Reflectance spectro-photometric curves, such as those described above, provide the necessary data. The results are expressed in one of two systems the tristimulus system in which the equivalent stimulus is a mixture of three standard primaries, or the heterogeneous-homogeneous system in which the equivalent stimulus is a mixture of light from a standard heterogeneous illuminant and a pure spectrum color (dominant wave-length-purity system). These systems provide a means of expressing the objective time-constant spectrophotometric results in numerical form, more suitable for tabulation and correlation studies. In the application to food work, the necessary experimental data have been obtained with spectrophotometers or certain photoelectric colorimeters. 

This initiator is aggregated but heterogeneous initiation is not harmful, provided the growing chains are dispersed as soon as they have reached a certain length. 

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-... 

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