Hansen space

Figure 11.57. Distance in Hansen space for plasticizers containing phthalates having alcohols of different lengths of hydrocarbon chains. [Data from Krauskopf L G Godwin A D, J. Vinyl Additive Technol., 5, No.2, June 1999, p. 107-12.]...

Introduction of a plasticizer causes separation of PVC chains relative to the concentration of the plasticizer (see Section 11.44.4 on discussion of the effect of plasticizer on free volume). Also the plasticizer type plays a role in this process. Figure 11.57 shows that the interaction radius of different plasticizers, expressed here by distance in Hansen space, increases with the size of the plasticizer molecule." Plasticizer concentration has similar effect on separation of chains and mobility of different molecules within the system. This modification of structure has implications on some properties discussed below. 

These three parameters can be treated as coordinates for a point in three dimensions, i.e., the Hansen space. The nearer some two molecules are in this space, the more likely they to be mutually soluble. The distance R between the Hansen parameters in the Hansen space can be calculated as ... 

Defusing the Global Warming Time Bomb, 2004. James Hansen—Director of NASA Goddard Institute for Space Studies, Scientific American, Vol. 290, Number 3, March. 

When the electrostatic properties are evaluated by AF summation, the effect of the spherical-atom molecule must be evaluated separately. According to electrostatic theory, on the surface of any spherical charge distribution, the distribution acts as if concentrated at its center. Thus, outside the spherical-atom molecule s density, the potential due to this density is zero. At a point inside the distribution the nuclei are incompletely screened, and the potential will be repulsive, that is, positive. Since the spherical atom potential converges rapidly, it can be evaluated in real space, while the deformation potential A(r) is evaluated in reciprocal space. When the promolecule density, rather than the superposition of rc-modified non-neutral spherical-atom densities advocated by Hansen (1993), is evaluated in direct space, the pertinent expressions are given by (Destro et al. 1989)... 

In the case when = and = , knowing is a parameter that does not depend on space, we obtain the decomposition of the held introduced by Hansen [40] ... 

U.S. Patent Appl. 345458, 1984 Hansen, K.C. Yaws, C. L. (United States National Aeronautics and Space Administration) Chem. Abstr. 1984, 700, 88140. 

Some years ago in a continuing effort to understand phase diagrams, I had discovered [3] the following empirical rules among more than 300 binary phase diagrams reported in the literature (Hansen, Elliot Shunk) [4,5,6], The metallic radii, Ra, Rb, used are from INTERATOMIC DISTANCES (The Chemical Society, London, 1958) [7] and the structural notation follows that described in Handbook of Lattice Spacing and Structure of Metals (Pearson, 1958) [8]).. 

Chemically bound water is most reasonably defined as including that present in interlayer spaces, or more firmly bound, but not that present in pores larger than interlayer spaces. As will be seen in Chapter 8, the distinction between interlayer space and micropores is not sharp water adsorbed on surfaces of pores further blurs the definition. From the experimental standpoint, the determination is complicated by the fact that the amount of water retained at a given RH depends on the previous drying history of the sample and on the rate at which water is removed. An approximate estimate is obtained by equilibrating a sample, not previously dried below saturation, with an atmosphere of 11% RH (F12,F13,F14). Saturated aqueous LiCl HjO gives the required RH (partial pressure of water vapour = 2,7 torr at 25°C). To achieve apparent equilibrium in a reasonable time (several days), the sample must be crushed and the system evacuated the salt solution should be stirred, at least intermittently. Young and Hansen (Y5) found the composition of the C-S-H in C3S paste thus... 

It is clear that the evidence for vicinal hydration of macromolecules in solution may be indirect or circumstantial, but it cannot be readily dismissed. A vast literature exists on the effects of temperature on rates of enzymatic reactions. It is our view that in many cases, where sufficiently closely spaced data are available, distinct changes in the rate of enzymatic reactions occur at or very near 15°, 30°, 45°, and 60°C. It thus seems reasonable to assume that vicinal water is present and manifests its existence by affecting the rates of the reactions. For a fuller discussion of the evidence for the occurrence of kinks in enzymatic rate data, see Drost-Hansen (1971, 1973) and Etzler and Drost-Hansen (1979). 

When plotted in three dimensions, the Hansen parameters provide an approximately spherical volume of solubility for each polymer in Sj, Sp, 6h space. The scale on the dispersion axis is usually doubled to improve the spherical nature of this volume. The distance of the coordinates (6j, 6p, 61) of any solvent i from the center point (6, 5, S ) of the solubility sphere of polymer j is... 

Hansen F, Tackmann K, Jeltsch F, Staubach C, Thulke H-H. 2001. If space changes all — the small-scale epidemiology of the fox tapeworm. In Menzies FD, Reid SWJ, editors, Proceedings SVEPM. Noordwijkerhout (NL). p 73-85. 

There is now no time left. The train has left the station. The climate is warming. The best we can do now is minimize the impact. The only resolution is for humans to move to a fundamentally different energy pathway within a decade, according to James Hansen, director of NASA s Goddard Institute for Space Studies and a leading... 

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