1.Ohshima, Kz., J. Mater. Sci. 31, 519 (1996).CrossRefGoogle Scholar

2. Examples of production methods for our metal pigments are disclosed in the following patents: Brit. Pat. No. 2,068,923 and 2,072,639; US Ser. No. 230,024 and 422,351; USP No. 4,469,507.Google Scholar

3.Tagawa, K., Matsunaga, M., Ohshima, Kz., Hiramatsu, M., Ishibashi, T., and Mikami, J., IEEE Trans. Magn. MAG–22, 729 (1986).CrossRefGoogle Scholar

4. It is confirmed that the small amounts of S or Na, which are typical chemical impurities remaining in the pigment unavoidably, do not result in the increase of the acidic or basic sites. It seems that the existence of Si and/or Al components used in the chemical modification on the goethite particles is the dominant cause of generation of the acidic/basic sites: Thomas, C. C., Ind. Eng. Chem. 41, 2564 (1946); K. Tanabe, Solid Acids and Bases (Kodansha, Tokyo, Japan, 1970).CrossRefGoogle Scholar

5.Tanabe, K., Matsuzaki, I., Fukuda, Y., Kobayashi, T., Kubo, K., and Tanabe, K., Shokubai (means “Catalyst”) 11, 211 (1969) (written in Japanese).Google Scholar

6. Its most popular type is known as “VAGH” made by UCC of U.S.A.Google Scholar

7. An alkylation of phenol by alcohols is one of the most typical catalytic reactions belonging to the application of this phenomenon.Google Scholar

8. The “simple mathematical model” was developed as follows: First, we prepared carefully nine samples of the metal pigments with “wide” range of [SSA (m₂/gr), σs (emu/gr), A (μeq/m₂), B (μeq/m₂)]: {56.1, 121, 5.28, 5.72}, {48.8, 127, 4.36, 2.84}, {45.5, 125, 4.86, 1.31}, {54.6, 123, 3.73, 1.93}, {47.1, 124, 3.59, 2.25}, {55.1, 121, 4.46, 5.22}, {59.7, 121, 3.40, 1.52}, {54.5, 126, 3.24, 1.47}, and {53.7, 129, 2.63, 1.19}. The estimated values of RA for these samples were 46.1, 20.8, 14.6, 29.6, 20.4, 45.4, 37.6, 15.8, and 29.7 mgr/gr, respectively. Next, to this sample series, we applied the regression analysis by assuming RA = Co + ΣCi^*Pi, where Pi's denote “independent” variables, SSA, σs, A, and B for i − 1, 2, 3, and 4, respectively, and Ci's are the corresponding fitting parameters, whereas Co is an adjustable constant. We obtained Co of 46.2 and Ci's for i = 1 to 4 of +1.19, −0.676, −1.97, and +4.39 with the correlation coefficient of 92.6%, when the above-mentioned units are used. This resultant formula means that RA increases when SSA either B increases, and/or σs either A decreases.Google Scholar

9. RA can be estimated as a function of SSA, σs, A, and B: RA − RA (SSA, σs, A, B). Then, to predict the “experimental” value of RA with the specific values of SSA and σs as a function of A and B from the original experimental values of RA, we used Taylor's expansion method. For example, for SSA and σs of 55 m₂/gr and 125 emu/gr, respectively, RA (55, 125, A, B) − RA (SSA, σs, A, B) − C₁^* (SSA-55) − C₂^* (σs-125), because δRA (Pi's)/δPi − Ci for i − 1 to 4. Note the “negative” sign for shifting the original experimental values to the specific state. For the present sample series, RA (55, 125, A, B) were 42.1, 29.5, 25.9, 28.7, 29.1, 42.6, 29.3, 17.1, and 34.0 mgr/gr, respectively. Next, we estimated RA (55, 125, 4, B) or RA (55, 125, A, 5) as a function of B or A, by the “shifting” formula, RA (55, 125, A, B) − C₃^*(A-4) or RA (55, 125, A, B − C₄^* (B-5). The results were 44.6, 30.3, 27.6, 28.2, 28.3, 43.5, 28.1, 15.6, and 31.3 mgr/gr for RA (55, 125, 4, B) or 38.9, 39.0, 42.1, 42.2, 41.2, 41.6, 44.6, 32.6, and 50.7 mgr/gr for RA (55, 125, A, 5), respectively. See Fig. 2 of the text.Google Scholar