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Determination of fractal dimension of metal dendrites in jelly polymers

Keywords:

T.V. Khecalo


The work contains definitions of fractal dimensions of the metal dendrites in jellies of polymers. We studied the influence of different factors (origin of jelly, salt, metal – seeding, shape of the vessel) on the size of fractal dimension. We used water solutions of high molecular substances: starch, gelatin, agar; metal – seeding (zinc, iron), four salts (lead, copper, tin and silver salts); two shapes of vessels (vertical – test tube, radial – Petri dish). It was established that the shape of dendrite depended on the origin of the jelly and the nature of metal-seeding. The fractal dimension was determined by four methods: 1) the method of counting of the number of cells σ × σ needed for the fractal covering, as the function of the step; 2) the method of determination of the number of geometric features, which σ × σ in this growth; 3) the method of determination of square of fractal according to the mass of imaging as the function of magnification factor; 4) the method of determination of square of fractal according to the brightness of imaging as the function of magnification factor. The value of dendrites’ fractal dimension corresponds to the literature data of the same objects and are in the interval of 1,00 ≤ Д < 2,0 The dimension depends on the origin of the jelly and the form the vessel. Is this dendrite a true fractal or depends on the origin of jelly, salt, metal-seeding and the form of the vessel. Only the part of dendrites was true, having fractional dimensions. Physic-chemical system «Metal dendrites in polymers’ jellies» can be used as a model of fractal object in laboratory practice on physics or colloidal chemistry for students of pharmaceutical specialties in medical universities.
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