Fractal Materials and Their Functional Properties

Abstract

Fractal, a mathematical concept, has been utilized to develop some functional materials by the present author and his coworkers. Fractal surfaces show super water-and even oil-repellent property due to their very large surface area. In order to realize the super water-repellent fractal surfaces some waxes (alkylketene dimer and triglycerides) were employed. These waxes interestingly form the fractal surfaces spontaneously. The formation mechanism of the fractal structures on the wax surfaces has been made clear. The waxes which form the fractal surfaces have a meta-stable crystalline phase when solidified from their melts, and then transform to the thermodynamically stable crystal. During this phase transition process, the wax surfaces become fractal. For practical applications in future, durable super water-repellent and highly oil-repellent fractal surfaces have been synthesized by the electrochemical polymerization of an alkylpyrrole and the coating them with a fluorinated alkylsilane-coupling agents. In the final part of this article, the creation of a fractal body, not the surfaces, with a novel template method is mentioned. Such a fractal body is expected to show some interesting and unique functional properties.

A continuum framework for mechanics of fractal materials I: from fractional space to continuum with fractal metric

“…In this background, the impossibility to define ) ( 2 i c and 3 c in a unique way is an intrinsic feature of mapping from two mutually orthogonal fractal coordinates ( i χ and ) (i ∂ Α ) associated with decomposition (12) into three orthogonal fractal coordinates ) , , ( [41]. So, in essence, this is a price one has to pay in order to deal with fractals which cannot be treated within the approach based on the Cartesian decomposition (6). Fortunately, this does not impose serious limitations, since we need not to know explicit functional forms of 3 c and )…”

“…Once again, let us first consider the special case of fractal domain (6). In the corresponding fractal continuum (16) Fig.…”

“…However, (micro-)structures of real heterogeneous materials frequently possess formidably complicated architecture exhibiting statistical scale invariance over many length scales [3,4]. Examples range from gels [5], polymers [6], and biological materials [7] to rocks [8], soils [9], and carbonate reservoirs [10]. For such materials the classical homogenization methods are inapplicable, because heterogeneities play an important role on almost all scales.…”

“…These include the scale-invariant spatial and size distributions of solid phases and/or defects (e.g. pores or fractures), long-range correlations in the mass (or pore) density distribution, fractal geometry of fracture, pore, and crumpling networks, among others [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. A key advantage of the fractal approach is the possibility to store the data relating to all scales of observation using a relatively small number of parameters that define a structure of greater complexity and rich geometry [22].…”

Bulk synthesis of ordered macroporous silica particles for superhydrophobic coatings

“…9e, which implies that superhydrophobic surface was successfully imposed due to the multi-scale structure of the macroporous particle film. Therefore, the Cassie-Baxter theory can be applied for interpreting the enhanced hydrophobicity of the porous surface from the following equation [35][36][37][38].…”