With the aid of mathematics, materials chemistry enables dimension travel, unveiling that all properties of materials are governed by their dimension.

It has been known that nanoparticles, for example, exhibit quite different properties from the bulk samples of the same materials. Yet nobody knows why. We discovered a control method of the fractal dimensions of any solid sample, enabling systematic and detailed examination of various physical properties of samples with different dimensions. As a result we discovered the universal relationship between physical properties and fractal dimensions.

From heavenly bodies to human cells, everything in this universe? possesses finite dimensions in three directions in space, namely everything in the real world is three-dimensional, according to Euclidean geometry. However thin or small an object is fabricated by nanotechnology, the dimensions can not be altered. Accordingly, it has been firmly believed that nobody could change or control the dimensions of real matter. However, if we pay attention to fractal dimensions instead, dimension control is possible in a facile way.
We prepared a series of mixed powder samples with the same material but with different fractal dimensions, corresponding to a different mixed ratio between the substance of interest and wax. Using these samples, we examined their structures and various physical properties in detail. We also examined different materials with different properties to confirm the universality of the results. With the aid of theoretical calculation based on original models and methods, we discovered that there is a universal relationship between the sample fractal dimensions and their physical properties, such as electrical conduction and magnetism. This could be a newly unveiled principle of nature, where the dimension of matter governs all its physical and mechanical properties.

Reference URL: https://doi.org/10.1039/D1CP04709D

Bibliographic Information

Universal relationship between sample dimensions and cooperative phenomena: Effects of fractal dimension on electronic properties of high-TC cuprate observed using electron spin resonance. Toshio Naito and Yoshiaki Fukuda. Physical Chemistry Chemical Physics (2022). DOI: 10.1039/D1CP04709D. Advanced Online Publication on 2021 (December 14), Selected as a Hot Article on 2022 (February 2).

Fundings

• Grant-in-Aid for Scientific Research (C) (23540432) from JSPS

Media

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  Fractal bodies in bubbles

  The word “fractal” originates from “fractional”. Few could imagine fractal bodies with non-integer dimensions between two-dimensional (a plane) and three-dimensional (a cube, for example) figures. However, there are many fractal bodies around us such as clouds and coastlines, indicating fractal shapes are the most natural and fundamental forms of existence in nature. Our finding of the universal relationship between physical properties and sample dimensions indicates that the dimensions also govern all kinds of physical and mechanical properties as a principle of nature.

  credit : Toshio Naito, Ehime University
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  Gradual variation in the dimension of fractal bodies (1)

  The stereoscopically arranged cubes are fractal bodies with different dimensions. The largest yellow body belongs to 2.5-dimensional bodies, while the smallest blue body belongs to three-dimensional bodies. The reduction in the fractal dimension corresponds to an increase of the void spaces in the bodies. In our study, the void spaces are filled with special wax which plays no role in the physical properties.

  credit : Toshio Naito, Ehime University
  Usage Restriction : Please get copyright permission

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  Gradual variation in the dimension of fractal bodies (2)

  The series of blue and yellow fractal bodies possess slightly different fractal dimensions from each other. The largest yellow body belongs to 2.5-dimensional bodies, while the smallest blue body belongs to three-dimensional bodies. The reduction in the fractal dimension corresponds to an increase of the void spaces in the bodies. In our study, the void spaces are filled with special wax which plays no role in the physical properties.

  credit : Toshio Naito, Ehime University
  Usage Restriction : Please get copyright permission