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In physics, natural units are physical units of measurement in which only universal physical constants are used as defining constants, such that each of these constants acts as a coherent unit of a quantity. For example, the elementary charge e may be used as a natural unit of electric charge, and the speed of light c may be used as a natural unit of speed. A purely natural system of units has all of its units defined such that each of these can be expressed as a product of powers of defining physical constants. Through nondimensionalization, physical quantities may then be redefined so that the defining constants can be omitted from mathematical expressions of physical laws, and while this has the apparent advantage of simplicity, it may entail a loss of clarity due to the loss of information for dimensional analysis. It precludes the interpretation of an expression in terms of constants, such as e and c, unless it is known which units (in dimensionful units) the expression is supposed to have. In this case, the reinsertion of the correct powers of e, c, etc., can be uniquely determined. Planck units The Planck unit system uses the following defining constants: c, ħ, G, k_B, where c is the speed of light, ħ is the reduced Planck constant, G is the gravitational constant, and k_B is the Boltzmann constant. Planck units form a system of natural units that is not defined in terms of properties of any prototype, physical object, or even elementary particle. They only refer to the basic structure of the laws of physics: c and G are part of the structure of spacetime in general relativity, and ħ is at the foundation of quantum mechanics. This makes Planck units particularly convenient and common in theories of quantum gravity, including string theory. Planck considered only the units based on the universal constants G, h, c, and kB to arrive at natural units for length, time, mass, and temperature, but no electromagnetic units. The Planck system of units is now understood to use the reduced Planck constant, ħ, in place of the Planck constant, h.

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Planck units

In particle physics and physical cosmology, Planck units are a set of units of measurement defined exclusively in terms of four universal physical constants, in such a manner that these physical constants take on the numerical value of 1 when expressed in terms of these units. Originally proposed in 1899 by German physicist Max Planck, these units are a system of natural units because their definition is based on properties of nature, more specifically the properties of free space, rather than a choice of prototype object.

Natural units

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Natural systems have marvelously utilized copper complexes featuring sulfur-coordinating ligands, known as blue copper proteins, as efficient electron-transfer mediators in biological processes. Copper complexes with sulfur-coordinating ligands have been attempted as redox mediators in dye-sensitized solar cells (DSCs), the performance of which is not yet satisfactory and still remains less well explored. Herein, we report the application of new copper complexes bearing a tetradentate polythioether ligand, (S-4)Cu (1(2+/+), S-4 = 1,4,8,11-tetrathiocyclotetradecane), as a redox mediator in DSCs in comparison with its N-4-tetradentate counterpart (N-4)Cu (2(2+/+), N-4 = 1,4,8,11-tetramethyl-1,4,8,11-tetraazacyclotetradecane). Impressively, the changes of coordination atoms from N to S positively shift the formal redox potential of the copper complexes by 600 mV, leading to a remarkably high photovoltage approaching 1.0 V. This is one of the highest photovoltage values reported thus far for DSCs based on copper redox mediators.

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