The equilibrium state of bifilar helix as element of metamaterials

Abstract

In the present article, we study the long bifilar helix in which electric currents are quasi-stationary, i.e. the wavelength of the electromagnetic field is much longer than the turn of the helix. All components of the force acting on a physically small element of one helix from the other helix having a big length are calculated. The case when the currents in the two helices have the same direction relative to the x axis is considered. The dependence of the radial component of the force of interaction between two helices on the pitch angle is determined. At various pitch angles the helices can attract and repel each other while the direction of the current does not change. It is found the value of pitch angle when two helices do not interact and bifilar helix, formed by them, is in equilibrium state.

Optical Forces Acting on a Double DNA-Like Helix, Its Unwinding and Strands Rupture

“…These radial components of the forces describe the mutual attraction or repulsion of two helices and exist both for a symmetrical double helix and in the case of mutual shift of two helices along their common axis. It has been shown that there exists a certain equilibrium helix pitch angle (α 0 ≈ 38 deg) at which the radial component of the magnetic force vanishes, which means the absence of radial attraction or repulsion of the elementary current in the second helix with respect to the entire first helix [44,45]. At this particular angle α 0 the force radial component of the helices' magnetic interaction changes sign.…”

“…In this regard, the result obtained in this article appear promising: the direction of the radial force of electric currents attraction or repulsion in two helical strands depends on the double helix pitch angle. The critical pitch angle of the double helix, at which the radial force of the magnetic interaction of two helices changes its direction, is α 0 ≈ 38 deg [44,45]. At the same time, the DNA helix in its natural condition is characterized by the pitch angle α exp = 28.4 deg [47,48].…”

“…The positive Z-component of the magnetic or electric force means the radial attraction of the elementary part of the second helix to the first one, while the negative value of Z component means the radial repulsion force. Figure 4 demonstrates an interesting feature: there exists a certain equilibrium helix pitch angle (α 0 ≈ 38 deg) at which Z-component of the magnetic force vanishes, which means that there is no radial attraction or repulsion of the elementary current in the second helix with respect to the entire first helix [44]. At this particular angle α 0 , the radial component of the magnetic interaction force of the helices' changes sign.…”

“…Here, as above, the "+" sign corresponds to a right-handed helix, and the "−" sign corresponds to a left-handed one. Using Formulae ( 43) and (44), and averaging in time, we arrive at…”

“…The excitation states of a long bifilar helix with quasi-stationary distributions of electric currents have already been studied earlier in [44,45]. Whereas the article by Semchenko et al [44] studies a two-fold symmetrical double stranded helix, paper [45] is devoted to an asymmetrical DNA-like helix. This particular excitation state is realized when the wavelength of excitation is much longer than the length of the helical turn.…”