Resonant Dipolar Coupling of Microwaves with Confined Acoustic Vibrations in a Rod-shaped Virus

Abstract

In this letter, we treat a rod-shaped virus as a free homogenous nanorod and identify its confined acoustic vibration modes that can cause strong resonant microwave absorption through electric dipolar excitation with a core-shell charge distribution. They are found to be the n = 4N-2 modes of the longitudinal modes of the nanorods, where N is an integer starting from 1 and n is the mode order quantum number. This study was confirmed by measuring the microwave absorption spectra of white spot syndrome virus (WSSV), which is a rod-shaped virus. This is also the first study to identify the "dipolar-like" mode in a rod-shaped nano-object. Our study is not only an important step to achieve rapid and sensitive detection of rod-shaped viruses based on their microwave spectroscopic features and a non-contact method to measure the Young's modulus of rod-shaped viruses, but also is critical to formulate an efficient epidemic prevention strategy to deactivate viruses with the structure-resonant microwaves.

Figure 1

Longitudinal standing waves in a nano-cylinder. (a) Coordinate of a nano-cylinder; L: length of cylinder; a: radius of cylinder. $u_r,u_{\theta },u_z\mathrm{are}\mathrm{displacement}\mathrm{of}\mathrm{r},\mathrm{\theta },\mathrm{z}$. (b) Schematic showing the core (red part) and shell (blue part) structure of a nano-cylinder with different charges. a is the radius of the whole cylinder, and L is the length of the whole cylinder. a’ is the radius of core, and L’ is the length of core; Dimension ratio = L’/L = a’/a. (c) Displacement of the longitudinal standing waves in a nano-cylinder. Brown and light blue curves represent the distribution of displacement when both ends have largest displacement. Dark blue and light green arrows indicate the direction of displacement at ends and center of the cylinder, respectively.

Figure 2

White spot syndrome virus. The (a) length and (b) diameter distribution of white spot syndrome virus (WSSV) as summarized by its (c) transmission electron micrographs.

Figure 3

Microwave resonant absorption spectra of WSSV after removing the contributions from the background. (a) First set of measurement with a 65 GHz measurement bandwidth. (b) Second set of measurement with a 18 GHz measurement bandwidth.

Figure 4

Microwave absorption spectrum measurement. (a) Schematic top view of a microfluidic channel sticking on top of a coplanar waveguide (CPW). (b) Photos showing the microfuidic channel integrated CPW on the test fixture, the 1 ml syringe, and details regarding the contact between CPW and test fixture.

Figure 5

Longitudinal modes and vibrational frequencies. (a) A figure showing the measured resonant microwave absorption frequency (red solid triangles) as a function of the longitudinal mode order. Relationships based on Eq. 6 are shown in blue and green lines, assuming longitudinal sound velocities of 1920m/s and 2450 m/s respectively. The dot dash line shows the relationship with a longitudinal sound velocity of 2100 m/s. (b) Schematic showing a nano-capsule and its inner core. a is the radius of the capsule and hemispheroid, L-2a is the length of the center cylinder; and L is the total length of the capsule. Similarly, a’ is the radius of core, and L’ is the length of core. (c) The FEM simulation result of the n = 2 longitudinal mode vibration of a nano-cylinder with a 0.5 dimension-ratio between the core and shell. Color bar represents the displacement field. T: Period; $\mathrm{\Delta }p$: difference of dipole moment between the balance state and the maximum compression/extension state. (d) The FEM simulation result of the n = 2 longitudinal mode vibration of a nano-capsule with a 0.5 dimension-ratio between the core and shell.