Vibrations of Dimers of Mechanically Coupled Nanostructures: Analytical and Numerical Modeling

Abstract

The coupling effects affecting the vibrations of two close nanostructures (e.g., two metal nanoplates or nanospheres separated by a thin dielectric layer) may considerably alter their vibrational eigenfrequencies, as demonstrated by several recent experimental studies. In this work, we present theoretical investigations of these coupling processes based on a continuum mechanics approach, considering various systems composed by two identical nanostructures mechanically coupled by a spacer made of a different material and computing their eigenfrequencies as a function of the spacer thickness. We first discuss the vibrations of stacked slabs, a one-dimensional problem which can be treated analytically. The more complex configurations of dimers of rods or spheres coupled by a finite cylindrical spacer are then treated numerically. In all cases, the frequency shifts occuring for thin spacers can be simply interpreted as a modification of the boundary conditions of the problem as compared to the single nanostructure case, while those predicted near specific spacer thicknesses are ascribed to an avoided crossing effect, happening when the individual building blocks of the dimers (nanostructures and spacer) present common eigenfrequencies.

Development of Intelligent CAD Technology for New Longitudinal Shell-Side Heat Exchange Equipment

“…(3) Database management system: the HECAD knowledge base system includes knowledge base, graphic base, and database; the HECAD system uses database technology to manage fact base and knowledge base; the knowledge in the expert system can be managed and represented by the database structure and processing method after certain processing [15] (4) Scheme design: according to the resources in the public database, the scheme design calls out the assembly schematic diagram of the heat exchange equipment to be designed from the assembly instance library. From the assembly diagram, you can see the basic structure of each part of the heat exchanger; if you are not satisfied, return to the menu of the design task management module and select it again; if you are satisfied, you can carry out the integrated design from the process design to component structure (5) Process design: according to the patented technology of the center, we use our process design method to design; the designers input the original design information such as user requirements and design process parameters into the computer through the system human-computer interaction interface and automatically enter the public database of the control structure; the reasoning process which is a rule-based reasoning mechanism is employed (6) Structural design: the structural design of the parts of the HECAD system adopts the CBR method.…”

Energy Dissipation for Nanometer Sized Acoustic Oscillators

“…This means that within this model nanoscale plates on a solid surface behave the same way (have the same quality factors) as macroscale plates with the same d / h ratio. In the following we present results from this analysis in a similar way to that in ref , where the theory for nanoplate dimers without a substrate was presented and discussed.…”

“…For this model we choose oscillating functions for the displacement in the plate and spacer layer and propagating waves for the substrate. The boundary conditions are stress-free conditions at the top surface ( z = d + h ) and continuity of displacement and stress at the inner surfaces ( z = d and z = 0). , This yields five equations that have a nontrivial solution when the determinant of the corresponding matrix is zero (see Supporting Information for details). After a little manipulation the solution can be written as the following eigenvalue equation: where the eigenvalue ξ = ω h / c 1 and c i and ρ i are the longitudinal speeds of sound and densities of the different materials (1 = plate, 2 = spacer layer, and 3 = substrate).…”

Optomechanic Coupling in Ag Polymer Nanocomposite Films

“…The well-established scaling, f (1,2) ∼ c t D –1 , of the quadrupolar mode in PVP conforms to the scaling in air with the transverse sound velocity, c t = 1250 m/s, of elastically isotropic Au. However, the frequency of the quasi-translational mode depends on the matrix elasticity as supported by eigenmode 2D (axial) calculations. , …”

“…However, the frequency of the quasi-translational mode depends on the matrix elasticity as supported by eigenmode 2D (axial) calculations. 15,16 Few reports focused on the vibration modes of sizeable (100−200 nm) Au NPs in PVP or in supported nanodevices utilizing BLS. 14,17,18 and PA, 13,19−21 of single Au and Au dimer NPs using two lasers at 532 and 647 nm (polarized along the dimer long axis), respectively.…”