James Chen

Abstract

Dynamic analysis of nano/micro bio-sensors based on a multiscale atomistic/continuum theory is introduced. We use a generalized finite element method (GFEM) to analyze a bio-sensor which has 3 × Na ×Np degrees of freedom, where Np is the number of representative unit cells and Na is the number of atoms per unit cell. The stiffness matrix is derived from interatomic potential between pairs of atoms. This work contains two studies: (1) the resonance analysis of nano bio-sensors with different amount of target analyte and (2) the dependence of resonance frequency on finite element mesh. We also examine the Courant-Friedrichs-Lewy (CFL) condition based on the highest resonance frequency. The CFL condition is the criterion for the time step used in the dynamic analysis by GFEM. Our studies can be utilized to predict the performance of micro/nano bio-sensors from atomistic perspective.

The shift of first fundamental frequency

Two different distributions of hybridization are studied. The first one assumes that the distribution is always uniform. The second one assumes the hybridization is randomly distributed based on hybridization percentage. In other words, if 40% of total target mass is attached, 40% of the whole surface is randomly covered. In Fig. 1, the numerical results show that these two cases are very similar. It implies the hybridization distribution does not affect the dynamic performance of micro/nano bio/chemical sensor.

Mesh dependence Test II for the 120-lattice specimen

It is observed the first resonance frequency is approaching a constant value as the finite element size approaching the lattice constant. This constant value is the same as one would observe from MD simulation. If the number of finite elements is small, then the finite element model tends to be stiffer than the one with more elements. In other words, the model with less number of elements makes the specimen artificially and mistakenly stiff. It explains why the first resonance frequency drops to instead of rising to the constant value. It is also seen that the finite element size which converges to the constant value is around one tenth of the specimen length. It means for specimen with length of 120 lattices, the element size needs to be at most 12 lattice constants.

CFL Condition (Time Step) vs. specimen size in one element

CFL Condition (Time Step) vs. Number of Finite Elements (in One Dimension). The specimen size is fixed to 6 lattice constants (in one dimension)

Figure 1 shows that the maximum time step, , is almost a constant due to the nonlocal effect, especially when the number of lattices is sufficiently large. In this case the specimen size changes from 1 lattice to 1000 lattices (in one dimension) but all in one finite element. Figure 2 shows when the number of elements increases, the maximum resonance frequency becomes larger and hence the required time step is getting smaller. In this case, the specimen size is fixed as lattices but the number of elements ranges from 1 to 6 in all directions.

Related Publication

1. James Chen and J. D. Lee, “Atomistic Analysis of Micro/Nano Bio-sensors”,Interaction and Multiscale Mechanics, 3, 111-121, 2010
2. James Chen and James D. Lee, Dynamic Characteristics of Nano/Micro Biosensors in Multiscaling of Synthetic and Natural systems with Self-Adaptive Capability, National Taiwan Univresity of Science and Technology, 77-80, 2010
3. James Chen and J. D. Lee, “Dynamic Characteristics of Nano/Micro Biosensors”, 12th International Congress on Mesomechanics (MESOMECHANICS 2010), Taipei June 2010
4. James Chen and J. D. Lee, "Dynamic Analysis of Biosensors", APS March Meeting, Portland, OR, 2010 (Accepted)