An energy model for nanomechanical deflection of cantilever-DNA chip

Nanomechanical behavior of cantilever-DNA chip in label-free biodetection is investigated by the energy method. First, using an equation of state for DNA liquid crystals and an alternative two-variable model for laminated cantilever beams, a relationship between chip energy and some factors, such as nanogeometrical, physical, chemical characteristics of DNA molecules, microscopical geometric dimension, macroscopical mechanical properties of chip, etc., is formulated in consideration of electrostatic energy, hydration energy and configurational fluctuations of DNA layer as well as mechanical energy of chip. Second, theoretical predictions of nanomechanical deflection of DNA chip by the minimum principle of energy are compared with experimental data in Wu's experiments. Third, the influence of stochastic interchain distances and stochastic elastic modulus on chip deflection is investigated. The validity of the simplified two-layer-beam model is also studied. Numerical results show that chip deflection enhances with the increase in length of DNA chains, and the interchain distances should be carefully controlled no less than 4 nm during the process of probe molecules self-assembly.