Time-dependent behaviors due to various mismatch strains are very important to the reliability of micro-/nano-devices.This paper aims at presenting an analytical model to study the viscoelastic stress relaxation of the laminated microbeam caused by mismatch strain.Firstly,Zhang’s two-variable method is used to establish a mechanical model for predicting the quasi-static stress relaxation of the laminated microbeam.Secondly,the related analytical solutions are obtained by combining the differential method and the eigenvalue method in the temporal domain.Finally,the influence of the substrateto-film thickness/modulus ratio on the relaxation responses of the laminated microbeam subject to a step load of the mismatch strain is studied.The results show that the present predictions are consistent with the previous theoretical studies.Furthermore,the thickness dependence of stress relaxation time of the laminated microbeam is jointly determined by the intrinsic structural evolution factors and tension-bending coupling state;the stress relaxation time can be controlled by adjusting the substrate-to-film thickness/modulus ratio.
Boundary constraint induced inhomogeneous effects are important for mechanical responses of nano/micro-devices.For microcantilever sensors,the clamped-end constraint induced inhomogeneous effect of static deformation,so called the clamped-end effect,has great influence on the detection signals.This paper is devoted to developing an alternative mechanical model to characterize the clamped-end effect on the static detection signals of the DNA-microcantilever.Different from the previous concentrated load models,the DNA adsorption is taken as an equivalent uniformly distributed tangential load on the substrate upper surface,which exactly satisfies the zero force boundary condition at the free-end.Thereout,a variable coefficient differential governing equation describing the non-uniform deformation of the DNA-microcantilever induced by the clamped-end constraint is established by using the principle of minimum potential energy.By reducing the order of the governing equation,the analytical solutions of the curvature distribution and static bending deflection are obtained.By comparing with the previous approximate surface stress models,the clamped-end effect on the static deflection signals is discussed,and the importance of the neutral axis shift effect is also illustrated for the asymmetric laminated microcantilever.
For the first time, the connection between surface stress and nanoscopic interac- tions of DNA adsorbed on microcantilever is established by combining Strey＇s mesoscopic liquid crystal theory and Stoney＇s formula. It is shown that surface stress depends not only on biomolec- ular interactions of DNA biofilm but also on mechanical properties of cantilever. Considering the correlativity between grafting density and chain length of DNA chain, we discuss the differences between DNA-microcantilever system and DNA solution system. The major theoretical achieve- ment of this model is to identify the main contributions to surface stress under different detection conditions. This provides guidelines for designing new biosensors with high sensitivity and improved reliability.
In microcantilever-based label-free biodetection technologies, deflection changes induced by adsorptions of double-stranded DNA （dsDNA） molecules on Au-layer surface are greatly affected by the mechanical, thermal and electrical properties of DNA biofilm. In this paper, the elastic properties of dsDNA biofilm are studied. First, the Parsegian＇s empirical potential based on a mesoscopic liq- uid crystal theory is employed to describe the interaction energy among coarse-grained DNA cylinders. Then, con- sidering a Gaussian distribution of DNA interaxial distance, the thought experiment method is used to derive an analyti- cal expression for Young＇s modulus of DNA biofilm with a stochastic packing pattern for the first time. Results show that Young＇s modulus of DNA biofilm is on the order of 10 MPa. These findings could provide a simple and effective method to evaluate the mechanical properties of soft biofilm on snbstrate.
