Achievable accuracy of resonating nanomechanical systems for mass sensing of larger analytes in GDa range

Measurement of larger analytes such as many chemical and biological structures or viruses in gigadalton (GDa) range is a reminding fundamental task in analytical chemistry and life sciences, which can be possibly resolved with the resonating nanomechanical systems. Common approaches to mass sensing with these systems model the bound analyte as a point particle and assume the analyte does not change the vibrational mode shapes. However, for larger analytes their stiffness and size not only affect the resonant frequencies but also cause the significant changes in the vibrational mode shapes making their measurement highly challenging and still under-explored problem. Here, we develop a 3D model capable to accurately predict the resonant frequencies and vibrational mode shapes of the resonating nanomechanical systems with the bound analyte of arbitrary properties and size. Then, we examine in details the impact of analyte properties, size and its position of attachment on the resonant frequencies and vibrational mode shapes and, correspondingly, resolve a dispute over the achievable detection limits of the nanomechanical systems, especially for mass sensing of larger analytes. Furthermore, we identify three different sensing regimes, that is, the ultra-light, light and heavy, for which the effects of the analyte mass, stiffness, its size and the position of attachment on the accuracy of the determined mass can be separated. For the ultra-light regime (mass ratio < 10⁻³) the analyte stiffness and its size affect notably the resonant frequencies, the point mass approximation is inaccurate and the analyte can be identified by its mass and stiffness. For the light regime the point mass approximation is accurate, while for the heavy one (mass ratio > 2∙10⁻²) the mass effect dominates the frequency response and alters the vibrational mode shapes which, for the common approaches, yields the errors in the determined analyte mass. Finally, we also propose an easily accessible approach for the identification of larger analytes (in GDa range) that does not require the advanced computational tools or experimental setup, applicable to the majority of the clamped-clamped ends resonating nanomechanical systems.