Compact and modular system architecture for a nano-resonator-mass spectrometer

Mass measurements in the mega-to giga-Dalton range are essential for the characterization of natural and synthetic nanoparticles, but very challenging to perform using conventional mass spectrometers. Nano-electro-mechanical system (NEMS) based MS has demonstrated unique capabilities for the analysis of ultra-high mass analytes. Yet, system designs to date included constraints transferred from conventional MS instruments, such as ion guides and high vacuum requirements. Encouraged by other reports, we investigated the influence of pressure on the performances of the NEMS sensor and the aerodynamic focusing lens that equipped our first-generation instrument. We thus realized that the NEMS spectrometer could operate at significantly higher pressures than anticipated without compromising particle focusing nor mass measurement quality. Based on these observations, we designed and constructed a new NEMS-MS prototype considerably more compact than our original system, and which features an improved aerodynamic lens alignment concept, yielding superior particle focusing. We evaluated this new prototype by performing nanoparticle deposition to characterize aerodynamic focusing, and mass measurements of calibrated gold nanoparticles samples. The particle capture efficiency showed nearly two orders of magnitude improvement compared to our previous prototype, while operating at two orders of magnitude greater pressure, and without compromising mass resolution.

The quality factor  was calculated from the fit of nano-resonator frequency response such as  =  0 /, where  0 is the resonance frequency and  is full width at half maximum.An example of measurement fitting is shown in the Supplementary Figure 1.Supplementary Table 1.Lengths of every resonator beam of the array.

NEMS index
NEMS length

Mass resolution
Mass resolution   is an important parameter for mass spectrometry and for NEMS-MS technique, it depends on the resonator geometry and the frequency fluctuations.It is defined as: Where   is the effective mass of the resonator and   is the frequency fluctuation which can be measured using the Allan deviation.In our case, for 0.1 second integration time, its typical value is ranging from   = 1 × 10 −7 to   = 3 × 10 −7 .Mass resolution has been computed for every NEMS and the results are reported in Supplementary Table 2.It slightly varies -depending on the length of the beam -between 0.12 MDa to 0.16 MDa for mode 1 and between 0.14 MDa to 0.18 MDa for mode 2.
Supplementary Table 2. Mass resolution of every NEMS of the array.

Simulations
In order to compute the particle trajectories, the flow field was first computed using the commercial CFD finite-element solver of COMSOL.The flow was assumed to be laminar, stationary, compressible, viscous and axisymmetric.The boundary conditions specified in Supplementary Figure 4 were used.
Supplementary Figure 4. Computational domain and boundary conditions to compute the velocity, density and pressure fields across an aerodynamic lens. ̇ is the mass flowrate and   is the downstream pressure.
The velocity, density and pressure fields are used to compute particle trajectory.The forces applied to the particles are the drag force  ⃗  and the Langevin force  ⃗  .
Where the drag force is given by: being the fluid dynamic viscosity,   the particle diameter,   the Cunningham correction slip factor and  ⃗  the relative velocity.
The Langevin force is given by: Where  ⃗ is a zero-mean, unit-variance-independent Gaussian random vector,   is the kinematic viscosity,   is the Boltzmann constant,   is the fluid temperature,   is the fluid density,   is the particle density and Δ is the time step.
This differential equation was derived using the velocity Verlet algorithm, and implemented in Python code.The numerical scheme of the lagrangian tracking has been presented elsewhere (Reynaud et al., 2021).In order to check this method, it has been applied to a specific lens simulated in the literature by (Wang et al., 2005) and showed good agreement (cf.Supplementary Figure 5 and Supplementary Figure 6).Energy dissipation in nano-resonators Using the model developed by (Trzpil et al., 2021), the contribution of each phenomena over the quality factor were quantified.The calculations were done for a 9 µm long, 300 nm wide and 160 nm thick beam.The lower value is the one due to the support and compares well with the measurement under vacuum.Those results indicate that the energy losses through the support are predominant over thermoelastic and acoustic losses.
NEMS #1 length = 9 µm  0,1 28.4 MHz   4.65 × 10 3  ℎ 2.12 × 10 5   1.13 × 10 13 experiments of (Dominguez-Medina et al., 2018) were used.We only took into account the experiments featuring ESI nebulization, since this is the technique that has been used to spray GNP.The capture efficiency was computed for one single NEMS since the number of used devices can vary from an experiment to the other and the objective was to compare performances of NEMS-MS system generations.
SEM micrographs and dimensions of the nano-resonators used in this work.

Table 3 .
(Dominguez-Medina et al., 2018)ens are presented in Supplementary Table3.They also correspond to the lens used and characterized by(Dominguez-Medina et al., 2018).Aerodynamic lens dimensions.Dorifice corresponds to the orifice diameter of each lens, Lspacer corresponds to the distance between the lens i and the lens i+1.PLO stands for pressure limiting orifice and AN stands for acceleration nozzle.All dimensions are in millimeters.