On the Optimality Assessment of Nanoparticle Size Spectrometry and Its Association to the Entropy Concept
Particle size distribution, the most important
characteristics of aerosols, is obtained through electrical
characterization techniques. The dynamics of charged nanoparticles
under the influence of electric field in Electrical Mobility
Spectrometer (EMS) reveals the size distribution of these particles.
The accuracy of this measurement is influenced by flow conditions,
geometry, electric field and particle charging process, therefore by
the transfer function (transfer matrix) of the instrument. In this work,
a wire-cylinder corona charger was designed and the combined fielddiffusion
charging process of injected poly-disperse aerosol particles
was numerically simulated as a prerequisite for the study of a
multichannel EMS. The result, a cloud of particles with no uniform
charge distribution, was introduced to the EMS. The flow pattern and
electric field in the EMS were simulated using Computational Fluid
Dynamics (CFD) to obtain particle trajectories in the device and
therefore to calculate the reported signal by each electrometer.
According to the output signals (resulted from bombardment of
particles and transferring their charges as currents), we proposed a
modification to the size of detecting rings (which are connected to
electrometers) in order to evaluate particle size distributions more
accurately. Based on the capability of the system to transfer
information contents about size distribution of the injected particles,
we proposed a benchmark for the assessment of optimality of the
design. This method applies the concept of Von Neumann entropy
and borrows the definition of entropy from information theory
(Shannon entropy) to measure optimality. Entropy, according to the
Shannon entropy, is the ''average amount of information contained in
an event, sample or character extracted from a data stream''.
Evaluating the responses (signals) which were obtained via various
configurations of detecting rings, the best configuration which gave
the best predictions about the size distributions of injected particles,
was the modified configuration. It was also the one that had the
maximum amount of entropy. A reasonable consistency was also
observed between the accuracy of the predictions and the entropy
content of each configuration. In this method, entropy is extracted
from the transfer matrix of the instrument for each configuration.
Ultimately, various clouds of particles were introduced to the
simulations and predicted size distributions were compared to the
exact size distributions.