We present a physical model for the effective electrical conductivity and the associated percolation behavior in CB-based polymer nanocomposites exhibiting a 3D conductive network structure. In ...conductive nanocomposites, the fillers, e.g., carbon black nanoparticles form a three dimensional (3D) network in a polymer matrix. Assuming attached carbon black nanoparticles give rise to nanoparticles with ellipsoidal shapes, the effects on the electrical conductivity of the nanocomposite are investigated by considering the variations of (a) the thickness and conductivity of the interphase region, (b) the conductivities of the filler and the matrix, (c) the size and the aspect ratio of the ellipsoids, (d) the volume fraction, and (e) the electron tunneling distance and the potential barrier height. The presence of an interphase layer is shown to exert a dominant effect on the behavior of the effective electrical conductivity and the associated percolation behavior. To validate the theoretical model, polymer nanocomposites were prepared by incorporating different concentration of CB within polyvinylidene fluoride matrix which shows an approximately 14 orders of magnitude of jump in the conductivity at percolation. The model predicts the value of percolation threshold for CB/PVDF nanocomposite as
P
c
(vol%) = 1 which is in good agreement with the experimental percolation threshold value of
P
c
(vol%) = 1. Also, the present model accurately predicts the reported experimental behavior of the electrical conductivity in a variety of CB-filled nanocomposites employing different polymer matrices, namely polyethylene terephthalate, high density polyethylene, polypropylene, nylon, polyurethane, and natural rubber, over the entire range of the volume fractions. Notably, the model allows accurate computation of the percolation thresholds for conductive nanocomposites at very low volume fractions.
Graphical Abstract
Coronavirus disease 2019 (COVID-19) is a newly emerging human infectious disease caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Early diagnosis is essential to reducing the ...transmission rate and mortality of COVID-19. PCR-based tests are the gold standard for the confirmation of COVID-19, but immunological tests for SARS-CoV-2 detection are widely available and play an increasingly important role in the diagnosis of COVID-19. Nanomechanical sensors are biosensors that work based on a change in the mechanical response of the system when a foreign object is added. In this paper, a graphene-based nanoresonator sensor for SARS-CoV-2 detection was introduced and analyzed by using the finite element method (FEM). The sensor was simulated by coating a single-layer graphene sheet (SLGS) with a specific antibody against SARS-CoV-2 Spike S1 antigen. In the following, the SARS-CoV-2 viruses were randomly distributed on the SLGSs, and essential design parameters of the nanoresonator, including frequency shift and relative frequency shift, were evaluated. The effect of the SLGS size, aspect ratio and boundary conditions, antibody concentration, and the number of viruses variation on the frequency shift and relative frequency shift were investigated. The results revealed that, by proper selection of the nanoresonator design variables, a good sensitivity index is achievable for identifying the SARS-CoV-2 virus even when the number of the viruses are less than 10 per test. Eventually, according to the simulation results, by using SLGS geometry determination, an analytical relationship is presented to predict the limit of detection (LOD) of the sensor with the required sensitivity index. The results can be applied in designing and fabricating specific graphene-based nanoresonator sensors for SARS-CoV-2.
The variability response function (VRF) is generalized to statically determinate Euler Bernoulli beams with arbitrary stress-strain laws following Cauchy elastic behavior. The VRF is a Green's ...function that maps the spectral density function (SDF) of a statistically homogeneous random field describing the correlation structure of input uncertainty to the variance of a response quantity. The appeal of such Green's functions is that the variance can be determined for any correlation structure by a trivial computation of a convolution integral. The method introduced in this work derives VRFs in closed form for arbitrary nonlinear Cauchy-elastic constitutive laws and is demonstrated through three examples. It is shown why and how higher order spectra of the random field affect the response variance for nonlinear constitutive laws. In the general sense, the VRF for a statically determinate beam is found to be a matrix kernel whose inner product by a matrix of higher order SDFs and statistical moments is integrated to give the response variance. The resulting VRF matrix is unique regardless of the random field's marginal probability density function (PDF) and SDFs.
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