The STOE model of XRD machine has been used to perform X-ray diffraction analysis (Fig. 3). X-ray diffraction spectroscopy was performed to investigate the crystalline properties of calcium carbonate and activated carbon. For structural analysis, X-ray diffraction, Bragg angles 2θ are between 5 and 90 degrees, and the source of Cu copper with a wavelength of λ = 1/54 angstroms In this model, the diffraction observed at angles 24 and 46 with low intensity is related to the graphite structure of activated carbon. Which refers to the crystal plates (002) and (101) graffiti, respectively. Calcium carbonate with calcite crystalline phase shows diffusions at angles of 23, 29, 36, 39, 43, 47 and 49.Which refers to the crystal plates (012), (104), (110), (013), (202), (018) and (016). Measurement crystallinity in this sample was calculated by the Debye‐Scherrer method and the value of 22 nm was obtained. In XRD analysis, the angle and intensity of the peaks contain information from the sample that can be used to determine the atomic structure and phase of the diffuser plates. Materials are available in crystalline and amorphous forms. In the XRD diagram, amorphous spheres have wide peaks. The intensity ratio of these peaks can be used to determine the crystallinity The size of the crystals and the micro-strains are effective factors in the width of the peaks. Obviously, the larger the crystal area and the smaller the lattice defects, the smaller the width of the peaks. As can be seen in (Fig. 3) narrow width of strips Self-determinants of crystallites in the nano range.

XRD diffraction peaks from calcium carbonate and activated carbon

Figure 4 shows the FESEM analysis images of optimal filter based on the compositions of calcium carbonate, ethylene glycol, cellulose, polyethylene and activated carbon.

FESEM images of optimal filter a 400 µm scale b 10 µm scale

As seen in the pictures improved filter have interconnected pores, pores and channels that represent an effective filter for better gas absorption. Because the more porosity and pores, the more pollutants are absorbed. The BET analysis was used to evaluate the porosity and effective surface measurement characteristics for filter. This analysis determines the pore diameter, surface area, hole volume and hole size distribution of nanoparticles. The effective surface of a substance is extracted from this line graph. In (Fig. 5a) the blue dots represent the absorption and red dots indicate excretion. As can be seen from the (Fig. 5a), the amount of absorption increases with the increase of the inlet gas pressure. Figure 5b shows the BET analysis of gas desorption. A comparison between the absorption and desorption diagrams is shown in (Fig. 5c).

a Filter gas adsorption, b Filter gas desorption c comparison between adsorption and desorption BET analysis

Since the absorption and desorption curves are close to each other and exceed two 0.5 and approximately two points at 0.3, the two curves are stuck together, it means that the diameter of the holes is very small and a few nanometers and in our structure there are both meso and micro. It is necessary to perform an efficiency test and pressure drop to identify suitable filters. Figure 6 shows the efficiency and permeability of filter as function of particles size. The test device of partner company of standard nanoscale technologists was used. This device is able to test efficiency, pressure drop and air permeability. This device is capable of supplying incoming air flow from 910 lit/min to 200 lit/min and pressure drop from zero to 1200 Pa. The efficiency can be obtained from [13, 14]:

$$}\left( \% \right)\, = \,\left( - N_ }} }}} \right)\, \times \,100$$

(1)

where N1 is the number of particles entering the device test and N2 is the number of particles passing through the filter. As can be seen in the Fig. 6, the efficiency of filter for particles with 100 nm size was 95% and by increasing the particle diameter, the permeability was decreased. The permeability can be obtained from [13, 14]:

$$}\left( \% \right)\, = \,1 - E\left( \% \right)\, = \,\left( }} }}} \right)\, \times \,100$$

(2)

where E(%) is the efficiency of the filter, N1 is the number of particles entering the device test and N2 is the number of particles passing through the filter. Figure 6 also shows the filter permeability for 100 nm particles was 5%. The goal of pressure drop analysis is to determine the pressure difference of unit under test when air passes through it under predetermined conditions. The pressure drop can be obtained from [13, 14]:

$$\Delta P\, = \, - \left( }}} \right)$$

(3)

where E(%) is the efficiency of the filter, Qf is the quality factor of the filter.The pressure drop was 213 Pa for a flow air 30 L/min. The carbon nanomaterials such as activated carbon, graphene and carbon nanotubes were used in filters for different application like indoor air cleaning, environmental pollution, life science and health [15,16,17]. Mallakpour and et al. [18], reviewed the fabrication of air filters for control the spread of COVID-19 based on the metals, metallic oxide, metal ions, carbon-based nanomaterials, biopolymers and other natural materials. They reported carbon nanomaterials due to construction, chemical stability and antimicrobial behavior have been employed widely in air filters and have an efficiency between 64 and 99.999%. In the Ref. [19], graphene-based air filters for COVID-19 has been investigated. They reported the efficiency of filter for sub-micron particulate filtration (0.3 µm) was 94.3%. The coronavirus filter based on the calcium carbonate/ethylene glycol/cellulose/polyethylene/activated carbon effectively absorbs respiratory fluid droplets that carry many viruses, including coronaviruses, which are produced by coughing, talking and breathing, and are suspended in the air for hours. Compare our results with other report show good agreement in the efficiency of filter performance.

Comparison between filter efficiency and permeability