Novel Machine Learning-Based Method for Estimation of the Surface Area of Porous Silica Particles

This work reports a novel and quick method to estimate the surface area of porous materials. Conventionally, surface area measurement requires the BET method/N2 adsorption experiment which is time-consuming. In this work, we developed a method based on machine learning (ML) and the adsorption of a conductive dye on porous materials. The rate and quantity of dye adsorption, which is characterized by dynamic measurement of conductivity, provide an indirect measure of surface area and zeta potential. An ML-based soft sensor is developed to relate the measured conductivity profiles with surface area and zeta potential. A phenomenological model on dye adsorption is also developed, validated, and used to augment experimental data for training the soft sensor. The developed method was tested for porous silica particles with a range of surface areas (250–1100 m2/g) and zeta potential (−17 mV: −29 mV). The developed soft sensor was able to estimate the surface area and zeta potential quite well. The developed approach and method reduce overall measurement time for surface area from several hours to a few minutes. The method can potentially be implemented in continuous plants producing porous materials like silica.


Calibration graph
Figure S1 shows a linear relation between conductivity and concentration of dye, based on calibration of dye concentration.

Error bar on conductivity profiles
Dye adsorption experiments were repeated for three times and error bars for conductivity profiles of various silica particles via experimental repetition were provided in Figure S2.

Optimazation of concentration for zeta potential measurement
Zeta potential measurement for Merk sample with different concentrations (0.833, 1.66, 2.5, 3.33, 4 mg/mL) with three repetitions.According to Figure S3, to concentrations 1.66 mg/mL and 2.5 mg/mL demonstrated lower standard deviation:

Result of BET analysis
The isotherm adsorption and desorption of N2 in BET analysis for four silica samples, as displayed in Table 1, was shown in Figure S4.
These reversible isotherm plots are the forms of isotherm obtained with the micropores and mesopores adsorbent and represent unrestricted monolayer-multilayer adsorption.The beginning of the almost linear middle section of the isotherm often indicates the stage at which monolayer coverage is complete and multilayer adsorption about to begin.The hysteresis is usually attributed to the thermodynamic or network effects or the combination of these two effects.The high steepness of the isotherms indicates the relatively high pore size uniformity and facile pore connectivity, and the less steepness presents narrow slit-like pores, particles with internal voids of irregular shape and broad size distribution, hollow spheres with walls composed of ordered mesoporous silica.Also, the extended double-sided arrow shows the larger surface area

Surface area calculation for mixed samples
Calculation of surface area for a mix of particles in different sizes: i=1, 2, 3, …, n S: surface area, (m 2 /g) m: weight, (g) Example:

Particle pore size distribution
We have used the BJH method 4 to measure pore size distributions of all the silica particles used in this work.The results are shown here in Figure S5:

Zeta potential modelling
The surface charge density (σ) is calculated using the following equation 5 : where C M is the acidic or basic reagent concentration, V is the reagent volume, m is the weight of powder, and S is the BET specific area.

Figure S2 .
Figure S2.Error bars for normalized conductivity profiles of various silica particles via experimental repetition

Figure S3 .
Figure S3.Zeta potential measurement for Merk sample with different concentrations

Figure S4 .
Figure S4.Isotherm adsorption and desorption of N 2 for silica samples with different surface area in BET test.

Figure S5 :
Figure S5: Pore size distribution for silica samples.