rus
Issue #1/2022
V.V.Zalipaev, D.Yu.Kobtsev, D.О.Zinchenko, О.V.Andreeva
STRUCTURE CHARACTERISATION OF NANOPOROUS SILICATE MATRICES BY OPTICAL METHODS
STRUCTURE CHARACTERISATION OF NANOPOROUS SILICATE MATRICES BY OPTICAL METHODS
10.22184/1993-8578.2022.15.1.28.33
INTRODUCTION
Nanoporous silicate matrices (NPSM) derived from biphase borosilicate glass [1] are of significant interest for a number of modern scientific and technical fields due to a number of useful properties. NPSM samples in the form of plane-parallel plates possess high transparency in visible and near-infrared regions of spectrum, high chemical, thermal, radiation resistance and physical-mechanical strength close to the properties of solid silicate glass. This opens up significant perspectives for their use in optical experiments as the basis for the development of optical elements for various applications (e.g., optofluidic elements [2–3]) and for investigation of the properties of substances in the nanoscale dispersed state [4–5].
The optical methods developed for continuous media are often used to characterise the internal structure of transparent objects. However, a key feature of nanoporous media is scattering, which is determined by the size of non-uniformities and their wavelength dependence [6–7].
A number of parameters are used to characterise the internal structure properties of NPSM, among which the most important, from the point of view of practical application, are the pore size and the free volume of the sample occupied by pores (Vp). In practice, the value of Vp is determined quite simply by the weight method [8] – by the weight of the sample in air-dry state and when the pores are filled with water. At the same time, the determination of pore size (and pore size distribution) is a rather complex scientific and technical task, which is currently solved by methods of porometry, and requires special equipment. The most common is the BET-method. It consists in finding the surface area of a solid body by adsorption of some substances. In the case of porometry measurements, dispersion (grinding) of the sample in question is required. The study of nanoporous matrices occupies a niche in the scientific community activity. In order to obtain a material that will have the desired properties, it is important to develop not only the technology for obtaining samples with stable and reproducible characteristics, but also the quality control methods applied to manufactured samples. As a rule, the existing methods are developed to characterize quality of optical surfaces. At the same time, the optical quality of NPSMs is determined by the internal porous structure of the sample which characterisation may not always be achieved by the methods developed for assessing the optical parameters of homogeneous (solid) non-porous materials.
In addition, the substance quantity to be tested should normally be in the range of a few grams. The laboratory-made NPSM samples are small, weighing tenths of a gram, and are produced in small batches [1]. Thus, the problem of non-destructive testing and appropriate techniques for characterising the structure of NPSMs is important in their manufacture and use.
This paper describes an approach to solve this problem using optical measurements and mathematical modeling of the relevant characteristics.
RESEARCH METHODS
Experiment. The optical density (D) and transmittance (T) of the samples were measured on an Evolution 300 spectrophotometer in the 200÷900 nm wavelength range. The measurements were taken in air-dry condition of the samples relative to air. The samples were plane-parallel plates with dimensions of 15 × 20 mm and a thickness of 1 mm.
Two types of NPSM-7 (sample 1) and NPSM-17 (sample 2), which differ in their internal porous structure, were studied [1]. Figure 1 shows the attenuation (optical density) and transmittance spectra of different types of samples. As shown in [6–7], the decrease of transmittance of NPSM samples with decreasing wavelength of radiation is caused by two main reasons – absorption by components of the initial glass (silicate framework) and scattering on the porous structure. As noted in the cited papers at λ > 350 nm, the main contribution to the decrease in transmittance of the samples in the visible region of the spectrum is due to scattering on the porous structure. At λ > 600 nm, both types of NPSM samples in air-dry state have high transparency, T > 0.8.
Theory. The mathematical model. Let us consider a Gaussian beam at its normal incidence onto a plane-parallel plate filled with a randomly inhomogeneous medium. When passing through such a sample, the intensity of the beam, as it exits the plate of thickness d, is determined as follows:
, (1)
where I0 – beam intensity at the inlet, t1, t2 – the beam coefficients of the plate interfaces [9], which are defined by the expressions:
, (2)
where n – the refractive index of the external homogeneous medium in relation to the plate, and nef – effective optical refractive index of a randomly heterogeneous medium. As a result, the dielectric permittivity of a randomly inhomogeneous medium is defined as:
(3)
where ñ – random fluctuation of the optical refractive index of a randomly heterogeneous medium. According to [10], when describing the scattered field on random non-uniformities with the Born first approximation, the extinction coefficient σ0 can be estimated with a Gaussian quadratic correlation function (homogeneous and isotropic random process):
, (4)
where <ñ> – mean square of the fluctuation of the optical refractive index, lc – correlation radius. It should be noted that <ñ> = 0. So, in this case we get the extinction coefficient as follows:
, (5)
where k = k0(nef)1\2, k0 = 2π/λ ‑ is the wave number in a vacuum. Using the exponential correlation function, we obtain:
, (6)
for the extinction coefficient we get the following expression:
. (7)
As a result, it can be assumed that the wave dependences of the transmittance spectra of nanoporous samples are approximated by two dependences:
, (8)
where I0 - beam intensity at the inlet, I1, and I2 - beam intensity at the medium outlet at different extinction coefficients.
The transmission coefficient T is determined as follows:
Т1,2 (λ) = I1,2(λ)/I0. (9)
RESULTS
Spectral characteristics of two types of nanoporous silicate matrices were measured.
Transmission spectra of optical radiation of investigated samples are described using dependence (8). Figure 2 (a, b) shows experimental dependences of transmission spectra of the optical radiation of nanoporous samples 1 and 2 and two theoretical curves Т1(λ) and Т2(λ), obtained by using the following values of mathematical model parameters: nef = 1.275, < ñ2 > = 0.39, lc=0.001 nm и < ñ2 > = 0.17, lc=0.0009 nm for sample 1, nef = 1.225, < ñ2 > = 0.4, lc=0.0012 nm и < ñ2 > = 0.22, lc=0.00095 nm for sample 2. As can be seen from the above data, both calculated curves Т1(λ) and Т2(λ) describe the experimental dependence well.
CONCLUSIONS
The obtained results indicate that the proposed approach to description of the nanoporous silicate matrix as a random non-uniform medium allows to correctly describe the spectral characteristics of nanoporous samples in the visible and near-infrared spectral range if the parameters of the mathematical model are selected accordingly.
This makes it possible to further improve the used methodology in order to be able to compare the parameters of the mathematical model with the physical parameters of the nanoporous structure of the studied samples.
PEER REVIEW INFO
Editorial board thanks the anonymous reviewer(s) for their contribution to the peer review of this work. It is also grateful for their consent to publish papers on the journal’s website and SEL eLibrary eLIBRARY.RU.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Nanoporous silicate matrices (NPSM) derived from biphase borosilicate glass [1] are of significant interest for a number of modern scientific and technical fields due to a number of useful properties. NPSM samples in the form of plane-parallel plates possess high transparency in visible and near-infrared regions of spectrum, high chemical, thermal, radiation resistance and physical-mechanical strength close to the properties of solid silicate glass. This opens up significant perspectives for their use in optical experiments as the basis for the development of optical elements for various applications (e.g., optofluidic elements [2–3]) and for investigation of the properties of substances in the nanoscale dispersed state [4–5].
The optical methods developed for continuous media are often used to characterise the internal structure of transparent objects. However, a key feature of nanoporous media is scattering, which is determined by the size of non-uniformities and their wavelength dependence [6–7].
A number of parameters are used to characterise the internal structure properties of NPSM, among which the most important, from the point of view of practical application, are the pore size and the free volume of the sample occupied by pores (Vp). In practice, the value of Vp is determined quite simply by the weight method [8] – by the weight of the sample in air-dry state and when the pores are filled with water. At the same time, the determination of pore size (and pore size distribution) is a rather complex scientific and technical task, which is currently solved by methods of porometry, and requires special equipment. The most common is the BET-method. It consists in finding the surface area of a solid body by adsorption of some substances. In the case of porometry measurements, dispersion (grinding) of the sample in question is required. The study of nanoporous matrices occupies a niche in the scientific community activity. In order to obtain a material that will have the desired properties, it is important to develop not only the technology for obtaining samples with stable and reproducible characteristics, but also the quality control methods applied to manufactured samples. As a rule, the existing methods are developed to characterize quality of optical surfaces. At the same time, the optical quality of NPSMs is determined by the internal porous structure of the sample which characterisation may not always be achieved by the methods developed for assessing the optical parameters of homogeneous (solid) non-porous materials.
In addition, the substance quantity to be tested should normally be in the range of a few grams. The laboratory-made NPSM samples are small, weighing tenths of a gram, and are produced in small batches [1]. Thus, the problem of non-destructive testing and appropriate techniques for characterising the structure of NPSMs is important in their manufacture and use.
This paper describes an approach to solve this problem using optical measurements and mathematical modeling of the relevant characteristics.
RESEARCH METHODS
Experiment. The optical density (D) and transmittance (T) of the samples were measured on an Evolution 300 spectrophotometer in the 200÷900 nm wavelength range. The measurements were taken in air-dry condition of the samples relative to air. The samples were plane-parallel plates with dimensions of 15 × 20 mm and a thickness of 1 mm.
Two types of NPSM-7 (sample 1) and NPSM-17 (sample 2), which differ in their internal porous structure, were studied [1]. Figure 1 shows the attenuation (optical density) and transmittance spectra of different types of samples. As shown in [6–7], the decrease of transmittance of NPSM samples with decreasing wavelength of radiation is caused by two main reasons – absorption by components of the initial glass (silicate framework) and scattering on the porous structure. As noted in the cited papers at λ > 350 nm, the main contribution to the decrease in transmittance of the samples in the visible region of the spectrum is due to scattering on the porous structure. At λ > 600 nm, both types of NPSM samples in air-dry state have high transparency, T > 0.8.
Theory. The mathematical model. Let us consider a Gaussian beam at its normal incidence onto a plane-parallel plate filled with a randomly inhomogeneous medium. When passing through such a sample, the intensity of the beam, as it exits the plate of thickness d, is determined as follows:
, (1)
where I0 – beam intensity at the inlet, t1, t2 – the beam coefficients of the plate interfaces [9], which are defined by the expressions:
, (2)
where n – the refractive index of the external homogeneous medium in relation to the plate, and nef – effective optical refractive index of a randomly heterogeneous medium. As a result, the dielectric permittivity of a randomly inhomogeneous medium is defined as:
(3)
where ñ – random fluctuation of the optical refractive index of a randomly heterogeneous medium. According to [10], when describing the scattered field on random non-uniformities with the Born first approximation, the extinction coefficient σ0 can be estimated with a Gaussian quadratic correlation function (homogeneous and isotropic random process):
, (4)
where <ñ> – mean square of the fluctuation of the optical refractive index, lc – correlation radius. It should be noted that <ñ> = 0. So, in this case we get the extinction coefficient as follows:
, (5)
where k = k0(nef)1\2, k0 = 2π/λ ‑ is the wave number in a vacuum. Using the exponential correlation function, we obtain:
, (6)
for the extinction coefficient we get the following expression:
. (7)
As a result, it can be assumed that the wave dependences of the transmittance spectra of nanoporous samples are approximated by two dependences:
, (8)
where I0 - beam intensity at the inlet, I1, and I2 - beam intensity at the medium outlet at different extinction coefficients.
The transmission coefficient T is determined as follows:
Т1,2 (λ) = I1,2(λ)/I0. (9)
RESULTS
Spectral characteristics of two types of nanoporous silicate matrices were measured.
Transmission spectra of optical radiation of investigated samples are described using dependence (8). Figure 2 (a, b) shows experimental dependences of transmission spectra of the optical radiation of nanoporous samples 1 and 2 and two theoretical curves Т1(λ) and Т2(λ), obtained by using the following values of mathematical model parameters: nef = 1.275, < ñ2 > = 0.39, lc=0.001 nm и < ñ2 > = 0.17, lc=0.0009 nm for sample 1, nef = 1.225, < ñ2 > = 0.4, lc=0.0012 nm и < ñ2 > = 0.22, lc=0.00095 nm for sample 2. As can be seen from the above data, both calculated curves Т1(λ) and Т2(λ) describe the experimental dependence well.
CONCLUSIONS
The obtained results indicate that the proposed approach to description of the nanoporous silicate matrix as a random non-uniform medium allows to correctly describe the spectral characteristics of nanoporous samples in the visible and near-infrared spectral range if the parameters of the mathematical model are selected accordingly.
This makes it possible to further improve the used methodology in order to be able to compare the parameters of the mathematical model with the physical parameters of the nanoporous structure of the studied samples.
PEER REVIEW INFO
Editorial board thanks the anonymous reviewer(s) for their contribution to the peer review of this work. It is also grateful for their consent to publish papers on the journal’s website and SEL eLibrary eLIBRARY.RU.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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