JP6018565B2 - Calculation method of pore parameters of transparent porous material - Google Patents

Description

  The present invention relates to a method for calculating pore parameters of a transparent porous body, and more specifically, the average pore radius, pore number density, optical constant (effective refractive index), and ratio of a porous body transparent to visible light. The present invention relates to a method for calculating a surface area and the like from a transmittance measurement result.

A porous body transparent to light in the ultraviolet / visible region with a wavelength range of 0.2 to 0.8 μm, such as porous silica glass, (1) transmits light in the visible region (0.35 to 0.8 μm). It has two characteristics: transparency and (2) gas adsorption characteristics of adsorbing gas molecules because it has a specific surface area (total surface area of the substance per gram) reaching several hundred m ² / g. . By utilizing these two characteristics, various utilization techniques such as utilization for optical elements and utilization for gas detection elements have been proposed for porous silica glass. When porous silica glass is used as a gas detection element, for example, gas detection is performed by supporting a porous silica glass with a dye that selectively reacts with a specific detection target gas and changes color (coloring or fading) in the visible region. Create an element. When this gas detection element is used, it is possible to manufacture an ultra-small storage type sensor. (See Patent Documents 1 and 2).

  The gas detection element of this accumulation type gas sensor is composed of two elements: a porous body serving as a base material for supporting a dye, and a dye supported in the pores of the porous body.

  Here, in order to evaluate the performance of a gas sensing element made of a transparent porous material such as porous silica glass, the pore parameters of the transparent porous material, specifically, the average pore radius, the pore number density , Optical constant (effective refractive index), and specific surface area must be calculated. The average pore diameter, specific surface area, etc. of transparent porous materials are conventionally measured by adsorbing a saturated vapor (adsorbate) of nonpolar molecules such as nitrogen gas to the pore surface in an isothermal state, and measuring the adsorption isotherm and desorption isotherm. It has been derived by analyzing the measured adsorption / desorption isotherm. For example, the specific surface area (BET specific surface area: specific surface area based on the adsorption theory of Brunauer, Emmett, Teller) is an adsorption isotherm in which the ratio of the vapor pressure to the saturated vapor pressure is about 0.2 to 0.35. It is calculated | required by analyzing (refer nonpatent literature 1). Furthermore, the pore size distribution is obtained by analyzing the adsorption isotherm or desorption isotherm using a technique such as the Dollimore-Heal method (see Non-Patent Document 2).

  In any method, the adsorption / desorption isotherm of the transparent porous body to be analyzed must be accurately measured in order to obtain the pore parameters.

  Here, the adsorption / desorption isotherm is measured by a volumetric method in which the amount of adsorbate adsorbed on the sample is determined from the relationship between the gas volume and pressure, and the amount of adsorbate adsorbed on the basis of changes in the sample weight. There are two methods, the gravimetric method to be determined.

  In the former capacity method, the amount of adsorbate adsorbed is estimated from the pressure change before and after adsorption using an approximate equation of state for the adsorbate. The measurement principle is very simple, but measurement errors occur due to the accuracy of the pressure sensor that measures pressure in addition to temperature, the accuracy of dead volume measurement, and the vacuum leakage of the entire measurement system. Need attention. Moreover, it takes a long time to measure the adsorption / desorption isotherm by the volume method, and therefore the automation of the measurement can be considerably advanced.

  On the other hand, the measurement of adsorption / desorption isotherm by the latter weight method does not require the dead volume as in the volume method, but it is necessary to measure the weight change accurately, and the difference between the thermostat temperature and the sample temperature is reduced. However, the influence of thermal convection and the change in weight due to buoyancy and adsorption to the container must be corrected. It is also susceptible to vibration and static electricity from a thermostatic chamber. Furthermore, compared to the volumetric method, there are few automated devices for performing adsorption / desorption isotherm measurement by the gravimetric method. To change the vapor pressure of the adsorbate, raise the temperature of the adsorbate above its gas-liquid phase transition point, and measure the adsorption isotherm, but control the temperature so that the sample temperature and the thermostat temperature match as much as possible. This is important for improving measurement accuracy. Similarly, when measuring a desorption isotherm, the thermostat temperature is lowered contrary to the above. Therefore, since the influence of the temperature change is great, it is necessary to keep the entire apparatus in a constant temperature state.

Japanese Patent No. 3934008 Japanese Patent No. 3700807 Japanese Patent No. 5032352 Japanese Patent No. 5192341

Seiichi Kondo, Tatsuo Ishikawa, Ikuo Abe, "Adsorption Chemistry" (Maruzen Co., Ltd., 1991), pp.40-46. D. Dollimore and G. R. Heal, J. Appl. Chem., 14, 109 (1964). Shigeo Ogawa, Yoko Maruo, 1 / λ4 light scattering during drying of Vycor porous glass, 2008 Proceedings of the 55th Joint Conference on Applied Physics, 20080327 (published), 1st volume , P. 179 M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (1969, Academic, New York), p. 37, Eq. (3.2.24).

  In any of the above two methods for measuring adsorption isotherm, since the adsorbate is actually adsorbed on the sample surface and measured, the measurement result depends sensitively and delicately on the surface condition of the sample to be measured. To do. Therefore, regarding the pretreatment of the sample, a process of removing impurities, adhering gas, etc. from the sample to be measured is necessary (degassing process). In addition, in the measurement of adsorption isotherm, in the volume method, multiple pressure measurements, dead volume measurement, etc., in the gravimetric method, mass display monitoring, buoyancy correction, adjustment of the temperature of the entire device, etc. Have to go through. Therefore, the measurement of the adsorption isotherm is complicated and takes time, including proper pretreatment of the sample. Even non-porous solid samples usually require about 8 hours without failure to measure a set of adsorption / desorption isotherms. When the object to be measured is a porous body, it takes a longer time and usually requires a whole day and night. Furthermore, in the measurement method in which the adsorbate is directly adsorbed on the sample, nonpolar gas needs to be adsorbed on the wall surface of the pores connected to the surface of the porous body, and isolated pores (such as bubbles) existing in the porous body. If there is, there is no adsorption in the first place, and such isolated pores are not detected.

  The present invention takes into account various limitations such as the inherent limitations and problems of the conventional method, and the complexity and time of operation, and only from the optical properties exhibited by the transparent porous body, the average pore radius, The present invention relates to a method for calculating pore number density, effective refractive index, specific surface area and the like in a short time.

  In order to achieve the above object, the present invention provides a method for calculating a pore parameter of a transparent porous body by a computer, wherein the transparent processed into a parallel plate shape. Obtaining a parallel plate thickness and a porosity of a porous body; and obtaining a transmittance spectrum of the transparent porous body, wherein the transmittance spectrum is measured by wavelength sweeping in a visible region. And plotting the logarithm of the transmittance spectrum and dividing by the parallel plate thickness of the transparent porous body against the inverse fourth power of the wavelength divided by the refractive index of the skeleton member of the transparent porous body; Calculating a slope parameter and a vertical axis intercept by performing linear regression analysis on the value obtained by taking the logarithm of the plotted transmittance spectrum and dividing the value by the parallel plate thickness; Calculating the reflectance at the interface between the air and the porous body, calculating the effective refractive index of the transparent porous body from the reflectance at the porous body interface, and calculating the average fineness of the transparent porous body from the slope parameter. Calculating the pore radius and the pore number density.

  The invention according to claim 2 is the method according to claim 1, further comprising a step of calculating a specific surface area of the transparent porous body using the porosity and the average pore radius. It is characterized by.

  The invention according to claim 3 is the method according to claim 1 or 2, wherein the transparent porous body is cleaning with acetone, ethanol, and ultrapure water to improve transparency. In addition, the cleaning is performed individually or in combination of two or more, and each cleaning is performed a plurality of times.

  The invention according to claim 4 is the method according to claim 3, wherein when the transparent porous body is porous silica glass, the transparent porous body is 0.1% in the washing step. The transparent porous body is further subjected to a light etching treatment with diluted hydrofluoric acid.

  The invention according to claim 5 is the method according to claims 1 to 4, wherein the transparent porous body is heated to 150 ° C. or more for 6 hours or more in a vacuum after being washed by the washing. Further, the method is further characterized in that a drying step of drying by storing dry nitrogen after overheating is further performed.

  The invention described in claim 6 is a pore parameter measurement system, which is connected to a spectrophotometer for measuring a transmittance spectrum of the transparent porous body, and the spectrophotometer. And a computer executing the described method.

  The invention described in claim 7 is a computer-readable storage medium, wherein a program for causing a computer to execute the method described in claim 1 or 2 is stored.

  According to the technique of the present invention, in the calculation of the pore parameters of the transparent porous body, while paying close attention to the prior art, without undergoing pretreatment that takes a long time, and measurement of adsorption and desorption isotherm over almost all day and night, By simply measuring the transmittance of the transparent porous body, approximate values of pore parameters such as average pore radius, pore number density, effective refractive index, and specific surface area can be easily obtained in a short time.

It is a flowchart which shows the process of the calculation method of the pore parameter concerning one Embodiment of this invention. It is a figure which shows the detail of the flow of the pore parameter calculation in an Example. It is a figure which shows the pre-processing process by the organic solvent of a transparent porous body. It is a figure which shows the light etching by the diluted hydrofluoric acid of the porous silica glass sample. It is a block diagram which shows the structure of the pore parameter measurement system used in the Example of this invention. It is a graph which shows the transmittance | permeability spectrum of a transparent porous body sample. It is a flowchart which shows the detail of the method of a pore parameter extraction in a present Example. ln _e (1 / T) / medium in opposite fourth power of the wavelength of d (1 / λ ⁴⁾ the dependence is a chart showing the results of linear regression analysis. It is a graph which shows the nitrogen gas adsorption / desorption isothermal curve of the transparent porous body measured with the capacity | capacitance type automatic adsorption amount apparatus in a prior art. It is a graph which shows the pore size distribution calculated | required by the prior art.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

  FIG. 1 is a flowchart showing the steps of a pore parameter calculation method according to an embodiment of the present invention. The pore parameter calculation method shown in FIG. 1 is a “processing / cleaning step” in which a transparent porous body to be evaluated is processed into a parallel flat plate shape, and cleaning is performed to improve the transparency of the transparent porous body as necessary. And a “measurement / analysis step” for measuring the light transmittance of the porous body to be evaluated and processing the data.

In addition, the “measurement / analysis process” includes the following six processes.
First step: After giving the approximate value of the porosity of the porous body to be evaluated, the wavelength is swept in the visible region (wavelength 0.35 to 0.8 μm), and the transmittance spectrum is measured.
Second step: A value obtained by taking the logarithm of the transmittance of the transparent porous body and dividing it by the parallel plate thickness is plotted against the inverse fourth power of the wavelength divided by the refractive index of the skeleton member of the transparent porous body.
Third step: The slope parameter and the vertical axis intercept are obtained by linear regression analysis of the inverse wavelength fourth power plot of the logarithmic transmittance created in the second step.
Fourth step: The reflectance at the interface between air and the porous body is calculated from the vertical axis intercept obtained in the third step, and the effective refractive index of the transparent porous body is calculated from the calculated reflectance.
-5th process: The average pore radius and pore number density of a transparent porous body are calculated using the inclination parameter obtained from the 3rd process.
-6th process: The specific surface area of a transparent porous body is calculated using this approximate value of the said porosity, and the average pore radius obtained at the 5th process.

  A slight decrease in the transmittance spectrum in the visible region of the transparent porous body is not an absorptive material such as coloring but depends on the inverse fourth power of the incident light wavelength. Therefore, it can be said that the slight decrease in the transmittance spectrum is due to Rayleigh scattering caused by the nanopores (see Non-Patent Document 3, Patent Documents 3 and 4). Therefore, in the present embodiment, by utilizing this fact, the effective average pore radius and pores of the transparent porous body can be obtained from the measurement result of the transmittance spectrum without using the conventional adsorption / desorption isotherm analysis. Pore parameters such as number density, effective refractive index, and specific surface area can be obtained, and their values are on the same order as the conventional method.

  Next, calculation of each pore parameter in the “measurement / analysis step” will be described together with physical properties on which the present invention is based on the optical properties of the transparent porous body.

In general, in a medium having a uniform composition and a homogeneous structure, it has been experimentally found that the intensity of light attenuates exponentially with the transmission distance L of light in the medium, and Lambert's law As
I _meas = I _ref · exp (−α · L)
Is displayed.

Here, I _ref is the intensity of incident light (also referred to as reference light), I _meas is the transmitted light intensity of the sample, L is the transmission distance (or optical path length) of light in the medium, and α is a property specific to the substance. Called absorption coefficient.

When the light source wavelength is λ ₀ (unit: μm), the transmittance spectrum T (λ ₀ ) has an intensity I _meas (λ ₀ ) of transmitted light and an intensity I _ref (reference light) of the reference light obtained at the wavelength λ ₀ . λ ₀ ).

The basic condition for the medium to be transparent is that the absorption coefficient α (λ ₀ ) at the wavelength λ ₀ is very small. If the absorption coefficient α (λ ₀ ) varies greatly depending on the wavelength of visible light, the medium is colored. It will be. If it is colorless and transparent, the absorption coefficient does not change at a specific wavelength in the visible range. A transparent porous body usually has many nano-sized pore groups in the medium, but being transparent to visible light means that the distribution of pore groups in the medium is uniform. It means that there is no non-uniformity on a scale that is structurally comparable to the wavelength of visible light. In such a case, the porous body can be regarded as a non-absorbing and optically uniform medium. However, there is little scattering due to the difference in refractive index between the nanopore and the medium. The wavelength of incident light is about 350 nm even on the short wavelength side compared to a hole diameter on the order of several tens of nm, and the ratio of the wavelength of incident light to the hole diameter is about 1/10. From this, it can be seen that the scattering by the nanopores does not depend on the shape thereof and becomes Rayleigh type scattering. In addition, these pore groups are considered to be uniformly distributed in the nanoporous body, and scattering by each pore occurs incoherently. As a result, the scattering intensity per unit volume of the transparent nanoporous porous material may be the sum of the scattering effects from each scatterer. The number of pores (= scatterers) per unit volume is N (having a dimension that is the inverse of the volume), and the intensity of light is I. The light intensity attenuation due to scattering is
−dI / dx = N · C _sca · I
Can be described. Here, C _sca has a dimension of an area as a scattering cross section of one scatterer. For a scatterer population, introducing turbidity τ (having the dimension of the inverse of distance) instead of the above absorption coefficient,
τ = N · C _sca
Can be written.

When the differential equation is solved in consideration of the surface reflectivity r at each interface between the air and the transparent nanoporous porous material, the transmittance spectrum T (λ ₀ ) for the material of thickness d is (First step).
T (λ ₀ ) = I _meas (λ ₀ ) / I _ref (λ ₀ ) = (I−r) ² · exp (−τ · d) (1)

Here, the medium 1 light beam refractive index _{n 1 (air:} n 1 = 1.0003) from medium 2 of refractive index _{n 2} (absorption unless if real refractive index in a transparent porous _{body: n} 2) The surface reflection coefficient r is

It is represented by

For a Rayleigh scatterer, its scattering cross section C _sca is

(See Non-Patent Document 4). However, V ₁ is the volume of the pores acting as a scatterer, assuming spherical single scatterer average radius r _p,

Given in. Also, λ is the wavelength of light inside the medium 2, and λ ₀ is the wavelength in vacuum,
λ = λ ₀ / n ₂
Given in. M is the ratio between the refractive index n ₁ of the medium ₁ and the refractive index n ₂ of the medium 2;
m = n ₁ / n ₂
Given in.

By the way, the porosity φ (dimensionalless amount) is defined as the volume ratio of the portion other than the solid portion constituting the skeleton with respect to the volume V of the entire porous body sample. When the volume of the skeleton portion of the porous body is _{V skelton, V p} (total volume of pores) volume air gap portion,
V _p = V−V _skeleton
Therefore, the porosity φ is defined by the following equation.

Since the volume of pores acting as a scatterer is V ₁ and the number of pores per unit volume (pore number density) is N, the product N · V ₁ is equal to the porosity φ of the porous body. There is nothing else.
φ = N · V ₁ (6)

The turbidity defined by τ = N · C _sca takes into account equations (3) and (6),
N · V ₁ ² = φ · V ₁
It is proportional to

Taking the natural logarithm of both sides of equation (1) and dividing it by the sample thickness d, the turbidity τ is proportional to the inverse fourth power of the wavelength, so that the linear dependence on the horizontal axis 1 / λ ⁴ Should show gender. That is,

It becomes. That is, ln _e (1 / T) / d is created from the transmittance spectrum T and plotted against the inverse fourth power (1 / λ ⁴ ) of the corresponding in-medium wavelength (λ = λ ₀ / n ₂ ). Then (second step), it is expected to be placed on a straight line with a slope β and a vertical intercept C (third step).

  The slope parameter β has a volume dimension, and combining the equations (3), (4), (6),

It becomes. Solving this equation (8) with respect to the volume V ₁ of the pores, when combined with equation (4), the scatterer, that is, the average radius r _p of the pores is obtained (step 4). Furthermore, when the pore volume V ₁ is combined with the equation (6), the number density N of the scatterers, that is, the pores can be calculated (fifth step).

  On the other hand, the vertical axis intercept C has the dimension of the reciprocal of the length, and when the second equation of Equation (7) is solved for r so as to satisfy the condition 0 <r <1, As the reflectance r of

Is obtained. If equation (9) is equivalent to equation (2) and solved for the effective refractive index n ₂ of the porous body,

It becomes.

  Finally, a specific surface area representing an internal surface area per unit mass of the porous body is derived using various amounts obtained from the transmittance measurement (sixth step).

The total internal surface area S _p of a porous body having N spherical pores per unit volume is theoretically S _p = (4πr _p ² ) · N
It becomes. On the other hand, the When the porous body apparent density and ρ [kg / ^{m 3],} and the density ρ _skelton [kg / ^{m 3]} of the skeleton portion, a relationship of ρ = (1-φ) ρ skelton. Accordingly, the specific surface area σ [m ² / kg] indicating the total pore surface area per unit mass of the porous body is

Is calculated by

The total volume V _p for a spherical pore is theoretically V _p = V ₁ · N
Since given by the ratio contained in the final term of equation _{(11) (S p / V} p) is equal to 3 / _{r p} Combined with equation (4). Note that when assuming cylindrical through hole having a radius _{r p} as the pores, the ratio _{(S p} / _V p) is equal to 2 / _{r p.}

[Example]
As an embodiment of the present invention, a specific application example of the above principle will be described in detail with reference to the drawings.

  FIG. 2 shows details of the flow of pore parameter calculation in the embodiment. As described with reference to FIG. 1, there are two components of the pore parameter calculation method: a “processing / cleaning step” first and a “measurement / analysis step” second. First, in the “processing / cleaning step”, a test sample is prepared and pretreated. Next, in the “measurement / analysis step”, the transmittance spectrum of the test sample is measured, the measured transmittance spectrum is analyzed, and the pore parameters are calculated. In this example, a “verification step” is provided as a reference, but in the “verification step”, the parameters extracted by the parameter calculation method of this example were obtained from the conventional adsorption / desorption isotherm. Compared with the results, the validity is evaluated.

In this example, pore parameters are calculated using Corning Vycor 7930 (Thirsty Glass) porous silica glass having a nominal pore diameter of 4.2 nm as a specific transparent porous body to be applied. As shown in Table 1, the nominal value of the average pore diameter of this silica glass sample (transparent porous body sample) is 4.2 to 4.6 nm. When measured by the conventional BET method, the specific surface area is about 195 to 195. 200 [m ² / g].

[Processing / cleaning process]
First, the “processing / cleaning process” will be described.

  In the processing / cleaning process, the sample is processed (sample preparation process). In processing the transparent porous body sample to be measured into a parallel flat plate shape, the thickness d of the sample is set to a thickness within a measurable range, and the vertical and horizontal sizes of the sample are measured for the transmittance. The size is arbitrarily selected according to the measurement optical system. In this embodiment, the sample holder of the spectrophotometer for measuring the transmittance spectrum was adapted.

  In this example, as a sample preparation, a transparent porous body serving as a sample is processed into a parallel flat plate having a thickness of about 1 mm and a width and width of about 8 mm × 8 mm.

  Next, the transparent porous material sample is washed (cleaning step). If the transparent porous material sample shows yellowing due to adsorption of organic matter and its oxidation, the organic solvent itself is removed to remove the yellowing. Wash with. As a washing process with an organic solvent, washing with acetone, ethanol, or ultrapure water, each alone or in combination of two or more, and each washing more than once, for a transparent porous body sample to be measured, Implemented as pre-measurement processing.

  In general, when the transparent porous body is left in the atmosphere for a long time, the organic substance is adsorbed in the pores, and thus tends to yellow. In order to remove the influence of these organic contaminants when measuring the light transmittance, the transparent porous material sample was firstly acetone (purity 99%), ethanol (purity 99.5%), and ultrapure water (18 MΩ · cm). Need to be cleaned using Here, the examples are developed on the assumption that the transparent porous body is not eroded by the organic solvent.

  When the transparent porous material is eroded by these organic solvents, the following cleaning cannot be performed. Instead, it may be switched to washing with an acid such as hydrochloric acid or sulfuric acid. Regarding the solvent used for cleaning, it is necessary to determine the chemical composition of the porous material to be cleaned after careful examination.

  3A and 3B are diagrams showing a cleaning process of the transparent porous body with an organic solvent. FIG. 3A shows a cleaning process, and FIG. 3B shows a drying process after cleaning.

  As shown in FIG. 3A, the cleaning procedure is performed by first immersing the transparent porous material sample in a container filled with acetone, and further immersing the container itself in an ultrasonic cleaner filled with water. For 10 minutes. This step is repeated three times with fresh acetone after every 10 minutes of washing. Next, after rinsing all the samples with pure water, as shown in FIG. 3 (a), it is immersed again in a new container filled with ethanol, and the container itself is further placed in an ultrasonic cleaner filled with water. Soak and sonicate for 10 minutes. Repeat this step three times. After rinsing the sample again with pure water, in order to remove a trace amount of residual ethanol, again, as shown in FIG. 3 (a), the transparent porous body sample was immersed in a container filled with ultrapure water, This container is immersed in an ultrasonic cleaner filled with water and subjected to ultrasonic cleaning for 10 minutes. Repeat this three times.

  Finally, the transparent porous body sample is dried (drying step). In the drying step, as shown in FIG. 3B, the transparent porous body sample is sufficiently dried by storing it in a desiccator in which dry nitrogen is passed for about 6 hours. Further, as another drying method, the transparent porous body sample washed in the washing step may be heated to 150 ° C. or higher in a vacuum for 6 hours or longer, and stored in dry nitrogen after overheating to dry the transparent porous body sample. .

  Here, when the transparent porous body to be measured is porous silica glass, the light etching treatment with 0.1% diluted hydrofluoric acid is measured in addition to the cleaning step prior to performing the measurement / analysis step. It can also be implemented as a pretreatment. In the case where the transparent porous body to be measured is porous silica glass, the transparency can be further improved by chemically etching the sample surface with dilute hydrofluoric acid.

  4 shows light etching with dilute hydrofluoric acid on a transparent porous glass sample of porous silica glass, FIG. 4 (a) shows dilute hydrofluoric acid etching, and FIG. 4 (b) shows cleaning with running water after etching. .

  As an etching step, as shown in FIG. 4A, the transparent porous body sample is immersed in a Teflon (registered trademark) container filled with a diluted hydrofluoric acid solution having a concentration of 1% for 1 minute. When dipping, a Teflon chip holder is used to handle the sample.

  Next, as shown in FIG. 4B, after light etching with dilute hydrofluoric acid, the sample is immersed in ultrapure water running water for 20 minutes for rinsing, thereby removing a trace amount of hydrofluoric acid.

  In fact, through this step, it is possible to keep the transparent porous body sample in an optically transparent state even after heating to about 450 ° C. in a vacuum.

  Finally, returning to FIG. 3 (b), the sample is sufficiently dried by storing it in a desiccator in which dry nitrogen is passed for about 6 hours.

[Measurement and analysis process]
The “measurement / analysis process” will be described in detail.

  First, the pore parameter measurement system used in the measurement / analysis process of the present embodiment will be described. FIG. 5 is a block diagram showing the configuration of the pore parameter measurement system used in this embodiment.

  The pore parameter measurement system 500 includes a spectrophotometer 510 that measures the transmittance spectrum of the transparent porous body sample 501, and the transmittance spectrum of the transparent porous body sample 501 that is measured by the spectrophotometer 510. And an analysis computer 520 for measuring pore parameters. The spectrophotometer 510 and the analysis computer 520 may be connected by wire or wirelessly.

  The spectrophotometer 510 detects the visible light transmitted through the transparent porous sample 501, the light source 511 that irradiates the transparent porous sample 501 with visible light, the sample chamber 512 into which the transparent porous sample 501 to be measured is inserted, and And a calculation unit that calculates a transmittance spectrum from the detected visible light.

  The spectrophotometer 510 for measuring the transmittance spectrum is a U-3500 spectrophotometer manufactured by Shimadzu Corporation. Since the transparent porous body sample had a size of about 8 mm square, it was measured by attaching it to an aluminum sample holder (plate) having a hole diameter of 6 mm.

  Next, the procedure of the “measurement / analysis step” will be described.

First, the transmittance spectrum in the visible region is measured (corresponding to the first step in FIG. 1). In this step, the transparent porous body sample 501 that has undergone the above processing / cleaning step is inserted into the sample chamber 512 of the spectrophotometer 510, and the wavelength (λ ₀ ) of the light source 511 is a wavelength in the visible region of 0.35 to 0.8 μm. The transparent porous body sample is irradiated within the range, and the transmitted light intensity I _meas (λ ₀ ) is detected by the detection unit 513. The detected transmission high intensity I _meas (λ ₀ ) is input to the calculation unit 514, and the calculation unit 514 calculates the transmitted light intensity I _meas (λ ₀ ) and the reference light intensity I _ref (λ ₀ ) from the equation (1). ) To convert to transmittance T (λ ₀ ). This is a measurement that can be easily performed with a standard double beam spectrophotometer.

  FIG. 6 is a chart showing the transmittance spectrum of the transparent porous material sample measured by this step. In the porous silica glass used as this sample, absorption considered to be caused by the silica glass itself is observed at 0.33 μm or less on the short wavelength side. On the other hand, the visible region of 0.35 to 0.8 μm is almost transparent, and the transmittance in this region exceeds 90%.

  Next, the pore parameter is calculated from the transmittance spectrum measured by the above process. FIG. 7 is a flowchart showing details of the pore parameter calculation method in the present embodiment. The pore parameter calculation method is performed by a pore parameter analysis computer 520 connected to a spectrophotometer for measuring a transmittance spectrum.

The pore parameter calculation is first started in step 701, and in step 702, a measurement file name and initial parameters are input to the computer 720. As initial parameters, sample thickness (d), porosity (φ), and effective refractive index n ₂ of the transparent porous body to be analyzed are input.

In step 703, the transmittance spectrum T (λ ₀ ) obtained by the above process is taken into the computer 720 from the spectrophotometer 510, and the computer 720 proceeds with the analysis according to the equation (7).

In step 704, the in-medium wavelength λ (= λ ₀ / n ₂ ) is calculated. In this embodiment, employing a porous silica glass since it is targeted to be measured, as tentatively first starting value of the effective refractive index n ₂ of the refractive index 1.45 of the silica skeleton transparent porous body.

In Step 705, the amount ln _e {1 / T (λ ₀ )} / d obtained by dividing the transmittance spectrum T (λ ₀ ) by logarithm and dividing by the sample thickness d according to the left side of the equation (7) Then, the inverse fourth power 1 / λ ⁴ of the wavelength λ in the medium is plotted on the horizontal axis. Steps 703 to 705 in FIG. 4 show details of the second step in FIG.

A plot of ln _e {1 / T (λ ₀ )} / d obtained in step 705 with respect to the inverse fourth power 1 / λ ⁴ of the in-medium wavelength is a linear function shown in the right side of equation (7) in step 706. By curve fitting, values of the slope parameter β and the vertical axis intercept C are obtained. Step 706 in FIG. 7 shows details of the third step in FIG.

In step 707, the reflectance r of the single interface is obtained using the value of the vertical axis intercept C obtained from the linear regression analysis and the equation (9), and the reflectance r is substituted into the equation (10). A new effective refractive index n ₂ of the body is calculated. Step 707 in FIG. 7 shows details of the fourth step in FIG.

In step 708, the new effective refractive index n ₂ and the first starting value n, which are the first calculated values obtained using the equations (9) and (10) from the value of the vertical intercept C obtained from the linear regression analysis. ₂ to obtain the refractive index error | δ |. If the difference | δ | exceeds the allowable error, in step 709, an intermediate value between the first calculated value n ₂ and the first starting value n ₂ is set so that the error | δ | The new second starting value n ₂ is adopted and the process returns to step 704 again. The linear regression analysis in steps 704 to 707 is repeated to obtain the second calculated value n ₂ again. By repeating this calculation loop until the difference | δ | becomes smaller than the allowable error, the final solution can be reached with high accuracy.

FIG. 8 is a chart showing the results of linear regression analysis of the inverse fourth power 1 / λ ⁴ dependence of the wavelength in the medium of ln _e {1 / T (λ ₀ )} / d in step 705. FIG. Is the first time (calculated with the first starting value), and FIG. 8B is a diagram showing the result after convergence. FIG. 8A shows an initial result when the refractive index n ₂ = 1.45 is used, and FIG. 8B shows a case where the effective refractive index n ₂ = 1.3179 converged by the calculation loop is reached. It is a result.

As shown in FIG. 8B, finally, values of β = 9.499513 × 10 ⁻⁷ [μm ³ ] and C = 3.791246 × 10 ⁻⁵ [μm ⁻¹ ] are obtained, respectively.

  Table 2 shows the effective refractive index, the vertical axis intercept, and the single reflectance by the iterative calculation loop (steps 704 to 709) shown in FIG. It can be seen that the value of the vertical axis intercept hardly changes even after repeated calculation.

In step 710, it solves the above equation (8) with respect to the volume _{V 1,} by combining with Equation (4), the scatterer, i.e., obtaining an average radius _{r p} of the pores. Further, if the volume V ₁ is combined with the equation (6), the pore number density N can also be calculated. Since the density of the silica skeleton ρ _skelton = 2.65 [g / cm ³ ], the specific surface area σ can also be calculated using the equation (11). The results are summarized in Table 3.

  Step 710 in FIG. 7 shows details of the fifth step and the sixth step in FIG.

  The pore parameter calculation method according to the present embodiment is included in a program module, and a computer executable instruction executed on a target real processor or a virtual processor is executed in the pore parameter analysis computer 520. Can be explained in a general context. Computer-executable instructions for program modules may be executed within a local computing environment or in a distributed computing environment.

  In addition, the pore parameter calculation method of this embodiment can be described in the general context of computer-readable media. Computer readable media can be any available media that can be accessed within a computing environment. By way of example, and not limitation, within a computing environment, computer-readable media includes memory, storage, communication media, and any combination of the foregoing.

"Verification process"
In the “verification process”, the parameters extracted by the parameter determination method of this example are compared with the results obtained from the conventional adsorption / desorption isotherm, and the results of the pore parameter determination method of this example are validated. Assess sex.

  In order to obtain the pore diameter distribution, an adsorption / desorption isotherm is determined using a capacity type automatic gas adsorption device (BELSORP-mx) in order to obtain the specific surface area and average pore radius of the transparent porous body. This apparatus can automatically measure the amount of nitrogen gas adsorbed on the inner wall surface of the porous body. Next, the pore diameter distribution is obtained from the adsorption isotherm using the Dollimore and Heal method (Non-Patent Document 2).

  In the conventional method, the adsorption / desorption isotherm was determined for the same porous silica glass sample used in this example.

  Prior to this adsorption amount measurement, the porous silica glass sample was subjected to the washing step shown in the Examples, and then heated in a vacuum at about 450 ° C. for 6 hours to dry the moisture adsorbed inside the pores. After drying, the adsorption and desorption isotherm of nitrogen gas at 77K was measured for the porous silica glass sample.

FIG. 9 shows a nitrogen gas adsorption / desorption isotherm of porous silica glass. The horizontal axis represents the relative value of the nitrogen gas pressure with respect to the saturated vapor pressure at the liquid nitrogen temperature, and the vertical axis represents the adsorption amount. The adsorption isotherm and desorption isotherm show hysteresis characteristics typical of mesoporous porous materials. The adsorption isotherm is subjected to BET analysis in the range of relative pressure P / P ₀ = 0.02 to 0.5 to obtain a value of σ = 207 [m ² / g] as the specific surface area.

  When this value is compared with the value derived by the method of the present invention shown in Table 3, the value according to the present invention is about 70% (= 145/207) of the value obtained by the conventional method. I understand. In this parameter determination method, a spherical shape is assumed as the geometric shape of the pores. On the other hand, considering that the conventional method assumes a cylindrical pore shape, the values obtained by this evaluation method and the conventional method Although the values obtained by are not given the same value, they are given values of the same order, so it is concluded that the method has sufficient accuracy as a pore parameter determination method by a simple method.

  FIG. 10 shows the pore diameter distribution of the porous silica glass. This is obtained by analyzing the adsorption / desorption isotherm shown in FIG. 9 by the Dollimore-Heal method (non-patent document 2).

  When the adsorption isotherm is analyzed, a broad pore diameter distribution curve having a peak per pore diameter of 6.4 nm is obtained. On the other hand, when the desorption isotherm is analyzed, a sharp pore size distribution curve having a remarkable peak at a pore diameter of 4.2 nm is obtained.

According to the parameter determination method of the present invention, as shown in Table 3, the average pore radius (r _p ) is 2.95 nm for the first time and 3.35 nm after convergence, and the diameter (d _p ) When converted, 5.9 nm (first time) and 6.7 nm (after convergence) are obtained, respectively.

  From this result, it can be seen that the pore parameter determination method according to the present invention is almost the same on the order, but the result is very close to the pore size distribution based on the adsorption isotherm.

501 Transparent porous body sample 510 Spectrophotometer 511 Light source 512 Sample chamber 513 Detector 514 Calculation unit 520 Computer for analysis

Claims (7)

A method of calculating pore parameters of a transparent porous body by a computer connected to a spectrophotometer,
Inputting the parallel plate thickness and porosity of the transparent porous material processed into a parallel plate shape into the computer in advance;
Inputting the transmittance spectrum of the transparent porous body measured in the spectrophotometer into the computer, wherein the transmittance spectrum is measured by wavelength sweeping in the visible region; and
Plotting the logarithm of the transmittance spectrum and dividing by the parallel plate thickness of the transparent porous body against the inverse fourth power of the wavelength divided by the refractive index of the skeleton member of the transparent porous body;
A value obtained by taking the logarithm of the plotted transmittance spectrum and dividing by the parallel plate thickness is subjected to linear regression analysis to calculate a slope parameter and a vertical axis intercept;
Calculating the reflectance at the air and porous body interface from the vertical axis intercept;
Calculating the effective refractive index of the transparent porous body from the reflectance at the porous body interface;
Calculating the average pore radius and pore number density of the transparent porous body from the slope parameter;
A method comprising the steps of:   The method according to claim 1, further comprising calculating a specific surface area of the transparent porous body using the porosity and the average pore radius.   The transparent porous body is a cleaning with acetone, ethanol, and ultrapure water for improving the transparency, and each cleaning is performed individually or in combination of two or more, and each cleaning is performed more than once. 3. The method according to claim 1 or 2, wherein:   When the transparent porous body is porous glass, the transparent porous body is further subjected to a light etching process of the transparent porous body with 0.1% diluted hydrofluoric acid in the cleaning step. Item 4. The method according to Item 3.   The transparent porous body is further subjected to a drying process in which the transparent porous body is cleaned by the cleaning, heated to 150 ° C or higher in vacuum for 6 hours or more, and stored after being heated and dried and stored in dry nitrogen. The method according to any one of 1 to 4. A spectrophotometer for measuring the transmittance spectrum of the transparent porous body;
A computer connected to the spectrophotometer,
A pore parameter measurement system, wherein the method according to claim 1 or 2 is executed.   A computer-readable storage medium storing a program for causing a computer to execute the method according to claim 1.

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