Usage: in control and measurement technology to study the filtration and hydraulic properties of filter materials, in particular to determine the pore size distribution. The essence of the invention: the speed and time of free flow of a given mass of gas located in a sealed chamber under excess pressure is measured through dry and liquid-impregnated samples at the same pressure drop across them. The pore size distribution is calculated from the relation F i F =W ci T ci /W at i T at i where F i is the total area of open pores at the i-th pressure drop on the sample soaked in liquid; F is the total area of through pores of all sizes in the material; W ci , W at i - the gas velocity through the dry and liquid-impregnated samples at the i-th pressure drop across them, T ci , T at i - the time of flow of a given mass of gas through the dry and liquid-saturated samples at the i-th pressure drop across them.
The invention relates to control and measuring technology, namely, to the field of studying the filtration and hydraulic properties of filter materials, and can be used to assess their quality indicators. There is a known method for determining the pore size distribution, in the implementation of which an integral dependence of the change in the area of opening pores in a sample soaked in liquid on the pressure drop across it is obtained. The disadvantage of this method is the low sensitivity of gas flow control, due to the fact that the chain of series-connected elements is not reversible, which reduces the accuracy of determining the pore size distribution. The closest to the claimed technical solution is a method for determining the basic parameters of the structure of porous permeable bodies, which consists of passing gas under pressure through dry and liquid-impregnated samples. However, the known method has the disadvantages that when mathematically processing the characteristics of gas flow versus pressure, a graphical differentiation of the experimental dependencies is performed, which significantly reduces the accuracy of the method and increases the complexity due to the large amount of calculations. The purpose of the proposed method is to increase the accuracy and reduce the complexity of determining the pore size distribution. This goal is achieved by measuring the speed and time of free flow of a given mass of gas located in a sealed chamber under excess pressure through dry and liquid-impregnated samples at the same pressure drop across them, and the pore size distribution is calculated from the relation = , where F i - the total area of open pores at the i-th pressure drop on a sample soaked in liquid: F - the total area of through pores of all sizes in the material; W ci , W at i - gas velocity through dry and liquid-impregnated samples at the i-th pressure drop across them; T ci , T at - time of flow of a given mass of gas through dry and liquid-impregnated samples at the i-th pressure drop across them. A comparative analysis of the proposed solution with the prototype shows that the proposed method differs from the known one in that the pore size distribution is determined by the ratio of the products of velocities and free flow times of a given mass of gas located in a sealed chamber under excess pressure through dry and liquid-impregnated samples at the same pressure difference across them. Thus, the claimed method meets the invention criterion of “novelty”. A technical solution is known in which a gas enclosed in a chamber is passed through reference and controlled samples soaked in liquid. However, the sequence of actions used in it does not make it possible to determine the pore size distribution, which is determined in the claimed technical solution. This gives grounds to conclude that the proposed solution meets the “significant differences” criterion. Comparison of the flow of a given mass of gas under excess pressure in a sealed chamber through dry and liquid-impregnated samples provides, at the same pressure drop across them, the possibility of determining the proportion of open pore area in a liquid-impregnated sample in relation to the products of the velocities and times of gas flow through these samples. In accordance with the Boyle-Mariotte law, for a given mass of gas, the process of its outflow from the chamber is characterized by the constancy of the product of pressure and the occupied volume. Therefore, the change in gas pressure from its initial value to the residual pressure value in the chamber characterizes the same amount of gas passing through dry and liquid-saturated samples, with the same pressure drop across them in the specified range. Since as the pressure drop decreases, the area of open pores in a sample soaked in liquid decreases, while in a dry sample it remains constant, the product of the speed and time of flow of equal specific volumes of gas will be inversely proportional to the ratio of the open pore areas of these samples at the same value of the pressure drop across them. The proposed method for determining the pore size distribution is implemented as follows. An excess pressure P is created in a sealed chamber, the value of which must be equal to or slightly greater than the opening pressure of the smallest pore size, determined by the well-known Cantor dependence for equilibrium capillary pressure. In this case, the given mass of gas will occupy the volume U. By opening the fast-acting valve, the free flow of gas through the sample soaked in liquid is ensured. The pressure in the chamber will change from its initial value to some residual value, characterizing the size of the maximum pores. For each fixed value of gas outflow pressure in the specified range of its fall, the outflow velocity and time are measured using known methods. The speed and time of gas flow through a dry sample are measured at the same fixed values of gas pressure in the specified range of its drop. The amount of gas passing through a sample soaked in liquid is determined by the dependence U1 i = W at i T at i F i , where W at i is the gas flow rate through the sample soaked in liquid at the i-th pressure drop across it; T ati is the time of flow of a given mass of gas through a sample soaked in liquid at the i-th pressure drop across it; F i is the total area of open pores in a sample soaked in liquid at the i-th pressure drop across it. Since U1 i =U2 i, and F = const, where U2 i is the amount of gas passing through a dry sample at the i-th pressure drop across it; F is the total area of through pores of all sizes in the material, then = .
Claim
METHOD FOR DETERMINING PORE SIZE DISTRIBUTION, which consists in passing gas under pressure through dry and liquid-impregnated samples located in a sealed chamber, and calculating the desired parameter, characterized in that at the same pressure drop on the samples, the speed and time of free flow of a given mass of gas is measured, and the pore size distribution is calculated from the relation
= ,
where F i is the total area of open pores at the i-th pressure drop across the sample soaked in liquid;
F is the total area of through pores of all sizes in the material;
W ci , W at i - gas velocity through dry and liquid-impregnated samples at the i-th pressure drop across them;
T ci , T at - time of flow of a given mass of gas through dry and liquid-impregnated samples at the i-th pressure drop across them.
Such characteristics can be estimated in several ways from desorption isotherms. Brockhoff and Lineen provide a fairly detailed review of this issue. In addition to the labor-intensive technique of accurately measuring adsorption isotherms, most methods involve performing separate calculations for a large number of intervals of the isotherm in question. However, with a significantly improved method of measuring and issuing the results obtained, the ability to process the received data and compile programs for calculating pore sizes on a computer, such work is greatly simplified,
There are currently two types of commercial instruments available to perform this type of measurement. One uses a vacuum system, just like the original method
BET (Micromeritics instrument) and in the other a gas flow system (Quantachrome instrument). An isotherm with 10-15 equilibrium points can be measured within a few hours, and specific surface area values and pore size distributions can be obtained quite quickly.
Over the past century, various mathematical approximations have been developed to calculate the pore size distribution.
Most methods involve constructing a t* curve, since it is necessary to take into account the fact that adsorption occurs on a relatively smooth surface in the absence of pores and the adsorption film turns out to be several molecular layers thick before the vapor pressure reaches the value p/po = 1D corresponding to the formation of liquid. Obviously, in such a thick film, consisting of several layers, the properties of nitrogen will not be the same as for a normal liquid. As already noted, determining pore sizes requires not only the use of the Kelvin equation to calculate the sizes of pores that are filled with liquid nitrogen, which has the properties of a normal liquid, but also knowledge of the thickness of the adsorption film on the inner surface of the pores that are not yet filled with nitrogen.
To obtain experimental data that takes into account film thickness, the silica under study must not contain micropores. Harris and Singh studied a number of such silica samples (with a specific surface area of less than 12 m2/g) and showed the possibility of drawing an isotherm averaged over the samples they examined in the form of a dependence of vjvm on pipe. However, since then, numerous studies have been carried out on corresponding non-porous silicas to accurately determine t-values. Bebris, Kiselev and Nikitin “prepared a very homogeneous wide-pore silica, not containing micropores, by heat treating fumed silica (aerosil) in water vapor at 750 ° C, obtaining the specified silica with a specific surface area of about 70-80 m2 / g and pores with a diameter of about 400 A Generally accepted values of film thickness t for various values of p!po when using nitrogen are based on data from Lippens, Linsen and de Boer and de Boer, Linsen and Osinda.
In table 5.4 shows typical ^-values depending on p/p0. The following equation allows one to calculate film thickness using most of the published data based on average t values at p/po pressures above 0.3:
T_ 4.58 ~ Mg/V/>o)I/3
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Table 5.4 Partial pressure of nitrogen and film thickness of nitrogen adsorbed on a non-porous surface at a temperature of - 195°C (according to data) |
As described by Brockhoff and Linsen, many researchers have contributed to the development of methods for calculating pore size distributions from adsorption isotherms. The original approach and general equation developed by Barrett, Joyner and Halenda were completed by Peirce and later by Cranston and Inkley. Subsequent developments of this problem have been described in detail by Greg and Singh.
Cranston and Inkley method. Cranston and Inkley (39), using the known film thickness t of adsorbed nitrogen on the inner walls of the pores along with filling the pores with nitrogen according to the mechanism described by the Kelvin equation, developed a method for calculating the volume and size of pores from the desorption or adsorption branches of the isotherm. The calculation is carried out in the section of the isotherm above p/po>0.3, where there is already an adsorbed at least monomolecular layer of nitrogen.
The method is a stepwise calculation procedure, which, although simple, provides for such calculations at each successive stage. A desorption isotherm consists of a series of experimental points, each of which contains data on the measured volume of adsorbed gas at a certain pressure. Starting from the point p/po = 1.0 with completely filled pores, the pressure is reduced stepwise and at each stage the adsorbed volume is measured (this applies to the desorption isotherm, but the calculation procedure will be the same when considering the adsorption isotherm). As the pressure decreases from the value pi/p0 to Pr/Poi, the following provisions are true:
1. A volume of liquid nitrogen AVuq evaporates from the pores, thereby forming a gas with a volume AVg, which is usually expressed in cubic centimeters under normal conditions per 1 g of adsorbent.
2. The volume AVnq of liquid nitrogen, which was removed from the pores in the range of their radius sizes between r i and r2, leaves a nitrogen film of thickness t2 on the walls of these pores.
3. In pores emptied at previous stages, the thickness of the nitrogen film on the walls decreases from t\ to t2.
A reader unfamiliar with this issue may benefit from the schematic representation of the process shown in Fig. 5.11. The figure shows a cross section of a sample with idealized cylindrical pores that vary in diameter. It can be seen that when the pressure in the system decreases from pі (position A) to p2 (position B), the thickness of the nitrogen film on the walls of the emptied capillaries decreases from tx to t2, the amount of liquid nitrogen decreases as a result of desorption and at the same time the number of empty pores increases.
In position A (Fig. 5.11) there is one partially filled pore with a diameter of 2r in which liquid nitrogen is currently in equilibrium with steam at pressure px. Similarly, in position B we have one pore with a diameter of 2r2, which contains liquid nitrogen, which is in equilibrium at pressure p2. In these pores, the radius is determined as fp = t + rk, where rz is the radius calculated from the Kelvin equation at a given pressure. Calculations are based on the following equations. Let L be the length equal to the total length of all emptied pores with radii in the range from r to r2, and let r be the average value of the radius. Then the total volume of evaporated liquid nitrogen Vuq at this stage is equal to
Vuq = 3.14 (rp - t2f L + (t2- tx) Z L
Where A is the surface of the adsorption film remaining in the indicated emptied pores.
The average volume of pores with radius g is
A V р = nfpL Eliminating the value L, we get
Since rv - t = ru, where Γk is found from the Kelvin equation, then
The volume of released gas, measured at pressure p and temperature TC, corresponds to the volume of liquid
Vid = 2 377"_
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Rice. 5.11. Diagram of an imaginary adsorbent with a set of cylindrical pores shown in section when nitrogen is adsorbed at two pressures and pr - A pressure pi. All pores with a radius less than n are filled with liquid adsorbed substance. The adsorption film has a thickness tu and radius Kelvin in the pore, Filled under the influence of surface tension, is equal to g, . B - pressure Pr (P2 Those born as the pressure dropped from pt to pe (see text). |
The area A of the internal surface of the pores under consideration, assuming that they are cylindrical, turns out to be equal to
A -2 (Vp/rr) ■ 104
Where Vp is expressed in cubic centimeters, and the radius gr is expressed in angstroms.
Using desorption data, calculations begin at p/p0 near 1.0, when the pores are essentially filled with liquid nitrogen. Cranston and Inkley described step-by-step calculations of pore volume and pore surface area emptied. Nevertheless, the detail of such consideration will be useful.
Calculations are performed at each stage at a fixed pressure, starting with filled pores and a relative pressure p/po close to 1.0. For each stage the following values are calculated:
1. Average? b. of two Kelvin radii Tk, and Tr at the corresponding pressures pі and p2, expressed in angstroms. Each value is calculated from the Kelvin equation
4.146 Gk~ lgPo//>
2. Film thicknesses 11 and t2 at pressures рх and р2, expressed in angstroms. Each thickness t is taken from the tables or determined from the equation
T - 4.583/(lg Po/r)"/3
3. Average pore radius gr in this interval:
Gr = 0.5 [g + g k, + t2)
4. The value of t=t\ - t2, expressed in angstroms.
5. Volume of desorbed liquid nitrogen AVnq per unit mass of the adsorbent, AVuq = 1.55-10-3 AVg, cm3/g, where AVg is the volume of released nitrogen gas, reduced to normal conditions, cm3.
6. The volume of liquid nitrogen lost at this stage due to the thinning of films on the pore walls and equal to (A0"(Z^)> where 2 A is the surface of the walls of all pores emptied during the desorption process at all previous stages (or AL for the first stage The indicated volume is equal to (At) (£ A) 10~4 and has the dimension cm3, since At is expressed in angstroms, and
In square meters.
7. AA - 2(AVnq) Рр 104.
8. The value of £ A is found by summing all the DA values from the previous stages.
The specified calculation process is necessary at each stage of such a stepwise method. A series of calculations are performed for each stage in turn as the pressures decrease, and the results are tabulated.
The total pore volume Vc, starting from p/po = 0.3 and up to the largest value of p/po, is simply the sum of the AViiq values obtained at each stage. As a rule, a graphical dependence of Vc on log gr is drawn.
The total surface Ls is the total sum of AL values obtained at each stage. If there are no micropores, then Ac usually amounts to values reaching 85-100% of the surface area determined by the BET method. Since the latter is obtained by measurements in the region of lower values of p/p o from 0 to 0.3, such agreement indicates the absence of micropores in the sample.
Cranston and Inkley came to the conclusion that for many silica gels it is advisable to use the considered method in the opposite direction, starting from the value p/p0 = 0.3 and carrying out measurements and calculations at subsequent stages as the adsorption isotherm is obtained.
Hougen provided further discussion of the Cranston and Inkley method and provided some useful nomograms. However, it turned out to be not so easy to translate the system of equations into a method of practical calculations, which is why the calculation of the stages discussed above was shown in such detail.
The pore size distribution can be estimated from the ^-diagram according to data from Brockhoff and de Boer.
Micropores. Special problems arise when measuring and characterizing extremely small pores. It is impossible in this book to give an overview of all the vast literature that has appeared over the past decade, but an attempt will be made to describe some aspects of this problem, accompanied by examples.
According to Brunauer, it is generally accepted that "the mechanism of adsorption of molecules in micropores is not well understood." Singh stated in 1976 that “no reliable method has been developed for determining the micropore size distribution.” It is clear, however, that adsorption in micropores is fundamentally different from adsorption on the surface of the walls of wide pores and on open surfaces, and that the molecules in such fine pores are subject to the attraction of the surrounding solid and are in a state of strong compression. Dubinin discussed the theory of adsorption under such conditions, which includes the concept of “micropore volume,” which more accurately describes the process than the concept of the surface of such pores.
According to Okkers, the specific surface area in microporous materials cannot be determined if the radius of the micropore is less than 12 A. This author used the term “submicropore”, meaning by this concept
the same as other researchers, including Eyler, who used the term "micropore". Ockers summarized the possible application of a number of equations that have been proposed for the smallest pore sizes.
As clearly demonstrated by Brockhoff and Linsen, micropores can be detected by studying adsorption isotherms depicted as /-curves. If on the graph the line depicting the dependence of Va on / deviates downwards towards the /-axis, then this is an indication of the presence of micropores in the sample. Similar graphs obtained by Mikhail are presented in Fig. 5.12 for two silica gels. Since the values of the specific surface areas of the samples are close, the lines on the /-diagrams have approximately the same slope. For silica gel A, which is microporous and dense, the /-curve begins to deviate downwards towards the /-axis at a relative pressure p/po = 0.1. For mesoporous silica gel B, which has a low density, the /-curve deviates upward at approximately p/po = 0.5, i.e., when wide pores begin to fill. In such gels, which have pores of uniform size, it is easy to demonstrate the presence of micropores. However, for many
In many silica gels, a large proportion of the surface belongs to mesopores and only a small part belongs to micropores. In this case, the deviation from linearity on the /-curve is difficult to determine. Mieville studied solid materials of mixed structure that had mesopores and micropores. He applied the /-diagram method and showed that in such a sample with a mixed structure, 10% are micropores.
Using the as-diagram, Singh showed the presence of meso-pores by deviation from linearity with respect to the a-axis at higher values of as. The presence of micropores is proven by the deviation of the curve towards the as-axis at lower cc values. s. Extrapolation of the linear section to the x-axis allows us to determine the volume of micropores (Fig. 5.13). The authors of the work conducted further research in this direction with a large set of silicas and gave an explanation for the deviations based on the concepts of micropores and mesopores.
Ramsay and Avery obtained data on the adsorption of nitrogen in dense compressed microporous silicas. They plotted their data using the equation
Pyrogenic silica powder with a particle size of 3-4 nm was pressed to obtain pore volumes of 0.22-0.11 cm3/g (silica packing densities were 67-80%), which corresponded to the formation of pores with a diameter of 22-12 A. In the graphs, presented in the coordinates of the specified equation, a decrease in the slopes of the lines for a series of samples is visible, which indicates changes occurring in them in the region from complete filling of the pore volume to a monolayer coating (when a monolayer of adsorbate fills the thinnest pores). In this work, the constant C on the graph plotted in BET coordinates had a value of 73 for the original, unpressed powder and increased from 184 to more than 1000 with time. how the pore diameter decreased from 22 to 12 A.
“Model pore” (MP) method. Brunauer, Mikhail and Bodor developed a method for determining the characteristic pore size distribution, including even part of the area occupied by micropores.
Using the Cranston-Inkley method, which also includes the /-curve and the Kelvin equation, curves characterizing the porous structure of the sample can be calculated for pores with radii from 10 to 150 A. However, the results obtained depend on the assumption made about the cylindrical shape of the pores. Since in fact Since the pores are not cylindrical, the calculation of the pore size distribution does not reflect the real state of affairs, especially in the presence of small pores.
In the “model pores” method, the concept of hydraulic radius “rh” is introduced, defined as rh = V/S, where V is the volume of the porous system and 5 ■ is the surface of the pore walls. The ratio applies to pores of any shape. The V and S values are calculated from adsorption or desorption isotherms. When desorption occurs and some group of pores is emptied, a monolayer of nitrogen molecules remains on their walls at a pressure p. The empty space of the pore is called the “core”. This value represents the desorbed volume ■ as the pressure decreased from p0 to p.
This method differs from the Cranston and Inkley method in that it uses the Kiselev equation instead of the Kelvin equation
U ds = Ar da "
Where y is surface tension; ds is the surface that disappears as the pore fills; - change in chemical potential, da - the number of liquid molecules located in the pore. (The Kelvin equation is a special case of the above Kiselev equation if cylindrical pores are considered.) The change in chemical potential is calculated by the equation -Ар = = -RT In (р/р0). Integration gives
S = -\ - RT In da
Where ah is the number of adsorbed molecules at the beginning of the hysteresis loop and as is the number of adsorbed molecules at saturation.
The last equation is integrated graphically in stages:
1. During the desorption of ai moles of a substance, the relative pressure p/po decreases from 1.0 to 0.95.
2. The resulting volume of all cores will be equal to the product of a\ and the molar volume of the adsorbate; for the case of nitrogen it is 34.6 a/cm3.
3. Si-surface area of the formed cores is determined by the equation
Integration is carried out graphically.
4. rh is the hydraulic radius equal to the resulting volume of the cores (stage 2) divided by the surface area of such cores (stage 3).
Then at the nth stage, when an mole is desorbed, the following is observed:
1. Decrease in relative pressure p/po from rp/po to pn-l/po-
2. The resulting volume of the cores is 34.6 ap cm3. However, when the substance is desorbed, some volume is added
Adsorbate v„ from the walls of the pores formed on the previous
Stages. This volume vn is calculated based on the construction of the /-curve, which makes it possible to determine the value of At, i.e., the decrease in the thickness of the liquid film over the entire total surface of the cores formed up to this point. The volume is thus equal to the product of At and the total surface of the cores. The introduction of such an amendment is a key point in the calculation.
3. The difference a„ - vn gives the value of the volume of newly formed cores at the nth stage.
4. The surface area of the new cores Sn is determined by graphical integration, as in the previous stages.
The above explanation is sufficient to show the difference between this “corrected model pore method” and the Cranston-Inkley method. For a more detailed description of the method and examples of calculations, you must refer to the original source.
In most cases, the “model pore” method gives a smaller value of the pore radius at the maximum of the distribution curve than that obtained by the Cranston and Inkley method. For example, for samples with pore radii in the range of 5-10 A when using the desorption isotherm according to this method the radius value at the maximum of the distribution curve was obtained to be about 6 A, and using the Cranston-Inkley method 10 A. Hannah et al.
For a wide range of different silica gels, good agreement in pore sizes was obtained using nitrogen or oxygen as an adsorbate at two different experimental temperatures. In some cases noted in this work, silica samples contained both micro- and mesopores.
Standard for determining pore sizes. Howard and Wilson
We described the use of the “model pores” method on a sample of mesoporous silica Gasil(I), consisting of spheres with an average radius of 4.38 nm, packed with a coordination number of 4. Such silica is one of the standards
SCI/IUPAC/NPL for determination of specific surface area and can also be used as a standard for determination of pore sizes and for calibration of equipment operating on the principle of the BET method over the entire pressure range.
The MP method was demonstrated by Mikhail, Brunauer and Baudot. They showed the applicability of this method to the study of micropores, and the “corrected model pore method” to the study of large pores. When this method is applied to silica gel, which has both micro- and mesopores, the MP method gives an aggregate value of the pore surface area that is consistent with the value found by the BET methods. This fact indicates that, despite the objections raised against the use of the BET method for studying microporous samples, this method can hopefully provide reliable data on specific surface areas even in these cases.
The detailed examination of the pore structure of five silica gels by Hagemassy and Brunauer can be considered typical of work of this kind in which the pore structure was assessed using the MP method. This article compared water and nitrogen vapor as adsorbates, and the data obtained were in fairly good agreement, giving pore diameters at the maxima of the distribution curves of 4.1 and 4.6 A, respectively. However, for adsorbents that have any hydrophobic surface areas, nitrogen must be used.
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Supermicro - |
The basis for this proposed classification is that supermicropores and mesopores, but not micropores, can be subjected to detailed study.
The MP method was criticized, followed by a refutation of the criticisms.
Ultramicropores or submicropores. Such pores have a radius of less than 3 A. The mechanism by which such pores are filled has remained the main topic of discussion. Obviously, if the smallest known gas molecule (helium) is not able to penetrate into a pore, then the pore simply does not exist, since this is confirmed
An experiment. Thus, the lower limit of pore sizes at which these pores can be detected depends on the size of the adsorbate molecule used.
The main issue is to consider the situation where a molecule enters a pore whose diameter is less than twice the size of the molecule. In this case, the van der Waal interaction is very strong, and the heat of adsorption is noticeably higher than on a flat surface. Therefore, such a situation differs from the one when the formation of a single polymolecular? loya or capillary filling of pores.
According to Dollimore and Heale, pores that are probably 7-10 A in diameter when determined from nitrogen adsorption isotherms are actually only 4-5 A in diameter. Submicropores in silica gel prepared from sol particles only ~ 10 A turn out to be so small that even krypton molecules cannot enter them. Monosilicic acid is known to polymerize rapidly at low pH values to form particles of approximately the same size. Dollimore and Hill prepared such a gel using the freeze-drying method of a 1% solution of monosilicic acid at a temperature below 0°C. Since a large amount of water was removed during evaporation and freezing, the pH value of the system during the gelation process was 1-2, i.e., exactly the value when the slowest growth of particles is observed. Such silica could be called “porous”, since helium molecules (and only these molecules) penetrated into such “pores.” Note that helium molecules also penetrate into fused quartz, so with the generally accepted approach, such silica is considered non-porous.
Isosteric heat of adsorption. The heat of adsorption in micropores turns out to be abnormally high. Singh and Ramakrishna found that through careful selection of adsorbates and the use of the a5 method of investigation, it was possible to distinguish between capillary adsorption and adsorption at high-energy surface sites. It was shown that in the p/po range of 0.01-0.2, the isosteric heat of nitrogen adsorption on silica gel not containing mesopores remains essentially constant at a level of 2.0 kcal/mol. On silica gel containing mesopores, a drop in heat is observed from 2.3 to 2.0 kcal/mol, and on microporous silica gel the isosteric heat drops from 2.7 to 2.0. Isosteric heat qst under - is read from adsorption isotherms using the Clausius-Cliperon equation.
Microporosity can simply be characterized by plotting the dependence of isosteric heat on p/p0, obtained from nitrogen adsorption isotherms.
Calorimetric studies of microporosity were carried out, in which the heat released during the adsorption of benzene on silica gel was measured. They confirmed that adsorption energy was highest in micropores and measured the surface area that was still available for the adsorption of nitrogen molecules at different stages of benzene adsorption.
Dubischin characterized microporosity using the equation
Where a is the amount of adsorbed substance; T - absolute temperature; Wo is the maximum volume of micropores; v* is the molar volume of the adsorbate; B is a parameter that characterizes the size of micropores.
In the case when the sample contains pores of two sizes, then a is expressed as the sum of two similar terms that differ in the values of Wо and B.
At constant temperature the equation takes the form
Where C in O can be calculated from adsorption isotherms and converted into Wо and B values. Dubinin used this method to obtain the characteristics of a silica gel sample containing micropores with diameters in the range of 20-40 A. This method is still being refined.
Adsorbates that vary in molecular size. Such adsorbates can be used in research by constructing /-curves in order to obtain the size distribution of micropores. Mikhail and Shebl used substances such as water, methanol, propanol, benzene, hexane and carbon tetrachloride. The differences in the data obtained were associated with the pore size of the silica sample, as well as the degree of hydroxylation of its surface. The molecules of most of the listed adsorbates are not suitable for measuring the surfaces of silicas containing fine pores.
Bartell and Bauer had previously carried out studies with these vapors at temperatures of 25, 40 and 45°C. Fu and Bartell, using the surface free energy method, determined the surface area using various vapors as adsorbates. They found that the surface values in this case were generally consistent with the values determined from nitrogen adsorption.
Water can be used to measure the surface of solid materials containing micropores of a size that makes it difficult for relatively large nitrogen molecules to penetrate them. The MP method, or “corrected model pore method,” was used by the authors of the work to study hydrated calcium silicate.
Another way to determine microporous characteristics is to take measurements at relative pressures near saturation. The differences in adsorption volumes show that this pore volume and size does not allow large selected adsorbate molecules to penetrate into them, while the smallest molecules used, such as water molecules, show “complete” penetration into these pores, determined by the adsorption volume .
When the micropores are too small for methanol or benzene molecules to enter, then they are still able to absorb water. Vysotsky and Polyakov described a type of silica gel that was prepared from silicic acid and dehydrated at low temperature.
Greg and Langford developed a new approach, the so-called pre-adsorption method, to identify micropores in coals in the presence of mesopores. First, nonane was adsorbed, which penetrated into the micropores at 77 K, then it was pumped out at ordinary temperature, but the micropores remained filled. After this, the sample surface was measured using the BET nitrogen method in the usual way, and the results of this determination were consistent with the geometrically measured surface that was found by electron microscopy. A similar pre-adsorption method for studying micropores can certainly be used with silica, but in this case, a much more polar adsorbate would probably have to be used to block the micropores, such as decanol.
X-ray scattering at small angles. Ritter and Erich used this method and compared the results obtained with adsorption measurements. Longman et al. compared the scattering method with the mercury indentation method. Even earlier, the possibilities of this method were described by Poraj-Kositz et al., Poroda and Imelik, Teichner and Carteret.
18 Order No. 250
Mercury pressing method. Mercury does not wet the silica surface, and high pressure is required to force liquid mercury into the small pores. Washburn derived the equation
Where p is the equilibrium pressure; a - surface tension of mercury (480 dynes/cm); 0 - contact angle between mercury and the pore wall (140°); gr - pore radius.
From this equation it follows that the product pgr = 70,000 if p is expressed in atmospheres and grp in angstroms. Mercury can penetrate into pores with a radius of 100 A at pressures above 700 atm. Therefore, very high pressures must be applied to penetrate mercury into micropores.
One problem is that unless the silica gel is very strong, the structure of the sample is destroyed by the external pressure of the mercury before the mercury can penetrate into the fine pores. It is for this reason that the method of measuring nitrogen adsorption isotherms is preferable for research purposes. However, for strong solids like industrial silica catalysts, mercury porosimetry is much faster, not only in terms of performing the experiment itself, but also in processing the data to construct pore size distribution curves.
Commercial mercury porosimeters are widely available, and improved versions of this method are described in the works. De Wit and Scholten compared the results obtained by mercury porosimetry with the results of methods based on nitrogen adsorption. They concluded that the mercury indentation method is unlikely to be used to study pores whose diameter is less than 10 nm (i.e., a radius less than 50 A). In the case of pressed Aerosil powder, the pore radius, determined by the indentation of mercury, at the maximum of the distribution curve turned out to be about 70 A, while the nitrogen adsorption method gave values of 75 and 90 A when calculating the distribution curve by different methods. The discrepancy may be due to a curved mercury meniscus with a radius of about 40 A, which has a lower (almost 50%) surface tension than in the case of mercury contact with a flat surface. According to Zweitering, there is excellent agreement between these methods when the pore diameter is around 30 nm. Frevel and Kressley presented a detailed description of the operation of a commercial mercury porosimeter (or penetrometer), the introduction of the necessary corrections, and the actual method for calculating pore sizes. The authors also gave theoretical porosimetric curves for the cases of different packings of spheres of uniform size.
, micropores , monodisperse , morphology of nanostructures , nanopowder , nanopores , nanostructure , nanoparticle Determination of the dependence of the number (volume, mass) of particles or pores on their size in the material under study and the curve (histogram) describing this dependence. Description
The size distribution curve reflects the dispersion of the system. In the case when the curve looks like a sharp peak with a narrow base, i.e. particles or pores have almost the same size, they speak of a monodisperse system. Polydisperse systems are characterized by distribution curves that have broad peaks with no clearly defined maxima. If there are two or more clearly defined peaks, the distribution is considered bimodal and polymodal, respectively
.It should be noted that the calculated particle (pore) size distribution depends on the model adopted for interpreting the results and the method for determining the particle (pore) size, therefore the distribution curves constructed according to various methods for determining the particle (pore) size, their volume, specific surfaces, etc. may vary
.The main methods for studying the particle size distribution are statistical processing of data from optical, electron and atomic force microscopy, and sedimentation. The study of pore size distribution is usually carried out by analyzing adsorption isotherms using the BJH model. Authors
Links- Manual of Symbols and Terminology // Pure Appl. Chem. - v.46, 1976 - p. 71
- Setterfield Ch. Practical course of heterogeneous catalysis - M.: Mir, 1984 - 520 p.
- Karnaukhov A.P. Adsorption. Texture of dispersed and porous materials - Novosibirsk: Nauka, 1999. - 470 p.
Methods for certification and control of nanomaterials and diagnostics of their functional properties
Porous materials, including filters
See also in other dictionaries:
membrane, track- Term membrane, track Term in English track etched membrane Synonyms Abbreviations Related terms dialysis, membrane Definition Thin crystalline layers, metal foils or films (usually polymer, 5–25 microns thick), system ...
nanopowder- Term nanopowder Term in English nanopowder Synonyms Abbreviations Related terms hydrothermal synthesis, dispersity, sol-gel transition, sol-gel process, compaction of nanopowders, cryopowder, crystallite, BET, method, BJH method,... ... Encyclopedic Dictionary of Nanotechnology
adsorption isotherm- Term adsorption isotherm Term in English adsorption isotherm Synonyms Abbreviations Related terms adsorption, BET, method, BJH method, size distribution (pores, particles) Definition Dependence of the amount of adsorbed substance... ... Encyclopedic Dictionary of Nanotechnology
monodisperse- The term monodisperse The term in English monodisperse Synonyms Abbreviations Related terms nanopowder, size distribution (pores, particles) Definition A system is called monodisperse if the particles (pores) included in its composition have... ... Encyclopedic Dictionary of Nanotechnology
micropores- Term micropores Term in English micropores Synonyms Abbreviations Related terms macropores, nanopores, porous material, porometry, sorbent, molecular sieves, micromorphology, size distribution (pores, particles), porosity, pores... ... Encyclopedic Dictionary of Nanotechnology
macropores- The term macropores The term in English macropores Synonyms Abbreviations Related terms mesopores, micropores, nanopores, porous material, porometry, micromorphology, size distribution (pores, particles), porosity, pores Definition Pores... ... Encyclopedic Dictionary of Nanotechnology
mesopores- Term mesopores Term in English Synonyms Abbreviations Related terms macropores, mesoporous material, morphology of nanostructures, nanopores, porous material, porometry, sorbent, micromorphology, size distribution (pores, particles),... ... Encyclopedic Dictionary of Nanotechnology
nanopores- The term nanopores The term in English nanopores Synonyms Abbreviations Related terms macropores, mesopores, micropores, morphology of nanostructures, nanoobject, nanoporous material, porous material, porosimetry, size distribution (pores,... ... Encyclopedic Dictionary of Nanotechnology
critical micelle temperature- Term critical temperature of micelle formation Term in English Krafft temperature Synonyms Krafft temperature Abbreviations Related terms amphiphilic, amphoteric surfactant, hydrophobic interaction, colloid chemistry, colloidal... ... Encyclopedic Dictionary of Nanotechnology
small angle neutron scattering- Term small angle neutron scattering Term in English small angle neutron scattering Synonyms Abbreviations MNR, SANS Related terms size distribution (pores, particles) Definition elastic scattering of a neutron beam on inhomogeneities... Encyclopedic Dictionary of Nanotechnology
morphology of nanostructures- Term morphology of nanostructures Term in English morphology of nanostructures Synonyms Abbreviations Related terms aggregate, hydrothermal synthesis, mesopores, morphology, nanowhisker, nanofiber, nanocapsule, nanoencapsulation, bulbous... ... Encyclopedic Dictionary of Nanotechnology
nanostructure- Term nanostructure Term in English nanostructure Synonyms Abbreviations Related terms biomimetic nanomaterials, capsid, microphase separation, multifunctional nanoparticles in medicine, nanoionics, exfoliation, distribution over... ... Encyclopedic Dictionary of Nanotechnology
nanoparticle- The term nanoparticle The term in English nanoparticle Synonyms Abbreviations Related terms "smart" materials, biocompatible coatings, hydrothermal synthesis, electrical double layer, dispersion-hardening alloys, capsid, cluster... Encyclopedic Dictionary of Nanotechnology
Highly dispersed, highly porous and other traditional materials including submicron fragments- SubsectionsSorbents based on colloidal systemsCarbon materialsNanostructured polymers, fibers and composites based on themPorous materials, including filtersArticles"smart" compositesfibers, carbon desorptiondialysiscolloid... Encyclopedic Dictionary of Nanotechnology
Methods for diagnostics and research of nanostructures and nanomaterials- SubsectionsProbe methods of microscopy and spectroscopy: atomic force, scanning tunneling, magnetic force, etc. Scanning electron microscopy Transmission electron microscopy, including high resolution Luminescent... ... Encyclopedic Dictionary of Nanotechnology
Adsorbents used:
1) Nitrogen (99.9999%) at liquid nitrogen temperature (77.4 K)
2) If the customer provides reagents, it is possible to carry out measurements using various, incl. liquid adsorbents: water, benzene, hexane, SF 6, methane, ethane, ethylene, propane, propylene, n-butane, pentane, NH 3, N 2 O, He, Ne, Ar, Xe, Kr, CO, CO 2 ( after agreement with RC specialists).
Working range of absolute pressure - 3.8 10 -9 - 950 mm Hg. Art.
Instrumental measurement error - 0.12-0.15%
It is possible to measure the adsorption rate at specified relative pressures. It is also possible to measure the isosteric heat of adsorption (if the user provides liquefied gases different in temperature from liquid nitrogen for a low-temperature bath).
Required characteristics:
1) it is desirable to have information about the absence/presence of porosity in the sample; if present, the nature of the porosity (micro- and meso-), the order of magnitude of the specific surface area
2) purpose of the study: BET surface, pore size distribution and pore volume (isotherm hysteresis loop and/or low pressure region) or complete adsorption isotherm
3) the maximum permissible temperature of sample degassing in vacuum (50-450°C with 1°C increments, recommended for oxide materials 150°C, for microporous materials and zeolites 300°C).
Sample requirements and notes:
1) Adsorption isotherm measurements are carried out only for dispersed (powdery) samples.
2) The minimum required amount of an unknown sample is 1 g (if the specific surface area of the sample is more than 150 m 2 /g, then the minimum amount is 0.5 g, if the specific surface area exceeds 300 m 2 /g, then the minimum amount is 0.1 g). The maximum amount of sample is 3-7 g (depending on the bulk density of the material).
3) Before measurement, samples must be degassed in a vacuum when heated. The sample must first be dried in an oven; no toxic substances must be released during degassing; the sample must not react with the glass measuring tube.
4) The minimum specific surface area of the material used for measurement is 15 m 2 /g (may vary depending on the nature of the surface and composition of the sample).
5) Determination of the specific surface area using the BET method, due to theoretical limitations, is impossible for materials with microporosity.
6) When measuring nitrogen adsorption from the gas phase, determining the pore size distribution is possible for pores with a width/diameter of 0.39 – 50 nm (when using the BDC method up to 300 nm, depending on the sample). The construction of a pore size distribution curve is made on the basis of various structural models: slit-like, cylindrical or spherical pores; It is impossible to determine the pore shape from the adsorption isotherm; this information is provided by the user.
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ASSESSMENT OF PORE VOLUME DISTRIBUTION
BY SIZE OF NANO-SIZED POLYMER COMPOSITE MATERIALS
Many properties of polymer composite materials, including nanosized ones, depend not only, and in some cases not so much on their chemical nature, but on their physical structure. Among the structural parameters that determine the target characteristics of many materials is the size of voids or pores between the structural elements of solids. Moreover, in the same sample, individual pores can vary significantly in size. Pore size distribution is one of the main indicators of the operational suitability of polymer materials used as sorbents, fibers, films, membranes. Therefore, experimental methods for assessing the pore volume distribution by size occupy a central place in the characterization of any nanomaterial both in research practice and in nanotechnology.
The main experimental approach to measuring the pore volume distribution by size of solid dispersed materials is the method of low-temperature sorption of nitrogen vapor at the solid/gas interface. Its advantages are: rapidity, universal nature, ease of sample preparation, accuracy and reproducibility. The theoretical concepts underlying this method have proven their high experimental reliability. Therefore, the sorption method has actually become the standard method for characterizing any nanomaterial. This was facilitated by the development of a new generation of instruments for sorption measurements. These include the TriStar 3020 automatic analyzer manufactured by Micromeritics (USA).
This laboratory work: “Measuring the distribution of pore volume by size of nanomaterials by the sorption method using the TriStar 3020 analyzer” aims to train students to work on this modern equipment.
TARGET laboratory work “Measuring the pore volume distribution by size of nano-sized materials using an automatic gas adsorption surface and porosity analyzer TriStar 3020” - obtaining skills in the experimental study of adsorption processes on modern equipment and obtaining a pore volume distribution curve by size for nano-sized materials.
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BASIC DEFINITIONS.
Adsorption- enrichment (i.e. positive adsorption, or simply adsorption) or depletion (i.e. negative adsorption) of one or more components in the interfacial layer.
Sorption- adsorption on a surface, absorption by penetration of molecules into the lattice of a solid and capillary condensation in the pores.
Adsorbate (sorbate)– a gaseous or liquid substance that is sorbed at the adsorbent boundary
Physical adsorption– adsorption due to short-range nonspecific van der Waals forces
Chemical adsorption(chemisorption) – sorption due to specific chemical interactions with the formation of stable surface compounds
Adsorption (sorption) isotherm– dependence of the sorbed amount on gas (steam) pressure at a constant temperature. The shape of the sorption isotherm characterizes the morphology and physicochemical properties of the sorbent surface and the nature of its interaction with the sorbate
Units amount of adsorbed substance – mol/g adsorbent. When sorption of gases, the amount of adsorbed substance is often expressed in cm3 of gas at N. u. / 1 g adsorbent
BRIEF THEORY.
There are many types of porous systems. Both in different samples and in the same sample, individual pores can vary significantly in both shape and size. Of particular interest in many cases may be the transverse size of the pores, for example the diameter of cylindrical pores or the distance between the walls of slit-like pores.
The classification of pores by size proposed is officially accepted by the International Union of Pure and Applied Chemistry (IUPAC) (Table 1). This classification is based on the following principle: each pore size interval corresponds to characteristic adsorption properties, which are expressed in adsorption isotherms.
Table 1. Classification of pores by size .
Pore name | Pore sizes, nm |
Micropores Mesopores (transition pores) Micropores |
IN micropores due to the proximity of the pore walls, the potential for interaction with adsorbed molecules is much greater than in wider pores, and the magnitude of adsorption at a given relative pressure (especially in the region of low values p/ p0) is correspondingly also larger. IN mesopores capillary condensation occurs; A characteristic hysteresis loop is observed on the isotherms. Macropores so wide that it is impossible for them to study the adsorption isotherm in detail due to its proximity to the straight line p/p0 = 1 To obtain complete information about the nature of the porous structure of the sorbent, it is necessary to obtain differential distribution curves of the pore volume along their DCR radii.
To calculate the DCR, it is necessary to determine the radii of pores located in a real sorbent (r) and the volumes that pores of a given radius have (DV).
For sorbents with a mixed type of pores, isotherms usually have an S-shape with sorption hysteresis (Fig. 1). The presence of the latter indicates the occurrence of capillary condensation in the pores.
Rice. 1 Sorption isotherm on a mesoporous sorbent.
As is known, in this case, a concave meniscus of condensed liquid is formed between the adsorption layers on the pore walls (Fig. 2) with a radius of curvature rк, which can be calculated using the Thomson-Kelvin equation modified for adsorption data
Fig..2. Section of a cylindrical pore.
rk – radius of the cortex, rm – radius of the meniscus in the Kelvin equation;
t is the thickness of the adsorption film.
(1)
Where r/r0- relative pressure of steam in equilibrium with a meniscus having a radius of curvature rm, s is the surface tension of the liquid, Vmol is its molar volume, R is the universal gas constant; T – absolute temperature.
It must be borne in mind that during capillary condensation the pore walls are already covered with an adsorption film, the thickness t which is determined by the relative pressure (Fig. 2). Thus, capillary condensation occurs not in the pore itself, but in its “core” - the so-called “crust”. This means that the Kelvin equation allows us to determine not the size of the pore itself, but the size of its “crust”.
The pore radius will be equal to:
Where t – thickness of the adsorption layer.
As is known, during the sorption process at low p/ps values, the thinner pores of the sorbent are filled, and as the pressure increases, increasingly larger pores are filled. On the contrary, the desorption process begins with larger pores, and as the pressure decreases, increasingly finer pores are released. This step-by-step process of filling or emptying pores can be used to calculate the DCR. However, it should be taken into account that in the direct process of sorption, air molecules may remain on the pore walls, making it difficult to wet the pore walls with condensed liquid. Air is gradually displaced from the pores by the sorbed liquid, and at p/ps = 1 it is almost completely displaced. Therefore, the reverse process - desorption - is no longer complicated by the presence of air. This is one of the possible reasons for sorption hysteresis, i.e., the lag of the sorption isotherms from the desorption isotherms and leads to a different radius of curvature of the meniscus of the condensed liquid in the same pores during the process of sorption and desorption. Therefore, it is more correct to calculate pore radii using desorption isoters.
To calculate the DCR. The desorption isotherm is divided into a number of sections at certain intervals p/ ps(»0.05). According to ur. 1, the lower r1 and upper r2 values of the radii of pores released in this area are calculated.
The average radius of pores released at each stage is
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This kind of calculation is performed for each stage of desorption.
To construct the DCR at each stage of desorption, the values of the radius intervals are also calculated https://pandia.ru/text/80/219/images/image008_81.jpg" alt="IMG_2322" width="193" height="228">!} 
Fig.3. Fig.4.
General view of the Tristar 3020 analyzer. Sample degassing station
The station allows you to prepare up to 6 samples simultaneously. Samples can be kept in a vacuum or in an inert gas (helium) at a given temperature from room temperature to 4000C.
The Tristar 3020 analyzer operates under the control of a specialized computer program in the Windows environment.
Based on the obtained sorption and desorption isotherms, the specified parameters of the porous structure of the samples are automatically calculated.
As a report on measuring the DCR, the device can produce tabular data on nitrogen sorption, sorption isotherm graphs. As a report on measuring the total pore volume, the device can produce tabular data on the sorption of nitrogen vapor, sorption isotherm graphs, a summary report, which presents the specific surface area values , total pore volume and average pore radius of the studied sample., and distribution curves of pore volume over radii.
PROGRESS.
Preparing a sample for research
1. In an analysis test tube, take a sample of the nanomaterial to determine the specific surface area on an analytical balance with an accuracy of 0.0001 g. The optimal amount is about 300 mg. For samples with a small specific surface area (less than 1 m2/g), the amount should be increased to 1 g.
2. Degas the sample using a degassing station, for which:
Place the weighed test tube with the sample in the degassing station and connect it to the vacuum line. Set the degassing temperature. Note: The degassing temperature must be no less than 200 below the glass transition temperature of the material.
Warm up the sample for the specified time.
Weigh the tube at the end of degassing and determine the mass of the sample.
3. Secure the test tube with the degassed sample in one of the 3 ports of the analyzer at the top of the working chamber.
Preparing the analyzer for operation .
1.Pour liquid nitrogen into the Dewar flask included with the analyzer. Place the filled Dewar flask on the lifting table of the device.
2. Close the plastic doors.
3. Supply helium and nitrogen gases into the analyzer by turning the gas connection taps located on the gas cylinder pressure gauges
4. Connect the fore-vacuum pump, located behind the analyzer and connected to it with a vacuum hose, to the AC power supply.
5. Turn on the mains power switch located on the rear panel of the analyzer.
Activation of the measurement control program
1. Turn on the computer that is included in the installation. Launch the TriStar program. The program will check the connection between the computer and the analyzer. After the check is completed, the program's working window will appear.
2. Create a file of information about the sample under study, following the path:
File →Open→ Sample Information
3. Fill out the sample card: sample name, operator’s name, customer’s name,
mass of the sample.
4. On the Analysis Conditions tab, select the analysis conditions: ADSDES. OK.
4. On the Report Options tab, select the same report output program: ADSDES. OK.
6. Indicate in which port the test tube with the test sample is located. We follow the path Unit1 → Sample Analysis, a window appears. In it, opposite the port, for example, Port 1, click the Browse button. From the list, select a sample that will be filmed in this port.
7. Start the experiment - click Start.
Further operation of the TriStar analyzer occurs automatically
During operation, in the working window of the program there is an installation diagram for which
The current gas pressure in the manifold and test tubes and the position of the valves are displayed.
The status bar indicates the current process.
By switching to the Operation option, you can see the current results
Rice. 6 Window of the TRISTAR 3020 analyzer program with an installation diagram and an indication of the current process
EXERCISE
After completing the experiment, study and print the general report, tabular data, adsorption-desorption isotherm graph, pore volume distribution curve by radius. Analyze the results obtained. Draw a conclusion about the nature of the porosity of the studied sample
