SH/T 0572-1993 Calculation method for catalyst pore size distribution (calculation method from nitrogen desorption isotherm)

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1. Method number / full name / English name / replacement relationship

• Standard number: SH/T 0572-93 (confirmed in 2004)
• Chinese name: Calculation method for catalyst pore size distribution (calculation method from nitrogen desorption isotherm)
• English name: not provided in the available source
• Replacement relationship: not provided in the available source
• Drafting unit: drafted under the responsibility of the Research Institute of Petroleum Processing; main drafters Wang Shizhen and Li Guoying
• Reference adoption: American Society for Testing and Materials standard ASTM D4641-88 "Standard Method for Calculating Pore Size Distribution of Catalysts from Nitrogen Desorption Isotherm" (original text written as "ASTM natal[unreadable separator]88", requires confirmation against the source standard (source-text extraction))
• Approval/implementation: approved by China Petrochemical Corporation 1993-08-19, implemented on 1994-05-01

2. Scope of application and non-applicability

• This standard specifies the method for calculating the pore size distribution of a sample from the nitrogen desorption isotherm.
• Applicable to catalysts and their supports containing pores with pore radii of 1.5～50 nm.
• Not applicable: no explicit non-applicability clause is provided in the available source.

3. Method principle

• The pore size distribution is determined by calculation from the data of the desorption branch of the nitrogen adsorption isotherm.
• The adsorption of nitrogen includes the multimolecular adsorption film of nitrogen on the pore walls and the capillary condensate of nitrogen in the "inner core" of the pores.
• The relationship between the equilibrium relative pressure and the pore radius at which capillary condensation occurs at that time is given by the Kelvin formula.
• During desorption, thinning of the multimolecular adsorption layer occurs in pores from which the capillary condensate had previously been emptied; calculating the thinned volume requires the surface area and radius of the film that has been exposed.
• In principle, this calculation process can be applied to both the adsorption branch and the desorption branch; in practical application, except for ink-bottle-shaped pore isotherms in which the desorption branch suddenly closes with the adsorption branch, the desorption branch data are generally used for calculation.
• This standard basically follows the B-J-H (Barret, Joyner and Halenda) calculation method, but some simplifications have been made.
• Note: When calculating with the adsorption branch, it is recommended to use the Cranston Inkley calculation procedure.
• An open cylindrical pore model is adopted, the pores are not interconnected, and they act independently of one another during adsorption or desorption.

4. Reagents and materials (purity / preparation)

• Not provided in the available source (this standard is a calculation method standard and does not list reagents and materials items).

5. Instruments and equipment

• Not provided in the available source (the determination of experimental data follows GB/T 5816).

6. Recommended operating conditions

• Experimental data required for calculation: a series of relative pressures [Pd(i)/P0(i)] and a corresponding series of nitrogen adsorption amounts (unit cm³STP/g).
• The determination of experimental data follows the method specified in GB/T 5816, adsorbing to saturation, then desorbing little by little until near Pd/P0 = 0.25, with at least 20 points measured.
• Observe the region above Pd/P0 = 0.95: if the sample does not contain pores with radius greater than 50 nm, then in a region where Pd/P0 is close to 1 the isotherm remains almost horizontal, and it is relatively simple to determine the upper limit of the pore distribution and select the relative pressure point at which calculation starts; if the sample contains pores with radius greater than 50 nm, the isotherm rises rapidly when Pd/P0 is near 1, the total pore volume is difficult to determine, and the upper limit of the pore size distribution can only be determined relatively.
• In most cases, the starting relative pressure can be selected as 0.98, corresponding to an upper limit of pore radius of 50 nm (original text "Mo rn", requires confirmation against the source standard (source-text extraction)); if necessary, interpolation can be used to determine the nitrogen adsorption amount Vde corresponding to the starting relative pressure point.
• Calculation termination point: the relative pressure falls between 0.25 and 0.30 (equivalent to between radii 1.16～1.30 nm).
• Note: The Kelvin formula is no longer valid at low relative pressures, and is invalid for pores with radius less than 1.0～1.5 nm; the lower limit differs among different adsorption systems, and the lower limit of pore size distribution calculation is difficult to determine accurately.
• Other alternative methods for determining the calculation termination point:
  • a. Use the closure point of the hysteresis loop in the low relative pressure region (generally representing the starting point of irreversible capillary condensation within the pore structure of the sample).
  • b. Compare the ΣΔVp value in column 16 of Table 1 with the Vde value in the first row of column 9; when the value of ΣΔVp is equal to or greater than the first starting Vde value, the calculation terminates; if the sample contains micropores, this termination method is not used.
  • c. V-t Graphical method to determine the starting point of capillary condensation: plot the amount of adsorbed nitrogen against the t value to form a V-t plot; the point at which the V-t curve bends upward represents the starting point of capillary condensation, and the relative pressure corresponding to this point can be used as the calculation termination point; this method can detect reversible capillary condensation phenomena that the isotherm cannot detect, and this termination method is recommended for more refined work.

7. Sampling and sample preparation

• Not provided in the available source (the report is required to give the sample name, pretreatment conditions, and degassing conditions, see Section 11).

8. Analysis procedure

The calculation process requires many calculation steps and is best completed with the aid of a table (Table 1):

• List the experimentally measured relative pressure values Pd(i)/P0(i) in order from high to low in column 1 of Table 1; the relative pressure value in row 1 of column 1 is the selected starting relative pressure value; values with relative pressure lower than 0.25 need not be listed.
• Multiply the experimentally determined nitrogen adsorption amount Vda (cm³STP/g) by the conversion factor 1.5468 (derived from Vc = 34.67 cm³/mol) to convert it to liquid nitrogen volume Vde (mm³/g) and list it in column 9.
• Table 1 Pore size distribution calculation table column headers (source-text extraction has much noise, some column names require confirmation against the source standard):
  1. Pd/P0
  2. rk / nm
  3. r̄k / nm
  4. t / nm
  5. Δt / nm
  6. rp / nm
  7. r̄p / nm
  8. Q
  9. Vde / mm³/g
  10. ΔVT / mm³/g
  11. ΔVf / mm³/g
  12. ΔVk / mm³/g
  13. ΔVp / mm³/g
  14. ΔSp / m²/g
  15. ΣΔSp / m²/g
  16. ΣΔVp / mm³/g
• In column 2, rk is calculated according to the Kelvin formula (Equation 1, Equation 2).
• In column 4, t is calculated according to the Harkins-Jury formula (Equation 3).
• In column 8, when rk > 3 nm or Δt < 1% rk, Q = (r̄p/r̄k)².
• In column 11, ΔVf = 0.85 × Δt × ΣΔSp (Equation 6).
• In column 12, ΔVk = ΔVT − ΔVf.
• In column 13, ΔVp = ΔVk × Q.
• In column 14, ΔSp = 2 × (ΔVp / r̄p) (Equation 5).
• 6.3 The pore radius rk (nm) corresponding to each relative pressure is calculated using the Kelvin formula (Equation 1): RT ln(Pd/P0) = 2γVL / rk In the formula, T, γ, and VL are as in 3.2; R is the gas constant, whose value is 8.314 J/(K·mol). When T = 77.35 K, γ = 8.88 mN/m, VL = 34.67 cm³/mol, Equation (1) becomes Equation (2): rk = 0.9574 / ln(Pd/P0) (source-text extraction displayed as "0.9574 / [unreadable sign]ln(Pd[unreadable character]'o)", requires confirmation against the source standard (source-text extraction)) List the calculated rk values in column 2; for each adjacent pair of rk values, obtain the average rk and list it in column 3.
• 6.4 At each relative pressure, the average thickness of the multimolecular adsorption layer of nitrogen on the pore walls is t; use the Harkins-Jury formula (Equation 3) to calculate the film thickness t (nm) corresponding to each relative pressure: t = [13.99 / (0.034 − log(Pd/P0))] × 10⁻¹ (source-text extraction displayed as "13.99 / 0.034[unreadable sign]log(Pd/Po) x 10-1", requires confirmation against the source standard (source-text extraction)) List the calculated t values in column 4; list the differences between adjacent t values in column 5.
• 6.5 The radius rp of the cylindrical pore model is equal to the "inner core" radius rk plus the film thickness t, that is, the value in column 2 plus the corresponding value in column 4 gives the rp value, which is listed in column 6; calculate the average r̄p of two adjacent values and list it in column 7.
• 6.6 Calculate from the values in column 7 and column 3: Q = (r̄p/r̄k)², used to correct the “core” volume to the volume of each group of pores; the “core” volume refers to the portion of the pores filled by capillary condensate; list the calculated Q values in column 8. This Q value is a simplified value; for the cylindrical pore model, the exact Q value should be calculated according to equation (4): Q = [r̄p / (r̄k + Δt/2)]² (source-text extraction is shown as “4[unreadable symbol] L rp l( rk+AWZ”, requires confirmation against the source standard (source-text extraction)) For rk > 3 nm or Δt < 1% rk, Q can be simplified to (r̄p/r̄k)².
• 6.7 The amount of nitrogen desorbed ΔVT caused by a decrease in relative pressure can be obtained from the difference between two adjacent values in column 9, and is listed in column 10; each ΔVT value consists of two parts of nitrogen volume: one part is the capillary condensate emptied when the relative pressure decreases, and the other part is the thinning of the multilayer adsorbed film on the pore walls of pores that had already lost capillary condensate in previous steps; the 1th ΔVT in row 2 of column 10 includes only the desorbed capillary condensate alone, because it is assumed that at the highest relative pressure all pores are filled with capillary condensate, and no thinning of the adsorbed film occurs at the first decrease in relative pressure.
• 6.8 In order to obtain the pore volume value ΔVp for each group of pores having an average pore radius r̄p, the calculation of the preceding row must be made; the ΔVf in column 11 is the amount of nitrogen by which the multilayer adsorbed layer on the pore walls thins during desorption; for row 2, ΔVf = 0, and ΔVT is equal to the “core” volume ΔVk filled by capillary condensate, ΔVk × Q = ΔVp, and the ΔVp thus obtained is listed in row 2 of column 13.
• 6.9 The pore wall surface area ΔSp of pores with pore volume ΔVp (m²/g) is calculated according to equation (5): ΔSp = 2 × ΣΔVp / r̄p (source-text extraction is shown as “2x[unreadable symbol]VF / rp”, requires confirmation against the source standard (source-text extraction)) The ΔSp values calculated from the ΔVp values in column 13 and the corresponding r̄p values in column 7 are listed in column 14; the cumulative surface area value ΣΔSp is calculated by adding the ΔSp value to all previous-row ΔSp values in column 14, and is listed in column 15; the ΣΔVp value is calculated by adding the ΔVp value in column 13 to all previous ΔVp values, and is listed in column 16.
• 6.10 Calculate the liquid nitrogen volume ΔVf from the thinning of the multilayer adsorbed film from the total exposed pore surface area ΣΔSp and the decrease in film thickness Δt; the ΣΔSp used is the value taken from the preceding row, see equation (6): ΔVf = 0.85 × Δt × ΣΔSp List the ΔVf value in column 11; subtract the ΔVf value from the ΔVT value to obtain the ΔVk value, and list it in column 12; multiply ΔVk by the corresponding Q value in column 8 to obtain the ΔVp value, and list it in column 13; then calculate ΔSp, ΣΔSp and ΣΔVp according to the procedure of clause 6.9. Note: Here a simplification has been made for obtaining the ΔVf value; Appendix A gives a detailed explanation for obtaining ΔVf and the source of coefficient 0.85.
• 6.11 Repeat the calculation for each row of data according to the procedure of clause 6.10 until the relative pressure falls between 0.25 and 0.30.
• 6.12 The last ΣΔSp value in column 15 is the total cumulative surface area value; the last ΣΔVp value in column 16 is the total cumulative pore volume value. Note: The comparison of the total cumulative surface area value with the BET specific surface area measured in the low relative pressure region is an empirical check of the internal consistency of the pore size distribution calculation; if the assumed pore model is relatively close to the actual pore system in the sample, these two values should be very consistent; in practice it shows that these two values usually differ by no more than ±5%, but a difference of ±20% is also common; if the BET surface area is significantly greater than the cumulative surface area, the difference between the two may be caused by the presence of micropores; when the difference between the two is greater than 20%, care should be taken in interpretation.

Appendix A (reference item) Calculation of the volume of thinning of the physical adsorption layer:

• A1 Barrett, Joyner and Halenda propose obtaining the nitrogen volume ΔVf(i) of the thinning of the multilayer adsorbed film (mm³/g), calculated according to equation (A1): ΔVf(i) = Δt(i) Σ C(j) ΔSp(j) (equation A1) Where: i and j are respectively the desorption step sequence numbers; t is the adsorbed layer thickness (nm); C(j) = [r̄p(j) − t(j)] / r̄p(j) (equation A2); ΔSp(j) is the surface area of the group of pores emptied at step j (m²/g); r̄p(j) is the average pore radius of the group of pores emptied at step j (nm); t̄(j) is the average adsorbed layer thickness at desorption at step j (nm).
• A2 The C value varies with different pore groups, and because the t value is a function of relative pressure, for a specific pore group the C value also changes gradually with relative pressure; changes in the C value make the calculation of ΔVf very time-consuming; experience shows that for a specific adsorbent a constant C value can give a very approximate pore size distribution value; because the C value for any pore size varies between 0.72 and 0.97, this standard adopts an intermediate value 0.85 to derive the value of ΔVf [see equation (6)]; the C value may also use other values instead of 0.85; when the C value is constant, equation (A1) becomes equation (A3): ΔVf(i) = C Σ Δt(i) Σ ΔSp(j) (equation A3, source-text extraction is shown as “AVf(i )=c[unreadable separator]At(i)[unreadable symbol]ASP(j)”, requires confirmation against the source standard (source-text extraction)) In more precise work, it is recommended to use varying C values; the C values differ for different pore groups, and for the same pore group the C value also differs at different relative pressures.

9. Qualitative and Quantitative and Calculation Formulas

• Kelvin Formula (equation 1): RT ln(Pd/P0) = 2γVL / rk
• Equation (2): rk = 0.9574 / ln(Pd/P0) (when T = 77.35 K, γ = 8.88 mN/m, VL = 34.67 cm³/mol)
• Harkins-Jury Formula (equation 3): t = [13.99 / (0.034 − log(Pd/P0))] × 10⁻¹
• Equation (4): Q = [r̄p / (r̄k + Δt/2)]² (exact value); under the simplified condition rk > 3 nm or Δt < 1% rk, Q = (r̄p/r̄k)²
• Equation (5): ΔSp = 2 × ΣΔVp / r̄p
• Equation (6): ΔVf = 0.85 × Δt × ΣΔSp
• Equation (A1): ΔVf(i) = Δt(i) Σ C(j) ΔSp(j)
• Equation (A2): C(j) = [r̄p(j) − t(j)] / r̄p(j)
• Equation (A3): ΔVf(i) = C Σ Δt(i) Σ ΔSp(j)
• Conversion: Vde (mm³/g) = Vda (cm³STP/g) × 1.5468 (derived from Vc = 34.67 cm³/mol)
• Cumulative pore volume: ΣΔVp (column 16); cumulative surface area: ΣΔSp (column 15)
• Differential plot: formed with the ΔVp/Δrp value as the vertical axis and the r̄p values in column 7 as the horizontal axis (can also be derived from the slope of the cumulative curve)

10. Precision

• This calculation method is suitable for determining the pore volume distribution of samples containing mesopores.
• The calculated values depend on which branch of the isotherm is used, on the assumed pore model, and on the film thickness values used and how the film thickness correction is handled, so it is impossible to specify precision for this calculation method.

11. Report

The report shall include the following contents:

• 7.1 Sample name, pretreatment conditions and degassing conditions, and note that the desorption isotherm and the assumed cylindrical pore model are used.
• 7.2 Provide a table or graph consisting of the cumulative pore volume data in column 16 and the corresponding pore radius rp values in column 6. The vertical axis of the cumulative pore volume plot is the ΣΔVp value (mm³/g), using arithmetic coordinates; the horizontal axis is the corresponding pore radius or pore diameter (nm), using logarithmic coordinates or arithmetic coordinates. The cumulative pore volume distribution plot is generally a smooth curve with one or several inflection points, at which the change in pore volume is also relatively large (as shown in Figure 1).
• 7.3 The report should also give a differential plot; the differential curve can be derived from the slope of the cumulative curve, or constructed by using the ΔVp/Δrp value calculated from the data in columns 13 and 6 of Table 1 as the vertical axis and the r̄p values in column 7 as the horizontal axis (as shown in Figure 2).

12. Normative references

• GB/T 5816 Determination of specific surface area of catalysts and adsorbents

13. Source and verification

This page is an AI translation of the available Chinese method card. Human verification is pending. It is not an official translation of the standard. Check the source standard and product certificate before use.

14. Quick reference for questions and answers