Report of the key CCQM-K136 - bipm.org · Ural Scientific Research Institute for Metrology,...

Ural Scientific Research Institute for Metrology,

ROSSTANDART, RUSSIA

Report of the key CCQM-K136

Measurement of porosity properties (specific adsorption, BET

specific surface area, specific pore volume and pore diameter) of

nanoporous Al2O3

REPORT B

Pilot laboratory

Ural Scientific Research Institute for Metrology, ROSSTANDART, Ekaterinburg (UNIIM)

Laboratory for metrological assurance of nanoindustry, analysis of spectral methods and

reference materials (251)

Co-piloting laboratory

BAM Federal Institute for Materials Research and Testing.

Division 1.3 “Structure Analysis”

With participation of:

UNIIM: Egor Sobina

BAM: Dr. Franziska Emmerling

INMETRO: Rodrigo de Santis Neves., Carlos E. Galhardo, Eveline De Robertis

NIM: Hai WANG

NMIJ: Kohei Mizuno

Ekaterinburg 2016

2

Table of content

1 ABSTRACT ................................................................................................................................................. 3

2 INTRODUTION .......................................................................................................................................... 4

3 LIST OF PARTICIPANTS ............................................................................................................................. 5

4 SAMPLES .................................................................................................................................................. 6

5 INSTRUCTIONS TO PARTICIPANTS .......................................................................................................... 10

6 METHODS OF MEASUREMENT............................................................................................................... 11

7 RESULTS AND DISCUSSION ..................................................................................................................... 13

7.1 Uncertainty ...................................................................................................................................... 13

7.3 Formulas .......................................................................................................................................... 14

7.4 Specific adsorption at P/Po=0.990 ................................................................................................... 16



7.7 BET specific surface area .................................................................................................................. 23

7.8 Specific pore volume ........................................................................................................................ 25

7.9 Average pore diameter .................................................................................................................... 27

7.10 Discussion ...................................................................................................................................... 29

8 EQUIVALENCE STATEMENTS .................................................................................................................. 30

9 CONCLUSIONS ........................................................................................................................................ 30

10 HOW FAR THE LIGHT SHINES STATEMENT ........................................................................................... 30

11 ACKNOWLEDGEMENTS ......................................................................................................................... 31

12 REFERENCES ......................................................................................................................................... 31

Appendix A – Technical Protocol ............................................................................................................... 32

CCQM-K136/ CCQM-P180.......................................................................................................................... 32

Measurement of porosity properties (specific adsorption, BET specific surface area, specific pore

volume and pore diameter) of nanoporous Al2O3) .................................................................................... 32

Appendix B –CCQM-P180 (parallel to K136) .............................................................................................. 35

Measurement of porosity properties (specific adsorption, BET specific surface area, specific pore

volume and pore diameter) of nanoporous Al2O3) .................................................................................... 35

3

1 ABSTRACT

The CCQM-K136 key comparison for determination of the porosity properties of

aluminum oxide has been organized jointly by the surface and micro/nano analysis working

groups of CCQM to test the abilities of the metrology institutes to measure the porosity

properties (specific adsorption, BET specific surface area, specific pore volume and pore

diameter) of nanoporous Al2O3.

Ural Scientific Research Institute for Metrology (UNIIM) acted as the coordinating

laboratory for this comparison with BAM Federal Institute for Materials Research and Testing

(BAM) as co-coordinating laboratory. Five NMIs and one DI participated in this key

comparison. All participants used a gas adsorption method, here nitrogen adsorption at 77.3 K,

for analysis according to the international standards ISO 15901-2 and 9277.

4

2 INTRODUTION

Specific nitrogen adsorption, BET specific surface area1, specific pore volume

2 and pore

diameter3 in nanoporous solids are highly relevant parameters because they are often used for

the specification of a vast majority of porous materials and substances (sorbents, catalytic

agents, cross-linkers, zeolites, etc) used in advanced technology.

There are already CMC claims for measurement of porosity properties (BET specific

surface area, specific pore volume and pore diameter) at BAM and UNIIM. However, an

underpinning key comparison has never been carried out yet.

The aim of this comparison CCQM-K136 is to support National Metrology Institutes

(NMIs) and Designated Institutes (DIs) demonstrating the validity and comparability of the

procedure they employ for the measurement of porosity characteristics. The validity and

comparability of the procedures used needed to underpin the capabilities and measurement

services in the field of porosity and specific surface area measurements.

1 BET specific surface area by ISO 9277 ABET

2 Single point total pore volume according to the Gurvich rule (see e.g. Gregg and Sing 1982)

determined from the adsorption branch of the isotherm at relative pressure P/Po = 0.990 3 Average (hydraulic) pore diameter (expressed as ratio 4·V0.99/ ABET)

5

3 LIST OF PARTICIPANTS

Five institutes have taken part in the key comparison. Table 1 contains the full names

of all participating NMI/DIs and contact persons.

Table 1 List of participants

Institute Abbrev. Country Contact persons

Federal Institute for Materials

Research and Testing

BAM Germany Franziska Emmerling

National Institute of Metrology,

Quality and Technology

INMETRO Brazil Rodrigo de Santis

Neves

Carlos E. Galhardo,

Eveline De Robertis

National Metrology Institute P.R.

China

NIM China Hai WANG

National Metrology Institute of Japan NMIJ Japan Kohei Mizuno

Ural Scientific Research Institute for

Metrology

UNIIM Russia Egor Sobina

6

4 SAMPLES

The source of the sample is a 500 g batch of commercial sorbent (aluminum oxide)

which was grinded using a disk mill (Pulverisette 13, Fritsch GmbH) and a mortar grinder

(Pulverisette 2, Fritsch GmbH).

After homogenization of the shared sample its homogeneity and stability were

characterized by the pilot lab UNIIM. Homogeneity test results are presented in table 2.

Table 2 Results of homogeneity testing between bottles (2 replicates for each bottle, S - standard

deviation, r = difference; S(BET) - BET specific surface area)

Bottle S(BET), m2/g r, m

2/g S, m

2/g

1 208,26 205,82 2,45 1,73

2 207,71 206,94 0,77 0,54

3 208,32 206,69 1,64 1,16

4 207,69 206,82 0,87 0,61

5 207,13 207,52 0,39 0,28

6 209,25 205,53 3,72 2,63

In order to estimate the uncertainty contribution related to inhomogeneity hu , a one way

Analysis of Variances (ANOVA) was carried out with experimental data (table 1). The standard

uncertainty hu for the Al2O3 powder (see Table 3 and 4) was calculated according to ISO Guide

35 using the Equations (1) and (2).

among within

h

MS MSu

n

(1)

42

(n 1)

withinh

MSu

n N

, (2)

where N=6 is the number of bootles and n=2 is the number of replicates.

Table 3 ANOVA analysis of data in table 2

bottle number Sum Average Dispersion

1 2 414,0813 207,0407 2,995128

2 2 414,6524 207,3262 0,294758

3 2 415,009 207,5045 1,340867

4 2 414,5054 207,2527 0,374286

5 2 414,6522 207,3261 0,077225

6 2 414,7882 207,3941 6,920688

Table 4 ANOVA analysis of data in table 2 (SS - sum of squares; Df – number of degrees of

freedom; MS - the average sum of the squares; F –Fisher’s criterion)

source SS Df MS F

Among 0,24243216 5 0,048486 0,024237

Within 12,0029515 6 2,000492

Sum 12,2453837 11

standard uncertainties due to

inhomogeneity, uh -

Equation (1)

standard uncertainties due to

inhomogeneity, uh 0,76 m2/g Equation (2)

relative standard uncertainties due

to inhomogeneity, uho 0,37 %

7

Stability test results of BET specific surface area for the aluminum oxide powder are

presented in Table 5 and Figure 1. The powder was stored in bottles under laboratory condition

(temperature was (20±5) oC; atmosphere pressure was (96±10) kPa, humidity was not more than

80 %).

Table 5 Results of measurement of BET specific surface area of aluminum oxide

№ Date BET specific surface area, m2/g

1 23.12.2014 208,26

2 24.12.2014 205,82

3 26.12.2014 207,71

4 27.12.2014 206,94

5 30.12.2014 208,32

6 31.12.2014 206,69

7 01.01.2015 207,69

8 03.01.2015 206,82

9 13.01.2015 207,13

10 14.01.2015 207,52

11 15.01.2015 209,25

12 16.01.2015 205,53

13 29.09.2015 206,36

14 30.09.2015 206,41

15 01.10.2015 207,05

16 02.10.2015 205,50

17 03.10.2015 204,93

18 05.10.2015 205,27

19 21.03.2016 204,02

20 22.03.2016 205,61

mean of stability test, Xs 206,64

standard deviation of the data of key comparison

participants, S 1,38

Xs+S 208,02

Xs-S 205,26

slope, b -0,0054

standard uncertainty of slope, slopeu 0,0013

standard uncertainty due to long-term (in)stability, su 0,67

relative standard uncertainty due to long-term

(in)stability, sou , % 0,32

time measurements in key comparison, maxt , days 120

8

Fig.1 - Stability test results for the shared aluminum oxide powder sample.

Data in Table 5 was accounted using linear regression method. The standard uncertainty

due to instability was calculated using formula:

2 2

max maxs slopeu t u bt , (3)

where b is the slope, slopeu is the standard uncertainty of the slope and maxt - is the time

span of measurements in the key comparison.

The statistical evaluation of homogeneity and stability testing results indicated that the

relative standard uncertainty due to inhomogeneity was 0.4 % and instability was 0.3 %.

However, these contributions are significantly lower than the target relative uncertainty of

measurement (1-3) %.

After investigation of homogeneity and stability, a 500 g portion was selected from the

middle fraction of the batch and homogenised again in a large bottle. This homogenised

portion was then transferred to 5 glass bottles closed with silicone lined plastic caps, each

containing about 5 g of the material. Eight bottles were randomly selected from the set of 15

bottles.

These bottles were distributed to the participants by using DHL on 14 September 2015.

INMETRO did not receive this bottle and UNIIM sent one more to INMTERO on 30 October

15. All bootles arrived at their destination without damage. The dispatch dates and receipt

dates are given in Table 6.

The deadline for reporting results was set by end of February 2016 in order to prepare a

presentation for discussion at the CCQM SAWG meeting in April 2016. All participants

reported their results in time (with exception of INMETRO, see above).

S(BET) = -0,0054t + 207,38

195,00

197,00

199,00

201,00

203,00

205,00

207,00

209,00

211,00

213,00

215,00

17.11.2014 25.02.2015 05.06.2015 13.09.2015 22.12.2015 31.03.2016

BE

T s

pec

ific

su

rfac

e ar

ea, m

2 /g

Date

Mean of stability test results + 1s

Mean of stability test results - 1s

9

Table 6 Sample sent dates, receipt dates and report dates

Institute Sample No. Sample dispatch

date Sample receipt date Date report sent

BAM 02 21 September 2015 01 October 2015 22 December 2015

INMETRO 05 21 September 2015/

30 November 2015 11 December 20015 11 March 2016

NIM 03 21 September 2015 08 October 2015 18 February 2016

NMIJ 04 21 September 2015 05 October 2015 29 February 2016

UNIIM 01 01 September 2015 01 September 2015 05 October 2015

10

5 INSTRUCTIONS TO PARTICIPANTS

The technical protocol was sent to each participant by e-mail. The technical protocol

(appendix A) contained background information, timing of the comparison and information on

the participating institutes. Information about sample preparation and recommended

measurement conditions were also given.

Each participant used the gas adsorption method for the measurement of the specific

adsorption of nitrogen, BET specific surface area, specific pore volume and pore diameter of

Al2O3 as defined in ISO 15901-2 [1] and ISO 9277 [2].

Some details about measurement procedure of the gas adsorption method was

recommended in the technical protocol shown below.

Please perform at least 5 replicate measurements on separate aliquots of Al2O3. The

recommended minimum sample amount is about 0.5 gram for each run.

Sample pretreatment

Heat the sample Al2O3 for degassing in a vacuum (1-2) Pa with a rate of 10 oC/min to

250 oC, then hold temperature at 250

oC for at least 5 hour. Afterwards, allow the sample to cool

slowly back to ambient temperature.

Measurement of the complete Isotherm (adsorption branch) at 77.3 K and specific

adsorption of nitrogen at P/Po=0.100; P/Po=0.300; P/Po=0,990.

First isotherm data point should be taken at P/Po=0.01, last adsorption isotherm data

point should be taken at P/Po=0.995. An intermediate adsorption isotherm data point should be

taken at P/Po=0.095; P/Po=0.100; P/Po=0.105; P/Po=0.295; P/Po=0.300; P/Po=0.305;

P/Po=0.985; P/Po=0.990; P/Po=0.995 (non-ideal correction factor, equal to 0.464·10-6

Pa-1

for

nitrogen at 77.35 K).

BET specific surface area

Determine the BET specific surface area S using at least 10 isotherm data points at the

adsorption branch of the isotherm within relative pressure range 0.05≤P/Po≤0.30 (cross selection

area for the N2 molecule in the monolayer: aN2 = 0.162 nm2).

Specific pore volume (Gurvich) [3]

The Single Point Total Pore Volume V according to the Gurvich rule should be

determined from the adsorption branch of the isotherm at relative pressure P/Po=0,990.

Average pore diameter D (hydraulic pore diameter)

Please use the relationship D=4V/S.

Participants were requested to provide the results for the values of specific adsorption

nitrogen, BET specific surface area, specific pore volume and pore diameter of Al2O3. The

results should be reported accompanied by a full uncertainty statement (including a combined

standard uncertainty and an expanded uncertainty with a coverage factor applied). In addition

the report should include technical details on measurement procedure, traceability links (as

calibrations) and uncertainty contributions. Each of report should include tabular reports and

graphs for the isotherm (dependence specific adsorption from relative pressure) and for the BET

calculation.

11

6 METHODS OF MEASUREMENT

Five participants have used the gas adsorption method for the measurement of the

porosity properties and reported details of their procedure in their reports or additional

information. Some details on measurements as derived from the reports are given in Table 7 and

Table 8.

Table 7 Details of sample pretreatment

Institute Approx.

sample mass, g Sample pretreatment

Corrected for

buoyancy

BAM 0.5544-

0.7138

Sample was heated for degassing in vacuum with the

ramp rate of 10℃/min to 110℃, held at the

temperature and then heated to 250°C (10℃/min) and

then held for 6 hours. Afterwards, the sample cooled

slowly to ambient temperature.

no

INMETRO 0.5029-

0.5798

Prior to each experiment the sample was heated in a

vacuum, with heating rate of 10 °C/min, from 25 to

250 °C and kept at 250 °C for 5 hours. Afterwards,

the sample was slowly cooled back to 25 °C.

no

NIM ~ 0.45

Sample was heated for degassing in vacuum with the

ramp rate of 10℃/min to 250℃ and then held for 6

hours to meet the outgas pressure rise less than

0.0067 Pa/min. Afterwards, the sample cooled slowly

to ambient temperature. Weight loss by the degassing

process was 8.3 % in average.

no

NMIJ ~ 0.47

The samples were heated in a vacuum of (2–4) Pa

with rate of 12 °C/min to 250 °C and kept at 250 °C

for 5 hours. Afterwards, the samples were cooled

slowly back to ambient temperature. Weight loss by

the degassing process was 7.5 % in average.

no

UNIIM 0.399 -

0.7794

Heat the sample Al2O3 for degassing in a vacuum

(1-3) Pa with rate of 10 oC/min to 250

oC, then hold

temperature at 250 oC for 5 hours. Afterwards, allow

the sample to cool slowly back to ambient

temperature. Weight loss by the degassing process

was 6.7 % in average.

yes

12

Table 8 Details of gas adsorption procedures used

Institute Adsorbat

Type of

instrument and

producer

Traceability

BAM N2

ASAP 2020

company

Micromeritics,

USA

CRM BAM P-106

INMETRO N2

Autosorb-1

company

Quantachrome

Instruments, USA

AB 265-S/FACT (Mettler Toledo) scale with 0.01

mg resolution and standard uncertainty = 0.02 mg,

BCR®-173

NIM N2

Autosorb-1-MP

company

Quantachrome

Instruments, USA

- balance (readability up to 0.1mg) to weigh samples

were calibrated using E2,

- temperature and pressure transducers were also

calibrated and their indications can be traceable to

corresponding national measurement standards,

- volume of adsorbed N2 gas traceable to national

measurement standard of solid density

- NIM CRMs for inert gas physical adsorption

NMIJ N2

BELSORP-mini II

company

Microtrac

Apparatus used in the measurement was validated

using a certified reference material (CRM)

BAM-P105 before and after the series of

experiments. Measured values of P105 fell within

their expanded uncertainties. Balance was calibrated

with 40 g weights by an ilac-MRA accredited

laboratory.

UNIIM N2

ASAP 2020MP

company

Micromeritics,

USA

- high precision resistance thermometer PTSV-1-1

with a measurement range of 10 to 60 ° C, expanded

uncertainty (k=2) 0.002 ºC, manufactured by the

Federal state unitary enterprise “VNIIFTRI”,

Moscow, Russia, and the twin channel precision

temperature measuring device MIT 2.05

manufactured by the limited liability company

“IzTekh”, Zelenograd, Russia;

- mass comparator CCE 2004 with a measurement

range of 0.0001 to 2500g, standard deviation 0.0002

g, manufactured by“Sartorius Weighing Technology

GmbH”, Germany;

- 2 kg scale weight (accuracy class E1),

manufactured by CJSC “Sartogosm”;

- high precision pressure sensor Baratron 690A with

a measurement range of 0 to 133 300 Pa, relative

expanded uncertainty (k=2) 0.05 %, manufactured

by “MKS Instruments”, Germany

13

7 RESULTS AND DISCUSSION

7.1 Uncertainty Participants have used different approaches for calculation of the porosity properties

uncertainty by gas adsorption method and have taken into account different sources of

uncertainty to establish their budget of uncertainty, see Table 9.

Table 9 Details about sources of uncertainty

Institute Tabular reports for

the isotherm

Accounted sources of uncertainty

BAM +

Type A

- repeatability measurement of the sample (type A),

- repeatability measurement of the CRM BAM P-106,

- deviation between certified value of the CRM BAM P-106 and arithmetic

mean of measurement results of the CRM BAM P-106.

Type B

- uncertainty of certified value of the CRM BAM P-106.

INMETRO +

Type A - repeatability measurement of the sample, fitting.

Type B - mass of sample, temperature, pressure, volumes.

NIM -

Type A - repeatability measurement of the sample, fitting

Type B - mass, temperature, pressure and volumes.

NMIJ +

Type A

- repeatability measurement of the sample.

- deviation between certified value of the CRM BAM P-105 and arithmetic

mean of measurement results of the CRM BAM P-105

Type B

- mass of sample, uncertainty of certified value of the CRM BAM P-105

UNIIM +


Type B - mass of sample, temperature, pressure, volumes, molar volume of ideal gas.

Uncertainty for specific surface area was calculated by Monte-Carlo method.

14

7.3 Formulas

A consistency check was performed according to the CCQM guidance note [4] using the

algorithm as shown below

2

21

1

/

1/

mi i

u mi

i

i

x u xx

u x

, (4)

2

2

1

mi u

obs

i i

x x

u x

, (5)

where ix is the result of participant i, u x is the standard uncertainty of x and m is the total

number of participants of the key comparison.

After calculations using formulas (4), (5) was compared, 2

obs with m-1 and with 2

0.05,m 1

the 95 percentile of 2 with m-1 of freedom ( 2

0.05,m 1 - has been taken from Microsoft Excel).

If 2 1obs m , it is normally safe to proceed with the assumption that the results are

mutually consistent and that the uncertainties account fully for the observed dispersion of values.

If 2 2

0.05,m 11 obsm the data provides no strong evidence that the reported

uncertainties are inappropriate, but the remains a risk that additional factors are contributing to

the dispersion. Refer to the prior working group decision on presumptive consistency and

proceed accordingly.

If 2 2

0.05,m 1obs the data should be considered mutually inconsistent.

Candidates of the key comparison reference value (KCRV) were estimated following the

CCQM guidance note [4] using different approaches. Results and uncertainties were taken from

the reports as they were. Formulas for calculation are shown below.

Arithmetic mean

1

1 m

i

i

x xm

, (6)

2

2 1

1

m

i

i

x x

u xm m

, (7)

where ix - is the result of the value of i NMI, u x - is the standard uncertainty of x .

Uncertainty-weighted mean

1

m

u i i

i

x w x

, (8)

2

2

1

1/

1/

i

i m

i

i

u xw

u x

, (9)

2

21

11/

m

i

iu

u xu x

, (10)

15

where iu x - is the standard uncertainty of ix .

Median

/2 /2 1

1 /2

1,

2

,

m m

m

x x even m evenmed x

x m odd

, (11)

2 2

2u med x

m

, (12)

1.483 imed d , (13)

where i id x med x .

Mandel-Paule

1

m

MP i i

i

x w x

, (14)

2 2

2 21

1

1

i

i m

i i

u x u qw

u x u q

, (15)

2

1

1MP m

i

i

u x

w

. (16)

where 2u q is the estimated additional variance from iterative procedure.

The DerSimonian-Laird procedure

11

1 m

u i i

i

x w xW

, (17)

2

1i

i

wu x

, (18)

1

1

m

i

i

W w

, (19)

2

1

1 2 1

1

max 0,/

m

i i u

i

w x x m

W W W

, (20)

2

2

1

m

i

i

W w

, (21)

1

m

DL i i

i

x w x

, (22)

12

12

1

i

i m

i

i

u xw

u x

, (23)

16

2

2 1

1

m

i i DL

iDL

i

w x x

u xw

. (24)

Huber estimate 2 (H15)

15

1

1 m

H i i

i

W xW

, (25)

15

min 1,i

i H

kW

x

, (26)

2

15 15

1H Hu

e , (27)

where 15H is a robust scale estimate of standard deviation delivered simultaneously in iterative

estimation of 15H and e is the efficiency (0.95 k =1.345).

7.4 Specific adsorption at P/Po=0.990 The reported values of the specific adsorption of nitrogen at P/Po=0.990 and the uncertainties of

all results are summarized in Table 10. Estimations of candidates KCRV have been obtained by

different approaches (arithmetic mean, uncertainty weighted mean, median, Mandel-Paule, the

DerSimonian-Laird procedure, Huber estimate 2 (H15)) are presented in Table 10. The same

results are displayed graphically in Figures 2 and 3.

It is proposed to use the median as a robust assessment of the KCRV because:

2 2

0.05,m 1obs , in this case the data is mutually inconsistent,

The uncertainties do not vary significantly (except for the uncertainty reported by NMIJ),

There is one extreme value according to /i ix med x u x ,

According to figure 2, the transformed distribution for reported results of NMI for the

specific adsorption of nitrogen at P/Po=0.990 is asymmetric,

Because the values of specific adsorption of nitrogen at P/Po=0.990 are primary data

obtained by the gas adsorption method for the calculation of the specific pore volume and pore

diameter, it is supposed to use the median as the KCRV for these values, too.

17

Table 10 – Reported values of specific adsorption of nitrogen at P/Po=0.990 and uncertainties

№

NMI/DIS

Specific adsorption of

nitrogen at P/Po=0.990,

mol/kg

Combined standard

uncertainty, uc, mol/kg

Expanded uncertainty,

U(k=2), mol/kg

di, mol/kg

U(di), mol/kg

Verdict

1 UNIIM 18.59 0.10 0.20 -0.31 0.36 +

2 ВАМ 18.71 0.07 0.14 -0.19 0.33 +

3 INMETRO 18.90 0.17 0.33* 0.00 0.44 +

4 NMIJ 19.011 0.019 0.038 0.110 0.300 +

5 NIM 19.08 0.17 0.34 0.18 0.45 +

Median 18.90 0.15 0.30 КСRV

Mean 18.86 0.09 0.18

Uncertainty weighted mean 18.978 0.018 0.036

Mandel-Paule 18.85 0.09 0.18 DerSimonian-Laird 18.85 0.09 0.19 Huber estimate 2 (H15) 18.86 0.10 0.21

Consistency test Conclusion 2

obs 2

0.05,m 1 m-1 2 2

0.05,m 1obs

34.24 9.49 4 inconsistent

* k=2.23

18

Figure 2 Error bars show standard uncertainty. The solid and dashed horizontal lines are the

median, upper and low limits of the corresponding standard uncertainty respectively.

Figure 3 Degrees of equivalence di and expanded uncertainty U（di）(k=2)

17,50

17,70

17,90

18,10

18,30

18,50

18,70

18,90

19,10

19,30

19,50

19,70

19,90

UNIIM ВАМ INMETRO NMIJ NIM median mean weightedmean

Spec

ific

adso

rpti

on o

f N

2 a

t

P/P

o=

0,9

90, m

ol/

kg

-1,00

-0,80

-0,60

-0,40

-0,20

0,00

0,20

0,40

0,60

0,80

1,00

UNIIM ВАМ INMETRO NMIJ NIM

di f

or

spec

ific

ad

sorp

tion

of

N2

at

P/P

o=

0.9

90, m

ol/

kg

transformation

normal

KCRV-median

19

7.5 Specific adsorption at P/Po=0.300 The reported values of the specific adsorption of nitrogen at P/Po=0.300 and the

uncertainties of all results are summarized in Table 11. Estimations of candidates KCRV have

been obtained by different approaches (arithmetic mean, uncertainty weighted mean, median,

Mandel-Paule, the DerSimonian-Laird procedure, Huber estimate 2 (H15)) are presented in

Table 11. The same results are displayed graphically in Figures 4 and 5.


2 2

0.05,m 11 obsm , in this case the data provide no strong evidence that the reported

uncertainties are inappropriate,


There are two extreme value according to /i ix med x u x ,


specific adsorption of nitrogen at P/Po=0.300 is unimodal and close to the Gaussian

distribution. In this case different estimations of KCRV are very close and are in good

agreement with each other.


№ NMI/DIS

Specific adsorption of


mol/kg

Combined standard



U(k=2), mol/kg

di, mol/kg

U(di), mol/kg

Verdict

1 INMETRO 2.944 0.037 0.074* -0.011 0.076 +

2 UNIIM 2.955 0.010 0.019 0.000 0.026 +

3 NMIJ 2.955 0.003 0.006 0.000 0.019 +

4 ВАМ 2.971 0.011 0.023 0.016 0.029 +

5 NIM 2.998 0.028 0.056 0.043 0.059 +

median 2.955 0.009 0.018 КСRV

mean 2.965 0.005 0.010

Uncertainty weighted mean 2.956 0.003 0.006

Mandel-Paule 2.957 0.003 0.007

DerSimonian-Laird 2.957 0.003 0.007 Huber estimate 2 (H15) 2.961 0.007 0.013


obs 2

0.05,m 1 m-1 2 2

0.05,m 11 obsm

4.17 9.49 4

the data provides no

strong evidence that the

reported uncertainties

are inappropriate

* k=2.20

20




2,80

2,90

3,00

3,10

3,20

INMETRO UNIIM NMIJ ВАМ NIM median mean weightedmean

Spec

ific

adso

rpti

on o

f N

2 a

t

P/P

o=

0,3

00, m

ol/

kg

-0,10

-0,08

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

0,10

0,12

INMETRO UNIIM NMIJ ВАМ NIM

di fo

r sp

ecif

ic a

dso

rpti

on o

f N

2 a

t

P/P

o=

0.3

00

, m

ol/

kg

transformation

normal

KCRV-median

21

7.6 Specific adsorption at P/Po=0.100 The reported values of the specific adsorption of nitrogen at P/Po=0.100 and the uncertainties of

all results are summarized in Table 11. Estimations of candidates KCRV have been obtained by

different approaches (arithmetic mean, uncertainty weighted mean, median, Mandel-Paule, the

DerSimonian-Laird procedure, Huber estimate 2 (H15)) are presented in Table 12 (only results

of key comparison participants have been used for calculation KCRV). The same results are

displayed graphically in Figures 6 and 7.

It is proposed to use the median as a robust assessment of the KCRV, because:

2 2

0.05,m 11 obsm in this case the data provide no strong evidence that the reported



There is one extreme value according to /i ix med x u x .


specific adsorption of nitrogen at P/Po=0.100 is unimodal. In this case different

estimations of KCRV are very close and are in good agreement with each other. In any

way it is supposed to use median for calculation of KCRV.


№

NMI/DIS

Specific adsor-ption of nitrogen

at P/Po=0.100,

mol/kg

Combined standard



U(k=2), mol/kg

di, mol/kg

U(di), mol/kg

Verdict

1 INMETRO 2.173 0.015 0.032* -0.022 0.033 +

2 NMIJ 2.191 0.002 0.004 -0.004 0.014 +

3 UNIIM 2.195 0.0075 0.015 0.000 0.020 +

4 ВАМ 2.203 0.0085 0.017 0.008 0.022 +

5 NIM 2.226 0.020 0.040 0.031 0.042 +

median 2.195 0.0066 0.013 КСRV

mean 2.198 0.0086 0.017

weighted mean 2.1918 0.0019 0.0037

Mandel-Paule 2.195 0.006 0.012 DerSimonian-Laird 2.1942 0.0036 0.0072 Huber estimate 2 (H15) 2.1963 0.0045 0.0089


obs 2

0.05,m 1 m-1 2 2

0.05,m 11 obsm

6.75 9.49 4

the data provides no strong

evidence that the reported

uncertainties are

inappropriate

* k=2.15

22

Figure 6 Error bars show standard uncertainty. The solid and dashed horizontal lines are the median, upper and low limits of the corresponding

standard uncertainty respectively.


2,000

2,050

2,100

2,150

2,200

2,250

2,300

INMETRO NMIJ UNIIM ВАМ NIM median mean weightedmean

Spec

ific

adso

rpti

on o

f N

2 a

t

P/P

o=

0,1

00, m

ol/

kg

-0,08

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

INMETRO NMIJ UNIIM ВАМ NIM

di f

or

spec

ific

ad

sorp

tio

n o

f N

2 a

t

P/P

o=

0.1

00

, m

ol/

kg

transformation

normal

KCRV-median

23

7.7 BET specific surface area

The reported values of BET specific surface area and the uncertainties of all results are

summarized in Table 9. Estimations of candidates KCRV have been obtained by different

approaches (arithmetic mean, uncertainty weighted mean, median, Mandel-Paule, the

DerSimonian-Laird procedure, Huber estimate 2 (H15)) are presented in Table 13 (only results

of key comparison participants have been used for calculation KCRV). The same results are

displayed graphically in Figures 8 and 9.


2 2



The uncertainties do not vary significantly.

There are two extreme value according to /i ix med x u x .

Table 13 – Reported values of BET specific surface area and uncertainties

NMI/DIS

BET

specific

surface

area, m2/g

Combined

standard

uncertainty,

uc, m2/g

Expanded

uncertainty,

U(k=2), m2/g

di, m2/g

U(di) ,

m2/g Verdict

INMETRO 205.6 0.72 1.6* -0.4 1.6 +

UNIIM 205.90 0.47 0.94 -0.10 1.15 +

NMIJ 206.0 1.1 2.2 0.0 2.3 +

ВАМ 207.4 0.8 1.6 1.4 1.7 +

NIM 208.9 1.6 3.2 2.9 3.3 +

median 206.00 0.33 0.66 КСRV

mean 206.8 0.6 1.2

weighted mean 206.23 0.33 0.66

Mandel-Paule 206.39 0.48 0.97

Der Simonian-Laird 206.36 0.42 0.83

Huber estimate 2 (H15) 206.6 0.5 1.0


obs 2

0.05,m 1 m-1 2 2

0.05,m 11 obsm

6.16 9.49 4

the data provides no strong

evidence that the reported

uncertainties are inappropriate

* k=2.23

24




201,0

202,0

203,0

204,0

205,0

206,0

207,0

208,0

209,0

210,0

211,0

INMETRO UNIIM NMIJ ВАМ NIM median mean weightedmean

BE

T s

pec

ific

su

rfac

e ar

ea,

m2/g

-5,0

-4,0

-3,0

-2,0

-1,0

0,0

1,0

2,0

3,0

4,0

5,0

INMETRO UNIIM NMIJ ВАМ NIM

di fo

r B

ET

spec

ific

surf

ace

area

,

m2/g

KCRV - median

25

7.8 Specific pore volume

The reported values of specific pore volume and the uncertainties of all results are summarized

in Table 10. Estimations of candidates KCRV have been obtained by different approaches

(arithmetic mean, uncertainty weighted mean, median, Mandel-Paule, the DerSimonian-Laird

procedure, Huber estimate 2 (H15)) are presented in Table 14. The same results are displayed

graphically in Figures 10 and 11.

It is proposed to use the median as a robust assessment of the KCRV, because:

2 2



The uncertainties do not vary significantly.

There are two extreme value according to /i ix med x u x .

Table 14 – Reported values of specific pore volume and uncertainties

№

NMI/DIS

Specific pore volume, cm

3/g

Combined standard

uncertainty, uc, cm

3/g


U(k=2), cm

3/g

di, cm

3/g

U(di), cm

3/g

Verdict

1 UNIIM 0.6450 0.0036 0.0072 -0.012 0.012 +

2 ВАМ 0.6487 0.0024 0.0048 -0.008 0.011 +

3 INMETRO 0.657 0.006 0.012* 0.000 0.015 +

4 NMIJ 0.659 0.009 0.018 0.002 0.021 +

5 NIM 0.663 0.007 0.014 0.006 0.017 +

median 0.657 0.005 0.010 КСRV

mean 0.6545 0.0033 0.0067

weighted mean 0.6500 0.0018 0.0036

Mandel-Paule 0.6522 0.0033 0.0065

DerSimonian-Laird 0.6520 0.0032 0.0064

Huber estimate 2 (H15) 0.6545 0.0039 0.0078


obs 2

0.05,m 1 m-1 2 2

0.05,m 11 obsm

8.32 9.49 4



reported uncertainties are

inappropriate

* k=2.20

26




0,6200

0,6300

0,6400

0,6500

0,6600

0,6700

0,6800

0,6900

UNIIM ВАМ INMETRO NMIJ NIM median mean weightedmean

Sp

ecif

ic p

ore

vo

lum

e, c

m3/g

-0,050

-0,040

-0,030

-0,020

-0,010

0,000

0,010

0,020

0,030

0,040

0,050

UNIIM ВАМ INMETRO NMIJ NIM

di f

or

spec

ific

pore

volu

me,

cm

3/g

KCRV - median

27

7.9 Average pore diameter

The reported values of average pore diameter and the uncertainties of all results are summarized

in Table 11. Estimations of candidates KCRV have been obtained by different approaches

(arithmetic mean, uncertainty weighted mean, median, Mandel-Paule, the DerSimonian-Laird

procedure, Huber estimate 2 (H15)) are presented in Table 15 (only results of key comparison

participants have been used for calculation KCRV). The same results are displayed graphically

in Figures 12 and 13.


2 2

0.05,m 1obs , in this case the data is mutually inconsistent,

The uncertainties do not vary significantly (except for the uncertainty reported by BAM).

There is one extreme value according to /i ix med x u x .

Table 15 – Reported values of specific pore volume and uncertainties

№

NMI/DIS

Average pore

diameter, nm

Combined standard

uncertainty, uc, nm

Expanded uncertainty, U(k=2), nm

di, nm

U(di), nm

Verdict

1 ВАМ 12.51 0.07 0.14 -0.19 0.22 +

2 UNIIM 12.53 0.07 0.14 -0.17 0.22 +

3 NIM 12.70 0.10 0.20 0.00 0.26 +

4 INMETRO 12.78 0.11 0.23 0.08 0.28 +

5 NMIJ 12.80 0.21 0.42 0.10 0.45 +

median 12.70 0.083 0.17 КСRV

mean 12.67 0.06 0.12

weighted mean 12.594 0.041 0.081

Mandel-Paule 12.62 0.06 0.12

Der Simonian-Laird 12.62 0.06 0.12

Huber estimate 2 (H15) 12.67 0.091 0.18


obs 2

0.05,m 1 m-1 2 2

0.05,m 11 obsm

7.03 9.49 4



reported uncertainties

are inappropriate

* k=2.20

28




12,00

12,10

12,20

12,30

12,40

12,50

12,60

12,70

12,80

12,90

13,00

13,10

13,20

ВАМ UNIIM NIM INMETRO NMIJ median mean weightedmean

Av

erag

e p

ore

dia

met

er, n

m

-0,50

-0,45

-0,40

-0,35

-0,30

-0,25

-0,20

-0,15

-0,10

-0,05

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,45

0,50

ВАМ UNIIM NIM INMETRO NMIJ

di,

nm

KCRV - median

29

7.10 Discussion

The key comparison CCQM K-136 has demonstrated very good agreement between the

five participating NMIs/DIs concerning the porosity characteristics determination. NMIJ presented optimistic uncertainty for specific adsorption of nitrogen because only

uncertainty of type А and uncertainty of the balance were taken into account for calculation of

expanded uncertainty.

30

8 EQUIVALENCE STATEMENTS

The equivalence statements have been calculated according to the BIPM guideline . The

degree of equivalence (and its uncertainty) between a NMI result and the KCRV has been

calculated according to the following equations:

i i refd x x , (28)

222 2cov ,i i ref i refU d u x u x x x , (29)

where id is the degree of equivalence between the NMI result xi and the KCRV xref ,

and U (di ) is the expanded uncertainty (k = 2) of the id calculated by combining the standard

uncertainty u(di ) of the NMI result xi and the standard uncertainty u xref of the KCRV xref (it is

supposed that cov ,i refx x is ineligible).

The equivalence statements for CCQM-K136 are given in Table 10-15 and Figures 3, 5,

7, 9, 11 and 13.

9 CONCLUSIONS

Good agreement between the participating laboratories for measurement porosity

properties as specific adsorption of nitrogen, BET specific surface area, specific pore volume

and pore diameter of nanoporous Al2O3 has been observed in the key comparison. The median

of all results is proposed for the calculation of the KCRV. The agreed use of the median and

its uncertainty based on the median of the absolute deviations (MAD) as the KCRV have been

accepted at the SAWG meeting in April 2016.

10 HOW FAR THE LIGHT SHINES STATEMENT Successful participation in the key comparisons CCQM-K136 can be used to underpin

CMC claims addressing the measurement of the specific adsorption of nitrogen (in the range of

0.1-100 mol/kg), the BET specific surface area (in the range of 1-1500 m2/g), the specific

volume (in the range of 0.1-1.5 cm3/g) and the average pore diameter (in the range of 2-100 nm)

of aluminum oxide as well as other mesoporous samples determined with a method matching the

scope of the international standard ISO 9277.

The measurands of the key comparison are method-defined (model dependent)

parameters. The values are determined on the basis of the BET model described in ISO 9277 and

ISO 15901-2. Under the condition that this model is applied as an integral part of the traceability

statement, the measured values are traceable to the base units of the SI via calibrated

measurements of the quantities of pressure, temperature, volume and mass.

Key comparison CCQM-K136 cannot be used to underpin CMC claims for

macroporous/nonporous solids with low specific surface area (<1 m2/g) and for microporous

solids with pore size (<2 nm).

The parallel Pilot Study CCQM P-180 cannot be used to underpin CMC claims.

31

11 ACKNOWLEDGEMENTS UNIM gratefully acknowledges collaboration with BAM, especially thanks are due to

Dr. Franziska Emmerling (BAM), Dr. Wolfgang Unger (BAM, SAWG) and Dr. Yuri Kustikov

(VNIIM). Many thanks are due to all of colleagues at the participant institutes delivering data.

12 REFERENCES

1. ISO 15901-2:2006 Pore size distribution and porosity of solid materials by mercury

porosimetry and gas adsorption – Part 2: Analysis of mesopores and macropores by gas

adsorption International Organization for Standardization, Geneva (2006).

2. ISO 9277:2010 Determination of the specific surface area of solids by gas adsorption –

BET method. International Organization for Standardization, Geneva (2010).

3. Gregg, S. J., Sing, K. S. W., Adsorption, Surface Area and Porosity. Academic Press,

London 1982.

4. CCQM Guidance note: Estimation of a consensus KCRV and associated Degrees of

Equivalence. Version: 10.

32

Appendix A – Technical Protocol CCQM-K136/ CCQM-P180

Measurement of porosity properties (specific adsorption, BET specific surface area, specific pore volume and pore diameter) of nanoporous Al2O3)

Technical protocol

1. Introduction

Specific nitrogen adsorption, BET specific surface area, specific pore volume and pore

diameter in nanoporous solids are highly relevant parameters because they are often used for the

specification of a vast majority of porous materials and substances (sorbents, catalytic agents,

cross-linkers, zeolites, etc) used in advanced technology. To check the comparability of

measurement protocols at NMIs and DIs adressing the porosity properties of technologically

relevant nanoporous solids, a key comparison is launched by the Surface Analysis Working

Group at CCQM/BIPM. Under certain conditions (see attachment) expert labs from non-

NMI/DIs are allowed to participate in a parallel Pilot Study CCQM-P180 which follows the

same rules as the key comparison.

The comparison is being carried out for the purpose to enable participating NMIs and DIs

to claim CMCs as detailed in table 1.

Table 1 Layout of CMC claims to be underpinned by key comparison CCQM-K 136

Meas. Serv.

Category

Matrix

Measurand

Dissemination Range of

Measurement Capability

Range of Expanded Uncertainties as

Disseminated

Analyte or

component Quantity From To Unit From To Unit

Cov.

factor

Advanced

Materials

Aluminum

oxide

Aluminum

oxide

Specific

adsorption

of nitrogen

0.1 50 mol/kg mol/kg 2

Advanced

Materials

Aluminum

oxide

Aluminum

oxide

BET

specific surface area

100 300 m2/g m2/g 2

Advanced

Materials

Aluminum

oxide

Aluminum

oxide

Specific Pore

Volume

0.1 1.5 cm3/g cm3/g 2

Advanced

Materials

Aluminum

oxide

Aluminum

oxide

Pore

diameter 2 50 nm nm 2

2. Measurand and reporting

Mandatory measurand values for CCQM-K136/ CCQM-P180) are specific adsorption of

nitrogen, BET specific surface area, specific pore volume and pore diameter of Al2O3.

Each participant shall report the results for the values of specific adsorption nitrogen,

BET specific surface area, specific pore volume and pore diameter of Al2O3. The results should

be reported accompanied by a full uncertainty statement (including a combined standard

uncertainty and an expanded uncertainty with a coverage factor applied). In addition, the report

should include technical details on the measurement procedure, traceability links (as

calibrations) and uncertainty contributions. Each report should include tabular reports and graphs

for the isotherm (dependence specific adsorption from relative pressure) and for the BET

calculation.

33

3. Guidance values and target uncertainty

Analyte/matrix: The test material used for the comparisons is nanoporous Al2O3. A range

of characteristic parameters and target uncertainty are shown in table 2.

Table 2

Quantity Range

Target relative

expanded uncertainty

Specific adsorption of nitrogen at P/Po=0.100* (1-3) mol/kg

(1-3) %



BET specific surface area (150-250) m2/g

Specific pore volume (0.3-1.0) cm3/g

Average pore diameter (5–20) nm

* it is primary information from instrument. If relative pressure is not exactly equal 0,10 or 0,30

and 0,99. Please calculate specific adsorption using linear regression using three nearest points.

4. KCRVs

The processing of measurement results of the specific adsorption nitrogen, specific

surface area, specific pore volume and pore diameter submitted to the pilot lab will be

carried out according to the following documents:CCQM Guidance note: Estimation of a

consensus KCRV and associated Degrees of Equivalence (version: 6, Date 2010-03-01,

Draft)

Cox M.G. “The evaluation of key comparison data” [1]

Jorg W.Muller. “Possible Advantages of a Robust Evaluation of Comparisons” [2].

5. Methods of measurement

Each participant should use the gas adsorption method for the measurement of the

specific adsorption nitrogen, BET specific surface area, specific pore volume and pore diameter

of Al2O3 as defined in ISO 15901-2 [3] and ISO 9277 [4].

Some details about measurement procedure of the gas adsorption method are shown

below

Please perform at least 5 replicate measurements on separate aliquots of Al2O3. The

recommended minimum sample amount is about 0.5 gram for each run.

Sample pretreatment

Heat the sample Al2O3 for degassing in a vacuum (1-2) Pa with a rate of 10 oC/min to

250 oC, the hold temperature at 250

oC for at least 5 hours. Afterwards, allow the sample to cool

slowly back to ambient temperature.

Measurement of the complete Isotherm (adsorption branch) at 77.3 K and specific

adsorption of nitrogen at P/Po=0.100; P/Po=0.300; P/Po=0,990.

First isotherm data point should be taken at P/Po=0.01, last adsorption isotherm data

point should be taken at P/Po=0.995. An intermediate adsorption isotherm data point should be

taken at P/Po=0.095; P/Po=0.100; P/Po=0.105; P/Po=0.295; P/Po=0.300; P/Po=0.305;

P/Po=0.985; P/Po=0.990; P/Po=0.995 (non-ideal correction factor, equal to 0.464·10-6

Pa-1

for

nitrogen at 77.35 K).

BET specific surface area

Determine the BET specific surface area S using at least 10 isotherm data points at the

adsorption branch of the isotherm within relative pressure range 0.05≤P/Po≤0.30 (cross selection

area for the N2 molecule in the monolayer: aN2 = 0.162 nm2).

Specific pore volume (Gurvich) [5]

The Single Point Total Pore Volume V according to the Gurvich rule should be

determined from the adsorption branch of the isotherm at relative pressure P/Po=0,990.

Average pore diameter D (hydraulic pore diameter)

34

Please use the relationship D=4V/S.

6. Planned time schedule

call for participants: by end of November 2014

latest registration of participant: by end of July 2015 (updated)

latest arrival of samples at participants: by end of September 2015

latest report of results: by end of February 2016

report A: by end of April 2016

report B: by end of July 2016

7. Samples

A bottle is planned to contain about 5 g of Al2O3.

8. Pilot laboratory

Laboratory for metrological assurance of nanoindustrie, analysis of spectral methods and

reference materials (251)

NMI’s name and abbreviation Ural Scientific Research Institute for Metrology, ROSSTANDART, Ekaterinburg

(UNIIM)

The postal address: 4, Krasnoarmeiskaya St., Ekaterinburg, Russian Federation, 620000

Head of Laboratory 251, Egor Sobina

Telephone / Fax +7 (343) 217-29-25, 217-85-96

E-mail: [email protected], [email protected]

Co-piloting laboratory

BAM Federal Institute for Materials Research and Testing.

Division 1.3 “Structure Analysis”

9. References

1. Cox M.G. The evaluation of key comparison data, Metrologia 39 (2002) 589-595.

2. Jorg W.Muller. Possible Advantages of a Robust Evaluation of Comparisons, Journal

of Research of the National Institute of Standards and Technology Vol.105, No.4

(2000) 551-555.

3. ISO 15901-2 Pore size distribution and porosity of solid materials by mercury

porosimetry and gas adsorption – Part 2: Analysis of mesopores and macropores by gas

adsorption International Organization for Standardization, Geneva (2006).

4. ISO 9277 Determination of the specific surface area of solids by gas adsorption – BET

method. International Organization for Standardization, Geneva (2010).

5. Gregg, S. J., Sing, K. S. W., Adsorption, Surface Area and Porosity. Academic Press,

London 1982.

mailto:[email protected]

35

Appendix B –CCQM-P180 (parallel to K136) Measurement of porosity properties (specific adsorption, BET specific surface area,

specific pore volume and pore diameter) of nanoporous Al2O3)

LNE participated in pilot study CCQM-P180 (parallel to K136). LNE used a gas

adsorption method of analysis. Table B.1 contains the full names of LNE and contact persons.

The dispatch dates and receipt dates are given in Table B.2. Some details on measurements as

derived from the reports are given in Table B.3 - B.5.

Table B.1

Institute Abbrev. Country Contact

persons

Kind of

comparison

Laboratoire

National de

métrologie et

d‘Essais

LNE France Laurent

Devoille,

Nicolas Feltin

Pilot

Table B.2 Sample sent dates, receipt dates and report dates

Sample No. Sample dispatch date Sample receipt date Date report sent

06 21 September 2015 24 September 2015 11 March 2016

Table B.3 Details of sample pretreatment

Approx. sample

mass, g Sample pretreatment

Corrected for

buoyancy

~ 0.5 Evacuation phase: 1 hour at 90 °C. Heating phase: 4 hours

at 250 °C. no

Table B.4 Details of gas adsorption procedures used

Adsorbat

Type of

instrument and

producer

Traceability

N2

ASAP2020

company

Micromeritics,

USA

- reference material supplied by Micromeritics (MSDS

Silica-Alumina, P/N 004/16821/00, Lot A-501-52)

- balance (ref. Sartorius TE64), calibrated prior to

measurements with a 50 g mass (ref. Zwickel ZW665,

class E2)

Some details about the results and sources of uncertainty are given in Table B.5.

Table B.5 Details about sources of uncertainty

Tabular reports for

the isotherm

Accounted sources of uncertainty

-


Type B - mass of sample, calibration of ASAP 2020.

36

The reported values of porosity characteristics and the uncertainties of all results are

summarized in Table B.6 (only results of key comparison participants have been used for

calculations KCRV). The same results are displayed graphically in Figures B.1 and B6.

Table B.6 The reported values of porosity characteristics and the uncertainties

Porosity

property Values

Combined

standard

uncertainty,

uc, mol/kg

Expanded

uncertainty,

U(k=2),

mol/kg

КСRV u(КСRV) di,

mol/kg

U(di),

mol/kg Verdict

Specific

adsorption of

nitrogen at

P/Po=0.990,

mol/kg

18.365 0.174 0.348 18.901 0.149 -0.536 0.458 -

Specific

adsorption of nitrogen at

P/Po=0.300,

mol/kg

2.904 0.028 0.056 2.9550 0.0091 -0.0511 0.0587 +

Specific adsor-ption of


mol/kg

2.147 0.023 0.046 2.1950 0.0066 -0.0476 0.0480 +

BET specific

surface area,

m2/g

202.82 6.31 12.62 206.00 0.33 -3.18 12.64 +

Specific pore

volume, cm3/g 0.6373 0.0802 0.1604 0.6570 0.0050 -0.0197 0.1607 +

Average pore

diameter, nm 12.57 1.51 3.01 12.700 0.083 -0.131 3.015 +

37

Figure B.1 Error bars show standard uncertainty. The solid and dashed horizontal lines are the




17,50

17,70

17,90

18,10

18,30

18,50

18,70

18,90

19,10

19,30

19,50

19,70

19,90

UNIIM ВАМ INMETRO NMIJ NIM LNE

Sp

ecif

ic a

dso

rpti

on

of

N2

at

P/P

o=

0,9

90

, m

ol/

kg

KC PS

2,80

2,90

3,00

3,10

3,20

INMETRO UNIIM NMIJ ВАМ NIM LNE

Spec

ific

adso

rpti

on o

f N

2 a

t

P/P

o=

0,3

00, m

ol/

kg

KC PS

38





2,000

2,050

2,100

2,150

2,200

2,250

2,300

INMETRO NMIJ UNIIM ВАМ NIM LNE

Sp

ecif

ic a

dso

rpti

on

of

N2 a

t

P/P

o=

0,1

00

, m

ol/

kg

197,0

199,0

201,0

203,0

205,0

207,0

209,0

211,0

INMETRO UNIIM NMIJ ВАМ NIM LNE

BE

T s

pec

ific

su

rfac

e ar

ea,

m2/g

KC PS

KC PS

39





0,6000

0,6100

0,6200

0,6300

0,6400

0,6500

0,6600

0,6700

0,6800

0,6900

0,7000

0,7100

0,7200

UNIIM ВАМ INMETRO NMIJ NIM LNE

Sp

ecif

ic p

ore

vo

lum

e, c

m3/g

KC PS

10,00

10,50

11,00

11,50

12,00

12,50

13,00

13,50

14,00

ВАМ UNIIM NIM INMETRO NMIJ LNE

Av

erag

e p

ore

dia

met

er, n

m

KC PS

Report of the key CCQM-K136 - bipm.org · Ural Scientific Research Institute for Metrology,...

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Transcript of Report of the key CCQM-K136 - bipm.org · Ural Scientific Research Institute for Metrology,...