T Plot Adsorption

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The classical Van't Hoff plot appears meaningless and its linear behavior a mere accident. Results from nonlinear chromatography confirm these conclusions and provide explanations. The retention factors seem to fulfill the Van't Hoff equation, not the Henry constants corresponding to the different types of adsorption sites. Adsorption Kinetics Integrated form of equation for second order reaction is t/q = 1/k2.qe 2 + t/qe The plot t/q versus t should give a straight line if second order kinetic model is applicable 12/9/2015Priy Brat Dwivedi, PhD 21 22.

. Adsorption as a macroscopic (thermodynamic) phenomenon. Equilibrium thermodynamics and adsorption isotherms: Langmuir and BET isotherm. The adsorption energy: Initial adsorption energy and a-priori heterogeneity. Coverage dependence of the adsorption energy: lateral interactions and a-posteriori heterogeneity.
Adsorption has been an alternative technique for heavy metal removal at low concentrations, and it depends on the adsorbent surface area, surface morphology, pore size distribution, polarity and functional groups attached to the adsorbent surface (Ali et al.

A Practical Guide to Isotherms of ADSORPTION on Heterogeneous Surfaces

Micromeritics's ASAP2405 report explained (AWM)

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Device: ASAP2405 - 6-channel automatic sorption analyzer, (Micromeritics Corp., USA)

Sample: experimental active carbon RIB (Norit BV, Netherlands)

Adsorbate: N₂ at 78K

In this measurement/report:

Relative pressure range: 0.05 - 0.99

Analyses: adsorption/desorption isotherms,

BET and Langmuir specific surface area

t-plot (Harkins-Jura equation)

BJH (Barret-Joyner-Halenda) surface/volume mesopore analysis (adsorption/desorption)

All Figures are drawn according to the reported isotherm data by me (AWM).

Micromeritics Instrument Corporation

ASAP 2405N V1.01 ADSORBATE: NITROGEN PAGE 1

SAMPLE DIRECTORY/NUMBER: DATA1 /142 START 08:37:51 06/26/98

SAMPLE ID: R/B COMPL 19:41:49 06/26/98

SUBMITTER: REPRT 09:35:18 06/29/98

OPERATOR: SAMPLE WT: 1.1288 g

STATION NUMBER: 3 EQUIL INTERVAL: 5 sec FREE SPACE: 97.4868 cc

ANALYSIS LOG

RELATIVE PRESSURE VOL ADSORBED ELAPSED TIME SATURATION

PRESSURE (mmHg) (cc/g STP) (HR:MN) PRESS.(mmHg)

x=p/p_spV_atimep_s

3:02 751.057

0.0587 44.071 314.2087 3:27

0.0792 59.454 323.3588 3:47

0.1324 99.427 337.2521 4:07

0.1441 108.249 339.3304 4:16

0.1673 125.636 342.7346 4:26

0.2003 150.418 346.7142 4:37

0.2483 186.494 351.5293 4:48

0.3459 259.759 359.5118 5:01 ◄◄◄ p/p_s≈0.4 - hysteresis loop

5:03 750.953

0.4457 334.689 366.2021 5:13

0.5572 418.388 373.2755 5:27

0.6436 483.263 379.0942 5:37

0.7470 560.855 387.4077 5:54

0.7969 598.292 391.7355 6:02

0.8348 626.691 395.1406 6:09

0.8701 653.209 398.2824 6:17

0.9019 677.018 400.7671 6:23

0.9198 690.459 402.3520 6:28

0.9364 702.939 404.1616 6:33

0.9500 713.115 406.0604 6:39

0.9619 722.018 408.0504 6:44

0.9689 727.219 409.6730 6:48

0.9757 732.356 411.6911 6:53

0.9812 736.465 413.5470 6:5716 ◄◄◄ V_t=V(p/p_s≈0.98)

0.9835 738.199 414.6281 7:01

7:05 750.540

0.9878 741.345 416.8401 7:06

0.9892 742.436 418.0067 7:10

0.9947 746.546 420.8760 7:16 < ◄◄◄ p close to p_s

0.9810 736.272 419.6332 7:19

0.9719 729.402 418.1166 7:23

0.9643 723.688 416.7538 7:27

0.9643 723.688 416.5946 7:28

0.9534 715.483 414.5608 7:34

0.9380 703.899 412.4948 7:40

0.9296 697.563 411.3706 7:44

0.9031 677.722 409.2945 7:50

0.8642 648.473 407.3190 7:57

0.8286 621.755 405.7912 8:04

0.8027 602.331 404.9170 8:08

0.7285 546.619 402.5403 8:16

0.6567 492.754 400.3286 8:23

0.5546 416.080 396.8762 8:33

9:07 750.178

0.4544 340.847 370.4437 9:29 ◄◄◄ p/p_s≈0.4 - hysteresis loop

0.3507 263.102 360.4513 9:44

0.2492 186.944 352.1268 9:58

0.2003 150.288 347.0935 10:10

0.1536 115.191 341.1276 10:23

0.1018 76.394 330.9598 10:41

0.0517 38.814 310.9733 11:05

Adsorption/desorption isotherm of N₂ on active carbon RIB (Norit), T=78K

Micromeritics Instrument Corporation

ASAP 2405N V1.01 ADSORBATE: NITROGEN PAGE 4

SAMPLE DIRECTORY/NUMBER: DATA1 /142 START 08:37:51 06/26/98

SAMPLE ID: R/B COMPL 19:41:49 06/26/98

SUBMITTER: REPRT 09:35:18 06/29/98

OPERATOR: SAMPLE WT: 1.1288 g

STATION NUMBER: 3 EQUIL INTERVAL: 5 sec FREE SPACE: 97.4868 cc

BET SURFACE AREA REPORT

BET SURFACE AREA: 1190.1411 +/- 26.5809 sq. m/g

SLOPE: 0.003682 +/- 0.000081

Y-INTERCEPT: -0.000025 +/- 0.000011

C: -148.159561

VM: 273.394623 cc/g STP

CORRELATION COEFFICIENT: 9.99276E-01

RELATIVE VOL ADSORBED 1/

PRESSURE (cc/g STP) [VA(Po/P - 1)]

x=p/p_sV_ay_BET=1/[V_a(1/x – 1)

0.0587 314.2087 0.000198

0.0792 323.3588 0.000266

0.1324 337.2521 0.000452

0.1673 342.7346 0.000586

0.2003 346.7142 0.000722

Adsorption isotherm of N₂ on active carbon RIB (Norit), T=78K – linear form of BET equation

This method gives reliable results for solids that do not contain large amount of micropores or supermicropores and mesopores are rather large, i.e. surface of the solid may be well approximated by the flat surface. S_BET[m²/g] = 4.35·V_a,BET[cc/g STP] – determined from the linear plot.

Micromeritics Instrument Corporation

ASAP 2405N V1.01 ADSORBATE: NITROGEN PAGE 6

SAMPLE DIRECTORY/NUMBER: DATA1 /142 START 08:37:51 06/26/98

SAMPLE ID: R/B COMPL 19:41:49 06/26/98

SUBMITTER: REPRT 09:35:18 06/29/98

OPERATOR: SAMPLE WT: 1.1288 g

STATION NUMBER: 3 EQUIL INTERVAL: 5 sec FREE SPACE: 97.4868 cc

LANGMUIR SURFACE AREA REPORT

LANGMUIR SURFACE AREA: 1576.9810 +/- 5.7505 sq. m/g

SLOPE: 0.002760 +/- 0.000010

Y-INTERCEPT: 0.000026 +/- 0.000001

b: 0.009364

VM: 362.257965 cc/g STP

CORRELATION COEFFICIENT: 9.99980E-01

RELATIVE VOL ADSORBED 1/

PRESSURE (cc/g STP) [VA*Po/P]

x=p/p_sV_ay_L=1/[V_a/x]

T Plot Adsorption Meaning

0.0587 314.2087 0.000187

0.0792 323.3588 0.000245

0.1324 337.2521 0.000393

0.1673 342.7346 0.000488

0.2003 346.7142 0.000578

Adsorption isotherm of N₂ on active carbon RIB (Norit), T=78K – linear form of Langmuir equation

(This method gives results that are applicable for strongly microporous solids, having only small share of mesopores. Though Langmuir model has nothing to do with micropores, it approximates well enough the course of adsorption in micropores close to micropore saturation.
For microporous solid – having practically no “external area”, the “specific surface area” obtained formally from this analysis should be replaced by the “micropore volume” or adsorption capacity. However, specific surface area may be still used for comparisons) S_L[m²/g] = 4.35·V_a,L[cc/g STP] – determined from the linear plot.

Micromeritics Instrument Corporation

ASAP 2405N V1.01 ADSORBATE: NITROGEN PAGE 8

SAMPLE DIRECTORY/NUMBER: DATA1 /142 START 08:37:51 06/26/98

SAMPLE ID: R/B COMPL 19:41:49 06/26/98

SUBMITTER: REPRT 09:35:18 06/29/98

OPERATOR: SAMPLE WT: 1.1288 g

STATION NUMBER: 3 EQUIL INTERVAL: 5 sec FREE SPACE: 97.4868 cc

MICROPORE ANALYSIS REPORT

MICROPORE VOLUME: 0.353311 cc/g

MICROPORE AREA: 765.7809 sq. m/g

EXTERNAL SURFACE AREA: 424.3603 sq. m/g

SLOPE: 27.434721 +/- 2.557187

Y-INTERCEPT: 228.414215 +/- 10.229213

CORRELATION COEFFICIENT: 9.87217E-01

RELATIVE STATISTICAL VOL ADSORBED

PRESSURE THICKNESS,(A ) (cc/g STP)

x=p/p_st_HJV_a

0.0587 3.325 314.2087

0.0792 3.510 323.3588

0.1324 3.916 337.2521

0.1441 3.998 339.3304

0.1673 4.155 342.7346

0.2003 4.371 346.7142

0.3459 5.316 359.5118

0.4457 6.028 366.2021

0.5572 6.970 373.2755

THICKNESS VALUES USED IN THE LEAST-SQUARES ANALYSIS

WERE BETWEEN 3.500 AND 5.000 A . ◄◄◄◄ thickness range (3.54Å =t_mono)

0.500

t = [ 13.9900/( 0.0340 - log(P/Po))] ◄◄◄◄ HJ equation

SURFACE AREA CORRECTION FACTOR IS 1.000.

In this t-plot report:

EXTERNAL SURFACE AREA, S_ext = SLOPE*4.3532*t_mono(surface for pores larger than micropores)

MICROPORE VOLUME, V_micro = Y-INTERCEPT*0.0015468 (recalculates[cc/g STP]into[cc/g])

MICROPORE AREA, S_micro = S_BET - S_ext

Adsorption isotherm of N₂ on active carbon RIB (Norit), T=78K – t-plot (de Boer)

For microporous solids the Halsey (aka Frenkel-Halsey-Hill, FHH) isotherm equation is also often used in t-plot. However, this equation produces negative micropore volume estimates for solids with small amounts of micropores. Generally, the HJ isotherm is more reliable in this respect. If the low pressure data (micropore range) is available, the t/F-plot (by Kadlec) may be used. The most general is the a_s-method (alpha-s) which relies on comparison of sample isotherm with isotherm measured on some standard adsorbent.

Micromeritics Instrument Corporation

ASAP 2405N V1.01 ADSORBATE: NITROGEN PAGE 10

SAMPLE DIRECTORY/NUMBER: DATA1 /142 START 08:37:51 06/26/98

SAMPLE ID: R/B COMPL 19:41:49 06/26/98

SUBMITTER: REPRT 09:35:18 06/29/98

OPERATOR: SAMPLE WT: 1.1288 g

STATION NUMBER: 3 EQUIL INTERVAL: 5 sec FREE SPACE: 97.4868 cc

BJH (Barret-Joyner-Halenda) pore distribution

BJH ADSORPTION PORE DISTRIBUTION REPORT ◄◄◄◄ ADSORPTION

PORE DIAMETER AVERAGE INCREMENTAL CUMULATIVE INCREMENTAL CUMULATIVE

RANGE DIAMETER PORE VOLUME PORE VOLUME PORE AREA PORE AREA

(A ) (A ) (cc/g) (cc/g) (sq. m/g) (sq. m/g)

d_max - d_mind_aΔVΣΔV(d < d_min)ΔSΣΔS(d < d_min)

1813.6- 1599.0 1692.6 0.001922 0.001922 0.045 0.045

1599.0- 1195.7 1339.1 0.003665 0.005587 0.109 0.155

1195.7- 1050.2 1113.3 0.001800 0.007387 0.065 0.220

1050.2- 817.0 904.1 0.003110 0.010498 0.138 0.357

817.0- 640.6 707.0 0.003424 0.013922 0.194 0.551

640.6- 526.5 572.0 0.002779 0.016701 0.194 0.745

526.5- 404.3 448.9 0.003447 0.020148 0.307 1.052

404.3- 320.2 352.1 0.003355 0.023503 0.381 1.433

320.2- 255.6 280.3 0.003252 0.026755 0.464 1.898

255.6- 210.3 228.3 0.002903 0.029657 0.509 2.406

210.3- 160.3 178.2 0.004728 0.034385 1.061 3.468

160.3- 126.9 139.4 0.006349 0.040735 1.822 5.289

126.9- 103.8 112.8 0.007203 0.047938 2.555 7.844

103.8- 83.6 91.2 0.009598 0.057536 4.208 12.052

83.6- 59.2 66.7 0.020065 0.077601 12.038 24.090

59.2- 47.1 51.5 0.014658 0.092259 11.392 35.482

47.1- 36.6 40.2 0.019253 0.111512 19.150 54.632

36.6- 29.8 32.3 0.019838 0.131349 24.551 79.183

29.8- 24.5 26.5 0.026617 0.157967 40.196 119.379

24.5- 22.2 23.2 0.017230 0.175197 29.719 149.098

22.2- 20.6 21.3 0.015188 0.190385 28.484 177.582

20.6- 19.5 20.0 0.013890 0.204275 27.712 205.294

19.5- 19.0 19.3 0.009011 0.213286 18.713 224.007

BJH estimates of pore volume and surface area distributions correspond here to the cylindrical pore model (compare any pair of(4ΔV/ΔS) and (d_d) )

Micromeritics Instrument Corporation

ASAP 2405N V1.01 ADSORBATE: NITROGEN PAGE 17

SAMPLE DIRECTORY/NUMBER: DATA1 /142 START 08:37:51 06/26/98

SAMPLE ID: R/B COMPL 19:41:49 06/26/98

SUBMITTER: REPRT 09:35:18 06/29/98

OPERATOR: SAMPLE WT: 1.1288 g

STATION NUMBER: 3 EQUIL INTERVAL: 5 sec FREE SPACE: 97.4868 cc

BJH (Barret-Joyner-Halenda) pore distribution

BJH DESORPTION PORE DISTRIBUTION REPORT ◄◄◄◄ DESORPTION

PORE DIAMETER AVERAGE INCREMENTAL CUMULATIVE INCREMENTAL CUMULATIVE

RANGE DIAMETER PORE VOLUME PORE VOLUME PORE AREA PORE AREA

(A ) (A ) (cc/g) (cc/g) (sq. m/g) (sq. m/g)

d_max - d_mind_dΔVΣΔV(d < d_min)ΔSΣΔS(d < d_min)

3670.6- 1041.1 1228.9 0.002072 0.002072 0.067 0.067

1041.1- 708.4 812.0 0.002572 0.004644 0.127 0.194

708.4- 560.9 617.1 0.002349 0.006993 0.152 0.346

560.9- 432.7 479.9 0.003857 0.010850 0.322 0.668

432.7- 327.9 365.4 0.003681 0.014531 0.403 1.071

327.9- 289.9 306.4 0.002041 0.016572 0.266 1.337

289.9- 213.0 239.2 0.003800 0.020371 0.636 1.973

213.0- 153.5 173.1 0.003706 0.024078 0.856 2.829

153.5- 122.5 134.2 0.002989 0.027067 0.891 3.720

122.5- 106.8 113.4 0.001730 0.028796 0.610 4.330

106.8- 77.9 87.4 0.005084 0.033880 2.328 6.658

77.9- 61.5 67.5 0.005109 0.038989 3.029 9.687

61.5- 46.8 51.8 0.008903 0.047892 6.880 16.567

46.8- 37.3 40.7 0.086943 0.134835 85.467 102.034

37.3- 30.1 32.7 0.027577 0.162412 33.715 135.749

30.1- 24.6 26.6 0.021850 0.184263 32.864 168.613

24.6- 22.2 23.2 0.015267 0.199530 26.314 194.927

22.2- 20.0 20.9 0.020243 0.219773 38.692 233.619

20.0- 17.5 18.5 0.041958 0.261730 90.566 324.185

BJH estimates of pore volume and surface area distributions correspond here to the cylindrical pore model (compare any pair of(4ΔV/ΔS) and (d_d) )

Micromeritics Instrument Corporation

ASAP 2405N V1.01 ADSORBATE: NITROGEN PAGE 24

SAMPLE DIRECTORY/NUMBER: DATA1 /142 START 08:37:51 06/26/98

SAMPLE ID: R/B COMPL 19:41:49 06/26/98

SUBMITTER: REPRT 09:35:18 06/29/98

OPERATOR: SAMPLE WT: 1.1288 g

STATION NUMBER: 3 EQUIL INTERVAL: 5 sec FREE SPACE: 97.4868 cc

SUMMARY REPORT

AREA

BET SURFACE AREA: 1190.1411 sq. m/g

LANGMUIR SURFACE AREA: 1576.9810 sq. m/g

SINGLE POINT SURFACE AREA AT P/Po 0.2003: 1207.0052 sq. m/g

BJH CUMULATIVE ADSORPTION SURFACE AREA OF PORES

BETWEEN 17.0000 AND 3000.0000 A DIAMETER: 224.0069 sq. m/g

BJH CUMULATIVE DESORPTION SURFACE AREA OF PORES

BETWEEN 17.0000 AND 3000.0000 A DIAMETER: 324.1851 sq. m/g

MICROPORE AREA: 765.7809 sq. m/g

VOLUME

SINGLE POINT TOTAL PORE VOLUME OF PORES LESS THAN

1195.7146 A DIAMETER AT P/Po 0.9835: 0.641347 cc/g

BJH CUMULATIVE ADSORPTION PORE VOLUME OF PORES

BETWEEN 17.0000 AND 3000.0000 A DIAMETER: 0.213286 cc/g

BJH CUMULATIVE DESORPTION PORE VOLUME OF PORES

BETWEEN 17.0000 AND 3000.0000 A DIAMETER: 0.261730 cc/g

MICROPORE VOLUME: 0.353311 cc/g

PORE SIZE

AVERAGE PORE DIAMETER (4V/A BY LANGMUIR): 16.2677 A

BJH ADSORPTION AVERAGE PORE DIAMETER (4V/A): 38.0855 A

BJH DESORPTION AVERAGE PORE DIAMETER (4V/A): 32.2939 A

Area occupied by the adsorbate S_a [m²/g]= 4.35·V_a [cc/g STP]

Single point BET area: S_1p(x≈0.2)=4.35·(1-x)·V_a(x)

Volume occupied by the adsorbate V_liq [cc/g] = 0.0015468·V_a [cc/g STP]

(2V/A) => 2 · “pore volume” / “pore area” – average “hydraulic” pore diameter (slit-shaped pores)

(4V/A) => 4 · “pore volume” / “pore area” – average “hydraulic” pore diameter (cyllindrical pores)

(6V/A) => 6 · “pore volume” / “pore area” – average “hydraulic” pore diameter (spherical pores)

where: “pore volume” is the amount adsorbed [cc/g STP] recalculated into “adsobate volume” [cc/g]

Average pore diameter is calculated from Single point Total pore volume, V, and Langmuir (here for microporous solids) or BET (other solids) surface area, A.

BJH ads/des average pore diameter is the average mesopore diameter calculated as above from S_meso and V_meso

The use of Langmuir area estimate for microporous solids has very limited sense (and should be used only for comparisons between adsorbents). It comes from practical reasons – the shape of adsorption isotherm on microporous solids close to completion of micropores is generally more similar to Langmuir isotherm close to monolayer filling than to BET multilayer. Thus, in 0.05 – 0.2 region such experimental isotherm is more likely to follow the Langmuir than BET isotherm course. If the solid contains comparable amounts of micropores and meso- + macropores, then neither model may simulate such behavior properly.

The (4V/A) term used in estimation of pore average sizes corresponds to the assumed cylindrical model of pores. However, this assumption “sits” also in BJH estimates of pore volume and surface area distributions!

Adsorption/desorption isotherm of N₂ on active carbon RIB (Norit), T=78K.

Differential mesopore size distribution DV/Dd (BJH method).

Differences betwee ads/des result from discrepancies between adsorbate structure and the model of open-ended cylindrical capillaries

Adsorption/desorption isotherm of N₂ on active carbon RIB (Norit), T=78K.

Differential logarytmic mesopore size distribution DV/Dlog₁₀d (BJH method) (large pores are emphasized)Differences betwee ads/des result from discrepancies between adsorbate structure and the model of open-ended cylindrical capillaries

Adsorption/desorption isotherm of N₂ on active carbon RIB (Norit), T=78K.

T-plot Adsorption

Cumulative distribution of of mesopore volume V(2r<d) (BJH method).

Differences betwee ads/des result from discrepancies between adsorbate structure and the model of open-ended cylindrical capillaries

Adsorption/desorption isotherm of N₂ on active carbon RIB (Norit), T=78K.

Cumulative distribution of of mesopore surface area S_meso(2r<d) (BJH method).

Differences betwee ads/des result from discrepancies between adsorbate structure and the model of open-ended cylindrical capillaries

Adsorption/desorption isotherm of N₂ on active carbon RIB (Norit), T=78K.

Differential distribution of mesopore surface area DS/Dd (BJH method).

T Plot Adsorption Definition

Differences betwee ads/des result from discrepancies between adsorbate structure and the model of open-ended cylindrical capillaries

T Plot Adsorption Isotherm

Adsorption/desorption isotherm of N₂ on active carbon RIB (Norit), T=78K.

Differential logarithmic distribution of mesopore surface area DS/Dlog₁₀d (BJH method) (large pores are emphasized).Differences betwee ads/des result from discrepancies between adsorbate structure and the model of open-ended cylindrical capillaries

Micromeritics's ASAP2405 report explained (AWM)

T Plot Adsorption Meaning

MICROPORE VOLUME, Vmicro = Y-INTERCEPT*0.0015468 (recalculates[cc/g STP]into[cc/g])

MICROPORE AREA, Smicro = SBET - Sext

BJH (Barret-Joyner-Halenda) pore distribution

T-plot Adsorption

T Plot Adsorption Definition

T Plot Adsorption Isotherm

T Plot Adsorption Method

MICROPORE VOLUME, V_micro = Y-INTERCEPT*0.0015468 (recalculates[cc/g STP]into[cc/g])

MICROPORE AREA, S_micro = S_BET - S_ext