Skip to main content
SpringerLink
Log in

Identification of mass transfer resistances in microporous materials using frequency response methods

  • Published:
Adsorption Aims and scope Submit manuscript

Abstract

The frequency response (FR) method, a pseudo-steady state relaxation technique employing perturbation frequency, plays an essential role in discriminating between multi-kinetic mechanisms in microporous materials for separation and catalytic processes. Experimental and theoretical principles are reviewed for three frequency response methods, including one commonly used batch system with volume perturbation and two recently developed flow-through systems with pressure or concentration oscillation. Even though these methods have different overall transfer functions, they can be linked closely through the adsorbed-phase functions, which account for individual or coupling of mass transfer resistances and heat effects. Mass transfer resistances include micropore diffusion, macropore diffusion, surface barriers, and external film resistance. By judicious application of FR methods, it is not only possible to identify dominating mass transfer resistances but also to extract reliable mass transfer coefficients based on corresponding mathematical models. Representative examples to display the ability of the FR methods in studies of zeolites, carbon molecular sieves, and other microporous materials are discussed. Mixture studies and future developments, including nonlinear frequency response and chemical reactions, have also been briefly described.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

; Figure b reprinted with permission from Hossain et al. [55])

Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

(Adapted with permission  from Giesy and LeVan [15])

Fig. 11

(Adapted with permission from Van-Den-Begin and Rees [10])

Fig. 12
Fig. 13

Figure c adapted with permission from Liu et al. [23])

Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Abbreviations

A :

Heat transfer area, m2

C 0 :

Initial molar concentration of adsorbate, mol/m3

C s :

Heat capacities of the adsorbent, J/(g K)

C p :

Heat capacities of the gas, J/(mol K)

D :

Micropore diffusivity, m2/s

D ii :

Main-term diffusivities in a mixture, m2/s

D ij :

Cross-term diffusivities in a mixture, m2/s

D p :

Macropore diffusivity, m2/s

f :

Frequency, Hz

G :

Overall transfer function

G n :

Adsorbed-phase transfer function

k :

Specific heat ratio of gas, or the LDF mass transfer coefficient

K :

Equilibrium constant related to the gradient of the adsorption isotherms

k B :

Barrier resistance coefficient or surface permeability, m/s

K V :

Dimensionless equilibrium constant used in VSFR, defined as Ms (RT/V0) (dn/dP)0

K p :

Equilibrium constant defined as dn/dP, mol/(kg bar)

M s :

Adsorbent mass, kg

n :

Adsorbed amount, mol/kg

n * :

Adsorbed amount in equilibration, mol/kg

h :

Heat transfer coefficient, W/(m2 K)

l 3 :

Lumped parameter for a non-isothermal model as \((\eta /s)\left[\sqrt{s/\eta } \mathrm{coth}\left(\sqrt{s/\eta} \right)-1\right]\)

P :

Pressure, bar

P B :

Pressure response in the absence of adsorbents

P Z :

Pressure response in the presence of adsorbents

P 0 :

Initial equilibrium and reference pressure for a system with adsorbent, bar

R:

Universal gas constant, Pa m3 mol−1 K−1

R c :

Radius of micropore crystal or microparticle, m

R p :

Radius of adsorbent macroparticle, m

t :

Time, s

T :

Temperature, K

T o :

Initial temperature, K

V :

Working volume, m3

V 0 :

Equilibrium volume, m3

V 1 :

Inlet volume for a CSFR system, m3

V b :

Adsorption bed void volume in a CSFR, m3

α:

Lumped heat-transfer rate, J/(K s)

β bm :

Dimensionless parameter to describe the relative contribution of surface permeation and intrinsic diffusion for a sphere microparticle

δ :

Intensity function in Eq. 3

δin :

In-phase function

δout :

Out-of-phase function

δ c :

Dimensionless in-phase function

δ s :

Dimensionless out-of-phase function

ε p :

Macropore or pellet porosity

λ:

Heat of adsorption (taken to be negative), kJ/mol

µ :

Mean value of Gaussian distribution

η :

Parameter for D/r2, 1/s

η M :

Effective macropore diffusion time constants defined in Eq. 26, 1/s

ω:

Angular frequency of oscillation, rad/s

ν:

Dimensionless frequency as (2ω/η)1/2

ρ :

Density of the adsorbent, kg/m3

σ 2 :

Variance of the Gaussian distribution

φ:

Phase lag

ΔP :

Amplitude of pressure change in a system

ΔF :

Amplitude of flow rate change in system

∆V :

The oscillation amplitudes of the system volume, m3

Γ :

Thermodynamic factor

References

  1. Brzić, D., Petkovska, M.: Some practical aspects of nonlinear frequency response method for investigation of adsorption equilibrium and kinetics. Chem. Eng. Sci. 82, 62–72 (2012)

    Google Scholar 

  2. Petkovska, M., Do, D.D.: Nonlinear frequency response of adsorption systems: isothermal batch and continuous flow adsorbers. Chem. Eng. Sci. 53(17), 3081–3097 (1998)

    CAS  Google Scholar 

  3. Cartigny, J., Giermanskakahn, J., Delara, E.C.: Frequency response method in the study of methane diffusion in three cation-exchanged zeolites A. Zeolites 14(7), 576–581 (1994)

    CAS  Google Scholar 

  4. Hossain, M.I., Holland, C.E., Ebner, A.D., Ritter, J.A.: Mass transfer mechanisms and rates of CO2 and N2 in 13X zeolite from volumetric frequency response. Ind. Eng. Chem. Res. 58(47), 21679–21690 (2019)

    CAS  Google Scholar 

  5. Onyestyák, G., Valyon, J., Rees, L.V.C.: A frequency-response study of diffusion and adsorption of C1– C5 alkanes and acetylene in zeolites. In: Unger, K.K., Kreysa, G., Baselt, J.P. (eds.) Studies in Surface Science and catalysis, vol. 128, pp. 587–592. Elsevier, Amsterdam (2000)

    Google Scholar 

  6. Rees, L.V.C., Shen, D.: Frequency-response measurements of diffusion of sorbates in zeolites. In: Derouane, E.G., Lemos, F., Naccache, C., Ribeiro, F.R. (eds.) Zeolite Microporous Solids: Synthesis, Structure, and Reactivity, pp. 151–166. Springer Netherlands, Dordrecht (1992)

    Google Scholar 

  7. Shen, D., Rees, L.V.C.: Diffusivities of benzene in HZSM-5, silicalite-I, and NaX determined by frequency-response techniques. Zeolites 11(7), 666–671 (1991)

    CAS  Google Scholar 

  8. Shen, D.M., Rees, L.V.C.: Frequency response technique measurements of p-xylene diffusion in silicalite-1 and-2. J. Chem. Soc. Faraday Trans. 89(7), 1063–1065 (1993)

    CAS  Google Scholar 

  9. Song, L., Rees, L.V.C.: Adsorption and diffusion of cyclic hydrocarbon in MFI-type zeolites studied by gravimetric and frequency-response techniques. Microporous Mesoporous Mater. 35–36, 301–314 (2000)

    Google Scholar 

  10. Van-Den-Begin, N.G., Rees, L.V.C.: Diffusion of hydrocarbons in silicalite using a frequency-response method. In: Jacobs, P.A., Santen, R.A.V. (eds.) Studies in Surface Science and Catalysis, vol. 49, pp. 915–924. Elsevier, Amsterdam (1989)

    Google Scholar 

  11. Yasuda, Y.: Detection of surface resistance in a gas/porous-adsorbent system by frequency response method. Bull. Chem. Soc. Jpn. 64(3), 954–961 (1991)

    CAS  Google Scholar 

  12. Yasuda, Y.: Frequency response method for investigation of various dynamic phenomena occurring simultaneously in a gas/zeolite system. In: Weitkamp, J., Karge, H.G., Pfeifer, H., Hölderich, W. (eds.) Zeolites and Related Microporous Malerials: Slaie of the Art, vol. 84, pp. 1331–1338. Elsevier, Amsterdam (1994)

    Google Scholar 

  13. Yasuda, Y., Sugasawa, G.: A frequency response technique to study zeolitic diffusion of gases. J. Catal. 88(2), 530–534 (1984)

    CAS  Google Scholar 

  14. Yasuda, Y., Yamamoto, A.: Zeolitic diffusivities of hydrocarbons by the frequency response method. J. Catal. 93(1), 176–181 (1985)

    CAS  Google Scholar 

  15. Giesy, T.J., LeVan, M.D.: Mass transfer rates of oxygen, nitrogen, and argon in carbon molecular sieves determined by pressure-swing frequency response. Chem. Eng. Sci. 90, 250–257 (2013)

    CAS  Google Scholar 

  16. Giesy, T.J., Wang, Y., LeVan, M.D.: Measurement of mass transfer rates in adsorbents: new combined-technique frequency response apparatus and application to CO2 in 13X zeolite. Ind. Eng. Chem. Res. 51(35), 11509–11517 (2012)

    CAS  Google Scholar 

  17. Onyestyák, G., Valyon, J., Hernádi, K., Kiricsi, I., Rees, L.V.C.: Equilibrium and dynamics of acetylene sorption in multiwalled carbon nanotubes. Carbon 41(6), 1241–1248 (2003)

    Google Scholar 

  18. Tovar, T.M., Mahle, J.J., Knox, C.K., LeVan, M.D.: 110th anniversary: molecular structure effects on mass transfer of C10 hydrocarbons in BPL activated carbon. Ind. Eng. Chem. Res. 58(33), 15271–15279 (2019)

    CAS  Google Scholar 

  19. Valyon, J., Ötvös, Z., Onyestyák, G., Rees, L.V.C.: The sorption dynamics of propane, i-butane and neopentane in carbon nanotubes. In: Llewellyn, P.L., Rodriquez-Reinoso, F., Rouqerol, J., Seaton, N. (eds.) Studies in Surface Science and Catalysis, vol. 160, pp. 439–446. Elsevier, Amsterdam (2007)

    Google Scholar 

  20. Wang, Y., Levan, M.D.: Nanopore diffusion rates for adsorption determined by pressure-swing and concentration-swing frequency response and comparison with Darken’s equation. Ind. Eng. Chem. Res. 47(9), 3121–3128 (2008)

    CAS  Google Scholar 

  21. Reyes, S.C., Sinfelt, J.H., DeMartin, G.J., Ernst, R.H., Iglesia, E.: Frequency modulation methods for diffusion and adsorption measurements in porous solids. J. Phys. Chem. B 101(4), 614–622 (1997)

    CAS  Google Scholar 

  22. Hossain, M.I., Glover, T.G.: Kinetics of water adsorption in UiO-66 MOF. Ind. Eng. Chem. Res. 58(24), 10550–10558 (2019)

    CAS  Google Scholar 

  23. Liu, J., Wang, Y., Benin, A.I., Jakubczak, P., Willis, R.R., LeVan, M.D.: CO2/H2O adsorption equilibrium and rates on metal-organic frameworks: HKUST-1 and Ni/DOBDC. Langmuir 26(17), 14301–14307 (2010)

    CAS  PubMed  Google Scholar 

  24. Wang, Y., Paur, C.S., Ravikovitch, P.I.: New development in flow-through pressure-swing frequency response method for mass-transfer study: ethane in ZIF-8. AlChE J. 63(3), 1077–1090 (2017)

    CAS  Google Scholar 

  25. Cavers, M., Davidson, J.M., Harkness, I.R., McDougall, G.S., Rees, L.V.C.: Novel frequency response techniques for the study of kinetics in heterogeneous catalysis. In: Froment, G.F., Waugh, K.C. (eds.) Studies in Surface Science and Catalysis, vol. 122, pp. 65–72. Elsevier, Amsterdam (1999)

    Google Scholar 

  26. Lai, J.L., Song, L.J., Liu, D.S., Qin, Y.C., Sun, Z.L.: A frequency response study of thiophene adsorption on HZSM-5. Appl. Surf. Sci. 257(8), 3187–3191 (2011)

    CAS  Google Scholar 

  27. Onyestyak, G., Valyona, J., Rees, L.V.C.: The skeletal isomerization of n-butene over ferrierite catalysts. Appl. Surf. Sci. 196, 401–407 (2002)

    CAS  Google Scholar 

  28. Qin, Y.C., Gao, X.H., Zhang, H.T., Zhang, S.H., Zheng, L.G., Li, Q., Mo, Z.S., Duan, L.H., Zhang, X.T., Song, L.J.: Measurements and distinguishment of mass transfer processes in fluid catalytic cracking catalyst particles by uptake and frequency response methods. Catal. Today 245, 147–154 (2015)

    CAS  Google Scholar 

  29. Rees, L.V.C., Onyestyak, G.: Frequency-response characterization of acid sites in zeolite catalysts using NH3 as the probe molecule. Microporous Mesoporous Mater. 28(2), 293–303 (1999)

    CAS  Google Scholar 

  30. Teixeira, A.R., Qi, X., Chang, C.C., Fan, W., Conner, W.C., Dauenhauer, P.J.: On asymmetric surface barriers in MFI zeolites revealed by frequency response. J. Phys. Chem. C 118(38), 22166–22180 (2014)

    CAS  Google Scholar 

  31. Naphtali, L.M., Polinski, L.M.: A novel technique for characterizations of adsorption rates on heterogeneous surfaces. J. Phys. Chem. 67(2), 369–375 (1963)

    CAS  Google Scholar 

  32. Yasuda, Y.: Frequency response method for study of the kinetic behavior of a gas-surface system. 2. An ethylene-on-zinc oxide system. J. Phys. Chem. 80(17), 1870–1875 (1976)

    CAS  Google Scholar 

  33. Yasuda, Y.: Determination of vapor diffusion coefficients in zeolite by the frequency response method. J. Phys. Chem. 66, 1913–1917 (1982)

    Google Scholar 

  34. Yasuda, Y.: Frequency response method for study of the kinetic details of a heterogeneous catalytic reaction of gases: 1. Theoretical treatment. J. Phys Chem. 97, 3314–3318 (1993)

    CAS  Google Scholar 

  35. Yasuda, Y., Matsumoto, A., Oda, R.: Reaction rate spectroscopy for a catalyzed reaction of gases. Bull. Chem. Soc. Jpn. 77, 1973–1986 (2004)

    CAS  Google Scholar 

  36. Yasuda, Y., Mizusawa, H., Kamimura, T.: Frequency response method for investigation of kinetic details of a heterogeneous catalyzed reaction of gases. J. Phys. Chem. B. 106, 6706–6712 (2002)

    CAS  Google Scholar 

  37. Yasuda, Y., Nomura, K.: Frequency response method for study of the kinetic details of a heterogeneous catalytic reaction of gases. 2. A methanol conversion to olefins. J. Phys Chem. 97, 3319–3323 (1993)

    CAS  Google Scholar 

  38. Yasuda, Y., Suzuki, Y., Fukada, H.: Kinetic details of a gas/porous adsorbent system by the frequency response method. J. Phys. Chem. 95(6), 2486–2492 (1991)

    CAS  Google Scholar 

  39. Jordi, R.G., Do, D.D.: Analysis of the frequency response method for sorption kinetics in bidispersed structured sorbents. Chem. Eng. Sci. 48(6), 1103–1130 (1993)

    CAS  Google Scholar 

  40. Jordi, R.G., Do, D.D.: Analysis of the frequency-response method applied to nonisothermal sorption studies. Chem. Eng. Sci. 49(7), 957–979 (1994)

    CAS  Google Scholar 

  41. Bourdin, V., Grenier, P., Meunier, F., Sun, L.M.: Thermal frequency response method for the study of mass-transfer kinetics in adsorbents. AlChE J. 42(3), 700–712 (1996)

    CAS  Google Scholar 

  42. Giermanska-Kahn, J., Cartigny, J., Cohen De Lara, E., Sun, L.M.: Heat effect and intercrystalline diffusion of light n-alkanes in zeolite NaX measured by frequency response method. Zeolites 17, 365–372 (1996)

    CAS  Google Scholar 

  43. Sun, L.M., Bourdin, V.: Measurement of intracrystalline diffusion by the frequency response method: analysis and interpretation of bi-modal response curves. Chem. Eng. Sci. 48, 3783–3793 (1993)

    CAS  Google Scholar 

  44. Sun, L.M., Bourdin, V., Grenier, P., Meunier, F.: Measurement of adsorption dynamics using the thermal frequency response method. In: LeVan, M.D. (ed.) Fundamentals of Adsorption, pp. 889–896. Kluwer Academic Publishers, Boston, Massachusetts (1996)

    Google Scholar 

  45. Sun, L.M., Do, D.D.: Frequency response analysis of a closed diffusion cell with two resonators. Adsorption 2(4), 265–277 (1996)

    CAS  Google Scholar 

  46. Sun, L.M., Meunier, F., Grenier, P., Ruthven, D.M.: Frequency-response for nonisothermal adsorption in biporous pellets. Chem. Eng. Sci. 49(3), 373–381 (1994)

    CAS  Google Scholar 

  47. Sun, L.M., Meunier, F., Karger, J.: On the heat effect in measurements of sorption kinetics by the frequency response method. Chem. Eng. Sci. 48(4), 715–722 (1993)

    CAS  Google Scholar 

  48. Shen, D.M., Rees, L.V.C.: Study of fast diffusion in zeolites using a higher harmonic frequency response method. J. Chem. Soc. Faraday Trans. 90, 3011–3015 (1994)

    CAS  Google Scholar 

  49. Shen, D.M., Rees, L.V.C.: Analysis of bimodal frequency-response behavious of p-xylene diffusion in silicalite-1. J. Chem. Soc. Faraday Trans. 91, 2027–2033 (1995)

    CAS  Google Scholar 

  50. Song, L.J., Rees, L.V.C.: Adsorption and transport of n-hexane in silicalite-1 by the frequency response technique. J. Chem. Soc. Faraday Trans. 93(4), 649–657 (1997)

    CAS  Google Scholar 

  51. Valyon, J., Onyestyak, G., Rees, L.V.C.: A frequency-response study of the diffusion and sorption dynamics of ammonia in zeolites. Langmuir 16(3), 1331–1336 (2000)

    CAS  Google Scholar 

  52. Rees, L.V.C., Shen, D.: Characterization of microporous sorbents by frequency-response methods. Gas Sep. Purif. 7(2), 83–89 (1993)

    CAS  Google Scholar 

  53. Bourdin, V., Germanus, A., Grenier, P., Karger, J.: Application of the thermal frequency response method and of pulsed field gradient NMR to study water diffusion in zeolite NaX. Adsorption 2(3), 205–216 (1996)

    CAS  Google Scholar 

  54. Bourdin, V., Sun, L.M., Grenier, P., Meunier, F.: Analysis of the temperature frequency response for diffusion in crystals and biporous pellets. Chem. Eng. Sci. 51(2), 269–280 (1996)

    CAS  Google Scholar 

  55. Hossain, M.I., Holland, C.E., Ebner, A.D., Ritter, J.A.: 110th anniversary: new volumetric frequency response system for determining mass transfer mechanisms in microporous adsorbents. Ind. Eng. Chem. Res. 58(37), 17462–17474 (2019)

    CAS  Google Scholar 

  56. Boniface, H.A., Ruthven, D.M.: Chromatographic adsorption with sinusoidal input. Chem. Eng. Sci. 40, 2053–2061 (1985)

    CAS  Google Scholar 

  57. Harkness, I.R., Cavers, M., McDougall, G.S.: Simultaneous determination of diffusion and adsorption properties of microporous sorbents under continuous flow conditions by frequency response methods: propane in silicalite-1. PCCP 5(20), 4708–4717 (2003)

    CAS  Google Scholar 

  58. Leder, F., Butt, J.B.: The dynamic behavior of a fixed-bed catalytic reactor. AlChE J. 12(6), 1057–1063 (1966)

    CAS  Google Scholar 

  59. Park, I.S.: Frequency response analysis of the constant molar flow semi-batch adsorption vessel containing core-shell composites. Korean J. Chem. Eng. 27(3), 955–961 (2010)

    CAS  Google Scholar 

  60. Park, I.S.: Frequency response of the adsorption vessel loaded with inert core adsorbents. Korean J. Chem. Eng. 22(6), 960–963 (2005)

    CAS  Google Scholar 

  61. Park, I.S., Kwak, C., Hwang, Y.G.: Frequency response of continuous-flow adsorber for multicomponent system. Korean J. Chem. Eng. 17(6), 704–711 (2000)

    CAS  Google Scholar 

  62. Sward, B.K., LeVan, M.D.: Frequency response method for measuring mass transfer rates in adsorbents via pressure perturbation. Adsorption 9(1), 37–54 (2003)

    CAS  Google Scholar 

  63. Wang, Y., LeVan, M.D.: Mixture diffusion in nanoporous adsorbents: development of Fickian flux relationship and concentration-swing frequency response method. Ind. Eng. Chem. Res. 46(7), 2141–2154 (2007)

    CAS  Google Scholar 

  64. Wang, Y., Sward, B.K., LeVan, M.D.: New frequency response method for measuring adsorption rates via pressure modulation: application to oxygen and nitrogen in a carbon molecular sieve. Ind. Eng. Chem. Res. 42(18), 4213–4222 (2003)

    CAS  Google Scholar 

  65. Glover, T.G., Wang, Y., Levan, M.D.: Diffusion of condensable vapors in single adsorbent particles measured via concentration-swing frequency response. Langmuir 24(23), 13406–13413 (2008)

    CAS  PubMed  Google Scholar 

  66. Wang, Y., Mahle, J.J., Furtado, A.M.B., Glover, T.G., Buchanan, J.H., Peterson, G.W., LeVan, M.D.: Mass transfer and adsorption equilibrium for low volatility alkanes in BPL activated carbon. Langmuir 29(9), 2935–2945 (2013)

    CAS  PubMed  Google Scholar 

  67. Deisler, P.F., Wilhelm, R.H.: Diffusion in beds of porous solids: measurement by frequency response techniques. Ind. Eng. Chem. 45(6), 1219–1227 (1953)

    CAS  Google Scholar 

  68. Giesy, T.J., LeVan, M.D.: Contributions to frequency response models for mass transfer in adsorbents. Chem. Eng. Sci. 116, 745–751 (2014)

    CAS  Google Scholar 

  69. Wang, Y., LeVan, M.D.: Master curves for mass transfer in bidisperse adsorbents for pressure-swing and volume-swing frequency response methods. AlChE J. 57(8), 2054–2069 (2011)

    CAS  Google Scholar 

  70. Onyestyak, G., Rees, L.V.C.: Frequency response study of adsorbate mobilities of different character in various commercial adsorbents. J. Phys. Chem. B 103(35), 7469–7479 (1999)

    CAS  Google Scholar 

  71. Yasuda, Y.: Frequency response method for study of the kinetic behavior of a gas-surface system 1 Theoretical treatment. J. Phys. Chem. 80(17), 1867–1869 (1976)

    CAS  Google Scholar 

  72. Giesy, T.J., Mitchell, L.A., LeVan, M.D.: Mass transfer of binary mixtures of oxygen and argon in a carbon molecular sieve. Ind. Eng. Chem. Res. 53(22), 9221–9227 (2014)

    CAS  Google Scholar 

  73. Shen, D.M., Bulow, M., Lemcoff, N.O.: Mechanisms of molecular mobility of oxygen and nitrogen in carbon molecular sieves. Adsorption 9(4), 295–302 (2003)

    CAS  Google Scholar 

  74. Yasuda, Y.: Frequency response method for investigation of gas/surface dynamic phenomena. Heterogen. Chem. Rev. 1, 3–24 (1994)

    Google Scholar 

  75. Song, L., Rees, L.V.C.: Frequency response measurements of diffusion in microporous materials. In: Karge, H.G., Weitkamp, J. (eds.) Adsorption and Diffusion, pp. 235–276. Springer, Berlin, Heidelberg (2008)

    Google Scholar 

  76. Reyes, S.C., Iglesia, E.: Frequency response techniques for the characterization of porous catalytic solids. In: Spivey, J.J., Agarwal, S.K. (eds.) Catalysis, vol. 11, pp. 51–92. The Royal Society of Chemistry, Cambridge (1994)

    Google Scholar 

  77. Bourdin, V., Gray, P.G., Grenier, P., Terrier, M.F.: An apparatus for adsorption dynamics studies using infrared measurement of the adsorbent temperature. Rev. Sci. Instrum. 69(5), 2130–2136 (1998)

    CAS  Google Scholar 

  78. Kramers, H., Alberda, G.: Frequency response analysis of continuous flow systems. Chem. Eng. Sci. 2, 173–181 (1953)

    CAS  Google Scholar 

  79. Tovar, T.M., Zhao, J., Nunn, W.T., Barton, H.F., Peterson, G.W., Parsons, G.N., LeVan, M.D.: Diffusion of CO2 in large crystals of Cu-BTC MOF. J. Am. Chem. Soc. 138(36), 11449–11452 (2016)

    CAS  PubMed  Google Scholar 

  80. Ruthven, D.M., Kärger, J., Brandani, S., Mangano, E.: Sorption kinetics: measurement of surface resistance. Adsorption (2020). https://doi.org/10.1007/s10450-020-00257-w

    Article  Google Scholar 

  81. Sun, L.M., Zhong, G.M., Gray, P.G., Meunier, F.: Frequency-response analysis for multicomponent diffusion in adsorbents. J. Chem. Soc. Faraday Trans. 90(2), 369–376 (1994)

    CAS  Google Scholar 

  82. Chmelik, C., Kärger, J.: The predictive power of classical transition state theory revealed in diffusion studies with MOF ZIF-8. Microporous Mesoporous Mater. 225, 128–132 (2016)

    CAS  Google Scholar 

  83. Zhang, C., Lively, R.P., Zhang, K., Johnson, J.R., Karvan, O., Koros, W.J.: Unexpected molecular sieving properties of zeolitic imidazolate framework-8. J. Phys. Chem. Lett. 3, 2130–2134 (2012)

    CAS  PubMed  Google Scholar 

  84. Krokidas, P., Castier, M., Moncho, S., Brothers, E., Economou, I.G.: Molecular simulation studies of the diffusion of methane, ethane, propane, and propylene in ZIF-8. J. Phys. Chem. C 119(48), 27028–27037 (2015)

    CAS  Google Scholar 

  85. Bülow, M., Schlodder, H., Rees, L.V.C., Richards, R.E.: Molecular mobility of hydrocarbon ZSM5/silicalite systems studied by sorption uptake and frequency response methods. In: Murakami, Y., Iijima, A., Ward, J.W. (eds.) Studies in Surface Science and Catalysis, vol. 28, pp. 579–586. Elsevier, Amsterdam (1986)

    Google Scholar 

  86. Caro, J., Hǒcevar, S., Kärger, J., Riekert, L.: Intracrystalline self-diffusion of H2O and CH4 in ZSM-5 zeolites. Zeolites 6(3), 213–216 (1986)

    CAS  Google Scholar 

  87. Talu, O., Sun, M.S., Shah, D.B.: Diffusivities of n-alkanes in silicalite by steady-state single-crystal membrane technique. AlChE J. 44(3), 681–694 (1998)

    CAS  Google Scholar 

  88. Shen, D., Rees, L.V.C.: Diffusion of benzene, p-xylene and their mixture in silicalite-1 using a frequency response technique. In: von Ballmoos, R., Higgins, J.B., Treacy, M.M.J. (eds.) Proceedings from the ninth international zeolite conference. pp. 45–54. (1993a)

  89. Shen, D.M., Rees, L.V.C.: Adsorption and diffusion of n-butane and 2-butane in silicalite-1. Zeolites 11(7), 684–689 (1991)

    Google Scholar 

  90. Song, L.J., Sun, Z.L., Rees, L.V.C.: Experimental and molecular simulation studies of adsorption and diffusion of cyclic hydrocarbons in silicalite-1. Microporous Mesoporous Mater. 55(1), 31–49 (2002)

    CAS  Google Scholar 

  91. Wang, Y.: Combined heat transfer and surface barrier resistances for propane in commercial ZIF-8 crystals by pressure-swing frequency response. In preparation. (2021)

  92. Yasuda, Y., Matsumoto, K.: Straight-and cross-term diffusion coefficients of a two-component mixture in micropores of zeolites by frequency response method. J. Phys. Chem. 93, 3195–3200 (1989)

    CAS  Google Scholar 

  93. Yasuda, Y., Yamada, Y., Matsuura, I.: Zeolitic diffusivities of binary gas mixtures by the frequency response method. In: Murakami, A.I.Y., Ward, J.W. (eds.) Studies in Surface Science and Catalysis, vol. 28, pp. 587–594. Elsevier, Amsterdam (1986)

    Google Scholar 

  94. Wang, Y., LeVan, M.D.: Investigation of mixture diffusion in nanoporous adsorbents via the pressure-swing frequency response method. 2. Oxygen and nitrogen in a carbon molecular sieve. Ind. Eng. Chem. Res. 44(13), 4745–4752 (2005)

    CAS  Google Scholar 

  95. Chen, Y.D., Yang, R.T.: Predicting binary Fickian diffusivities from pure-component Fickian diffusivities for surface diffusion. Chem. Eng. Sci. 47(15), 3895–3905 (1992)

    CAS  Google Scholar 

  96. Wang, Y., LeVan, M.D.: Investigation of mixture diffusion in nanoporous adsorbents via the pressure-swing frequency response method. 1. Theoretical treatment. Ind. Eng. Chem. Res. 44(10), 3692–3701 (2005)

    CAS  Google Scholar 

  97. Petkovska, M.: Nonlinear frequency response of isothermal adsorption controlled by pore-surface diffusion. Bull. Chem. Technol. Maced. 18(2), 149–160 (1999)

    CAS  Google Scholar 

  98. Petkovska, M.: Non-linear frequency response of non-isothermal adsorption controlled by micropore diffusion with variable diffusivity. J. Serb. Chem. Soc. 65(12), 939–961 (2000)

    CAS  Google Scholar 

  99. Petkovska, M.: Nonlinear frequency response method for investigation of equilibria and kinetics of adsorption systems. Surfactant Sci. Ser. 130, 283–327 (2006)

    CAS  Google Scholar 

  100. Petkovska, M., Petkovska, L.T.: Use of nonlinear frequency response for discriminating adsorption kinetics mechanisms resulting with bimodal characteristic functions. Adsorption 9(2), 133–142 (2003)

    CAS  Google Scholar 

  101. Brzić, D., Petkovska, M.: Nonlinear frequency response measurements of gas adsorption equilibrium and kinetics: new apparatus and experimental verification. Chem. Eng. Sci. 132, 9–21 (2015)

    Google Scholar 

  102. Brzić, D., Petkovska, M.: Nonlinear frequency response analysis as a tool for identification of adsorption kinetics: case study—pore-surface diffusion control. Math. Probl. Eng. (2019). https://doi.org/10.1155/2019/7932967

    Article  Google Scholar 

  103. Marcelin, G., Lester, J.E.: Effect of supports on the energetics of carbon monoxide chemisorption on Rhodium catalysts. React. Kinet. Catal. Lett. 28(2), 281–286 (1985)

    CAS  Google Scholar 

  104. Schrieffer, J.R., Sinfelt, J.H.: Frequency response analysis of surface reactions in flow systems. J. Phys. Chem. 94(3), 1047–1050 (1990)

    CAS  Google Scholar 

  105. Yasuda, Y.: Frequency response method for the study of kinetics of a heterogeneous catalytic reaction of gases. J. Phys. Chem. 93, 7185–7190 (1989)

    CAS  Google Scholar 

Download references

Acknowledgements

The author thanks Ned Corcoran and Ben McCool for providing valuable suggestions and support for the work.

Author information

Authors and Affiliations

  1. Corporate Strategic Research, ExxonMobil Research and Engineering, 1545 Route 22 East, Annandale, NJ, 08801, USA

    Yu Wang

Authors
  1. Yu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu Wang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y. Identification of mass transfer resistances in microporous materials using frequency response methods. Adsorption 27, 369–395 (2021). https://doi.org/10.1007/s10450-021-00305-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10450-021-00305-z

Keywords

Search

Navigation