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Isotropic and anisotropic properties of adsorption-induced deformation of porous carbon materials

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Abstract

In the present work, the issues of isotropic/anisotropic character of adsorption-induced deformation of carbon adsorbents were addressed. A simple model of microporous zones of carbon adsorbents was developed in terms of their structure determined by a raw material and activation conditions. The model made it possible to evaluate the number of micropores (~ 1020 g−1) and the number of microporous nanocrystals with micropores (denoted as an elementary microporous zone, EMZ) ~ 1011 g−1 for four carbon adsorbents differing in raw material and activation conditions. The equiprobable orientation of the EMZ in activated carbons nullifies the influence of the anisotropic structure of nanocrystallites on the changes in macroscopic dimensions of the adsorbents stimulated by adsorption. The assumption was confirmed by the dilatometry measurements of the CO2 adsorption-induced deformation for the commercial activated carbon Sorbonorit-4 granules, which were deposited parallel and perpendicular to the vertical axis of the dilatometer. The adsorption-induced strain isotherms did not depend on the orientation of the Sorbonorit-4 granules and exhibited the non-monotonic character. The initial contraction of the adsorbent was followed by its expansion with increasing pore filling. The contraction–expansion transition, as well as the contraction magnitude, were found to be temperature-dependent within the temperature range from 216.6 to 393 K. The compressibility and triaxial compression modulus of Sorbonorit-4 were evaluated over the temperature range from 216.6 to 293 K. The temperature dependences of both parameters were approximated by exponential functions. The triaxial compression modulus of Sorbonorit-4 decreased from 42 to 10 GPa and the compressibility increased by five times with a rise in temperature from 216.6 to 293 K.

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Abbreviations

AUK:

: Carbon adsorbent

AR-V:

: Carbon adsorbent

BET:

: Brunauer–Emmett–Teller method

D-R:

: Dubinin–Radushkevich equation

EDX:

: Energy dispersive X-ray

EMZ:

: Elementary microporous zone

NLDFT:

: Non-local density functional theory

PSA:

: Pressure swing adsorption

PSD:

: Particle size distribution

QSDFT:

: Quenched solid density functional theory

SAXS:

: Small-angle X-ray scattering

SEM:

: Scanning electron microscopy

TCLE:

: Temperature coefficient of linear expansion

TVFM:

: Theory of volume filling of micropores

a :

Adsorption of carbon dioxide (mmol g−1)

E 0 :

Characteristic adsorption energy of standard steam in terms of benzene (kJ mol−1)

H S :

Half-width of micropore in the slit-like pore model (nm)

I :

Intensity of scattered X-rays (a.u.)

K 0 :

Empirical coefficient (kJ⋅nm mol−1)

K a :

Triaxial compression modulus (GPa)

l :

Size of an elementary microporous zone (nm)

l nc :

Side of the nanocrystallite (nm)

L o :

Initial length of the adsorbent (mm)

L :

Length of the adsorbent, taking into account the deformation, depending on the amount of adsorption (mm)

N :

Number of EMZ per adsorbent mass unit (g−1)

p :

Internal pressure of the adsorbate in the pores (MPa)

P :

Pressure (MPa)

P s :

Saturated steam pressure (MPa)

P kin :

Kinetic pressure in a liquid (MPa)

q :

Scattering vector (nm−1)

r :

Average radius of the carbon wall of the micropore (nm)

R G :

Radius of gyration (nm)

R S :

Radius of micropore in the spherical pore model (nm)

R T :

Radius of micropore in the cylindrical pore model (nm)

S me :

Specific surface of mesopores (cm2 g−1)

S mi :

Surface of intercrystalline micropores (cm2 g−1)

S BET :

Specific surface area of the adsorbent determined by BET method (cm2 g−1)

T :

Temperature (K)

T cr :

Critical temperature of carbon dioxide (K)

u c(η):

Measurement uncertainty for the relative linear deformation of the adsorbent (%)

U(η):

Extended uncertainty (%)

V 0 :

Specific reduced volume of regenerated adsorbent with micropores (cm3 g−1)

V a :

Volume of the adsorbent, taking into account the deformation, depending on the amount of adsorption (cm3 g−1)

V :

Specific volume of liquid (cm3 g−1)

V me :

Specific volume of mesopores (cm3 g−1)

V mz :

Specific volume of microporous zones (cm3 g−1)

V c :

Specific volume of the nonporous adsorbent skeleton (cm3 g−1)

V mi :

Specific volume of micropores (cm3 g−1)

V S :

Total pore volume obtained from the low temperature nitrogen adsorption at the relative pressure P/Ps = 0.99 (cm3 g−1)

x :

Half-width of the micropore (nm)

X me :

Half-width of slits (mesopores) formed by the neighbouring EMZ cubes

Z :

Total number of micropores per adsorbent mass unit (g−1)

z :

Number of micropores in EMZ (g−1)

α :

Number of sides of the EMZ cubes involved in the formation of the mesopore

γ a :

Adsorbent compressibility (bar−1)

η:

Relative linear deformation (%)

θ :

Scattering angle of X-rays relative to the incident beam

λ :

Wavelength of X-ray monochromatic radiation (nm)

ρ c :

Density of the adsorbent skeleton (g cm−3)

ω :

Volume of one micropore (nm3)

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Acknowledgements

The experiments were carried out with the use of equipment of the Center of Physical Methods of Investigations of the A.N. Frumkin Institute of Physical Chemistry and Electrochemistry of Russian Academy of Sciences. We thank A.A. Shiryaev and V.V. Vysotskii for their help in the SAXS and SEM experiments and constructive suggestions.

Funding

The research was carried out within the State Assignment of the Russian Federation (Project No. 0081-2019-0018).

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Authors and Affiliations

  1. A. N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Leninsky Prospect, 31, Bld. 4, Moscow, Russian Federation, 119071

    A. V. Shkolin, I. E. Men’shchikov, E. V. Khozina, V. Yu. Yakovlev & A. A. Fomkin

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  1. A. V. Shkolin
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  2. I. E. Men’shchikov
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  3. E. V. Khozina
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  4. V. Yu. Yakovlev
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Contributions

Conceptualization: AAF, AVS; methodology, AVS, AAF; software, IEM, VYuY.; validation, AAF, AVS; formal analysis, IES; investigation, IEM, AVS; resources AVS; data curation: AVS, EVK; writing—original draft preparation: AVS, IEM, AAF; writing—review and editing, EVK, VYuY; visualization: AVS, IEM, EVK; supervision, AAF; project administration, AAF, IEM, funding acquisition: AAF. All authors have read and agreed to the published version of the manuscript.

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Correspondence to A. V. Shkolin.

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The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

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Shkolin, A.V., Men’shchikov, I.E., Khozina, E.V. et al. Isotropic and anisotropic properties of adsorption-induced deformation of porous carbon materials. Adsorption 29, 237–253 (2023). https://doi.org/10.1007/s10450-022-00370-y

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