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Dynamic column breakthrough experiments for measurement of adsorption equilibrium and kinetics

• Published: 30 September 2020
• Volume 27 , pages 397–422, ( 2021 )

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• Nicholas Stiles Wilkins 1 ,
• Arvind Rajendran 1 &
• Shamsuzzaman Farooq   ORCID: orcid.org/0000-0002-6501-5540 2  

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This paper provides a set of comprehensive guidelines for the use of dynamic column breakthrough experiments to measure single and multi-component equilibria and kinetics. Recommendations are made for the design of the experimental rig, experimental procedures, and data processing methods to minimize errors and increase data reliability. Designing experiments to identify the transport mechanism, and quantitatively interpreting the breakthrough responses via modeling and optimization are also enumerated. Results reported in relevant published literature are also used to illustrate the ideas and concepts.

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The zero length column technique to measure adsorption equilibrium and kinetics: lessons learnt from 30 years of experience

Integrated uncertainty quantification and sensitivity analysis of single-component dynamic column breakthrough experiments

Equilibrium loadings and adsorption isotherm model parameters estimated from multi-component breakthrough curves

Abbreviations.

Cross-sectional area (m 2 )

Fluid concentration (mol/m 3 )

Heat capacity (J/mol/K)

Diameter (m)

Diffusivity (m 2 /s)

Convective heat transfer coefficient (W/m 2 /K)

Heat of adsorption (J/mol)

LDF coefficient (s −1 )

Henry’s constant (–) or thermal conductivity (W/m/K)

Molecular mass (g/mol)

Nusselt number (–)

Total pressure (Pa)

Peclet number (–)

Solid-phase loading (mol/m 3 )

Solid-phase equilibrium loading (mol/m 3 )

Standard flow (SLPM)

Radius or micropore position (m)

Macropore position (m)

Reynolds number (–)

Universal gas constant (Pa m 3 /mol/K)

Schmidt number (–)

Sherwood number (–)

Mean residence time (s)

Temperature (K)

Interstitial velocity (m/s)

Mole fraction (–)

Axial position (m)

Velocity distribution or \(\frac{\left(1-{\varepsilon }_{\mathrm{p}}\right){K}_{\mathrm{c}}}{{\varepsilon }_{\mathrm{p}}}\) in Fig.  11

Defined by Eq.  21

Void fraction

\(\frac{{D}_{\mathrm{c}}L}{{r}_{\mathrm{c}}^{2}{v}_{\mathrm{in}}}\)

Collision integral

Pore or viscosity

Collision diameter

Barrier or blank response

Column, crystal or micropore

Outer column

Corrected response

Inner column

Effective parallel Knudsen and surface contribution

Experimental

Index or component

Initial state of column

Inlet or initial

At zero flow

Outlet or outer

Surface or solid

True response

Effective value in the axial direction

Initial or limiting

Back-pressure regulator

Breakthrough curve

Carbon molecular sieve

Constant volume (volumetry)

• Dynamic column breakthrough

Engelhard titanosilicate

Linear driving force

Mass flow controller

Mass flow meter

Metal–organic framework

Mass spectrometer

Needle valve

Point-by-point correction

Pressure indicator

Pressure swing adsorption

Standard liters per minute

Temperature indicator

Tank in series correction

Zero-length column

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Wilkins, N.S., Rajendran, A. & Farooq, S. Dynamic column breakthrough experiments for measurement of adsorption equilibrium and kinetics. Adsorption 27 , 397–422 (2021). https://doi.org/10.1007/s10450-020-00269-6

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Received : 04 June 2020

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Published : 30 September 2020

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DOI : https://doi.org/10.1007/s10450-020-00269-6

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Effects of Structure and Composition of Adsorbents on Competitive Adsorption of Gaseous Emissions: Experiment and Modeling

Adam verner, jonáš tokarský, tomáš najser, lenka matějová, kateřina mamulová kutláková, václav peer.

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Correspondence: [email protected]

Received 2023 Jan 31; Revised 2023 Feb 9; Accepted 2023 Feb 11; Collection date 2023 Feb.

Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( https://creativecommons.org/licenses/by/4.0/ ).

Dangerous gases arising from combustion processes must be removed from the air simply and cheaply, e.g., by adsorption. This work is focused on competitive adsorption experiments and force field-based molecular modeling of the interactions at the molecular level. Emission gas, containing CO, NO, SO 2 , and CO 2 , was adsorbed on activated carbon, clay mineral, silicon dioxide, cellulose, or polypropylene at two different temperatures. At 20 °C, activated carbon had the highest NO and SO 2 adsorption capacity (120.83 and 3549.61 μg/g, respectively). At 110 °C, the highest NO and SO 2 adsorption capacity (6.20 and 1182.46 μg/g, respectively) was observed for clay. CO was adsorbed very weakly, CO 2 not at all. SO 2 was adsorbed better than NO, which correlated with modeling results showing positive influence of carboxyl and hydroxyl functional groups on the adsorption. In addition to the wide range of adsorbents, the main novelty of this study is the modeling strategy enabling the simulation of surfaces with pores of controllable sizes and shapes, and the agreement of the results achieved by this strategy with the results obtained by more computationally demanding methods. Moreover, the agreement with experimental data shows the modeling strategy to be a valuable tool for further adsorption studies.

Keywords: gaseous emission, competitive adsorption, molecular modeling, morphology, adsorbent structure

1. Introduction

In recent years, more than ever before, the importance of monitoring the evolution of the amount of pollutants in the environment has increased [ 1 ]. People and nature in general need optimal conditions for their efficient functioning, which is related to the reduction of destructive factors and the increase of constructive factors in the environment. Manufacturing industry is accompanied by the disruption of natural resources during the acquisition of input materials, a number of chemical reactions or energy processes during production, and last but not least, the disposal of waste, i.e., unused or unusable products. The main sources of pollution include the manufacturing and processing industry [ 2 ] as well as the energy industry [ 3 ] and transportation [ 4 ], with which the increasing production of specifically air pollutants is connected.

Despite the fact that thermochemical conversion is beginning to be replaced by the use of renewable resources worldwide, the combustion process of various materials (coal, gas, heating oils, wood, biomass, etc.) still contributes significantly to air pollution [ 5 , 6 ]. Even with the effective use of plant waste [ 7 , 8 ], it is still challenging to monitor and reduce the risks related to the production of arising pollutants. While solid pollutants consist primarily of particulate matter of various grain sizes and NH 3 , gaseous pollutants mainly include CO 2 , CO, SO 2 , nitrogen oxides (NO x ) [ 9 , 10 ], volatile organic compounds and polycyclic aromatic hydrocarbons [ 6 , 10 ]. Solid particles released during the combustion process can be easily captured by various types of solid or liquid filter systems. However, the removal of emission gases from the air is generally more complex, due to the gaseous state of the pollutants, the required chemical selectivity, etc. The most studied is CO 2 removal from the air [ 11 ]. Absorption of CO 2 in gas-liquid systems with methanol, poly-(ethylene glycol) dimethyl ether [ 12 ] or amine solutions [ 13 ] as absorbing phases was investigated. However, adsorption methods in gas-solid systems, i.e., weaker physisorption or stronger chemisorption [ 11 , 14 , 15 ], are used more often. The most effective adsorption materials for CO 2 include activated carbons [ 16 , 17 ], zeolites [ 18 ], porous oxides (e.g., calcium oxides [ 19 ] or silica gel [ 20 ]), hydrotalcites [ 21 ], amines [ 22 ] or metal-organic frameworks [ 11 , 23 , 24 ].

On the other hand, the adsorption mechanisms and suitable adsorbents of NO x , CO, and SO 2 have been considerably less investigated. Research on CO and NO adsorption using Pd catalysts [ 25 ], possibly Au alloys [ 26 ] or various modifications of activated carbon [ 27 ] should be mentioned. In the case of SO 2 and NO, adsorption mechanisms on modified activated carbon [ 27 , 28 ] and bimetallic surfaces containing noble and transition metals [ 29 ] were investigated. Zeolites are also efficient adsorbents of CO 2 , SO 2 , and NO [ 30 ].

Research works mostly deal with specific adsorption materials for a specific gas, but materials in various forms sorbing several types of emission gases at the same time by the mechanism of competitive adsorption have not yet been sufficiently investigated. There is also a lack of research on interactions at the molecular level during the competitive adsorption of emission gases. Therefore, in this work, the process of competitive adsorption of emission gases on different materials with different physical and chemical properties was studied both experimentally and via force field-based molecular modeling. Activated carbon is extensively researched and modeled in connection with adsorption [ 31 , 32 , 33 , 34 ]. Therefore, it was used for comparing the obtained data and verifying the modeling strategy. Adsorbent materials whose potential in the field of competitive adsorption of emission gases has not yet been established were used, and adsorption capacities were determined. Unlike DTF modeling methods that are usually used, the modeling strategy introduced here enabled the creation of larger models with pores of precisely controllable sizes and shapes. The influence of chemical and structural factors on competitive adsorption was clarified, which can be used further in research on other materials or as a prediction tool of adsorption.

2. Materials and Methods

2.1. materials.

Adsorption experiments were carried out using a special emission gas (EG) having concentrations of emission components similar to the real concentrations produced during the combustion of various alternative fuels, such as biomass, sewage sludge, etc. [ 35 ]. The EG consisted of 197.3 vol. ppm NO (199.9 w / w ppm), 197.3 vol. ppm SO 2 (426.8 w / w ppm), 395 vol. ppm CO (373.6 w / w ppm), and 9.96 vol. % CO 2 (14.80 w / w %) in nitrogen (SIAD Czech s.r.o., Ostrava, Czech Republic). In addition, the nitrogen was also used to purge the adsorption path.

The following materials commonly used in hazardous chemical spill incidents were used as adsorbents in this study: activated carbon (AC; MA C6 D40 CZ, Resorbent, s.r.o., Ostrava, Czech Republic), clay (CL; Bentonite Puranit, LIPERA s.r.o., Velke Bilovice, Czech Republic), and (from REO AMOS s.r.o., Ostrava, Czech Republic) silicon dioxide (SiO 2 ), cellulose (CEL) and polypropylene (PP).

2.2. Characterization of Samples

A photoelectron spectrometer with a hemispherical VG SCIENTA R3000 analyzer (Prevac, Rogów, Poland) was used for XPS analysis of AC. The photoelectron spectra were recorded using a monochromatized aluminum Al Kα source ( E = 1486.6 eV) and a low-energy electron flood gun (FS40A-PS). The base pressure in the analysis chamber was 5·10 −9 mbar. Spectra were recorded with a constant pass energy of 100 eV for the survey and high-resolution spectra. The binding energy scale was calibrated using the Au 4f7/2 line of a cleaned gold sample at 84.0 eV. The composition and chemical surrounding of the sample surface were investigated on the basis of the areas and binding energies of O 1s and C 1s photoelectron peaks. The fitting of high-resolution spectra was performed using CasaXPS software.

The moisture content of the samples was determined by Kern ABT 320-4NM (Kern & Sohn GmbH, Balingen, Germany). Particle density was determined by measuring the volume of the sample in water and the weight with MA 110.R laboratory scale (RADWAG Váhy s.r.o., Šumperk, Czech Republic). Atmospheric pressure and pressure in the adsorption system were measured with GPB 3300 (GHM-Greisinger s.r.o., Regenstauf, Germany) and Kimo MP 210 (Kimo Instruments, Mumbai, India), respectively. The concentration of NO, SO 2 and CO was measured by the infrared spectrometer PG-350 (Horiba, Palaiseau, France). Nitrogen physisorption at 77 K was measured using 3Flex apparatus (Micromeritics, Norcross, CA, USA). Prior to physisorption analysis, each material was degassed under pressure of 0.6 bar and temperature of 350 °C. This step was done for all materials to release physisorbed moisture. After such pre-treatment, the nitrogen adsorption–desorption isotherms at 77 K of all materials were measured for the relative pressure range p / p 0 ~1 × 10 −7 –0.99. Nitrogen adsorption–desorption data were processed using BET theory, the t-plot method and the BJH method applied on the adsorption branch of the nitrogen adsorption–desorption isotherm, by using either the Carbon Black STSA standard isotherm (for carbonaceous materials) or Broekhoff-De Boer standard isotherm (for inorganic materials). The slit or cylindrical-pore geometry of mesopores and macropores characterized by pore width or diameter, respectively, were assumed. From measured data, it was possible to reliably obtain the specific surface area, S BET (m 2 /g), the mesopore–macropore surface area, S meso (m 2 /g), the micropore volume, V micro (mmliq 3 /g) and mesopore–macropore size distribution characterized by the pore width or diameter. The net pore volume, V net (mm 3 liq/g), was evaluated from the adsorbed amount of nitrogen at p / p 0 ~0.99. The micropore size distribution was evaluated from the adsorbed amount of nitrogen at p / p 0 ~1 × 10 −7 –0.05 using the Horwath–Kawazoe solution and assuming the slit-pore geometry for both carbonaceous and inorganic materials.

X-ray powder diffraction (XRPD) patterns were recorded under Co Kα irradiation ( λ = 0.1789 nm, U = 35 kV, I = 25 mA) using the Bruker D8 Advance diffractometer (Bruker AXS, Karlsruhe, Germany) equipped with a fast position sensitive detector VÅNTEC 1. Measurements were carried out in the reflection mode, powder samples were pressed in a rotational holder, and a goniometer was used with the Bragg–Brentano geometry in 2θ range from 3 to 80°, step size 0.03°. The phase composition was evaluated using database PDF 2 Release 2020 (International Centre for Diffraction Data).

2.3. Sample Preparation

The powder samples (AC, CL, SiO 2 ) were crushed and sieved into three granulometric fractions—0.16–0.315 mm, 0.315–0.63 mm, 0.63–1.00 mm ( Table 1 )—to ensure laminar flow in the adsorption chamber (Ad) whose inner tube diameter was 10 mm. CEL and PP were used in their original form, i.e., pellets and nonwoven, respectively. Each type of sample was used in its wet and dried state. The samples were dried in a drying oven Binder FP 400.

Basic information about the adsorbing materials used, such as particle density and material humidity, and its forms and labeling.

AC—activated carbon, CL—clay, SiO 2 —silicon dioxide, CEL—cellulose, PP—polypropylene.

Particle density and humidity of the adsorbents were determined, and the samples were labeled according to the granulometric fraction ( Table 1 ).

2.4. Adsorption System

The adsorption experiments took place in a closed system consisting of PTFE hoses, stainless steel fittings, the stainless steel Ad and analytical instruments ( Figure 1 ). The Ad was a stainless steel tube with an inner diameter of 10 mm. A volume of 3 cm 3 was calculated from the volume of the catalyst V cat according to the formula:

where Q V is volumetric gas flow rate per hour (0.5 L/min = 30,000 cm 3 /h) and GHSV is gas hourly space velocity (10,000 h −1 ) [ 36 ].

Diagram of adsorption apparatus with fittings. EG—emission gas, N 2 —nitrogen, P—pressure gauge, Ad—adsorption chamber, An—analyzer, OUT—overflow branch.

The gas traveled from the gas cylinders (EG—emission gas, N 2 —nitrogen) through the pressure gauge (P) and the adsorbent (Ad) to the analyzer (An) at a speed of 0.5 L/min (analyzer parameter). The rest was discharged through the overflow branch (OUT) ( Figure 1 ).

First, the entire adsorption apparatus was filled with nitrogen (including the Ad branch). Subsequently, the source gas was switched from N 2 to EG through the branch without Ad. The measurement of the concentration of emission components with the analyzer was switched on. As soon as the concentration values stabilized, thereby determining the actual concentrations of gaseous components in EG, the gas path was switched to the Ad branch, where adsorption took place. The measurement was terminated after the initial concentration was again reached (the actual concentration in the EG bottle). The measurement took place at 20 °C (with wet adsorbents) and 110 °C (with dried adsorbents and Ad in the drying oven Binder FP 400 (Binder GMBh, Tuttlingen, Germany). Each sample was measured three times and the results were averaged.

The total amount of each adsorbed gaseous component was obtained by integrating the area between the adsorption curve and the original concentration value of the given emission component, and using the ideal gas equation (where the amount of substance n is expressed as m / M ) for expressed mass m of the adsorbed gas component:

where p (Pa) is pressure in the adsorption system, V (dm 3 ) is volume of the adsorbent, M (g·mol −1 ) is molar mass of the gaseous component, R (J·K −1 ·mol −1 ) is the gas constant, and T (K) is temperature in the adsorption system [ 37 ].

Adsorbed mass m was related to one gram of wet or dried adsorbent expressed in μg/g.

2.5. Atomistic Models and Modeling Strategy

Building of the initial models of EG molecule and adsorbent surface, geometry optimizations, molecular dynamics, and energy calculations were carried out in Biovia Materials Studio 7.0 (MS) modeling environment [ 38 ]. Triclinic unit cells of CEL (a = 8.549 Å, b = 9.568 Å, c = 10.000 Å, α = 102.10°, β = 106.54°, γ = 55.46°), and PP (a = 8.348 Å, b = 13.505 Å, c = 10.000 Å, α = 75.68°, β = 39.54°, γ = 61.01°), both containing two polymer chains, were created according to Chen et al. [ 39 ] and Verenich et al. [ 40 ], respectively ( Figure 2 ).

XRPD diffractogram proving the crystalline phase in ( a ) CEL and ( b ) PP. ( c ) Determination of clay phases in clay material. CEL—cellulose, PP—polypropylene.

AC orthorhombic unit cell (a = b = 2.460 Å, c = 6.670 Å, α = β = 90°, γ = 120°) was prepared according to Wyckoff [ 41 ]. SiO 2 trigonal (a = b = 4.913 Å, α = β = 90°, γ = 95.18°) and MUS monoclinic unit cells (a = 5.194 Å, b = 8.996 Å, c = 20.096 Å, α = β = 90°, γ = 120°, layer thickness ~6.7 Å, interlayer distance ~3.3 Å) were imported from the MS database. Substitutions and interlayer cations were added to MUS so that MUS and NON unit cells met the chemical formulas ( K 0.86 N a 0.10 ) ( A l 1.90 F e 0.05 2 + M g 0.06 F e 0.02 3 + T i 0.01 ) ( S i 3.02 A l 0.98 ) O 10 ( O H ) 1.99 F 0.01 and ( C a 1.50 N a 0.5 ) ( F e 1.84 3 + A l 0.15 M g 0.02 □ 0.99 ) ( S i 3.46 A l 0.38 F e 0.16 3 + ) O 10 ( O H ) 2 , respectively, according to Weiss et al. [ 42 ]. Chemical formulas of prepared MUS and NON models were ( K 180 N a 18 ) ( A l 334 F e 9 2 + M g 11 F e 4 3 + T i 2 ) ( S i 540 A l 180 ) O 1800 ( O H ) 358 F 2 and ( C a 270 N a 90 ) ( F e 330 3 + A l 25 M g 5 □ 180 ) ( S i 620 A l 70 F e 30 3 + ) O 1800 ( O H ) 360 , respectively. CEL, PP, SiO 2 , and AC periodic unit cells were enlarged to ~50 × 50 Å with a surface height and additional vacuum slab height of 50 Å and 350 Å, respectively. The CEL, PP, SiO 2 , and AC surfaces were further modified to simulate nanopores with dimensions of (width × height) ~30 × 30 Å ( Figure 3 ) and molecular pores with dimensions of 5.1 × 7.1 Å (CEL), 6.5 × 5.9 Å (PP), 5.6 × 5.7 Å (SiO 2 ), and 5.9 × 6.3 Å (AC) ( Figure 4 ).

Nanopores in the ( a ) CEL, ( b ) PP, ( c ) SiO 2 , and ( d ) AC surfaces with spots where the NO or SO 2 molecule was placed: (1) bottom, (2) corner, (3) side. NO or SO 2 molecules were also placed on the AC surfaces with -COOH or -OH groups added, e.g. ( e ) bottom_COOH and ( f ) bottom_OH. CEL—cellulose, PP—polypropylene, SiO 2 —silicon dioxide, AC—activated carbon.

Molecular pores in the ( a ) CEL, ( b ) PP, ( c ) SiO 2 , and ( d ) AC surfaces with spots (M) where the NO or SO 2 molecule was placed. CEL—cellulose, PP—polypropylene, SiO 2 —silicon dioxide, AC—activated carbon.

Due to the XPS analysis of AC adsorbents establishing 3.67 % carboxyl and 4.61 % hydroxyl groups on the surface, models with -COOH (bottom_COOH, corner_COOH, cavity_COOH) and -OH (bottom_OH, corner_OH, cavity_OH) added to the bare AC surfaces (bottom, corner, cavity) were also prepared ( Figure 3 e,f). The main advantage of using this approach to building AC models based on a graphitic structure is the possibility it offers of creating pores and cavities of controllable sizes [ 43 ].

MUS and NON periodic unit cells were enlarged to ~50 × 50 Å with a surface containing two clay layers with two interlayers and a vacuum slab added with a height of 350 Å. NO and SO 2 molecules were placed on various spots of the surfaces ( Figure 5 ). Three models were created for each “EG molecule/adsorbent surface spot” combination.

Molecular models of MUS ( a ) surface, ( b ) edge; and NON ( c ) surface and ( d ) edge—with spots where the NO or SO 2 molecule was placed: (1) surface, (2) interlayer, (3) edge. MUS—muscovite, NON—nontronite.

An MS/Forcite module was used for geometry optimization of each model. The COMPASS force field parameterized atoms and assigned their charges [ 44 ], which was verified for CEL [ 45 ], PP [ 46 ], SiO 2 [ 47 ], and AC [ 43 ]. A universal force field, with the QEq module setting charges, was used for models containing MUS and NON [ 48 ].

The Smart algorithm (implemented in MS) with 5·10 5 steps was used. Convergence thresholds for displacement, force, and energy were 5·10 −5 Å, 5·10 −3 kcal·mol −1 ·Å −1 , and 1·10 −4 kcal·mol −1 , respectively. Cell parameters were not optimized. Interaction energy ( E int ; kcal/mol) was calculated for each optimized model from potential energies ( E p ) using the following equation:

where E p 1 is E p of a whole model, E p 2 is E p of a surface, and E p 3 is E p of a NO/SO 2 molecule. The lower the E int value was, the stronger the interaction between NO/SO 2 and the surfaces.

For molecular dynamics, periodic models of AC, MUS, and NON with dimensions of ~17 × 17 Å (α = β = 90°) were prepared. The AC model contained three graphene layers, while the MUS and NON models contained two clay layers with one interlayer. All models had a vacuum slab, 1000 Å high, perpendicular to the surfaces. A total of 28 NO and 28 SO 2 molecules were evenly placed on one side of the surfaces. The MD/Forcite module and COMPASS or Universal force field for AC or MUS/NON models, respectively, were used for molecular dynamics with NVT ensemble, Nosé thermostat, random initial velocities, 293 K temperature, and 5 ns total simulation time.

3. Results and Discussion

3.1. physisorption.

Nitrogen physisorption measurements ( Figure 6 a,c,e; Table 2 ) proved that individual groups of adsorbents differ very much concerning their textural properties. According to the surface area and porosity, the adsorbents used can be ordered as follows (from largest to smallest): AC > CL > SiO 2 > CEL > PP.

(left: ( a , c , e )) Measured nitrogen adsorption–desorption isotherms at 77 K, (right: ( b , d , f )) evaluated mesopore–macropore-size distributions of adsorbents and (inset) evaluated micropore size distributions of adsorbents: ( a , b ) AC; ( c , d ) CL; ( e , f ) SiO 2 . AC1-3, CL1-3, SiO 2 1-3—activated carbon, clay, and silicon dioxide respectively (1-3—three granulometric fractions; see Table 1 ), V a —adsorbed volume of nitrogen, STP—standard temperature and pressure, p/p 0 —relative pressure, dV/dlog(w) —derivation of adsorbed volume of nitrogen divided by derivation of logarithm of pore width, dV/dw pore —derivation of adsorbed volume of nitrogen divided by derivation of pore width, dV/dlog(d) —derivation of adsorbed volume of nitrogen divided by derivation of logarithm of pore diameter.

Determined textural properties of adsorbents.

* Since adsorbent belongs to meso–macroporous solids, the mesopores surface area S meso equals the specific surface area S BET . AC1-3, CL1-3, SiO 2 1-3—activated carbon, clay, and silicon dioxide, respectively (1-3—three granulometric fractions; see Table 1 ), CEL—cellulose, PP—polypropylene; S BET —specific surface area, S meso —mesopore–macropore surface area, V micro —micropore volume, V net —net pore volume, n. d.—not defined.

AC showed the type I adsorption isotherm according to IUPAC classification [ 49 ], typical for microporous materials ( Figure 6 a). Evaluated textural parameters ( Table 2 ) and pore-size distributions ( Figure 6 b and insets) definitively correspond to this feature. AC showed micropores of 0.48 nm width with a volume of 359–376 mm 3 liq/g, and mesopore surface area in the range of 114–209 m 2 /g. With increasing particle-size fraction in the range of 0.16–1 mm, the mesopore surface area and net pore volume of AC logically decreases with no effect on micropore volume.

CL showed the mixed I + IV type of adsorption isotherm (according to IUPAC classification) typical for mesoporous materials with broad mesopores/macropores and some micropores ( Figure 6 c,d). CL possessed ~14 mm 3 liq/g of micropores of ~0.6 nm width ( Figure 6 d inset) and broad mesopores/macropores of 47–50 m 2 /g surface area ( Figure 6 d). There are no differences between individual particle-size fractions of CL, the properties of individual particle-size fractions being identical.

Concerning SiO 2 , these samples show the type III adsorption isotherm (according to IUPAC classification) with narrow steep hysteresis loop ( Figure 6 e), typical for macroporous/nonporous materials with large macropores, which corresponds to the pore-size distributions shown in Figure 6 f, proving the presence of macropores having diameter >100 nm. Textural properties (i.e., pore surface area, net pore volume) of SiO 2 are comparable; there are no differences among particle-size fractions. PP and CEL belong among nonporous materials with very low surface area.

3.2. Emission Gas Adsorption

With the exception of PP, all adsorbent materials were able to adsorb at least one of the EG components ( Table 3 ). CO 2 was adsorbed on none of the adsorbents. Adsorption of CO on SiO 2 was not observed at any temperature. Granulometry had a significant effect on the adsorbed amount of gases—the smaller the particles, the more adsorbed EG. At the adsorption temperature of 20 °C, AC on average adsorbed the most amount of both NO (9× higher than CL, 20× higher than CEL; Table 3 ) and SO 2 (1.5× higher than CL, 3× higher than CEL, and 54× higher than SiO 2 ; Table 3 ). At the adsorption temperature of 110 °C, all of the adsorbents adsorbed NO in very small amounts in contrast to SO 2 , which was adsorbed significantly more on average, and most on CL (6× higher than on AC, 7× higher than on CEL and 82× higher than on SiO 2 ; Table 3 ). CEL was the only one to adsorb CO at 20 °C (33.55 μg/g). on average, CL adsorbed the most amount of CO at 110 °C.

The adsorbents in the wet and dried state and their adsorption capacities for different molecules (NO, SO 2 , CO) at different adsorbent temperatures (20 and 110 °C).

AC1-3, CL1-3, SiO 2 1-3—activated carbon, clay, and silicon dioxide, respectively (1-3—three granulometric fractions; see Table 1 ), CEL—cellulose, PP—polypropylene.

During the adsorption of NO on AC, there was a significant competitive effect between NO and SO 2 at both temperatures ( Figure 7 and Figure 8 ). As soon as most of the AC adsorption sites were occupied by SO 2 molecules and the adsorbed amount began to decrease ( t = 550–950 s at 20 °C, 40–70 s at 110 °C; Figure 7 ), SO 2 began to replace NO molecules, resulting in NO forced desorption. The more porous the AC (smaller granulometric fraction), the earlier the desorption effect occurs (represented by AC1, AC2, and AC3 borderlines in Figure 7 ).

The dependence between SO 2 adsorption and NO desorption at the temperature of 20 °C. AC1, AC2, and AC3 border lines represent the beginning of the NO desorption effect for each adsorbent. AC1-3—activated carbon at different granulometric fractions (see Table 1 ).

The adsorption curves showing NO adsorption on AC at adsorbent temperatures of ( a ) 20 °C and ( b ) 110 °C. The curves also show forced the desorption effect in the ranges of ( a ) 630–2150 s and ( b ) 43–93 s. AC1-3—activated carbon at different granulometric fractions (see Table 1 ).

At the temperature of 20 °C, a total of 214.32/92.66 μg/g of NO was adsorbed/desorbed on AC1, 163.92/60.86 μg/g on AC2, and 106.51/30.03 μg/g on AC3 ( Figure 8 ). This phenomenon was investigated in more detail using molecular dynamics (see Section 3.3 ). Forced desorption was not observed with any other adsorbent.

In the case of AC, the adsorption maximum of NO was reached gradually ( Figure 8 ), while the SO 2 adsorption maximum of SO 2 occurred immediately after the EG flow started ( Figure 9 ). The same was observed during SO 2 adsorption on CL, SiO 2 and CEL ( Figure 10 and Figure 11 ).

The adsorption curves showing SO 2 adsorption on AC at adsorbent temperatures of ( a ) 20 °C and ( b ) 110 °C. AC1-3—activated carbon at different granulometric fractions (see Table 1 ).

The adsorption curves showing SO 2 adsorption on CL at adsorbent temperatures of ( a ) 20 °C and ( b ) 110 °C. CL1-3—clay at different granulometric fractions (see Table 1 ).

The adsorption curves showing SO 2 adsorption on SiO 2 at adsorbent temperatures of ( a ) 20°C and ( b ) 110 °C. ( c ) The adsorbing curve showing SO 2 adsorption on CEL at adsorbent temperatures of 20°C and 110 °C. SiO 2 1-3—silicon dioxide at different granulometric fractions (see Table 1 ), CEL—cellulose.

3.3. Molecular Modeling

CO 2 adsorption was not observed on any of the adsorbents, and CO was only adsorbed in negligible amounts and only at a temperature of 110 °C. Therefore, these two EG components were not molecularly modeled. Molecular dynamics clarified the competitive adsorption process of NO and SO 2 on the most adsorbing materials, i.e., AC (having the most specific adsorption process; Figure 12 ) and CL (MUS and NON). It showed NO forced desorption caused by SO 2 adsorption. Consequently, it was found with geometry optimization that SO 2 showed a lower E int with the surfaces than NO ( Figure 13 a,b), which correlated with the molecular dynamics results. The SO 2 molecules gradually occupied the top of the first surface, and the bottom of the second one. According to the notation “EG molecule_EG molecules number on the top of the surface/on the bottom of the surface_in the vacuum slab”, there were SO 2 _12/13_3 on AC, SO 2 _10/9_9 on MUS, and SO 2 _7/7_14 on NON ( Figure 12 ), while most NO molecules were expelled away from the surfaces (NO_3/3_22 for AC, NO_0/2_26 for MUS, and NO_1/1_26 for NON; Figure 12 ). The molecular dynamics results correspond to the experimentally determined sorption capacities, when higher sorption capacities were measured for SO 2 than for NO; and at 20 °C (293 K), AC showed higher sorption capacity than CL (MUS/NON; Table 3 ).

The initial molecular models containing 28 SO 2 and 28 NO molecules on the ( a ) MUS, ( b ) NON, and ( c ) AC surfaces. ( d ) The initial AC cell with EG molecules and the vacuum slab. The models after molecular dynamics showing the preference of SO 2 over NO molecules during the adsorption process on the ( e ) MUS, ( f ) NON, and ( g ) AC surfaces. MUS—muscovite, NON—nontronite, AC—activated carbon; EG—emission gas.

The E int comparison of models containing NO/SO 2 at different sites of ( a ) AC surface without or with -COOH/-OH groups and ( b ) MUS/NON surfaces. AC—activated carbon, MUS—muscovite, NON—nontronite, E int —interaction energy.

Due to the established correlation of molecular dynamics and geometry optimization results, the other models were only geometry optimized with one EG molecule on the surfaces in order to determine E int and observe molecular interactions in more detail.

Geometry optimization showed the suitability of the chemical composition of all sorbent materials for NO and SO 2 adsorption. An attractive interaction with NO or SO 2 was observed for all models containing AC. Average E int of models containing NO was 2× higher than models containing SO 2 on AC ( Figure 13 a). NO interacted most strongly with the cavities, cavity_COOH ( E int = −8.312 kcal/mol) and cavity_OH. The second strongest NO interactions were observed with the AC corner surfaces ( E int = −5.962 kcal/mol). In the case of SO 2 , the strongest interactions were observed for cavity_COOH ( E int = −15.360 kcal/mol) and cavity_OH. Corner_COOH ( E int = −13.877 kcal/mol) showed the second strongest interactions with SO 2 . These findings prove that the interaction of NO/SO 2 with AC is stronger, the more numerous surface atoms participating in the non-bonding interaction. The presence of the functional groups (mainly -COOH) is another important factor supporting the strength of AC interaction with NO/SO 2 via hydrogen bonds.

NO showed the strongest interaction with the MUS surface ( E int = −28.785 kcal/mol) and NON interlayer ( E int = −16.177 kcal/mol). The lowest E int showed the model containing SO 2 at the MUS edge ( E int = −52.357 kcal/mol); and the second strongest SO 2 interaction was with MUS and NON edge ( Figure 13 b). The MUS and NON interlayers in most cases showed a positive E int (repulsive force) with NO and SO 2 , due to a large number of cations in the interlayer of clay minerals causing a strong interaction between clay layers, and making it impossible for NO or SO 2 to penetrate. At the same time, these cations occupied all chemically suitable sites for interaction with NO and SO 2 . The average E int of models containing SO 2 on MUS and NON is significantly lower than in the case of models with NO.

All models containing NO placed at all sites of the CEL, PP and SiO 2 surfaces showed a weak negative interaction energy. The strongest interaction ( E int = −10.936 kcal/mol; Figure 14 a) was achieved in the case of NO lying in the corner of SiO 2 . The second lowest E int (−8.137 kcal/mol; Figure 14 a) was achieved for NO placed in the CEL cavity. SO 2 interacted with CEL, PP and SiO 2 surfaces several times stronger. The model with the strongest interaction of SO 2 in the CEL cavity showed 5× lower E int (−55.491 kcal/mol; Figure 14 b) than the model with the strongest interaction with NO. The second strongest interaction ( E int = −27.872 kcal/mol; Figure 14 b) was shown by SO 2 on the SiO 2 bottom. The average E int of models containing NO/SO 2 on PP was the highest.

The E int comparison of models containing ( a ) NO and ( b ) SO 2 at different sites of CEL, PP and SiO 2 surfaces. CEL—cellulose, PP—polypropylene, SiO 2 —silicon dioxide, E int —interaction energy.

3.4. Adsorption Factors

The importance of chemical ( E int ) and textural ( S BET , S meso , V micro , V net ) properties on the adsorption capacity of adsorbents was determined ( Table 4 ). AC adsorption capacity was high for both NO and SO 2 , which was mainly correlated with the large surface area in spite of high E int values (i.e., weak interactions). The high CL adsorption capacity was due to a combination of both chemical and textural properties. A dominant factor of low SiO 2 and PP adsorption capacity was primarily textural properties (despite strong interactions). The high CEL adsorption capacity was mainly provided by the presence of functional groups strongly interacting with SO 2 molecules.

Determining the importance of E int or textural properties ( S BET , S meso , V micro , V net ) on adsorption capacity of the adsorbents having 0.16–0.315 mm granulometry.

* denotes dominant adsorption factor, i.e., chemical ( E int ) or textural ( S BET , S meso , V micro , V net ). AC—activated carbon, CL—clay, SiO 2 —silicon dioxide, CEL—cellulose, PP—polypropylene, S BET —specific surface area, S meso —mesopore–macropore surface area, V micro —micropore volume, V net —net pore volume, n. d.—not defined, E int —interaction energy.

Furthermore, agreement between the experiment and molecular modeling was generally more common for lower sorption capacities for NO (corresponding to higher E int values, i.e., weaker interaction) compared to higher SO 2 capacities (corresponding to lower E int values, i.e., stronger interaction).

In general, a significantly lower E int can be observed for models containing a molecule in a molecular pore (mainly CEL), which appears to be an ideal combination of chemical (more non-bonding interactions) and structural/steric (molecule size correlates with pore size) factors. The agreement of the force field-based molecular modeling results and experimental data demonstrate the modeling strategy used to be a suitable tool for analysis and prediction of interactions during the sorption process at the molecular level.

However, other modeling studies performed using more computationally demanding DFT methods have led to similar results for interactions between AC and NO/SO 2 [ 32 , 34 ]. Wang et al. [ 34 ] reported the same behavior of NO on AC—the strongest interactions were observed on AC basal plane (compare with “side” in Figure 13 a), weaker interactions with -OH group (compare with “bottom_OH” in Figure 13 a), and the weakest with -H (compare with “bottom” in Figure 13 a). Zhao et al. [ 32 ] found the same E int trend for SO 2 on AC, where the molecule interacted most strongly with -COOH groups (compare with “bottom_COOH” in Figure 13 a), more weakly with -OH (compare with “bottom_OH” in Figure 13 a), and the weakest with -H (compare with “bottom” in Figure 13 a).

The comparison demonstrates the usefulness of computationally less demanding force field-based molecular modeling in adsorption research. It also reveals that there is no need to take into account the partial amorphousness of AC, e.g., by a large amount of polyaromatic hydrocarbons [ 32 ]. Approximation of AC using graphite, which additionally enables the preparation of pores of the required size, is sufficient for the given purpose.

4. Conclusions

In this work, the competitive adsorption of emission gas, containing CO, NO, SO 2 and CO 2 , on adsorption materials with different chemical compositions was studied.

CO 2 was not adsorbed on any material. CO was adsorbed in small amounts and mainly at a temperature of 110 °C on AC, CL and CEL. At 20 °C, the AC showed the highest NO and SO 2 sorption capacity. At 110 °C, the highest NO and SO 2 sorption capacity was found for the CL.

The strongest interactions were exhibited between NO/SO 2 and corner or cavity surface types due to the larger number of interacting atoms. Carboxyl and hydroxyl functional groups strengthened the interaction of AC mainly with SO 2 , where hydrogen bonds were formed. NO and SO 2 showed attractive interactions with MUS and NON mainly on the surface and edge. Strong interactions between clay layers and interlayer cations prevented the penetration of NO and SO 2 into the interlayer space.

The dominant factor determining the sorption capacity of AC, SiO 2 and PP was textural (surface area, porosity)—while in the case of CEL, it was the chemical factors (chemical composition, functional groups). Both textural and chemical factors played an important role in adsorption on CL.

The effects of competitive adsorption of emission components on sorption capacity were determined and further clarified using force field-based molecular modeling. The modeling strategy made it possible to simulate surfaces with different and controllable structural character. Geometry optimization and molecular dynamics results agreed well with experimental data allowing the modeling strategy to be further used in studies of interactions during adsorption, or for a prediction of adsorption phenomena.

Author Contributions

Conceptualization, A.V.; methodology, A.V. and J.T.; software, A.V. and J.T.; validation, A.V. and T.N.; formal analysis, A.V., L.M. and K.M.K.; investigation, A.V. and T.N.; resources, J.K. and V.P.; data curation, A.V.; writing—original draft preparation, A.V.; writing—review and editing, J.T.; visualization, A.V.; supervision, J.T.; project administration, A.V.; funding acquisition, A.V. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data is contained within the article.

Conflicts of Interest

The authors declare no conflict of interest.

Funding Statement

This work was supported by the Doctoral grant competition VSB—Technical University of Ostrava, reg. no. CZ.02.2.69/0.0/0.0/19_073/0016945 within the Operational Programme Research, Development and Education, under project DGS/TEAM/2020-005 “Low-potencial waste heat recovery”. Large Research Infrastructure ENREGAT supported by the Ministry of Education, Youth and Sports of the Czech Republic (project No. LM2018098) also contributed to the realization of this work.

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