Abstract
Adsorption isotherms generated by the Elution by Characteristic Point Method were used to determine the local adsorption equilibrium distribution (AEqD) on commercial zeolite BEA 150 extrudate pellets at room temperature. The linear sugar alcohol sorbitol and the circular sugar fructose were used as sensor molecules since both showed a rather strong adsorption with a typical type I isotherm. The expectation maximization method was transferred into a MATLAB code to calculate the most probable AEqD explaining the experimental data. The resulting distribution favors a bi-site Langmuir model that is in good agreement with the pore sizes of this zeolite, the critical diameters of the adsorptive molecules and gas phase experiments conducted previously. In summary, both molecules are too big to enter the zigzag channels of the zeolite. Instead they occupy two different binding sites in the straight channels and at the intersections between the straight and the zigzag channels. Therefore, sugars and sugar alcohol can be a good sensor to investigate the interaction between a zeolite crystal and adsorptive molecules in the liquid phase.
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Abbreviations
- AED:
-
Adsorption energy distribution
- AEqD:
-
Adsorption equilibrium distribution
- BEA150:
-
Dealuminated β-zeolite with Si/Al = 75
- ECP:
-
Elution by characteristic point
- EM:
-
Expectation maximization
- PM:
-
Peak maximum
- \({{c}_{0}}\) :
-
Initial concentration in the liquid phase, \(\text{m}{{\text{g}}_{\text{Adsorbtive}}}\ {{\text{L}}^{-1}}\)
- \({{c}_{\text{e}}}\) :
-
Equilibrium concentration, \(\text{m}{{\text{g}}_{\text{Adsorbtive}}}\ {{\text{L}}^{-1}}\)
- \({{c}_{i}}\) :
-
Concentration of component i, \(\text{m}{{\text{g}}_{\text{Adsorbtive}}}\ {{\text{L}}^{-1}}\)
- \(c_{\text{i}}^{{}^\circ }\) :
-
Dimensionless concentration of component i
- \({{c}_{i,max}}\) :
-
Maximum concentration of component i, \(\text{m}{{\text{g}}_{\text{Adsorbtive}}}\ {{\text{L}}^{-1}}\)
- \({{c}_{i,min}}\) :
-
Minimum concentration of component i, \(\text{m}{{\text{g}}_{\text{Adsorbtive}}}\ {{\text{L}}^{-1}}\)
- \({{E}_{\text{A}}}\) :
-
Adsorption energy, \(\text{J}\ \text{mol}^{-1}\)
- \({{E}_{\text{solute}}}\) :
-
Adsorption energy of the solute, \(\text{J}\ \text{mol}^{-1}\)
- \({{E}_{\text{solvent}}}\) :
-
Adsorption energy of the solvent, \(\text{J}\ \text{mol}^{-1}\)
- \(f\) :
-
Adsorption equilibrium distribution, \(\text{m}{{\text{g}}_{\text{Adsorbate}}}\ \text{g}_{\text{Adsorbent}}^{-1}\)
- \(K\) :
-
Binding coefficient, \(\text{L}\ {{\text{g}}^{-1}}\)
- \({{K}_{0}}\) :
-
Pre-exponential factor, \(\text{mL}\ {{\text{g}}^{-1}}\)
- \(K_{i}^{Ex}\) :
-
Excess adsorption equilibrium constant,\(\text{mL}\ {{\text{g}}^{-1}}\)
- \({{m}_{0}}\) :
-
Mass of liquid, g
- \({{m}_{\text{acc}}}\) :
-
Accumulated mass, g
- \({{m}_{\text{Ad}}}\) :
-
Mass of adsorbent, g
- \({{\dot{m}}_{\text{conv}}}\) :
-
Mass flow by convection, \(\text{g}\ {{\text{s}}^{-1}}\)
- \({{\dot{m}}_{\text{disp}}}\) :
-
Mass flow by dispersion, \(\text{g}\ {{\text{s}}^{-1}}\)
- \({{\dot{m}}_{\text{t}}}\) :
-
Mass flow into zeolite particles, \(\text{g}\ {{\text{s}}^{-1}}\)
- \({{q}_{i}}\) :
-
Real loading of component i, \(\text{m}{{\text{g}}_{\text{Adsorbate}}}\ \text{g}_{\text{Adsorbent}}^{-1}\)
- \(q_{i}^{\text{Ex}}\) :
-
Excess loading of component i, \(\text{m}{{\text{g}}_{\text{Adsorbate}}}\ \text{g}_{\text{Adsorbent}}^{-1}\)
- \({{q}_{\text{S}}}\) :
-
Saturation loading, \(\text{m}{{\text{g}}_{\text{Adsorbate}}}\ \text{g}_{\text{Adsorbent}}^{-1}\)
- \(R\) :
-
Universal gas constant \(\text{J}\ \text{mo}{{\text{l}}^{-1}}\ {{\text{K}}^{-1}}\)
- \(t\) :
-
Time, s
- \(T\) :
-
Temperature, K
- \({{u}_{\text{m}}}\) :
-
Velocity of the fluid, \(\text{m}\ {{\text{s}}^{-1}}\)
- \({{V}_{\text{dead}}}\) :
-
Dead volume of the apparatus, L
- \({{V}_{\text{inj}}}\) :
-
Injection volume, L
- \({{V}_{\text{L}}}\) :
-
Volume of the liquid, L
- \({{V}_{\text{R}}}\) :
-
Retention volume of a substance, L
- \({{V}_{\text{S}}}\) :
-
Concentration-dependent system dead volume, L
- \(w\) :
-
Band velocity, \(\text{m}\ {{\text{s}}^{-1}}\)
- \(x\) :
-
Length, m
- \({{\varepsilon }_{\text{t}}}\) :
-
Total porosity of the bed in the column, \(\text{m}_{\text{void}}^{3}\ \text{m}_{\text{total}}^{-3}\)
- \(\theta\) :
-
Local isotherm model, 1
- \({{\rho }_{p}}\) :
-
Density of the pellet, \(\text{g}\ {{\text{L}}^{-1}}\)
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Acknowledgements
This work was supported by German Research Foundation (DFG) under Grant No. SCHO 842/9-2. We gratefully acknowledge receipt of zeolite extrudates from Clariant Company. We also thank Dr. Ingo Kampen, Institute for Particle Technology at TU Braunschweig, for supplying the crushed zeolite extrudate and Marcus Möbius and Toni Gossmann for helpful discussions.
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Hartig, D., Schwindt, N. & Scholl, S. Using the local adsorption equilibrium distribution based on a Langmuir type adsorption model to investigate liquid phase adsorption of sugars on zeolite BEA. Adsorption 23, 433–441 (2017). https://doi.org/10.1007/s10450-017-9873-6
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DOI: https://doi.org/10.1007/s10450-017-9873-6