, Volume 24, Issue 1, pp 105–120 | Cite as

Chromium adsorption into a macroporous resin based on vinylpyridine–divinylbenzene copolymers: thermodynamics, kinetics, and process dynamic in a fixed bed column

  • José Antonio Arcos-Casarrubias
  • Martín R. Cruz-Díaz
  • Judith Cardoso-Martínez
  • Jorge Vázquez-Arenas
  • Francisco Vidal Caballero-Domínguez


The synthesis of the poly(4-vinylpyridine-co-ethylvinylbenzene) resin is investigated and its performance to remove Cr(VI) from aqueous solutions is evaluated as a function of pH using batch and fixed bed column adsorptions. The rate of Cr(VI) removal is observed to increase as the pH solution shifts to acidic conditions due to an enhanced protonation of the 4-vinylpyridine group in the polymer, which favors its electrostatic attraction with Cr(VI) oxyanions. This finding is supported with Density Functional Theory (DFT) calculations, revealing that the interaction between \({\text{CrO}}_{4}^{{2 - }}\) (predominant species at pH < 6) and protonated 4VP is more favorable than a bond formed with \({\text{HCrO}}_{4}^{ - }\) species (pH > 6) due to a higher charge delocalization arising in the O atoms. Experimental isotherms are approximated with the Langmuir and Radke-Prausnitz adsorption models. This former approach generates the best fitting to the data, whereby it was incorporated into a nonlinear transient model to account for the Cr(VI) adsorption in a fixed bed, and evaluating its capacity to predict experimental adsorption data. The model enables to infer that the resin presents a fast kinetic for Cr(VI) sorption, and the Cr(VI) intra-particle diffusion across the adsorbent pores is the rate-determining step for sorption.


Vinylpyridine–divinylbenzene copolymer Chromium adsorption Mathematical modelling Fixed bed column Density functional theory 



Area of transversal section of the column (cm2)


Mass transfer specific area (cm−1)


The equilibrium concentrations in the liquid phase (mg Cr L−1)


The initial concentrations in the liquid phase (mg Cr L−1)


Concentration of Cr(VI) in the bulk fluid phase (mg L−1)


Feed concentration of Cr(VI) in the bulk fluid phase (mg L−1)

\({C_{{\text{Cr}}\left( \delta \right)}}\)

Concentration of Cr(VI) in the layer (mg L−1)


The effluent Cr(VI) concentrations through the bed (mg L−1)


Axial dispersion coefficient in the fluid phase (cm2 min−1)


Equivalent diameter of the adsorbent particle (cm)


Molecular diffusivity of Cr(VI) (cm2 min−1)


Volumetric flow rate (cm3 min−1)


Mass flux (g cm−2 min−1)


Mass transfer coefficient in external liquid film (cm min−1)


Constant related to the free adsorption energy (L mg−1)


Mass transfer coefficient in the adsorbent (min−1)


Fixed bed length (cm)


Radke-Prausnitz constant


Mass of resin (g)


Dimensionless exponent


Number of experimental data points


Water swelling capacity


Average concentration of Cr(VI) adsorbed in the adsorbent (mg g−1)


Amount of chromium adsorbed per unit weight of resin at equilibrium (mg g−1)


Maximal adsorption capacity (mg g−1)


Constant Radke-Prausnitz


Total Cr(VI) adsorbed on the copolymer at different time (mg g−1)


Chromium adsorption rate (g g−1 min−1)


Least squared error function


Time (min)


Velocity (cm min−1)


Volume of the solution (L)


Dimensionless parameter


Weight of the swollen resin (g)


Weight of the dried resin (g)

Greek Letters

\({\beta _{RPIII}}\)

Radke-Prausnitz exponent


Density of the fluid phase (g cm−3)


Density of the bed (g L−1)


Column void fraction


Viscosity of the fluid phase (g cm−1 min−1)



This work was supported by the Mexican Council for Science and Technology (CONACyT, Grant Number CB-220232).


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© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.División de Ingeniería Química y BioquímicaTecnológico de Estudios Superiores de EcatepecEcatepec de MorelosMexico
  2. 2.Departamento de Ingeniería y Tecnología, Facultad de Estudios Superiores Cuautitlán Campo UnoUniversidad Nacional Autónoma de MéxicoCuautitlan IzcalliMexico
  3. 3.Departamento de FísicaUniversidad Autónoma Metropolitana-IztapalapaMexicoMexico
  4. 4.Centro Mexicano para la Producción más LimpiaInstituto Politécnico NacionalMexico CityMexico

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