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Analysis of the swelling or shrinking kinetics of crosslinked hydrophilic polymers by mathematical modeling

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Abstract

The developed kinetic physical and mathematical model of a crosslinked hydrophilic polymer swelling process in aqueous solutions of low molecular weight compounds is presented. The model was tested on 13 combinations of “polymer-solution”. The experimental results of measuring the swelling kinetics can be described by considering the flows caused by the difference in chemical potential of the water and solute inside/outside the swollen polymer, as well as the effect of elastic forces in the polymer. The calculation results are in a good agreement with experimental data.

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Abbreviations

\(a_w \) :

Water activity in the solution under study (dimensionless)

\(c_0 \) :

The solute concentration in the external solution (mol/l)

\(c_b \) :

The solute concentration in the surface layer (average) (mol/l)

\(c^{*}\) :

The solute concentration on the border of polymer gel (PG) (mol/l)

\(\bar{{c}}\) :

The solute concentration in the external solution phase (ES) of the PG (mol/l)

D :

The solute diffusion coefficient in the external solution (m\(^{2}\)/s)

\(E_v \) :

The specific amount of polar groups in the dry polymer (g-eq/l)

h :

The thickness of surface layer (m)

\(n_w \) :

The specific water of polymer sorption (mol H\(_{2}\)O/mol pol. gr.)

Q :

The amount of solute in the PG (mol)

p :

Parameters characterizing influence of the nature and concentration of solute on the number of hydrogen bonds in the polymer gel [(mol/l)\(^{-1}\)]

\(S, S_{\max } \) :

Current and maximum visible surface area of the PG (m\(^{2}\))

t :

Time (s)

\(V,V_{\max } \) :

Current and maximum volume of the PG (m\(^{3}\))

\(V_0 \) :

Volume of the PG immersed in water (m\(^{3}\))

\(V_r ,V_s ,V_f \) :

The volume of dry polymer, the volume of adsorbed water and the volume of the external phase solution (or “free” water), respectively (m\(^{3}\))

\(V_f^{eq}\) :

The volume of the ES phase which is in equilibrium with concentration of the electrolyte in the external solution (m\(^{3}\))

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Authors and Affiliations

  1. Department of Physics, Moscow Lomonosov State University, Moscow, Russia

    Mikhail G. Tokmachev

  2. Department of Chemistry, Moscow Lomonosov State University, Moscow, Russia

    Nikolai B. Ferapontov & Alexandr N. Gagarin

Authors
  1. Mikhail G. Tokmachev
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  2. Nikolai B. Ferapontov
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  3. Alexandr N. Gagarin
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Correspondence to Mikhail G. Tokmachev.

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Tokmachev, M.G., Ferapontov, N.B. & Gagarin, A.N. Analysis of the swelling or shrinking kinetics of crosslinked hydrophilic polymers by mathematical modeling. J Math Chem 55, 142–152 (2017). https://doi.org/10.1007/s10910-016-0676-x

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