Korean Journal of Chemical Engineering

, Volume 36, Issue 12, pp 2047–2059 | Cite as

A modified non-equilibrium lattice fluid model based on corrected fractional free volume of polymers for gas solubility prediction

  • Abolfazl JomekianEmail author
  • Bahamin Bazooyar
  • Seyed Jalil Poormohammadian
  • Parviz Darvishi
Separation Technology, Thermodynamics


We propose a model based on non-equilibrium lattice fluid (NELF) theory and corrected fractional free volume of polymers to effectively and accurately predict the solubility of gases in different polymers. The method to achieve this purpose is based on the utilization of NELF model infinite dilution solubility coefficient (S0) as the base of predictive calculations. To account for the isolated pore in the polymer matrix in density estimation, a fractional free volume correction factor (β) was introduced in NELF model. The modified NELF model was successfully applied for prediction of solubility of C3H8 and CO2 in polyethylene oxide (PEO) and CO2 in polyethylene terephthalate (PET), isotactic polypropylene (i-PP), polyetherimide (PEI), polymethyl methacrylate (PMMA) and polyethyl methacrylate (PEMA) with adjustments in β value and depth of diffusion of gases in polymer matrix (ζ) at different pressures and temperatures. This work involves multi-objective optimization using genetic algorithm of MATLAB toolbox with adjusted settings. It applies to find the optimum temperature at which the minimum standard deviation of β for different gas-polymer systems is obtained. β showed the same trend of change with temperature as the constrained pressure imposed on the amorphous phase in semi-crystalline polymers. A cubic correlation for standard deviation for β versus temperature was obtained which was able to anticipate the changing trend of β at different temperatures. The chi-square test results verified that compared with original NELF model, a more accurate model for prediction of gas solubilities in polymers has been proposed.


NELF Model Solubility Prediction Infinite Dilution Solubility Fractional Free Volume Correction Factor Chi-square Test 


English Letters


total Helmholtz free energy [J]


Helmholtz free energy density at nonequilibrium state [J mol−1]


numbers of moles of penetrants


Universal gas constant [J mol−1 K−1]


characteristic temperature of the mixture of gases [K]


characteristic temperature of pure component i [K]


dimensionless temperature


molar average number of lattice sites occupied by a molecule in the mixture


molar number of lattice sites occupied in the mixture by molecules of species i


number of lattice sites occupied by a mole of pure component i


volume occupied by a mole of lattice sites of pure substance [m3 mol−1]


infinite dilution solubility coefficient [m3(STP) m−3 Pa]


characteristic pressure of pure component i [Pa]

\({\rm{\Delta p}}_{i,j}^*\)

pressure binary interaction parameter between penetrants i and j [Pa]


concentration of penetrant in matrix of polymer [mol m−3]


molecular weight of penetrant (i=1) or polymer (i=2) [kg mol−1]


molecular flux of penetrant in polymer [mol m−2 s−1]


diffusion coefficient of penetrant in polymer [m2 s−1]


diffusion coefficient of solute in polymer [kgsolute·kgpolymer−1]


molecular separation at collision [nm]


Boltzmann constant


fractional free volume [FFV]


the direction of diffusion [µm]

Greek Letters

\(\widetilde\rho \)

dimensionless density [kg m−3]


lattice fluid characteristic density [kg m−3]

\(\rho _i^*\)

characteristic density of pure component i [kg m−3]

\(\rho _2^0\)

density of polymer in very low pressures [kg m−3]


density of penetrant molecule (i=1), density of polymer (i=2) [kg m−3]


volume fraction of component i

\(\mu _i^{NE}\)

non-equilibrium chemical potential of component i [J mol−1]


binary adjustable parameter


energy of molecular attraction [kg m−2 s−2]


fractional free volume correction factor


depth of diffusion of penetrant in polymer matrix [µm]




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This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.


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Copyright information

© The Korean Institute of Chemical Engineers 2019

Authors and Affiliations

  • Abolfazl Jomekian
    • 1
    Email author
  • Bahamin Bazooyar
    • 2
  • Seyed Jalil Poormohammadian
    • 3
  • Parviz Darvishi
    • 3
  1. 1.Esfarayen University of TechnologyEsfarayenIran
  2. 2.Department of Design and Engineering, School of Creative Arts and EngineeringStaffordshire UniversityStoke-on-TrentUK
  3. 3.Chemical Engineering Department, School of EngineeringYasouj UniversityYasoujIran

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