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A new interpretation of chemical potential in adsorption systems and the vapour–liquid interface

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Abstract

Chemical potential is a fundamental thermodynamic quantity that is constant everywhere in uniform or non-uniform systems at equilibrium. Because it is not a mechanical variable, its clear interpretation is elusive and its relationship to the energetics of the molecules that make up the system has not been established. In this work, we present a link between the chemical potential and molecular energetics, using a kinetic Monte Carlo scheme. We illustrate this new interpretation using argon as a model species giving examples for adsorption on a graphite surface and for a bulk vapour-liquid equilibrium (VLE). It was found that in either an adsorbed phase or a bulk liquid phase, the chemical potential is associated with repelling molecules, despite the number of these molecules being very small. In a rarefied phase it is associated with attracting molecules. In the interfacial regions in an adsorption system or in a VLE, the energetics of the repelling and attracting molecules contribute equally to the chemical potential.

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References

  • Baierlein, R.: The elusive chemical potential. Am. J. Phys. 69(4), 423–434 (2001)

    Article  CAS  Google Scholar 

  • Battaile, C.C.: The kinetic Monte Carlo method: foundation, implementation, and application. Comput. Methods Appl. Mech. Eng. 197(41–42), 3386–3398 (2008)

    Article  Google Scholar 

  • Bennett, C.H.: Efficient estimation of free energy differences from Monte Carlo data. J. Comput. Phys. 22(2), 245–268 (1976)

    Article  Google Scholar 

  • Fan, C., Do, D.D., Nicholson, D., Ustinov, E.: Chemical potential, Helmholtz free energy and entropy of argon with kinetic Monte Carlo simulation. Mol. Phys. 112(1), 60–73 (2013a)

    Article  CAS  Google Scholar 

  • Fan, C., Do, D.D., Nicholson, D., Ustinov, E.: A novel application of kinetic Monte Carlo method in the description of N2 vapour–liquid equilibria and adsorption. Chem. Eng. Sci. 90, 161–169 (2013b)

    Article  CAS  Google Scholar 

  • Frenkel, D.: Simulations: the dark side. Eur. Phys. J. Plus 128(1), 10 (2013)

    Article  Google Scholar 

  • Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)

    Article  CAS  Google Scholar 

  • Job, G., Herrmann, F.: Chemical potential—a quantity in search of recognition. Eur. J. Phys. 27(2), 353 (2006)

    Article  CAS  Google Scholar 

  • Kofke, D.A., Cummings, P.T.: Quantitative comparison and optimization of methods for evaluating the chemical potential by molecular simulation. Mol. Phys. 92(6), 973–996 (1997)

    Article  CAS  Google Scholar 

  • Michels, A., Wijker, H., Wijker, H.: Isotherms of argon between 0°c and 150°c and pressures up to 2900 atmospheres. Physica 15(7), 627–633 (1949)

    Article  CAS  Google Scholar 

  • Moore, S.G., Wheeler, D.R.: Chemical potential perturbation: extension of the method to lattice sum treatment of intermolecular potentials. J. Chem. Phys. 136(16), 164503 (2012)

    Article  CAS  PubMed  Google Scholar 

  • Nguyen, V.T., Do, D.D., Nicholson, D., Ustinov, E.A.: Application of the kinetic Monte Carlo method in the microscopic description of argon adsorption on graphite. Mol. Phys. 110(18), 2281–2294 (2012)

    Article  CAS  Google Scholar 

  • Nguyen, V.T., Tan, S.J., Do, D.D., Nicholson, D., Application of kinetic Monte Carlo method to the vapour–liquid equilibria of associating fluids and their mixtures. Mol. Simul. (2015). https://doi.org/10.1080/08927022.2015.1067809

    Article  Google Scholar 

  • Shing, K.S., Gubbins, K.E.: The chemical potential in dense fluids and fluid mixtures via computer simulation. Mol. Phys. 46(5), 1109–1128 (1982)

    Article  CAS  Google Scholar 

  • Steele, W.A.: The physical interaction of gases with crystalline solids: I. Gas-solid energies and properties of isolated adsorbed atoms. Surf. Sci. 36(1), 317–352 (1973)

    Article  CAS  Google Scholar 

  • Tan, S.J., Do, D.D., Nicholson, D., An efficient method to determine chemical potential of mixtures in the isothermal and isobaric bulk phase with kinetic Monte Carlo simulation. Mol. Phys. (2015). https://doi.org/10.1080/00268976.2015.1090634

    Article  Google Scholar 

  • Tan, S., Do, D.D., Nicholson, D., Development of a grand canonical-kinetic Monte Carlo scheme for simulation of mixtures. Mol. Simul. (2016a). https://doi.org/10.1080/08927022.2015.1136824

    Article  Google Scholar 

  • Tan, S.J., Do, D.D., Nicholson, D., A new kinetic Monte Carlo scheme with Gibbs ensemble to determine vapour–liquid equilibria. Mol. Simul. (2016b). https://doi.org/10.1080/08927022.2016.1233548

    Article  Google Scholar 

  • Tan, S., Prasetyo, L., Zeng, Y., Do, D.D., Nicholson, D.: On the consistency of NVT, NPT, µVT and Gibbs ensembles in the framework of kinetic Monte Carlo—fluid phase equilibria and adsorption of pure component systems. Chem. Eng. J. 316, 243–254 (2017)

    Article  CAS  Google Scholar 

  • Ustinov, E.A.: Thermodynamics and simulation of hard-sphere fluid and solid: Kinetic Monte Carlo method versus standard Metropolis scheme. J. Chem. Phys. 146(3), 034110 (2017)

    Article  CAS  PubMed  Google Scholar 

  • Ustinov, E.A., Do, D.D.: Two-dimensional order-disorder transition of argon monolayer adsorbed on graphitized carbon black: kinetic Monte Carlo method. J. Chem. Phys. 136(13), 134702 (2012a)

    Article  CAS  PubMed  Google Scholar 

  • Ustinov, E.A., Do, D.D.: Application of kinetic Monte Carlo method to equilibrium systems: vapour-liquid equilibria. J. Colloid Interface Sci. 366(1), 216–223 (2012b)

    Article  CAS  PubMed  Google Scholar 

  • Ustinov, E.A., Do, D.D.: Thermodynamic analysis of ordered and disordered monolayer of argon adsorption on graphite. Langmuir 28(25), 9543–9553 (2012c)

    Article  CAS  PubMed  Google Scholar 

  • Widom, B.: Some topics in the theory of fluids. J. Chem. Phys. 39(11), 2808–2812 (1963)

    Article  CAS  Google Scholar 

  • Widom, B.: Potential-distribution theory and the statistical mechanics of fluids. J. Phys. Chem. 86(6), 869–872 (1982)

    Article  CAS  Google Scholar 

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Acknowledgements

This project is supported by the Australian Research Council (Grant # DP160103540).

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Correspondence to D. D. Do.

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Tan, S., Loi, Q.K., Do, D.D. et al. A new interpretation of chemical potential in adsorption systems and the vapour–liquid interface. Adsorption 24, 425–430 (2018). https://doi.org/10.1007/s10450-018-9957-y

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  • DOI: https://doi.org/10.1007/s10450-018-9957-y

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