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Modeling elastic properties of Vycor glass saturated with liquid and solid adsorbates

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Abstract

A combination of ultrasonic experiments with gas adsorption is a promising tool for improved characterization of nanoporous materials. The use of ultrasound requires understanding of the effects of adsorbates on the elastic properties of nanoporous medium. This issue is not trivial, because nanostructured materials, as well as nanoconfined matter, may exhibit physical properties that differ substantially from the properties of “normal” bulk materials. In this paper, we investigate the change of elastic properties of Vycor glass filled with adsorbed liquid and solid argon within the context of elasticity and compare the modeling results with the ultrasonic measurements. The modeling requires the knowledge of solid moduli of Vycor glass and the pore geometry, which cannot be measured directly. Instead, we estimate these parameters from the dry moduli using so-called Differential Effective Medium (DEM) theory, in which the pores are assumed to be of spheroidal shape characterized by a single aspect ratio. Predictions of the Gassmann equation give an excellent fit to the measured elastic moduli of Vycor glass completely filled with liquid argon at temperature 80 K. Estimates of the DEM show a reasonable agreement with ultrasonic measurements on the elastic moduli of Vycor glass fully saturated with solid argon at 74 K in shear modulus but a significant overestimate in bulk modulus. This might be due to the effects of the confinement on the moduli of argon in nanopores. Although the validation and generalization of this conclusion requires further laboratory experiments for a number of well characterized solid–fluid systems, our finding shed light on the understanding of elastic properties of nanoporous materials mixed with adsorbates in various phases. These results provide steps toward development of methods for ultrasonic characterization of confined fluid and solid phases.

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References

  • Amberg, C., McIntosh, R.: A study of adsorption hysteresis by means of length changes of a rod of porous glass. Can. J. Chem. 30(12), 1012–1032 (1952)

    Article  CAS  Google Scholar 

  • Anderson, M., Swenson, C.: Experimental equations of state for the rare gas solids. J. Phys. Chem. Solids 36(3), 145–162 (1975)

    Article  CAS  Google Scholar 

  • Balzer, C., Cimino, R.T., Gor, G.Y., Neimark, A.V., Reichenauer, G.: Deformation of microporous carbons during N2, Ar, and CO2 adsorption: insight from the density functional theory. Langmuir 32(32), 8265–8274 (2016)

    Article  CAS  Google Scholar 

  • Barker, J., Dobbs, E.: CXX. Measurement of the elasticity of solid argon with an ultrasonic interferometer. Lond. Edinb. Dubl. Phil. Mag. 46(381), 1069–1080 (1955)

    Article  CAS  Google Scholar 

  • Bentz, D.P., Garboczi, E.J., Quenard, D.A.: Modelling drying shrinkage in reconstructed porous materials: application to porous Vycor glass. Model. Simul. Mater. Sci. Eng 6(3), 211 (1998)

    Article  CAS  Google Scholar 

  • Berryman, J.G.: Long-wavelength propagation in composite elastic media II. Ellipsoidal inclusions. J. Acoust. Soc. Am. 68(6), 1820–1831 (1980)

    Article  Google Scholar 

  • Berryman, J.G.: Origin of Gassmann’s equations. Geophysics 64(5), 1627–1629 (1999)

    Article  Google Scholar 

  • Biot, M.A.: Theory of propagation of elastic waves in a fluid-saturated porous solid. I. Low frequency range. J. Acoust. Soc. Am. 28(2), 168–178 (1956)

    Article  Google Scholar 

  • Charnaya, E., Plotnikov, P., Michel, D., Tien, C., Borisov, B., Sorina, I., Martynova, E.: Acoustic studies of melting and freezing for mercury embedded into Vycor glass. Physica B 299(1–2), 56–63 (2001)

    Article  CAS  Google Scholar 

  • Cleary, M.P., Lee, S.-M., Chen, I.-W.: Self-consistent techniques for heterogeneous media. J. Eng. Mech 106(5), 861–887 (1980)

    Google Scholar 

  • Coasne, B., Czwartos, J., Sliwinska-Bartkowiak, M., Gubbins, K.E.: Effect of pressure on the freezing of pure fluids and mixtures confined in nanopores. J. Phys. Chem. B 113(42), 13874–13881 (2009)

    Article  CAS  Google Scholar 

  • Dobrzanski, C.D., Maximov, M.A., Gor, G.Y.: Effect of pore geometry on the compressibility of a confined simple fluid. J. Chem. Phys 148(5), 054503 (2018)

    Article  Google Scholar 

  • Evans, R., Stewart, M.C.: The local compressibility of liquids near non-adsorbing substrates: a useful measure of solvophobicity and hydrophobicity? J. Phys. Condens. Matter 27(19), 194111 (2015)

    Article  CAS  Google Scholar 

  • Gassmann, F.: Über die Elastizität poröser Medien. Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich. 96, 1–23 (1951)

    Google Scholar 

  • Gor, G.Y.: Adsorption stress changes the elasticity of liquid argon confined in a nanopore. Langmuir 30(45), 13564–13569 (2014)

    Article  CAS  Google Scholar 

  • Gor, G.Y.: Bulk modulus of not-so-bulk fluid. In: Poromechanics VI, Sixth Biot Conference on Poromechanics, pp. 465–472 (2017). https://doi.org/10.1061/9780784480779.057

  • Gor, G.Y., Gurevich, B.: Gassmann theory applies to nanoporous media. Geophys. Res. Lett. 45(1), 146–155 (2018)

    Article  Google Scholar 

  • Gor, G.Y., Siderius, D.W., Rasmussen, C.J., Krekelberg, W.P., Shen, V.K., Bernstein, N.: Relation between pore size and the compressibility of a confined fluid. J. Chem. Phys 143(19), 194506 (2015)

    Article  Google Scholar 

  • Gor, G.Y., Siderius, D.W., Shen, V.K., Bernstein, N.: Modulus–pressure equation for confined fluids. J. Chem. Phys. 145(16), 164505 (2016)

    Article  Google Scholar 

  • Gor, G.Y., Huber, P., Bernstein, N.: Adsorption-induced deformation of nanoporous materials—a review. Appl. Phys. Rev. 4(1), 011303 (2017)

    Article  Google Scholar 

  • Gregg, S.J., Sing, K.S.W.: Adsorption, surface area and porosity. Ber. Bunsenges. Phys. Chem. 86(10), 957 (1982)

    Google Scholar 

  • Hashin, Z., Shtrikman, S.: A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11(2), 127–140 (1963)

    Article  Google Scholar 

  • Huber, P.: Soft matter in hard confinement: phase transition thermodynamics, structure, texture, diffusion and flow in nanoporous media. J. Phys. Condens. Matter 27(10), 103102 (2015)

    Article  Google Scholar 

  • Jones, T.D.: Pore fluids and frequency-dependent wave propagation in rocks. Geophysics 51(10), 1939–1953 (1986)

    Article  Google Scholar 

  • Keeler, G., Batchelder, D.: Measurement of the elastic constants of argon from 3 to 77 degrees K. J. Phys. C Solid State Phys. 3(3), 510 (1970)

    Article  CAS  Google Scholar 

  • Knorr, K., Wallacher, D., Huber, P., Soprunyuk, V., Ackermann, R.: Are solidified fillings of mesopores basically bulk-like except for the geometric confinement? Eur. Phys. J. E 12(1), 51–56 (2003)

    Article  CAS  Google Scholar 

  • Kolesnikov, A., Georgi, N., Budkov, Y.A., Möllmer, J., Hofmann, J., Adolphs, J., Gläser, R.: Effects of enhanced flexibility and pore size distribution on adsorption-induced deformation of mesoporous materials. Langmuir 34, 7575–7584 (2018)

    Article  CAS  Google Scholar 

  • Kowalczyk, P., Balzer, C., Reichenauer, G., Terzyk, A.P., Gauden, P.A., Neimark, A.V.: Using in situ adsorption dilatometry for assessment of micropore size distribution in monolithic carbons. Carbon 103, 263–272 (2016)

    Article  CAS  Google Scholar 

  • Kuster, G.T., Toksöz, M.N.: Velocity and attenuation of seismic waves in two-phase media: part I. Theoretical formulations. Geophysics 39(5), 587–606 (1974)

    Article  Google Scholar 

  • Landers, J., Gor, G.Y., Neimark, A.V.: Density functional theory methods for characterization of porous materials. Colloids. Surf. A Physicochem. Eng. Asp 437, 3–32 (2013)

    Article  CAS  Google Scholar 

  • Mavko, G., Jizba, D.: Estimating grain-scale fluid effects on velocity dispersion in rocks. Geophysics 56(12), 1940–1949 (1991)

    Article  Google Scholar 

  • Mavko, G., Mukerji, T., Dvorkin, J.: The rock physics handbook: tools for seismic analysis of porous media. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  • Maximov, M.A., Gor, G.Y.: Molecular simulations shed light on potential uses of ultrasound in nitrogen adsorption experiments. Langmuir 34(51), 15650–15657 (2018)

    Article  CAS  Google Scholar 

  • Milton, G.W.: The theory of composites. Cambridge University Press, Cambridge (2002)

    Book  Google Scholar 

  • Molz, E., Wong, A.P., Chan, M., Beamish, J.: Freezing and melting of fluids in porous glasses. Phys. Rev. B 48(9), 5741 (1993)

    Article  CAS  Google Scholar 

  • Müller, T.M., Gurevich, B., Lebedev, M.: Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks—a review. Geophysics 75(5), 75A147–175A164 (2010)

    Article  Google Scholar 

  • Norris, A.: A differential scheme for the effective moduli of composites. Mech. Mater. 4(1), 1–16 (1985)

    Article  Google Scholar 

  • Nygård, K.: Local structure and density fluctuations in confined fluids. Curr. Opin. Colloid Interface Sci. 22, 30–34 (2016)

    Article  Google Scholar 

  • O’Connell, R.J., Budiansky, B.: Viscoelastic properties of fluid-saturated cracked solids. J. Geophys. Res. 82(36), 5719–5735 (1977)

    Article  Google Scholar 

  • Page, J., Liu, J., Abeles, B., Herbolzheimer, E., Deckman, H., Weitz, D.: Adsorption and desorption of a wetting fluid in Vycor studied by acoustic and optical techniques. Phys. Rev. E 52(3), 2763 (1995)

    Article  CAS  Google Scholar 

  • Schappert, K., Pelster, R.: Elastic properties and freezing of argon confined in mesoporous glass. Phys. Rev. B 78(17), 174108 (2008)

    Article  Google Scholar 

  • Schappert, K., Pelster, R.: Freezing behavior of argon layers confined in mesopores. Phys. Rev. B 83(18), 184110 (2011)

    Article  Google Scholar 

  • Schappert, K., Pelster, R.: Continuous freezing of argon in completely filled mesopores. Phys. Rev. Lett. 110(13), 135701 (2013a)

    Article  Google Scholar 

  • Schappert, K., Pelster, R.: Elastic properties of liquid and solid argon in nanopores. J. Phys. Condens. Matter 25(41), 415302 (2013b)

    Article  Google Scholar 

  • Schappert, K., Pelster, R.: Influence of the Laplace pressure on the elasticity of argon in nanopores. Europhys. Lett. 105(5), 56001 (2014)

    Article  Google Scholar 

  • Schappert, K., Pelster, R.: Experimental method for the determination of adsorption-induced changes of pressure and surface stress in nanopores. J. Phys. Condens. Matter 29(6), 06LT01 (2016)

    Article  Google Scholar 

  • Shimizu, H., Tashiro, H., Kume, T., Sasaki, S.: High-pressure elastic properties of solid argon to 70 GPa. Phys. Rev. Lett. 86(20), 4568 (2001)

    Article  CAS  Google Scholar 

  • Siderius, D.W., Mahynski, N.A., Shen, V.K.: Relationship between pore-size distribution and flexibility of adsorbent materials: statistical mechanics and future material characterization techniques. Adsorption 23(4), 593–602 (2017)

    Article  CAS  Google Scholar 

  • Smith, T.M., Sondergeld, C.H., Rai, C.S.: Gassmann fluid substitutions: a tutorial. Geophysics 68(2), 430–440 (2003)

    Article  Google Scholar 

  • Thommes, M., Cychosz, K.A.: Physical adsorption characterization of nanoporous materials: progress and challenges. Adsorption 20(2–3), 233–250 (2014)

    Article  CAS  Google Scholar 

  • Thommes, M., Smarsly, B., Groenewolt, M., Ravikovitch, P.I., Neimark, A.V.: Adsorption hysteresis of nitrogen and argon in pore networks and characterization of novel micro-and mesoporous silicas. Langmuir 22(2), 756–764 (2006)

    Article  CAS  Google Scholar 

  • Thommes, M., Kaneko, K., Neimark, A.V., Olivier, J.P., Rodriguez-Reinoso, F., Rouquerol, J., Sing, K.S.: Physisorption of gases, with special reference to the evaluation of surface area and pore size distribution (IUPAC Technical Report). Pure Appl. Chem. 87(9–10), 1051–1069 (2015)

    Article  CAS  Google Scholar 

  • Ustinov, E., Do, D.: Effect of adsorption deformation on thermodynamic characteristics of a fluid in slit pores at sub-critical conditions. Carbon 44(13), 2652–2663 (2006)

    Article  CAS  Google Scholar 

  • Wallacher, D., Knorr, K.: Melting and freezing of Ar in nanopores. Phys. Rev. B 63(10), 104202 (2001)

    Article  Google Scholar 

  • Warner, K., Beamish, J.: Ultrasonic measurement of the surface area of porous materials. J. Appl. Phys. 63(9), 4372–4376 (1988)

    Article  CAS  Google Scholar 

  • Wu, T.: The effect of inclusion shape on the elastic moduli of a two-phase material. Int. J. Solids Struct. 2(1), 1–8 (1966)

    Article  Google Scholar 

  • Zimmerman, R.W.: Compressibility of sandstones, vol. 29. Elsevier, New York (1990)

    Google Scholar 

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Acknowledgements

The authors thank the sponsors of the Curtin Reservoir Geophysics Consortium and China Scholarship Council (CSC) for financial support, and Stanislav Glubokovskikh and Patrick Huber for useful discussions.

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Authors and Affiliations

  1. Department of Exploration Geophysics, Curtin University, GPO Box U1987, Perth, WA, 6845, Australia

    Yongyang Sun & Boris Gurevich

  2. CSIRO Energy, 26 Dick Perry Avenue, Kensington, WA, 6151, Australia

    Boris Gurevich

  3. Otto H. York Department of Chemical and Materials Engineering, New Jersey Institute of Technology, Newark, NJ, USA

    Gennady Y. Gor

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  1. Yongyang Sun
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Correspondence to Gennady Y. Gor.

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Sun, Y., Gurevich, B. & Gor, G.Y. Modeling elastic properties of Vycor glass saturated with liquid and solid adsorbates. Adsorption 25, 973–982 (2019). https://doi.org/10.1007/s10450-019-00123-4

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