Skip to main content
Log in

Stress and strain during supercritical drying

  • Original Paper: Modeling, computational tools and theoretical studies of sol-gel and hybrid materials
  • Published:
Journal of Sol-Gel Science and Technology Aims and scope Submit manuscript

Abstract

Supercritical drying avoids capillary forces, but damaging stresses can be generated during solvent exchange, pressurization, and depressurization. Each of those steps has been analyzed, so the duration of the process can be minimized without risk to the sample. This work, which was initiated in collaboration with Professor Jean Phalippou’s group, is reviewed. Poromechanics is the study of stresses and strains resulting from interaction of the solid and liquid phases in a porous material. For example, if a gel is immersed in another liquid for solvent exchange, the gel network may undergo a transient contraction if the original pore liquid diffuses out faster than the replacement liquid diffuses in; poromechanical analysis quantifies the resulting stresses and indicates whether there is a risk of cracking. In the preparation of aerogels, when the pressure in the autoclave is decreased, the higher pressure inside the aerogel causes it to expand, which may result in cracking. Poromechanics reveals the rate of depressurization that can be imposed without creating damaging stresses. We also show that the sensitivity of gels to pore pressure can be exploited to measure their permeability to gases and liquids by observing the response to small loads or changes in temperature.

A dilatometer incorporated into the autoclave measures dilatation of the gel during the supercritical drying cycle, and poromechanical analysis allows extraction of the permeability from the measured strain. Similar analyses are used to minimize the cycle time while avoiding damaging stresses during the solvent exchange, pressurization, and heating, and depressurization steps.

Highlights

  • Poromechanics quantifies supercritical drying stresses during solvent exchange, pressurization and heating, and depressurization.

  • Supercritical drying duration is minimized by accounting for the pressure dependence of permeability, viscosity and compressibility.

  • By monitoring strain of the aerogel during depressurization, permeability can be measured as a function of pressure.

  • The permeability of gels is found from their response to small loads or changes in temperature.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Hdach H, Woignier T, Phalippou J, Scherer GW (1990) “Effect of aging and pH on the modulus of aerogels”. J Non-Cryst Solids 121:202–205

    Article  Google Scholar 

  2. Pauthe M, Quinson JF, Hdach H, Woignier T, Phalippou J, Scherer GW (1991) Autoclave treatment effect on silica alcogel sructure. J Non-Cryst Solids 130:1–7

    Article  Google Scholar 

  3. Woignier T, Phalippou J, Larnac G, Pernot F, Scherer GW (1992) Evolution of mechanical properties during the alcogel-aerogel-glass process. J Non-Cryst Solids 147&148:672–680

    Article  Google Scholar 

  4. Alaoui AH, Woignier T, Phalippou J, Scherer GW (1998) Room temperature densification of aerogel by isostatic compression. J Sol-Gel Sci Technol 13:365–369

    Article  Google Scholar 

  5. Duffours L, Woignier T, Phalippou J (1995) “Plastic behaviour of aerogels under isostatic pressure”. J Non-Cryst Solids 186:321–327

    Article  Google Scholar 

  6. Woignier T, Quinson JF, Pauthe M, Repellin Lacroix M, Phalippou J, Scherer GW (1994) The sintering of silica aerogels studied by thermoporometry. J Sol-Gel Sci Technol 2:277–282

    Article  Google Scholar 

  7. Scherer GW, Calas S, Sempéré R (1998) Densification kinetics and structural evolution during sintering of silica aerogel. J Non-Cryst Solids 240:118–130

    Article  Google Scholar 

  8. Biot MA (1941) General theory of three-dimensional consolidation. J Appl Phys 12:155–164

    Article  Google Scholar 

  9. Biot MA, Willis DG (1957) The elastic coefficients of the theory of consolidation. J Appl Mech 24:594–601

    Google Scholar 

  10. Coussy O (2004) Poromechanics. Wiley, West Sussex, England

    Google Scholar 

  11. Wang HF (2000) Theory of Linear Poroelasticity. Princeton Univ. Press, Princeton, NJ, p 287

    Google Scholar 

  12. Coussy O (2005) Poromechanics of freezing materials. J Mech Phys Solids 53:1689–1718

    Article  Google Scholar 

  13. Sun Z, Scherer GW (2010) Effect of Air Voids on Salt Scaling. Cem Concr Res 40:260–270

    Article  Google Scholar 

  14. Coussy O, Brisard S (2009) Prediction of drying shrinkage beyond the pore isodeformation assumption. J Mech Mater Struct 4(2):263–279

    Article  Google Scholar 

  15. Scherer GW (2015) Drying, shrinkage, and cracking of cementitious materials. Transport Porous Med 110(2):311–331

    Article  Google Scholar 

  16. Coussy O (2006) Deformation and stress from in-pore drying-induced crystallization of salt. J Mech Phys Solids 54:1517–1547

    Article  Google Scholar 

  17. Flatt RJ, Caruso F, Aguilar Sanchez AM, Scherer GW (2014) Chemomechanics of salt damage in stone. Nat Commun 5:4823

    Article  Google Scholar 

  18. Bear J (1972) Dynamics of fluids in porous media. American Elsevier, New York, NY

    Google Scholar 

  19. Scherer GW (2004) Characterization of saturated porous bodies. Concr Sci Eng 37:21–30

    Google Scholar 

  20. Scherer GW (1989) Drying gels: VII. Diffusion during drying. J Non-Cryst Solids 107:135–148

    Article  Google Scholar 

  21. Scherer GW (1994) Stress in aerogel during depressurization of autoclave: I. theory. J Sol-Gel Sci Technol 3:127–139

    Article  Google Scholar 

  22. Woignier T, Phalippou J, Hdach H, Scherer GW (1990) Mechanical properties of silica alcogels and aerogels. In: Zelinski BJJ, Brinker CJ, Clark DE, Ulrich DR eds. Better Ceramics Through Chemistry IV. Mat Res Soc, Pittsburgh, PA, p 1087–1099

    Google Scholar 

  23. M.P. Vukalovich, V.V. Altunin (1968) Thermophysical properties of carbon dioxide (Collet’s, London)

  24. Zhang Z, Scherer GW (2017) Supercritical drying of cementitious materials. Cem Concr Res 99:137–154

    Article  Google Scholar 

  25. Fabbri A, Corvisier J, Schubnel A, Brunet F, Goffé B, Rimmele G, Barlet-Gouédard V (2009) Effect of carbonation on the hydro-mechanical properties of Portland cements. Cem Concr Res 39:1156–1163

    Article  Google Scholar 

  26. Penoncello SG, Lemmon EW, Jacobsen RT, Shan Z (2003) A fundamental equation for trifluoromethane (R-23). J Phys Chem Ref Data 32:1473–1499

    Article  Google Scholar 

  27. H. Hdach (1992) Interaction liquide—solide dans les gels de silice: effet de la température, (Liquid-solid interaction in silica gels: effect of temperature), Doctoral thesis, Univ. Montpellier, France

  28. Brinker CJ, Scherer GW (1990) Sol-Gel Science. Academic Press, New York, NY, Ch. 6

    Google Scholar 

  29. Scherer GW, Hdach H, Phalippou J (1991) Thermal expansion of gels: a novel method for measuring permeability. J Non-Cryst Solids 130:157–170. Erratum: J. Non-Cryst Solids 194 (1996) 326

    Article  Google Scholar 

  30. Scherer GW (1992) Stress development during supercritical drying. J Non-Cryst Solids 145:33–40

    Article  Google Scholar 

  31. Scherer GW, Swiatek RM (1989) Measurement of permeability: II. Silica Gel. J Non-Cryst Solids 113:119–129

    Article  Google Scholar 

  32. Scherer GW (1994) Measuring permeability by the thermal expansion method for rigid or highly permeable gels. J Sol-Gel Sci Technol 3:31–40

    Article  Google Scholar 

  33. Scherer GW (1989) Effect of shrinkage on modulus of silica gel. J Non-Cryst Solids 109:183–190

    Article  Google Scholar 

  34. Scherer GW (1992) Bending of gel beams: method of characterizing mechanical properties and permeability. J Non-Cryst Solids 142:18–35

    Article  Google Scholar 

  35. Scherer GW (2000) Measuring permeability of rigid materials by a beam-bending method: I. Theory. J Am Ceram Soc 83:2231–2239. Erratum, J Am Ceram Soc. 87 [8] (2004) 1612–1613

    Article  Google Scholar 

  36. Scherer GW, Prévost JH, Wang Z-H (2009) Bending of a poroelastic beam with lateral diffusion. Int J Solids Struct 46:3451–3462

    Article  Google Scholar 

  37. Scherer GW (1997) Effect of drying on properties of silica gel. J Non-Cryst Solids 215:155–168

    Article  Google Scholar 

  38. Scherer GW (1995) Viscoelasticity and permeability of silica gels. Faraday Discus 101:225–234

    Article  Google Scholar 

  39. Sharp KG, Scherer GW (1997) Interaction of formic acid with the silica gel network. J Sol-Gel Sci Technol 8:165–171

    Google Scholar 

  40. Scherer GW (1994) Relaxation of a viscoelastic gel bar: I. Theory. J Sol-Gel Sci Technol 1:169–175

    Article  Google Scholar 

  41. Gross J, Scherer GW (2003) Dynamic pressurization: novel method for measuring fluid permeability. J Non-Cryst Solids 325:34–47

    Article  Google Scholar 

  42. D.H. Bangham and R.I. Razouk (1938) “The swelling of charcoal. Part V. The saturation and immersion expansions and the heat of wetting”. Proc Roy Soc. London A CLXVI 572–586

  43. L.J. Klinkenberg (1941) The permeability of porous media to liquids and gases, Drill Proc. API-41 200–213

  44. Scherer GW, Smith DM, Stein D (1995) Deformation of aerogels during characterization. J Non-Cryst Solids 186:309–315

    Article  Google Scholar 

  45. Scherer GW, Smith DM, Qiu X, Anderson JM (1995) Compression of aerogels. J Non-Cryst Solids 186:316–320

    Article  Google Scholar 

  46. Reichenauer G, Scherer GW (2000) Nitrogen adsorption in compliant materials. J Non-Cryst Solids 277:162–172

    Article  Google Scholar 

  47. Reichenauer G, Scherer GW (2001) Extracting the pore size distribution of compliant materials from nitrogen adsorption. Colloids Surf A 187-188:41–50

    Article  Google Scholar 

Download references

Acknowledgements

In 1989, the author had the pleasure of spending 3 months as a visitor in the group of Jean Phalippou. That began a long and stimulating collaboration, much of the fruit of which is reviewed in the present paper. Jean became more than a colleague: he was a friend and a role model as a teacher and scientist. Jean will be missed, but he will be remembered with great affection.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to George W. Scherer.

Ethics declarations

Conflict of interest

The author declares that they have no conflict of interest.

Electronic supplementary material

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Scherer, G.W. Stress and strain during supercritical drying. J Sol-Gel Sci Technol 90, 8–19 (2019). https://doi.org/10.1007/s10971-018-4808-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10971-018-4808-6

Keywords

Navigation