Diffusion rate of polyethylene glycol into cell walls of red pine following vacuum impregnation


Rates of penetration of polyethylene glycol (PEG) molecular weight (MW) 1,000, 2,000, and 4,000 from 30% aqueous solutions into hydrated cell walls of red pine samples following vacuum impregnation were estimated by examining retained swelling of the samples after different post-treatment conditioning times. To model PEG diffusion into wood cell walls, a hollow cylinder diffusion model was developed and diffusion coefficients were estimated and compared to those determined with a plane membrane diffusion model. The models gave similar results. The diffusion coefficient of PEG MW 1,000 at room temperature was estimated to be in the order of 10−13 m2/s, while the penetration rates of both PEG 2,000 and 4,000 were about an order lower. These findings indicate that treatments of wood by PEG can be significantly shorter than present practices of soaking green samples in solution if the samples are vacuum/pressure impregnated with PEG solution.

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Fig. 1
Fig. 2
Fig. 3
Fig. 4


\( \sqrt t \) :

Square root of time

D :

Diffusion coefficient


Equilibrium moisture content


Fiber saturation point


Longitudinal direction

M :

Total amount of substance diffused into the cell walls at equilibrium

M t :

Amount of substance diffused into the cell walls at any time t


Molecular weight


Molecular weight distribution


Polyethylene glycol


Radial direction

R h_PEG :

Hydrodynamic radius of PEG molecule in water solution

R h_wat :

Hydrodynamic radius of water molecule


Retained swelling upon treatment, %


Scanning transmission electron microscope coupled with energy dispersive X-ray analyzer


Tangential direction

\( V_{\text{TR}}^{\text{D}} \) :

Dry volume of samples upon treatment, cm3

\( V_{\text{UNTR}}^{\text{D}} \) :

Initial volume of freeze-dried samples, cm3

η PEG :

Viscosity of aqueous PEG solution

η wat :

Viscosity of water


  1. Andreoli TE, Dennis WV, Weigl AM (1969) The effect of Amphotericin B on the water and nonelectrolyte permeability of thin lipid membranes. J Gen Physiol 53:133–156. doi:10.1085/jgp.53.2.133

    Article  CAS  Google Scholar 

  2. Basmadjian D (1999) The art of modeling in science and engineering. Chapman and Hall/CRC, Boca Raton, FL, 237 pp

  3. Carslaw HS, Jaeger JC (1959) Conduction of heat in solids. Clarendon Press, Oxford, pp 332–333

    Google Scholar 

  4. Choong ET (1965) Diffusion coefficients of softwoods by steady-state and theoretical methods. For Prod J 15(1):21–27

    Google Scholar 

  5. Cooper PA (1996) Rate of swelling of vacuum-impregnated wood. Wood Fiber Sci 28(1):28–38

    CAS  Google Scholar 

  6. Cooper PA (1998) Diffusion of copper in wood cell walls following vacuum treatment. Wood Fiber Sci 30(4):382–395

    CAS  Google Scholar 

  7. Crank J (1970) The mathematics of diffusion. Oxford University Press, London, pp 45, 62

  8. Dohmen MPJ, Pereira AM, Timmer JMK, Benes NE, Keurentjes JTF (2008) Hydrodynamic radii of polyethylene glycol in different solvents determined from viscosity measurements. J Chem Eng Data 53(1):63–65. doi:10.1021/je700355n

    Article  CAS  Google Scholar 

  9. Ericson HD, Schmidt RN, Laing JR (1968) Freeze-drying and wood shrinkage. For Prod J 18(6):63–68

    Google Scholar 

  10. Fee CJ, Van Alstine JM (2004) Prediction of the viscosity radius and the size exclusion chromatography behavior of PEGylated proteins. Bioconjug Chem 15(6):1304–1313. doi:10.1021/bc049843w

    Article  CAS  Google Scholar 

  11. Hoffmann P (1989) HPLC for the analysis of polyethylene glycols (PEG) in wood. In: Conservation of wet wood and metal. Proceedings of the ICOM conservation working groups on wet organic archaeological materials and metals. Western Australian Museum, Perth, Australia, pp 41–60

  12. Ishimaru Y, Inoue E, Sadoh T, Nakato K (1986) Dimensional stability of wood with adsorbed polyethylene glycol. I. Effect of molecular weight. Mokuzai Gakkaishi 32(11):888–895

    CAS  Google Scholar 

  13. Jeremic D, Cooper P, Heyd D (2006) PEG bulking of wood cell walls as affected by moisture content and nature of solvent. Wood Sci Technol 41(7):597–606. doi:10.1007/s00226-006-0120-7

    Article  CAS  Google Scholar 

  14. Jeremic D, Cooper P, Brodersen P (2007) Penetration of poly(ethylene glycol) into wood cell walls of red pine. Holzforschung 61(3):272–278. doi:10.1515/HF.2007.068

    Article  CAS  Google Scholar 

  15. Kirincic S, Klofutar C (1999) Viscosity of aqueous solutions of poly(ethylene glycol)s at 298.15 K. Fluid Phase Equilib 155(2):311–325. doi:10.1016/S0378-3812(99)00005-9

    Article  CAS  Google Scholar 

  16. Kitani Y, Ohsawa J, Nakato K (1970) Adsorption of polyethylene glycol on water-swollen wood versus molecular weight. Mokuzai Gakkaishi 16(7):326–333

    Google Scholar 

  17. Mantanis GI, Young RA, Rowell RM (1994) Swelling of wood. Part II. Swelling in organic liquids. Holzforschung 48(6):480–490

    CAS  Google Scholar 

  18. Mantanis GI, Young RA, Rowell RM (1995a) Swelling of wood. Part III. Effect of temperature and extractives on rate and maximum swelling. Holzforschung 49(3):239–248

    CAS  Article  Google Scholar 

  19. Mantanis GI, Young RA, Rowell RM (1995b) Swelling of wood. Part IV. A statistical model for prediction of maximum swelling of wood in organic liquids. Wood Fiber Sci 27(1):22–24

    CAS  Google Scholar 

  20. Panshin AJ, de Zeeuw C (1970) Textbook of wood technology, vol 1, 3rd edn. McGraw-Hill Inc., New York, p 123

    Google Scholar 

  21. Stamm AJ (1959) Bound-water diffusion into wood in the fiber direction. For Prod J 9(1):27–32

    CAS  Google Scholar 

  22. Stamm AJ (1960) Bound-water diffusion into wood in the across-the-fiber direction. For Prod J 10(10):524–528

    CAS  Google Scholar 

  23. Stamm AJ (1964) Factors affecting the bulking and dimensional stabilization of wood with polyethylene glycols. For Prod J 14(9):403–408

    Google Scholar 

  24. Thomas DK, Charlesby A (1960) Viscosity relationship in solutions of polyethylene glycols. J Polym Sci 42(139):195–202. doi:10.1002/pol.1960.1204213922

    Article  CAS  Google Scholar 

  25. Wallstrom L, Lindberg KAH, Johansson J (1995) Wood surface stabilization. Holz Roh Werkst 53:87–92

    Article  Google Scholar 

  26. Yata S, Mukudai J, Kajita H (1979) Morphological studies on the movement of substances into the cell wall of wood. II. Diffusion of copper compounds into the cell wall. Mokuzai Gakkaishi 25(3):171–176

    Google Scholar 

  27. Yata S, Mukudai J, Kajita H (1981a) Morphological studies on the movement of substances into the cell wall of wood. III. Diffusion of zinc compounds into the cell wall. Mokuzai Gakkaishi 27(11):761–766

    CAS  Google Scholar 

  28. Yata S, Mukudai J, Kajita H (1981b) Morphological studies on the movement of substances into the cell wall of wood. IV. Diffusion of hexavalent chromium into the cell wall. Mokuzai Gakkaishi 27(12):821–827

    CAS  Google Scholar 

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Jeremic, D., Quijano-Solis, C. & Cooper, P. Diffusion rate of polyethylene glycol into cell walls of red pine following vacuum impregnation. Cellulose 16, 339 (2009). https://doi.org/10.1007/s10570-008-9255-z

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  • Wood
  • Cell wall
  • Diffusion
  • Cylinder
  • Plane
  • Polymer
  • Polyethylene glycol
  • MW