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Licensed Unlicensed Requires Authentication Published by De Gruyter June 1, 2005

Small angle scattering in the Porod region from hydrated paper sheets at varying humidities

  • Christopher J. Garvey , Ian H. Parker , Robert B. Knott and George P. Simon
From the journal


The microscopic changes in the structure of paper at different equilibrium moisture contents were examined using the novel technique of contrast variation small angle neutron scattering (SANS). Contrast variation, by appropriate selection of the H2O:D2O ratio, was used to simplify the scattering from hydrated paper to a two-phase approximation. The two phases were paper polymers (cellulose, lignin and hemicelluloses) and a phase consisting of water and voids. The two-phase approximation is justified by consideration of the chemistry and density of each of the polymer species belonging to paper, and by matching the scattering length density of the sorbed moisture to air. The neutron intensity at the higher scattering angles examined was successfully fitted using the Porod law, which is applicable to scattering from a two-phase system at the high scattering angle limit. This limit is related to the specific surface area between the two phases. The limiting scattered intensity of neutrons was found to increase with increasing moisture content for a range of paper materials. It is concluded that the sorption of water increased the limiting intensity because water disrupted polymer-polymer bonding. The Porod law also predicts the slope of the intensity/scattering angle curve at the high scattering angle limit.


Corresponding author. Australian Nuclear Science and Technology Organisation, PMB 1, Menai NSW 2234, Australia. E-mail:


Adamson, A.W. (1990) Physical Chemistry of Surfaces. Wiley-Interscience, New York. pp. 647–648.Search in Google Scholar

Beaucage, G. (1995) Approximations leading to a unified exponential/power-law approach to small angle scattering. J. Appl. Cryst.28:717–728.10.1107/S0021889895005292Search in Google Scholar

Brunauer, S., Copeland, L.E., Kantro, D.L. (1966) The Langmuir and BET Theories. In: The Solid-Gas Interface, Vol. 1. Ed. Flood, E.A. Marcel Dekker, New York. pp. 77–104.Search in Google Scholar

Cranshaw, J., Vickers, M.E., Briggs, N.P., Heenan, R.K., Cameron, R.E. (2000) The hydration of TENCEL® cellulose fibres studied using contrast variation in small angle neutron scattering. Polymer41:1873–1881.10.1016/S0032-3861(99)00331-6Search in Google Scholar

CRC Handbook of Chemistry and Physics. CRC Press, Cleveland, 2000. pp. 15–25.Search in Google Scholar

Feigin, L.A., Svergun, D.I. - Structure Analysis by Small Angle X-ray and Neutron Scattering. Plenum Press, New York, 1969. pp. 107–14.Search in Google Scholar

Fisher, E.W., Herchenroder, P., Manley, R.S.J., Stamm, M. (1976) Small-angle scattering of selectively deuterated cellulose. Macromolecules11:213–217.Search in Google Scholar

Garvey, C.J., Simon, G.P., Knott, R.B., Whittaker, A.K., Parker, I.H. (2001) An Experimental Study by NMR and SANS of the Hydration of Paper Sheets. In: Proceedings of the 12th Fundamental Symposium of Papermaking, University of Oxford. Vol. 1, pp. 359–380.Search in Google Scholar

Greenland, D.J., Quirk, J.P. (1964) Determination of the total specific surface areas of soils by adsorption of cetyl pyridinium bromide. J. Soil Sci.15:178–191.10.1111/j.1365-2389.1964.tb02217.xSearch in Google Scholar

Guinier, A., Fournet, G. - Small-Angle Scattering of X-rays. John Wiley and Sons, New York, 1955.Search in Google Scholar

Hammouda, B., Krueger, S., Glinka, C.J. (1993) Small angle neutron scattering at National Institute for Standards and Technology. J. Res. Inst. Stand. Technol.98:31–46.10.6028/jres.098.003Search in Google Scholar

Hermans, P.H., Heikens, D., Weidinger, A. (1959) A quantitative investigation on the X-ray small angle scattering of cellulose fibres. Part II The scattering power of various cellulose fibres. J. Polymer Sci.35:145–165.Search in Google Scholar

Higgins, J.S., Benoît, H.C. - Polymers and Neutron Scattering. Clarendon Press, Oxford, 1994.Search in Google Scholar

Hill, T.L. - An Introduction to Statistical Thermodynamics. Dover, New York, 1986. pp. 134.Search in Google Scholar

Howsman, J.A., Sisson, W.A. (1954) In: Cellulose and Cellulose Derivatives. Eds Ott, E., Spurlin, H.M., Graffin., M.V. Vol. 1, 2nd Edition, Interscience, New York. pp. 231–316.Search in Google Scholar

Jakob, H.F., Tschegg, S.E., Fratzl, P. (1986) Hydration Dependence of the Wood-Cell Wall Structure in Picea abies. A Small-Angle X-ray Scattering Study. Macromolecules29:8435–8440.Search in Google Scholar

Klenkova, N.I., Ivashkin, G.P. (1963) Internal surface area and capillary structure of native and mercerized cellulose. J. Appl. Chem. USSR36:398–408.Search in Google Scholar

Koberstein, J.T., Morra, B., Stein, R.S. (1980) The determination of diffuse-boundary thicknesses of polymers by small-angle X-ray scattering. J. Appl. Cryst.13:34–45.10.1107/S0021889880011478Search in Google Scholar

Krässig, H.A. - Cellulose: structure, accessibility, and reactivity. Gordon and Breach, Yverdon, 1992.Search in Google Scholar

Kratky, O., Miholic, G. (1963) Small-angle investigations with absolute intensity measurments on regenerated, air-swollen cellulose. J. Polym. Sci.Part C2:449–476.Search in Google Scholar

Li, J-C., Benham, M.J., Howe, L.D., Ross, D.K. (1989) Neutron and X-ray scattering: complementary techniques. Inst. Phys. Conf. Ser.101:155–168.Search in Google Scholar

Luzzati, V., Witz, J., Nicolaieff, A. (1961) Determination of mass and dimensions of proteins in solution by x-ray scattering measured on an absolute scale. J. Molec. Biol.3:367–378.10.1016/S0022-2836(61)80050-8Search in Google Scholar

Manley, R.S.J. (1963) Hydrolysis of cellulose triacetate crystals. J. Polymer Sci.Part A1:1893–1899.10.1002/pol.1963.100010604Search in Google Scholar

Mitropoulos, A.C., Kanellpoulos, N.K., Stefanpoulos, K.L., Heenan, R.K. (1998) Scattering by Curved and Fractal Surfaces. J. Colloid Interface Sci.203:229–230.10.1006/jcis.1998.5550Search in Google Scholar

Müller, M., Czihak, C., Schober, H., Nishiyama, Y., Vogl, G. (2000) All disordered regions of native cellulose show common low-frequency dynamics. Macromolecules33:1834–1840.10.1021/ma991227lSearch in Google Scholar

National Institute of Standards and Technology Center for Neutron Research. - NCNR SANS Data Acquisition Manual, US Department of Commerce, Gaithersburg, 1999.Search in Google Scholar

Nissan, A.H. (1976) H-bond dissociation in hydrogen bond dominated solids. Macromolecules9:840–850.10.1021/ma60053a026Search in Google Scholar

Perrin, P., Prud’homme, R.E. (1994) SAXS measurements of interfacial thickness in amorphous polymer blends containing a diblock copolymer. Macromolecules27:1852–1860.10.1021/ma00085a029Search in Google Scholar

Porod, G. (1951) The x-ray small angle scattering of close packed colloid systems. I. Kolloid-Z.124:83–114.10.1007/BF01512792Search in Google Scholar

Porod, G. (1952) The x-ray small angle scattering of close packed colloid systems. II. Kolloid-Z.125:108–122.10.1007/BF01526289Search in Google Scholar

Roberts, G.A.F. (1996) In: Paper Chemistry. Ed. Roberts, J.C. Blackie Academic, Glasgow.Search in Google Scholar

Salmén, N.L., Back, E.L. (1977) The influence of water on the glass transition temperature of cellulose. Tappi J.60(12):137–140.Search in Google Scholar

Salmén, N.L., Back, E.L. (1980) Moisture-dependant thermal softening of paper evaulated by its elastic modulus. Tappi J.63(6):117–121.Search in Google Scholar

Schwartz, M. - Principles of Electrodynamics. Dover, New York, 1987. pp. 223–224.Search in Google Scholar

Sears, V.F. (1992) Neutron scattering length and cross sections. Neutron News3:26–37.10.1080/10448639208218770Search in Google Scholar

Standards Australia (2001) AS/NZS 1301.209s, Methods of test for pulp and paper (metric units)-Laboratory processing of pulp-PFI mill method.Search in Google Scholar

Statton, W.O. (1956) Crystallite regularity and void content in cellulose fibres as shown by small angle X-ray scattering. J. Polymer Sci.22:385–397.10.1002/pol.1956.1202210204Search in Google Scholar

van de Hulst, H.C. - Light Scattering by Small Particles. Dover, New York, 1986. pp. 3.Search in Google Scholar

Published Online: 2005-06-01
Published in Print: 2004-08-01

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