Cellulose

, Volume 19, Issue 2, pp 313–318 | Cite as

The role of the Ekenstam equation on the kinetics of cellulose hydrolytic degradation

LETTER TO THE EDITOR

Abstract

The meaning of the Ekenstam equation (1/DP − 1/DP°) = kt is shortly discussed. Several misleading statements about its application to cellulose hydrolysis are underlined in order to improve the reliability of kinetic analyses. To this end, some further simple analyses are suggested to the experimentalists.

Keywords

Degree of polymerisation Size exclusion chromatography Paper degradation 

List of symbols

DP°, DP

Degree of polymerisation

k

Rate constant of hydrolysis (mol g−1 t−1) for the Ekenstam equation; (t−1) for first-order kinetics

k1,0

Initial rate constant (Emsley and Stevens model)

k2

Rate constant of decrease of k1,0

LODP

Levelling-off degree of polymerisation

M0

Zero-order momentum of a Mw distribution

M1

First-order momentum of a Mw distribution

Mw

Molecular weight

Initial amount of scissile units

S

Number of broken bonds (scissions)

Sn(0)

nth derivative of the function S(t) at t = 0

References

  1. Calvini P (2005) The influence of levelling-off degree of polymerisation on the kinetics of cellulose degradation. Cellulose 12:445–447CrossRefGoogle Scholar
  2. Calvini P (2010) What went wrong with the kinetics of cellulose degradation? In: Lejeune A, Deprez T (eds) Cellulose: Structure and Properties. Derivatives and Industrial Uses. Nova Science Publishers, NY, pp 417–426Google Scholar
  3. Calvini P, Gorassini A (2006) On the rate of paper degradation: lessons (learned) from the past. Restaurator 27:275–290CrossRefGoogle Scholar
  4. Calvini P, Conio G, Princi E, Vicini S, Pedemonte E (2006) Viscometric determination of dialdehyde content in periodate oxycellulose Part II. Topochemistry of oxidation. Cellulose 13:571–579CrossRefGoogle Scholar
  5. Calvini P, Gorassini A, Merlani AL (2008) On the kinetics of cellulose degradation: looking beyond the pseudo zero order rate equation. Cellulose 15:193–203CrossRefGoogle Scholar
  6. Cheng Y, Brown KM, Prud’homme RK (2002) Preparation and characterization of molecular weight fractions of guar galactomannans using acid and enzymatic hydrolysis. Int J Biol Macromol 31:29–35CrossRefGoogle Scholar
  7. Dupont A-L, Mortha G (2004) Comparative evaluation of size-exclusion chromatography and viscometry for the characterisation of cellulose. J Chromatog A 1026:129–141CrossRefGoogle Scholar
  8. Emsley AM, Stevens GC (1994) Kinetics and mechanisms of the low-temperature degradation of cellulose. Cellulose 1:26–56CrossRefGoogle Scholar
  9. Emsley AM, Heywood RJ, Ali M, Eley CM (1997) On the kinetics of degradation of cellulose. Cellulose 4:1–5CrossRefGoogle Scholar
  10. Evans R, Wallis AFA (1989) Cellulose molecular weights determined by viscometry. J Appl Polym Sci 37:2331–2340CrossRefGoogle Scholar
  11. Feller RL, Lee SB, Bogaard J (1986) The kinetics of cellulose degradation. In: Needles HL, Zeronian SH (eds) Historic textile and paper materials: conservation and characterization. Adv Chem Ser 212, Am Chem Soc, Washington, DC, pp 329–346Google Scholar
  12. Gehlen MH (2009) Approximate solution of the autocatalytic hydrolysis of cellulose. Cellulose 16:1069–1073CrossRefGoogle Scholar
  13. Gilbert R, Jalbert J, Tétreault P, Morin B, Denos Y (2009) Kinetics of the production of chain-end groups and methanol from the depolymerization of cellulose during the ageing of paper/oil systems. Part 1: Standard wood kraft insulation. Cellulose 16:327–338CrossRefGoogle Scholar
  14. Glaus MA, Van Loon R (2004) Cellulose degradation at alkaline conditions: long-term experiments at elevated temperatures. Nagra Tech Report 03–08:1–70Google Scholar
  15. Guaita M, Chiantore O, Luda MP (1990) Monte Carlo simulations of polymer degradations. 1. Degradations without volatilization. Macromolecules 23:2087–2092CrossRefGoogle Scholar
  16. Håkansson H, Ahlgren P (2005) Acid hydrolysis of some industrial pulps: effect of hydrolysis conditions and raw material. Cellulose 12:177–183CrossRefGoogle Scholar
  17. Herdan G (1953) Fitting of polymer distributions of molecular weights by the method of moments. J Polym Sci 10(1):1–18CrossRefGoogle Scholar
  18. Hill DJT, Le TT, Darveniza M, Saha T (1996) A study of the degradation of cellulosic insulation materials in a power transformer. Part III. Degradation products of cellulose insulation paper. Polym Degrad Stab 51:211–218CrossRefGoogle Scholar
  19. Lauriol J-M, Comtat J, Froment P, Pla F, Robert A (1987) Molecular weight distribution of cellulose by on-line size exclusion chromatography—low angle laser light scattering. Holzforschung 41:165–169CrossRefGoogle Scholar
  20. Łojewski T, Zięba K, Knapik A, Bagniuk J, Lubańska A, Łojewska J (2010) Evaluating paper degradation progress. Cross-linking between chromatographic, spectroscopic and chemical results. Appl Phys A 100:809–821CrossRefGoogle Scholar
  21. Łojewski T, Zięba K, Kołodziej A, Łojewska J (2011) Following cellulose depolymerization in paper: comparison of size exclusion chromatography techniques. Cellulose 18:1349–1363CrossRefGoogle Scholar
  22. Marx-Figini M (1986) The acid-catalyzed degradation of cellulose in the range of medium and low degrees of polymerization. Makromol Chem 187:679–687CrossRefGoogle Scholar
  23. McShane CP, Rapp KJ, Corkran JL, Gauger GA, Luksich J (2002) Aging of Kraft paper in natural ester dielectric fluid. In: Proceedings of IEEE 2002 14th international conference on dielectric liquids (ICDL), Graz (Austra) July 7–12, pp 173–177Google Scholar
  24. Montroll E (1941) Molecular size distributions and depolymerization reactions in polydisperse systems. J Am Chem Soc 63:1215–1220CrossRefGoogle Scholar
  25. Pavasars I, Hagberg J, Borén H, Allard B (2003) Alkaline degradation of cellulose: mechanisms and kinetics. J Polym Environment 11(2):39–47CrossRefGoogle Scholar
  26. Potthast A, Rosenau T, Kosma P (2006) Analysis of oxidized functionalities in cellulose. In: Klemm D (ed) Polysaccharides II, Adv Polym Sci 205, Springer, Berlin, pp 1–48Google Scholar
  27. Potthast A, Kostic M, Schiehser S, Kosma P, Rosenau T (2007) Studies on oxidative modification of cellulose in the periodate system: Molecular weight distribution and carbonyl group profiles. Holzforschung 61:662–667CrossRefGoogle Scholar
  28. Potthast A, Schiehser S, Rosenau T, Kostic M (2009) Oxidative modifications of cellulose in the periodate system—Reduction and beta-elimination reactions. Holzforschung 63:12–17CrossRefGoogle Scholar
  29. Sawoszczuk T, Barański A, Łagan JM, Łojewski T, Zięba K (2008) On the use of ASTM closed vessel tests in accelerated ageing research. J Cult Herit 9:401–411CrossRefGoogle Scholar
  30. Schult T, Hjerde T, Optun OI, Kleppe PJ, Moe S (2002) Characterization of cellulose by SEC-MALLS. Cellulose 9:149–158CrossRefGoogle Scholar
  31. Sharples A (1971) Degradation of cellulose and its derivatives. A. Acid hydrolysis and alcoholysis. In: Bikales NH, Segal L (eds) Cellulose and cellulose derivatives Vol V pt V, 2nd edn. Wiley-Intescience, NY, pp 991–1006Google Scholar
  32. Stephens CH, Whitmore PM, Morris HR, Bier ME (2008) Hydrolysis of the amorphous cellulose in cotton-based paper. Biomacromolecules 9:1093–1099CrossRefGoogle Scholar
  33. Stol R, Pedersoli JL, Poppe H, Kok WTh (2002) Application of size exclusion electrochromatography to the microanalytical determination of the molecular mass distribution of celluloses from objects of cultural and historical value. Anal Chem 74:2314–2323CrossRefGoogle Scholar
  34. Whitmore PM, Bogaard J (1994) Determination of the cellulose scission route in the hydrolytic and oxidative degradation of paper. Restaurator 15: 26-45 http://www.cmu.edu/acrc/Publications/h%20and%20o%20degradation.pdf. Accessed 21 December 2011
  35. Zervos S, Moropoulou A (2005) Cotton cellulose ageing in sealed vessels. Kinetic model of autocatalytic depolymerization. Cellulose 12:485–496CrossRefGoogle Scholar
  36. Zou X, Uesaka T, Gurnagul N (1996) Prediction of paper permanence by accelerated ageing I. Kinetic analysis of the aging process. Cellulose 3:243–267CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Istituto per la Tutela delle Opere Grafiche (ITOG)Zero BrancoItaly

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