The kinetics of the spontaneous, proton- and AlIII-catalysed hydrolysis of 1,5-anhydrocellobiitol - Models for cellulose depolymerization in paper aging and alkaline pulping, and a benchmark for cellulase efficiency

Article abstract of DOI:10.1139/v05-168

The kinetics of the spontaneous, proton- and Al^III-catalysed hydrolyses of the Cl-O4′ bond in 1,5-anhydrocellobiitol have been measured at elevated temperatures (125.0-220.0°C). Data for the first two processes extrapolate to the expression k = (8.6 ± 2.1 × 10^-16) + (1.4 ± 0.2 × 10^9-pH) s^-1 at 25°C. These room-temperature figures were used to model cellulose depolymerization by the af Ekenstam equation. The spontaneous process is too slow to contribute to loss of paper strength on aging, and even the acid-catalysed process is significant only below -pH 4.0. However, the spontaneous hydrolysis readily accounts for the reduction of cellulose degree of polymerization (DP) during alkaline (e.g., kraft) pulping of cellulose fibres. Efficient electrophilic catalysis by Al ^III was observed at 150.0°C in 0.1 mol/L succinate buffers of room temperature pH 3.05 and 3.35 (k₂ = 8.1 ± 0.4 ± 10^-3 and 4.2 ± 0.2 × 10^-3 (mol/L) ^-1 s^-1, respectively). The apparent activation energy of the Al^III-catalysed process was 31 ± 4 kJ mol^-1, lower than that of the proton-catalysed path, suggesting the electrophilic catalysis increases in importance as the temperature approaches ambient. Consequently, it appears that the culprit in the impermanence of "rosin-alum"-sized paper is Al^II, directly acting as a Lewis acid, not the Al^III hydration sphere as a Bronsted acid. Conservation measures should either address this or be generic (e.g., low-temperature storage).

Full text of DOI:10.1139/v05-168

1
516
The kinetics of the spontaneous, proton- and AlIII-
catalysed hydrolysis of 1,5-anhydrocellobiitol —
Models for cellulose depolymerization in paper
aging and alkaline pulping, and a benchmark for
1
cellulase efficiency
John William Baty and Michael L. Sinnott
III
Abstract: The kinetics of the spontaneous, proton- and Al -catalysed hydrolyses of the C1—O4′ bond in 1,5-anhydro-
cellobiitol have been measured at elevated temperatures (125.0–220.0 °C). Data for the first two processes extrapolate
to the expression k = (8.6 ± 2.1 × 10– ) + (1.4 ± 0.2 × 10
16
–9-pH
) s at 25 °C. These room-temperature figures were
–1
used to model cellulose depolymerization by the af Ekenstam equation. The spontaneous process is too slow to contrib-
ute to loss of paper strength on aging, and even the acid-catalysed process is significant only below ~pH 4.0. However,
the spontaneous hydrolysis readily accounts for the reduction of cellulose degree of polymerization (DP) during alka-
III
line (e.g., kraft) pulping of cellulose fibres. Efficient electrophilic catalysis by Al was observed at 150.0 °C in
.1 mol/L succinate buffers of room temperature pH 3.05 and 3.35 (k = 8.1 ± 0.4 × 10 and 4.2 ± 0.2 × 10 (mol/L)–1 s ,
–
3
–3
–1
0
2
III
–1
respectively). The apparent activation energy of the Al -catalysed process was 31 ± 4 kJ mol , lower than that of the
proton-catalysed path, suggesting the electrophilic catalysis increases in importance as the temperature approaches am-
bient. Consequently, it appears that the culprit in the impermanence of “rosin-alum”-sized paper is Al , directly acting
III
III
as a Lewis acid, not the Al hydration sphere as a Brønsted acid. Conservation measures should either address this or
be generic (e.g., low-temperature storage).
Key words: cellulose, hydrolysis, kraft pulping, paper conservation, rosin-alum sizing.
Résumé : Opérant à des températures élevées (125,0 à 220,0 °C), on a mesuré les vitesses des réactions d’hydrolyse,
spontanée et catalysées par le proton ou l’aluminium(III), de la liaison C1—O4′ du 1,5-anhydrocellobiitol. Les données
–
16
–9-pH
–1
pour les deux premiers processus conduisent à l’expression k = (8,6 ± 2,1 × 10 ) + (1,4 ± 0,2 × 10
) s extra-
polée à 25 °C. On a utilisé ces valeurs à la température ambiante comme modèle pour la dépolymérisation de la cellu-
lose par l’équation de af Ekenstam. Le processus spontané est trop lent pour contribuer à une perte de la force du
papier avec l’âge; le processus catalysé par un acide n’est significatif qu’à des pH inférieurs à environ 4,0. Toutefois,
l’hydrolyse spontanée permet d’expliquer facilement la réduction du degré de polymérisation (DP) de la cellulose du-
rant le traitement alcalin (kraft) des fibres de cellulose. On a observé une catalyse électrophile efficace par
l’aluminium(III) à 150,0 °C, dans des tampons de succinate, à la température ambiante et à des pH de 3,05 et 3,35
k2 = 8,1 ± 0,4 × 10–3 et 4,2 ± 0,2 × 10 (mol/L)
–3
–1 –1
s
respectivement). L’énergie d’activation apparente pour le pro-
(
–
1
cessus catalysé par l’aluminium(III) est de 31 ± 4 kJ mol , inférieure à celle du processus catalysé par le proton, ce
qui suggère que la catalyse électrophile augmente en importance lorsque la température tend vers la température am-
biante. En conséquence, il semble que le coupable de la non permanence du papier collage à la rosine et à l’alun serait
l’aluminium(III) qui agirait directement comme acide de Lewis et non pas la sphère d’hydratation de l’aluminium(III)
qui agirait comme un acide de Brønsted. Les mesures de conservation devraient tenir compte de ces conclusions ou
être génériques, tel qu’un entreposage à basse température.
Mots clés : cellulose, hydrolyse, pulpage alcalin, conservation du papier, traitement à la rosine et à l’alun.
[
Traduit par la Rédaction] Baty and Sinnott 1524
Received 20 April 2005. Published on the NRC Research Press Web site at http://canjchem.nrc.ca on 25 November 2005.
2
J.W. Baty. School of Materials, University of Manchester, POB 88, Sackville Street, Manchester, M60 1QD, UK.
3
M.L. Sinnott. School of Applied Sciences, University of Huddersfield, Queensgate, Huddersfield, HD1 3DH, UK.
1
This article is part of a Special Issue dedicated to organic reaction mechanisms.
Present address: 1201 Lincoln Mall, Apt. 400, Lincoln, NE 68508-2800, USA.
Corresponding author (e-mail: m.l.sinnott@hud.ac.uk).
2
3
Can. J. Chem. 83: 1516–1524 (2005)
doi: 10.1139/V05-168
© 2005 NRC Canada

Baty and Sinnott
1517
Introduction
boxylates (–0.82) (14). The former generates a solvent-
equilibrated tetrahydropyranyl cation; the latter is an unam-
biguous S 2 (A D ) reaction. The pK of methanol is 15.54
The loss of mechanical strength of cellulose fibres with
age is an important limiting factor in the preservation of pa-
per documents and, to a lesser extent, textiles. The degrada-
tion of paper in particular threatens much of our written
cultural heritage (1). Loss of paper strength is associated
with a decrease in the degree of polymerization (DP) of the
cellulose in the paper fibres (2a). Some depolymerization
arises from initial oxidation of the hydroxyls in cellulose to
carbonyl groups, which can then promote E1cb-like elimina-
tion of O4 and its substituent, leading to cellulose chain
cleavage. The oxidation can arise from excess use of oxida-
tive bleaching agents or photooxidation (3).
However, much paper degradation (particularly that occur-
ring under conditions of archival storage) does not occur by
these routes, and appears to be a hydrolysis. Hydrolytic deg-
radation is confirmed by the detection of glucose, cellobiose,
and cellotriose in naturally aged papers (4). Paper is 4%–9%
water by weight (5), and the aqueous hydrolysis of the
β(1→4) link in the noncrystalline regions of the cellulose fi-
bre is the depolymerization route.
N
N
N
a
(15); whereas that for the 2-OH of glucose is 14.0 (16), and
the 4-OH is likely to be similar. Further, it seems as if the
β(1→4) linkage between two hexopyranose units is some-
what crowded: equilibrium constants for the hydrolysis of
lactose and allolactose (the β(1→6) isomer) at 37 °C are
152 ± 19 mol/L and ~44 mol/L, respectively (17). It seemed
likely that the spontaneous hydrolysis of 1,5-anhydrocello-
biitol would be faster than that of methyl β-D-glucopyrano-
side by over one order of magnitude because of electronic
effects, and a factor of ~2 through steric acceleration. Were
this to be the case at room temperature, spontaneous hydro-
lysis would be a major contributor to paper degradation.
Paper from around the middle of the 19th century until
about the mid-1970s loses mechanical strength compara-
tively quickly, so that 19th and early 20th century documents
can be in worse condition than books and papers from the
17th and 18th centuries. The culprit is “rosin-alum” sizing
(sizing with diterpene acids and aluminium sulfate — not
KAl(SO ) ·12H O), invented in 1800 and widespread by the
4
2
2
We here report studies of the kinetics of hydrolysis of 1,5-
anhydrocellobiitol by spontaneous and electrophile-catalysed
routes. We also report data on the hydrolysis of this com-
pound by the well-known acid-catalysed mechanism, but at
high-temperature and (room-temperature) pH 3.1–4.0, to
permit comparison with the first two routes without large ex-
trapolation of acid strength. This compound, rather than
cellobiose itself, was used as the model for the β(1→4) link
in cellulose to avoid the carbonyl group rearrangement and
elimination reactions, which had vitiated a previous attempt
to measure the rate of spontaneous hydrolysis of a β(1→4)
glucan link (6).
1840s (18). Paper conservators have hitherto assumed that
rosin-alum-sized paper principally degrades via the proton-
catalysed mechanism, with the aluminium hydration sphere
acting as a source of protons (19). Policies of mass deacidi-
fication of documents have followed from this assumption
(20) despite occasional paper technology studies suggesting
the picture was more complicated. For example, differing ac-
tivation energies from differential thermal analyses led Parks
to conclude, “Sulfuric acid has a destabilizing effect qualita-
tively different from that of [aluminium sulfate]…” (21).
Bara½ski et al. (22) measured the macroscopic kinetics of
the degradation of Al (SO ) -impregnated papers and con-
2
4 3
cluded that mixed-control-type kinetic equations, taking into
account other processes, were required. In 1993, it was re-
marked “Considering that rosin sizing is still widely used af-
ter 140 years, and that in commercial operations aluminium
compounds are invariably involved, it is a matter for some
astonishment that we still do not know for certain the exact
mechanism by which aluminium compounds affect perma-
nence…” (23).
The spontaneous hydrolysis of 2,4-dinitrophenyl glyco-
sides has been known for some time (7) and effects of gly-
cone structure have been studied in detail (8). Since the
glucopyranosyl cation is “too unstable to exist” in contact
with an anionic leaving group (9), such hydrolyses are SN2
(
A D ) reactions with “exploded” transition states with little
N N
bonding to either nucleophilic water or the leaving group
10). Multiple kinetic isotope effects with fluoride as a leav-
(
We hypothesized that AlIII species in rosin-alum-sized pa-
per might be directly acting as electrophiles rather than as a
source of protons. The hypothesis had a chemical precedent
in the electrophilic catalysis of the hydrolysis of 8-
quinolinyl β-D-glucopyranosides by first-row transition metal
ing group support such a picture (11). The logkhyd vs. pH
plot for 2,4-dinitrophenyl β-galactopyranoside was horizon-
tal between pH 2 and 8, that for p-nitrophenyl β-
glucopyranoside between pH 3 and 6 (12). However, the ex-
pectation that the horizontal region for such plots would get
smaller as the leaving group became worse was confounded
by the recent discovery of a spontaneous hydrolysis pathway
for methyl glycosides. Wolfenden et al. (13) measured the
rates of methyl β- and α-D-glucopyranoside and -ribofuranoside
hydrolysis at 180–260 °C and observed rates independent of
the buffer room-temperature pH between 7 and 11. Their
data for methyl β-D-glucopyranoside extrapolate to a rate of
II
ions (24, 25) and a possible biochemical one in the Mg -de-
pendence of the hydrolysis of O-glycosides by the lacZ β-
galactosidase of Escherichia coli (26). A preliminary report
III
of catalysis of 1,5-anhydrocellobiitol hydrolysis by Al has
been published (27); we now report full details and apply the
measured rate data to the depolymerization of cellulose,
modelled with the af Ekenstam equation.
The proton-catalysed hydrolysis of cellulose has received
much attention over the years. Macroscopic kinetic studies
have been prompted by technology, such as the industrial
manufacture of microcrystalline cellulose (28), the develop-
ment of biomass fuels and feeds (29, 30a), the acid pulping
of biomass for paper (30b), and the permanence and conser-
vation of cellulosic textiles and paper (31, 32). The acid-
–
15 –1
4
.7 ± 2.1 × 10
s
at 25 °C, a figure they noted may be of
significance to paper degradation. We considered that depar-
ture of the 4-anion of glucose might be faster than that of
methoxide for steric and electronic reasons. The anticipated
β value of the spontaneous hydrolysis of glycosides is ex-
lg
pected to be between that for the spontaneous hydrolyses of
aryloxytetrahydropyrans (–1.18) and methoxymethyl car-
©
2005 NRC Canada

1
518
Can. J. Chem. Vol. 83, 2005
catalysed hydrolysis of glycosides in general has been exten-
sively studied. Pyranosides hydrolyse by initial protonation
of the exocyclic oxygen atom followed by C1-O1 fission. In
the case of alkyl glycosides, the protonation step is a pre-
equilibrium one (i.e., specific acid catalysis) (33, 34). Any
nucleophilic involvement is questionable. The leaving group
is electrically neutral (and, with a late transition state, results in
degrade rapidly at high temperatures to carboxylic acids and
other compounds (13, 40). To accommodate these, a ratio of
10:1 molar ionic strength buffer to molar substrate was se-
lected for all reactions conducted. The pH of all samples
was measured at room temperature and rechecked with
narrow-range pH paper after exposure. Oxygen – acid buffer
systems, with small heats of ionization, were used to mini-
mize dpH/dT. Further criteria for buffer suitability were
solubility in the chromatographic mobile phase and nonin-
terference with detection. For HPLC–RI, succinic acid –
succinate buffers (pH 3.0–4.0) were selected. For HPAE–PAD,
acetic acid – acetate (pH 4.7), monobasic phosphate – dibasic
phosphate (pH 5.9–7.5), and dibasic phosphate – tribasic
phosphate (pH 9.6–10.7) were used.
We considered general acid catalysis of substrate hydroly-
sis by buffers highly unlikely in these studies. General acid
catalysis of glycosides is favoured where acidic leaving
groups make the conjugate acid of the substrate too unstable
to exist (34). The mode of acid catalysis of the hydrolysis of
p-nitrophenyl glucopyranoside changes from general at
β ~ 0). Recent work on 2-deoxy-β-glucopyranosyl pyridinium
lg
salts, with likewise an electrically neutral leaving group,
suggests that the rate-determining step is formation of a sol-
–
+
vent-separated ion-pair-molecule complex (i.e., X //Glu Py)
35). An analogous process would explain the dependence of
(
acid-catalysed hydrolysis reactions on the nature, but not the
nucleophilicity, of anions present (33, 36). Limited data for
the hydrolysis of 1,5-anhydrocellobiitol in mildly acid media
were therefore obtained, largely to establish the “turnround”
point on the pH–rate profile, and to compare to the
electrophile-catalysed process.
Materials and methods
4
5 °C to specific at 75 °C (41).
The Al ion has a complicated aqueous coordination
III
1
,5-Anhydrocellobiitol
((4-O-β-D-glucopyranosyl)-1,5-
chemistry, with certain insoluble species predominating un-
der certain conditions (42). Therefore, in the electrophilic
catalysis study, samples were monitored for any loss of ho-
mogeneity. Samples exhibiting a loss of homogeneity were
anhydro-D-glucitol) was prepared according to Zhang (37),
who adapted Fletcher’s route to 1,5-anhydroglucitol (38).
Reduction of ethyl (heptacetyl-β-cellobiosyl) xanthate with
Raney nickel afforded hepa-O-acetyl-1,5-anhydrocellobiitol,
mp 194 to 195 °C (lit. value (39) mp 194 to 195 °C).
Zemplén deacetylation afforded a material mp of 170 °C
discarded because of the risk of crystal entrainment. The
III
Al ion was added as Al (SO ) ·nH O, the salt employed in
2
4 3
2
2
0
the rosin-alum-sizing method. In the study comparing the
rates of proton vs. electrophilic catalysis, concentrations of
Al (SO ) ranging from 0 to 20 mmol/L were employed.
(
(
(
decomp.), lit. value (39) mp 172 °C (decomp.), [α] 29°
D
lit. value 29.3). Spin-decoupled 13C NMR 10 lines, d 103
C1), double intensity 76.5 (C6 and C6′), and 79.5 (C5 and
2
4 3
C5′).
Reaction solutions containing 1,5-anhydrocellobiitol sub-
strate in buffer (including, where applicable, catalysts or cat-
alytic controls) were sealed inside small ampoules made
from melting point capillaries (Fisher Scientific Co.) and
submerged into a thermostatted oil bath (Labovisco-PMT
Tamson TC 9E). Oil temperatures were verified using a mer-
cury-in-glass thermometer calibrated by the UK National
Physical Laboratory, Teddington. After various time inter-
vals the ampoules were removed, opened, and the propor-
tions of 1,5-anhydrocellobiitol and 1,5-anhydroglucitol
analyzed by high-performance liquid chromatography – re-
fractive index detection (pH 3.0–4.0, all components by
Gilson Medical Instruments, Inc., supplied by Anachem
Ltd., Luton, Beds, UK, except the column by YMC (YMC-
Polyamine II)) or high-performance anion exchange chroma-
tography – pulsed amperometric detection (pH 4.7–11.0, all
components by Dionex (UK) Ltd., Camberley, Surrey, UK,
including the CarboPac PA-10 column). Because of the high
surface area of the capillaries and the exposure time of hours
to days, warm-up and cool-down times were negligible.
The concentration of substrate in the sample solutions was
selected for optimal detection. For refractive index detection
Results and discussion
The spontaneous hydrolysis of 1,5-anhydrocellobiitol
Figure 1 shows log k for hydrolysis of 1,5-anhydro-
1
0 obs
cellobiitol as a function of room-temperature pH at three
temperatures; individual constants are listed in the Supple-
4
mentary material. The gradients of these plots are 0.017 ±
0.005 at 220.0 °C, 0.007 ± 0.004 at 200.0 °C, and 0.005 ±
0.012 at 170.0 °C, effectively zero. The alkaline degradation
mechanisms of 1,5-anhydrocellobiitol observed by Brandon
occurred in NaOH solution (0.5–2.5 mol/L, H_ 14–15) (43a)
and are therefore unlikely to be important in our pH range.
As expected, a pH-independent reaction similar to methyl β-
D-glucopyranoside has been observed. At 220.0 °C, where
the two sets of data can be compared without extrapolation,
the rate for 1.5-anhydrocellobiitol is about an order of mag-
nitude faster than for methyl β-D-glucopyranoside (log k
=
10 obs
–4.66 ± 0.03 and ~–5.8, respectively), confirming our analy-
sis of electronic and steric effects. The E from data at
a
–
1
220.0, 200.0, and 170.0 °C is 149 ± 2 kJ mol at (room-
–
1
temperature) pH 7.5, and 151 ± 2 kJ mol at (room-
(
HPLC) this was 10 mmol/L and for pulsed amperometric
temperature) pH 9.6. An average figure for the entropy
–
4
‡
detection (HPAE) it was 3.07 × 10 mol/L. One hydrolysis
product of 1,5-anhydrocellobiitol, glucose, is expected to
change of activation at ambient temperature (∆S 5°C) is cal-
2
–
1
–1
culated to be –38 ± 3 J mol K .
4
Supplementary data for this article are available on the Web site or may be purchased from the Depository of Unpublished Data, Document
Delivery, CISTI, National Research Council Canada, Ottawa, ON K1A 0S2, Canada. DUD 4045. For more information on obtaining mate-
rial refer to http://cisti-icist.nrc-cnrc.gc.ca/irm/unpub_e.shtml.
©
2005 NRC Canada

Baty and Sinnott
1519
Fig. 1. kobs vs. room-temperature pH. The pH dependence of the
spontaneous hydrolysis of 1,5-anhydrocellobiitol measured at
three temperatures.
Fig. 2. DP vs. t at 25 °C. Calculated from af Ekenstam eq. [1],
substituting a DP of 1300 and the extrapolated values for k
from methyl β-D-glucopyranoside (13) and 1,5-anhydrocellobiitol.
0
25 °C
-
-
-
-
-
-
4.5
5.0
5.5
6.0
6.5
7.0
1
1
300
200
DP
100
1
4
6
8
10
Room-temperature pH
20.0 °C 200.0 °C 170.0 °C
12
1
000
0
400
800
1200
2
t (years)
Our E figure is significantly higher than the value from
a
Wolfenden et al. (13) for the spontaneous hydrolysis of
Methyl β-
D-glucopyranoside
–
1
methyl β-D-glucopyranoside (124 ± 6 kJ mol ), but is in line
with their unpublished results on the spontaneous hydrolysis
1,5-Anhydrocellobiitol
–
1
of trehalose (155 kJ mol , personal communication from R.
Wolfenden). The value for the spontaneous hydrolysis of
methyl β-D-glucopyranoside is similar to that of several 2,4-
the model. The periodic crystalline regions of native cellu-
lose, which are sites of very limited aqueous chemistry, are
therefore neglected. Therefore, our results will overestimate
the true rate of cellulose depolymerization by a particular
mechanism.
Figure 2 models cellulose depolymerization due to the
spontaneous hydrolysis mechanism over time at 25 °C. The
–
1
dinitrophenyl β-D-glycopyranosides (108–126 kJ mol ),
1
0
which, however, react some 10 -fold faster (8). Our value
‡
5°C
for ∆S
is lower than has been observed in other sponta-
2
neous hydrolysis systems, but not as low as observed
by Wolfenden et al. (13) for methyl β-D-glucopyranoside
–1
(
–99.6 ± 3.1 J mol–1 K ). The difference in our E for 1,5-
DP used (1300) is that commonly taken for the cellulose in
a
0
anhydrocellobiitol from the value obtained by Wolfenden et
al. (13) for methyl β-D-glucopyranoside is such that while
the spontaneous hydrolysis of 1,5-anhydrocellobiitol is faster
at the temperatures tested, it extrapolated to lower rates at
softwood kraft pulp (2b, 46); the specific rate constants used
are that previously given for 1,5-anhydrocellobiitol and that
reported by Wolfenden et al. (13) for methyl β-D-glucopy-
ranoside. These models strongly suggest that spontaneous
–
16 –1
ambient temperatures (8.6 ± 2.1 × 10
s
at 25.0 °C as
-
hydrolysis is not likely to be a problem encountered in neu
tral and alkaline papers in archives. The retained DP of
1250 after 1000 years is far more than the ~400 at which
against 4.7 ± 2.1 × 10– s ). It may be that departure of
methoxide requires immobilization of a water molecule as
proton donor, but that departure of the glucose 1-anion or 4-
anion does not.
15
–1
~
brittleness becomes a problem in paper (2a).
A major element of the kraft process of paper pulping is
the “cook phase” in which wood chips are exposed to condi-
tions of pH 12–14 and 170–173 °C for roughly 90 min after
warm-up (47). In this process, a DP loss from the
biosynthetic ~10 000 (30c) to ~1300 occurs (2b). This loss
in DP has been attributed to alkaline degradation mecha-
nisms including β-alkoxy elimination (also known as the
“peeling reaction” because it proceeds endwise) and uni-
molecular nucleophilic substitution that results from hydroxyl
ionization. Previous molecular model studies of this process
have not identified a spontaneous hydrolysis mechanism
(43b, 48–50).
True endoglucanases have kcat values around 30 s–1 when
acting on long cellooligosaccharides (44). They therefore
achieve a rate enhancement of ~3 × 1016 over the uncatalysed
mechanism measured with our model.
Depolymerization of cellulose modelled using the af
Ekenstam equation
af Ekenstam derived eq. [1] relating the degree of poly-
merization to the first-order rate constant for the cleavage of
a specific linkage. Random chain fission and rates of cleav-
age independent of position in the chain were assumed (45).
ln(1 – DPt–1) – ln(1 – DP –1) = –kt
Figure 3 plots DP vs. t, showing the depolymerization of
cellulose because of spontaneous hydrolysis modelled with
1,5-anhydrocellobiitol using the af Ekenstam eq. [1] and a
[
1]
0
where DP and DP are the degrees of polymerization ini-
0
t
tially and at time t, respectively, and k is the first-order mi-
croscopic rate constant for cleavage of an individual linkage,
assumed to be invariant across the chain. Whilst this equa-
tion is normally used to calculate k from DP data, we re-
versed the process, inputting k from our model studies. This
assumes that the cellulose is in dilute aqueous solution, like
DP value of 10 000. The specific rate constant used in this
0
–
7
–1
model (3.5 ± 0.3 × 10 s ) is the average value of two data
series obtained with good precision at 170.0 °C. (See Fig. 1
and Supplementary material). As previously argued, the hy-
4
drolysis of 1,5-anhydrocellobiitol observed at these pH val-
ues will be exclusively due to the spontaneous hydrolysis
©
2005 NRC Canada

1
520
Can. J. Chem. Vol. 83, 2005
Fig. 3. DP vs. t at 170.0 °C. Depolymerization of cellulose dur-
ing kraft cooking owing exclusively to spontaneous hydrolysis,
modelled with 1,5-anhydrocellobiitol using af Ekenstam eq. [1]
and a DP of 10 000. The k value used is an average of two
data series (pH 7.5 and 9.6) obtained at 170.0 °C. Inset: Detail
of depolymerization (40–90 min).
Fig. 4. log k vs. pH. The pH dependence of the specific acid
catalysis of 1,5-anhydrocellobiitol (150.0 °C).
1
0 obs
Room-temperature pH
0
obs
3
.0 3.2 3.4 3.6 3.8 4.0
-4.2
1
0 000
-
-
-
-
4.6
5.0
5.4
5.8
8
6
4
2
000
000
000
000
0
1
000
500
0
1
50.0 °C, HPLC
log10 k = -1.0916(pH) - 1.1522
DP
olation to 25.0 °C gives a value of 4.5 ± 0.7 × 10–13 s–1, 525
times faster than the spontaneous hydrolysis. Equating
log [H ] with measured pH at 25.0 °C gives a second-
order rate constant for the proton-catalysed reaction of 1.4 ±
.2 × 10 (mol/L) s . For the hydrolysis at 25.0 °C, we
can thus write eq. [2], valid from very acidic conditions to
pH 12.3.
4
0
60
60
80
100
100
+
–
1
0
–
9
–1 –1
0
~
0
20
40
t (min)
80
[
2]
khyd, 25 °C = (8.6 ± 2.1 × 10–16
(1.4 ± 0.2 × 10–9-pH) s–1
)
+
mechanism. As shown in the inset of Fig. 3, this model pre-
dicts that spontaneous hydrolysis alone reduces the DP of
the cellulose to 502 ± 37 after 90 min under kraft cooking
conditions, which is appreciably shorter than the actual DP
after kraft cooking. An overestimate of DP loss, however, is
expected here for two reasons. First, as previously noted,
this model assumes that all of each cellulose chain is solu-
ble. Second, in native wood chips, cellulose is part of a com-
posite in which the matrix is (hydrophobic) lignin. On the
introduction of the wood chips into the digester, only the
surface of the chips is in contact with the kraft cooking li-
quor. Nonetheless, the reduction in DP is so large as to point
unambiguously to the spontaneous hydrolysis mechanism as
a primary mechanism of cellulose depolymerization in the
kraft process.
Therefore, the acid-catalysed hydrolysis becomes compa-
rable with the spontaneous one only at pH 6.0.
The activation energy calculated for hydrolysis in succinic
acid buffers of room-temperature pH 3.5 will include the heat
–
1
of ionization of succinic acid. The value (140 ± 1 kJ mol )
is close to activation energies measured with stoichiometric
–
1
concentrations of mineral acids (e.g., 141.3 kJ mol for
–
1
methyl β-D-glucopyranoside, 138.8 kJ mol for 2-propyl β-
–
1
D-glucopyranoside, or 134.2 kJ mol for the sterically
acclerated 1-adamantyl β-D-glucopyranoside (51)), which do
not include such a contribution. Therefore, the heat of ion-
ization of succinic acid appears to be low, as is expected for
an oxygen acid.
Given the relation between DP and paper strength, sponta-
neous hydrolysis is the primary mechanism in limiting the
strength of papers made from kraft pulp.
Modelling depolymerization using the af Ekenstam
equation
Figure 5 models the depolymerization of cellulose in pa-
per fibres (DP ≅ 1300) using af Ekenstam eq. [1] inputting
0
(4.5 ± 0.7 × 10– s ) for
13
–1
The proton-catalysed hydrolysis of 1,5-anhydro-
cellobiitol
the extrapolated value of k
2
5.0 °C
1,5-anhydrocellobiitol at pH 3.5. The other pH values were
calculated from the pH 3.5 extrapolated value, assuming
rates that were first-order in protons. The af Ekenstam equa-
tion will overestimate the rate of hydrolysis, since it assumes
an aqueous environment throughout all cellulose chains. It is
clear that even paper of pH 3.5 — at the lower end of the
range of even “acid” papers — will have a usable lifetime of
several decades before it reaches the failure criterion of
DP = 400, the point at which paper becomes unusably brittle
(2a). Although of greater significance than spontaneous hy-
drolysis, it seems unlikely that proton catalysis plays a major
role in paper aging.
The slope of the plot (Fig. 4) of log k (150.0 °C) vs.
1
0 obs
room temperature pH between pH 3.1 and 4.0 has a value of
.09 ± 0.04, showing the expected 1:1 dependence of the
1
specific rate constant to proton concentration. The pH
changes were brought about by changing the buffer ratio in
the same buffer system (succinic acid – succinate), which
means that changes of pH within the series are temperature-
independent, even if the change in absolute pH with temper-
ature is large.
The E obtained from k (room-temperature pH 3.5) be-
a
obs
–
1
tween 140.0 and 175.0 °C, is 140 ± 1 kJ mol (27). Extrap-
©
2005 NRC Canada

Baty and Sinnott
1521
III
Fig. 5. Four hundred years of aging: DP vs. t at 25 °C. The
depolymerization of cellulose in papermaking fibres modelled us-
Fig. 6. k vs. [M ]. First-order rate constants for hydrolysis of
1,5-anhydrocellobiitol (150.0 °C) as a function of added trivalent
metal sulfates (27).
ing af Ekenstam eq. [1], substituting 1300 for DP , and specific
0
rate constants obtained from the model compound, 1,5-anhydro-
cellobiitol. The rate at pH 3.5 (succinic acid – succinate buffer,
Al(III) pH = 3.35 ±
0.02
–4
2
2
1
1
5
.5×10
.0×10
.5×10
III
no Al ) was extrapolated. All other pH values were calculated
+
from the extrapolated rate based on first-order kinetics in H .
Al(III) pH = 3.05 ±
0.02
1
400
–4
La(III) pH = 3.32
±
0.05
1150
–
4
-
k (s )
1
9
6
4
00
50
00
DP
–4
.0×10
–
5
.0×10
0
100
200
300
400
t (years)
0.0
0
5
10
15
20
25
pH = 3.5, rate extrapolated
III
M ] (mmol/L)
[
pH = 4.0, rate calculated from
extrapolated pH 3.5 value
Presumably, this is due to protonated aluminium species
being more electrophilic than unprotonated ones. Alu-
minium(III) exists in a variety of coordination compounds
under papermaking conditions and it is not certain whether
this particular pH dependence will extend to other pH
ranges. It does suggest, however, that the relative impor-
tance of electrophilic catalysis to proton catalysis under am-
pH = 4.5, rate calculated from
extrapolated pH 3.5 value
pH = 5.5, rate calculated from
extrapolated pH 3.5 value
III
The Al -catalysed hydrolysis of 1,5-anhydrocellobiitol
bient conditions will be pH-independent (27).
III
Figure 6 shows the effect of added Al (SO ) and
At 20 mmol/L of Al , k was measured at 150.0 and
2
4 3
obs
La (SO ) on kobs for hydrolysis (150.0 °C) of 1,5-
125.0 °C in buffers of room-temperature pH 3.33, and gave
2
4 3
–
1
anhydrocellobiitol (10 mmol/L) in 100 mmol/L succinate
buffers with the room-temperature pH values shown. The
an E value of 109 ± 3 kJ mol (27). This is appreciably
a
lower than the value for proton-catalysed hydrolysis, sug-
gesting that the electrophilic pathway will increase in impor-
tance as the temperature is lowered. Although the proton-
III
III
much greater effect of Al than La establishes that the in-
crease in rate is not due to a change in ionic strength. (Al-
though maximum added salt concentration was only 20%
catalysed pathway contributes ~10% to k at 20 mmol/L of
obs
III
that of the buffer, if the concept of ionic strength, defined as
Al at 150.0 °C, the lower energy of activation means that
2
1
/2 Σc z , is applicable to these concentrated solutions, it is
this contribution, small anyway, decreases with temperature.
Conceivably, a kinetically equivalent pathway of hydroly-
i i
not constant, since we used salts of a divalent anion and tri-
valent cation (27)).
Competitive chelation of Al by succinate, substrate hy-
III
sis could proceed, not from the coordination of Al with
III
cellulose as in Scheme 1, but from the kinetically equivalent
III
droxyls, and substrate glycosidic oxygen is expected, with
nucleophilic attack by an Al -coordinated oxygen atom on
III
Al in solution likely to be completely coordinated by the
the conjugate acid of the substrate as in Scheme 2. However,
as discussed in the Introduction, the sensitivity of such pro-
cesses to nucleophilicity varies from weak to imperceptible.
For example, in 2,4-dinitrophenolate production from 2,4-
dinitrophenyl β-D-glucopyranoside, Bennet and Sinnott (53)
showed sodium azide (1.0 mol/L) increased the rate by only
40%.
succinate and sulfate (42). Because of this anation, the rate
of hydrolysis is expected to be lower than that which would
be observed with AlCl , which possesses a noncoordinating
3
cation (42, 52). Despite anation, unambiguous effects over
the control are still observed. A clear pH dependence in the
rate of the electrophilic hydrolysis is noted in this pH range.
The apparent second-order rate constant at pH 3.05 is 8.1 ±
Electrophilic catalysis by AlIII was demonstrated with
mmol/L concentrations of catalyst and substrate in homoge-
neous solution. In rosin-alum-sized paper there is more than
enough aluminium to catalyse such a process: Priest et al.
–
3
–1 –1
0
1
.4 × 10 (mol/L) s ; at pH 3.35 it is 4.2 ± 0.2 ×
–
3
–1 –1
0
(mol/L) s , showing approximate proportionality of
the second-order rate constant to the proton concentration.
5
5
2
In the preliminary communication, an error of 10 in these derived constants, immediately apparent from the displayed graphs, was unfortu-
nately made.
©
2005 NRC Canada

1
522
Can. J. Chem. Vol. 83, 2005
Scheme 1. 1,5-Anhydrocellobiitol, showing a possible coordina-
tion pattern for Al (27). Coordination by O6′ is speculative, but
has a possible precedent in the intramolecular conversion of lac-
Fig. 7. DP vs. t at 25 °C. The depolymerization of cellulose in
papermaking fibres modelled using af Ekenstam eq. [1], substi-
III
tuting a DP of 1300 and k
for 1,5-anhydrocellobiitol hydro-
0
25 °C
tose into allolactose by the lacZ β-galactosidase of E. coli where
lyses as labelled.
II
Mg may be the electrophile (26).
OH
1200
0 mmol/L Al(III),
pH= 3.54
OH
O
HO
O
DP
20 mmol/L Al(III),
pH = 3.33
HO
HO
O
8
00
(
III)
OH
O
Al
H
L
L
400
Scheme 2. A kinetically equivalent pathway to the electrophile-
0
25
50
t (days)
75
100
catalysed hydrolysis: hydrolysis proceeding from nucleophilic
III
substitution of an Al -coordinated oxygen atom. This mecha-
nism is deemed unlikely to cause the observed acceleration be-
cause of the minimal effect of even very strong nucleophiles in
these systems (52).
Fig. 8. Four hundred years of aging at –20 °C: DP vs. t at
25 °C. The depolymerization of cellulose in papermaking fibres
under cold storage conditions. Modelled using the af Ekenstam
OH
eq. [1], substituting 1300 for DP , and specific rate constants ob-
0
H
tained from the model compound, 1,5-anhydrocellobiitol.
OH
O
+
O
HO
1400
HO
HO
O
1
150
00 DP
650
OH
O
9
OH
(III)
Al
L
L
4
00
0
100
200
300
400
(
54) found a range of 1.3%–6.7% Al (SO ) (average 3.8%)
t (years)
2
4 3
per weight of oven-dried 20th century papers (AAS of acid
extracts). Thus, in principle, concentrations of Al in the
molar range are possible in the 5%–7% aqueous phase in
such papers, although in practice much of the aluminium
will be precipitated or adsorbed.
0
mmol/L Al(III), pH = 3.54
III
20 mmol/L Al(III), pH = 3.33
ues from 20 mmol/L Al (SO )
catalysed 1,5-
2
4 3
anhydrocellobiitol samples (room temperature pH 3.33) ex-
trapolated to 25 °C. This model suggests that paper of this
composition would be extremely impermanent, reaching the
failure criterion of DP ≅ 400 after 96 days. Such imperma-
nence will be exaggerated, particularly as raising the pH will
decrease the electrophilicity of the aluminium in the paper
sheet. However, Murray (57), implicating rosin-alum sizing
soon after its introduction, commented, “One letter which I
had forwarded by post fell to pieces by the way…”. Even
papers of such pronounced impermanence can be preserved
for centuries using the preservation technique of cold stor-
age. The same kobs values used in Fig. 7 (20 mmol/L
Al (SO ) , pH 3.33), but extrapolated to –20 °C, are plotted
Mechanism of electrophilic catalysis of 1,5-anhydro-
III
cellobiitol hydrolysis by Al
Given the rate of water exchange in the inner sphere of
III
III
Al (55), ligand exchange about Al is unlikely to be rate-
determining. The identities of these ligands in the model
system will include aquo, sulfate, and succinate, whilst in
the paper sheet they will be many and various. Particularly
given that in crystalline cellulose I the conformation about
C5-C6 is the usually disfavoured tg conformation (56), the
III
possibility exists that Al is chelated as shown in Scheme 1
in the productive complex. A possible biochemical precedent
for 6-OH coordination may be found in the intramolecular
conversion of lactose into allolactose by E. coli β-
2
4 3
using af Ekenstam eq. [1] in Fig. 8.
II
galactosidase, which contains an active-site Mg (26). Alu-
minium(III), which has a similar Pauling ionic radius (50
pm) to Mg (65 pm), is expected to coordinate in a similar
Conclusions
II
manner.
The spontaneous hydrolysis of the β(1→4) link in cellu-
lose, modelled in 1,5-anhydrocellobiitol, is too slow to con-
tribute to reduction in degree of polymerization of cellulose
Figure 7 models the depolymerization of cellulose using
the af Ekenstam eq. [1] inputting 1300 for DP and k val-
0
obs
©
2005 NRC Canada

Baty and Sinnott
1523
(
and hence loss of paper strength) during aging of paper un-
13. R. Wolfenden, X. Lu, and G. Young. J. Am. Chem. Soc. 120,
der archival storage conditions, but does completely account
for the reduction in cellulose DP during kraft pulping. The
proton-catalysed pathway is adequate to account for reduc-
tion in cellulose DP during aging only of the most acidic pa-
pers. Efficient electrophilic catalysis by Al has been
demonstrated, and is likely to be the origin of the imperma-
nence of all rosin-alum-sized papers.
6814 (1998).
1
4. G.-A. Craze and A.J. Kirby. J. Chem. Soc. Perkin Trans. 2,
54 (1978).
5. P. Ballinger and F.A. Long. J. Am. Chem. Soc. 82, 795 (1960).
3
1
III
16. H. Nielsen and P.E. Sörensen. Acta Chem. Scand. Ser. A, 37,
05 (1983).
1
1
7. A.C. Elliott, K. Srinvasan, M.L. Sinnott, P.J. Smith, J.
Bommuswamy, Z. Guo, B.G. Hall, and Y.L. Zhang. Biochem.
J. 282, 155 (1992).
Whilst more work is needed to determine the details of
III
the Al -catalysed hydrolysis, it is clear that programs of
1
1
8. D. Hunter. Papermaking: the history and technique of an an-
document deacidification (such as that currently under way
in the US Library of Congress (20)) will have, at best, a di-
rect effect only on the most acidic of papers, and only the in-
direct one of reducing the electrophilicity of metal ions on
other acid papers. Deacidification procedures that add metals
cient craft. Dover, New York. 1943. p. 523.
9. For example, see the introduction in: D.J. Priest and M. Farrar.
In Proceedings of symposium 88, Ottawa, Ontario, 3–7 Octo-
ber 1988. Edited by H.D. Burgess. Canadian Institute of Con-
servation, Ottawa, Ontario. 1994. p. 255.
(
especially deacidification by dimethyl cadmium) are likely
2
0. The Library of Congress. Saving the written word: Library of
Congress awards mass deacidification contract. Press release
[online]. Available from http://www.loc.gov/today/pr/2001/01-
155.html [accessed 25 March 2005]. 2001.
to be counterproductive.
It would appear that generic document storage techniques
should be more widely adopted. The preservation technique
of cold storage, widely used to preserve photographic mate-
rials, slows the rate of all detrimental reactions and does not
entail the chemical alteration of the object. If a chemical al-
teration is absolutely necessary, it should at least target the
21. E.J. Parks. Tappi J. 54, 537 (1971).
22. A. Bara½ski, R. Dziembaj, A. Konieczna-Molenda, J.M.
Lagan, and S. Walas. Pol. J. Chem. Technol. 6, 1 (2004).
2
2
2
2
3. N. Gurnagul, R.C. Howard, X. Zou, T. Uesaka, and D.H. Page.
J. Pulp Paper Sci. 19, J160 (1993).
4. C.R. Clark, R.W. Hay, and I.C.M. Dea. J. Chem. Soc. D, 13,
III
real culprit of impermanence, e.g., complex the Al ion in
rosin-alum-sized papers with fluoride.
7
94 (1970).
5. C.R. Clark and R.W. Hay. J. Chem. Soc. Perkin Trans. 2, 1943
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6. M.L. Sinnott. Chem. Rev. 90, 1171 (1990).
(
Acknowledgements
We thank the Textiles and Paper Group, School of Mate-
rials, University of Manchester, for two years of postgradu-
ate support for JWB, and Dr. Yazmin Hernandez and
Dr. Richard Hughes, University of Huddersfield, for help
with operation of the HPAEC-PAD system.
27. J. Baty and M.L. Sinnott. Chem. Commun. (Cambridge), 7,
866 (2004).
28. For example, see: Enerex Botanicals Ltd. Microcrystalline cel-
lulose I.P.: the excipient of choice [online]. Available from
http://www.enerex.ca/articles/microcrystalline_cellulose.htm
[
accessed 18 April 2005]. 1997–2004.
2
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5
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2005 NRC Canada