Chemorheological analysis and model-free kinetics of acid catalysed

furfuryl alcohol polymerization

Nathanael Guigo, Alice Mija,* Luc Vincent and Nicolas Sbirrazzuoli

Received 25th May 2007, Accepted 24th July 2007

First published as an Advance Article on the web 8th August 2007

DOI: 10.1039/b707950h

The complete curing of furfuryl alcohol (FA), was studied by chemorheological analysis and

model-free kinetics under isothermal and non-isothermal modes. Polymerization of FA under

acidic catalysis involves complex reactions, with several steps (such as condensations and

Diels–Alder cycloadditions). To account for the polymerization complexity, kinetic analysis of

DSC data was performed with a model-free isoconversional method. The obtained

Ea-dependencies were closely-correlated with the variation of complex viscosity during curing.

Linear condensations are predominant during the early curing stage and are followed by two

distinct stages of branching cycloadditions. Gelation and vitrification, identified by rheometric

measurements, were associated with a decrease of the overall reaction rate that becomes

controlled by diffusion of small oligomers. Before vitrification, the rate of crosslinking is limited

by the mobility of longer polymer chains and diffusion encounters a large energy barrier due to

the cooperative nature of the motions, leading to higher Ea values.

Introduction

Vegetable biomass represents a sustainable solution to replace

petroleum-based chemicals. In particular, hemicellulose con-

stitutes an important source of monomers such as furfuryl

alcohol (FA). This latter is obtained by conversion of furfural

and can react with Brønsted or Lewis acidic catalysts to form a

black, cross-linked macromolecule.1 At an industrial scale, FA

is usually converted into prepolymers and these furanic resins

represent excellent eco-friendly precursors for wood impreg-

nation2 and for elaborating composite materials3,4 or wood

adhesives.5 Currently, for this type of resin, the control of

prepolymerization is an important issue and requires careful

application of processing conditions. A perfect knowledge of

the chemorheological behaviour of the reactive polymer sys-

tem during processing is very important in order to determine

optimum process parameters, adapted to the aimed applica-

tion. As it is the case for many thermosets, viscosity of FA

prepolymers is strongly dependent on the evolution of tem-

perature and the extent of conversion during curing. The

variation of the viscosity is also a key parameter which may

govern the chemical reactions at the microscopic scale.

The polymerization reaction of furfuryl alcohol has been

previously studied under different experimental conditions.6–13

The reported step-growth curing mechanisms can be separated

into two stages. In the first stage, under acid catalysis, the

methylol group of one furan ring condenses with the C5

position of another furan ring with dehydration.1 Furan rings

connected by methylene linkages create linear oligomers,14 as

shown in Scheme 1. In the second stage, these linear oligomers

are cross-linked into black materials. It is postulated3,6,10,15,16

that these oligomers are branched together mostly due to

Diels–Alder cycloadditions between the furan rings (diene)

and the dihydrofuranic cycles (dienophile). Despite these

previous investigations, the overall kinetics of this complex

curing process (i.e., linear growth of chains and crosslinking)

still remain imperfectly understood. According to Milkovic,17

the overall mechanism involves many steps that are likely to

have different activation energies. The contribution of these

steps into the overall cure rate should generally vary with both

temperature and extent of curing. This means that the effective

activation energy determined from the overall rate measure-

ments is likely to be a function of these two variables. A kinetic

study based on empirical models could be ineffective if the

reaction models are unknown. For this reason, an alternative

solution is to use model-free isoconversional methods. These

methods require no hypotheses on the reaction mechanism

and allow for evaluation of the apparent activation energy as a

function of the extent of conversion. Consequently, changes in

curing mechanisms are associated with the variation of appar-

ent activation energy.

The objective of the present study is to get a better under-

standing of the curing behaviour of FA and to highlight

changes in mechanisms during both resinification and cross-

linking. For this purpose, the curing of FA catalyzed with

maleic anhydride (MA) was investigated by infrared spectro-

scopy (IR), rheometry and by differential scanning calorimetry

(DSC) under both isothermal and non-isothermal conditions.

DSC data were treated with an advanced isoconversional

method in order to yield the dependence of activation energy

on conversion. To our knowledge, this work reports the first

chemorheological study combining model-free kinetics and

rheological data for the study of FA polymerization. In

particular, we demonstrate that this type of analysis allows

us to obtain consistent results from isothermal and non-

Thermokinetic Group, Laboratory of Chemistry of Organic andMetallic Materials C.M.O.M., Institute of Chemistry of Nice,University of Nice—Sophia Antipolis, 06108 Nice Cedex 2, France.E-mail: mija@unice.fr

This journal is �c the Owner Societies 2007 Phys. Chem. Chem. Phys., 2007, 9, 5359–5366 | 5359

PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics

isothermal data, and also to get important correlations with

the rheological behavior during curing.

Experimental

Materials

Furfuryl alcohol (FA) is a light-yellow liquid (Mw = 98.10 g

mol�1, b.p. = 170 1C, purity 498%). It was generously

supplied by TransFurans Chemicals BVBA (Belgium) and

was used as received. An anhydride, maleic anhydride (MA)

(Mw = 98.06 g mol�1, m.p. = 51–56 1C, purity 499%), was

used as acid catalyst to induce homopolymerization of FA and

was obtained from Aldrich Chemical Co. MA was totally

dissolved in water (50% aqueous solution) and was mixed in

FA solution at a weight ratio of FA : MA = 100 : 2 under

vigorous mechanical stirring. The fresh mixtures were imme-

diately analyzed to avoid prepolymerization at ambient

temperature.

Experimental techniques

DSC measurements were performed on a Mettler-Toledo DSC

821e equipped with STARr software. Computations for

kinetic evaluation were performed using both internally-writ-

ten software, regularly upgraded,18–20 and the ‘‘advanced

model-free kinetics’’ STARr software option. Temperature

and enthalpy calibrations were done by using indium and zinc

standards. Volatilization of polycondensation by-products

occurs during the curing of FA and, consequently, high-

pressure stainless steel crucibles (ME-51140404) were used

instead of aluminium crucibles because they can withstand a

vapour pressure of up to 15 MPa. Samples of approximately

10 mg were placed into sealed pans. The DSC measurements

of FA polymerization were conducted at the heating rates of 1,

2, 4 and 6 1C min�1. A blank run was subtracted for each

heating rate experiment. The DSC runs under isothermal

conditions were carried out at 110, 120, 130, 140, and

150 1C, respectively. The second heating of the cured samples

did not show any residual heat release.

Infrared spectroscopy (IR) was used to monitor the struc-

tural changes after different stages of polymerization. The IR

spectra were recorded on a Perkin Elmer Spectrum BX II

spectrophotometer. The attenuated total reflectance (ATR)

mode was used to characterize starting monomer (FA), PFA

prepolymer in the gelled state and also the PFA thermoset

(totally cured polymer). To prepare samples for IR, a first

DSC scan was performed to determine the relationship be-

tween a and T. Then, the prepolymer in the gelled state was

obtained by directly curing the FA monomer in DSC crucibles

at 1 1C min�1 to a temperature of 113 1C, corresponding to aB 0.54. Then, the sample was quickly quenched to �10 1C.

The same procedure was applied to obtain the totally cured

polymer (heated to T = 220 1C, a B 1).

Rheological measurements were conducted on oscillating

mode with parallel plate geometries (40 mm diameter and

1 mm gap) of a Bohlin C-VOR rheomether with strain

convection heating. The linear viscoelastic range of the mate-

rial at its liquid and solid state was evaluated by a strain sweep

to determine a deformation that can be used to measure

complex viscosity during the whole polymerization process.

Measurements were carried out on auto stress mode with a

frequency of 1 Hz, and a deformation of 0.05%. Time to

gelation was estimated as the point where storage (G0) and loss

modulii (G00) curves intersect. The polycondensation reaction

is accompanied by a water release, leading to the formation of

empty spaces between the plates. Due to this modification of

geometry during experimentation, the measured viscosities are

relative values.

Theoretical calculations

The overall rate of reactions is commonly described by the

following equation:21

dadt¼ kðTÞf ðaÞ ð1Þ

Scheme 1

5360 | Phys. Chem. Chem. Phys., 2007, 9, 5359–5366 This journal is �c the Owner Societies 2007

where dadtis the reaction rate, a is the conversion degree, k(T) is

the rate constant, t is the time, T is the temperature, and f(a)is the reaction model. The dependence of the rate constant

is described by the Arrhenius law:

kðTÞ ¼ A exp � E

RT

� �ð2Þ

where E is the activation energy, A is the preexponential factor

and R is the gas constant.

The reaction rate is generally determined by the rates of

both chemical reaction and diffusion22 The ratio of the

characteristic times of chemical reaction and diffusion deter-

mines which of these two processes is rate limiting. According

to Debye,23 the relaxation time for a molecule is directly

proportional to viscosity:

t ¼ 4pa3ZkBT

ð3Þ

where Z is the viscosity of the medium, a is the molecular

radius, kB is Boltzmann’s constant. This suggests viscosity as a

crucial factor of diffusion control. Eyring’s theory of viscos-

ity24 gives rise to the Arrhenius type of temperature depen-

dence:

Z ¼ Z0 expEZ

RT

� �ð4Þ

where EZ is the activation energy of the viscous flow, Z0 is thepreexponential factor. Eqn (4) usually holds for liquids well

above their Tg. At temperatures closer to Tg, the temperature

dependence of viscosity follows the WLF equation.25 The

diffusion activation energy, Ed can be obtain as follows

Ed ¼ �Rd ln kd

dT�1¼ EZ þ RT : ð5Þ

If RT is much smaller than EZ, Ed is practically equal to EZ,

which was experimentally found by several workers.24 Then,

substitution of the Arrhenius equation for k gives the apparent

activation energy, Ea:

Ea ¼ �Rd ln kef

dT�1

� �¼ ðEZ þ RTÞkþ EkZ

kþ kZð6Þ

where E is the activation energy of a chemical reaction. Eqn

(6) suggests that depending on the temperature, the apparent

activation energy, Ea, may take values between E and EZ.

Furthermore, the Ea dependence should be different for the

cures performed under a different temperature range.

The simplest isoconversional method proposed by Fried-

man26 allows the activation energy E to be determined for each

given conversion degree, and can be expressed as:

lndadt

� �a;i¼ ln½Aaf ðaÞ� �

Ea

RTa;ið7Þ

where the subscript i denotes the ordinal number of a non-

isothermal experiment conduced at the heating (or cooling)

rate bi. Eqn (7) allows the activation energy E to be determined

for each given conversion degree (a). The heat flow measured

in DSC is proportional to both overall heat release and cure

rate. In differential scanning calorimetry (DSC), the conver-

sion degree is defined as the ratio between the heat exchanged

at time ti (Hi) and the total heat released by the reaction (Q):

ai ¼Hi

Q¼R tit1ðdH=dtÞi dtR t2

t1ðdH=dtÞi dt

: ð8Þ

The quantity (dH/dt)i represents the heat flux measured in

DSC at time ti, t1 is the time corresponding to the first

integration bound and t2 to the second integration.

An advanced isoconversional method has been developed in

order to be applicable for any temperature programming, and

was used in this study.27,28 According to this method, for a set

of n experiments carried out at different heating programs,

Ti(t), the activation energy is determined at any particular

value of a by finding the value of Ea that minimizes the

function

FðEaÞ ¼Xni¼1

Xnjai

J½Ea;TiðtaÞ�J½Ea;TjðtaÞ�

ð9Þ

Henceforth, the subscript a denotes the values related to a

given extent of conversion. In eqn (9), the integral:

J½Ea;TiðtaÞ� �Zta

ta�Da

exp�Ea

RTiðtÞ

� �dt ð10Þ

is evaluated numerically for a set of experimental heating

program. Integration is performed over small time segments,

allowing for the elimination of a systematic error that occurs

in the usual integral methods when Ea varies significantly with

a. In eqn (10), a is varied from Da to 1� Da with a step Da =

m�1, where m is the number of intervals chosen for analysis.

The integral, J in eqn (10) is evaluated numerically by using

the trapezoid rule. The minimization procedure is repeated for

each value of a to determine the Ea-dependence.29 An advan-

tage of the advanced isoconversional method is that it employs

exactly the same computational algorithm to evaluate the Ea-

dependence from both isothermal and nonisothermal data.

The apparent activation energy calculated by isoconversional

methods is a global energy that may include several chemical

reactions (multi-step kinetics) as well as physical transforma-

tions (evaporation, gelation, vitrification). These methods can

take into account for the change from a chemically controlled

reaction to a reaction controlled by the change in viscosity or

by diffusion.20,34,35,37

Results and discussion

Evolution of structure during FA polymerization

Partial or complete polymerization of the FA monomer has

been performed in order to study the evolution of structure

during polymerization and to highlight the DA reactions. Fig.

1 shows the IR spectra of starting FA monomer, those of PFA

prepolymer at the gelled state and also the PFA when com-

pletely cured. The comparison of the three spectra reveals

some important band-modifications as a consequence of poly-

merization. As observed in Fig. 1, the polymerization leads to

a strong decrease of the –OH stretching band at 3450 cm�1

and those corresponding to the furanic bands around 1500,

1015, 920 and 880 cm�1. A new band develops at 1560 cm�1

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and can be attributed to a CQC skeletal stretch vibration in

the furan ring interconnected to the furan–CH2–furan group

after formation of oligomers by a condensation reaction

(Scheme 1a). The formation of chromophores during poly-

merization (Scheme 1b) is accompanied by an increase in the

relative intensity of theQCH–dihydroxyfuran rings’ stretch-

ing band at 3150 cm�1 together with the decrease of the

furan–CH2–furan stretching band at 2930 cm�1. The evidence

of Diels–Alder cycloaddition is marked by the appearance of a

non-aromatic CQC weak band at 1670 cm�1 in the PFA

thermoset. The occurrence of the carbonyl signal at 1712 cm�1

points out the formation of a ketonic structure by a furan ring-

opening reaction. However, these are considered side reac-

tions, and lead to intermediate products that do not influence

the overall rate of polymerization.30

Non-isothermal measurements

Normalized non-isothermal DSC curves of FA polymerization

are shown in Fig. 2. The heat released during non-isothermal

polymerizations of FA was combined and traced with the

corresponding variation of the extent of conversion with

temperature (Fig. 2). The non-isothermal DSC curves were

used to estimate the total heat release of reaction, Q. Integra-

tion of the DSC peaks resulted in decreasing Q values of 709,

685, 620, and 593 J g�1 for the respective heating rates 1, 2, 4,

and 6 1C min�1.

Milkovic et al.17 observed two distinct exothermic DSC

peaks for the polymerization of FA with p-toluene sulfonic

acid. These stages were attributed to the extension of the

polymerization reaction, followed by a distinct stage of cross-

linking. As seen in Fig. 2, a single exothermic DSC peak is

observed in the case of FA polymerization. These DSC data

were used for the evaluation of the dependence of the apparent

activation energy, Ea, on conversion, as shown in Fig. 3. In

parallel is plotted the variation of the complex viscosity in

order to highlight rheological changes during polymerization.

According to this Ea-dependence, it can be concluded that the

non-isothermal acid-catalyzed polymerization follows multi-

step kinetics expressed by different apparent activation ener-

gies. The obtained Ea values are in agreement with the data

previously reported by Milkovic et al.17 of 73 and 106 kJ

mol�1 using the Kissinger method. The Kissinger method

allows the computation of a single activation energy value

based on the evolution of the temperature of the peak

maximum with the heating rate.

At the beginning of the reaction, (a o 0.10) the Ea values

decrease from 70 to 55 kJ mol�1. Such a decrease of Ea during

the initial cure stages has already been observed for an epoxy-

novolak system in a previous work.31 This behaviour was

explained by a diffusion controlled kinetic due to the high

viscosity of the medium and Ea was correlated to EZ. However,

the system under investigation had a higher initial viscosity

(B102 Pa s), and the viscosity decreased strongly with increas-

ing temperature in the initial stages (a o 0.20). In other

cases,32 the Ea decrease during the initial cure stages was

interpreted by a control of an autocatalytic step. According

to Fig. 3, the viscosity of the medium has a low initial value,

corresponding to the viscosity of the small FA oligomers and

remains constant until a B 0.10–0.15, in perfect agreement

Fig. 1 IR spectra of FA monomer (a), PFA prepolymer (b) and PFA

totally cured polymer (c).

Fig. 2 DSC data (solid line) of the heat released during nonisother-

mal polymerizations of FA and the corresponding variation of extent

of conversion with temperature (dashed line). The heating rate of each

experiment (in 1C min�1) is indicated by each curve.

Fig. 3 Variation in the effective activation energy with conversion

obtained for FA polymerization under nonisothermal conditions b =

1–6 1C min�1 (open triangles) and evolution of the complex viscosity

at 4 1C min�1 (solid line).

5362 | Phys. Chem. Chem. Phys., 2007, 9, 5359–5366 This journal is �c the Owner Societies 2007

with the Ea decrease. This quasi-constant viscosity value

results from the competition between the temperature-depen-

dence of viscosity and the increase of molecular weight. Thus,

this suggests that the decreasing shape of Ea cannot be

attributed to a diffusion-controlled rate but rather to an

autocatalytic mechanism that corresponds with the formation

of the active species for the first stage of condensation. Under

acidic conditions, the chain reaction starts by the formation of

a furyl carbenium active center able to react with the mono-

mer.33 This active center is regenerated at every step, allowing

the reaction to continue. The viscosity increases when suffi-

cient active species are generated and condensation reactions

start to become predominant (a B 0.15; this marks the end of

control by an autocatalytic step).

For 0.10o a o 0.40, Ea values are around 60 kJ mol�1 and

quasi-constant on conversion, suggesting that a single reaction

dominates in this conversion range.34 According to previous

studies35,36 the value of 60 kJ mol�1 is typical for condensation

reactions of hydroxymethyl groups into methylene phenolic

bridges in phenol–formaldehyde (PF) systems. The accepted

mechanism of polycondensation of FA is close to that of PF.

Indeed, the polycondensation of FA starts by linear condensa-

tion of a hydroxymethyl group to a furan ring and formation

of a methylene furanic linkage (Scheme 1). According to this

mechanism, the Ea values can be attributed to self condensa-

tion reactions that occur predominantly until a B 0.40.

Formation of linear oligomers occurs for this stage which is

expressed by a quasi-exponential increase of viscosity of the

medium. This increase is generally observed for the curing of

thermosets before gelation. Additionally, water is an impor-

tant by-product of this polycondensation process (B18.35%

w/w) and can have a transient plasticizing effect on viscosity

only in the early cure stage (0 o a o 0.30), where the FA

oligomers have still a relatively low molecular weight. More-

over, due to the high temperature of polymerization

(4100 1C), the water is rapidly vaporized from the mixture.

For 0.40 o a o 0.45, Ea increases suddenly from 60 to

about 70 kJ mol�1, revealing a change in the reaction mechan-

ism. In this range, the Diels–Alder cycloadditions can start

between oligomers formed in the previous step. The kinetics of

Diels–Alder cycloadditions have been extensively studied, and

the reported activation energies of furanic diene cycloaddi-

tions on different dienophiles are ranging about 68 kJ mol�1

(UV-Vis),37 83.6 kJ mol�1 (ab initio),38 101.2–105.1 kJ mol�1

(DSC),39 82.3–95.3 kJ mol�1 (ab initio),40 77.3–145.0 kJ mol�1

(ab initio),41 72.2–86.6 kJ mol�1 (RMN).45 These values are in

agreement with ours and, therefore, this change in the reaction

rate at a B 0.45 could be attributed to the [4 + 2] cycloaddi-

tions between the furanic diene and the dihydrofuranic dieno-

phile. Endo and exo Diels–Alder cycloadducts cannot be

distinguished because they are formed with very close activa-

tion energies42 (differences of about B2–4 kJ mol�1). More-

over, at this extent of conversion, the observed material

becomes dark-coloured due to conjugated sequences.6 Forma-

tion of DA cycloadducts is confirmed by the appearance of

specific peaks registered in IR spectra (Fig. 1). Development of

interconnections between cycloadducts is still correlated with a

continue increase of the viscosity medium in this region as

shown in Fig. 3.

For 0.45 o a o 0.63, Ea decreases from 70 to 50 kJ mol�1.

In this conversion interval, the gelation process takes place as

shown in Fig. 4. The gel point of the system, taken as cross-

over between G0 and G00 as seen in Fig. 4, is about agel E 0.52.

At the gel point, the growing oligomer chains, obtained by

Diels–Alder cycloadditions, reach an unique, giant macromo-

lecule, by connections between the furanic rings. When gela-

tion takes place, the molar mass becomes infinite and the

viscosity increases. This implies a low molecular mobility

which induces the decrease of the overall reaction rate that

becomes controlled by diffusion of unbranched small oligomer

chains. This is mostly due to an inherent increase in viscosity

after branching cycloadditions and results in a decrease of Ea.

A similar decrease of Ea after gelation has been previously

reported for the epoxy/amine crosslinking37 and has been

attributed to the beginning of a diffusion-controlled rate. This

latter change in the kinetic regime is easily observable upon the

evolution of viscosity. Indeed, for 0.63 o a o 0.72, the

viscosity reaches a constant value (plateau). As explained

above for the initial cure stage, these apparent constant values

of viscosity demonstrate a complex temperature dependence,

which is a superposition of two phenomena. Firstly, at a

constant value of the molecular weight, viscosity decreases

with increasing temperature. Secondly, an increase in the

temperature accelerates the cure and promotes an increase in

molecular weight and viscosity.

For 0.63 o a o 0.85, the apparent activation energy

increases to about 100 kJ mol�1 (a E 0.85). The variation of

the polymerization rate leads to a dramatic change of viscos-

ity. We observe a final exponential increase of viscosity that is

clearly indicating the continuation of crosslinking reactions.

Because the temperature increases linearly in non-isothermal

experiments, the chain mobility increases and the chemical

reactions can be reactivated.

Thus, the increase of Ea to about 100 kJ mol�1 could be

explained by the contribution of further Diels–Alder

Fig. 4 Variation of G0 (open symbol), G00 (solid symbol) during non

isothermal cure at 4 1C min�1 (circle) and isothermal cure at 120 1C

(triangles).

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cycloadditions to the cure rate. In the gelled state, the pre-

viously-formed longer chains are branched together by further

cycloaddition reactions leading to three-dimensionally cross-

linked materials. At this stage of the reaction, the rate of

crosslinking is limited by the mobility of longer polymer

chains and diffusion encounters a large energy barrier due to

the cooperative nature of the motions, leading to higher Ea

values.20,43

For a Z 0.85, Ea reaches a maximum, 100 kJ mol�1 and

starts to decrease at vitrification (a Z 0.90). The monomer

molecules become frozen in their positions in the glassy state

that results in a virtual cessation of the reaction. The curing

rate in the glassy state becomes controlled by diffusion of

small, unreacted functions still present in the medium and

chemical reactions are considerably reduced.20 This means

that vitrification causes a dramatic decrease in molecular

mobility leading to a decrease of the effective activation energy

with increasing extent of reaction.

The Diels–Alder cycloadditions have the particularity of

being thermally reversible3,6,14–16 and retro Diels–Alder reac-

tions may occur at higher temperatures. However, according

to rheological measurements presented in Fig. 3, the viscosity

still continues to increase with the increasing extent of the

reaction and reaches a plateau at av E 0.90, indicating that the

system is in the glassy state. The vitrification of the polyfur-

furyl alcohol network is confirmed by the observation of a

glass transition temperature obtained during a second heating

of the cured sample in DMA. As shown in Fig. 5, the

maximum of tan d (G00/G0) can be used as an estimate of glass

transition temperature at Tg(non-iso) E 115 1C. Such observa-

tions cancel the hypothesis of retro Diels–Alder reactions,

because conversion back to oligomers (by scission of polymer

crosslinks) would have been accompanied by a decline of

viscosity as previously observed for certain furanic copoly-

mers.16 Moreover, corroborating with the structural IR char-

acterization, the formation of the chromophore is confirmed in

the final thermoset PFA by continuous increase of the

QCH–dihydroxyfuran rings’ stretching band at 3150 cm�1

compared to PFA prepolymer (Fig. 1). The intensity of furanic

bands at 1500 or 1015 cm�1 continues to decrease with

increasing extent of conversion confirming that no conversion

back to furanic oligomers has occurred through retro Diels–

Alder reaction. Furthermore, the strong decrease in intensity

of the –OH stretching band at 3450 cm�1 reveals that the final

product is totally cured.

Isothermal measurements

The isothermal DSC thermoanalytical curves are shown in

Fig. 6. A blank run has been carried out at each isothermal

temperature to evaluate the stabilization of the pan after

introduction into the furnace. The obtained isothermal DSC

data have been integrated to evaluate the total heat released of

isothermal reactions. The latter varies as 579, 560, 607, 620

and 647 J g�1 for the temperatures of 110, 120, 130, 140, and

150 1C. For all isothermal measurements, a shoulder appears

in the first part of the DSC curves indicating a change in the

reaction rate.

The advanced isoconversional method was applied on these

isothermal data and the resulting dependency associated with

viscosity changes were reported in Fig. 7. In isothermal mode,

the maximum heat released is about 647 J g�1, while it is

709 J g�1 (amax B 1) in the non-isothermal mode. In order to

compare isothermal and non-isothermal dependencies, abso-

lute values of a were plotted in Fig. 7, instead of relative

values. This means that the value amax,iso B 0.91 is taken as the

maximum value reached in isothermal mode.

At the beginning of the reaction (a o 0.15), we observe a

slight increase from 65 to 75 kJ mol�1 in Ea values that is

attributed to formation of the active species for the first stage

of condensation. In comparison with non-isothermal experi-

ments (Fig. 3), the Ea-dependence has an opposite behaviour

for this first conversion interval. This can be explained by the

fact that in the non-isothermal mode the active center forma-

tion started at low temperatures and conversion. In the

isothermal mode, the active species appears, at a certain

temperature, in time. To compare isothermal and non-iso-

thermal data, we must keep in mind that the temperature

domain ranges between 110–150 1C for the former and

Fig. 5 Variation of tan d obtained by rheometric measurements at 4 1C

min�1 of samples already cured under non-isothermal mode at 4 1C

min�1 (solid line) and under isothermal mode at 120 1C (dashed line).

Fig. 6 DSC data (solid line) of the heat release during isothermal

polymerizations of FA and the corresponding variation of the extent

of conversion with time (dashed line). The temperature of each

experiment (in 1C) is indicated by each curve.

5364 | Phys. Chem. Chem. Phys., 2007, 9, 5359–5366 This journal is �c the Owner Societies 2007

between 60–220 1C for the latter data. This could explain why

the autocatalytic stage is only predominant at the early stages

of the non-isothermal cure, corresponding to lower tempera-

tures. In this conversion interval, the viscosity remains con-

stant because only low molecular weight oligomers and water

are formed.

For 0.15 o a o 0.40, the general shape of the Ea-depen-

dence is in agreement with non-isothermal data suggesting

that formation of linear oligomers by condensation reactions

is predominant for this stage. The apparent activation energy

of the polycondensation step appears to be around 75 kJ

mol�1. In this region, the viscosity registered only a slight

increase. As suggested for non-isothermal conditions, water

has a plasticizing effect. The viscosity increases slightly be-

cause the growth of the chain length during condensation

reactions is compensated by the plasticizing effect of water

formed in the same reaction.

Due to the higher activation energy of Diels–Alder cycload-

ditions, these first branching reactions between linear chains

start at earlier conversion degree in non isothermal experi-

ments. This explains why for this region, in non isothermal

experiments, we observe a more marked viscosity increase in

comparison with the isothermal mode.

As previously described for non-isothermal data, the

Diels–Alder cycloadditions become predominant for 0.40 oa o 0.45. This step is characterized by a sudden Ea-increase

associated with an exponential increase of complex viscosity.

In isothermal curing, the Ea value increases to about 87 kJ

mol�1 for aB 0.45. The Diels–Alder reactions become the rate

limiting step for a B 0.40–0.50. This conversion range corre-

sponds to the region were the shoulders is observed on the

isothermal DSC curves (Fig. 6).

In isothermal mode the gel point is obtained for a B0.50–0.52 as seen in Fig. 4 (T = 120 1C). In the range

0.45 o a o 0.70, Ea decreases to about 55 kJ mol�1, suggest-

ing that the cure kinetics become controlled by diffusion of

molecules in the gelled media. At this stage, the molar mass

becomes infinite and the viscosity increases exponentially.

Compared to non isothermal data, we do not observe a

plateau of viscosity in this region. In the isothermal mode

the viscosity is not temperature-dependent, and only the

increase of molecular weight is determinant on its evolution.

Then, as observed for non-isothermal data, Ea goes on to

higher values. This confirms our hypothesis that a second

cycloadditions branching stage may occur at this conversion

range (0.70 o a o 0.85) and is associated with an increase in

Ea. This second branching stage is also marked by an increase

of the slope of the viscosity that start for a B 0.70 which

corresponds to the minimum value of the Ea. Because in

isothermal mode the temperature remains constant, the che-

mical reactions cannot be reactivated by the temperature

increase and the completion of the cure is lower than in non-

isothermal mode (amax,iso B 0.91). This explains why we do

not observe the Ea increase to such a high value of 100 kJ

mol�1, as was seen in the non-isothermal mode. As shown in

Fig. 5 (second heating), a peak maximum is observed at 70 1C

and is attributed to the glass transition temperature, Tg(iso), of

the sample cured under isothermal condition. This is an

indication that the system has reached the glassy state after

isothermal curing at 120 1C. As expected, Tg(iso) o Tg(non-iso),

confirming a lower completion of cure in isothermal mode. As

already mentioned, this experimental results support our

hypothesis that the Diels–Alder cycloadditions start at earlier

conversion degree in non isothermal conditions leading to a

higher degree of crosslinking.

For a 4 0.85, the system is in the glassy state and the Ea-

values start to decrease, as described previously for non-

isothermal data. Lower values of activation energy correspond

to diffusion of small unreacted molecules in the glassy state. As

in non-isothermal experiments (Fig. 3), the viscosity reaches a

plateau indicating that vitrification occurs. Similar trends are

highlighted in both isothermal and non-isothermal mode.

The complementary nature of DSC and rheometric data

gives new insights into the overall reaction mechanism of these

complex polymerizations. A sudden increase of Ea reflects a

change in the polymerization mechanism (condensations to

Diels–Alder cycloadditions). Condensation reactions still con-

tinue to occur, even for a 4 0.40, but are not the rate-limiting

step of the overall reaction. After gelation, the viscosity plays

an important role in the polymerization kinetics. Usually, a

decrease of Ea corresponds to a diffusion-controlled rate and is

associated with a plateau of viscosity (for gelation or vitrifica-

tion phenomena), whereas an increase of Ea corresponds to a

chemical controlled rate and is associated with an increase of

viscosity.

Conclusions

The polymerization of FA upon the action of an acidic

catalyst is a complex chemical process that supposes a linear

condensation step and a branching reaction step leading to a

black thermosetting material. The curing kinetics of this

monomer have not been extensively studied, although the

applications of FA based resins are increasingly important.

Isoconversional analysis associated with rheological data lead

to the conclusion that the overall curing of FA follows multi-

step kinetics controlled alternatively by chemical reactions and

Fig. 7 Variation in the effective activation energy with conversion

obtained for FA polymerization under isothermal conditions T=110,

120, 130, 140, 150 1C (open circles) and evolution of the complex

viscosity during cure at 120 1C (solid line).

This journal is �c the Owner Societies 2007 Phys. Chem. Chem. Phys., 2007, 9, 5359–5366 | 5365

diffusion. Linear condensations are predominant at the early

curing stage and the Diels–Alder reactions become rate-deter-

mining after the formation of the first oligomers. These first

cycloadditions cause an increase in the viscosity-inducing

gelation. At this stage of reaction, the overall cure rate

becomes controlled by the diffusion of oligomers. Finally,

the latter stage is marked by an increase of apparent activation

energy, explained by a different stage of cycloadditions in the

gelled state, leading to the final glassy materials. This stage of

reaction becomes controlled by diffusion of longer polymer

chains, while diffusion of small molecules in the gelled or

glassy state is associated with a decrease of Ea.

Nevertheless, this study also highlights some differences in

the development of the mechanisms between isothermal and

non-isothermal polymerizations. The material cured in non-

isothermal conditions presents higher degree of crosslinking,

leading to higher Tg values, because the Diels–Alder cyclo-

addition starts at an earlier stage of conversion.

Acknowledgements

The authors would like to acknowledge Transfurans Chemi-

cals, the partners of the ECOBINDERS project (http://

www.ecobinders.net) and the European Commission for

financial support (ECOBINDERS FP6-2003-NMP-SME-3

project ‘‘Furans and lignin based resins as eco-friendly and

durable solutions for wood preservation, panel, board and

design products’’).

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