moisture transport and dehydration in heated gypsum, an nmr study
TRANSCRIPT
Chemical Engineering Science 66 (2011) 4241–4250
Contents lists available at ScienceDirect
Chemical Engineering Science
0009-25
doi:10.1
� Corr
E-m
journal homepage: www.elsevier.com/locate/ces
Moisture transport and dehydration in heated gypsum, an NMR study
G.H.A. van der Heijden, L. Pel �, H.P. Huinink, K. Kopinga
Department of Applied Physics, Transport in Permeable Media, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
a r t i c l e i n f o
Article history:
Received 25 October 2010
Received in revised form
24 May 2011
Accepted 14 June 2011Available online 23 June 2011
Keywords:
Heat transfer
Porous media
Multiphase flow
NMR
Gypsum
Phase change
09/$ - see front matter & 2011 Elsevier Ltd. A
016/j.ces.2011.06.024
esponding author. Tel.: þ31402473406; fax:
ail address: [email protected] (L. Pel).
a b s t r a c t
Nuclear magnetic resonance (NMR) is used to non-destructively measure the moisture and dehydration
profiles in gypsum during one sided heating to temperatures of 400 1C reflecting the conditions during
fire. The temperature and moisture profiles are recorded simultaneously. The gypsum used in the
experiments was extensively characterised using TGA, DSC, MIP, and NMR. The influence of the initial
moisture content on the drying and dehydration processes was tested by varying the moisture content
of the samples: capillary saturated, 50% RH, and 0% RH.
By calibrating the NMR signal with moisture content we have shown that it is possible to not only
measure free or absorbed water with NMR, but also measure the degree of hydration of the gypsum.
Furthermore, by comparing the NMR signal decays it is possible to distinguish between these two water
populations. The measured water profiles reveal that during one sided heating of a gypsum sample the
dehydration inside is taking place in a two-step reaction. Furthermore, the profiles indicate that the
vapour produce by the dehydration reactions condensates and thereby increases the local moisture
content. The condensated water forms a so-called moisture peak behind the dehydration front.
To our knowledge the measurements described in this article are the first quantitative in-situ
evidence for the existence of two dehydration fronts in gypsum during one sided heating. Furthermore,
the built up of a moisture peak in gypsum behind the dehydration front has not been reported in the
literature to our knowledge. The NMR heating experiments presented in this paper can be used to
evaluate and validate hygro-thermal models in the field of fire research on building materials.
& 2011 Elsevier Ltd. All rights reserved.
1. Introduction
The question of how a porous building material responds to afire is one of the main questions in fire safety. During a fire, abuilding material can suddenly be heated up to temperatures ofapproximately 1000 1C. At temperatures above 100 1C water insidethe pores will start to boil. Simultaneously, in materials such asconcrete and gypsum, chemically bound water will be released bydehydration of the porous matrix. The released water vapour has tobe transported through the porous material. If the material has alow permeability, the vapour pressure inside the material willincrease. Furthermore, close to the heated surface a large tempera-ture gradient can generate stresses in the surface. In addition, thedehydration reactions will decrease the strength of the material.These three processes can result in a sudden (explosive) failure ofthe material (Khoury, 2000). The question of how a material reactsto a fire has been raised for numerous building materials such asconcrete (Aitcin, 2003; Khoury, 2000), fired-clay brick (Nguyen
ll rights reserved.
þ31402434853.
et al., 2009; O’Garra et al., 2003), and gypsum (Ang and Wang, 2004,2009; Mehaffey et al., 2008; Fejean et al., 2003).
The research on fire behaviour of building materials is gen-erally focussed on large scale fire testing. These tests are expen-sive, require large equipment, and do not give any physical insightin processes such as evaporation, boiling, and dehydration. In mostof these large scale tests only the temperature is recorded, and theoverall outcome after the test is evaluated. In this way, one of themost important factors: the moisture content is left out of theequation. The presence of moisture during heating can have alarge effect on different material properties such as: the heatcapacity, the heat conductivity, and the dehydration kinetics. As aconsequence of the dehydration the porous structure and hencepermeability is changed. A better understanding of the underlyingphysical processes will help to improve materials to become betterfire resistant. At the same time, minimizing the need for expensivelarge scale fire testing.
To this purpose, we have recently developed a nuclear mag-netic resonance (NMR) setup to measure the moisture transport inheated building materials. With this NMR setup, it is possible tonon-destructively measure the evolution of the moisture contentinside a porous building material while it is heated (van derHeijden et al., 2007, 2009). In the literature, to our knowledge, no
G.H.A. van der Heijden et al. / Chemical Engineering Science 66 (2011) 4241–42504242
detailed moisture profiles during heating of building materials canbe found.
In this paper we present moisture, temperature, and dehydra-tion profiles of gypsum. Gypsum was chosen as a benchmarkmaterial for different reasons. First, all of the above-mentionedmechanisms such as boiling and dehydration take place ingypsum. The dehydration reaction(s) take place at well definedand relatively low temperatures. Secondly, it is widely used as abuilding material in different applications such as plasterboard orbuilding blocks. The large latent heat stored in free and chemi-cally bound water, combined with a low thermal conductivitymake it an excellent insulating and fire retarding material. There-fore, gypsum plasterboard is used as a protective barrier for theload bearing wood or steel frame it is attached to. Thirdly, it is avery clean material from an NMR point of view, because it doesnot contain any paramagnetic impurities.
In Section 2, a brief introduction is given into theory behindNMR. The NMR setup and the other experimental methods arealso discussed. The gypsum used in our experiments is charac-terised in Section 3. The measured moisture and temperatureprofiles from the heating experiments will be presented in Section4. Conclusions and outlook will be given in Section 5.
2. Materials and methods
NMR is used to measure the one-dimensional moisture con-tent distribution in a gypsum sample. In this section, a shortoverview of NMR is given. For a more detailed overview of NMR,the reader is referred to Vlaardingerbroek and den Boer (2003).
2.1. NMR
When a nucleus with a net nuclear magnetic moment is placedin an external magnetic field B0, the magnetic moment willprecess around this field at a certain resonance frequency. Thisresonance frequency is the so-called the Larmor frequency fl (Hz),which is proportional to the magnetic field fl ¼ gB0. Here, g is thegyromagnetic ratio (for hydrogen g ¼ 42.58 MHz/T). In our caseB0 ¼ 1.5 T, resulting in a resonance frequency of 63.9 MHz.
The individual magnetic moments all contribute to a netnuclear magnetisation. In equilibrium this magnetisation isaligned parallel to B0. The direction of the magnetisation can bemanipulated by applying a radio-frequent magnetic field B1 at theresonance frequency. If two suitably chosen radio-frequent pulsesare applied, the magnetisation induces a signal in the measure-ment coil, which is the so-called the ‘Hahn spin-echo’ (Hahn,1950). The signal intensity S of the Hahn spin-echo is given by(Vlaardingerbroek and den Boer, 2003)
S¼ kM0ðTÞ 1�exp �TR
T1
� �� �exp �
TE
T2
� �: ð1Þ
In this equation M0 (T) is temperature dependent equilibriummagnetisation, T1 and T2 are relaxation times, TE is the time afterwhich an echo is recorded, TR the time between two successivespin-echo measurements, and k is a proportionality constant. TheNMR signal S decreases exponentially for increasing TE with acharacteristic relaxation time T2, which is caused by spin–spininteractions. In technological porous materials, the relaxationtime T2 ranges from 0.1 to 1 ms. A medical NMR (MRI) scannercan record a spin-echo after about 5 ms, which means that evenwith a T2 of 1 ms the signal has decreased by a factor of 10�3.Therefore, we use a home-built dedicated NMR scanner, whichhas the capability of measuring the spin-echo after 200 ms.
The spin–lattice interactions cause the magnetisation to re-align with the main magnetic field. The spin–lattice relaxation
process has a characteristic time T1. In order to obtain a maximumsignal from the Hahn spin-echo experiment, the minimum repeti-tion time TR between two successive spin echoes is determined byT1 (TRZ4T1).
If the water molecules have enough time to diffuse around andprobe the pore space, the spin–spin relaxation time T2 of water ina porous material can contain information on the pore sizes. Thereason is that a water molecule has a higher chance to relax nearthe pore surface than in bulk volume. The relaxation time ofwater in a pore T2,pore can therefore be related to the volume V, thesurface area ~S, the surface relaxivity r2 of the pore (Brownsteinand Tarr, 1979) by
1
T2,pore¼
1
T2,bulkþr2
~S
V: ð2Þ
The bulk relaxation time T2,bulk is often much larger than T2,pore andthe first term on the right-hand side can often be neglected. Bymeasuring the signal decay curve, a distribution of the relaxationtimes can be calculated by using an inverse Laplace routine, i.e., amulti-exponential fit. If the surface relaxivity is known, the T2
distribution can be used to obtain a pore size distribution. Notethat only pores which are filled with water are probed.
The equilibrium magnetisation M0 is temperature dependent. Itis well known that due to the temperature-dependent Boltzmanndistribution of nuclear magnetic moments in a magnetic field, themagnetisation and hence the measured signal is inversely propor-tional to the absolute temperature (Gultekin and Gore, 2005).Therefore, in a non-isothermal quantitative NMR experiment oneneeds to correct the measured signal for the temperature at whichthe signal was measured. Furthermore, a correction for thetemperature dependence of the relaxation times is needed. How-ever, in the case of gypsum this temperature dependence of therelaxation is negligible.
In a homogeneous magnetic field B0 all 1H nuclei have the sameresonance frequency, and as a result a signal from the entire sampleis obtained. One can selectively excite the nuclei in a limitedvolume by making the magnetic field position dependent. Byapplying a gradient it is possible to measure spatial distributionsof water. In our experiments the modified magnetic field is given by
BðxÞ ¼ B0þGz, ð3Þ
where x is the position along the direction of the gradient G
(T m�1). By varying the frequency of B1 the signal can be measuredat different positions in the sample without moving the sample.
2.2. NMR setup
The experiments were performed in a home-built NMR setupespecially designed for moisture measurements on heated build-ing materials. A schematic diagram of the setup is shown in Fig. 1.The setup is placed in the bore of a 1.5 T whole-body medicalscanner (Gyroscan, Philips), which is used to provide the mainmagnetic field. The diameter of the bore is 650 mm, providingample space for our setup. Two coils in an anti-Helmholtzconfiguration (diameter 350 mm) provide a constant magneticfield gradient G in the direction of B0. The magnitude of thegradient is about 100 mT m�1, yielding a theoretical spatialresolution of 3 mm in our experiments. A home-built bird-cagecoil is used for sending the RF pulses (B1), and receiving the NMRsignal from the sample. The coil is 140 mm long and has adiameter of 140 mm. A bird-cage type coil is used because itgenerates a homogeneous B1 field perpendicular to the long axis ofthe cylindrical sample. Therefore, the coil can be placed parallel tothe main magnetic field, providing optimal use of the availablespace inside the bore. A high power RF amplifier (3.6 kW) wasused in order to achieve relative short RF pulses (50 ms) in a large
G.H.A. van der Heijden et al. / Chemical Engineering Science 66 (2011) 4241–4250 4243
volume coil. The complete setup is enclosed by a Faraday shield inorder to reduce the RF noise, and to protect the electronic systemsof the medical scanner.
The sample is heated with an array of four 100 W halogenlamps, capable of generating a heat flux of 12 kW m�2. Thereflectors of the lamps are gold plated to ensure maximumreflection of infrared radiation. The heat flux from the lamp wascalibrated calorimetrically and varies linearly with the electricalpower applied to the lamp (van der Heijden et al., 2009). Theinitial heating rate of the sample surface is 20 1C/min.
2.3. Materials
The cylindrical gypsum samples used in the experiments werecut from larger gypsum blocks, and have a diameter of 80 mm anda length of 100 mm. The samples were pressed in a PTFE holderleaving only the front end of the cylindrical sample open formoisture to escape. Furthermore, the samples were insulatedusing 3 cm of mineral wool, minimizing the temperature gradientin the radial direction to less than 10% of the longitudinal gradient.In this way, both moisture and heat transport are limited to onedimension. For the sample holder PTFE was used, because it doesnot contain any hydrogen, which could cause an unwanted back-ground signal. Thermocouples (type K) were fitted in pre-drilledholes with a diameter of 1 mm. The holes were closed using PTFE
0.01 0.1 1 10 1000.0
0.1
0.2
0.3
pore
vol
ume
(ml/g
)
r (μm)
3 -3
Fig. 2. (a) MIP results for gypsum. (b) Sorption isotherm of gyp
G
B1
r
z
B0
gradient coils
externalFaraday cage
RF coil
insulationsample
10 cm
Al2O3 tube
lamp array
flowFaraday shield
Fig. 1. Schematic diagram of the NMR setup. A whole-body 1.5 T MRI scanner
provides the main magnetic field B0. Two coils in an anti-Helmholtz configuration
provide a constant magnetic field gradient G of 100 mT m�1. A bird-cage coil with
a diameter of 140 mm is used for both sending RF pulses B1 and receiving the NMR
signal. The bird-cage coil is constructed on an Al2O3 tube, because during the
experiment high temperatures are reached. An array of four 100 W halogen lamps
is used to heat the sample, which is thermally insulated and positioned within the
bird-cage coil.
tape. The gypsum samples were pre-conditioned at three differentmoisture contents: capillary saturated, and a moisture contentcorresponding to 0 and 50% RH, respectively. The capillarysaturated sample was placed under water until a constant masswas obtained. The 0 and 50% RH samples were stored approxi-mately 6 months at 20 1C at the respective relative humiditiesuntil a constant mass was obtained.
Before the heating is started one moisture and temperatureprofile is measured to record the initial state of the sample. Eachsubsequent moisture profile is divided by the reference moistureprofile to correct for the inhomogeneous RF coil profile. The timebetween two successive profiles is about 3–4 min in each experi-ment. To prevent hot vapour, which is coming out of the sample,from condensing on ‘cold’ surfaces inside the coil, air of 1–2% RHwas blown over the sample surface.
3. Characterisation of gypsum
We have characterised the gypsum which was used in theexperiments. For this purpose, we have used mercury intrusionporosimetry (MIP), thermal gravimetric analysis (TGA), differentialscanning calorimetry (DSC), moisture sorption. NMR was also usedto characterise the gypsum. It was used to obtain additionalinformation on gypsum, and/or to complement the results obtainedby other techniques. We have divided the characterisation in twoparts: the pore size distribution of gypsum and the effect of heatingon gypsum.
3.1. Pore size distribution
Gypsum is a dihydrate of calcium sulphate (CaSO4 �2H2O),which is formed by mixing plaster (CaSO4 �
12 H2O) and water in
the correct proportions. The hydration reaction which takes place is
CaSO4 �12 H2OðsÞþ3
2H2OðlÞ-CaSO4 � 2H2OðsÞþDHhyd: ð4Þ
This exothermic hydration reaction will release an amount of energyDHhyd. The porous structure being formed is built up from plate- andneedle-shaped gypsum crystals. The crystals form a crosslinkednetwork, resulting in a solid porous material. The porosity rangesfrom 0.36 to 0.61 m3 m�3, depending on the water to plaster ratio(w=p) (Jaffel et al., 2006; Singh and Middendorf, 2007). The gypsumused in our experiments has a porosity of 0.44 m3 m�3 (w/p ¼ 0.5),which was measured using vacuum saturation.
3.1.1. MIP and sorption isotherm
The pore size distribution of the hydrated gypsum was mea-sured using MIP (see Fig. 2a). The results clearly show onedominant pore size of about 223 mm. The absorption branch of
0.00
0.01
0.02
0.03
abso
rbed
vol
ume
(mm
)
RH (%)0 20 40 60 80 100
sum. Capillary saturated moisture content ¼ 0.4 m3 m�3.
G.H.A. van der Heijden et al. / Chemical Engineering Science 66 (2011) 4241–42504244
the sorption isotherm was measured to verify the results obtainedby MIP (see Fig. 2b). In the range of 0–97% RH the moisturecontent does not increase significantly. Above 97% RH a sharpincrease in moisture content can be seen. This RH corresponds topore sizes of approximately 0:5 mm and larger. This is in agree-ment with the MIP data. Under average atmospheric conditions ina building (50% RH) the used gypsum contains only a few percentof free moisture.
3.1.2. NMR
In the one sided heating experiments the distribution of themoisture over the gypsum sample is measured with NMR.However, NMR can also be used to characterise the water filledporous structure of gypsum. The pore space of gypsum is built upby entangled needle- or plate-shaped crystals. The spin–spinrelaxation time (T2) distribution of water in gypsum can giveinformation on the interaction of water molecules with the porewalls. In Fig. 3a, the NMR signal as a function of time is shown fora saturated gypsum sample. An inverse Laplace transform of theexponential decay curve (inset graph) clearly shows a bi-expo-nential behaviour, which is typical for gypsum (Jaffel et al., 2006).The relaxation times can be related to a pore size via the surfacerelaxivity (r2 � 5 mm s�1, Jaffel et al., 2006). The top axis of the T2
distribution graph displays the estimated pore size from the NMRexperiment. Although the pore sizes obtained by NMR are a factorof 4 smaller, one must keep in mind that the results wereobtained by two completely different measurement techniques.The bi-exponential behaviour represents two different waterpopulations present in the porous structure. Both populationshave a strong interaction with the pore surface. The fact that thedecay shows a clear bi-exponential behaviour indicates that theexchange due to diffusion of water molecules between the twowater populations is small (Brownstein and Tarr, 1979). In fact, itwas shown that for a water to plaster ratio lower than 0.6 there isno exchange possible between the two water populations due tothe geometry of the pore space (Jaffel et al., 2006).
Let us now take a closer look at how the pore space can berepresented. In Fig. 3b, a schematic view of the pore sizes ingypsum is shown (picture recreated after Filippov et al., 1996).The water between the entangled gypsum needles and platesaccounts for the long relaxation times and the dominant pore sizeas measured by MIP and sorption isotherm. The water populationwith the faster decay can be related to regions where the gypsumcrystals are more densely packed or to pores inside the gypsumcrystals (Halperin et al., 1994; Jehng et al., 1996; Filippov et al.,1996).
0.00 0.25 0.50 0.75100
101
102
103
104
105
1 10 100 10000
50
100
150
2000.1
Mxy
(a.u
.)
t (s)
1 r (μm)
Inte
nsity
(a.u
.)
T2 (ms)
Fig. 3. (a) Transverse nuclear magnetisation as a function of time as measured in satura
revealing two dominant relaxation regimes. (b) Schematic representation of the porous
up from entangled needle and plate-shaped crystals.
3.2. Thermal characterisation
3.2.1. DSC and TGA
As we have mentioned in Section 3.1, the pore space ofgypsum is created by hydrated crystals. If the temperature isincreased the reverse process of hydration, called dehydration,will result in release of chemically bound water from the gypsumcrystals. As a consequence the pore geometry and as a conse-quence the permeability and the strength of the gypsum willchange. In case of fire, the temperature at the heated surface of agypsum wall or plasterboard will rise quickly. At 100 1C the freewater will start to boil, and the gypsum will start to dehydrate.Under ‘open’ conditions (water vapour is free to escape) thefollowing dehydration reaction takes place:
CaSO4 � 2H2OðsÞþDHdehyd-CaSO4ðsÞþ2H2OðgÞ: ð5Þ
This endothermic reaction requires a total energy of 625 kJ/(kg drygypsum), which accounts for both the separation of water mole-cules from the crystal structure (150 kJ/kg (Thomas, 2002)) as wellas evaporation of the released dehydration water. The reactionwill take place from 90 to 150 1C The dehydration reaction wasmeasured using DSC. The results are shown in Fig. 4. In the opencase, one peak is measured.
In a closed system, the water vapour cannot freely escape fromthe reaction front. The released water vapour will act as an inhibitorfor the dehydration reaction. As a result the reaction will take placein two steps (Axenenko and Thorpe, 1996; Wullschleger and Wakili,2008; Mehaffey et al., 2008):
CaSO4 � 2H2OþDHdehyd,1-CaSO4 �12 H2Oþ3
2H2O,
CaSO4 �12 H2OþDHdehyd,2-CaSO4þ
12H2O: ð6Þ
In the first step the dihydrate is partially dehydrated to thehemihydrate. Only part of the energy needed for the completedehydration is used (450 kJ/kg). During the second step thehemihydrate is fully dehydrated. The temperatures at which thesereactions take place and the temperature gap between the tworeactions both depend on the partial vapour pressure (Mcadie,1964). The influence of vapour pressure on the dehydrationreactions was measured using DSC (see Fig. 4). Three experimentsare shown: the two extreme cases are an open pan, and a closedpan. The intermediate experiment was created by using a pan witha hole (0.5 mm). Under influence of the vapour pressure the onsetof the first reaction shifts to higher temperatures. Furthermore,the temperature gap between the first and second reactionincreases at higher vapour pressures.
slow decay
fast decay
ted gypsum. In the inset: inverse Laplace transform of the exponential decay curve,
structure of gypsum, adapted from (Filippov et al., 1996). The pore structure is built
0 50 100 150 200 250 300-25
-20
-15
-10
-5
0
5 %
Δm (%
)
T (°C)
closedopen
15 %
50-30
-20
-10
0
closed mediumopen
Q (m
W)
100 150 200 250T (°C)
Fig. 4. (a) Heat evolution during heating of gypsum as measured with DSC. Three different experiments are shown: open pan, closed pan, and an intermediate condition.
The intermediate condition was created by making a small hole (0.5 mm) in the pan. The samples were heated from 25 1C to 250 1C with 10 1C min�1. (b) Mass vs.
temperature curves of gypsum during heating as measured by TGA. Two different measurements were performed, one with a closed pan (50 mm pinhole lid) and one with
an open pan. Samples were heated from 25 1C to 300 1C at 10 1C min�1.
0.0 0.1 0.2 0.3 0.40
500
1000
1500
2000
2500Heat capacity
c (k
J / k
g K
)
moisture content (m3 m-3)
0.0
0.1
0.2
0.3
0.4
Thermal conductivity�
(W /
mK
)
Fig. 5. Heat conduction and heat capacity of gypsum measured as a function of
moisture content. The lines indicate the theoretical increase of the heat capacity
and thermal conductivity assuming a linear dependence with the moisture
content.
0.75 0.80 0.85 0.90 0.95 1.000
200
400
600
800
1000
1/2H2OSi
gnal
(a.u
.)
Relative mass (-)
3/2H2O
α = 0 α = 1
Fig. 6. Measured NMR signal of dry gypsum during slow dehydration. The signal is
shown as a function of the relative mass of the sample. A relative mass of
1 corresponds to complete hydration (a ¼ 1).
G.H.A. van der Heijden et al. / Chemical Engineering Science 66 (2011) 4241–4250 4245
The open and closed dehydration experiments were alsomeasured with a TGA. The mass-temperature curves are shownin Fig. 4. The same behaviour as in the DSC experiment isobserved in the TGA experiment, confirming the two-step releaseof first 3
2 and next 12 H2O, respectively.
3.2.2. Thermal properties
The heat capacity and thermal conductivity of the gypsumsamples were obtained by measuring the temperature profilesand heat flux during heating. The temperature on one side of thesample was instantly raised, and the temperature response of thematerial was measured to obtain the heat capacity. The thermalconductivity was obtained from the steady state temperatureprofile. The results are shown as a function of saturation in Fig. 5.It can be seen that the moisture content has a large influence onboth parameters. The two lines show that the theoretical increaseof the heat capacity and thermal conductivity assuming a lineardependence with the moisture content.
3.2.3. NMR
All water molecules are probed in an hydrogen NMR experi-ment, whether they are chemically bound, absorbed to a porewall, or surrounded by other water molecules. In the previousNMR section we focussed on the free moisture content inside the
gypsum pore space. In this section we will try to measure thechemically bound water with NMR. To this purpose, a gypsumsample was dried at 20 1C under a 0% RH atmosphere until aconstant mass was obtained. In this way, almost no free moistureis present in the pore space.
The mobility of a water molecule will determine the trans-verse relaxation time of the corresponding NMR signal. The watermolecules which are adsorbed or chemically bond to the porousmatrix have a much shorter relaxation time (T2o100 ms) thanbulk water (T2 ¼ 3 s) or water inside a pore (100 ms o T2 o 3 s)(Halperin et al., 1994). Although the relaxation time of thesewater molecules is extremely short, the large amount of water ingypsum makes it possible to measure the signal originating fromthe chemically bound water molecules.
If the NMR signal can be related to the amount of chemicallybound water, the signal can be used to obtain the degree ofhydration of gypsum. To test whether our setup is capable ofmeasuring the degree of hydration, a gypsum sample was dried at20 1C. The sample was then dehydrated during 5 days in an ovenat a temperature of 105 1C. The NMR signal and the mass of thesample were monitored simultaneously. The results are shown inFig. 6. The measured NMR signal is plotted against the relative
G.H.A. van der Heijden et al. / Chemical Engineering Science 66 (2011) 4241–42504246
mass of the gypsum sample, which represents the degree ofhydration (a). Where a¼1 corresponds to fully hydrated and a¼0to completely dehydrated. A linear fit of the data clearly showsthat the NMR signal can be directly related to the degree of(de)hydration.
The total NMR signal obtained from a gypsum sample at agiven relative humidity is thus a combination of both freehygroscopic water (long relaxation time), and chemically boundwater (short relaxation time).
4. Results
In this section the one sided heating experiments of gypsumwill be presented. Three experiments are presented, each withdifferent initial saturations of the gypsum sample: capillarysaturated, in equilibrium with 50% RH, and a dried sample. Theapplied heat flux was the same in all experiments: 12 kW m�2.
4.1. Heating of capillary saturated gypsum
For the first experiment, the gypsum sample is capillarysaturated (initial moisture content of 0.40 m3 m�3). In Fig. 7,the moisture content y and temperature profiles are shown. Theposition of 0 mm corresponds with the heated drying surface.Although the profiles were measured every 3 min, for sake ofclarity they are only shown for every 9 min. At the start of theexperiment the sample is at room temperature.
In general, two drying stages can be identified during drying ofa saturated porous material (van Brakel, 1980; Laurindo and Prat,1996; Yiotis et al., 2005). In the first drying stage the moistureremains homogeneously distributed throughout the sample. Themoisture transport is dominated by liquid flow through theporous material to the drying surface, where the moistureevaporates. When a certain critical moisture content is reached,the second drying stage starts. At this point the moisture phase inthe material is no longer percolating the material, and the liquidphase brakes up in smaller islands. In the second drying stage themoisture transport is pre-dominantly taking place via the vapourphase. A drying front develops, which will move through theporous material.
Depending on the heating rate, the first drying stage may beshortened or even absent. As long as the liquid moisture fluxtowards the surface is large enough to keep up with the evapora-tion flux from the surface, no drying or boiling front will develop.The maximum moisture flux which can be generated towards theheated surface is determined by the maximum capillary pressure
0 20 40 60 80 100
0
0.1
0.2
0.3
0.4
position (mm)
θ (m
3 m-3
)
1α
Fig. 7. Moisture (a) and temperature (b) profiles as measured during one sided heating
The initial moisture content y0 ¼ 0:40 m3 m�3 at 201. The horizontal dashed line indi
content. The y-axis is therefore split into two parts: free moisture y and chemically boun
(�). The temperatures as measured on the boiling front (X) and dehydration front (&
difference which can be generated over the sample. If themoisture flux is unable to keep up with the evaporation, thesurface will dry out and a drying or boiling front will develop.
In the case of gypsum, a first drying stage of homogenousdrying is observed (vertical arrow, Fig. 7). A small moisturegradient is present during the first drying stage, which has alsobeen observed in the non-isothermal drying of fired-clay brick(van der Heijden et al., 2009). This moisture gradient during thefirst drying stage is the result of the temperature gradientresulting from the intense one sided heating. During the firstdrying stage the temperature at the surface reaches 100 1C after20 min, while the back of the sample is still at room temperature.
At the end of the first drying period a clear drying frontdevelops (horizontal arrow). At this time, the average moisturecontent of the sample is approximately 0.12 m3 m�3, which isreferred to as the critical moisture content. The temperatures atthe drying front are marked in the temperature profiles (X).These temperatures were obtained by a linear interpolationbetween the two measured temperatures of the neighbouringthermocouples. Within the uncertainty of the experiment thetemperature at the drying front remains at 100 1C indicating thatthe drying front is in fact a boiling front. In the region where theboiling front has passed, the temperature increases further. Thetemperature at the surface reaches 300 1C. The moisture contentand boiling have a large influence on the heat conductivity andheat capacity of gypsum. This is clearly reflected by the twodifferent temperature gradients in the dry and wet part of thesample.
In Section 3.2, we have shown that we are able to measure thedegree of hydration of gypsum. In this experiment the tempera-tures near the surface are well above the dehydration tempera-tures for gypsum. In the moisture profiles (shown in Fig. 7) ahorizontal dashed line is shown to indicate the presumed bound-ary between free and chemically bound moisture. We havetherefore chosen to split the y-axis in two parts: hydration degree(a), and free moisture content (y). The front shows an extrainflection at an extremely low moisture content (lower arrow). Itappears as if a separate front is moving through the sample from0 to 15 mm. The temperature at this front is about 200 1C (&, seeFig. 7), which is in the temperature region of the seconddehydration reaction step (see Fig. 4). The first dehydration stepis not observed separately because the boiling front is moving tooclose together with the 1st dehydration front to be separatelyresolved in this experiment. The first dehydration reaction isexpected to take place at a temperatures between 100 and 150 1C(see Fig. 4). The observed boiling front is therefore most probablya combination of boiling water and the first dehydration step.
0 20 40 60 80 1000
100
200
300
400
position (mm)
T (°
C)
of capillary saturated gypsum. The time between two subsequent profiles is 9 min.
cates the presumed boundary between the free and chemically bound moisture
d a. The positions of the thermocouples are marked in the first temperature profile
) are marked in the temperature profiles.
G.H.A. van der Heijden et al. / Chemical Engineering Science 66 (2011) 4241–4250 4247
4.2. Heating of gypsum with 50% RH
In situ, building materials will have a moisture content inequilibrium with an environmental relative humidity. Therefore,in this experiment the gypsum was equilibrated at 50% RH. Thisrelative humidity was chosen close to the average humidity in abuilding. At this RH the gypsum has a very low moisture contentof 6�10�4 m3 m�3. Compared to the amount of chemicallybound water in gypsum (0.15 m3 m�3), this free water contentis only 0.4% of the total water content. The gypsum sample isinitially fully hydrated (a ¼1). Any increase of the signal abovethe maximum hydration degree of one must therefore originatefrom free moisture. Furthermore, we will use the term hydrogenprofiles since it is more suited in this experiment.
The moisture and temperature profiles are shown every4.7 min in Fig. 8. The magnitude of the signal at the start of thisexperiment is about 7% of the initial signal in the saturatedexperiment. If we compare this to the signal in the saturatedexperiment, it is of the same order of magnitude as the observeddehydration front (see Fig. 7). Based on the relaxation times andthe densities of free and chemically bound moisture, we canestimate the signal contribution of free moisture in Fig. 8a to be inthe order of 2%, which is smaller than the noise on the moistureprofiles.
Three observations can be made from the hydrogen profiles.First, a front is moving through the sample (horizontal arrow).The temperature at the front is about 100 1C. Dehydration istaking place since the hydration degree is lower than one. Basedon the temperatures, this front can be attributed to the firstdehydration reaction. The first dehydration reaction releases 75%of the chemically bound water. This water is released as watervapour, thereby increasing the local partial vapour pressure.
Secondly, behind the dehydration front, a significant increasein hydrogen content above a¼1 is observed. The increase insignal cannot be originating from chemically bound water, andmust be coming from free moisture. The maximum signalintensity at the peak of the hydrogen profile can be comparedwith the saturated experiment. The moisture content is approxi-mately 0.04 m3 m�3.
Thirdly, a second front can be observed moving through thesample behind the first front (indicated by the bottom arrow,hydrogen content between 0.45 and 0). The temperatures of thedehydration front are marked in the temperature profiles (&). Thetemperatures range from 200 1C at a position of 0 mm to 230 1Cfurther into the material, which is significantly higher than thefirst front. The temperatures measured on this front are compar-able to the temperatures related to the second dehydration of
0 20 40 60 80 100position (mm)
α (-
) 1.5 H2O
0.5 H2O
θ (m
3 m-3
)
0
0.5
10
0.04
Fig. 8. Hydrogen (a) and temperature (b) profiles during heating of gypsum in equilib
shown every 4.7 min. Initially the sample is fully hydrated (a¼1). Two separate
thermocouples are marked in the first temperature profile (�). The temperatures on thes
released in the first dehydration reaction, which results in an increase in free moisture
gypsum (see Fig. 4). Also, the temperatures are comparable to theobserved small dehydration front in the saturated experiment (seeFig. 7). This second front can therefore be identified as the seconddehydration reaction.
The build up of a moisture peak can be explained on the basis ofthe vapour pressure in the material. Close to the drying surface, thewater vapour can escape from the gypsum sample without diffi-culty. However, it can be seen that as the dehydration front reachesa position of approximately 30 mm from the surface the peak inhydrogen content starts to built up. As the dehydration front movesfurther into the sample the vapour released at the dehydrationfront is not only moving towards the heated surface, but alsotowards the back of the sample. The vapour moves into a region oflower temperatures, and as a result it will condensate. Thecondensing water is accumulating behind the dehydration front.
In a closed environment, TGA and DSC experiments haveshown that, under the influence of the partial vapour pressure,the dehydration of gypsum is a two-step process. The two frontsobserved in the hydration profiles are a clear indication thatinside the gypsum sample dehydration is taking place in twosteps. The temperatures on the two fronts are constant, indicatingthat the partial vapour pressures are not changing significantly.
4.3. Heating of dried gypsum
The gypsum sample was first dried before heating, in order toverify whether a small amount of moisture present in the previousexperiment has any influence on the dehydration kinetics and theobserved moisture peak built up. The sample was dried under acontrolled environment (1–2% RH and a temperature of 40 1C)until a constant mass was obtained. The hydrogen and tempera-ture profiles are shown every 4.1 min in Fig. 9. The gypsum sampleis initially fully hydrated (a ¼1). Any increase of the signal abovethe maximum hydration degree of one must therefore originatefrom free moisture. The initial heating rates of the two experi-ments were approximately the same.
When comparing the hydrogen content profiles of this experi-ment with the 50% RH experiment it can be seen that the sameresult is obtained. Two dehydration fronts can be identified, andan increase in free moisture content just behind the first dehy-dration front. This confirms our assumption that the initialhygroscopic moisture content is of no influence on the built upof a moisture peak. The vapour released in the first dehydrationreaction is the only origin for the increases of free moisturebehind the dehydration front. The peak starts to built up as thefront is at approximately 30 mm from the surface. Indicating thatcloser to the surface the vapour can escape from the sample.
0 20 40 60 80 1000
100
200
300
400
500
position (mm)
T (°
C)
rium with 50% RH. The initial moisture content is 6:10�4 m3 m�3. The profiles are
dehydration fronts can be observed (horizontal arrows). The positions of the
e fronts are marked in the temperature profiles (X, &). A large amount of water is
content y (see curved upward arrow).
0 20 40 60 80 100position (mm)
α (-
)
0 20 40 60 80 1000
100
200
300
400
500
position (mm)
T (°
C)
1.5 HO
0.5 HO
θ (m
3 m-3
)
0
0.5
10
0.04
Fig. 9. Hydrogen (a) and temperature (b) profiles during heating of dried gypsum. The profiles are shown for every 4.1 min. Initially the sample is fully hydrated (a¼ 1).
Two separate dehydration fronts can be observed (horizontal arrows). The positions of the thermocouples are marked in the first temperature profile (�). The temperatures
on these fronts are marked in the temperature profiles (X, &). A large amount of water is released in the first dehydration reaction, which results in an increase in free
moisture content y (see curved upward arrow).
50 100 150 200 250 3000
5
10
152 nd
40 mm
20 mm
10 mm
heat
ing
rate
(°C
min
-1)
T (°C)
5 mm1st
Fig. 10. Time derivative of the temperature at four thermocouple positions (5, 10,
20, and 40 mm) shown as a function of the temperature. The vertical dashed lines
indicate the positions of the two dehydration reactions.
G.H.A. van der Heijden et al. / Chemical Engineering Science 66 (2011) 4241–42504248
The temperatures on the two observed fronts are marked inthe temperature profiles (X, &). The temperature on the seconddehydration front is somewhat higher than in the previousexperiment, 300 1C compared to 250 1C. In both experiments thetemperatures on the two dehydration fronts are constant, indi-cating that the two reactions are temperature controlled.
The time derivative of the local temperature as a function oftemperature is shown for the five different thermocouple posi-tions in Fig. 10. We have chosen to use the temperature as thex-axis, so that the different curves can be compared. The influenceof the first dehydration reaction is observed in the heating rate atall thermocouple positions. The second dehydration step isonly noticed at a position of 5 mm, and not at the four otherpositions. It must be noted that the heat of dehydration of thesecond step is significantly smaller compared with the first step.Furthermore, in the experiments the second dehydration fronthas not progressed as far as the first dehydration front, typicallyonly 10–15 mm.
4.4. NMR relaxometry
We have introduced NMR relaxometry as a method forcharacterising the sizes of water filled pores. Furthermore, basedon the relaxation time a distinction could be made between free
and chemically bound water. In this section we will use NMRrelaxometry to verify whether the peak in hydrogen content is infact caused by an increase in free moisture. The NMR signal decaycurves were measured during the 50% RH experiment, at aposition of 50 mm from the heated surface. The two frontsmoving through the sample will pass this position. In this waythe evolution of both the moisture peak and dehydration frontscan be monitored in time. Analysis of the different relaxationcomponents present in the signal decay curves can be used toidentify the origin of the peak.
The results from the NMR relaxometry measurements areshown in Fig. 11a. The signal decay curves are shown at threedifferent times during the experiment. The bottom curve representsthe initial state of the sample before the experiment is started. Wecan identify two components in the exponential decay of the signal.A fast decay (T2 � 100 ms) which can be attributed to the chemicallybound water in gypsum, and a slower decay (T2¼ 3 ms) from the‘free’ water. The ratio between the amplitudes of the slow and thefast component is about 0.01, which is consistent with the lowmoisture content of 6�10�4 m3 m�3.
In Fig. 11b, the amplitudes of the two main components (short&, long J), and the normalised total signal (W) is plotted as afunction of temperature. As the sample is heated, the temperaturereaches 60 1C. At this temperature the long component starts toincreases, while the amplitude of the short component remainsconstant. At the same time the total signal increases, indicatingthat the long component is responsible for the signal increase.
The amplitude of the short component starts to decrease at atemperature of 80–90 1C. The amplitude decreases to about halfof the initial magnitude at a temperature of 130 1C. The seconddehydration should further decrease the magnitude to zero. At100 1C the long component starts to decrease along with the totalsignal. The decrease can be explained by boiling of water.
The fact that the free moisture content increases before dehy-dration is taking place indicates that the free moisture originatesfrom a position closer to the surface. The only sources of vapour isthe dehydration reaction. As a result of the steep temperaturegradient, a steep gradient in relative humidity is present. The watervapour will condense in the region just behind the dehydrationfront. The vapour released by the dehydration reaction itself willinfluence the dehydration kinetics. The increased vapour pressuresplits the dehydration process in two steps.
We have observed that the T2 of the slow component (freemoisture) increases from 1 to 3 ms as the amplitude of the peakincreases. The surface relaxivity of gypsum (see Section 3.1) canbe used to estimate the size of the condensation layer, which isabout 5–15 nm.
20 40 60 80 1000
100
200
300
400
500
position (mm)
T (°
C)
00
0.5
1
α (-
)
1ststep
2ndstep
T
Pv
H
vapourescape
vapourcondensing
0
θ (-
)
Fig. 12. The combined hydrogen (H, solid line) and temperature (T, dashed line)
profile at t ¼ 50 min. The moisture peak is indicated in grey. The temperature is
indicated on the left y-axis. The hydration degree (a), and the moisture content (y)
are shown on the right y-axis. The small horizontal arrows indicate the two
dehydration fronts. An approximate pressure peak (Pv, dash-dotted line) is shown
to illustrate that the vapour transport is directed in two directions. The vapour flux
back into the sample is responsible for the moisture peak built up (shown in grey).
0 1 2 3 4 5 6 7 8 9101
102
103
104
t (ms)
Sign
al (a
.u.)
time
hydrationwater
hygroscopicwater
20 40 60 80 100 120 1400.0
0.5
1.0
1.5 short T2long T2total signal
Ampl
itude
(-)
T (°C)
onsetdehydration
increasefree moisture
Fig. 11. (a) Three signal decay curves as measured at 50 mm from the heated surface. Two components can be identified: a fast decay and a slower decay. The fast and slow
decay can be associated to the chemically bound, and free water, respectively. (b) The amplitudes of the two decay components (short &, long J), and the total signal (W)
are shown in the right graph. The vertical dashed line indicates a temperature of 100 1C.
G.H.A. van der Heijden et al. / Chemical Engineering Science 66 (2011) 4241–4250 4249
4.5. Conceptual model
To summarize the different processes taking place in the twogypsum experiments, a schematic representation of the experimentis shown in Fig. 12. Three curves are shown: temperature (T),hydrogen content (H), and the approximated vapour pressure (Pv).The moisture peak is highlighted in grey. The dehydration reactions,especially the first dehydration step, are a large source of watervapour. The release of water vapour results in a local increase inpartial vapour pressure.
Initially, as the dehydration front is close to the surface thevapour can escape from the material. As the heating continues thefront moves further into the material increasing the resistance ofthe vapour flow towards the surface. The resistance to the vapourflow is determined by the vapour permeability. The maximum invapour pressure causes the vapour to be transported in twodirections (indicated by the double arrow). The vapour which istransported towards the drying surface will flow into a region ofhigher temperatures, and can exit the porous material at thedrying surface. However, the vapour which is transported towardsthe back of the sample will flow into a cooler region. The largegradient in temperature results in a large gradient in saturated
vapour pressure and hence relative humidity. At lower tempera-tures the relative humidity will increase resulting in condensationof moisture at a temperature of about 70 1C, corresponding to asaturated vapour pressure of 0.34 bar. The condensation of watervapour results in the built up of the observed moisture peak. Thefront position at which the built up of a moisture peak will startwill depend on the vapour permeability.
5. Conclusions
With our dedicated NMR setup it is possible to measure in anon-destructive way the moisture, hydration and temperaturedistributions in gypsum during intense heating. In this way, wewere able to measure both the free moisture as well as the(de)hydration profiles. The combined hydrogen content and tem-perature profiles give a unique insight in the moisture transportand dehydration kinetics inside the gypsum. The combination ofdetailed moisture content, hydration, and temperature profileshave not yet been reported in literature to our knowledge.
From the three different heating experiments with differentsaturations three important observations can be made. First,dehydration inside a gypsum wall is a two-step process. Theincrease in vapour pressure resulting from the first dehydrationreaction shifts the second dehydration reaction to higher tempera-tures of about 200–300 1C.
Secondly, the increase in partial vapour pressure resulting fromthe first dehydration reactions causes the vapour to diffuse in twodirections. Towards the heated surface, where the vapour canescape, and towards the back of the sample, where the vapour cancondensate. The increase in free moisture content was measuredand identified with NMR relaxometry.
The moisture, hydration, and temperature profiles obtained bythe NMR experiments can be used to validate existing heat andmass transfer models in gypsum. By combining the informationalready known from standard characterisation experiments withthe NMR data, a full set of parameters can be obtained. In thisway, validated moisture and heat transfer models will be able toaccurately predict the effect of a fire on a gypsum structure.
Nomenclature
B0
main magnetic field, T B1 radio-frequent magnetic field, T fl Larmor frequency, Hz G gradient, T/m Hhyd enthalpy of hydration, kJ/mol k proportionality constant
G.H.A. van der Heijden et al. / Chemical Engineering Science 66 (2011) 4241–42504250
M0
equilibrium magnetisation S NMR signal, a.u. ~S surface area poreT1
longitudinal relaxation time, s T2 transverse relaxation time, s TE echo-time, s TR repetition time, s x spatial coordinate, mGreek letters
a
degree of hydration g gyromagnetic ratio, MHz/T r2 surface relaxivity, m s�1Acknowledgements
This research was supported by the Dutch Technology Foun-dation, STW. The authors wish to thank Jef Noijen and HansDalderop for their help in the construction of the NMR setup andpreparation of the gypsum samples. Thanks to Jeroen Borghartsfor the gypsum characterisation measurements.
References
Aitcin, P.C., 2003. The durability characteristics of high performance concrete: areview. Cement and Concrete Composites 25 (4–5), 409–420.
Ang, C.N., Wang, Y.C., 2004. The effect of water movement on specific heat ofgypsum plasterboard in heat transfer analysis under natural fire exposure.Construction and Building Materials 18 (7), 505–515.
Ang, C.N., Wang, Y.C., 2009. Effect of moisture transfer on specific heat of gypsumplasterboard at high temperatures. Construction and Building Materials 23 (2),675–686.
Axenenko, O., Thorpe, G., 1996. The modelling of dehydration and stress analysisof gypsum plasterboards exposed to fire. Computational Materials Science 6(3), 281–294.
Brownstein, K.R., Tarr, C.E., 1979. Importance of classical diffusion in NMR studiesof water in biological cells. Physical Review A 19 (6), 2446.
Fejean, J., Lanos, C., Melinge, Y., Baux, C., 2003. Behaviour of fire-proofing materialscontaining gypsum, modifications induced by incorporation of inert filler.Chemical Engineering Research & Design 81 (A9), 1230–1236.
Filippov, A.V., Altykis, M.G., Khaliullin, M.I., Rachimov, R.Z., Lantsov, V.M., 1996.Study of the porous structure of hardened gypsum by pulsed nuclear magneticresonance. Journal of Materials Science 31 (16), 4369–4374.
Gultekin, D.H., Gore, J.C., 2005. Temperature dependence of nuclear magnetizationand relaxation. Journal of Magnetic Resonance 172 (1), 133–141.
Hahn, E.L., 1950. Spin echoes. Physical Review 80 (4), 580–602.Halperin, W.P., Jehng, J.Y., Song, Y.Q., 1994. Application of spin–spin relaxation to
measurement of surface-area and pore-size distributions in a hydratingcement paste. Magnetic Resonance Imaging 12 (2), 169–173.
Jaffel, H., Korb, J.P., Ndobo-Epoy, J.P., Morin, V., Guicquero, J.P., 2006. Probingmicrostructure evolution during the hardening of gypsum by proton NMRrelaxometry. Journal of Physical Chemistry B 110 (14), 7385–7391.
Jehng, J.Y., Sprague, D.T., Halperin, W.P., 1996. Pore structure of hydrating cementpaste by magnetic resonance relaxation analysis and freezing. MagneticResonance Imaging 14 (7–8), 785–791.
Khoury, G.A., 2000. Effect of fire on concrete and concrete structures. Progress inStructural Engineering and Materials 2, 429–447.
Laurindo, J.B., Prat, M., 1996. Numerical and experimental network study ofevaporation in capillary porous media. Phase distributions. Chemical Engi-neering Science 51 (23), 5171–5185.
Mcadie, H.G., 1964. Effect of water vapor upon dehydration of caso4.2h2o.Canadian Journal of Chemistry—Revue Canadienne de Chimie 42 (4), 792–800.
Mehaffey, J.R., Cuerrier, P., Carisse, G., 2008. A model for predicting heat transferthrough gypsum-board/wood-stud walls exposed to fire. Fire and Materials18, 297–305.
Nguyen, T.D., Meftah, F., Chammas, R., Mebarki, A., 2009. The behaviour ofmasonry walls subjected to fire: modelling and parametrical studies in thecase of hollow burnt-clay bricks. Fire Safety Journal 44 (4), 629–641.
O’Garra, M., Ali, F.A., Laverty, D., 2003. A numerical model for the behaviour ofmasonry under elevated temperatures. Fire and Materials 27 (4), 163–182.
Singh, N.B., Middendorf, B., 2007. Calcium sulphate hemihydrate hydration leadingto gypsum crystallization. Progress in Crystal Growth and Characterization ofMaterials 53 (1), 57–77.
Thomas, G., 2002. Thermal properties of gypsum plasterboard at high tempera-tures. Fire and Materials 26 (1), 37–45.
van Brakel, J., 1980. Mass transfer in convective drying. In: Mujumdar, A.S. (Ed.),Advances in Drying. Hemisphere Publishing Corporation, pp. 217–267 (Chapter 7).
van der Heijden, G.H.A., Bijnen, R.M.W., Pel, L., Huinink, H.P., 2007. Moisturetransport in heated concrete, as studied by NMR, and its consequences for firespalling. Cement and Concrete Research 37 (6), 894–901.
van der Heijden, G.H.A., Huinink, H.P., Pel, L., Kopinga, K., 2009. Non-isothermaldrying of fired-clay brick, an NMR study. Chemical Engineering Science 64(12), 3010–3018.
Vlaardingerbroek, M.T., den Boer, J.A., 2003. Magnetic Resonance Imaging, thirded. Springer Verlag.
Wullschleger, L., Wakili, K.G., 2008. Numerical parameter study of the thermalbehaviour of a gypsum plaster board at fire temperatures. Fire and Materials32 (2), 103–119.
Yiotis, A.G., Stubos, A.K., Boudouvis, A.G., Tsimpanogiannis, I.N., Yortsos, Y.C., 2005.Pore-network modeling of isothermal drying in porous media. Transport inPorous Media 58 (1–2), 63–86.