Water desorption from resorcinol-formaldehyde hydrogels and adsorptionin the resulting xerogels

Ivonne G. Escalona a,b, Cedric J. Gommes a, Nathalie Job a, Silvia Blacher a, Claudio G. Olivera-Fuentes b,Jean-Paul Pirard a, Angélique Léonard a,*

a Laboratory of Chemical Engineering, Department of Applied Chemistry, University of Liège, FNRS, Building B6c, Sart-Tilman, 4000 Liège, Belgiumb TADiP Group, Department of Thermodynamics and Transport Phenomena, Simón Bolívar University, Caracas 1080, Venezuela

a r t i c l e i n f o

Article history:Received 11 February 2008Received in revised form 6 June 2008Accepted 6 June 2008Available online 14 June 2008

Keywords:Water adsorption–desorptionResorcinol-formaldehyde xerogelsGAB modelPlastic deformation model

a b s t r a c t

Water desorption isotherms of resorcinol-formaldehyde (RF) hydrogels and subsequent water adsorptionisotherms of the resulting xerogels are determined using the static gravimetric method, at various tem-peratures. Isotherms obtained from samples synthesized at various pH are compared. Two differentmechanisms are involved in RF hydrogels water desorption. At large relative humidity the capillary ten-sion resulting from water removal induces a macroscopic shrinkage of the gel, whereas at low humiditywater is evaporated with no network deformation. These two mechanisms are analyzed using a plasticdeformation model and the Guggenheim-Anderson-de Boer (GAB) model, respectively. Adsorption iso-therms of RF xerogels are analyzed using the GAB model.

! 2008 Elsevier Inc. All rights reserved.

1. Introduction

Organic gels can be synthesized by sol–gel process via the poly-condensation of resorcinol (R) with formaldehyde (F) using sodiumcarbonate to modify the initial pH of the reacting solution [1]. Theobtained gels can afterwards be dried in subcritical conditionsleading to RF xerogels, and possibly pyrolyzed in an inert atmo-sphere to yield carbon xerogels [2–4]. The nanostructure of the ob-tained material is very sensitive to the synthesis and processingconditions [5]: depending on the pH of the precursor’s solutionand on the drying conditions, microporous, micro–mesoporous ormicro–macroporous carbons can be obtained. The meso–macro-pore texture is regulated by the synthesis and drying steps whilethe micropores are developed during the pyrolysis of the polymer.According to its tailorable pore texture, this carbon material can beused for many applications such as electrode materials for electri-cal double layer capacitors [6], materials for catalyst supports [7–9] and adsorbents.

The present study deals with the analysis of water desorptionisotherms from RF hydrogels, and with the subsequent wateradsorption isotherms in the resulting RF xerogels. The main moti-vation for this study is the prediction of the drying kinetics whenRF gels are dried in a convective dryer [10,11]. Indeed, at any stageof the drying process, the humidity of air at the surface of thematerial, i.e. in the boundary layer, depends on both the tempera-

ture and the water content of the material. At equilibrium, thisrelation between the sample water content and the humidity ofair in its surroundings at a given temperature is described by thewater desorption isotherm. Their determination is, therefore,needed as boundary conditions to solve the mass transfer equationwithin the dryer.

2. Materials and methods

2.1. Experimental

Hydrogels were produced by polycondensation of resorcinol (R)and formaldehyde (F), solubilized in water, in the presence of so-dium carbonate (C). The molar ratio of resorcinol/formaldehyde,R/F, and the dilution ratio, D, i.e. the Solvent/(R + F + C) molar ratio,were fixed at 0.5 and 5.6, respectively. The total amount of solventtakes into account the deionized water as well as the water and themethanol included in the formaldehyde solution. Three differentvalues of resorcinol/sodium carbonate molar ratio, R/C, weretested, chosen equal to 300, 500 and 1000, in order to modify thepH of the precursor’s solutions (6.6, 6.4 and 5.9, respectively).According to this composition, the fraction of the gels occupiedby the solid skeleton is estimated to be /0 = 26% of the totalvolume.

Resorcinol (VWR International, 99%) and sodium carbonate(UCB, 99.5%) were put together in a flask with deionized waterand stirred. After complete dissolution, formaldehyde (Aldrich,

1387-1811/$ - see front matter ! 2008 Elsevier Inc. All rights reserved.doi:10.1016/j.micromeso.2008.06.007

* Corresponding author. Tel.: +32 4366 4722; fax: +32 4366 2818.E-mail address: A.Leonard@ulg.ac.be (A. Léonard).

Microporous and Mesoporous Materials 117 (2009) 61–66

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37 wt.% in water, stabilized by 10–15 wt.% methanol) was addedand 2 ml of solution was poured into cylindrical glass molds witha diameter of 13 mm. Then, the samples were put in an ovenheated at 70 "C for gelation which typically may occur in severalhours if the initial solution pH is less than 6.8. The gels were after-wards aged for another 24 h at 70 "C [12].

Several methods can be used to determine moisture sorptionisotherms. The gravimetric technique, using saturated salt or sulfu-ric acid solutions, is the standard recommended method to obtaincomplete sorption isotherms [13]. This technique was used todetermine the water desorption isotherm of the RF hydrogelsand the water adsorption of the subsequent RF xerogels at 20, 50and 80 "C. Ten saturated salt solutions (Table 1) were selected tosettle different relative humidities (RH) ranging from 6% to 97%in a closed vessel in which the hydrogels or xerogels were placed.Relative humidity is defined as the ratio between the water vaporpressure at the surface of the material at any given temperatureand the vapor pressure of pure water at the same temperature.Analytic grade saturated salt solutions were prepared in ten differ-ent plastic containers. The moisture content of each hydrogel orxerogel was determined by weighing them periodically every3 days. This procedure was continued until a weight change lowerthan 0.1% was observed over 3 days. With this criterion, the longestexperiment took 12 days. The dry solid content of the samples wasdetermined at the end of the desorption stage by putting the sam-ples in an oven at 105 "C during 24 h. The equilibrium moisturecontent Weq was expressed on a dry basis, i.e. the amount of waterdivided by the amount of dried solid. Afterwards, the obtainedsamples, called RF xerogels, were put back in the ten containersfor the subsequent adsorption experiment. The water uptake wasperiodically measured until equilibrium was reached. Knowingthe initial dried sample mass, the equilibrium water content wasdetermined from the mass at the end of the adsorption stage.

2.2. Modeling methodology

A gel consists of two continuous phases: a liquid phase and a so-lid phase called the skeleton. In the course of water desorption, thegel first shrinks macroscopically at large relative humidity, underthe effect of the menisci that develop at the mouth of the poreson the outer surface of the material. When the relative humiditybecomes low enough, the evaporation front enters the material[14]. These two stages of desorption are governed by differentphysical mechanisms that require a specific modeling: a plasticdeformation model is used for the large humidity desorption[15], and the Guggenheim-Anderson-de Boer (GAB) model [16] isused to analyze the desorption and adsorption data for low humid-ity. A previous work comparing different water adsorption–desorption empirical isotherm models showed that the GAB

equations gave the best results [17]. The two models are describedbriefly in the next sections.

2.2.1. The plastic deformation modelThe equations presented in this section are discussed more

thoroughly in [18] for nitrogen desorption in compliant materialsand in [15] for methanol desorption. The compressive stress r(Pa) exerted by the menisci on the skeleton during the shrinkageof the material is related to the relative humidity, RH, by

r !Rg " TVm"

ln#RH$ 1%qqs

! "; #1$

where Rg is the ideal gas constant, T ("K) is the temperature, Vm (m3/kmol) is the molar volume of the solvent, q (kg/m3) is the bulk den-sity of the material, mass of the fluid not included, i.e. the mass drysolid phase divided by the volume of the gel, and qs (kg/m3) is theskeletal density, i.e. the mass of the dry solid phase divided by itsvolume. In the case of an ideal shrinkage, the volume reduction ofthe sample corresponds exactly to the volume of water evaporated.In this case, the relationship between the specific volume of theskeleton V (m3/kg), i.e. the total volume per unit mass of dry solid,and the moisture content Weq (kgwater/kgdry solid) expressed on a drybasis, is [12]:

V ! 1q ! 1

q1#Weq &

q1

qs$; #2$

where ql (kg/m3) is the density of the liquid. Combining Eqs. (1), (2)enables to determine, for any given value of Weq and RH, the com-pressive stress exerted on the skeleton of the gel

r ! Rg " TVm

Weq

Weq & q1=qs

# $ln#RH$: #3$

When the skeleton of the gel is submitted to a compressivestress r smaller than a given yield stress ry, it shrinks accordingto the following elastic law:

V ! V0 expqK0

! "; #4$

where V and V0 are the specific volume of the compressed skeletonand the unstressed skeleton, respectively. K0 is the elastic compres-sion modulus, defined as the volumetric stress over the volumetricstrain ratio; it describes the mechanical stiffness of the skeleton,when slightly compressed. Note that r is negative in Eq. (4). Whenthe compression stress exceeds the yield stress ry, it deforms plas-tically and Eq. (4) has to be replaced by [18]:

V ! Vy 1& mK0

#ry % r$# $%1

m

; #5$

wherem is a plastic hardening exponent that characterizes how thebulk modulus increases when the material is compressed, and Vy isthe yield volume, related to ry through:

Vy ! V0 expry

K0

! ": #6$

Combining Eqs. (2)–(6), the equilibrium water content in thegels is obtained, for any given value of RH, as a function of sixparameters V0, K0, m, Vy, ql and qs.

The practical fit of the data, when the gels undergo a pure com-pression, is done by taking the value V0 = 0.95 ' 103 kg/m3, whichsimply results from the composition of the gels, qs = 1.5 ' 103 kg/m3 [12], which is obtained from helium pycnometry done on thedry material, ql = 103 kg/m3, and m = 4. The latter value is a goodapproximation for RF gels, as notably reviewed in [19]. Therefore,the data are fitted by least-square minimization, with K0 and Vy

as only adjustable parameters.

Table 1Relative humidity for different saturated salt solutions used in the static gravimetricmethod, taken from Refs. [10,29]

Solution Relative humidity at 1 atm (±0.01%)

20 "C 50 "C 80 "C

LiBr 6.4 5.5 5.2LiCl 11.3 11.1 10.5KC2H3O2 22.5 18.9 15.1MgCl2 32.8 30.5 26.1K2CO3 43.2 42.7 41.1NaBr 58.0 50.9 51.4CuCl2 67.0 67.0 67.0NaCl 75.3 74.4 76.3KCl 84.3 81.2 78.9K2SO4 97.3 95.8 95.8

62 I.G. Escalona et al. /Microporous and Mesoporous Materials 117 (2009) 61–66

2.2.2. The GAB modelThe Guggenheim-Anderson-de Boer (GAB) sorption equation

[20–22], common in the field of the food technology [16], was usedto analyze the multilayer sorption of water. This model is a gener-alization of the BETmodel: it introduces a new constant (KG) relatedto the energy of interaction between the surface and the watermol-ecules in successive adsorbed layers. This enables one to describethe sorption of water in a broader range of relative humidities, RH(typically between 1% and 90%). The GAB equation is

Weq !WmCGKGRH

#1% KGRH$#1& #CG % 1$KGRH$; #7$

where Weq is the equilibrium moisture content of the material ex-pressed on a dry basis (kgwater/kgdry solid), RH is the relative humid-ity,Wm is the moisture content of the monolayer (kgwater/kgdry solid),CG is related to the difference of free enthalpy between the bulkysorbate and the sorbate in the first adsorbed monolayer, and KG isa measure of the difference in free enthalpies of the sorbate in suc-cessive monolayers. In the particular case of KG = 1, one recovers theBET model. The parameter identification was done using the so-called transformed GAB equation [13,23]. The model is consideredacceptable if the root mean squared error (RMSE) values are uni-formly scattered below 10%.

3. Results and discussion

3.1. Water desorption isotherms of RF hydrogels

Experimental data obtained during water desorption from RFhydrogels, for the three investigated temperatures and R/C ratiosare presented in Fig. 1. This figure presents the equilibrium mois-ture content of the samples as a function of RH, for three differenttemperatures. Initially, the water content of each hydrogel is closeto 1.85 kgwater/kgdry solid. At each considered temperature (20, 50and 80 "C), the desorption isotherms on gels obtained with differ-ent R/C coincide for RH < 50% and diverge for larger RH values. Inthe split zone, the higher the R/C value, the lower the equilibriummoisture content at any humidity. The effect of the R/C ratio is re-lated to the different texture of the samples. Indeed, a decrease ofthe R/C ratio leads to a decrease of the pore size in the wet gels,which will undergo a larger shrinkage during water removal [24].For each sample, the breaking of the curve at RH ( 67% roughlycorresponds to the end of shrinkage, as discussed further in Section3.3.

In the probed temperature range, at a given relative humiditythe equilibrium moisture content decreases with increasing tem-perature. This is shown in Fig. 2 for R/C = 300. The isotherms areclose to each other at the lowest temperature in the whole RHrange, whereas, moisture contents are quite different at 80 "C espe-cially for RH > 60%. These results are in good agreement with pre-vious studies [16]: for a given material, the equilibrium moisturecontent at a given relative humidity decreases with increasingthe temperature.

3.2. Water adsorption isotherms of RF xerogels

The experimental data obtained for water adsorption of RFxerogels are presented in Fig. 3. This figure shows the equilibriummoisture content, Weq, of the RF xerogels as a function of the rela-tive humidity, RH, at various temperatures. Adsorption isothermsexhibit the same tendency with regards to the influence of thetemperature and the R/C ratio as the desorption isotherms: theequilibrium moisture content decreases with increasing tempera-ture and at a given temperature and humidity, the equilibriummoisture content decreases with increasing R/C.

The data also exhibit an hysteresis for RH > 50% (Fig. 4): thedesorption is carried out on a hydrogel and the re-adsorption is

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1. 4

1. 6

1. 8

0 20 40 60 80 100

Weq

(kg

wat

er/ k

g dr

y so

lid)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 20 40 60 80 100

0. 0

0. 2

0. 4

0. 6

0. 8

1. 0

1. 2

1. 4

1. 6

1. 8

Weq

(kg

wat

er/ k

g dr

y so

lid)

0 20 40 60 80 100

Weq

(kg

wat

er/ k

g dr

y so

lid)

a

b

c

RH (%)

RH (%)

RH (%)

Fig. 1. RF hydrogels desorption isotherms experimental data for (e) R/C = 300, (h)R/C = 500 and (D) R/C = 1000 at (a) 20 "C, (b) 50 "C and (c) 80 "C. The full lines anddashed line represent the modeling by the GAB model and the deformation model,respectively.

I.G. Escalona et al. /Microporous and Mesoporous Materials 117 (2009) 61–66 63

carried out on the resulting xerogel. The hysteresis reflects the irre-versible shrinkage of the solid structure during desorption. Oncedried, the material cannot recover the full volume of the initialhydrogel.

3.3. Modeling of water desorption and adsorption

The shrinkage behavior of RF hydrogels was previously studiedunder various convective drying conditions [12]. These authorsobserved a final irreversible volume reduction of 10–15% forR/C = 1000, while the volume reduction is 45% and 60% forR/C = 500 and 300, respectively. In the case of an ideal shrinkage,i.e. the volume reduction corresponding exactly to the volume ofremoved water, Eq. (2) can be used to relate the macroscopicshrinkage to the loss of moisture content. This leads to [12]

VV0

! u0 1& qs

q1

! "W

# $; #8$

where V and V0 are the actual and initial specific volumes (m3/kg),respectively, u0 is the initial solid fraction of the hydrogel(u0 = 26%), W (kgwater/kgdry solid) is the water content defined on adry basis, ql is the density of water (103 kg/m3) and qs, i.e. the skel-etal density of the gel (1.5 ' 103 kg/m3 [12]). From Eq. (8) the watercontents corresponding to the end of shrinkage for R/C = 300, 500and 1000 are 0.43, 0.84 and 1.66 kgwater/kgdry solid, respectively.The calculated value corresponds well to the beginning of the hys-teresis, for instance around RH = 67% for R/C = 300, as indicated inFig. 4. This confirms that the first part of the desorption is irrevers-ible shrinkage.

Figs. 1 and 2 show the fit of the large humidity desorption iso-therm of the gel with R/C = 300 with the plastic deformation mod-el. The parameters obtained at each temperature for R/C = 300 byapplying the plastic deformation model to the high humiditydesorption are shown in Table 2. The values of K0 obtained fromthe fits are in agreement with values measured by beam bendingon RF samples of similar densities [25]. One observes from Table2 that K0 decreases when the temperature increases, which is com-mon to many materials, most notably thermoplastic polymericmaterials [25]. In this context, it has to be noted that the loweringof the equilibrium moisture content of that sample when increas-ing the temperature simply results from its skeleton becomingsofter.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 20 40 60 80 100

Weq

(kg

wat

er/ k

g dr

y so

lid)

RH (%)

Fig. 2. Moisture desorption isotherm of RF hydrogels for R/C = 300 at (D) 20 "C, (h)50 "C and (e) 80 "C. The full lines and dashed lines represent the modeling by theGAB model and the deformation model, respectively.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 20 40 60 80 100

RH (%)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

RH (%)

0 20 40 60 80 100

RH (%)

0 20 40 60 80 100

a

b

c

Weq

(kg

wat

er/ k

g dr

y so

lid)

Weq

(kg

wat

er/ k

g dr

y so

lid)

Weq

(kg

wat

er/ k

g dr

y so

lid)

Fig. 3. Adsorption isotherms experimental data in the RF xerogels for (e) R/C = 300,(h) R/C = 500 and (D) R/C = 1000 at (a) 20 "C, (b) 50 "C and (c) 80 "C. The solid line isthe fit with the GAB equation.

64 I.G. Escalona et al. /Microporous and Mesoporous Materials 117 (2009) 61–66

The GAB equation was used to analyze the desorption at the lowhumidity (RH < 67%) for gel with R/C = 300, and on the entirehumidity range of R/C = 500 and 1000. Figs. 1 and 2 show the dataadjustment using the GAB model. In order to determine the valuesof the parameters of the GAB equation, KG, Wm and CG, a parabolicregression derived from Eq. (1) was applied [23]. The obtained val-ues of the parameters at each temperature and R/C ratio are shownin Table 2. Decreasing R/C results in an increase of KG, while Wm

and CG remain almost unchanged.Taking into account that decreasing R/C results in xerogels with

a finer structure, as notably assessed by nitrogen physisorption[1,3,5,12,26,27], one could expect a decrease ofWm because it is re-lated to the specific surface area. The fact that it remains almostconstant hints at a phenomenological interpretation of the GABmodel. This is also confirmed by the KG being sometimes largerthan 1, which is not possible if that parameter is given its precisephysical meaning [28]. Values of KG larger than 1 simply reflectthe fact that the isotherms are bent upwards at large humidity,more than what would be possible from adsorption on a flat sur-face. In the present context differences in KG (i.e. in bending) pos-sibly reflect capillary evaporation in the samples with R/C = 300,the final xerogel of which is indeed known to be mesoporous,while the other two are macroporous [12].

Table 3 shows the estimated parameters of the GAB equationfor the adsorption branch. Here too, KG tends to increase when R/C decreases, i.e. when the pores become smaller [5]. Although KG

is now smaller than one, which in theory would be compatiblewith surface adsorption, the observed tendencies are the same asfor desorption. It is likely that it also has to be attributed to capil-lary condensation of water in the mesopores, the size of whichdecreasing when R/C decreases.

4. Conclusions

The static gravimetric method was used to determine waterdesorption isotherms on RF hydrogels, and subsequent wateradsorption isotherms on the resulting xerogels. The data were ana-lyzed with the GAB model and with a plastic deformation model, intheir respective application ranges. Although the GAB model theo-retically describes adsorption on a flat surface, its parameter KG canbe empirically used to assess the occurrence of capillarycondensation.

At low humidity, the data show that the moisture content of thesamples is roughly the same on desorption and adsorption: it de-pends mostly on the temperature and it is not found to be verysensitive to the texture of the samples. At high humidity, the mois-ture is different on desorption and on adsorption for all samples;furthermore, the moisture content is texture-dependent. On thedesorption branch, the samples undergo shrinkage driven by cap-illary forces. The differences in equilibrium moisture contentspoint to differences in mechanical stiffness of the samples: the datasuggest that the sample with R/C = 300 has the stiffest skeleton. Onthe adsorption branch, the moisture content is controlled by capil-lary condensation: the data suggest that samples with R/C = 300have the smallest pores, in agreement with independent character-ization data.

Acknowledgments

A.L., C.J.G. and N.J. are indebted to the Belgian Fonds de laRecherche Scientifique (FRS-FNRS) for a Research Associate posi-tion, and for Postdoctoral Researchers position, respectively;I.G.E, S.B., C.G.O. and J.P.P. acknowledge the ALFA Program of theE.U. (project ALFA II 0412 FA FI) for enabling fruitful scientific ex-changes between European Union and Latin America.

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0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 20 40 60 80 100

Weq

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Table 2Estimated parameters of the GAB and plastic deformation models for RF hydrogelsdesorption isotherms

Model GAB model Deformation model

T("C)

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(cm3/g)

Ko

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50 300 1.4 ± 0.1 0.05 44.0 ± 0.7 0.044 1.417 5.20 0.070500 1.2 ± 0.1 0.05 33.6 ± 0.8 0.031 – – –1000 1.2 ± 0.2 0.05 34.7 ± 1.4 0.028 – – –

80 300 1.2 ± 0.3 0.04 20.8 ± 1.2 0.130 1.746 1.08 0.070500 1.09 ± 0.06 0.04 26 ± 2 0.100 – – –1000 1.08 ± 0.06 0.03 41 ± 4 0.040 – – –

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Table 3Estimated parameters of the GAB model for adsorption isotherms of the RF xerogels

GAB Model

T ("C) R/C KG Wm CG RMSE

20 300 0.91 ±0.04 0.061 ±0.04 30 ±6 0.09500 0.73 ±0.07 0.061 ±0.07 39 ±7 0.041000 0.90 ±0.08 0.058 ±0.06 60 ±4 0.03

50 300 1.00 ±0.29 0.042 ±0.07 33 ±6 0.09500 0.98 ±0.07 0.044 ±0.09 40 ±7 0.081000 0.9 ±0.9 0.045 ±0.04 45 ±4 0.05

80 300 0.9 ±0.3 0.047 ±0.09 55 ±9 0.05500 0.8 ±0.6 0.050 ±0.07 43 ±4 0.061000 0.72 ±0.04 0.049 ±0.05 44 ±4 0.07

KG, Wm, CG: parameter of the GAB model, RMSE: root mean square error.

I.G. Escalona et al. /Microporous and Mesoporous Materials 117 (2009) 61–66 65

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