effects of pore sizes of porous silica gels on desorption activation energy of water vapour

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Applied Thermal Engineering 27 (2007) 869–876

Effects of pore sizes of porous silica gels on desorption activationenergy of water vapour

Xin Li, Zhong Li *, Qibin Xia, Hongxia Xi

Research Institute of Chemical Engineering, South China University of Technology, Guangzhou 510640, China

Received 17 November 2005; accepted 14 September 2006Available online 22 November 2006

Abstract

In this work, the effects of pore sizes of silica gel on desorption activation energy and adsorption kinetics of water vapour on the silicagels were studied. The isotherms and adsorption kinetic curves of water vapour on three kinds of silica gels with average pore diametersof 2.0 nm, 5.28 nm and 10.65 nm, respectively, were measured by the method of static adsorption, the desorption activation energies ofwater vapour on silica gels were estimated by using the TPD technique, and the effects of pore sizes of silica gel on adsorption kineticsand desorption activation energy were discussed. Results showed that the isotherm of water vapour on the A-type silica gel with theaverage pore diameter of 2 nm was of type I, which can be well described by the Langmuir model; the isotherms of water vapour onthe B-type and the C-type mesoporous silica gels with the average pore diameters of 5.28 nm and 10.65 nm, respectively, were of typeV; and at lower RH, the smaller the average pore size of the silica gel was, the smaller the adsorption rate constant was due to the dif-fusion resistance in the pores of the silica gels, while at a higher RH, the smaller the average pore size of the silica gel was, the larger theadsorption rate constant was. The desorption activation energies of water on the A-type, the B-type and the C-type silica gels wererespectively 35.54 kJ/mol, 31.41 kJ/mol and 26.16 kJ/mol, which suggested that the desorption activation energy of water on the silicagels increased as the pore sizes of the silica gels decreased.� 2006 Published by Elsevier Ltd.

Keywords: Silica gel; Pore size; Desorption activation energy; Adsorption kinetics; Water vapour adsorption

1. Introduction

Silica gel as a solid drying agent has been widely utilizedin dehumidification processes for their great pore surfacearea and good moisture adsorption capacity [1]. Since theadsorption performance of silica gel depends mainly onits surface area and pore distribution, the selection andcontrol of the pore structure are very important. Manyresearchers have done much work on the effect of the porestructure of the silica gels on the adsorption capacity ofwater vapour. Tashiro [2] pointed out that the pore volumewith pore sizes less than 2 nm was speculated to be relatedto the adsorption amount at lower relative humidities

1359-4311/$ - see front matter � 2006 Published by Elsevier Ltd.

doi:10.1016/j.applthermaleng.2006.09.010

* Corresponding author. Tel.: +86 20 87113501; fax: +86 20 87113735.E-mail address: [email protected] (Z. Li).

(RHs). Ng [3,4] found that the isotherm of water vapouron the silica gels with an average pore diameter of 2.2 nmcould be described by the Henry-type equation and theToth isotherm model. Chung [5] found that the adsorbedamount per unit volume of silica gel was increased withthe increasing of micropore zones of the silica gel.

The technology of dehumidification by adsorption con-sists of the adsorption and desorption processes. In recentyears, the amount of energy consumption in the regenera-tion process is considered to be responsible for the costof dehumidification. Therefore, the energy consumptionin the regeneration process has drawn considerable atten-tion. Kuei-Sen [6] pointed out that the regeneration ratewas not affected by the particle size of silica gel signifi-cantly. Chang [1] reported that the modified silica gelswould be regenerated at 90 �C for 0.5 h and that the silicagels with a larger pore volume could be regenerated easily

mailto:[email protected]

Fig. 1. Experimental apparatus for measuring adsorption kinetics andequilibrium.

870 X. Li et al. / Applied Thermal Engineering 27 (2007) 869–876

[3]. Ahmed [7] indicated that when an inclined-fluidized bedwas applied, a satisfactory regeneration rate was confirmedat regeneration temperature as low as 90 �C. Sukhmeet [8]studied the optimization of the regeneration air tempera-ture and bed-air velocity for a minimum energy input.Rong-Luan [9] found that if the adsorption isotherms ofwater vapour on the silica gel were of type I, the uptakecapacity at 298 K did not change significantly when regen-eration temperatures were varied in the range of 373–442 Kand 4–16 h. Nevertheless, a few desorption activation ener-gies of water vapour on the silica gels with different poresizes were reported up to now.

The purpose of the present work is to determine thedesorption activation energies of water vapour on the silicagels with different pore sizes, and discuss the effects of thepore sizes on desorption activation energies and the adsorp-tive properties of water vapour on silica gels.

2. Experimental section

2.1. Silica gels and reagents

Three kinds of silica gels (A-type, B-type and C-type)used in this study were purchased from Qingdao HaiyangChemical Co., Ltd and Special Silica Gel Factory (Qing-dao, China). Their particle sizes were in the range3–4 mm. Prior to use, they were dried at 413 K in a vacuumfor 4 h.

2.2. Nitrogen adsorption experiments

The specific surface area, pore volume, and average porediameter of samples were measured by nitrogen adsorptionat the liquid nitrogen temperature 77 K with the help ofMicromeritics gas adsorption analyzer ASAP 2010 machine.The silica gel sample was degassed at 573 K for 3 h in avacuum before the nitrogen adsorption measurements.The BET surface area was calculated from the adsorptionisotherms using the standard Brunauer–Emmett–Teller(BET) equation. The pore size distributions (PSD) weredetermined using Density Functional Theory (DFT) basedon statistical mechanics. The specific surface area and thepore volume of the gels were measured by the BET method.The average pore diameter DP = 4VP/SBET (assuming acylindrical shape of pores) was calculated from the BET sur-face area and pore volume.

2.3. Water vapour adsorption experiments

The adsorption isotherms and kinetic curves of thewater vapour on the silica gels at 303 K were separatelydetermined by means of the homemade apparatus withthe function of keeping constant temperature and humidityshown in Fig. 1. The apparatus consisted of an adiabaticsorption chamber and the temperature and humidity-con-trolling system. A micro-electronic balance was locatedwithin the adsorption chamber. Its accuracy was 0.0001 g.

The temperature and humidity of the sorption chambercan be adjusted and maintained constant by using the cycleof gas whose temperature and humidity can be adjusted.Its relative humidity (RH) was controlled by means of adehumidifier and a humidifier, with an accuracy of ±3%,and its temperature can be controlled with an accuracy of±0.5 �C.

2.3.1. Determination of adsorption kinetic curve of the water

vapour on the silica gels

Adsorption kinetic experiments were performed at atmo-spheric pressure by using the experimental apparatus shownin Fig. 1. Firstly, 2 g of fresh silica gel was introduced in anairtight flask with a cover, and then the flask was placed onthe micro-electronic balance located in the sorption cham-ber. Secondly, after the temperature and relative humidity(RH) within the sorption chamber was maintained ontosome designed values by means of its temperature andhumidity controllers, the flask was opened and thus theadsorption experiment may start, i.e. the weight of the sam-ple silica gel would be periodically recorded with the help ofthe electronic micro-balance as the adsorption occurred,and an adsorption kinetic curve giving the amountadsorbed of the water vapour on the silica gel as a functionof time was measured. Thirdly, the adsorption kineticexperiment ends when the weight of the sample got unvar-ied, meaning that the equilibrium had been achieved (the sil-ica gel was saturated with the water vapour). In order to getthe adsorption kinetic curves for the adsorption of the watervapour on various kinds of silica gels under the condition ofdifferent relative humidities, the adsorption kinetic experi-ments mentioned above were repeated separately at differ-ent relative humidities and on different silica gels, andthus these adsorption kinetic curves can be obtained.

2.3.2. Determination of isotherm of the water vapour on the

silica gels

Adsorption equilibrium experiments were carried out atatmospheric pressure in a similar way as stated above.Firstly, 2 g of fresh silica gel was introduced in an airtightflask with a cover, and then the flask was placed on anelectronic micro-balance located in the sorption chamber.

0 100 200 300 400 5000.000

0.005

0.010

0.015

0.020

0.025

A-type Silica gel

B-type Silica gel

C-type Silica gel

dV.(

dD)-1

, P

ore

volu

mes

/cm

3 .g-1.n

m-1

Pore Diameter (A)

Fig. 2. DFT pore size distributions.

0.0

N2

Vol

ume

adso

rbed

(cm

3 /g)

p/p0

0.2 0.4 0.6 0.8 1.00

100

200

300

400

500

A-Type silica gel

B-Type silica gel

C-Type silica gel

600

700

Fig. 3. The nitrogen adsorption isotherm on the three silica gels at 77 K.

X. Li et al. / Applied Thermal Engineering 27 (2007) 869–876 871

Secondly, after the temperature and relative humiditywithin the sorption chamber was maintained onto somedesigned values by means of its temperature and humiditycontrollers, the flask was opened using an internal mecha-nism and thus the adsorption of the water vapour on thesilica gel began. The weight of the sample increased gradu-ally as the adsorption was carried out. When the time ofthe adsorption was long enough(generally, about 200 hwere used), the weight of the sample hardly varied, whichindicated that the sample silica gel had been saturated withthe water vapour, and hence the equilibrium amountadsorbed of the water vapour on the unit silica gel corre-sponding to some relative humidity was obtained. Afterfinishing a series of Adsorption equilibrium experimentsunder the condition of different relative humidities, a seriesof adsorption phase equilibrium data of the water vapouron the unit silica gel can be obtained, and thus the plotof the equilibrium adsorption amounts of the water vapouron unit silica gel against its corresponding relative humid-ity yielded an isotherm of the water vapour on silica gel.

2.4. TPD experiments

The TPD experiments were conducted, respectively, atdifferent heating rates from 6 to 15 K/min. In each experi-ment, the sample that had adsorbed the water vapour waspacked in a stainless reaction tube whose inner diameterwas 0.3 cm and whose packed length was 0.5 cm. Subse-quently, the stainless tube was placed in a reaction furnaceand then heated in the high-purity N2 flow at a constantrate of 46.9 ml/min. The desorbed water vapour was mea-sured by using the GC-9501 chromatograph with a thermalconductivity detector (TCD) at the outlet of the stainlessreaction tube, and effluent curves were recorded, whichwere called the TPD curves. According to the experimentalTPD curves, the application of equation (8) can estimatethe activation energy for desorption of water on three kindsof silica gels with the average pore diameters of 2.0 nm,5.28 nm and 10.65 nm, respectively.

3. Results and discussion

3.1. Textural properties

According to IUPAC classification, pores within porousmaterials can be divided into micropore (width less than20 A), mesopore (width between 20 and 500 A) and macro-pore (width greater than 500 A). Fig. 2 shows the DFTpore size distributions of the silica gels. A sharp peakstretching toward the micropore region was observed inthe PSD curves of the A-type silica gel (at about 2 nm),while a distinct peak in the mesopore region could be seenin the PSD curves of the B-type and the C-type silica gel (atabout 5 and 10 nm, respectively). It meant that the microp-ores were dominant for the A-type silica gel, and the mes-opores were dominant for the B-type and the C-type silicagels in their structures. Fig. 3 shows the nitrogen adsorp-

tion isotherms of these silica gels. A steep increase in nitro-gen volume adsorbed at higher P/Po (by the mechanism ofcapillary condensation) suggested a relatively large contri-bution in mesopore range in the B-type and the C-type sil-ica gels. In the entire region of relative pressure, thenitrogen volume adsorbed was small for the A-type silicagel, indicating a low porosity. A flat linear portion at ahigher P/Po of the nitrogen adsorption isotherm for theA-type silica gel indicated a smaller contribution from mes-oporosity, whereas a steep increase in nitrogen volumeadsorbed at a higher P/Po and hysteresis phenomenon sug-gested a relatively large contribution in mesoporosity in theB-type and the C-type silica gels. The structure parametersof silica gels based on the nitrogen adsorption data aresummarized in Table 1. Among the three silica gels, theC-type silica gel possessed the largest total pore volume.

3.2. The isotherms of water vapour on the silica gels with

different average pore sizes

Fig. 4 shows the adsorption isotherms of the watervapour on the silica gels with different average pore sizes

Table 1Porous structure parameters of silica gels

Silicagels

BET surface area(m2/g)

Average porediameter (nm)

Volume of pores(cm3/g)

A 690.5 2.062 0.3560B 591.4 5.288 0.8179C 349.2 10.65 0.9555

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

Am

ount

ads

orpt

ed (

g/g)

Relative humidity (RH)

A-type Silica gel

B-type Silica gel

C-type Silica gel

Fig. 4. Isotherms of the water vapour on adsorption of the three silica gelsat 303 K.

0.2 0.4 0.6 0.8 1.00.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Am

ount

ads

orpt

ed (

g/g)

Relative humidity (RH)

The experiement datas

Langmuir, R=0.9953

Freundlich, R=0.9872

Fig. 5. The fitting of the water vapour adsorption isotherm on the A-typesilica gel.

0 2000 4000 6000 8000 10000 12000 140000.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

The

ads

orpt

ed w

ater

(g/

g)

The time (min)(T=303K,RH=10%)

A-type Silica gel

B-type Silica gel

C-type Silica gel

Fig. 6. Adsorption kinetic curves of the water vapour on the silica gels at303 K and 10% RH.


in air at 30 �C. It indicated that the adsorption isotherm ofthe water vapour on the A-type silica gel was of type I iso-therm, whereas the adsorption isotherms of the watervapour on the B-type and the C-type silica gels were of typeV isotherm [10]. At low relative humidity, the equilibriumamounts adsorbed of the water vapour on the A-type silicagel were the highest, while that on the C-type silica gel wasthe lowest. This was because at low RH the monomolecu-lar layer adsorption of the water vapour on the silica gelswas dominant [10], and the surface hydroxyl groups playedan important role in the adsorption. As a result, the lagerthe surface area of the silica gel, the higher the amountadsorbed of the water vapour was since the concentrationof hydroxyl groups was directly proportional to the specificsurface area of the amorphous silica gel [11]. The surfacearea of the A-type silica gel was the highest, while that ofthe C-type silica gel was the lowest, as indicated in Table1. The A-type silica gels, which adsorb much water aroundthe abundant active centres at low RHs, exhibited hydro-philic behaviour.

The isotherm of the water vapour on the A-type silicagel could be fitted by Langmuir (R = 0.9953) or Freundlich(R = 0.9872) model, as shown in Fig. 5. The Langmuirmodel was found to be in reasonable agreement with theexperimental data. This indicated that the adsorption ofthe water vapour on the A-type silica gel was the monomo-lecular layer adsorption.

It was noticed that for the B-type silica gel, the sharpincrease in uptake took place in the range of 60–85%RHs, and then it increased more slowly at higher RHs.This was because the filling of the micropores firstly

occurred, and then followed by capillary condensation inthe mesopores. For the C-type silica gel, the adsorptionof the water vapour increased very fast when the RH wasbetween 80% and 90%, due to its larger average pore sizeand larger pore volume in comparison with the B-type sil-ica gel, as indicated in Fig. 2.

The equilibrium amounts of the water vapour adsorbedon the three silica gels were very close to their total porevolume, respectively, at 100% RH, which meant that themaximum adsorption capacities of the silica gels were lim-ited, respectively, by their pore volumes. The amountadsorbed of the water vapour on the C-type silica gel waslarger than that adsorbed on the other silica gels, sincethe former had the largest pore volume.

3.3. The influence of relative humidity and average pore size

on adsorption rate constants

Figs. 6–9 show the kinetics curves of the water vapouradsorption on the silica gels at 303 K and different relativehumidities. It can be seen that the moisture sorption rateswere the highest during the initial adsorption stages andthen gradually became slow as the amount of adsorbedwater gradually increased. The adsorption kinetics of the

0 4000 8000 120000.00

0.05

0.10

0.15

0.20

0.25

The

ads

orpt

ed w

ater

(g/

g)


A-type Silica gel

B-type Silica gel

C-type Silica gel


0 4000 8000 12000 160000.0

0.1

0.2

0.3

0.4

The

ads

orpt

ed w

ater

(g/

g)


A-type Silica gel

B-type Silica gel

C-type Silica gel


0 16000 24000 32000 400000.0

0.2

0.4

0.6

0.8

1.0

The

ads

orpt

ed w

ater

(g/

g)

Time (min)

A-type Silica gel

B-type Silica gel

C-type Silica gel

8000



water vapour on the silica gels can be described by meansof Linear Driving Force (LDF) Model. The LDF modelwas expressed as follows [12,13]:

Mt

M e

¼ 1� e�kt ð1Þ

Rearranging Eq. (1) yields

1� Mt

M e

¼ e�kt ð2Þ

where Mt is the uptake at time t, Me is the equilibriumuptake and k is the rate constant. Figs. 10–13 showed thatthe plots of ln (1 �Mt/Me) versus time were linear with theslopes equal to the rate constants. It was found that theplots formed a straight line for >90% of the total uptakeat 303 K and different RHs. This suggested that the LDFmodel was suitable for the description of the water vapouradsorption on the silica gels studied.

Fig. 14 shows that the effects of RH on the adsorptionrate constants for water vapour adsorption on the threetypes of the silica gels. The results showed that the rate

0 4000 8000 12000

-4

-3

-2

-1

0

kA=2.977E-4S -1,R=-0.9990

kB=8.722E-4S -1,R=-0.9989

kC=0. 00133S -1,R=-0.9937

ln(1

-Mt/M

e)

Time (min)

A-type Silica gel

B-type Silica gel

C-type Silica gel

Fig. 10. Linear Dependence between ln (1 �Mt/Me) and time for analysis of water vapour adsorption kinetics using the LDF model at 303 K and10% RH.

0 2000 4000 6000 8000 10000 12000-5

-4

-3

-2

-1

0

kA=3.802E-4S-1,R=-0.9992

kB=0.00115S-1,R=-0.9842

kC=0.00367S

-1,R=-0.9967

ln(1

-Mt/M

e)

Time (min)

A-type Silica gel

B-type Silica gel

C-type Silica gel

Fig. 11. Linear dependence between ln (1 �Mt/Me) and time for analysisof water vapour adsorption kinetics using the LDF model at 303 K and45% RH.

0 4000 8000 12000-4

-3

-2

-1

0

kA=5.672E-4S-1,R=-0.9961

kB=1.790E-4S-1,R=-0.9957

kC=0.00115S-1,R=-0.9663

ln(1

-Mt/M

e)

Time (min)

A-type Silica gel

B-type Silica gel

C-type Silica gel


0 5000 10000 15000 20000 25000-5

-4

-3

-2

-1

0

A-type Silica gel

B-type Silica gel

C-type Silica gel

kA=0.00164S-1,R=-0.9811

kB=4.28477E-4S-1,R=-0.9662

kC=8.15998E-5S-1,R=-0.9954

ln(1

-Mt/M

e)

Time (min)


0 20 40 60 80 1000.000

0.001

0.002

0.003

0.004

0.005 A-type Silica gel

B-type Silica gel

C-type Silica gel

Rat

e co

nsta

nt (

s-1 )

Relative humidity (RH)%

Fig. 14. Variation of rate constants for water vapour adsorption on silicagels with RH at 303 K.


constants differ markedly for the different RH and the silicagels with different average pore size.

For the A-type silica gel with an average pore diameterof 2 nm, the rate constant of water vapour adsorptionincreased with increase of RH. When RH reached 80%, itled to a rapid increase in the rate constant due to the occur-ring of capillary condensation in higher RH.

For both the B-type and the C-type silica gels with theaverage pore diameters of 5.28 nm and 10.65 nm, respec-tively, the variation of their rate constants with RH showedthe same trend with a minimum and a maximum in the rateconstants, which was relative to the mechanisms of thewater vapour adsorption on these mesoporous silica gels.The isotherms of the water vapour on the B-type and theC-type mesoporous silica gels were of type V isotherm.The isotherm of type V represented mono- and multilayeradsorption plus capillary condensation [10]. It can be seenfrom Fig. 14 that the variation curves of the rate constants

with RH for water vapour adsorption can basically bedivided into three distinct regions. The first region wherethe relative humidity was less than 45% represented thatthe mono-adsorption was dominant and thus exhibited amonotonic increase in value of the rate constant of adsorp-tion with RH until it got a maximum. The second regionlies between RH > 45% and RH < 80% where the rate con-stant began to decrease with RH until it reached a mini-mum. The reason for this may possibly be that multilayeradsorption occurred, and was dominant in this adsorptionprocess. Since the adsorbate–adsorbate interactions in themultilayer adsorption processes were usually weaker thanthe interaction between the adsorbate molecules and theadsorbent surface, the adsorption process of the watervapour was slowed until the filling of mesopores occurred.The third region was when the relative humidity (RH) wasgreater than 80%, and led to an increase in the rate con-stant. The reason for this most possibly was that thegrowth of the cluster was filling up the mesopores of theB-type or C-type silica gel after the multilayer adsorption,and hence exhibited a rapid increase in the rate constants.

It can also be seen from Fig. 14 that at lower RH, thesmaller the average pore size of the silica gel was, the smal-ler the adsorption rate constant was due to the diffusionresistance [14] in pores of the silica gels, while at higherRH, the smaller the average pore size of the silica gelwas, the larger the adsorption rate constant was, becausethe capillary condensation easily occurred.

3.4. The effects of the pore sizes on desorption activation

energies

TPD technique is a technique of surface analysis [15]. Itis usually used to estimate binding energy between theadsorbate and the adsorbent, and activation energy ofdesorption [16–18], which can be used to value the adsor-bents and estimate adsorption isotherms [19]. Basically,some kind of adsorbate is adsorbed onto the adsorbent,

300 350 400 450

0

1

2

3

4

5

6

7 Tp=360.7K

Tp=356.9K

Tp=352.5K

Tp=347.1K

Tp=341.8K

ßH=8k/min

ßH=7k/min

ßH=6k/min

ßH=5k/min

ßH=4k/min

Des

orpt

ion

rate

Temperature (K)

Fig. 16. TPD spectrum of water on the type-B silica gel at differentheating rates.

300 350 400 4500

1

2

3

4

5

6

7

Tp=355.2K

Tp=359.3K

Tp=349.0K

Tp=343.7K

Tp=337.8K

ßH=4k/min

ßH=8k/min

ßH=7k/min

ßH=6k/min

ßH=5k/min

Des

orpt

ion

rate

Temperature (K)

Fig. 17. TPD spectrum of water on the type-C silica gel at differentheating rates.

-11.8 A-type Silica gel

B-type Silica gel


and then the adsorbent is heated with flowing of an inertgas in a controlled way such that the adsorbent tempera-ture varies linearly with time. As the temperature becomeshigh enough, the adsorbate will desorb gradually. In a TPDexperiment, a GC or a mass spectrometer is used to mea-sure the rate at which the adsorbate desorbs from theadsorbent. Using the TPD, one can know how stronglymolecules are bound to the surface of the adsorbent. TheTPD spectrum was a plot of the desorption rate of theadsorbate as a function of the sample temperature [15–19]. Desorption from a surface in a TPD experiment is usu-ally described by the Polanyi–Wigner equation,

rd ¼ �dhA

dt¼ k0h

nA expð�EA=RT Þ ð3Þ

the desorption reaction is assumed to follow first orderkinetics, the activation energy for desorption can be calcu-lated by

lnbH

RT 2p

!¼ � Ed

RT p

� �� ln

Ed

K0

� �ð4Þ

where n is the order of the desorption reaction, h is the frac-tional surface coverage, Tp is the peak desorption temper-ature, bH is the heating rate, Ed is the activation energy fordesorption, R is gas constant, and K0 is a constant that de-pends on the desorption kinetics.

TPD spectrums of water desorption from the A-type,the B-type and the C-type silica gels at different heatingrates are shown in Figs. 15–17. It can be seen that therewas an obvious peak in each TPD spectrum due to desorp-tion of the water vapour on the silica gels. A gradualincrease in the heating rate bH led to an increase in the peaktemperature Tp. The peak temperatures, Tp, can beobtained from the TPD spectra depicted in Figs. 15–17.Knowing the values of Tp for different heating rates, itwas possible to employ equation (8) to estimate the desorp-tion activation energy of water from the silica gels studied.Fig. 18 depicts the corresponding linear dependencies of

300 350 400 4500

1

2

3

4

5

6

7

8

Tp=345.1K

Tp=350.5K

Tp=355.0K

Tp=359.0K

Tp=362.5K

ßH=8k/min

ßH=7k/min

ßH=6k/min

ßH=5k/min

ßH=4k/min

Des

orpt

ion

rate

Temperature (K)

Fig. 15. TPD spectrum of water on the type-A silica gel at differentheating rates.

-2.96 -2.92 -2.88 -2.84 -2.80 -2.76

-12.6

-12.5

-12.4

-12.3

-12.2

-12.1

-12.0

-11.9

Y=-0.03219+4.274* X

Ed=35.54KJ/mol

Y=-1.338+3.778* X

Ed=31.41KJ/mol

Y=-3.046+3.146* XEd=26.16KJ/mol

ln(ß

H/R

Tp2 )

-103/Tp

C-type Silica gel

Fig. 18. Linear dependence between ln (RTp/bH) and 1/Tp for TPD ofwater on the silica gels.

the resulting plots of 1/Tp versus ln ðRT 2p=bHÞ for these sil-

ica gels. From the slope of these lines, activation energy Ed

Table 2Desorption peak temperatures of water at different heating rates and desorption activation energies of water on the silica gels

Adsorbent Desorption peak temperature (Tp, K) at different heating rates Activation energy of desorption(EA, kJ/mol)4 K/min 5 K/min 6 K/min 7 K/min 8 K/min

A-type 345.1 350.5 355.0 359.0 362.5 35.54B-type 341.8 347.1 352.3 356.9 360.7 31.41C-type 337.8 343.7 349.0 355.2 359.3 26.16


can be found out, and then k0 can also be obtained fromthe intercept of these lines on the y-axis, as shown inFig. 18. The calculation results of the desorption activationenergy of water on the A-type, the B-type and the C-typesilica gels are listed in Table 2. The desorption activationenergies of water on the A-type, the B-type and the C-typesilica gels were, respectively, 35.54 kJ/mol, 31.41 kJ/moland 26.16 kJ/mol. It suggested that the desorption activa-tion energy of water on the silica gels increased as the poresizes of the silica gels decreased. In other words, the smallerthe pore size of the silica gel was, the higher the desorptionactivation energy of water on the silica gel became. Thiswas because attraction forces acting on the water moleculefrom the surface force field on the surrounding wallsbecame stronger if the pore sizes of the silica gels weresmaller. As a result, the desorption activation energy ofwater on the A-type silica gel was the highest due to itssmallest average pore size, while that on the C-type silicagel was the lowest due to its largest average pore size forthe silica gels studied.

4. Conclusions

The isotherm of the water vapour on the A-type silicagel with an average pore diameter of 2 nm was of type I,which can be well described by the Langmuir model. Theisotherms of the water vapour on the B-type and the C-typemesoporous silica gels with average pore diameters of5.28 nm and 10.65 nm, respectively, were of type V. Atlower RH, the smaller the average pore size of the silicagel was, the smaller the adsorption rate constant was dueto the diffusion resistance in pores of the silica gels, whileat higher RH, the smaller the average pore size of the silicagel was, the larger the adsorption rate constant was. Thedesorption activation energies of the water vapour on theA-type, the B-type and the C-type silica gels were, respec-tively, 35.54 kJ/mol, 31.41 kJ/mol and 26.16 kJ/mol, sug-gesting that the desorption activated energy of water onthe silica gels increased as the pore sizes of the silica gelsdecreased.

Acknowledgements

The authors thank the National Natural Science Foun-dation of China (No. 20336020) and the Science and Tech-nology Foundation of the city of Guangzhou for financialsupports.

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effects of pore sizes of porous silica gels on desorption activation energy of water vapour

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