- Email: [email protected]
Roles of Capillary Condensation in Adsorption
Dr. Morio Okazaki, Professor at Department of Chemical Engineering, Kyoto Unversity, first joined Mitsubishi Rayon Co. Ltd. in 1956 when he graduated Kyoto University. After six years of industrial experience, he returned to Kyoto University and entered the graduate course in Chemical Engineering. He joined the faculty of Kyoto University in 1965 and he gained his doctoral degree by the dissertation entitled 'Transport Properties in Drying Process and Drying Characteristics' under Professor R. Toei at Kyoto University in 1975. His research interest, which started from a kinetic study of drying of porous materials, has been expanded and his current research interests include studies on transport phenomena of heat and mass in porous media, especially on transport properties concerning adsorption. He is the author of more than 90 papers mainly on adsorption, drying and heat transfer. He was a Visiting Associate Professor at the University of Wisconsin-Madison during the period from 1979 to 1980. Currently he serves as Editor-in-Chief of Journal of Chemical Engineering of Japan (Society of Chemical Engineers, Japan) and an editorial board member of Chemical Engineering and Processing (Elsevier Sequoia) and Separation Technology (Butterworth-Heinemann) .
Fundamentals of Adsorption Proc. lVth Int. Con$ on Fundamentals of Adsorption, Kyoto, May 17-22, 1992 Copyright 0 1993 International Adsorption Society
Roles of Capillary Condensation in Adsorption
Morio OKAZAKI Depamnent of Chemical Engineering, Kyoto University, Kyoto 60601, JAPAN
ABSTRACT
Hindrance effect of occurrence of capillary condensation of coexistingwater vapor was discussed on solvent-watervapor binary adsorption equilibrium in gas phase, as the first part. In the second part, transportkinetics of capillary-condensed phase in adsorptive porous material were consided In the last part, Capillary Phase-Separation, namely liquid-phase capillary condensation and its new application to estimation of adsorption from solution were suggested.
INTRODUCI'ION Strictly speaking, the capillary condensation, so-called Kelvin condensation, is not the interfacial phenomenon which takes place between a molecule and a solid surface, and is not included in the adsorption phenomena in a narrow sense,because it is brought about by deviation of the vapor-liquid equilibrium of a curved liquid surface from that of a flat surface. But even so, it has a great importance in adsorption in many aspects, especially in the engineering one. The author would like to discuss about the following three topics which have been studied by the author's group. (1) Influence of occurrence of capillarycondensation on binary adsorption equilibriain gas-phase (2) Transport of capillaqwondensedphase in porous solid (3) Liquid-phase capillarycondensation and its application to estimation of adsorption from solution 1. BINARY ADSORPTION EQULIBRIUM OF ORGANIC SOLVENT AND WATER VAPOR ON ACITVATEJl CARBON [11 In the adsorption process to remove and recover organic solvent vapor from exhaust process air by using activatedcarbon water vapor often coexists in the exhaust air. In most cases, the concentration of coexisting water vapor is much higher than that of solvent vapor. From the hydrophobic nature of the activatedcatbon, the adsorption equilibrium is not so hindered by the coexisting water vapor up to approximately0.2 to 0.3 in relative humidity. But the water vapor concentration often exceeds this level and it could hinder the adsorption of solvent vapor. In that case, it is important to evaluate the influenceof coexisting water vapor to the adsorption equilibrium of solvent vapor onto activated carbon.
1.1 AdsorptionModel Based on an idea that the birth and growth of capillary condensation phase of water vapor, which follow the Kelvin equation, should result in hindrance of the adsorption of organic vapor, we postulate a model as shown in Fig. 1. On the "dry*'surface of pores having the radius larger than the critical radius for the capillary condensation, the solvent vapor adsorption(qol) takes place. This adsorption equilibrium of the solvent vapor can approximately be given by the single component adsorption isotherm of the solvent vapor because of the hydrophobic nature of the surface of the activated carbon. The smaller pores than the critical pore, on the other hand, are filled with the capillary condensation phase(94, into which a certain amount of solvent vaPor(q,2)dissolves and a liquid-phase adsorption (903) onto the "wet" surface of the p s takes place following t he liiuid13
14
M. Okazaki
wet surface eq uilibri urn
surface r>rc)
condensed phase ( r
condense4 ( r(rc 1
phase
Fig. 1. Model for Binary Adsorption phase adsorption isotherm of dissolved solvent in aqueous solution. Finally the total amount of adsorbed solvent vapor (qo)is given by Eq. (1) 40 = 401 + 402 + 403
(1)
Here we p v i d e the following assumption. :On the dry surface there exists only vapor-phase adsorption of organic solvent and the amount adsorbed of water is negligibly small because the number of the hydmphilic sites are far fewer than the hydrophobic ones. Then, qol can be given as Eq. (2) 401 = 40"s D / s T =
40"(ST - SC)/ s T = 40"(1 - SC /ST)
(2)
where & is the gas-phase equilibriumamount adsorbed of the solvent vapor in the single component system, which can be given by the adsorption isotherm of solvent vapor on the activated carbon, ST the total surface area of the activated carbon, Sc the area of the "wet surface" and SD the one of the "dry surface". The net volume of the capillarycondensed water phase is given by subtracting the volume of the solvent adsorbed on the wet surface from Vc,the volume of the capillarycondensed phase, and then q02 can bt given by Eq. (3). 402 = pow0 ( vc (403 / P o )
(3)
where po is the density of the liquid solvent and wo the volume fraction of the solvent in the capillarycondensed phase which is a mixture of water and solvent. 403 is given by Eq. (4), in which 4003 is the equilibrium amount of liquid-phase adsorption at the composition of the capillary-condensed phase, which can be given through a separate experiment of liquid-phase adsorption of the dissolved solvent from the aqueous solution of the solvent. 403 = d $ C / ST
(4)
Similarly to Eq. (3), the amount adsorbed of water vapor as capillary-condensed phase is given by Eq. (5). 4w = Pw
(VC - (402+ 403) / P o )
(5)
1.2 Volume of Capillary-CondensedPhase and Surface Area of Wet Surface. Here we intend to predict the negative influence of coexisting water vapor on the adsorption of solvent vapor to activated carbon from the single component adsorption isotherms of each components. Figure 2 shows the adsorption isotherms in adsorption and &sorption steps of water vapor for two kinds of activated carbon, and physical propexties of the carbons are shown in Table 1. The singlecomponent adsorption isotherms of two kinds of water-soluble solvent vapor (Acetone and
Capillary Condensation in Adsorption
I5
Table 1. Physical Ropcm'es of Activafcd Carbans ShirasagiS HGI-780 Particle density 0.710 g/cc 0.787 g/cc Surfaceam 972m2/g 724 m2/g Pore volume 0.90 cc/g 0.85 cc/g
0.0
0.2
0.4
Pl = R'R
0.6
0.8
(-1
1.0
Fig. 2. Adsorption and Desorption Isothems of Water Vapor on Activated Carbon at 30'C
I
.-\
n
2 0.4"
0
I
I 1 1 1 1 4 1
Toluene Benzene
A A
I
IIOII
Methanol Acetone
Fig. 3.Adsorption Isotherms for Pure Components on Shirasagi S at 30'C Methanol) and two kinds of water-insolubleone (Benzene and Toluene) are shown in Fig. 3. In the cases of solvent vapor, no hysteresis between the adsorption and desorption steps was observed. In olrler to evaluate the above-mentioned four amounts adsorbed of solvent and water vapor, it is necessary to calculate the volume of capillary-condensedwater V c and the surface area ratio S&T. Then we adopt the followingtwo assumptions. : Through the adsorption of water-soluble solvent vapor, the surface becomes -philic even in the adsorption step, and then the contact angle of the adsorption step comes close to that of the desorption step.
16
M.Okazaki
Fig. 4. Cumulative Pore Volume and Surface Area Curves '
$EEESat
:In the case of water-insolublesolvent, the contact angles for each step is essentially
in the sinde-cmponent water vapor adsorption.
The Kelvin equation for cylindricalpore is given as r ICOS a = -2aVr/{RT In@&,i)) and the cumulative surface area S from r =O to t =r is given by Eq.(7).
Then from &sorption-step isothermsin Fig.2, the cumulative pore volume and pore surface area can be given as a function of r lcosa, as shown in Fig.4. By using this figure. it is possible to calculate Vc and SC/STagainst partial pressure of adsorbate, and those values are independent of postulated shape of pore and the contact angle. Namely, even if we postulate slit pores for the activated carbon, the same values are obtained The Kelvin radius r of binary component system can also be determinedeasily using Eq. (6)through the vapor-liquid equilibrium and the surface tension of the liquid binary component system 1.3 Results and Discussion The adsorption equilibrium data of mixed gas of solvent and water vapors on activated carbon Shirasagi S (TakedaChemical Industries, Ltd.) observed at adsorption step are given in Tables 2-5. The relative pressures of solvent vapors adopted for experiment a~ 53x104-3.3~10-2for acetone, 2.7~10-2-1.7~10-1for methanol, 1.0~10-3-1.5~10-2for toluene and 3.8~10-4-5.0~10-3for benzene. On the other hand, the dative pressures of water vapor are approximatelyin the range of 0.64.9 for all of the mixed gas systems. The equilibria observed for the liquid-phaseadsorption are given by Eq. (8) using the mole fraction of solvent in solutionX.
The obtained values of parameters Cf and A are shown in Table 6. The 403 has the largest contribution to the total amount adsorbed of solvent among the three amounts, q01,qd and 403. This is due to the high relative pressures of water vapor resulting in quite large
Capillary Condensation in Adsorption
I7
Table 2. Adsutption Equilibrium of Mixed Vapor of Wafer-Soluble Solvent (Acetone) and Water to Shirasaai S at W C Po ( d g ) 0.150 0.716 1.337 2.83 1 6.123 9.284 Pw
%
40 (obs.) 40 @=w q w (obs-)
@l=W
qw
401 402 Qa3
25.6 0.104 0.369 0.043 0.03 1 0.323 0.377 0.001 O.OO0 0.030
25.6 0.200 0.369 0.092 0.089 0.259 0.296 0.002 O.OO0 0.087
23.1 0.233 0.295 0.129 0.122 0.225 0.248 0.005 O.OO0 0.117
24.5 0.268 0.346 0.195 0.206 0.135 0.145 0.005 O.OO0 0.201
23.8 0.295 0.325 0.236 0.25 1 0.089 0.091 0.007 O.OO0 0.244
22.2 0.297 0.183 0.276 0.281 0.059 0.038 0.01 1 O.OO0 0.270
Table 3. Adsorption Equilibrium of Mixed Vapor of Water-Soluble Solvent (Methanol) and Water to Shirasaai S at 30'C Po ( H g ) 4.420 4.493 4.635 6.524 6.848 28.43 1 Pw ( m m w 28.6 25.5 24.3 26.1 23.3 20.4
8(obs.1 40
40 @Met.) qw (obs.1 4w @-edict-) 401
402
an?
0.125 0.404 0.023
0.055
0.338 0.356 O.OO0 0.013 0.042
0.126 0.369 0.053 0.073 0.267 0.321 0.001 0.015 0.057
0.131 0.338 0.069 0.080 0.278 0.30 1 0.003 0.014 0.063
0.160 0.378 0.112 0.102 0.242 0.289 O.OO0 0.022 0.080
0.163 0.310 0.119 0.099 0.219 0.274 0.004 0.019 0.076
0.280 0.070 0.166 0.204 0.160 0.150 0.014
0.044
0.145
Table 4. Adsorption Equilibrium of Mixed Vapor of Water-Insoluble Solvent (Toluene) and Water to Shirasagi S at 30'C Po (mmHg) 0.037 0.077 0.546 0.038 0.075 0.315 Pw (mmHg) 23.5 23.5 23.5 20.4 20.4 20.4
%Ws.) 40
40 @=diet.) qw (0bS.j QW
40I
@dct-)
402 On?
0.275 0.315 0.242 0.248 0.084 0.067 0.034 O.OO0 0.214
0.305 0.3 15 0.270 0.265 0.048 0.049 0.037 O.OO0 0.228
0.344 0.315 0.318 0.311 0.013 0.001 0.042 O.OO0 0.269
0.275 0.070 0.259 0.249 0.0 18 O.OO0 0.061 O.OO0 0.189
0.305 0.070 0.289 0.270 0.013 O.OO0 0.067 O.OO0 0.203
0.340 0.070 0.320 0.309 0.010 O.OO0 0.075 O.OO0 0,234
Table 5. Adsorption Equilibrium of Mixed Vapor of Water-Insoluble Solvent (Benzene) and Water to Shirasagi S at 30'C Po (mmHg) 0.045 0.077 0.489 0.212 0.432 0.601 Pw (mmHg)
$
40 (obs.1
40 @ d c t . ) 4 w cobs.) 4w Wet.)
401
402
Qa?
22.8 0.170 0.270 0.110 0.094 0.229 0.199 0.033 O.OO0 0.061
22.5 0.201 0.220 0.133 0.125 0.178 0.151
0.044
O.OO0
0.08 1
22.4 0.260 0.200 0.269 0.237 0.03 1 0.019 0.084 O.OO0 0.154
28.1 0.243 0.399 0.142 0.169 0.196 0.207
0.006
O.OO0 0.163
27.9 0.255 0.390 0.212 0.225 0.147 0.134 0.008 O.OO0 0.217
27.9 0.263 0.390 0.220 0.250 0.121 0.106 0.008 O.OO0
0.242
18
M.Okazaki
Table 6 Parameters in Frtundlich EquatiOn for Shirasagi S System Cf n X Acetone-Water 8.67 1.61 10-4-10-2 Methanol - Water 0.37 2.08 - 3 x 10-1 Benzene-Water 8.47 2.88 10-6-10-4 Toluene-Water 1.20 7.78
f! P 0.4 C 0
01
z
01
-03 h
XI 0,
2 0.2
u m n
0.1 3 00
v
6 0.0
u
0.0 0.1 0.2 0.3 0 4 q . q w ( p r e d i c t e d ) [glg-carbon) (A: adsorption, D: desorption)
Fig. 5. Comparisons of Observed and predicted Results on Shirasagi S at 30'C
OW"
0.0 0.1
0.2
qo,qW (predicted
0.3
1
0.4
(glg- carbon]
(A: adsorption, D: desorption)
Fig. 6.Comparisons of Observed and predicted Results on Shirasagi S at 30'C amount of capillarycondensedwater. For smaller relative pressure of water vapor, the contribution of qol would be more significant. As far as the present experiments are concerned, the large contribution of q03 is thought to compensate appreciably the hindrance of qol by the coexisting water vapor especially in the case of water-insoluble solvent vapor. It should be noted that the contribution of 403 is unexpectedly significant. HindrMce effect of water vapor For the case of water-soluble solvent, the hindrance effect of coexisting water vapor is more significant to 40 than to qw. On the other hand, the effect is reversed for the case of water-insoluble solvent.
Capillary Condensation in Adsorption I9
Hysteresis between aclsorption and &sorption step The hysteresis of adsoqtion equilibrium does not appreciably exist for both adsorbates in case of water-soluble solvent. However, in case of water-insoluble solvent the hysteresis is found. Namely, qw of desorption ste is larger than that of adsorption step. On the other hand, qo of desorption step is smaller than at of adsarptian step. C-n of predicted to observed equilibria As seen in Tables 2-5 and Figs. 5 and 6 the predicted adsorption equilibria show fairy good agreements with the observed ones for all the four kinds of solvent vapor. Similar agreements 8n also conf'med for another activated carbon, HGI-780 (Takeda Chemical Industries,Ltd.)[ 13. Then it would be concluded that the proposed model shown by Fig. 1 is useful for evaluation of the hindrance effect of coexisting water vapor onto adsorption equilibrium of organic solvent vapor.
tK
2. R O E OF CAPILLARY (?ONDENSATIONIN MASS TRANSPORT IN ADSORPTIVE POROUS SOLID [2,3] 2.1 Su~face-Adsorbed Phase and Capillary-Condensed Phase Besides diffusion and flow of gas in the pure, the transport of physically a d s h e d gas molecules is important in evaluatingthe apperent mass transferrate thtou adsorptiveporous solid. In the range of low partial pressure of the adsorbate gas, monolayer sorption takes place, while multilayer adsorption gradually incnases with the pressure. As the pressure approaches the saturated pnssurt of the adsorbate, capillary condensation begins to occur in the small pores. This means that the molecules adsorbed in both monolayer and multilayergradually accumulate to become the capillarycondensed phase. Therefore, the "apparent adsorbed phase" should be divided into the two phases for interpretation of transport mechanism of the so-called "surface diffusion". The first one is the "adsorbed phase in n m w sense", that is the "surface-adsorbedphase", and the other the "capillarycondensed phase".
2
[Apparent AdsorbedPhase]= [Surface-Adsorbed phase] + [Capillary-Condensed Phase] 2.2 Transport Mechanisms When we accept an idea that the transport of the adsorbed phase is attributed to the migration of the surface-adsorbedmolecule exposed to the gas phase as shown in Fig. 7, the apparent motive force should be the gradient of the number density of those molecules along the surface of pore. Accordingly, the mechanism of this phase is based on a stochastic process in nature. The transfer mechanism of the capillarycondensedphase, on the other hand, is not based on a stochasticprocess. Consider that there is a certain gradient of amount of Condensed phase in a porous solid. Simply thinking, the capillary-condensedphase occupies pores in order of radius that is from the smallest pure to larger pore. Consequently, far a given porous solid the pons of larger radii will be occupied by condensed phase as increasing amount adsorbed as schematically shown in Fig. 7. The capillary suction pressure pc, which is given by Eq. (9), of left-hand side in Fig. 7 with larger amount adsarbed is smaller than that of right-hand side with lower amount adsorbed.
MOLECULE MIGRATION
VISCOUS FLOW
L
cr fl!&f I )
rc2r
r rc 1
(a)
0)
Fig. 7. Mechanism of Apparent SurfaceDifhsion (a) Adsorbed phase (b) Capillary-Condensed Phase
20
M.Okazaki
pc= -20cos$/r
(9)
when a i s the surface tension, 8 the contact angle between the adsahre and the solid surface and r the porc radius. Consequently, the flow of condensedphase is induced.
2.3 SurfaceDiffusion Fluxes When the overall surface diffusion permeability P is defined by Eq. (lo),
N =-PA(@/&) where N is the surface diffusion flux, A the cross-sectional area and dp/& the adsorbate partial pressure gradient, the permeability of the adsorbed phase can be expressedby Eq. (1 1). Pd =D& (&BET
19)((ST - SC)
ST)
(1 1)
where D sis the surface diffusion coefficient of surface-adsorbbd phase, pb the bulk density of porous solid, BET the hypothetical amount adsorbed calculated by the B.E.T.equation., ST the total surface area and Sc the surface m a of pores occupied by capillaryeondensed phase. If we adopt the random hopping model [41for transport kinetics of surface-adsorbedmolecule, Dscan be expressed by using two parameters of which physical meanings are clear. On the other hand, under some assumptions on pore structure and capillary-condensed phase configuration, the permeability of capillarycondensedphase can be given as Eq. (1 2),
where VCWTthe relative volumetric saturation by capillarycondensed phase, poC the Kozeny constant for the case that all pores are occupied by capillary-condensedphase, and ps the saturated vapor pressure of the adsorbate. Equation (12)has one adjusting parameter Finally the apparent surface diffusion coefficientcan be given as Eq. (13).
e.
k p p
= (pd + pc) (pb (dq 19))
(13)
Consequently, we should separately consider those two kinds of transport phenomena and regard the apparent surface diffusion as a simultaneous pracess of the molecular migration of the adsorbed phase on the solid surface which takes place only on the "dry surface" and the viscous flow of the capillarycondensedphase through wet pores. When the amount adsorbed is small, the contribution of the former mechanism predominates, and it is gradually replaced by the one of the latter mechanism as innease of the capillarycondensed phase.
2.4 Results and Discussion Figure 8 is an example of correlation by Eqs. (1 1) and (12). The two parameters of Eq. (1 1) used for the conelation have been determined by fitting the calculated permeabilitiesto the observed ones in the range of small amount adsorbed and pE determined in the range of large amount adsorbed to ensure the accurate determination of parameters. The permeability of the surface-adsorbed phase decreaseswith the adsorbate pressure mainly due to decreasing the available "dry surface" area On the other hand, the permeability of the capillary-condensed phase appwiably inneases. The sum of the two permeabilities 8n well correlated. Figure 9 is an alternativeexpmsion of the same data, and the agnements m also satisfactoryof course. Satisfactory correlationshave also been obtained with other several sets of obsewed penneabilities. In order to obtain another experimental evidence of the substantial difference in the nature of transport mechanism between the surface-adsorbed and the capillary-mdensedphase, we performed measurements of self surface diffusion flux of sulfur dioxide gas through a plate of Vycor glass by using a radio-active 35302 as shown in Fig. 10. In this experiment, the both sides of Vycor-glass so that any overall surfacediffusion of the surfaceplate are kept in the same total pmsure of
Sa
adsarbad and the capillarycondensedphase can not take place. Consequentlythe Observed flux of 3 5 S a can give the self surface diffusion permeability of
m.
Capillary Condensation in Adsorption
21
Fig. 8. Permeabilities of CF2C12 through Carbolac: Experimental Data by Carman and Raal[5]
10
CFzCIz- Carbolac -33.1.C
-
2I
I
monolayer amount I
I
I
I
I
0
0
Fig. 10. Measurement of Self-DiffusionFlux of S@ Using 35S@ Figure 11(a) is a comparison between the "usual"and the l'selft surface diffusion permeability in the range when the surface-adsorbedphase is dominant. The transport of the surface-adsorbedphase is based on random migration of exposed molecules, and then those two kinds of permeability is considemi to coincide each other. The expected agreement can c e d y be found in Fig. 1l(b). On the other hand, Fig. 11(b) shows a comparison fm the range in which the capillary-condensed phase is dominant. In contrast to Fig. 11(a), significant discrepancies between those two kinds of permeabilityart found in this figure.
22
M.Okazaki
Figure 12 is another expression of the same data. In the range of small amount adsorbed, the two permeabilitycoincides each other. But in the range of large amount, the concenlration de ndenct of self surface diffusion coefficient is in striking comast to usual surface diffusion c o e z e n t . c his clearly suggests that there exists a substantial diffemnce in the mechanism between diffusions of the surface-adsorbedphase and the capillary-condensedphase. The self surface diffusion flux is not viscous flow of capillary-condensed phase, but a liquid-phaseselfdiffusion flux through a net work of p a ~ e ssaturated with capillary-condensedphase.
'
-4
1
'
1
'
1
1
(
-
1
Surface self- diff usion - 1O'C
p" h
g 3 - L
-
;(
~
E
< c
x
a"
2-
A
A
Surface flow 1- A Surface self-diffusion 0
-
30'C
Ok,
0'
11201140 111 1111 60 00 100
O
0
p [kPal
L p [kP.l
Fig. 11. Permeabilities for Surface Flow and Surface Self-Diffusion of S0.r on Porous Vycor Glass
0
0
I
1
1
1
I
2
I
-I
--'I.---+-
3 9 [mol/kgl
I
4
5
Fig. 12. Surface Flow Coefficients and Surface Self-Diffusion Coefficientsof S@ on Porous Vycor Glass
Capillary Condensationin Adsorption
23
3. INTERPRETATION OF LIQUID PHASE ADSORPTION BY CAPILLARY PHASESEPARATION CONCEPT-Liquid-PhaSe "Capiuety Candensation" -[6] The capillary condensation can be interpretedas that the vap-liquid equilibriumof the adsorbateis deviated from that with a flat surface by the curvature of the liquid surface in narrow pons. This effect of the curvam should exist also in liquid-li uid uilibrium to yield a similar situation in liquid phase to the capillary condensation: a h i n d liqui liquid equilibrium could stand within a
"8-
pore, because of the presence of a curved interface of the two liquid phases. In other woTds, a phaseseparation can be possible at a concentrationless than the saturated concentration. Though Patrick and co-worken [7,8] first suggested the possibility of this phenomenon, the quantitative n a m of this phenomenon still remains unclear. Hen we call this phenomenon "CapillaryPhase-Separation (CPS)". Such a solute-rich phase would contribute to the amount adsorbed in liquid phase adsorption of a solute with limited solubility onto po~ousadsorbent. The appannt amount admrbed in liquid phase, then, consists of two modes of 'adsorption', namely, one associated with the affinity to the surface and the BS-phase. Hence the knowledge of the relation between the concentration and the CuNam enables us to interpret the adsorption isotherms of adsarbates with limited solubilities,to some extent, especially in higher range of relative concentration. In this work, the relation between the curvature of interface and concentration in liquid-liquid equilibrium was found Further, utilizing this concept,we proposed a method to estimate liquid phase adsorption isotherms in higher range of relative concentration from the information of pore characteristicsof solids, especially from nitrogen isotherms.
3.1 Lquid-LiquidEquilibrium with curved Interface Suppose that we have two equilibrium states including components A and B as shown in Fig. 13, namely, one with a flat interface and the other with a curved one existing within a pore which has a cylindrical shape, as an example, with radius r. The interface with the interfacial tension d contacts to the wall with the contact angle 8. The component A and B correspondto a solvent and adsorbate, respectively, in the case of adsorption. Besides, the a-phase and the B-phase comspond to a bulk phase and a portion of adsorbed phase, respectively.
Through a treatment of classical thermodynamics, and with the mechanical balance between the phases expressed by Young-Laplace equation, we obtain the relation between the radius and the equilibrium concentration C under the ideal dilute solution approximation, which is applicable to aqueous solutions of, for example, aromatic compounds or aliphatic compounds in general because of heir small solubilities.
where C, is the saturated concentration of the solute B in the solvent A and m0is the molar volume of the solute B. For other shape of the pore, the corresponding curvature should be substituted for 2cos6yr. Equation (14) for capillary phase-separation corresponds to the Kelvin equation for capillary u-phase (A-rich)
..intaface .. B-Phrn
@-rich)
I
(m
(I) Fig. 13 Two Equilibrium States
24
M.Okazaki
condensation. They have similar form to cach other. One has to be, however, careful whether Eq. (14) holds in a given system. A more complicated foxmula should be used in other cases.
3.2 Estimation of Liquid phase Adsorption Isotherms The solute-rich phase of the liquid-liquid equilibrium within a pore would be counted as amount adsorbed at a comxntration less than the saturated. Accordingly, the total amount adsorbed consists of two modes of adsorption, namely, the red adsorption which arises from physimhemical nature of the adsorbent surface, and the apparent amount which arises from the pore characteristicsof the adsorbentespecially in the meSOpOrc range. This concept is quite the same as that employed in port analysis of mesopomus solids by physisorption of gas. The two adsorption isotherms. namely, the isotherm in liquid phase and that in gaseous phase can now be connected by the pore size distribution function. Hence, a liquid phase adsorption isotherm can be estimated by taking the reversed pn>cedunof pane analysis starting frwn the pcm size distribution. Among the existing pore analysis methods, the one proposed by Dollimm and Heal 191 was used to detennine the distribution in this study. The determined distribution should be recognized as an effective pore size distributionbecause the panes may not be cylindrical. For the estimation of liquid phase isotherms,the statistical thickness of the adsorptionin liquid phase, t, was needed to count for the red adsorption amount and assumed to follow &&el-type fmula
By this assumption, we had only one unknown parameter, to in Eq.(15) for the estimation of liquid phase adsorption isotherms from the pole size distribution function. He-, in principle, the isotherm could be estimated with only one measured point for a given system. The to value should be unique for a given combination of solution and solid by definition. Accordingly,once to is determinedfor a combination, the to is applicable to other adsorbents of differentpore structure if the solid itself has the same chemical composition. The liquid phase adsaption isotherms were estimated with the reversed procedure of the pore analysis [9]. It is briefly explained below. The calculation started froma saturated state in which all the pores were filled with adsorbate. or solute. The value of unknown parameter to was postulated arbitrarily. In the first step, the CPS phases in the pores with the largest radii, which was determined from the pore size distribution, were displaced by the bulk solution and only the real adsorption phase remained in this range of pores. The amount adsorbed was calculated by subtraction and the corresponding concentration was determind with Eqs.(l4) and (15). In the succeeding steps, the decrease of the red adsorption phase was counted in addition to the disappearanceof the CPS phase. The calculation was repeated until the concentration became small enough so that the CPS phase would not contribute to the amount adsorbed, usually around C/Co= 0.2. The postulated to value was then adjusted until the best fit to measured isotherm data was obtained. Note that the estimated isotherms consist of discrete points since the calculation procedure is based on the discrete data points of pore size distribution.
3.3 Results and Discussion Adsorption isotherms of aqueous solutions of aromatic compounds onto porous adsorbents were measured by a conventionalbatch adsorption method at 308K. The concentrations were determined by an ultraviolet spectrophotometer. Nitrogen adsorption isotherms at 78K were measured by the constant volume method to obtain pan size distributionof the adsorbentsused. Typical mesoporous solids used included porous carbonblacksand macrmeticularadsorbents whose mean pore diameter ranged from 40 to 60 A. Some activated carbons wen also used. However the contribution of the CPS were quite small for this kind of solids since they have small mesoporc volumes, which resulted in only faint changes in mount adsorbed in the relative concentration range considered here. For mesoparous solids, on the other hand, the amount adsorbed varied significantly in the concentration range as shown in the followings. The method is of greater use for these kinds of admrbents.
Capillary Condensation in Adsorption
3
25
1.2
i::
1
1.0
0.4 0.2
0.0 0.0
0.2
0.4
0.6
0.8
1.o
Redwedconcentration c I C o [ - I Fig. 14 Adsorption Isotherm of Nitrobenzene from Aqueous Solution onto SP900 As an example, the experimental and estimated results of the adsorption of nitrobenzene from aqueous solution onto a macroreticular adsorbent SP900 provided by Mitsubishi Kasei corp. are shown in Figure 14. The solid line shows the estimated isotherm and the broken line, as a reference. shows an estimation using Eq.(15) only. The solid line agrees fairly well with the experimental data to show the effectivenessof the method proposed. The parameter to in this system was determined to be 5.9
A.
The agreementswere similar in other systems examined. The parameter r, was determined for each combination of a solute and a group of solids with same origin. Though the number of systems examined was limited, it was found that the parameter stayed almost cons t for a solute even with different solids (e.g., 5.9 A for nitrobenzene-macroreticular adsorbent, 5.8 for nitrobenzene-porous carbonblack) but varied much from one solute to another (e.g., 3.9 A for benzene-porous carbonblacks, 7.6 A for aniline-porous carbonblacks). Namely, there might be a possibility for an adsorbate to have a common value which is applicable to relatively wide variety of solids.
R
The insensitivityof the tovalue to the solid could be inteqmted as follows. In the concentration range studied here, the apparent coverage of solute exceeds unity, which implies more opportunity for an adsorbed molecule to interact with other adsorbed molecules. This situation for the molecule rtduccs the importance of the interaction with the solid. As a result, the influence of the solid-adsorbate interactionon the tovalue becomes less important and the adsorbate-adsorbateinteraction principally determines the r,.
This implies the possibility of a unique value existing for a given adsorbate,which can be applied to a relatively wide variety of solids. Then the estimation of liquid phase adsorption isotherms could be made without any measured data in liquid phase. It would need only the informationof the nitrogen isotherms. Other than u prion' estimation of the liquid phase adsurption isotherm, the knowledge of the parameter
to enables us to follow the reverse procedure starting from a liquid phase adsorption isotherm to obtain the pore size distribution of the solid in liquid phase. As seen in macroreticular adsorbents. some porous materials swell or shrink when immersed in a solvent. Conventionalmethods such as the nitrogen adsorption or mercury intrusion need evacuation before the measurement. The swollen or shrunk state in a solvent could not be obtained by these methods. Utilization of the CPS concept may enable us to obtain an in siru measurement of the pore characteristicsof these kinds of porous solids. However, nothing definite can be said in the present state of the research. Further investigation would be needed to clarify the possibility.
26
CONCLUSIONS 1. The influence of occmnce of water vapor capillary condensation on binary adsorption equilibrium of vapor mixture of organic solvent and water on activated carbon was considered. Dividing the apparent amount adsorbed of organic solvent vapor into three parts, namely (1) amount adsorbed on dry-surface, (2)amount dissolved into capillarycondensed water, and (3) amount adsorbed on wet-surface of porn occupied by capillnry-comienscd water, it was possible to evaluate the hindrance effect of coexisting water vapor on adsorption of organic solvent vapor for both adsorption and &sorption steps. Further it was pointed out that the amount adsorbed of solvent on wet-surface plays a significant role in the adsorpaonof solvent vapor. 2.The surface diffusion of apparent adsorbed phase in the adsorptive porous material, especially focusing on the transport of capillarycondensed phase, was discussed. It was shown that the apparent surface diffusion flux can be expressed as the sum of the fluxes of the surface-adsorbexi phase and the capillary-condensedphase. Through measurements of self surface diffusion flux, an another evidence of the difference in nature of transport mechanism between the surface-adsorbed phase and the capillary-condensed phase was found. 3. Based on the concept of phase separation at a concentrationless than the saturation within pore, a method to estimate liquid phase adsorption isorhem of a solute with limited solubility, from pore size distribution of solids,especially that of mesopore range was proposed. And good agreements were found in liquid phase adsarptionisotherms over four kinds of adsorbates!kin aqueous solutions onto three categories of six adsorbem, which showed the effectivenessof the method proposed. Utilizing this concept, we have a possibility to obtain pore characteristicsof swollen or shrunk solid immersed in a solvent.
REFERENCES 11 M.Okazaki, H.Tamon and R. Toei, J. Chem.Eng. Jpn., 11 (1978)209 21 H. Tamon, M.Okazaki and R.Toei, AIChE J.,27 (1981)271 31 M.Okazaki, H.Tamon. T. Hyodo and R. Toei, AIChE J., 27 (1981)1035 41 M.Okazaki, H.Tamon and R. Toei, AIChE J.,27 (1981)262 51 P. C.Carman and F. A. Raal, Proc. Roy. Soc., 201A (1951)38 61 M.Miyahara and M.Okazaki,Chem.Express, 7 (1992)601 71 W.A. Patrick and D.C.Jones,J. Phys. Chem., 29 (1925)1 81 W.A. Patrick and N.F. Eberman, J. Phys. Chem.,29 (1925)220 91 D.Dollimore and G.R.Heal,J . Appl. Chem., 14 (1964)109
Fundamentals of Adsorption Proc. lVth Int. Con$ on Fundamentals of Adsorption, Kyoto, May 17-22, 1992 Copyright 0 1993 International Adsorption Society
Roles of Capillary Condensation in Adsorption
Morio OKAZAKI Depamnent of Chemical Engineering, Kyoto University, Kyoto 60601, JAPAN
ABSTRACT
Hindrance effect of occurrence of capillary condensation of coexistingwater vapor was discussed on solvent-watervapor binary adsorption equilibrium in gas phase, as the first part. In the second part, transportkinetics of capillary-condensed phase in adsorptive porous material were consided In the last part, Capillary Phase-Separation, namely liquid-phase capillary condensation and its new application to estimation of adsorption from solution were suggested.
INTRODUCI'ION Strictly speaking, the capillary condensation, so-called Kelvin condensation, is not the interfacial phenomenon which takes place between a molecule and a solid surface, and is not included in the adsorption phenomena in a narrow sense,because it is brought about by deviation of the vapor-liquid equilibrium of a curved liquid surface from that of a flat surface. But even so, it has a great importance in adsorption in many aspects, especially in the engineering one. The author would like to discuss about the following three topics which have been studied by the author's group. (1) Influence of occurrence of capillarycondensation on binary adsorption equilibriain gas-phase (2) Transport of capillaqwondensedphase in porous solid (3) Liquid-phase capillarycondensation and its application to estimation of adsorption from solution 1. BINARY ADSORPTION EQULIBRIUM OF ORGANIC SOLVENT AND WATER VAPOR ON ACITVATEJl CARBON [11 In the adsorption process to remove and recover organic solvent vapor from exhaust process air by using activatedcarbon water vapor often coexists in the exhaust air. In most cases, the concentration of coexisting water vapor is much higher than that of solvent vapor. From the hydrophobic nature of the activatedcatbon, the adsorption equilibrium is not so hindered by the coexisting water vapor up to approximately0.2 to 0.3 in relative humidity. But the water vapor concentration often exceeds this level and it could hinder the adsorption of solvent vapor. In that case, it is important to evaluate the influenceof coexisting water vapor to the adsorption equilibrium of solvent vapor onto activated carbon.
1.1 AdsorptionModel Based on an idea that the birth and growth of capillary condensation phase of water vapor, which follow the Kelvin equation, should result in hindrance of the adsorption of organic vapor, we postulate a model as shown in Fig. 1. On the "dry*'surface of pores having the radius larger than the critical radius for the capillary condensation, the solvent vapor adsorption(qol) takes place. This adsorption equilibrium of the solvent vapor can approximately be given by the single component adsorption isotherm of the solvent vapor because of the hydrophobic nature of the surface of the activated carbon. The smaller pores than the critical pore, on the other hand, are filled with the capillary condensation phase(94, into which a certain amount of solvent vaPor(q,2)dissolves and a liquid-phase adsorption (903) onto the "wet" surface of the p s takes place following t he liiuid13
14
M. Okazaki
wet surface eq uilibri urn
surface r>rc)
condensed phase ( r
condense4 ( r(rc 1
phase
Fig. 1. Model for Binary Adsorption phase adsorption isotherm of dissolved solvent in aqueous solution. Finally the total amount of adsorbed solvent vapor (qo)is given by Eq. (1) 40 = 401 + 402 + 403
(1)
Here we p v i d e the following assumption. :On the dry surface there exists only vapor-phase adsorption of organic solvent and the amount adsorbed of water is negligibly small because the number of the hydmphilic sites are far fewer than the hydrophobic ones. Then, qol can be given as Eq. (2) 401 = 40"s D / s T =
40"(ST - SC)/ s T = 40"(1 - SC /ST)
(2)
where & is the gas-phase equilibriumamount adsorbed of the solvent vapor in the single component system, which can be given by the adsorption isotherm of solvent vapor on the activated carbon, ST the total surface area of the activated carbon, Sc the area of the "wet surface" and SD the one of the "dry surface". The net volume of the capillarycondensed water phase is given by subtracting the volume of the solvent adsorbed on the wet surface from Vc,the volume of the capillarycondensed phase, and then q02 can bt given by Eq. (3). 402 = pow0 ( vc (403 / P o )
(3)
where po is the density of the liquid solvent and wo the volume fraction of the solvent in the capillarycondensed phase which is a mixture of water and solvent. 403 is given by Eq. (4), in which 4003 is the equilibrium amount of liquid-phase adsorption at the composition of the capillary-condensed phase, which can be given through a separate experiment of liquid-phase adsorption of the dissolved solvent from the aqueous solution of the solvent. 403 = d $ C / ST
(4)
Similarly to Eq. (3), the amount adsorbed of water vapor as capillary-condensed phase is given by Eq. (5). 4w = Pw
(VC - (402+ 403) / P o )
(5)
1.2 Volume of Capillary-CondensedPhase and Surface Area of Wet Surface. Here we intend to predict the negative influence of coexisting water vapor on the adsorption of solvent vapor to activated carbon from the single component adsorption isotherms of each components. Figure 2 shows the adsorption isotherms in adsorption and &sorption steps of water vapor for two kinds of activated carbon, and physical propexties of the carbons are shown in Table 1. The singlecomponent adsorption isotherms of two kinds of water-soluble solvent vapor (Acetone and
Capillary Condensation in Adsorption
I5
Table 1. Physical Ropcm'es of Activafcd Carbans ShirasagiS HGI-780 Particle density 0.710 g/cc 0.787 g/cc Surfaceam 972m2/g 724 m2/g Pore volume 0.90 cc/g 0.85 cc/g
0.0
0.2
0.4
Pl = R'R
0.6
0.8
(-1
1.0
Fig. 2. Adsorption and Desorption Isothems of Water Vapor on Activated Carbon at 30'C
I
.-\
n
2 0.4"
0
I
I 1 1 1 1 4 1
Toluene Benzene
A A
I
IIOII
Methanol Acetone
Fig. 3.Adsorption Isotherms for Pure Components on Shirasagi S at 30'C Methanol) and two kinds of water-insolubleone (Benzene and Toluene) are shown in Fig. 3. In the cases of solvent vapor, no hysteresis between the adsorption and desorption steps was observed. In olrler to evaluate the above-mentioned four amounts adsorbed of solvent and water vapor, it is necessary to calculate the volume of capillary-condensedwater V c and the surface area ratio S&T. Then we adopt the followingtwo assumptions. : Through the adsorption of water-soluble solvent vapor, the surface becomes -philic even in the adsorption step, and then the contact angle of the adsorption step comes close to that of the desorption step.
16
M.Okazaki
Fig. 4. Cumulative Pore Volume and Surface Area Curves '
$EEESat
:In the case of water-insolublesolvent, the contact angles for each step is essentially
in the sinde-cmponent water vapor adsorption.
The Kelvin equation for cylindricalpore is given as r ICOS a = -2aVr/{RT In@&,i)) and the cumulative surface area S from r =O to t =r is given by Eq.(7).
Then from &sorption-step isothermsin Fig.2, the cumulative pore volume and pore surface area can be given as a function of r lcosa, as shown in Fig.4. By using this figure. it is possible to calculate Vc and SC/STagainst partial pressure of adsorbate, and those values are independent of postulated shape of pore and the contact angle. Namely, even if we postulate slit pores for the activated carbon, the same values are obtained The Kelvin radius r of binary component system can also be determinedeasily using Eq. (6)through the vapor-liquid equilibrium and the surface tension of the liquid binary component system 1.3 Results and Discussion The adsorption equilibrium data of mixed gas of solvent and water vapors on activated carbon Shirasagi S (TakedaChemical Industries, Ltd.) observed at adsorption step are given in Tables 2-5. The relative pressures of solvent vapors adopted for experiment a~ 53x104-3.3~10-2for acetone, 2.7~10-2-1.7~10-1for methanol, 1.0~10-3-1.5~10-2for toluene and 3.8~10-4-5.0~10-3for benzene. On the other hand, the dative pressures of water vapor are approximatelyin the range of 0.64.9 for all of the mixed gas systems. The equilibria observed for the liquid-phaseadsorption are given by Eq. (8) using the mole fraction of solvent in solutionX.
The obtained values of parameters Cf and A are shown in Table 6. The 403 has the largest contribution to the total amount adsorbed of solvent among the three amounts, q01,qd and 403. This is due to the high relative pressures of water vapor resulting in quite large
Capillary Condensation in Adsorption
I7
Table 2. Adsutption Equilibrium of Mixed Vapor of Wafer-Soluble Solvent (Acetone) and Water to Shirasaai S at W C Po ( d g ) 0.150 0.716 1.337 2.83 1 6.123 9.284 Pw
%
40 (obs.) 40 @=w q w (obs-)
@l=W
qw
401 402 Qa3
25.6 0.104 0.369 0.043 0.03 1 0.323 0.377 0.001 O.OO0 0.030
25.6 0.200 0.369 0.092 0.089 0.259 0.296 0.002 O.OO0 0.087
23.1 0.233 0.295 0.129 0.122 0.225 0.248 0.005 O.OO0 0.117
24.5 0.268 0.346 0.195 0.206 0.135 0.145 0.005 O.OO0 0.201
23.8 0.295 0.325 0.236 0.25 1 0.089 0.091 0.007 O.OO0 0.244
22.2 0.297 0.183 0.276 0.281 0.059 0.038 0.01 1 O.OO0 0.270
Table 3. Adsorption Equilibrium of Mixed Vapor of Water-Soluble Solvent (Methanol) and Water to Shirasaai S at 30'C Po ( H g ) 4.420 4.493 4.635 6.524 6.848 28.43 1 Pw ( m m w 28.6 25.5 24.3 26.1 23.3 20.4
8(obs.1 40
40 @Met.) qw (obs.1 4w @-edict-) 401
402
an?
0.125 0.404 0.023
0.055
0.338 0.356 O.OO0 0.013 0.042
0.126 0.369 0.053 0.073 0.267 0.321 0.001 0.015 0.057
0.131 0.338 0.069 0.080 0.278 0.30 1 0.003 0.014 0.063
0.160 0.378 0.112 0.102 0.242 0.289 O.OO0 0.022 0.080
0.163 0.310 0.119 0.099 0.219 0.274 0.004 0.019 0.076
0.280 0.070 0.166 0.204 0.160 0.150 0.014
0.044
0.145
Table 4. Adsorption Equilibrium of Mixed Vapor of Water-Insoluble Solvent (Toluene) and Water to Shirasagi S at 30'C Po (mmHg) 0.037 0.077 0.546 0.038 0.075 0.315 Pw (mmHg) 23.5 23.5 23.5 20.4 20.4 20.4
%Ws.) 40
40 @=diet.) qw (0bS.j QW
40I
@dct-)
402 On?
0.275 0.315 0.242 0.248 0.084 0.067 0.034 O.OO0 0.214
0.305 0.3 15 0.270 0.265 0.048 0.049 0.037 O.OO0 0.228
0.344 0.315 0.318 0.311 0.013 0.001 0.042 O.OO0 0.269
0.275 0.070 0.259 0.249 0.0 18 O.OO0 0.061 O.OO0 0.189
0.305 0.070 0.289 0.270 0.013 O.OO0 0.067 O.OO0 0.203
0.340 0.070 0.320 0.309 0.010 O.OO0 0.075 O.OO0 0,234
Table 5. Adsorption Equilibrium of Mixed Vapor of Water-Insoluble Solvent (Benzene) and Water to Shirasagi S at 30'C Po (mmHg) 0.045 0.077 0.489 0.212 0.432 0.601 Pw (mmHg)
$
40 (obs.1
40 @ d c t . ) 4 w cobs.) 4w Wet.)
401
402
Qa?
22.8 0.170 0.270 0.110 0.094 0.229 0.199 0.033 O.OO0 0.061
22.5 0.201 0.220 0.133 0.125 0.178 0.151
0.044
O.OO0
0.08 1
22.4 0.260 0.200 0.269 0.237 0.03 1 0.019 0.084 O.OO0 0.154
28.1 0.243 0.399 0.142 0.169 0.196 0.207
0.006
O.OO0 0.163
27.9 0.255 0.390 0.212 0.225 0.147 0.134 0.008 O.OO0 0.217
27.9 0.263 0.390 0.220 0.250 0.121 0.106 0.008 O.OO0
0.242
18
M.Okazaki
Table 6 Parameters in Frtundlich EquatiOn for Shirasagi S System Cf n X Acetone-Water 8.67 1.61 10-4-10-2 Methanol - Water 0.37 2.08 - 3 x 10-1 Benzene-Water 8.47 2.88 10-6-10-4 Toluene-Water 1.20 7.78
f! P 0.4 C 0
01
z
01
-03 h
XI 0,
2 0.2
u m n
0.1 3 00
v
6 0.0
u
0.0 0.1 0.2 0.3 0 4 q . q w ( p r e d i c t e d ) [glg-carbon) (A: adsorption, D: desorption)
Fig. 5. Comparisons of Observed and predicted Results on Shirasagi S at 30'C
OW"
0.0 0.1
0.2
qo,qW (predicted
0.3
1
0.4
(glg- carbon]
(A: adsorption, D: desorption)
Fig. 6.Comparisons of Observed and predicted Results on Shirasagi S at 30'C amount of capillarycondensedwater. For smaller relative pressure of water vapor, the contribution of qol would be more significant. As far as the present experiments are concerned, the large contribution of q03 is thought to compensate appreciably the hindrance of qol by the coexisting water vapor especially in the case of water-insoluble solvent vapor. It should be noted that the contribution of 403 is unexpectedly significant. HindrMce effect of water vapor For the case of water-soluble solvent, the hindrance effect of coexisting water vapor is more significant to 40 than to qw. On the other hand, the effect is reversed for the case of water-insoluble solvent.
Capillary Condensation in Adsorption I9
Hysteresis between aclsorption and &sorption step The hysteresis of adsoqtion equilibrium does not appreciably exist for both adsorbates in case of water-soluble solvent. However, in case of water-insoluble solvent the hysteresis is found. Namely, qw of desorption ste is larger than that of adsorption step. On the other hand, qo of desorption step is smaller than at of adsarptian step. C-n of predicted to observed equilibria As seen in Tables 2-5 and Figs. 5 and 6 the predicted adsorption equilibria show fairy good agreements with the observed ones for all the four kinds of solvent vapor. Similar agreements 8n also conf'med for another activated carbon, HGI-780 (Takeda Chemical Industries,Ltd.)[ 13. Then it would be concluded that the proposed model shown by Fig. 1 is useful for evaluation of the hindrance effect of coexisting water vapor onto adsorption equilibrium of organic solvent vapor.
tK
2. R O E OF CAPILLARY (?ONDENSATIONIN MASS TRANSPORT IN ADSORPTIVE POROUS SOLID [2,3] 2.1 Su~face-Adsorbed Phase and Capillary-Condensed Phase Besides diffusion and flow of gas in the pure, the transport of physically a d s h e d gas molecules is important in evaluatingthe apperent mass transferrate thtou adsorptiveporous solid. In the range of low partial pressure of the adsorbate gas, monolayer sorption takes place, while multilayer adsorption gradually incnases with the pressure. As the pressure approaches the saturated pnssurt of the adsorbate, capillary condensation begins to occur in the small pores. This means that the molecules adsorbed in both monolayer and multilayergradually accumulate to become the capillarycondensed phase. Therefore, the "apparent adsorbed phase" should be divided into the two phases for interpretation of transport mechanism of the so-called "surface diffusion". The first one is the "adsorbed phase in n m w sense", that is the "surface-adsorbedphase", and the other the "capillarycondensed phase".
2
[Apparent AdsorbedPhase]= [Surface-Adsorbed phase] + [Capillary-Condensed Phase] 2.2 Transport Mechanisms When we accept an idea that the transport of the adsorbed phase is attributed to the migration of the surface-adsorbedmolecule exposed to the gas phase as shown in Fig. 7, the apparent motive force should be the gradient of the number density of those molecules along the surface of pore. Accordingly, the mechanism of this phase is based on a stochastic process in nature. The transfer mechanism of the capillarycondensedphase, on the other hand, is not based on a stochasticprocess. Consider that there is a certain gradient of amount of Condensed phase in a porous solid. Simply thinking, the capillary-condensedphase occupies pores in order of radius that is from the smallest pure to larger pore. Consequently, far a given porous solid the pons of larger radii will be occupied by condensed phase as increasing amount adsorbed as schematically shown in Fig. 7. The capillary suction pressure pc, which is given by Eq. (9), of left-hand side in Fig. 7 with larger amount adsarbed is smaller than that of right-hand side with lower amount adsorbed.
MOLECULE MIGRATION
VISCOUS FLOW
L
cr fl!&f I )
rc2r
r rc 1
(a)
0)
Fig. 7. Mechanism of Apparent SurfaceDifhsion (a) Adsorbed phase (b) Capillary-Condensed Phase
20
M.Okazaki
pc= -20cos$/r
(9)
when a i s the surface tension, 8 the contact angle between the adsahre and the solid surface and r the porc radius. Consequently, the flow of condensedphase is induced.
2.3 SurfaceDiffusion Fluxes When the overall surface diffusion permeability P is defined by Eq. (lo),
N =-PA(@/&) where N is the surface diffusion flux, A the cross-sectional area and dp/& the adsorbate partial pressure gradient, the permeability of the adsorbed phase can be expressedby Eq. (1 1). Pd =D& (&BET
19)((ST - SC)
ST)
(1 1)
where D sis the surface diffusion coefficient of surface-adsorbbd phase, pb the bulk density of porous solid, BET the hypothetical amount adsorbed calculated by the B.E.T.equation., ST the total surface area and Sc the surface m a of pores occupied by capillaryeondensed phase. If we adopt the random hopping model [41for transport kinetics of surface-adsorbedmolecule, Dscan be expressed by using two parameters of which physical meanings are clear. On the other hand, under some assumptions on pore structure and capillary-condensed phase configuration, the permeability of capillarycondensedphase can be given as Eq. (1 2),
where VCWTthe relative volumetric saturation by capillarycondensed phase, poC the Kozeny constant for the case that all pores are occupied by capillary-condensedphase, and ps the saturated vapor pressure of the adsorbate. Equation (12)has one adjusting parameter Finally the apparent surface diffusion coefficientcan be given as Eq. (13).
e.
k p p
= (pd + pc) (pb (dq 19))
(13)
Consequently, we should separately consider those two kinds of transport phenomena and regard the apparent surface diffusion as a simultaneous pracess of the molecular migration of the adsorbed phase on the solid surface which takes place only on the "dry surface" and the viscous flow of the capillarycondensedphase through wet pores. When the amount adsorbed is small, the contribution of the former mechanism predominates, and it is gradually replaced by the one of the latter mechanism as innease of the capillarycondensed phase.
2.4 Results and Discussion Figure 8 is an example of correlation by Eqs. (1 1) and (12). The two parameters of Eq. (1 1) used for the conelation have been determined by fitting the calculated permeabilitiesto the observed ones in the range of small amount adsorbed and pE determined in the range of large amount adsorbed to ensure the accurate determination of parameters. The permeability of the surface-adsorbed phase decreaseswith the adsorbate pressure mainly due to decreasing the available "dry surface" area On the other hand, the permeability of the capillary-condensed phase appwiably inneases. The sum of the two permeabilities 8n well correlated. Figure 9 is an alternativeexpmsion of the same data, and the agnements m also satisfactoryof course. Satisfactory correlationshave also been obtained with other several sets of obsewed penneabilities. In order to obtain another experimental evidence of the substantial difference in the nature of transport mechanism between the surface-adsorbed and the capillary-mdensedphase, we performed measurements of self surface diffusion flux of sulfur dioxide gas through a plate of Vycor glass by using a radio-active 35302 as shown in Fig. 10. In this experiment, the both sides of Vycor-glass so that any overall surfacediffusion of the surfaceplate are kept in the same total pmsure of
Sa
adsarbad and the capillarycondensedphase can not take place. Consequentlythe Observed flux of 3 5 S a can give the self surface diffusion permeability of
m.
Capillary Condensation in Adsorption
21
Fig. 8. Permeabilities of CF2C12 through Carbolac: Experimental Data by Carman and Raal[5]
10
CFzCIz- Carbolac -33.1.C
-
2I
I
monolayer amount I
I
I
I
I
0
0
Fig. 10. Measurement of Self-DiffusionFlux of S@ Using 35S@ Figure 11(a) is a comparison between the "usual"and the l'selft surface diffusion permeability in the range when the surface-adsorbedphase is dominant. The transport of the surface-adsorbedphase is based on random migration of exposed molecules, and then those two kinds of permeability is considemi to coincide each other. The expected agreement can c e d y be found in Fig. 1l(b). On the other hand, Fig. 11(b) shows a comparison fm the range in which the capillary-condensed phase is dominant. In contrast to Fig. 11(a), significant discrepancies between those two kinds of permeabilityart found in this figure.
22
M.Okazaki
Figure 12 is another expression of the same data. In the range of small amount adsorbed, the two permeabilitycoincides each other. But in the range of large amount, the concenlration de ndenct of self surface diffusion coefficient is in striking comast to usual surface diffusion c o e z e n t . c his clearly suggests that there exists a substantial diffemnce in the mechanism between diffusions of the surface-adsorbedphase and the capillary-condensedphase. The self surface diffusion flux is not viscous flow of capillary-condensed phase, but a liquid-phaseselfdiffusion flux through a net work of p a ~ e ssaturated with capillary-condensedphase.
'
-4
1
'
1
'
1
1
(
-
1
Surface self- diff usion - 1O'C
p" h
g 3 - L
-
;(
~
E
< c
x
a"
2-
A
A
Surface flow 1- A Surface self-diffusion 0
-
30'C
Ok,
0'
11201140 111 1111 60 00 100
O
0
p [kPal
L p [kP.l
Fig. 11. Permeabilities for Surface Flow and Surface Self-Diffusion of S0.r on Porous Vycor Glass
0
0
I
1
1
1
I
2
I
-I
--'I.---+-
3 9 [mol/kgl
I
4
5
Fig. 12. Surface Flow Coefficients and Surface Self-Diffusion Coefficientsof S@ on Porous Vycor Glass
Capillary Condensationin Adsorption
23
3. INTERPRETATION OF LIQUID PHASE ADSORPTION BY CAPILLARY PHASESEPARATION CONCEPT-Liquid-PhaSe "Capiuety Candensation" -[6] The capillary condensation can be interpretedas that the vap-liquid equilibriumof the adsorbateis deviated from that with a flat surface by the curvature of the liquid surface in narrow pons. This effect of the curvam should exist also in liquid-li uid uilibrium to yield a similar situation in liquid phase to the capillary condensation: a h i n d liqui liquid equilibrium could stand within a
"8-
pore, because of the presence of a curved interface of the two liquid phases. In other woTds, a phaseseparation can be possible at a concentrationless than the saturated concentration. Though Patrick and co-worken [7,8] first suggested the possibility of this phenomenon, the quantitative n a m of this phenomenon still remains unclear. Hen we call this phenomenon "CapillaryPhase-Separation (CPS)". Such a solute-rich phase would contribute to the amount adsorbed in liquid phase adsorption of a solute with limited solubility onto po~ousadsorbent. The appannt amount admrbed in liquid phase, then, consists of two modes of 'adsorption', namely, one associated with the affinity to the surface and the BS-phase. Hence the knowledge of the relation between the concentration and the CuNam enables us to interpret the adsorption isotherms of adsarbates with limited solubilities,to some extent, especially in higher range of relative concentration. In this work, the relation between the curvature of interface and concentration in liquid-liquid equilibrium was found Further, utilizing this concept,we proposed a method to estimate liquid phase adsorption isotherms in higher range of relative concentration from the information of pore characteristicsof solids, especially from nitrogen isotherms.
3.1 Lquid-LiquidEquilibrium with curved Interface Suppose that we have two equilibrium states including components A and B as shown in Fig. 13, namely, one with a flat interface and the other with a curved one existing within a pore which has a cylindrical shape, as an example, with radius r. The interface with the interfacial tension d contacts to the wall with the contact angle 8. The component A and B correspondto a solvent and adsorbate, respectively, in the case of adsorption. Besides, the a-phase and the B-phase comspond to a bulk phase and a portion of adsorbed phase, respectively.
Through a treatment of classical thermodynamics, and with the mechanical balance between the phases expressed by Young-Laplace equation, we obtain the relation between the radius and the equilibrium concentration C under the ideal dilute solution approximation, which is applicable to aqueous solutions of, for example, aromatic compounds or aliphatic compounds in general because of heir small solubilities.
where C, is the saturated concentration of the solute B in the solvent A and m0is the molar volume of the solute B. For other shape of the pore, the corresponding curvature should be substituted for 2cos6yr. Equation (14) for capillary phase-separation corresponds to the Kelvin equation for capillary u-phase (A-rich)
..intaface .. B-Phrn
@-rich)
I
(m
(I) Fig. 13 Two Equilibrium States
24
M.Okazaki
condensation. They have similar form to cach other. One has to be, however, careful whether Eq. (14) holds in a given system. A more complicated foxmula should be used in other cases.
3.2 Estimation of Liquid phase Adsorption Isotherms The solute-rich phase of the liquid-liquid equilibrium within a pore would be counted as amount adsorbed at a comxntration less than the saturated. Accordingly, the total amount adsorbed consists of two modes of adsorption, namely, the red adsorption which arises from physimhemical nature of the adsorbent surface, and the apparent amount which arises from the pore characteristicsof the adsorbentespecially in the meSOpOrc range. This concept is quite the same as that employed in port analysis of mesopomus solids by physisorption of gas. The two adsorption isotherms. namely, the isotherm in liquid phase and that in gaseous phase can now be connected by the pore size distribution function. Hence, a liquid phase adsorption isotherm can be estimated by taking the reversed pn>cedunof pane analysis starting frwn the pcm size distribution. Among the existing pore analysis methods, the one proposed by Dollimm and Heal 191 was used to detennine the distribution in this study. The determined distribution should be recognized as an effective pore size distributionbecause the panes may not be cylindrical. For the estimation of liquid phase isotherms,the statistical thickness of the adsorptionin liquid phase, t, was needed to count for the red adsorption amount and assumed to follow &&el-type fmula
By this assumption, we had only one unknown parameter, to in Eq.(15) for the estimation of liquid phase adsorption isotherms from the pole size distribution function. He-, in principle, the isotherm could be estimated with only one measured point for a given system. The to value should be unique for a given combination of solution and solid by definition. Accordingly,once to is determinedfor a combination, the to is applicable to other adsorbents of differentpore structure if the solid itself has the same chemical composition. The liquid phase adsaption isotherms were estimated with the reversed procedure of the pore analysis [9]. It is briefly explained below. The calculation started froma saturated state in which all the pores were filled with adsorbate. or solute. The value of unknown parameter to was postulated arbitrarily. In the first step, the CPS phases in the pores with the largest radii, which was determined from the pore size distribution, were displaced by the bulk solution and only the real adsorption phase remained in this range of pores. The amount adsorbed was calculated by subtraction and the corresponding concentration was determind with Eqs.(l4) and (15). In the succeeding steps, the decrease of the red adsorption phase was counted in addition to the disappearanceof the CPS phase. The calculation was repeated until the concentration became small enough so that the CPS phase would not contribute to the amount adsorbed, usually around C/Co= 0.2. The postulated to value was then adjusted until the best fit to measured isotherm data was obtained. Note that the estimated isotherms consist of discrete points since the calculation procedure is based on the discrete data points of pore size distribution.
3.3 Results and Discussion Adsorption isotherms of aqueous solutions of aromatic compounds onto porous adsorbents were measured by a conventionalbatch adsorption method at 308K. The concentrations were determined by an ultraviolet spectrophotometer. Nitrogen adsorption isotherms at 78K were measured by the constant volume method to obtain pan size distributionof the adsorbentsused. Typical mesoporous solids used included porous carbonblacksand macrmeticularadsorbents whose mean pore diameter ranged from 40 to 60 A. Some activated carbons wen also used. However the contribution of the CPS were quite small for this kind of solids since they have small mesoporc volumes, which resulted in only faint changes in mount adsorbed in the relative concentration range considered here. For mesoparous solids, on the other hand, the amount adsorbed varied significantly in the concentration range as shown in the followings. The method is of greater use for these kinds of admrbents.
Capillary Condensation in Adsorption
3
25
1.2
i::
1
1.0
0.4 0.2
0.0 0.0
0.2
0.4
0.6
0.8
1.o
Redwedconcentration c I C o [ - I Fig. 14 Adsorption Isotherm of Nitrobenzene from Aqueous Solution onto SP900 As an example, the experimental and estimated results of the adsorption of nitrobenzene from aqueous solution onto a macroreticular adsorbent SP900 provided by Mitsubishi Kasei corp. are shown in Figure 14. The solid line shows the estimated isotherm and the broken line, as a reference. shows an estimation using Eq.(15) only. The solid line agrees fairly well with the experimental data to show the effectivenessof the method proposed. The parameter to in this system was determined to be 5.9
A.
The agreementswere similar in other systems examined. The parameter r, was determined for each combination of a solute and a group of solids with same origin. Though the number of systems examined was limited, it was found that the parameter stayed almost cons t for a solute even with different solids (e.g., 5.9 A for nitrobenzene-macroreticular adsorbent, 5.8 for nitrobenzene-porous carbonblack) but varied much from one solute to another (e.g., 3.9 A for benzene-porous carbonblacks, 7.6 A for aniline-porous carbonblacks). Namely, there might be a possibility for an adsorbate to have a common value which is applicable to relatively wide variety of solids.
R
The insensitivityof the tovalue to the solid could be inteqmted as follows. In the concentration range studied here, the apparent coverage of solute exceeds unity, which implies more opportunity for an adsorbed molecule to interact with other adsorbed molecules. This situation for the molecule rtduccs the importance of the interaction with the solid. As a result, the influence of the solid-adsorbate interactionon the tovalue becomes less important and the adsorbate-adsorbateinteraction principally determines the r,.
This implies the possibility of a unique value existing for a given adsorbate,which can be applied to a relatively wide variety of solids. Then the estimation of liquid phase adsorption isotherms could be made without any measured data in liquid phase. It would need only the informationof the nitrogen isotherms. Other than u prion' estimation of the liquid phase adsurption isotherm, the knowledge of the parameter
to enables us to follow the reverse procedure starting from a liquid phase adsorption isotherm to obtain the pore size distribution of the solid in liquid phase. As seen in macroreticular adsorbents. some porous materials swell or shrink when immersed in a solvent. Conventionalmethods such as the nitrogen adsorption or mercury intrusion need evacuation before the measurement. The swollen or shrunk state in a solvent could not be obtained by these methods. Utilization of the CPS concept may enable us to obtain an in siru measurement of the pore characteristicsof these kinds of porous solids. However, nothing definite can be said in the present state of the research. Further investigation would be needed to clarify the possibility.
26
CONCLUSIONS 1. The influence of occmnce of water vapor capillary condensation on binary adsorption equilibrium of vapor mixture of organic solvent and water on activated carbon was considered. Dividing the apparent amount adsorbed of organic solvent vapor into three parts, namely (1) amount adsorbed on dry-surface, (2)amount dissolved into capillarycondensed water, and (3) amount adsorbed on wet-surface of porn occupied by capillnry-comienscd water, it was possible to evaluate the hindrance effect of coexisting water vapor on adsorption of organic solvent vapor for both adsorption and &sorption steps. Further it was pointed out that the amount adsorbed of solvent on wet-surface plays a significant role in the adsorpaonof solvent vapor. 2.The surface diffusion of apparent adsorbed phase in the adsorptive porous material, especially focusing on the transport of capillarycondensed phase, was discussed. It was shown that the apparent surface diffusion flux can be expressed as the sum of the fluxes of the surface-adsorbexi phase and the capillary-condensedphase. Through measurements of self surface diffusion flux, an another evidence of the difference in nature of transport mechanism between the surface-adsorbed phase and the capillary-condensed phase was found. 3. Based on the concept of phase separation at a concentrationless than the saturation within pore, a method to estimate liquid phase adsorption isorhem of a solute with limited solubility, from pore size distribution of solids,especially that of mesopore range was proposed. And good agreements were found in liquid phase adsarptionisotherms over four kinds of adsorbates!kin aqueous solutions onto three categories of six adsorbem, which showed the effectivenessof the method proposed. Utilizing this concept, we have a possibility to obtain pore characteristicsof swollen or shrunk solid immersed in a solvent.
REFERENCES 11 M.Okazaki, H.Tamon and R. Toei, J. Chem.Eng. Jpn., 11 (1978)209 21 H. Tamon, M.Okazaki and R.Toei, AIChE J.,27 (1981)271 31 M.Okazaki, H.Tamon. T. Hyodo and R. Toei, AIChE J., 27 (1981)1035 41 M.Okazaki, H.Tamon and R. Toei, AIChE J.,27 (1981)262 51 P. C.Carman and F. A. Raal, Proc. Roy. Soc., 201A (1951)38 61 M.Miyahara and M.Okazaki,Chem.Express, 7 (1992)601 71 W.A. Patrick and D.C.Jones,J. Phys. Chem., 29 (1925)1 81 W.A. Patrick and N.F. Eberman, J. Phys. Chem.,29 (1925)220 91 D.Dollimore and G.R.Heal,J . Appl. Chem., 14 (1964)109