METHOD FOR THE CALCULATION OF EFFECTIVE DISTRIBUTION IN MOLECULAR SIEVE CARBON

PORE SIZE

Geza HORVATHand Kunitaro KAWAZOE Department of Chemical Engineering, University of Tokyo, Tokyo 113 Amethod for the calculation of effective pore size distribution from adsorption isotherms in molecular-sieve carbon is described. This method is more exact theoretically as well as practically than previously described methods. An average potential function has been determined inside the slit-like pores. With the help of this function the doubtful use of the Kelvin equation can be avoided at the scale of molecular dimensions. The method gives poor values for the larger pores but can be combined with the well-known Dollimore-Heal method at a pore size of 1.34 nm. Calculation is possible over a wide range of pore sizes. The calculation is shown through two examples from N2 isotherms at 77.4K. The model can be extended to other pore shapes as well as to other

adsorbent-adsorbate pairs.

Introduction Molecular-sieve activated carbon usually contains slit-like pores of the order of0.1 nm and the distances between the walls of slits are of the interest from the standpoint of separation processes. Kawazoe et

^ i,i2-i4) repOrtec[ studies carbons. of severalHowever, properties theseof activated

molecular-sieve

authors found no reported theoretical works on pore size distribution at the scale of molecular dimensions. Dollimore

and Heal2) have given a review and

criticism of previous methods used for the calculation

of pore size distribution.

They pointed out that their

improved method also had some problems

when

The calorimetric ^diff

face" of carbon atoms may be regarded as the "effective radius of the carbon atom."4) Therefore,

the pore size itself must be called the "effective pore size." This definition by Everett is in use in the case of micropores. For larger pores, the problem of the uncertain size of the "outer surface" is negligible. 1.

the molar integral

change of the free

energy (Gibbs function for T=constant):

AGads=AH*ds- TASads (1) The molar integral change of enthalpy on adsorption AHads=

-qdm-RT+K(Tp/9)(dn/dT)d

(2)

is16) Received February 6, 1983. Correspondence concerning this article should be addressed to K. Kawazoe, Dept. ofInd. Admin., Sci. Univ. ofTokyo, Noda 278. G. Horvath is now at Dept. of Unit Operations, Univ. of Chem. Eng., Veszprem, Hungary. 470

= AHv*p_ RT_ (dhf/dna)T

(3)

ASads=AStr+ASrot+ASyih

(4)

Except for ASl\ the terms of this equation are nearly constant, and we can write ASads= AStr(w/wJ +AS0 (5) The free energy change can be calculated from the gas-phase pressure. Combining this with the previous equation:

AGad* = RTln {p/p0) =AHads-

T(ASu(w/wJ

+AS0)

(6)

If we consider the limit of zlGads as p approaches p0, lim AStT(w/wJ=0

lim p->Po RT\n(p/po)=AHoads-

TASo=0

(7)

AHoads= TASo= -AHwap= - TASyaip

(8)

then Wecan also write

Theory

Consider

of qdlff is

The molar integral change of entropy is

pores approach molecular dimensions, because the

Kelvin equation had been used. This problem has been reported elsewhere also.9) In the micropore domain the so-called "outer sur-

definition

RTln (p/p0)

= - qdá"- RT+K(Tp/e)(8n/dT)d -

T(AS\w/wJ+AS0)

Supposing that K(T/3/6)(dn/dT)d can be simplified to RT\n(p/po)-AHvaP=

(9)

^ RT, the expression

-qdm-TASir{wlwJ

(10)

In the range of p/p0^pjpo>0, the above general equation is approximated into Eq. (12), since the adsorbed phase is considered similar to the liquid JOURNAL

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phase and then

Having molecular

I TAS^w/wJKlq^l

(ll)

-qdiff=RT\n(p/p0)-AHá"»

(12)

considered level16):

the definition

surfaces. The potential, originated from the interaction of the adsorbate molecules in a pore, increases the interaction

energy. The potential

NnAn+NAA,

(13)

l-r

we used the samelogic to obtain: RTln (p/po) = Uo +Pa

(14)

'