The Solution Theory Modeling of Gas Adsorption on Zeolites

1 The Solution Theory Modeling of Gas Adsorption on Zeolites 1

ARTHUR W. WOLTMAN and WILLIAM H. HARTWIG

Downloaded by 80.82.77.83 on March 17, 2017 | http://pubs.acs.org Publication Date: August 15, 1980 | doi: 10.1021/bk-1980-0135.ch001

The University of Texas at Austin, Austin, TX 78712

The adsorption of gas molecules on the interior surfaces of zeolite voids i s an ionic interaction with a characteristic potent i a l energy called the heat of adsorption. The molecular adsorption process results i n an exothermic attachment of the gas molecules to the surface of the voids, and i s characterized by a high order of specificity. Zeolites exhibit a high a f f i n i t y for certain gases or vapors. Because of their "effective" anionic frameworks and mobile cations, the physical bonds for adsorbed molecules having permanent electric moments (N2* NH3, H2O) are much enhanced compared with nonpolar molecules such as argon or methane. The functional relationship of amount of adsorption versus temperature and pressure for various zeolite-gas pairs i s extremel y complex, and as such, empirical or semi-empirical methods are commonly used to generate adsorption data. Recent work (1^, 2^, 3.) by the junior author and his colleagues on thermally cycled gas compression by adsorption/desorption of N2O and other gases i n zeolites created a need for a theory derived from f i r s t principles. Such a theory would be capable of accounting for the detailed physical behavior over a wide range of pressures, and thereby establish a reliable formalism to predict behavior and design apparatus. More important, however, i s the need for a unifying theory to support and accelerate further work on a l l aspects of zeolite research and their applications. Derivation of a Lattice Solid Solution Model A l a t t i c e theory of solutions has been proposed (U) to describe the adsorption-desorption phenomena i n zeolites. There are several reasons for this choice: (a) forming a solid solution by two substances i s analogous to the forming of an adsorbed phase in the cavities of a zeolite, (b) the theory of solutions i s well understood and i t s mathematical techniques powerful, and (c) since the state-of-the-art i n description of adsorption phenomena i n 1

Current address:

Shell Development Corp., Houston, Texas 77001

0-8412-0582-5/80/47-135-003$05.75/0 © 1980 American Chemical Society

Flank; Adsorption and Ion Exchange with Synthetic Zeolites ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

SYNTHETIC ZEOLITES


4

zeolites i s basically empirical, solution theory could provide constants that are pleasing because they are physically related to the actual phenomena. An implicit reason for this choice i s that a l a t t i c e solution model w i l l correspond to a localized adsorption model - i . e . , adsorption w i l l occur at localized points on the surface just as a l a t t i c e solution i s formed at the various l a t tice points. Therefore, a l a t t i c e "adsorption" model w i l l consider small-scale, localized gradients i n the electrostatic f i e l d . The mobile adsorption equations of Ruthven (5.), and others {§_>T), by their very nature, do not consider fine structure i n the electrostatic f i e l d . The solution i s assumed ideal. It i s incompressible; a l l l a t t i c e sites are f i l l e d with some species of molecule. A l l species of molecules at the l a t t i c e sites are of equal (or nearly equal) size. For physical reasons, only one molecule can occupy each l a t t i c e s i t e . Since there i s a distribution of adsorptive energies within the zeolite, corresponding to the l o c a l l y varying electrostatic f i e l d , the adsorption problem i s approached from the standpoint of a superposition of several solutions - a l l the sites in each being identical. The number of solutions that must be considered equals the number of different adsorptive energy sites that are found within the zeolite. The canonical ensemble partition function for a binary solution i s , Q(N ,N ,T) = W \ W B l A W B > AB where (a) there are A molecules and Ν Β molecules i n solution, (b) each molecule vibrates about a l a t t i c e site with a three-di mensional partition function of qA*?) or qg(T) independent of the state of occupation of neighboring sites, (c) the t o t a l energy of solution i s W, given by N

A

Î

B

e

[ 1 ]

A

β

W

Ν

ω

• ΑΑ ΑΑ

+

*A*Xb"vPbb

[ 2 ]

and where the % β and N^g are the number of nearest neighbor pairs of type AA, AB, and BB i n the solution and where the ω ^ , ω^β, and o>gg are the corresponding nearest neighbor interaction energies (more distant interaction energies assumed to be i n s i g nificantly small), and (d) g(NJJ,N^+Ng,N^g) i s the number of ways i n which N Β solution molecules can be distributed among the A B Positions i n the l a t t i c e so that there are nearest neighbor pairs of type A-B. The presence of nearest neighbor i n teractions indicates that adjacent sites, although they are char acterized by partition functions which are independent of the state of occupation of their neighbors, are not independent en tities. According to H i l l (&), due to the small correction for ex cess entropy As , "the approximation of random mixing can approp r i a t e l y be introduced, for molecules of l i k e size, i n l a t t i c e or c e l l solution theories that are otherwise f a i r l y sophisiticated." B

N

+ N

e


1.

WOLTMAN

Solution Theory Modeling

AND HARTWIG

5

Making use of the random mixing theory, the canonical ensemble partition function becomes CW

Q(N ,N ,T)=[< (T)e- AA/2kT N A

B

lA

]

A[(iB(T)e

-c B/2kT N WB

]

B

(HA+MR)'. _ r cu>NNB ι N !N ! 2kT(M +ll ) [3] where c i s the coordination number (number of nearest neighbors) and ω i s the mixing energy of solution and i s defined as A

expl

A


ω

Ξ

ω

ΑΑ

J

B

+

A

ω

B

2 ω

[ k ]

ΒΒ " Α Β

This canonical ensemble partition function predicts a first-order two dimensional phase transition as shown by H i l l (8^). The chemical potential μ of species Β i n binary solution i s found by the standard thermodynamic formula β

/binar y (soïuÎïon) _

-9lnQ(N ,N ,T)

B

A

B

or PB(SaSEIon) kT

=

^

(

«

^

J

+

InY

- ^(l-X )

2

B

[5]

d i a

where X i s the molar concentration of component Β i n solution and is defined as B

A

Β

Similarly the chemical potential p solution of Β i s PB(pu^solution)

=

B

of species Β i n a pure

^ ^ - c u ^ k T )

[ γ ]

The chemical potential of species Β i n a binary gas mixture above the solution i s y (binary gas)

P (T)

B

Bo

=

kT

" k T -

+

l

n

p

[ 8 ]

B

where u ( T ) i s an integration constant and i s only a function of T, and p i s the p a r t i a l pressure of species Β i n the gaseous phase. The chemical potential of species Β i n the unitary gas phase above a pure solution of Β i s Bo

B

y-o(one component gas) »

u« (T) •

+

**Bo


[ 9 ]

6

SYNTHETIC

ZEOLITES

where the ο subscript on ρ designates a pressure due only to the one component B, i.e., the p a r t i a l pressure due to Β above the solution i s equivalent to the t o t a l pressure above the solution. The solution problem i s solved for the equilibrium condition. This i s formally equivalent to stating that β ο

υ (binary gas)

μ (binary solution)

Ώ

B

Ώ

"

kT

B

[10]

kT

and pône component gas)

p_(pure solution) = — kT


kT

[11] 1

J

The following adsorption law i s obtained by combining Equations [6-9]: P

B\ _ cw /, „ x2 in(^) = i n ^ - ^ ( l - V

There i s a corresponding equation for species A. Development of the Adsorption Equation Parameters The two species i n the binary solution are designated as Β and Α. Β i s the adsorbate molecule and A i s the absence of an ad sorbed molecule at a particular adsorption site on the zeolite surface, called a "vacancy". Because of i t s definition, A i s equal i n size to the Β species molecule. As the gas pressure above the zeolite ( i . e . , ρ ) goes to larger values (P^P^Q) solution composition within the cavity goes toward a pure solu tion of adsorbed gas (X^-KL). As the gas pressure above the zeo l i t e goes to smaller values ( i . e . , P " * P K the amount of adsorp tion becomes less (Χβ"*0) and the solution composition within the cavity goes toward a pure solution of vacancies (X^-KL). This choice of solution species has the proper asymptotic nature. It has been stated that zeolites exhibit a distribution of adsorptive energies. This i s due to the complex structure with in the z e o l i t i c micropores and the strong dependence of electro static energies upon structure geometry. A discrete number of types of adsorption sites can be considered; the f i n i t e number i s dependent upon electrostatic and steric considerations. The most strongly adsorbing sites correspond to locations near the cations ( S U , SIII, etc.). After these positions are f i l l e d , the adsorb ate molecules seek positions i n the framework structure to mini mize repulsive forces between them on the zeolite surface, and at the same time to maximize adsorptive forces with the framework. T H E

β

A

Ao



1.

WOLTMAN AND HARTWIG

7


This further adsorption must occur on the weakly charged "anionic" framework. The term "anionic" i s used i n that each oxygen atom i n the framework must display a fractional negative charge for the zeolite crystal to be neutral. This fractional charge or "effective" charge implies the covalent character of the oxygen framework. The zeolite can be easily handled with solution theory i f the ionic/covalent physical nature of the zeolite i s treated mathematically as an ionic crystal l a t t i c e of cationic sites and "effective" anionic sites. The weak adsorption sites (or "ionic" sites) are i n secondary coordination spheres around the cations and i n positions corresponding to minimum-energy configuration and favorable steric location. The mixing energy term ω i s defined as the energy difference between (a) a pair of AA nearest neighbors and a pair of BB near est neighbors, and (b) two pairs of AB nearest neighbors. In the subtraction, the adsorbate-adsorbent interactions are exactly can c e l l i n g and ω i s equal to the adsorbate-adsorbate interaction. For most gas species the adsorbate-adsorbate interaction i s given by the Lennard-Jones potential equation 12

6

a>(r) = ke[(o/r) -(o/r) ]

[13]

where σ and ε are constants characteristic of the chemical species of colliding molecules. For polar gases (such as NH3) the inter action energy i s given by the Stockmayer Potential (9.) ω (

Γ

, θ

Α

, θ

, ψ

Β

[ 2 ο ο 8 θ

Β

Α

, φ

ΰ θ 8 θ

Β

Β

)

=

12

6

ke[(o/r) -(o/r) ]

- 8 ί η θ ^ ΐ η θ

Β

ο ο 8 ( ψ

Β

-

^ |

- φ ^ ) ]

[lU]

where the last term i s the dipole-dipole interaction energy, u andy^ are the dipole moments of the BB pair, θ and Θ are the angles of inclination of the polar axes to the l i n e of centers, and ψ and Φ are the angles subtended between the polar axes and perpendiculars passing through their centers. The molar concentration term, defined by Equation [6], i s the ratio of the number of adsorbate molecules i n a cavity to the t o t a l number of adsorbate molecules that could be i n one cavity at temperature T. This may be related to the mass of gas adsorbed per unit mass of zeolite (the x/m commonly found i n adsorption graphs) by the following equation for a heteroenergetic surface: Μ Ν Ν . B

β

Β

Β

Β

Φ; where Ν M M Ν ^ J

= = = =

-V*

^

number of cavities/unit c e l l of zeolite mass of a unit c e l l of zeolite mass/molecule of gas adsorbed number of sites per cavity with adsorptive energy part i c u l a r to the j^h solution molar concentration of Β species i n the j t h solution


SYNTHETIC ZEOLITES

8

and (*). = the x/m contribution (to the total adsorption) due to the 3 solution. th

3

This equation must be solved subject to the boundary condition = t o t a l number of adsorption sites, and the t o t a l number of adsorbed Β molecules i n the cavity when a l l solutions within the cavity go to saturation.

Ν = Σ Ν m j mj A,


This value of Ν i s solved by considering steric limitations of adsorbed molecuTes i n the volume of the cavity as saturation i s approached. The t o t a l x/m becomes

i

=

P i

JVw

=

T

[16] i s

The term P ( U j * ) the pressure at which the j^h solution becomes one-component B. This "saturation" pressure has been shown i n standard s t a t i s t i c a l mechanics texts (10) to be Eu

Ρ (ϋ^,Τ) = const(T)exp[tykTj

[IT]

Βο

where Uj i s the minimum energy necessary to remove the molecule from solution j ; i s negative because the attachment of molecules to the zeolite surface i s exothermic; and i s not affected by nearest-neighbor interactions (10). Several researchers (11, 12, 13, lh) have found that the zeo l i t e cavities t o t a l l y f i l l with gas molecules at pressures corres ponding to saturation pressures for their corresponding vapors. This saturation pressure, ρ (ΐ^,Τ), follows the semilogarithmic formula Βο

In P (U.,T) = C-D/T

[18]

Bo

where C and D are constants to be solved for, and p ( t h ,T) i s the saturation pressure corresponding to the particular solution with the smallest adsorptive potential and labelled i . Therefore, the saturation pressure for any solution j i s immediately found with the following formulae: BQ

PgiUj.D/pî^.T) = expUiyU^/kT]

[19]

= exp(C-D/T)exp[(Uj-U^)/kT]

[20]

and

The adsorbate-adsorbent interactions Uj, tL are found by ing a l l relevant electrostatic interactions. summing (Z e) lon-dipole energy:

= -

cos θ

[21a]

Ion-quadrupole energy: W „ = l ^ f ^ ( 3 c o s 6 - l ) 2


[21b]

1.


WOLTMAN AND HARTWIG

Polarization energy:

α (Ze) = _ I-ÉL W pol 2

Dispersion-Repulsion energy:

9

2

[21c]

[21d]

W. DR

where Ze = ionic charge r = gas-ion distance

= dipole moment of gas molecule Downloaded by 80.82.77.83 on March 17, 2017 | http://pubs.acs.org Publication Date: August 15, 1980 | doi: 10.1021/bk-1980-0135.ch001

Q = quadrupole moment of gas molecule m = mass of electron c = speed of light i n vacuum a

V i

= p o l a r i z a b i l i t i e s of gas and ion respectively = susceptibilities of gas and ion respectively

and θ

angle subtended by a line connecting the centers of the ion and gas molecule and the l i n e of axis of the dipole or quadrupole.

Summarizing, i n the idealized l a t t i c e theory of solutions, the system i s a condensed, incompressible solid solution contain ing N and Ν molecules of types A and Β at temperature T. The Woltman-Hartwig model treats the A and Β species as vacant and occupied adsorption sites, respectively, i n the zeolite cage. The Β molecules i n solution (adsorbed) are i n equilibrium with the Β molecules i n the gas above the solution. The Bragg-Williams ap proximation i s used in which the distribution of molecules at the various sites i n the solution, and also their average nearest neighbor interaction energy, are both treated as random. The molar concentration = Ν /(Ν + Ν ) , and the solution equation relating equilibrium pressure of component Β above the solution to i t s molar concentration i n solution i s A

β

β

Α

β

[22] where Τ i s the absolute temperature,ω i s mixing energy, and c i s the coordination number appropriate to each adsorption s i t e . The mixing energy i s the energy difference when two nearest neighbor A-B pairs are destroyed to form an AA pair and a BB pair. The mixing energy i s calculated on the basis of forces between mole cules on a l i n e parallel to the void surface. This yields ω = + ω £ - ^ ω ^ . The value of ρ i s pressure, corresponding to the f i l l i n g of the last sites to be occupied. The value of ρ^ i s a function of the interaction energy between the molecule β

β ο

Λ


SYNTHETIC ZEOLITES

10

Β and the ions i n the zeolite, and the force vector i s normal to the void surface. It has the form


P

B o

[23]

= exp(C-D/T)exp [(U^-U^/kT]

The values of C and D are evaluated at the c r i t i c a l point and normal boiling point. U. i s the v e r t i c a l molecule-cation inter action energy and U i s the corresponding molecule-anion term. U and ω are calculateâ as the sums of a l l the appropriate dielectric and Lennard-Jones potentials. The actual calculation of an x/m isotherm i s the superposition of several solution models. The principal one corresponds to the p a r t i a l f i l l i n g by molecules on the cation sites. The value of x/m i s a constant times Xg, summed over a l l sites, where the constant i s the molecular weight ratio. The solution model i s implemented for various gas-zeolite combinations( k). Where calculations are similar for the various gases, unnecessary repetition i s avoided. Sample calculations are given below i n abbreviated form. Adsorption Isotherms of Argon on Synthetic Zeolite LiX Experimental isotherms from Barrer and Stuart (15.) are used as a check on the present theory. Following the l i q u i d f i l l i n g theory of Dubinin ( l l ) and other (12, 13» 1*0, saturation values of 5C for Argon on LiX at the various experimental temperatures are as follows : £

(173°K) = 0.393

ÂT Ζ

(183°K) = 0.386

£

(19*+.5°K) = 0.378

-

(218°K) = 0 . 3 6 2

Using these limiting values, the saturation pressures, ρ , at which the zeolite cavities are completely f i l l e d are determined by the saturated vapor pressure-temperature semi-logarithmic formula extrapolated into the super-critical region (8^, £ , 1Ό, l l ) . These pressures correspond to the f i l l i n g of the weakly adsorbing sitesthe anionic sites. β ο

p- (173°K) = 9.8 χ 10 kPa 3


1.


WOLTMAN AND HARTWiG

11

P ( l 8 3 ° K ) = 1.26 χ lO^kPa Bo

P ( l 9 ^ . 5 ° K ) = 1.6k

χ 10 kPa U

Bo

P ( 2 l 8 ° K ) = 2.55 x lO^kPa


Bo

Calculation of interaction energies at the various l a t t i c e sites c a l l s for evaluation of the interactions of Equation [21]. The argon atoms are adsorbed one per cationic site due to steric and electrostatic reasons. The remaining argon atoms are adsorbed on the anionic sites. The gas kinetic diameter of the adsorbed atoms and the geometric distribution of cations within the cavity determine the favorable anionic l a t t i c e solution sites. The cationic and anionic l a t t i c e solution sites are i l l u s t r a t e d i n Fig ure 1. The l i n e of sight into the page i s equivalent to a perpen dicular to the connecting frame forming a section of the supercavi t y wall. Adsorption of the cation at SI, and the geometric arrangement of oxygen atoms and L i atom are i l l u s t r a t e d i n Figures 2 and 3 respectively. For this geometry, the interactions given in Table 1 occur. TABLE 1 W (L i-Ar) = -21.5 kJ/mole +

pol

W

(L i-Ar) = -0.222 kJ/mole +

digp

"ion-y^"^

=

"ion-Q^"^

=

0

k

J

/

m

o

l

e

W (0(2)-Ar) = -0.205 kJ/mole pQl

W

disp

( 0 ( 2 )

"

A r )

=

-°-

T 3 2

kJ/mole

W (0(U)-Ar) = -0.272 kJ/mole pQl

W (0(U)-Ar) = -1.12 D

kJ/mole

Charge shielding i s the resultant repelling force of the oxygen atoms 0(2) and 0(U) upon the induced dipole moment of the argon atom. W ^(0(2)-Ar) = 2 . 8 8 kJ/mole ind

W. (0(10-Ar) = 3.55 kJ/mole ndy

The net SII site interaction energy i s -13.15 kJ/mole. The net SIII site interaction energy i s approximately that of site II and i s taken as being equal to i t . For the anionic site shown i n Figure 1, the net interaction energy i s - 6 . 9 0 kJ/mole. The subscript j i n Equation [19] refers here to sites SII, SIII; the subscript i refers to the anionic sites. Therefore,


12

SYNTHETIC ZEOLITES


• Center of Super Cavity

• Ar ot SI •Ar ot anionic site

Figure 1. Cross section of a supercavity in zeolite LiX with adsorption on the anionic sites and site SII. The various oxygen distances are as given by Broussard and Shoemaker (16) and are 0(l)-0(2) — 2.8A, 0(l)-0(3) = 2.7À, O(l)-0(4) = 2.64A, and 0(3)-0(4) = 2.8A. The centers of the O(l) and 0(4) oxygen anions lie 1.45A out of and into the plane of the paper. The centers of the 0(2) and 0(3) anions lie on the plane of the paper.



1.

WOLTMAN AND HARTWIG

Figure 2.


13

Spatial arrangement of oxygen atoms, cation, and adsorbed gas atom at site SII. The Li* atom lies on the 6-membered ring.

0(2)

0(4)

0(4)

0(2)

0(2)

0(4)

Figure 3. The geometric arrangement of oxygen anions and lithium cation at site SII. The distances are from Broussard and Shoemaker (16), with the Li* cation on the 6-membered ring.


SYNTHETIC ZEOLITES

14 ( υ , 1T3°K) = 9.8 χ 10 kPa and Ρ 3

Ρ

Β ο

ρ

Ώ

Ώθ

Ρ

Β ο

±

Β ο

( ^ , 1T3°K) = 128 kPa

(U., 183°K) = 1.26 χ lO^kPa and ρ (U , l83°K) = 208 kPa 1 ϋο J Ώ

4

( υ , 19^.5°Κ) = 1.6k χ lO^kPa and P ( U J , 19k.5%)=3^5 kPa B q

±

(U., 218°K) = 2.55 x loStPa and ρ (U., 2l8°K) = 8 l l kPa 1 Ώθ J Calculation of the nearest neighbor interactions takes into account the coordination number as well as the energies determined from Equations [ 1 3 , l M , as appropriate, so i n general Ρ

Ώ

Ώ

DO


α

ΐ

ω

1

=

c

i i » i i

+

c

i J

a

[

i J -

2

U

]

The term U K ^ i s the nearest-neighbor adsorbate-adsorbate i n teraction energy between two anionic sites and i s calculated using the Lennard-Jones equation; a^j i s that between site SII and the anionic s i t e , and ω.. = ω.. = ω.· il ij ι The term c^ i s the number of nearest neighbors an adsorbate atom has when i t i s sited on the anionic s i t e . For adsorption, the term q i s the number of atoms adsorbed on the solution sites which are nearest neighbor to a particular anionic site when the "solution" becomes saturated. The c^ are composed of two terms ω

•i · · " · ° u · ς?ςτ

1

1251

The f i r s t term i s the number of nearest neighbors at anionic sites and i s temperature-dependent. The second term i s the number of nearest neighbors at site SII, and i s temperature-independent, and has a value of 1 since the site would then become more unfav orable than any other adsorption s i t e .

Θ

unfavorable situation

The nearest-neighbor interaction between two adsorbed Ar atoms on the surface i s repulsive and equal to k.27 kJ/mole. Thus, Ο . ( 1 Τ 3 ° Κ ) . 1 2 ^ 2 8 + 1 = 1.935 and for 1T3°K for 183°K for 19^.5°K

c o> = (1.935)(^.27) = 8.26 kJ/mole ±

±

οω ±

±

= 8.16 kJ/mole

CÛK = 8 . 0 3 kJ/mole


1.

for 218° Κ

cu ±

15


WOLTMAN AND HARTWiG

= 7.81 kJ/mole

±

For the sites SII, SIII, the product cju>j i s calculated i n the following manner: c.œ. = c..u>.. + c..u).. j3 33 33 Ji Ji = =ω = U.27 kJ/mole; - 0.0 kJ/mole. &

i i

The ω., i s the nearest-neighbor adsorbate-adsorbate interaction between atoms at SII, SIII and the anionic sites. 3 N

°3


N

Bi' Bi,sat

[26]

= N

+ N

Ai Bi

where the 3 i s the three-fold coordination to any site SII, and the factor i s the occupation factor of the anionic N

N

B

i

B

i

s

a

t

AI B i sites when the sites SII, SIII are f i l l e d . The product c*u)j for argon i s so small for a l l temperatures of interest that rc may be put equal to zero. The equations which define the two solutions (SII, SIII and anionic)are as follows:

W

W

T

)

2

•^ V ^ V ^ ' - i k ^ - V

- ^

>

i

^

h

i

^

1

2

^

1

-

[

}

c

2

7

]

[

2

ω

^

8

]

Solving these equations and superimposing the results gives the adsorption isotherm of argon on zeolite LiX. The constituent contributions due to SII, SIII sites and to anionic sites are shown i n Figure k for the temperature Τ = 173 Κ. Comparison of experimental curves with theoretical points i s given by Figure 5· The agreement between theoretical and experimental results i s extremely good. The trend noted, that theory predicted s l i g h t l y less adsorption than was found experimentally, could be due to capillary condensation, especially when P / P i s appreciable. B

Bo

Adsorption Isotherms of Nitrogen on Synthetic Zeolite NaX Experimental isotherms from Barrer and Stuart (15.) are used as an additional check on the present theory. Saturation values of for N on NaX at the various experimental temperatures are as follows: 2

Temp. X m

173°K .237

19U.5°K .225

218°K

273°K

.212

.186

SAT



16

SYNTHETIC ZEOLITES

.050h

Figure 4. Constituent contributions due to (Φ) (SII, SIII) sites and (x) anionic sites

ZO

AO

60

press. (kftO


60

1.

WOLTMAN AND

17


HARTWIG

The cationic and anionic l a t t i c e solution sites are i l l u s trated i n Figure 6. The = 17.78 kJ/mole; the = 10.96 kJ/ mole. The Uj = -25.65 kJ/mole; the Ui = -15.27 kJ/mole. Therefore, Ρ

υ

Βο^ ΐ

ρ

Κ

° *

=

1

,

5

3

x

1 0

k

^

P

a

(U.,19^.5°K) = 2.39 x 10

8 1 1 ( 1

P

U

Bo* J DO

1 U

Bo^ i

, 1 7 3

, 2 l 8

K

° ^

=

3

,

5

2

x

k

P (U.,273°K) = 6.70 χ 10

k

Bo

P

a

8 1 1 ( 1

p

K

° *

=

1

2

k

P

a

(U.,19^-5) = kO kPa

kPa and

k

Ώ

DO P

, 1 Τ 3

U

J

Bo* J»

2 1 8

*

=

1

2

0

k

P

a

kPa and P ( U j , 2 7 3 ) = 695 kPa Bo


For 173°K c .ω ι ι = 9-21 2kT

c

where now ψ ω^* and the product i i must be used i n i t s expanded form i i = i» + ω.. w

c

w

C i J

C

±3

C i i

m OÙ m

= 2.19

where now

et*). For 19U.5°K,

=

Φ

= 0.0 kJ/mole

c.u>. = 7.8U and

For 2l8°K, ^ |

= 6.6U and ^

For 273°K, ^ |

= U.76 and ^

= 1.8l

=

i.Uo

= 0.91

Comparison of experimental curves with theoretical points i s given by Figure 7 · The agreement between theoretical and experi mental results i s good at 19^.5°K, 2l8°K and 273°K. For 173°K, the theoretical results overpredict adsorption at small pressures and underpredict adsorption at high pressures. The discrepancy i s never more than 5-6$. Adsorption Isotherms of Ammonia on Na X Experimental isotherms from Barrer and Gibbons (17) are used as a further check on the present theory. Saturation values of jj- for NH3 on NaX at the various experimental temperatures are as follows :


SYNTHETIC ZEOLITES

18

•

Center of Super Cavity

N ot SiteS


2

Figure 6.

Cross section of supercavity in zeolite NaX; shown

nitrogen is adsorbed as


1.


WOLTMAN AND HARTWIG

Temp.

373°K

1+53°K

503°K

563°K

SAT

0.171

0.138

0.121

O.lOU

19


m

These saturation values are determined assuming that the NH3 enters the 3 cages of the zeolite NaX at temperatures - 100°C. According to Breck (18) and Barrer and Gibbons ( 1 7 ) , this i s a good assumption. NH^ i s similar to H2O i n that they both possess large dipole moments and are both small molecules. The presence of NH3 i n a zeolite i s chemically similar to the presence of H2O i n a zeolite. Therefore, the hydrated cation distribution i n zeolites i s prob ably more typical of NH3 adsorption i n zeolites than the dehydrat ed cation distribution. According to Breck (18), for hydrated zeolite X, cations are found i n sites SI, S I , SII, and SIV. Of these s i t e s , S I , SII, and SIV would a l l be adsorption l a t t i c e solution sites. The cationic and anionic l a t t i c e solution sites (in the supercavity of NaX) are i l l u s t r a t e d i n Figure 8. For NH3, the subscript j l w i l l refer to SII sites, the subscript j 2 w i l l refer to SI sites, and J3 w i l l refer to SIV sites. The anionic sites are two and are ( l ) i n the center U-membered ring of the connecting frame and (2) near the center of the 0 ( 2 ) - 0 ( l ) - 0 ( l ) t r i a d of oxygen atoms. For NH3, the subscript i l w i l l refer to the f i r s t anionic s i t e ; the subscript i 2 w i l l refer to the second anionic s i t e . 1

1

1

= -69.O kJ/mole, U

* - 6 9 . 0 kJ/mole, and U ^ = -71.1 kJ/ mole = -1+7.3 kJ/mole and \J = - 3 2 . 6 kJ/mole. The

The U The Ό

±1

±2

9-33 kJ/mole = ω The u >

ils)1

= «

2

=

ω

ΐ2-33

=

T

=

ω

ί2-ί2

=

e

The ^ j

l

e

j

3

_^.

ΐ 2

= ω . ^ = u). _

1 1 - J 2

The

J2

= 0.0 kJ/mole,

ω

8 1 1 ( 1

a

r

e η ο

* considered since adsorption i s

completed so rapidly on the sites SII and SIV. c

For U53°K, c

For 503°K,

w

i i 2kT

2Λ7,

c

2.22,

e

w

i i 2kT

C.UK

For 563°K,

2kT

1.99,

c

J i " j i = 12.1*3, and J 3 j 3 = 10.32. 2kT 2kT C

w

J i " j i = 11.19, and J 3 J 3 = 9.29. 2kT 2kT C

W

c J i " j i = 10.0, and 2kT 2kT

= 8.3.

Comparison of experimental curves with theoretical points i s given by Figure 9· The agreement between theoretical and experi mental results i s good at high pressures for a l l the temperatures considered. At low pressures (2-3 kPa) the discrepancy may be as much as 10J5 for the 100°C experimental curve, i t i s less for the other temperatures. Adsorption Isotherms of Nitrous Oxide on NaY Experimental isotherms generated by the present authors are also used as a check on the present theory. Saturation values of


SYNTHETIC ZEOLITES

22

m for N 0 on NaY at the various experimental temperatures are as follows : 2

Temp. X m

202°K

2kO°K

270°K

300°K

335°K

373°K

Λ63

.k3k

.Ul2

.39h

.371

.3h9

SAT

The subscript i refers again to the anionic sites; the subscript j refers to the cationic site SII. The ω.. = ω.. = 20.k2 kJ/mole. The Uj = - 2 9 . 8 kJ/mole; the U = -21.00 kî^moleî"* Therefore, 3

±

P ( U , 2 0 2 ° K ) = 2k3 kPa and p^JU, ,202°K) * 1 kPa i


Bo

P P

B o

1.16

(U.,2^K)

Bo

( U

i

, 2 T 0

K

° ^

=

2

,

8

6 x

χ 1 0 kPa and ρ 3

Ώ

BO

λ

°

k 3

P

a 8 1 1 ( 1P

U

Bo^ j

, 2 T

°°

K )

=

5

7

k

P

a

(U ,300°K) = 173 kPa j Ρτ>.,(< »335°K) = 1.17 x 10 kPa and p_ (U.,335°K) = U98 kPa *Bo i Ρ (ϋ.,300°Κ) Βο

5.92 χ 1 0 kPa and ρ

(U,,2U0°K)= 1^ kPa j

3

Ώ

4

BO

υ

xw

(U,,373°K) = 1250 kPa J The sites SII f i l l so quickly at Τ = 202°K and 2l*0°K that the

P (U.,373 K) 0

B0

2.13 x 10* kPa and p

D

DO

exponent

i s not considered.

Temp. C.U). 1 1

202°K

2U0°K

270°K

300°K

335°K

373°K

12.67

10.20

8.77

7.67

6.62

5.73

2kT Comparison of experimental points with theoretical points i s shown i n Figure 10. Agreement i s good at low pressure ( i . e . , ρ < 100kPa), and may d i f f e r by as much as 10$ at the higher pres sures. This error i s of the same order as that claimed by the existing, more empirical, models i n the literature. A systematic agreement i n shape i s noted, and the actual error may be i n the experimental data where "flotation" effects are serious for gravimetic measurements at elevated pressures. Summary The "solid-solution l a t t i c e theory" model of adsorption on zeolites has been shown to describe the experimental results i n the literature with accuracy comparable to a l l existing theories, even though these theories are i n many instances semi-empirical. Since the theory i s related to actual physical phenomena, systema t i c studies can be made of the effect on adsorption of changing the zeolite.


1.

x/n


Solution

WOLTMAN AND HARTWIG

u 111111 \jP 2oz$ ' n

11 1111

1'

1 1 11 1 1 1 1

Theory

1 11 1 1 1 1 1 1

i

1M 1

Modeling

1

M 1 1 1 111

1 ""1

1

23

111 M 11

1M

' i3 240TK

373* Κ

TROUS

0

Q

ti 11111111 1 1 1 1 1 I ι ι ι ι n ι ι 11 ι ι ι ι ι ι ι I Μ ι ι ι 11111 1 1 1 1 1 1 1 1 ι ι 1 1 1 1 11 i 1 1 1 1 » 1 1 » i n t

Ό.Ο

.70 1-50 2 . 4 0 3 - 3 0 4 . 2 0 5 . 1 0 6 . 0 0

NAY RDSOtfP

6-90

PRESSURE

Figure 10. Comparison of experimental points with theoretical points. The experimental points are related to the temperatures at which they were taken by the caption at the lower right of the graph. The theoretical points are connected by lines that are then labeled with the correct corresponding temperatures.


SYNTHETIC ZEOLITES

24

The model has "been tested for a wide variety of gas-zeolite combinations. Gases of increasing complexity were considered: Ar(non-polar), N (quadrupole moment, no dipole moment), N 0 (quadrupole moment, small dipole moment), and NH^ (large dipole moment, small quadrupole moment). The zeolites tested were a l l i n the synthetic faujasite family; however, they ranged from the cationrich zeolite X to the cation-poor zeolite Y. Cation geometries considered i n the tests were those typical of the dehydrated zeo l i t e form and those typical of the hydrated geometry (associated with NH^ adsorption). Two forms of representative cations were considered, L i and Na . It can be concluded that the "solid-solution l a t t i c e theory" model shows great promise i n describing adsorption on zeolites. The general shape of the zeolite adsorption isotherm ( i . e . , the roughly linear Henry's law i n i t i a l adsorption region, the expon ential "knee" of the isotherm, and the slowly increasing adsorp tion with pressure at higher pressures) are a l l predicted quali tatively and with good quantitative agreement. I n i t i a l heats of adsorption agree well with experimental values i n the literature. Future studies should indicate whether other thermodynamic quanti t i e s are as well predicted. 2

2


+

+

Acknowledgement s The work was supported, i n part, by NASA-Lyndon B. Johnson Space Center, Houston. The authors acknowledge the efforts and confidence of Mr. R. R. Richard of NASA; the experimental research of Dr. J . P. Masson, and the advice and criticism of Drs. H. Steinfink, J . Stark, and W. C. Duesterhoeft of the University of Texas at Austin. Abstract A s t a t i s t i c a l thermodynamic equation for gas adsorption on synthetic zeolites i s derived using solid solution theory. Both adsorbate-adsorbate and adsorbate-adsorbent interactions are c a l culated and used as parameters i n the equation. Adsorption iso therms are calculated for argon, nitrogen, ammonia, and nitrous oxide. The solution equation appears v a l i d for a wide range of gas adsorption on zeolites.

Literature Cited 1. Hartwig, W. H . , Steinfink, Η., Masson, J . P. and Woltman, A.W., Proc. 1976 Region V IEEE Conf., IEEE Cat. 76CH1068-6Reg5, 1976, p. 80. 2. Hartwig, W. H.,"Adv. in Cryogenic Engineering," Ed. by K. D. Timmerhouse, Plenum Publishing Co., Ν. Υ., 1978,23,435-447. 3. Hartwig, W. H . , Woltman, A. W., and Masson, J . P., Proc. 1978 Int'l. Cryogenic Eng'g. Conf., IPC Science and Technology Press Guildford, Surrey GU2 5AW, England.



1. WOLTMAN AND HARTWIG


25

4. Woltman, A. W., Ph.D. Dissertation, The University of Texas at Austin, Austin, Texas, March 1978. 5. Ruthven, D. Μ., Nature, Phys. Sci., 1971, 232(29), 70. 6. Coughlan, B., Kilmartin, S., McEntree, J., and Shaw, R. G., J. Colloid Interface Sci., 1975, 52, 386. 7. Derrak, R. I., Coughlin, K. F., and Ruthven, D. Μ., J . Chem. Soc., Faraday I, 1972, 68, 1947. 8. Hill, T. L . , "An Introduction to Statistical Thermodynamics," Addison-Wesley, 1962, pp. 246, 38l. 9. Hirschfelder, J. O., Curtiss, C. F., and Bird, R. B., "Molecu lar Theory of Gases and Liquids," Wiley, New York, N.Y., 1954. 10. Fowler, M. A. and Guggenheim, Ε. Α., "Statistical Thermodyna mics," London, England, Cambridge University Press, 1939. 11. Dubinin, Μ. Μ., J. Colloid and Interface Sci., 1967, 23, 487. 12. Harper, R. J., Stifel, G. R., and Anderson, R. Β., Canad. Jour. of Chem., 1969, 47, 4661. 13. Flock, J. W. and Lyon, D. Ν., J. of Chem. and Engin. Data, 1974, 19, 205. 14. Nakahara, T., Hirata, M. and Ohmori, T., J . of Chem. and Eng. Data, 1975, 20, 195. 15. Barrer, R. M. and Stuart, W. I., Proc. Roy. Soc., London, 1959, 249A, 464. 16. Broussard, L. and Shoemaker, D.P., J. Amer. Chem. Soc., 1960, 82, 1041. 17. Barrer, R. M. and Gibbons, R. Μ., Trans. Faraday Soc., 1963, 59, 2569. 18. Breck, D. W., "Zeolite Molecular Sieves," Wiley-Interscience, New York, N.Y., 1974. RECEIVED

April

24,

1980.


The Solution Theory Modeling of Gas Adsorption on Zeolites

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