SURFACE SCIENCE 3 (1965) 126-142 o North-Holland Publishing Co., Amsterdam

SORPTION AND FLOW IN GRAPHITE-ZEOLITE COMPACTS

I. HELIUM, ARGON AND NITROGEN

R. M. BARRER and J. H. PETROPOULOS

Physical Chemistry Laboratories, Chemistry Department, Imperial College, London

Received 1 September 1964

Revised manuscript 4 December 1964

Low porosity compacts of graphite and Linde Sieve zeolites NaA and CaA,16) have been studied as diffusion and sorption media for helium, argon and nitrogen. The zeolite crystals in the compacts were outgassed and also hydrated in different series of experi- ments. There was evidence of surface fluxes and also of intracrystalline flows. On the assumption that helium has a negligible intracrystalline or surface flow, the surface and intracrystalline diffusion coefficients of nitrogen have been evaluated. The tortuosity of the conduction paths in the compacts is, however, high. The sorption isotherms of the three gases have been measured, and the Henry’s law adsorption constants calculated and analysed in thermodynamic terms.

1. Introduction

In a number of porous media a substantial surface flow of sorbable gases

and vapours has been demonstrated lms), and there are considerable potenti-

alities for separating molecular mixtures by employing such micro-pore

systems7-lo). It has recently been pointed out that large fractionation

factors are theoretically possible using suitable molecular sieve crystallites

dispersed in another phasell). The fractionation will be improved the greater

the volume fraction of zeolite and the smaller the permeability of the other

phase. In the present work we have accordingly investigated a porous medium

composed of molecular sieve crystallites compacted under pressure with

finely divided graphite. The medium is potentially able to produce three

component flows: in the gas phase; on external surfaces of the solid particles:

and within the porous crystals. Such three-phase flow has been the subject of

theoretical analysisl2). A useful property of a successful graphite-zeolite

membrane would be that the molecular sieve component could be sealed by

allowing the zeolite to sorb water. The system is then permeable to other

species by surface and gas-phase flow only, and by difference an estimate of

the intra-zeolitic flux is possible.

126

(1) SORPTION AND FLOW IN GRAPHITE-ZEOLITE COMPACTS 127

2. Theoretical aspects of three-phase flow

2.1. THE STEADY STATEOF FLOW

We require means of measuring the gas-phase, surface and intracrystalline

components of the total flow, J, through the graphite-zeolite compacts.

Per unit cross-section of the plug, normal to the x-direction in which flow

occurs, we may write

In eq. (I), C,, C, and Ci are the numbers of molecules per unit volume of the

porous medium which are respectively in the gas phase, on surfaces, and

inside the zeolite. Jb, Ji and .I: are the corresponding flows passing through

the cross-section which are only in the gas phase, on surfaces, and inside the

zeolite crystals, and Dhs, D~,/p and Di, are the three associated diffusion

coefficients. The origin of the term p has been considered previouslyla).

However, these three fluxes are not usually measurable by the helium

calibration method. Helium can normally be regarded as flowing only in the

gas phase since it is so weakly adsorbed. If the helium flux, J:‘, is multiplied

by ~(Mn-_I~) h w ere MHe and M are the molecular weights of helium and

another gas, a flux Jg = Jze ,/(M,,/M) can be evaluated. However, Jg is less

than 56, while J, and Ji will be correspondingly greater than Ji and Ji. This

happens because of the discontinuous nature of the surfaces, or the zeolite

particles. Any flux, such as J,, arising from the existence of a mobile adsorbed

phase is partly in the gas phase, as the flux bridges gas gaps between suc-

cessive surface elements13). Thus, as an alternative to eq. (1) we shall be

concerned only with another division of the total flux given by

J=J.+Js+Ji=- D,,d~+D,dC,+~is~ P dx

=- (2)

When CL, Cg and Ci are the concentrations per unit volume of gas phase,

per unit area of surface, and per unit intracrystalline volume of porous

crystal, one has

c, = ec;, C, = AC;, Ci = VCl. (3)

In eqs. (3), E is the porosity (cm3 per cm3 of porous medium), A is the area

(cm’ per cm3>, and V is the intracrystalline free volume of zeolite (cm3 per

cm3 of medium). If in addition Henry’s law is valid for sorption on all

128 R. hi. BARRER AND J. H. PETROPOULOS

surfaces and within the zeolite, then

C; = k,C;, Cl = kiCi. (4)

k, and ki are the Henry’s law constants for sorption on external surfaces and

within the zeolite. Thus eq. (2) becomes

In the Henry’s law range and when molecular streaming occurs in the gas

phase the diffusion coefficients in eq. (5) do not depend on concentration,

and so

Jl Ak, D,, Vki _ = K,, = D,, + ~- 2 + -Di,

AC, EP 6

where Ktd is the permeability of the dehydrated graphite-zeolite compact,

referred to the gas-phase concentration drop across the compact.

When the zeolite crystals are hydrated the flux Ji vanishes, and so for the

permeability K,, of the compact one has

(7)

Provided hydration of the zeolite does not change the gas phase and surface

permeability we may subtract eq. (7) from eq. (6) and obtain

(K,, - K,,) = “,“i Di,.

Eq. (8) then serves to determine Di,.

2.2. THE TIME LAG

Provided in each plane, x, normal to the direction of flow, equilibrium is

maintained between gaseous, adsorbed and intracrystalline sorbate, and if

Henry’s law describes each sorption process, the time lag for the dehydrated

compact is 13)

l2 l2 1+!5+?

& L,=-=-

602, 6 D,+D,Ak,+D;l/k, E &

where D,, is the over-all diffusion coefficient based on the time lag, and D,,

D, and Di are averaged transient state diffusion coefficients for the three

component fluxes, As explained elsewhere 13) D,, D, and Di are not necessarily

(I) SORPTION AND FLOW IN GRAPHITE-ZEOLITE COMPACTS 129

the same as the corresponding coefficients DBs, D,,lp, and possibly Di,. If the zeolite crystals are hydrated the time lag becomes

l2 l2 L, = ~

6D,, =d--’ D,+D,%

&

(10)

In the derivation of both equations it is required that CB at x=0 is much

greater than C, at x= I, and C, at x= 0 is also constant. If gas phase and

surface flow are unchanged by hydrating the zeolite component, one may

combine eqs. (9) and (10) and obtain

If the diffusion process into the zeolite particles is slow, so that equilibrium

is not continuously maintained between the particles and the gas phase, one

may think of the crystals as functioning like sinks, and draining off sorbate

gradually from the flowing gas. This situation may be approximated by the

use of a suitable sink function, 4(t). The diffusion equation in the transient

state is then

-4(t). (12)

For eq. (12) to be valid as written, the net intracrystalline flux in the x-

direction must be negligible. A method due to Frisch ls) is then available for

obtaining the time lag. However, this equation will not be considered further

at present.

3. Experimental

Zeolite powders of Linde Sieve NaA or CaAis) were used with Acheson

Co. graphite powder (“Dag” dispersion 621) in preparing the compacts. The

mixture of powders was ground in a mortar, and then compressed into a plug

by additions of small successive portions, each addition being followed by

compression of the whole. The plug container was a specially hardened steel

cylinder and pressure was applied through closely fitting steel plungers.

Pressures used were as large as 87 tons/sq. in. At a constant pressure each

new portion was compressed to a definite extent, but previously compressed

portions were not significantly changed. The plug thickness was determined

from the separation of the extremities of the steel plungers, and the porosity

from the mass of each component taken, the density of the pure component,

and the volume of the plug. Porosity determinations had an accuracy of about

130 R. hf. BARRER AND J. H. PETROPOLJLOS

f 10%. The plugs eventually studied had the following compositions by

volume:

Plug A: 60% NaA+40% graphite

B : 40% NaA + 60% graphite

D : 40% NaA + 60% graphite

G: 60% CaA+40% graphite

H : 40% CaA + 60% graphite.

Membrane D differed from membrane B in that the preliminary grinding

of graphite-zeolite mixture was more prolonged.

Spectroscopically pure helium, argon and nitrogen were supplied by the

British Oxygen Company. Sorption and flow measurements were made using

volumetric apparatus similar to that described elsewhereiss6). In the flow

measurements the boundary conditions at the ingoing and outgoing faces

of the plug (x = 0 and x = 1 respectively) were

C,= constant at x=0 for all t

C,=O for O<x<f at t=O

C, at x = 1 is much less than C, at x= 0 for all t.

Permeabilities, time-lags and sorption isotherms were measured over a

range of pressures and temperatures. Sorption isotherms were obtained for

water-free zeolite powders, graphite powder, and on pieces of graphite-

zeolite compact or on compressed graphite. The flow experiments were

conducted on the plugs in several states:

State I - the zeolite component is hydrated

State II - the zeolite component is dehydrated

State III - the zeolite component is rehydrated.

The compacts in their holders reached states I, II and III as follows. The

hydrated compacts were pumped out for several days at temperatures rising

to 60-65 “C. This caused a partial loss of water from regions near x=0 and

x = 1 but was not expected to render the bulk of the zeolite crystals permeable

to diffusing gases. The plug thus treated is in state I. State II was reached by

outgassing the plug at temperatures rising gradually to 340-370 “C and

maintaining these temperatures for one to two weeks while constantly

outgassing. Even then owing to the length and compacted character of the

plugs traces of water were still being evolved. State III was attained by

allowing the compacts in State II to sorb water vapour at a temperature of

100 “C falling to 50 “C ,or less, over a period of about one month. The

compact was then pumped out as in reaching state I.

Diffusion cells and sorption bulb were immersed in water or oil thermo-

TA

BLE

1

Syst

em

Hen

ry’s

la

w c

onst

ant

Mea

n A

S0

mol

ecul

es

per

cm3

of s

orpt

ion

volu

me

>

AE

A

A0

mol

ecul

es

per

cm3

of g

as p

hase

(k

cals

/mol

e)

(cal

s/m

ole)

be

twee

n 0”

and

75

“C

(c

als/

mol

e-de

g)

s --

8

0 “C

23

“C

50

“C

75

“C

0

“C

23 “

C

50 “

C

75 “

C

He

- N

aA

0.69

0.

63

0.57

0.

52

- 78

0 20

5 27

0 36

5 45

5 -

3.52

(a

)*

f 0.

83

0.76

0.

69

0.63

10

1 16

2 24

2 32

4 -

3.1s

(b

)*

g ;!

He

- C

aA

0.70

0.

58

0.50

0.

40

- 13

00

200

320

450

640

- 5.

49

(a)

2 0.

82

0.68

0.

58

0.46

11

0 23

0 34

5 53

0 -

5.17

(b

) ;

NZ

- N

aA

70.6

37

.4

20.1

12

.2

- 44

30

- 23

10

- 21

30

- 19

30

- 17

30

- 7.

76

(a)

84.9

45

.0

24.2

14

.7

-240

0 -

2230

-

2040

-

1850

-

7.42

(b

) i m

Na-

CaA

20

4 94

.9

43.7

22

.6

- 55

20

- 28

80

- 26

80

- 22

20

- 18

30

- 10

.01

(a)

239

111.

3 51

.2

26.5

5

- 29

70

- 27

10

- 23

10

- 19

30

- 9.

96

(b)

” 0

Ar

- C

aA

25.1

15

.6

9.75

6.

76

- 33

60

- 17

60

- 16

15

- 14

60

- 13

20

- 5.

8s

(a)

9

30.1

18

.3

11.4

7.

93

- 18

50

- 17

10

- 15

60

- 14

30

- 5.

56

(b)

2

* In

all

lines

(a)

the

sor

ptio

n vo

lum

e is

tak

en

as t

he t

otal

in

trac

ryst

allin

e vo

lum

e;

in a

ll lin

es (

b) i

t is

thi

s vo

lum

e le

ss t

he f

ree

volu

me

of t

he s

odal

ite

cage

s.

132 R. M. BARRER AND I. H. PETROPOULOS

stats controlled to + 0.1 “C, or at most to + 0.2 “C. A high temperature oil

in the latter case formed a thermostat fluid suitable for use up to 175 “C.

4. Sorption of permanent gases

Before considering the flow measurements the membranes and their

components must be well characterised as sorbents of the permanent gases.

Isotherms were measured at O”, 23”, 50” and 75 “C for He-NaA, He-CaA,

Ar-CaA, N,-NaA, N,-CaA and N,- and Ar-graphite. In the range of

pressures below 15 cm Hg all isotherms save those of nitrogen in CaA at 0

and 23 “C obeyed Henry’s law. Even for the exceptions the limiting Henry’s

law isotherm slopes were readily obtained. The higher affinity of nitrogen as

compared with argon for CaA is known to be associated with the quadrupole

moment of nitrogen17* I*).

The thermodynamic distribution coefficient, k,, may be written lg) as

(13)

The chosen standard state in the gas phase is p= I atm (or Cg= l/RT) and

in the sorbed state also Cg= l/RT. These are states of high dilution, and

since the Henry’s law region is also one of relatively high dilution we may

assume in this region that f,/f, - 1 and so k, N k,. Also the energy of sorption,

AE, will be virtually identical with the standard energy of sorption, AE’.

The standard free energy and entropy of sorption, AA0 and AS’, are then

given by

and

AA0 = - RTln k, = - RTln k, (14)

AA0 = AE” - TAS’ = AE - TAS’. (15)

Some values of k,, k, and of AE, AA0 and AS0 are given in table I. Those

for helium are particularly interesting because k, is less than unity and AA0

is positive. This situation arises because although AE is exothermic its

influence is outweighed by the loss of thermal entropy, AS’, when helium is

entrained within the crystals.

It 1s often considered that negative adsorption in the sense of Gibbs’

adsorption equation cannot occur in a porous solid20). However, in the

present work the method of measuring sorption is such as to ensure that the

absolute amount rather than a Gibbs excess of intracrystalline sorption is

obtained. Thus, the volume of the empty sorption bulb is first determined,

and from it the total volume of the hydrated crystals subsequently introduced

is subtracted. The net volume is then used to evaluate the uptake of helium.

(I) SORPTION AND FLOW IN GRAPHITE-ZEOLITE COMPACTS 133

On outgassing the zeolite its zeolitic water is removed and a known intra-

crystalline volume is thereby created wherein the sorption occurs. If this

volume is added to the above net volume in calculating helium uptake, then

the Gibbs surface excess is evaluated. If it is not, then the absolute sorption

is evaluated. As noted above, we have used the latter procedure, and so

derive from our data absolute adsorptions. These are shown in figs. la and b

and demonstrate the consistency obtained. Sorption is, of course, slight and

is therefore prone to uncertainty of measurement, but, subject to a reser-

(b)

Press km Hg)

Fig. 1. (a) Isotherms for helium in NaA. (b) Isotherms for helium in CaA.

vation on this count, we have the first example in the Gibbs sense of negative

excess of helium in the intracrystalline volume.

In fig. 2a the isotherms for sorption of nitrogen and argon are shown for

the graphite powder. Finally, the linear relations between log k, and l/r

are shown for typical examples in fig. 2b. The difference in AE for nitrogen

in CaA and NaA (1090 cals/mole) may approximate to the energy difference

between the quadrupole-field gradient interactions in these two intracrys-

talline environments, since the dispersion + repulsion energy should be

virtually the same in both. Similarly the difference in AE for N,-CaA and

Ar-CaA (2160 cals/mole) may approximate to the total quadrupole energy

of the nitrogen in CaA, because again the dispersion + repulsion energy of

these two sorbates is very similar and argon has no quadrupole moment.

The close correspondence of dispersion + repulsion energy for argon and

134 R. M. BARRER AND J. H. PETROPOULOS

nitrogen is seen when AE is compared for these two gases on the non-polar

sorbent graphite. For Ar-graphite AE= - 4210 cals/mole and for N,-graphite

it is -4580 cals/mole.

For all the gas-zeolite systems of table I two values of the intracrystalline

sorption volume were taken, because in the crystals there are two kinds of

cavityzr), of which the largest with a free volume of -775 A3 is easily

accessible to He, Ar or N,. The smaller cavities with a free volume of

N 157 A3 may be accessible only with difficulty, at least to argon. Accordingly

Preis (cmHg)

x SW--=*-- _X---_:Z==+

-+- 1 I a I_

28 32 36 40

+ x lo3 (Tm OK)

Fig. 2. (a) Isotherms for NZ and Ar on the graphite used in preparing the graphite- zeolite compacts.

L Graphite-N2 B Graphite-Ar (b) The linear relationships between the logarithm of the Henry’s law constants and

l/T(Tin “K). -1~ NaA-He a CaA-N2 x CaA-He B CaA-Ar !: NaA-Nz

in lines (a) of table I the total free volumes are used, and in lines (b) the free

volumes of the largest cavities only are employed. This is seen to make minor

changes in AA0 and AS0 but not of course in AE.

The values of dS” are all negative, corresponding to loss of thermal

entropy when the sorbates are transferred from gas phase to sorbent.

Among the gas-zeolite systems -dS” increases as - AE increases. This

may be taken to mean greater restrictions in freedom of entrained gas as

-AE rises. For nitrogen in CaA, -AS0 is so large as to indicate that

rotational as well as translational motions in the gas phase become rocking

TA

BL

E 2

Ste

ady-

stat

e pe

rmea

bili

ty

coef

fici

ents

an

d ti

me-

lag

diff

usi

on

coef

fici

ents

of

hel

ium

in

gra

phit

e-ze

olit

e co

mpa

cts

KI

x lo

3 D

Z

x lo

3 fr

om

tim

e la

g, L

K

I~~I

KI~

z P

lug

Sta

te *

(c

m2

set-

I)

(cm

2 se

t-l)

of

plu

g 0

“C

23 “

C

50 “

C

75°C

0°

C

23 “

C

50 “

C

7s “

C

0°C

23

“C

50

“C

75

“C

A

I1

5.38

5.

24

5.00

4.

91

1.96

2.

06

2.11

2.

22

III

4.99

4.

77

4.71

-

2.31

2.

37

2.50

2 IS

c =I

8 %

v

B

II

1.98

1.

91

1.83

1.

84

1.30

1.

50

1.65

1.

75

1.58

1.

67

1.85

1.

91

F

III

1.59

1.

55

1.53

-

2.00

2.

05

2.10

-

1.95

2.

04

2.13

-

2 ?

I 1.

24

1.21

1.

16

- 1.

85

2.02

2.

11

$ D

II

2.

74

2.59

2.

50

2.50

1.

79

1.88

2.

00

2.09

5

III

2.89

2.

80

2.77

-

2.22

2.

33

2.41

-

B

? R

I 9.

42

9.35

9.

35

- 2.

47

2.48

2.

48

- 0

G

Ira

13.7

13

.6

13.3

13

.1

1.87

2.

05

2.18

2.

27

f:

;;I

IIb

15.1

14

.7

14.3

-

- 2.

22

2.30

-

8 II

I 12

.2

13.0

13

.4

- 2.

62

2.66

2.

62

- 5

1 1.

69

1.62

1.

58

- 1.

76

1.84

1.

94

- 2

H

II

2.97

2.

92

2.82

2.

76

1.51

1.

67

1.83

-

III

2.27

2.

21

2.18

-

2.09

2.

17

2.23

-

* I

=

hyd

rate

d;

II =

de

hyd

rate

d;

III

=

reh

ydra

ted.

136 R. M. BARRER AND J. H. PETROPOULOS

vibrations or vibrations respectively within the zeolite. The values of --AS’

may be compared with those given by Barrer and Reesrs) in their table 2 for

a number of sorptions obeying Henry’s law.

5. Diffusion and flow

5.1. HELIUM

Measurements of steady-state flow and of time-lags served for the evalu-

ation of permeability and diffusion coefficients as summarised in table 2.

The view that the intracrystalline flow of helium is insignificant is supported

in the case of plug B by the close similarity in the magnitudes of K, and D, in table 2. When a gas shows significant sorption the time-lag period increases

strongly and D, decreases to correspond, as may be seen by reference to

table 3. The changes observed in the sequence state t+state n-+state III of the

plugs indicate that these graphite-zeolite compacts are not fully stable, but

that most of the alteration in flow properties occurs on the first outgassing,

that is, between stages I and II.

On account of these changes the ratio of the permeability coefficients for

helium and nitrogen in table 2 may give more information regarding surface

and intracrystalline flow of nitrogen than absolute values of K, and D,. For

flows confined purely to the gas phase the ratio should be ,/(MNr/MHe)=2.65. In all compacts K ~“/K~’ departs further from the theoretical ratio when the

compact is dehydrated. The value 2.65 is reached only for plug G in state III,

so that in general there is a flux involving a sorbed phase of nitrogen,

probably mainly on the graphite surfaces in states I and III. However, even in

these states some zeolitic water may be removed especially near x=0 and

x=1 and very limited intracrystalline flow of nitrogen is possible in these

portions of the plug even in these two hydrated states.

5.2. ARC~N AND NtTROG~~

The permeability coefficients in the steady state may be considered either

in terms of the concentration gradients in the gas phase, as in eq. (2), and

the derived equations (6) and (7), or they may be considered as below in

terms of the gradient of the total concentration, C= (C, + C, + Ci):

(16)

In the region where Henry’s law governs the distribution of gas between the

gas phase and both the surface and the intracrystalline free volume in the

zeolite, one may proceed as previously (eqs. (3), (4) and (5)) and obtain a

TABLE

3

Per

mea

bili

ty

and

diff

usi

on

coef

fici

ents

fo

r n

itro

gen

an

d ar

gon

Hyd

rati

on

Kl

x

lo3

(cm

2 se

t-l)

K

Z x

lo

5 (c

m2

set-

l)

D2

x

lo5

(cm

2 se

t-l)

E

for

KZ

E

for

DZ

P

lug

stat

e of

Plu

g 0

“C

23 “

C

50 “

C

15 “

C

0°C

23

“C

50

“C

75

“C

0

“C

23 “

C

50°C

75

“C

--

(cal

s pe

r m

ole)

(a)

Arg

on

H

II

1.60

1.

41

1.21

1.

18

- -

- -

4.0

5.6

7.2

9.3

--

2100

II

I 0.

79

- _

- -

- 10

.7

- -

-

(b)

Nit

roge

n

A

II

2.74

2.

54

2.37

2.

22

1.56

2.

72

4.1

7.1

3.70

6.

9 11

.6

19.2

38

00

4100

II

I 2.

16

2.01

1.

88

- -

B

II

1.22

1.

14

0.99

0.

97

0.99

1.

73

2.76

4.

4 1.

66

3.19

5.

34

8.05

28

70

3820

11

1 0.

82

0.76

0.

12

- 57

.3

61.1

64

.1

23.0

30

.2

35.2

-

420

1600

I 0.

67

0.60

0.

55

- -

- -

- -

- -

-

D

II

1.53

1.

38

1.25

1.

20

1.24

2.

09

3.48

5.

4 2.

35

3.91

6.

8 10

.5

3300

38

20

III

1.30

1.

20

1.15

-

98

91

102

- 44

56

13

0 16

60

I 3.

82

3.71

3.

78

- -

- -

- -

G

Ira

1.3

6.7

6.1

6.2

1.40

2.

72

5.4

10.5

1.

87

3.51

1.

4 12

.8

4910

49

20

ub

6.8

6.6

6.2

- -

- -

- -

- -

III

4.6

4.9

5.1

- -

- -

-

I 0.

96

0.88

0.

81

- -

9.9

13.2

19

.8

H

11

1.96

1.

74

1.54

1.

41

0.53

1.

01

1.95

3.

37

0.76

I .

44

2.81

4.

59

4680

45

80

III

1.09

1.

02

0.98

-

76

83

81

- 6.

9 10

.5

13.7

70

0 21

20

138 R. M. BARRER AND 1. H. PETROPOULOS

a new permeability coefficient, K,, which is for the dehydrated and hydrated

states respectively

(17)

and

These coefficients may be compared directly with the corresponding diffusion

coefficients D,, and D,, of eqs. (9) and (10).

The relevant coefficients are summarised in table 3, along with values of

K,. The ratios D,/K, are greater than one when the plugs are in state II, but

are less than one if the plugs are in state III. This supports the viewrs) that

one cannot assume the identity of steady and transient state diffusion

coefficients. The change in the ratio between states II and III also demonstrates

the reality and importance of an intracrystalline flux in state II.

The permeabilities, K,, given by eqs. (6) and (7), have very small negative

temperature coefficients. Thus, the increase in D,,/p and in Di, with rising

temperature is not quite as large as the decrease in k, and ki. Both D,,/p and

Di, refer to fluxes J, and Ji partly in gas phasel4). The flux J, must, as noted

earlier, pass by evaporation across gas gaps between one element of surface

and the next before being re-constituted on the surface. This process requires

the full energy of vaporisation; in addition, however, molecules comprising

J, hop or flow along each element of surface with an energy of activation

smaller than the full energy of evaporation. The resultant energy of activation

for surface diffusion is thus somewhat less than the energy of evaporation.

A similar argument applies to the molecules comprising Ji which evaporate

in passing from one porous crystal to the next, and also diffuse through

successive crystals. Accordingly the small negative temperature coefficient is

readily understood. There is also a slight increase in D,, (or Dg) with rising

temperature, and there may be a temperature effect on the pore geometry.

Even the helium permeabilities of table 2 show small negative temperature

coefficient so that either helium has a component of flow of adsorbed or

intracrystalline gas, or there are changes restricting the flow channels with

rising temperature, or both.

The large positive temperature coefficients of K, and D, arise from the

(I) SORPTION AND FLOW IN GRAPHITE-ZEOLITE COMPACTS 139

denominators or (I+$)

in the relevant expressions such as eqs. (I 7) and (18). As expected from this

argument, the temperature coefficient when the denominator contains the

term I/ki/c is much greater than when this term is not present, for Vk,/c

for argon and nitrogen considerably exceeds Ak,/s or I. The Arrhenius

energies of activation in the last two columns of table 3 are smaller than the

energies of intracrystalline sorption in table 1, but especially in the compacts

containing CaA the differences in the two energies are not large.

5.3. ANALYSIS OF NITROGEN FLOW

One may now use the helium flow measurements to interpret the nitrogen

flux in terms of its three component fluxes, J,, J, and Ji, and the three

diffusion coefficients to correspond. The method is similar to that of Barrer

and Gabor la) and neglects any flow of sorbed helium. The gas phase flux, Jg,

and the diffusion coefficient Dgs, are given by Jg/Ji’ = Dgs/D~se = J(M,,/M).

Also from eq. (8) we may evaluate ( Vki/.z) Di, for the intracrystalline flow,

whence Ji/J,=( Vki/E)(Di,/D,,). Vki/ E is k nown from the sorption experiments,

and both Di, and Ji follow. Finally, the remaining flux J, = J-(Ji + Jg) is

obtained, and since J,/J,=(Ak,/&)(D,,/P)/D,,, we may derive OS,//?. The

adsorption results have already given Ak,/c. These flux ratios and diffusion

coefficients are summarised in table 4, lines I to 8. Next, in lines 9 and 10,

are given the energies of activation, EDis and E,,,, for Di, and D,,/p.

From the time lags for helium, D!e may next be found [L,,=1,/(60~‘)]

and then D, for nitrogen [Dg=Dre J(MH,/MN2)]. Next from eq. (10) for

nitrogen in compacts in state III, taking Ak,/& from the sorption data, one

can determine D,. As before, assuming that hydration of the zeolite does not

significantly alter flow and adsorption on external surfaces or the gas phase,

one may use eqs. (12) or (14) to evaluate Di, since Vki/E is known from the

adsorption experiments. In this way flux ratios and diffusion coefficients,

and finally an energy of activation for Di, were found and are given in table 4,

lines 11 to 19. In lines 20 to 22 are recorded the ratios of relevant pairs of

time-lag and steady-state diffusion coefficients.

One may also compare D, and D,, with the Knudsen flow diffusion

coefficient, DF’, which one would find in one long cylindrical capillary

having a volume to surface ratio equal to that in the actual porous mediumr3).

Then D,, = IC~~D~’ ; D, = K&):’

where DEgy’ =8E J 2RT ~

3A nM

TA

BL

E

4

Ana

lysi

s of

nitr

ogen

fl

ow d

ata

Plu

g

Tem

pera

ture

“C

_

(KJD

as)

deh

ydr.

W,/D

.s)

reh

ydr.

J,sl

J,s

2 m

Jss/

Js.

=:

-0”

(Des

x

103)

deh

ydr.

z (D

es

x 10

”)re

hyd

r.

s D

is

x IO

”

D,,

x IO

”

En,

, k

cals

ED

_ kc

&

(h/D

,)

deh

ydr.

(&/D

e)

reh

ydr.

9 h/

Js

m

z Js

iJsz

;

(De

x 10

3) d

ehyd

r.

.u

; (D

E

x 10

3) r

ehyd

r.

e c D

, x

lo6

D.

x lo

1

En,

k

cals

-~

(DE

/D&

re

hyd

r.

Ds/

D..

DiiD

iS

Dgc

kl

x lo

3

1 (K

J reh

ydr.

(K&

re

hyd

r.

A

B

I D

I

G

0 23

50

75

,

0 23

50

75

i

0 23

50

75

0

23

50

__7:

1.35

1.15

0.20

0.15

2.03

1.88

2.33

1.0%

1.29

1.

25

1.12

1.

05

0.17

0.

20

0.12

0.

05

I .98

1.88

I.80

1.

78

3.64

7.

62

1.48

1.

14

3.6

2.4

1.19

1.

68

1.03

* 1.

36

0.16

0.

32

0.36

1.85

0.

747

0.60

9.8

1.95

0.50

s

12.1

12

.6

13.2

13

.9

0.15

6 0.

14

0.13

5

0.03

33

0.30

0

1.59

I .4

3 1.

39

1.30

1.

24

1.19

*

0.29

0.

19

0.20

0.30

0.

24

0.72

, 0.

69

0.69

4

0.58

5 0.

571

3.22

3.

7s

6.52

0.75

4 1.

11

3.1

2.8

0.05

55

0.08

31

0.12

0,

0.38

3 0.

429

1.48

1.

41

1.32

1.

28

~

1.06

*i

1.22

1.

19

1.15

1.9

1.14

1.

10

1.00

1.

00

1.01

0.29

0.

27

0.22

0.

22

0.22

0.

19

0.14

0.19

0.

14

0.10

0.

00

0.00

0.

01

1.03

1 .o

s

WI’

y:

E

0.94

i :

:l,

::zd

53:

5.27

2.44

4.

0s

5.94

9.

71

2.40

4.

32

6.7~

0.48

5 0.

64

0.84

3.3

3.7

I .9

H

0 23

50

75

1.75

1.

59

1.45

1.

35

1.27

1.

22

1.19

1.

15’

0.48

0.

37

0.26

0.

20

0.27

0.

22

0.19

I.12

I.

10

I .06

1 .O

a

0.85

, 0.

834

0.82

3

1.46

2.

38

3.50

5.

10

0.54

0.

79

1.22

3.1

2.8

2.68

2.

52

2.12

0.

58

0.27

~

0.

04

0.50

0.

58

0.64

I

0.77

0.

79

0.82

I

0.9

22.3

39

.1

1.04

0.

91s

-

4.4

1.3

1.3s

1.

4

2.05

1.

2 _

5.6

7.0

10.5

8.53

8.

89

9.31

9.

8 8.

53

8.89

9.

31

9.8

12.1

12

.6

13.2

13

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8.53

8.

89

9.31

9.

8

0.09

0 0.

089

0.08

8

0.07

0 0.

066

0.06

2 ~

0.13

0.12

0.

11

0.38

0.

39

0.38

0.

10

0.09

4 0.

089

* F

rom

ex

trap

olat

ed

valu

es o

f K

I,

D~

s.

(I) SORPTION AND FLOW IN GRAPHITE-ZEOLITF COMPACTS 141

and legs and rcg are structure factors. In this way one finds the results in the

last three lines of table 4. Clearly the structure factors are small indicating

tortuous diffusion paths in the compact. This is expected since during

formation under compression the graphite flakes in the compact will tend

to orient with their basal surfaces normal to the direction of compression,

which is also that of flow.

The steady-state intracrystalline and surface fluxes are seen from table 4

to be smaller than the gas-phase flow. In plug B in state II the intracrystalline

flow in the transient state during the time-lag period is, however, considerably

larger than the gas-phase flux. The intracrystalline diffusion coefficients are

considerably smaller (in the range 10m6 to lo-’ cm2 see-‘) than the surface

diffusion coefficients (ca. 10m4 cm2 set-‘) and the gas-phase diffusion

coefficients (ca. lop3 cm2 set-‘). Dis, Q, OS,//3 and D, all refer of course to

flows which are partly in the gas phase (l.c.). In all cases the gas-phase

diffusion coefficients are similar though not equal in the dehydrated and the

rehydrated states of any compact. They differ considerably, however, among

the different plugs. On the other hand the intracrystalline diffusion coef-

ficients at a given temperature are all of similar magnitude in each compact,

as would be expected for a process of which a good part is occurring within

the same intracrystalline channel system.

The Arrhenius energies of activation for Di, and Di are all rather smaller

than the energies of sorption of nitrogen (table 1); those for D,,/j3 are

considerably less than the energy of sorption of nitrogen on graphite (l.c.).

Finally, in compact B transient-state (time-lag) diffusion coefficients all tend

to be larger than the corresponding steady-state values. Especially is this so

for Di and Di,.

6. Conclusion

As a result of this study it has been possible to demonstrate rather small

intracrystalline flows of nitrogen in dehydrated compacts of graphite with

Linde Sieve A in Na- and Ca-forms. The work points to several directions

in which further examination of such compacts is needed. First, one may

choose a vapour of enhanced sorbability (Part II). Second, one may try to

avoid the large tortuosity associated with the incorporation of flaky graphite,

by using other bonding agents. Third, one may employ zeolites more open

in structure than Linde Sieve A, such as Linde Sieve X or Norton Co.

Zeolon. These possibilities are being currently investigated.

One of us (J.H.P.) wishes to acknowledge with thanks the award of

an Esso Postdoctoral Fellowship which enabled him to take part in this

work,

142 R. M. BARRER AND J. H. PETROPOULOS

References

1) E. A. Flood, R. H. Tomlinson and A. E. Leger, Canad. J. Chem. 30 (1952) 389. 2) P. C. Carman and F. A. Haul, Proc. Roy. Sot. A209 (1951) 38. 3) R. M. Barrer and E. Strachan, Proc. Roy. Sot. A231 (1955) 52. 4) E. R. Gilliland, R. F. Baddour and L. J. Russell, J. Amer. Inst. Chem. Eng. 4 (1958)

90. 5) R. A. W. Haul and R. Peerbooms, Naturwiss. 5 (1958) 109. 6) R. Ash, R. M. Barrer and C. G. Pope, Proc. Roy. Sot. A271 (1963) 1. 7) D. H. Hagerbaumer and K. Kammermeyer, Chem. Eng. Prog. Symposium Series

No. 10, Collected Research Papers 50 (1954) 25. 8) K. Kammermeyer and D. H. Hagerbaumer, Jour. Am. Inst. Chem. Eng. l(l955) 215. 9) R. Ash, R. M. Barrer and C. G. Pope, Proc. Roy. Sot. A271 (1963) 19.

10) K. Kammermeyer and L. 0. Rutz, Chem. Eng. Prog. Symposium Series No. 24, Collected Research Papers 55 (1959) 163.

11) R. M. Barrer and J. H. Petropoulos, Brit. J. App. Phys. 12 (1961) 691. 12) R. Ash and R. M. Barrer, Trans. Farad. Sot. 59 (1963) 2260. 13) R. M. Barrer and T. Gabor, Proc. Roy. Sot. A251 (1959) 353. 14) R. M. Barrer and T. Gabor, Proc. Roy. Sot. A256 (1960) 267. 15) H. L. Frisch, J. Phys. Chem. 61 (1957) 93. 16) D. W. Breck, W. G. Eversole, R. M. Milton, T. B. Reed and T. L. Thomas, J. Amer.

Chem. Sot. 78 (1956) 5963. 17) G. L. Kington and A. C. Macleod, Trans. Farad. Sot. 55 (1959) 1799. 18) R. M. Barrer and W. I. Stuart, Proc. Roy. Sot. A249 (1959) 464. 19) R. M. Barrer and L. V. C. Rees, Trans. Farad. Sot. 57 (1961) 999. 20) cf. D. M. Young and A. D. Crowell, Physical Adsorption of Cases (Butterworth,

London, 1962) p. 1. 21) D. W. Breck and T. B. Reed, J. Amer. Chem. Sot. 78 (1956) 5972.