Study of the adsorption equilibrium of binary hydrocarbon mixtures on graphitized carbon black

,J. Rouquerol and K.S.W. Sing (Editors) lAdsorpticn at the gas-solid and liquid-solid interface © 1982 Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

75

STUDY OF THE ADSORPTION EQUILIBRIUM OF BINARY HYDROCARBON MIXTURES ON GRAPHITIZED CARBON BLACK

M. ALBRECHT, P. GLANZ and G.H. FINDENEGG Institut fur Physikalische Chemie, Ruhr-Universitat Bochum, D 4630 Bochum (F.R.G.)

ABSTRACT Three experimental methods for studying mixed-gas adsorption are discussed: (a) determination of the individual isotherms of the two components by direct measurements of their amounts adsorbed from the gas mixture;

(b) measurement of the weight

of adsorbed mixture along isotherms of constant gas-phase composition, and subsequent calculation of the composition of the adsorbate by the Gibbs adsorption equation; (c) determination of the initial slope of the partial isotherm of one component as a function of coverage of the surface by the other component, using a chromatographic technique (elution on a plateau). Preliminary results for the adsorption of hydrocarbon mixtures on graphitized carbon black are presented. Results for binary mixtures of C obtained by method (c) at BOoC are analysed in terms of the two6-hydrocarbons dimensional van der Waals equation of state. In this way the interaction parameter for pairs of unlike adsorbed molecules can be obtained.

INTRODUCTION Physical adsorption of gas mixtures is of considerable practical importance for gas separation and purification processes. Since the measurement of two- and multicomponent adsorption equilibria is complicated, several methods for estimating such data from pure-gas adsorption isotherms have been developed. Up-to-date reviews of the literature in this field are available (refs. 1-4). However, there have been very few reliable experimental data for the adsorption of gas mixtures on well-defined adsorbents with which to compare these theoretical models. To provide such data is of primary importance for further progress in this field. Experimental problems arise for mainly two reasons. First, adsorbents with a homogeneous surface have a rather low specific surface area, hence the amounts adsorbed are small. Second, the number of independent variables in mixed-gas adsorption is rather large; i.e., temperature, pressure, amount adsorbed, and the composition of both the adsorbate and the gas phase, in the case of a binary mixture. In conventional techniques for taking mixture adsorption data the gas-phase composition is varied at

76 constant pressure in a static system. A recent version of this principle has been published by Hall and Muller (ref. 5). In the present paper we discuss three alternative methods which have been set up in our laboratory. Two of these involve quasistatic measurements, of the individual isotherms of the two components, or of the weight of adsorbed mixture, respectively, over a range of pressures at constant gasphase composition. The third method is based on a dynamic (gas chromatographic) technique by which the initial slope of the partial isotherm of one component can be measured as a function of precoverage of the surface by the other component (refs.

6-~

a simplified version of this method had been described previously by Sloan and Mullins (ref. 8). The experimental techniques and the methods of calculating the adsorption isotherms from the raw data will be outlined in the next section. The experimental surface excess amounts can be identified with the absolute amounts of the adsorbed components under the experimental conditions of this study. Representative results for the adsorption of binary mixtures of hydrocarbons of equal number of carbon atoms onto graphitized carbon black will be presented. In the final section, the results obtained by the gas chromatographic method will be analysed in terms of a two-dimensional equation of state of the mobile mixed film of adsorbate. EXPERIMENTAL METHODS AND RESULTS Direct method In this method the adsorbed amounts of the two components are measured directly. The adsorption equilibrium of a mixture of known composition at given pressure is achieved by passing a stream of the gas mixture through the adsorption cell at a low flow rate (quasi-static conditions). The adsorbate is then eluted and transferred into a gas chromatograph for quantitative analysis. The absolute calibration of the chromatograph represents a major difficulty of this method. A similar principle for measuring individual isotherms of binary gas mixtures was described by Arnold (ref.

~.

The scheme of the apparatus used in our laboratory is shown in Fig. 1. During the equilibration period the gas mixture flows from the supply cylinder through the adsorption cell (volume ca. 6 ml, containing ca. 1.5 g of adsorbent) and is removed from the system by a pump. The gas flow rate (ca. 10 ml/min) is adjusted by a needle valve (V4). The pressure in the cell is kept constant to ± 0.2 mbar over the experimental range of pressures (25-1000 mbar) by a precision pressure controller. When adsorption equilibrium is established the cell is isolated by valves V1 and v2 and the rest of the apparatus is evacuated. In the. subsequent desorption period the mixed adsorbate is transferred from the adsorption cell into the chromatograph. The vapours are swept through a suitably sized loop of a gas sampling valve by a carrier gas which is adjusted to a constant flow-rate by a needle valve (V5). Gas samples are injected into the chromatograph at regular time intervals. The intervals (ca. 3 min) are chosen such that a new sample is injected shortly after the integration of the second

77

Pressure Control

T2 Row Rate Cell

Gas Mixture

Fig. 1. Schematic diagram of apparatus for measurement of individual adsorption isotherms: Barocel pressure controller with capacitance manometer pressure sensor (P1) and magnetic valve (MV) for pressure control of gas mixture and elution gas (He); T1, constant temperature bath for adsorption cell; GC, gas chromatograph with sample loop; P2 mercury manometer; D1, D2, dilution volumes for eluted vapours; T2, air thermostat for soap bubble flowmeter; V1 to V3 valves; V4, V5, needle valves. component peak of the previous sample has been completed. About 50 samples are drawn during the elution process. The total amount of component i eluted by the carrier gas is obtained from the relation

c.

n.

~

where

~

(t)

dt

V is

the volume flow rate in the sample loop and c (t) is the corresponding i volume concentration of vapour i at time t. Values of c (t) are obtained from the i individual peak areas printed out in the chromatogram using a calibration function to convert peak areas to concentrations. In this calibration, a mixed vapour/carrier gas stream is produced in a vapour saturator which can be thermostatted accurately over a range of SUfficiently low temperatures. The mole fraction of the vapour in the

= p~(T~ s }/p, where p~(T.i, s } is the saturation ~ vapour pressure at the temperature of the saturator and p is the total pressure in

mixed gas is obtained by the relation y.

the saturator. When this gas stream sweeps the sample loop of the chromatograph the

= YiPL/RTL' where PL is the total i pressure and T the temperature of the gas in the loop. L A calibration function of the form volume concentration of the vapour is given by c

C

i

(loop)

= f(peak

area)

was obtained for each component by fitting a polynomial to the calibration data which covered the whole range of observed peak areas.

78

Propane (1:1 mixture)

Propane(pure gas)

5

c 10·C

I

62S·C

° ,"O·C

3 0)2

Propene (1:1 mixture) n 10·C

625 ·C

° t.O·C

3 2

200 400 600 800

1000

p/mbar

100

200 300 400 500 p./mbar I

Fig. 2. Adsorption of propane and propene on Vulcan 3-G graphitized carbon black at 10, 25, and 40°C. left: Pure gas isotherms; Right: individual component isotherms vs. partial pressure for an equimolar propane + propene mixture. The amount of component i adsorbed at the solid adsorbent is obtained from the total amount in the adsorption cell, n

i,

and the amount of component i in the gas

phase of the adsorption cell, ni' by a

n.

1

=

g

n. - n .• 1

1

The latter quantity can be estimated accurately from the known volume, pressure and temperature of the adsorption cell and from the weight and density of the adsorbent. Representative results for the adsorption of binary mixtures of propane + propene on graphitized carbon black are shown in Fig. 2. The graphs on the right represent individual isotherms of the two components for an equimolar gas mixture. The corresponding pure gas isotherms of the two components are shown on the left. Indirect method The composition of the mixed adsorbate can also be obtained indirectly from a measurements of the total amount of adsorbate along a set of isotherms n = na(p) at a common temperature, when these isotherms have been measured along constant gas-

79 phase concentrations. This method was suggested by van Ness (ref. 1) and applied to some selected hydrocarbon systems by Friederich and Mullins (ref. 10). It is based on the thermodynamic formalism of the Gibbs adsorption equation for a binary adsorbate in equilibrium with an ideal gas. For constant temperature T this equation may be written as drr

- RTf +

d 1

x -y

np +

where f = na/A isotherms 'll

=

s

A y yA

A B

d

YA

o

(1)

is the surface concentration of the adsorbate. Spreading pressure

'll(p) for the adsorption of a gas mixture of constant gas-phase compo-

sition YA are thus obtained by integration of the corresponding experimental adsorption isotherms (2)

From the spreading pressure isotherms for a set of gas phase concentrations Y it is A possible to determine the derivative (d'll/dy) for a set of fixed pressures p; this A p

can be done either graphically or by fitting a theoretical isotherm equation to the mixed gas adsorption data (see Discussion). Solving Eq. (1) for the unknown composttion of the adsorbate at constant pressure p now yields

(3)

Adsorption isotherms for the total amount adsorbed at constant gas composition may be measured by conventional volumetric or gravimetric methods, provided that precautions can be taken to prevent a depletion of the more strongly adsorbed component near the adsorbent sample. The gravimetric method is usually more precise a. a but it measures the total mass of adsorbate m instead of n Since the conversion a a of m to n (or f) involves the mean molar mass of adsorbate,

the evaluation of x

A

XA(T,P'YA) requires an iterative procedure in that case, as

outlined in ref.1. In gravimetric adsorption measurements it is convenient to use a symmetrical beamtype electronic microbalance. In this case buoyancy corrections can be minimized by employing a combination of taring materials of different densities (e.g., quartz and gold) such that both the weight and the volume of adsorbent and tare weights becomes nearly equal (ref. 11).

80 In view of the complications inherent in the experimental determination of the individual component isotherms of a mixture, gravimetric measurements can also be used to test the consistency of these results directly i.e. by calculating rna from the experimental data of n

a

and n

A

a

B.

Dynamic method One important application of mixed gas adsorption is in the field of separation and purification of gases by gas/solid chromatography (GSC). It is of interest, therefore, to study mixed gas adsorption under conditions similar to those encountered in GSC. One is concerned here with finite-concentration chromatography, i.e. concentrations at which the non-linearity of the adsorption isotherms is revealed. A method has been developed in our laboratory to study the initial slope of the partial isotherm of one component of a binary mixture of vapours as a function of the surface concentration of the second component (refs. 6-7). It is based on the chromatographic 'Elution on a Plateau'

(or 'Step and Pulse') technique (refs. 12-13)

and its application to the determination of pure gas adsorption isotherms has been worked out by Dondi et al.

(ref. 14). The principle is as follows: A column containing

the adsorbent is first equilibrated with an adsorbable vapour A which is added to the inert carrier gas. When a constant concentration (mole fraction YA) has been established along the column ('plateau' or 'step' of A) a small pulse of an adsorbable vapour B is injected at column inlet. This perturbation causes two signals to appear in the chromatogram; one of these signals is caused by the perturbation of the adsorption equilibrium of component A and its retention time t

is essentially equal A to that of a pulse A injected on the plateau of A. The other signal (retention time

t arises from the adsorption of component B in the presence of component A. The B) variation of t with the gas phase concentration YA contains the information on B mixed gas adsorption. The technique requires, in addition to the usual equipment for precision GC measurements, a device to prepare a mixed stream of vapour and carrier gas of stable and adjustable composition. Furthermore, the sample size of the pulse must be small (peak height of the pulse, h

less than 5 % of the height of the step, h a p' s)' condition which can only be met by using a sensitive detector (FID) and by minimizing the baseline noise. A flow scheme of the chromatograph used in our laboratory is shown in Fig. 3. Vapour A is added to the carrier gas by a vapour diffusion cell DZ and its concentration YA is adjusted by a vapour saturation cell SZ in a similar way as in the calibration device for the gas

c~romatograph

described in the previous section

(Direct method). All important parts of the apparatus (pressure and flow rate controllers, injector, column, detector and flowmeter) are thermostatted. Experimental details are given elsewhere (ref. 15). Fig. 4 shows a representative chromatogram. When a steady plateau of vapour A has

81

...

L._._.,

Fig. 3. Schematic diagram of the chromatographic apparatus (dynamic method): M to M i S' manometers; T , air thermostat containing pressure controllers for carrier gas (He) i and detector gas supply; T , T thermostatted liquid baths for diffusion cell (D2) 3, and saturation cell (S2); 1 , T , constant temperature bath for adsorption column (S); 4 6 T T thermostats for injector (In) and flame ionization detector (FID); T S' S' 7, constant temperature bath for soap-tubble flowmeter (SB) , V , Vy stop valves; V 2' four port switching valve; V needle valve. Recording unit: V, amplifier; KS, 4' recorder; A/D,analog-to-digital converter; DT, digital quartz timer; D, digital printer; IL, interface for tape punch; L, tape punch.

h

1

h,o

_t

1>,.••

I I

t.---.l

:..--+-1.---_

I'-I

I

t=o

Fig. 4. Typical chromatogram (schematically) for a step of cyclohexane (A) and a pulse of n-hexane (B) (see text). been attained (step height hA,s) the detector signal is compensated to zero and the amplifier is set to highest sensitivity. The pUlse of vapour B is injected at t The signal with retention time tAmay be a negative peak or a small positive peak immediately followed by a negative peak, as in Fig. 4, depending on the relative

o.

82 adsorption affinities of the two vapours. It is more accurate to measure t pulse of A. The signal with retention time t

by a A is always positive. It is convenient

B to define the net retention quantities R and R A B,

V

1

R A

(tA-tM)~

R B

j(t B - tM)RT' am s s

RT

A

-j-

(4)

a m s s

V

(5)

is the gas holdup time, V is the volume flow rate of the mobile phase measuned M at column outlet, msa is the surface area of the adsorbent in the column and j is s the common pressure gradient correction factor.

where t

The quantities R and R are related to the derivative of the adsorption isotherm B A of pure component A, dfA/dPA' and to the initial slope of the partial isotherm of component B at given partial pressure PA (i.e., at given surface coverage 8 A), (afB/aPB)PA(PB~ 0) - (afB/apB)O' respectively, by

r P

R A

r P

R

B

where P

=

i

df

2dP 3p p3 _ 1 I

A dPA

3p 2dP p3 _ 1 I

( afB ) apB

0

p/po and P 0

(6)

I

=

(7)

pi/po (p represents the total pressure at some point along the

column: pap ~ p ). When the column pressure drop PI is sufficiently small the pressure correction term may be taken outside the integrals of Eqs. allowing the isotherm fA f

=

fB(PA'

PB~

=

(6) and (7)

fA (PA) and the initial slope of the isotherm

0) to be derived directly from the experimental R(YA) data, as out-

B lined in the work of Conder and Purnell (ref. 16). At a column pressure drop P

I>1.2 the isotherms cannot be evaluated directly but are obtained by fitting parametric

isotherm equations based on a relevant theoretical model. For this purpose the r.h.s. of Eqs.

(6) and (7) are inverted by expressing P as a function of the surface con-

centration of the adsorbed components. pure component A, p

= (f m/K)f(8)

Inserti~g

a parametric isotherm

equation for

, into Eq. (6) yields

(8)

where 8

i

and

eO

represents the surface coverage by component A at column inlet and

83 column outlet, respectively. The corresponding expression for RB(y

is obtained by A) inserting parametric equations for the partial isotherms of the two components (i,j) of a binary mixture, Pi =

(fm,i/Ki)F(8i,8j), into Eq.

r (

~~A

(7); we thus obtain

3

(9)

)

with

g(8)

f

2

(8)

(

P

aA) ae A

The parameters K., f 1.

/ (

8 -+0

B

P

a B) ae B

(10)

8-+0

B

. and the lateral interaction parameter for a mixed gas

m,l.

adsorption isotherm can be obtained from a set of RA(y

and RB(y data by Eqs. A) A) (10). For several reasons it is recommended, however, to evaluate the mixed gas

parameters from the ratio of the net retention of the two components, RB/R

A, same vapour-phase concentration Y rather than from R Combination of Eqs. A) B. yields

f

2(8)d8.

(B)-

(at the (B)-(10)

( 11)

Fig. 5 shows experimental retention results for the adsorption of C 6-hydrocarbons on graphitized carbon black at BOoC; in all cases hexane is the preadsorbed component A. Thus the top curve in Fig. 5 represents the retention RA(y

for single-gas A) adsorption of hexane. The pronounced maximum of this curve at a gas-phase concentration

-3

Y ~ 2·10 is caused by a point of inflection of the single-gas adsorption isotherm A (i.e., a maximum of the slope dfA/dPA) at a pressure PA ~ 4 mbar. The single-gas isotherms of hexane, 2-methylpentane, and cyclohexane for the same temperature (BOoC) are shown in Fig. 6 (ref. 15). The lower curves in Fig. 5 represent the retention for several isomeric c h y d r o c a r b o n s including benzene and cyclohexane. Fig. A) 6 shows a plot of the relative retention RB/R as a function of YA' The curves shown A in this figure were obtained by a fitting procedure based on Eq. (11), as outlined

RB(y

below.

7

84

• n OJ

L-

a

0.2

n-Hexane Benzene

v

2-Methylpentane

o

3-Methylpentane

o 2.3-Dimethylbutane

.0

E 'E

~

N

2.2-Dimethylbutone

• Cyclohexane

(5

E

\0

-

52 0.1 0::

14

10

6

2

Fig. 5. Retention R(y of the C as a function of mole fractionOY of A) 6-hydrocarbons A n-hexane in the mobile phase. Adsorbent: Sterling FT-G, column temperature 80 C, pressure drop PI = 1.1, flow rate 5.7 ml/min.

c6- hydrocarbons I SterlingFT-G 2.0

N

E o

/'

E

o....

\0

~

~~,

10 /

6

~

• .J.,.......

.x

5

10

p,/mbar

0

~42e 1801 991

15

Fig. 6. Single gas adsorption isotherms of n-hexane, 2-methylpentane and cyclohexane 0C on Sterling FT-G at 80 (gravimetric results) (from ref. 15).

85

• o " •

0.61-"'=c-~

2-Methylpenlane 3-Methylpentane 2,J-Di"",thylbutane Cyclohexane

0.2

2

6

10

Fig. 7. Plot of the ratio R IR at the same vapour phase concentration (relative retention) versus the mole ~ra~tion Y of n-hexane in the mobile phase. Parameters A of the curves see table.

DISCUSSION Isotherm equations for monolayer adsorption of single gases on homogeneous surfaces can be written in the form f

p

~

.

f(e)

K.

(12)

~

where f

m,~

. is the amount adsorbed per unit area at complete monolayer coverage and

K is Henry's law constant. Several isotherm equations for mobile monolayer adsorption i are based on two-dimensional equations of state (refs. 17-18). The two-dimensional van der Waals equation of state yields f (8) = 1

~

e exp [ 1

~

e - we]

(13)

where the parameter w accounts for attractive lateral interactions of adsorbate molecules. f

rm

m

l/LB,

and ware related to the familiar van der Waals parameters a and w

=

2a/BkT

B by

(14)

where L is the Avogadro constant and k is the Boltzmann constant. For mixed monolayers of two components A and B the following combining rules for a and B are commonly adopted (ref. 19):

86

(15)

where x

and x are the mole fractions in the adsorbed layer and a is a parameter AB B A characteristic of the attractive AB interaction. Inserting aM and aM into the van der

Waals equation of state yields the following individual component adsorption isotherms for a binary mixture of i and j:

r

m,~

.

- K - F(8

i

c

t

~

(16)

8.)

J

with F (8. ,8.) ~ J

EqS.

(17)

(16) and (17) may be fitted to the individual component isotherms of the mixed

gas adsorption data for propane + propene shown in Fig. 2. Care must be taken, however, to confine the fitting range to the monolayer region of the experimental data. In the application of the van der Waals model to the chromatographic data presented in Fig. 5 the function g(8) in Eqs. (9)-(11) becomes (18)

where

e

TABLE 1 Parameters of the van der Waals equation for adsorption of binary mixtures of oC). hydrocarbons on Sterling FT-G (80 Component A is hexane. K A

r m,A

cyclohexane

0.197

2,3-dimethylbutane

0.210

Component B

r

w' AB

w A

K B

3.42

3.16

0.045

2.7

4.4

3.59

2.96

0.089

3.2

3.2

m,B

3-methylpentane

0.210

3.59

2.96

0.112

3.0

3.3

2-methylpentane

0.210

3.59

2.96

0.125

2.6

3.5

K and K in A B

~mol

-1 -2 m mbar

, r m,A and r m,B in

~mol

-2 m

For the analysis of the experimental data the following procedure was adopted. At first, the R (YA) data for the single-gas adsorption of hexane were used to obtain A

87 best-fit values of the parameters fm,A and w by Eqs. (8) and A constants K and K were taken from the experimental retention B A values of K , fm,A w and K , the parameters fm,B and w~B A A' B fitting Eq. (11) in combination with Eqs. (13) and (18) to the

(13). The Henry's law at YA = O. With these were determined by experimental RB/R

data. The curves exhibited in Fig. 7 represent the best fit of Eq.

A

(11) to the

experimental results. The resulting best-fit values of the van der Waals parameters are summarized in Table 1. The values of fm,B and

w~B

are uncertain as a consequence

of mutual compensation problems in the fitting procedure. In order to obtain reliable values of

w~B

it will be necessary to determine fm,i of both components by chromato-

graphic single-gas measurements. This will provide a possibility to determine the interaction parameter for adsorbed AB pairs

2r

m,B

r m,A + r m,B by two independent experiments (viz., using vapour i as the preadsorbed component A and vapour j as component B, and vice versa). Measurements of such data are now in progress.

ACKNOWLEDGEMENT Part of this work has been supported by the Deutsche Forschungsgemeinschaft (DFG) under Grant No. Fi 235/6-2.

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~(1969)

464-473.

2

S. Sircar and A.L. Myers, Chem. Eng. Sci.,

3

C.E. Brown and D.H. Everett, in D.H. Everett (Ed.), Colloid Science (Specialist Periodical Reports), Vol. 2, The Chemical Society, London, 1975, Ch. 2.

4

M. Jaroniec, Thin Solid Films, 50(1978)

5

P.G. Hall and S.A. Muller, J. Chern. Soc. Faraday Trans. I, 74(1978) 948-959, 2265-2270.

6

W. von Rybinski and G.H. Findenegg, Ber. Bunsenges. Phys. Chern., 83(1979) 1127-1130.

7

~(1973)

489-499.

163-169.

W. von Rybinski, M. Albrecht and G.H. Findenegg, J. Chern. Soc. Faraday Symposium paper 2.

~(1981),

8

E.D. Sloan and J.C. Mullins, Ind. Eng. Chem. Fundamentals, 14(1975) 347-355.

9

J.R. Arnold, J. Amer. Chern. Soc., 2!(1949) 104-110.

10

R.O. Friederich and J.C. Mullins, Ind. Eng. Chern. Fundamentals,

11

J. Specovius and G.B. Findenegg, Ber. Bunsenges. Phys. Chem. 82(1978) 174-180, 84(1980) 690-696.

12

J.R. Conder and C.L. Young, Physicochemical Measurements by Gas Chromatography, Wiley, Chichester, 1979, Ch. 9.

~(1972)

439-445.

88 13

P. valentin and G. Guiochon, J. Chromatogr. Sci.,

14

F. Dondi, M.-F. Gonnord and G.Guiochon, J. Colloid Interface Sci., 303-315, 316-328.

~(1976)

56-63, 132-139. ~(1977)

15

W. von Rybinski, Dissertation, Ruhr-Universitat Bochum, 1980.

16

J.R. Conder and J.H. Purnell, Trans. Faraday Soc. 64(1968) 1505-1512, 3100-3111; 65(1969) 824-838, 839-848.

17

R.A. Pierotti and H.E. Thomas, in E. Matijevic (Ed.), Surface and Colloid Science, Vol. 4, Wiley-Interscience, New York, 1971, Ch. V, p. 213.

18

A. Patrykiejew, M.

19

S.E. Hoary and J.M. Prausnitz, Chem. Eng. Sci., 22(1967) 1025-1033.

Jaron~

and W. Rudzinski, Chem. Eng. J., 12(1978) 147-157.