DESORPTION TIMEOF CYCLOHEXANE AND BENZENE ON
A
NONUNIFORM SURFACE
403 1
Determination of the Average Desorption Time of Cyclohexane and Benzene on a Nonuniform Surface by Gas-Solid Partition Chromatography
by Claire Vidal-Madjar and Georges Guiochon Labordoire d u Professeur L. Jacque, Ecole Polytechnique, Paris 6 , France Accepted and Transmitted by The Faraday Society
( J u n e 24, 1966)
The average desorption time of cyclohexane and benzene on a nonuniform solid support (benzophenone on firebrick) has been experimentally determined by gas-solid partition chromatography from the value of the kinetic mass transfer term of the plate height sec for cyclohexane, while for benzene it depends on equation. This time is less than the temperature and varies between loV4and sec. This last value may be explained by the existence on this surface of active sites with higher adsorption energy. The differential enthalpy of adsorption of benzene on the most active sites of the surface which can be derived from the variation of the average desorption time with temperature was found to be between 11.5 and 14.5 kcal/mole, while the differential enthalpy of adsorption on the average surface, calculated from the variation of the retention volume of benzene with temperature, is only 8.3 kcal/mole.
Introduction The study of the adsorption properties of a solid support is conveniently made by gas-solid partition chromatography using a systematic investigation of the elution peaks of several organic compounds. Retention volumes and their variation with temperature are a measure of the solute-adsorbent interaction while the zone profile depends on the rate of desorption. However, whereas retention volume measurements have been extensively used to derive adsorption isotherms, heat of adsorption, and entropy of adsorption,lW4information derived from the zone profile has been much less used, probably because it is more difficult to account for. I n linear gas-solid partition chromatography the zone profile eluted out of the column has a gaussian shape. By definition the average plate height, R, is related to the standard deviation of the gaussian peak by
Several physical processes are responsible of the zone broadening during its elution: molecular diffusion in the gas phase, mass transfer in gas and liquid phases,
and unevenness of the carrier gas flow. Assuming that these processes are independent and symmetrical, we can calculate the plate height in terms of the sum of the individual variances of these proce~ses.~The result is known as the plate height equation,6 which may be written as
ZJ = HJ + C k j ~ o
(2)
I n this equation H , is the sum of the terms which originates in the gas phase (molecular diffusion, resistance to mass transfer, unevenness of the flow pattern, etc) ; all of these terms are proportional to uJIg-’ and therefore are constant all along the column. According to Littlewood,6 H , is given by
(1) A. V . Kiselev, Gas Chromatog., Proc. S y m p . , 5th, Brighton, 1964, 238 (1965). (2) R. L. Gale and R. A. Beebe, J . Phys. Chem., 68, 555 (1964). (3) R. D. Oldenkamp and G. Houghton, ibid., 67, 597 (1963). (4) C. G, Scott. Gas Chromatog., Proc. S y m p . , 4th, Hamburg, 1962, 36 (1963). (5) J. C. Giddings, “Chromatography,” E. Heftmann, Ed., Reinhold Publishing Corp., New York, N. Y . , 1961, p 20. (6) A. B. Littlewood, A n a l . Chem., 38, 2 (1966).
Volume 7 1 , Number 12
-Vovember 1967
CLAIREVIDAL-MADJAR AND GEORGES GUIOCHON
4032
D, is measured at the outlet pressure; f and j are pres-
When benzophenone is coated on the diatomaceous supports, the result is quite different. The adsorbent has properties of type I1 and I11 adsorbents a t the same time. Specific interactions are observed with all compounds except paraffins. The ether peak has a large tailing even with a very low sample amount (less 9 (P4 - 1)(P2 - 1) than 0.1 pg). Its retention volume is 8 cm3/m2 of f = (4) adsorbent surface instead of 1cm3/m2on benzophenone8 (P3 - l)? coated graphitized carbon black, and its adsorption enthalpy is 2.5 kcal/mole more on the first packing . 3P?-1 (5) 3=2p3-1 than on the last. The difference between the two supports is much less for benzene peak; the retention volume and adsorption enthalpy are the same on both f varies only from 1 to 1.125 when inlet pressure varies supports; however, the benzene peak tails somewhat on from Po to infinity and may sometimes be neglected. the diatomaceous phase and never on the carbon black In the same conditionsj decreases from 1 to 0. phase, whatever the benzophenone ratio be. Ckin eq 2 is the term of resistance to mass transfer All of these results show that the surface of the adin the fixed phase and is known as the kinetic mass sorbent obtained by coating benzophenone on diatomatransfer term. This term has been related by Gidceous supports is heterogeneous, as could be expected dings to the average desorption times8 from the difficulties to coat an organic solid compound The main purpose of our work is to prepare new on a solid surface. The surface of the adsorbent obspecific adsorbents for gas chromatography from solid tained by coating benzophenone or anthraquinone on organic compounds. Hen-ever, crystals of organic graphitized carbon black is also heterogeneous,lo alcompounds have generally no mechanical stability and though the influence of the heterogeneity is much less have a very low specific surface; it is therefore necessary important for practical purposes. to disperse them on a solid support. Several solid We have studied the variations of the kinetic mass supports can be used. Our work originated from Scott's experiments on benzophenone-coated f i r e b r i ~ k . ~ transfer term of benzene and cyclohexane, and we discuss here the relations between this coefficient and the Excellent efficiencies can be obtained for alkanes desorption rate constant of these two compounds. when using this phase under the melting point of benzophenone. Unfortunately, the efficiency of the Experimental Section same column for polar compounds and even benzene The apparatus was made in our laboratory. The is quite poor and, especially with this last compound, columns can be thermostated at any temperature bevaries largely with experimental condition^.^ This 20 and f90" at & 0.1", with a water or a water tween observation leads us to make a more detailed study of and glycol bath. The inlet pressure of the column is the kinetic mass transfer term. regulated with a Negretti and Zambra valve. The I n a previous paperg we have discussed the properties flame ionization detector is of a design described by of the adsorbents obtained by coating benzophenone Halasz and Schreyer" with a grounded platinum burner on graphitized carbon black, crushed firebrick CZ2, and a platinum cage electrode. A splitting system12 and chromosorb W. Graphitized carbon black is a allows reproducible injection of very small samples well-known nonspecific adsorbent with a very homoin the column. geneous surface.' When benzophenone is coated on A splitting ratio of 1: 1000 is used for liquid samples this support, a new adsorbent is obtained which has and a ratio of 1:lO for methane. The other part of all the properties of an adsorbent of type I11 of Kisethe sample is discarded to the atmosphere. The lev's classification' as expected; nonspecific adsorption internal volume of the injector is 0.3 cm3; since it is is observed for saturated hydrocarbons, benzene, and ether' We'' for Other molecules with * bonds and (7) J. C.Giddings and P. D. Schettler, Anal. Chem., 36, 1483 (1964). unshared electron pairs. The adsorption enthalpy of (8) c. Giddings, ibid.,36, 1170 (1964). these molecules is lower than or near their vaporization (9) c. vid&Madjar and G. Guiochon, B U Z Z . sot. C h i n . France, 1096 enthalpy. Nolecules with acidic hydrogen, on the (1966). 5fOW-C. Vidal-Madjar and G. Guiochon, Separation Sci., 2, 155 contrary, such as alcohols and amines, undergo spe(IYO,). cific interaction With this they have a much (11) I. Halasa and G. Schreyer, Chem. Ingr-Tech., 32, 675 (1960). higher and their peaks (12) H.Bruderreck, W.Schneider, and I. Halasz, Advan. Chromatog., badly. 91 (1967); J . Gas Chromatog., 5, 217 (1967). sure correctmionfactors which allow for the influence of the zone expansion during its progression along the column.7 This results from the carrier gas decompression. f and j are given by the relations
J,
The Journal of Physical Chemistry
DESORPTION TIMEOF CYCLOHEXANE AND BENZENE ON A NONUNIFORM SURFACE
upstream to the splitter, its contribution to the apparatus dead volume is divided by the splitting ratio. The detector volume is 10 pl. These contributions are negligible compared to the column gas holdup of 5 cma. Columns were made with copper tubing of 2-mm i.d. and 2-m length. The sieved firebrick Cn (125160 p ) is acid-washed. The benzophenone is dissolved in acetone, the liquid is mixed up with firebrick, and the solvent is removed a t a temperature above the melting point of benzophenone (49"). The amount of the benzophenone deposited on the support is given as a percentage of the total weight of packing. The amount of solute injected into the column is about 0.1 bg, except when the influence of a large load is studied. The outlet linear velocity of the carrier gas is obtained from the retention time, t,, of an unretained component multiplied by j for the pressure correction
4033
where A(R/j)and Ao;Og/j)are, respectively, the differences between the values measured or interpolated for R / j on the two curves in Figure 1 and for j D g / jon the two curves in Figure 2 at the same value of 2. D, is the diffusion coefficient of the solute in the gas phase. It has been calculated according to the Chapman-Fnskog equation.la At 20°, D, is 0.073 and
t
r'
0.15
a'
5 0.10 IQ 0.05
Methane, which is not adsorbed by either the diatomaceous support or the benzophenone, is injected into the column at the same time as the solutes to be studied; so for each experimental determination of the plate height equation the outlet linear velocity is known with accuracy. The kinetio mass transfer term, c k , has been calculated as indicated by Giddings and Scbettler.' Two series of measurements of H at various values of the carrier gas velocity are carried out using two different carrier gases, hydrogen and argon. Equation 2 may be rearranged to
0
n/f
400
000
800
z , om-1.
Figure 1. Determination of the coefficients of the plate height equation for benzeng a t -9". Column (2 m) pgcked with 3% benzophenone on firebrick. Plot of R/f us. x : I, hydrogen; 11, argon.
0.30
g 0.20 As pointed out earlier, H , depends only on x = UO/D,. j/f is a function of uo as well as H / f . If the and jD,/f are plotted vs. experimental values of x = uo/Dg,for the two series of measurements, as was done in Figures 1 and 2, we have for a given valug of x
200
P,
1
I\I \ 0
200
000
400
800
z, om-1.
):(
2
=
H,(s)
+ Ckxt?)
(7")
where subscripts 1and 2 relate to the values obtained with hydrogen and argon as carrier gas, respectively. In these two equations x and H,(x) are fhe same. Therefore
Figure 2. Determination of the coefficients of the plate height equation for benzene a t -9". Column (2 m) packed with 3% benzophenone on firebrick. Plot of jD,/f v8. 2: I, hydrogen; 11, argon. ~~~
~
~~
~~
(13) J. 0.Hirschfelder, C. F. Curtiss, and R. B. Bird, "Molecular Theory of Gases and Liquids," John Wiley and Sons, Inc., New York, N. Y.,1964,p 639.
Volume 71,Number 1% November 1967
CLAIRE VIDAL-MADJAR AND GEORGES GUIOCHON
4034
0.34 cm2 sec-l for cyclohexane in argon and hydrogen, respectively, and 0.077 and 0.40 cm2 sec-l for benzene. The c k term of benzene at -9" is thus obtained from the curves given in Figures 1 and 2. The mean of ten values of C k obtained for x = 100, 200, . . . , lo00 cm-l is 0.60 msec, and the standard deviation is 0.02 msec. To measure c k with accuracy, it is necessary to work at great linear velocities where H , is well represented by eq 3. In the experiments discussed here the numerical values of the constants are a = 0.24, d, = 140 p , and y = 0.75. Equation 3 can also be written to compare the performances obtained with different carrier gases 27
H, = X
x + C,D,X + 1 +K ad,x
factor which characterizes the contribution of the axial diffusion, as suggested in the literature for packed columns.6 It has not been experimentally determined, which may introduce a small systematic error only in the lower velocity range. Least-square fit analysis of the experimental data obtained for cyclohexane and for benzene at z = 180 and at all temperatures studied give in each case the same numerical values: C,D, = 7 X cm2 and K = 40 X cm2. This result is a confirmation of the validity of eq 2, and a t the same time it indicates that the large dift
(9)
where C,D, is independent of the nature of the carrier gas; it is well known that the resistance to mass transfer in the gas phase is inversely proportional to the diffusion ~oefficient.~K and C, have been experimentally determined from a plot of [ ( H g / x )- (27/z2) 3 (1 ad,x) vs. x, which according to the theory should be a straight line that intercepts the x = 0 axis a t K C,D,. The slope of this straight line should be C,Dpd, = 3.36 X 10-3C,D, (Figure 3). The experimental points are in excellent agreement with this theoretical statement; the points corresponding to the experiments made with the two carrier gases are on a common straight line at high linear velocities ( x = 180). No data are shown, Figure 3, in the low velocity range where molecular diffusion in the gas phase is dominant. A value of 0.75 has been assumed for the tortuosity
+
0.15
a 0.10 I$
0.06
+
i
0.8
X
1
-
~~~
0
200
600
400
800
2,cm-1.
Figure 4. Determination of the kinetic mass transfer term of the plate height equation for benzene at 20" (same column as for Figures 1 and 2). Plot of i?/f vs. x: I, hydrogen; 11, argon.
0.16
0.10 o f
-
.= 0.4
A
t
X
0.05
-'
0.2 i
5 5 -
1
c
1
0
200
600
400 2.
cm-1.
Figure 3. Determination of the coefficients of the plate height equation for benzene. Plot of [(El&) - (27/x2)](l a d g ) us. x : I, hydrogen; 11, argon. Same conditions as for Figures 1 and 2.
+
The Journal of Phyeical Chemistry
0
200
400
600
800
2,cm-1.
800
Figure 5. Determination of the kinetic mass transfer term of the plate height equation for cyclohexane a t 20 and -9" (same column a8 for Figures 1 and 2). Plot of R/f us. x: I, 20" hydrogen; 11, 20" argon; 111, -9" hydrogen; IV, -9" argon.
DESORPTION TIMEOF CYCLOHEXANE AND BENZENE ON A NONUNIFORM SURFACE
4035
Table I : Kinetic Mass Transfer Term, Experimental Time of Desorption, and Calculated Value for a Perfectly Uniform Surface, Heterogeneity Factor, and Difference in the Adsorbent Energy of the Active Sites
-CyclohexaneT,OK R ck td
(exptl), msec (exptl), msec
i i
ido
cy
= 1
s
x IO5, msec x 10-4
AHl, koa1 mole-' x IO6, msec = 0 . 1 s x 10-4 AHl, kcal mole-' tdo
a
293 0.36
