Adsorption of chlorobenzene and benzene on γ-Al2O3

Article abstract of DOI:10.1023/A:1009573017700

Adsorption of chlorobenzene and benzene on γ-Al₂O₃ was investigated in the 413-572 K temperature region at an adsorbate partial pressure ranging from 2 to 1000 Pa. The adsorption isotherms were measured and the isosteric heats and th

Full text of DOI:10.1023/A:1009573017700

68
Russian Chemical Bulletin, International Edition, Vol. 50, No. 1, pp. 68—72, January, 2001
Adsorption of chlorobenzene and benzene on γ-Al2O3
L. D. Asnin,« A. A. Fedorov, and Yu. S. Chekryshkin
Institute of Technical Chemistry Ural Branch of the Russian Academy of Sciences,
13 ul. Lenina, 614000 Perm, Russian Federation.
Fax: +7 (342 2) 12 4375. E-mail: cheminst@mpm.ru
Adsorption of chlorobenzene and benzene on γ-Al2O3 was investigated in the 413—572 K
temperature region at an adsorbate partial pressure ranging from 2 to 1000 Pa. The adsorption
isotherms were measured and the isosteric heats and the entropy characteristics of adsorption
were determined. The experimentally found and theoretically calculated entropy changes upon
adsorption were compared. The mobility of the molecules of both adsorbates in the adsorption
layer was limited with respect to that predicted by the ideal two-dimensional gas model. The
mechanism of adsorption of benzene and chlorobenzene is discussed.
Key words: adsorption, thermodynamics of adsorption, alumina, chlorobenzene, benzene.
Calcination of boehmite at 723 Ê for 5 h gave γ-Al2O3. The
Study of adsorption of chlorobenzene (CB) on
phase composition of the products was checked at each step of
the synthesis by X-ray diffraction powder analysis on a DRON-2
diffractometer. The specific surface area of alumina, determined
γ-Al2O3 is important regarding the development of an
adsorption-catalytic method for the utilization of CB
contained in gas effluents. Previously, adsorption iso-
therms in the 900—23600 Pa range of partial pressures
have been measured.1 It was of interest to measure the
adsorption isotherm of CB on γ-Al2O3 for lower partial
pressures and to study the thermodynamics of this
process.
Some information about the mechanism of adsorp-
tion of CB on γ-Al2O3 can be gained from comparison
of thermodynamic characteristics of the adsorption equi-
librium of CB and benzene.
Determination of the heat of adsorption2,3 and ad-
sorption isotherms4 of benzene on Al2O3 is documented.
However, in none of these studies was γ-modification of
the oxide used, although the adsorption properties of
alumina depend substantially on the crystal form.5 There-
fore in this work, we studied the thermodynamics of
adsorption of benzene on γ-Al2O3.
–1
from low-temperature adsorption of nitrogen, was 160 m2 g
and the content of structural water corresponded to the formula
Al2O3•0.2H2O.
Adsorption isotherms were determined by chromatography6
on a Tsvet-500 chromatograph with a flame ionization detector.
Helium dried by commercial alumina and ÑaA zeolite was used
–1
as the carrier gas. The rate of the carrier gas was 30 mL min
.
The 0.2—0.315 mm fraction of γ-Al2O3 was used in the investi-
gations. The stainless-steel column (270½4 mm) was condi-
tioned at 573 K for 6—8 h prior to experiments. The weighed
portion of γ-Al2O3 in the column was 0.803 g.
Benzene (chemically pure grade) and CB were additionally
distilled and stored in tightly closed vessels over freshly calcined
NaA zeolite. Adsorbate samples were introduced into the col-
umn as a vapor through a heated dispensing cock. The gas—vapor
mixture was prepared by saturating helium with the vapor of the
compound in a saturator maintained at a constant temperature.
The detector was calibrated against neat liquids.
Adsorption isotherms of CB were determined in the tem-
perature range of 463—572 Ê, those of benzene, in the
413—473 Ê range. Variation of the carrier gas flow rate from 20
to 40 mL min–1 resulted in insignificant changes in the position
of the isotherm, i.e., the diffusion and kinetic broadening of the
chromatographic peak could be neglected under the experimen-
tal conditions.
The relative error of determination of the adsorbate partial
pressure (ð) and the excessive adsorption (Γ) was ∼7% and
remained virtually constant over the whole ranges of ð and Γ
studied. About half of this value is due to systematic errors.
The isosteric heat of adsorption (qst) was calculated from
the lnp—1/Ò plot. The absolute error of the calculation of lnp
was equal to the relative error of determination of ð. As noted
above, the latter value does not depend on ð; therefore, the
presence of the systematic error gives straight lines parallel to
the actual isotherm and having the same slope. Hence, the
systematic errors of determination of the adsorbate partial pres-
sure did not influence the accuracy of calculation of qst. This
value was subject only to random errors and, with a confidence
Experimental
Alumina was prepared by the scheme bayerite→boehm-
ite→γ-Al2O3.5 To prepare bayerite, a stoichiometric amount of
a 14% solution of NH3 (analytically pure grade) was added with
stirring at 303 Ê to a 0.5 Ì solution of AlCl3 (analytically pure
grade) and then the ðH of the suspension was brought to
10—11. The mixture was stirred at this temperature for 1 h,
–
filtered, washed on the filter to completely remove Ñl ions,
and dried at 363 Ê. The xerogel was suspended in distilled water
and the ðH of the suspension was brought to 11 by adding a
concentrated solution of NH3. After aging for 10 days, the
precipitate was filtered off, washed several times on the filter
with hot water, and dried at 383 Ê. The bayerite thus synthe-
sized was treated with a 20% solution of NH3 in an autoclave
for 10 h at 473 Ê to give boehmite. The precipitate of boehmite
was washed on the filter to a neutral pH and dried at 383 Ê.
Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 65—69, January, 2001.
1066-5285/00/5001-0068 $25.00 © 2001 Plenum Publishing Corporation

Adsorption of chlorobenzene and benzene on γ-Al2O3 Russ.Chem.Bull., Int.Ed., Vol. 50, No. 1, January, 2001
69
–1
probability of 0.95, it was equal to ∼3 and 4 kJ mol for CB
and benzene, respectively.
It is known that qst can be determined from the
equation
Based on the data on the accuracy of determination of ð, Γ,
and qst and using the rule for calculation of the inaccuracy for a
(logp)Γ = –qst/(RT) + const,
(1)
value determined indirectly,7 the errors of determination of the
–
differential entropy of an adsorbed substance (S s) and the
–
which does not take into account the temperature de-
pendence of qst, or from an equation that does take into
account this dependence in the first approximation8
corresponding standard value (S s°) were estimated to be 6.5,
and those for the change in the differential entropy upon
–
adsorption (∆S s) were found to be 6 J mol
K
.
–1
–1
$
$
qst (T ) + ∆CpT
RT
∆Cp
.
lnT + const′
(2)
(lnp)Γ = −
−
Results and Discussion
R
^
Here T is the simple average temperature over the
The resulting adsorption isotherms of benzene and
CB (Fig. 1) are well described by the Freundlich adsorp-
tion isotherm (FI), Γ = Ñð1/n, where Γ is the excessive
adsorption, mol g–1; ð is the partial pressure of the
adsorbate, Pa; and C and n are constants; the correlation
coefficient was r 2 > 0.998 in all cases.
As the temperature increases, the coefficient n, char-
acterizing the "degree of non-linearity" of the isotherm,
decreases approaching unity. For benzene, the depen-
dence of n on Ò in the temperature range studied can be
described by the function n(T ) = 560/T and for CB it
corresponds to the equation n(T ) = 0.345 + 394/T.
temperature range studied, which is equal to 508 and
439 Ê for CB and benzene, respectively; ∆Cp
=
Cp,ads – Cp,g, where ∆Ñð ≠ f (T ); Cp,ads and Cð,g are the
heat capacities of the adsorbate in the adsorbed and gas
phases, respectively. The subscript Γ means that this
isostere equation refers to a definite Γ value. In addition
to qst, Eq. (2) allows one to calculate ∆Ñð by means of
the Markwardt method.9
As shown by statistical analysis, the accuracy of
experimental data on the adsorption of CB permits the
calculation of qst from Eq. (2); the qst values calculated
from Eqs. (1) and (2) differ by no more than
0.5 kJ mol–1, which is much smaller than the error
associated with actual regression. It proved impossible to
process the data on benzene adsorption using Eq. (2).
The dependences of qst on Γ are shown in Fig. 2.
The ∆Ñð value for CB averaged over the range of
–1
Õ107/mol g
a
4
2
30
20
10
3
1
–1
–1
5
adsorptions studied amounts to 110±60 J mol
K
.
This value was used to convert the data on CB adsorp-
tion obtained for 508 Ê to 439 Ê, i.e., to the tempera-
ture for which the adsorption characteristics of benzene
were measured.
6
The heat capacity of CB in the adsorbed state is
much greater than its heat capacity in the gas phase
–1
(Cð,g(508) = 152.9 J mol
Ê
–1).10 A similar situation
was observed for adsorption of various hydrocarbons on
Silochrome11 and pentane on graphitized carbon
black (GCB).12
Since the number of degrees of freedom of molecules
upon adsorption decreases, the increase in the heat
0
200
400
600
p/Pa
Õ107/mol g
120
–1
b
8
10
–1
qst/kJ mol
7
80
11
9
70
1
65
40
60
2
3
55
0
200
400
600
800
1000
p/Pa
–1
0
5
10
15
Õ107/mol g
Fig. 1. Adsorption isotherms of chlorobenzene (a) at tempera-
tures of 463 (1), 473 (2), 493 (3), 513 (4), 533 (5), and 572 K
(6) and benzene (b) at 413 (7), 423 (8), 433 (9), 453 (10), and
473 Ê (11).
Fig. 2. Isosteric heats of adsorption vs. excessive adsorption for
chlorobenzene at 439 (1) and 508 Ê (2) and benzene at
439 Ê (3).

70
Russ.Chem.Bull., Int.Ed., Vol. 50, No. 1, January, 2001
Asnin et al.
capacity of a substance in the adsorbed phase with
respect to that in the gas phase can be due to the
interaction between the adsorbed molecules and the
adsorbent surface. This interaction proves to be the
channel of the transfer of energy from the adsobate
molecule to the portion of the surface in the close
vicinity of the site of adsorption. Thus, some part of the
surface below the adsorbed species is involved in the
energy distribution over degrees of freedom; it is this
process that determines the increases the heat capac-
dependences, available from the literature.10,16 The value
ð0 = 101325 Pa was taken as the standard pressure. The
known relation
~
^
~
^
^
Sg(T,Γ) = Sg°(T ) – Rln[p (T,Γ)/p0],
^
where p(T,Γ) is the equilibrium partial pressure of the
^
adsorbate at the temperature T and adsorption Γ, makes
it possible to pass from the standard entropy to equilib-
–
–
rium entropy. The calculated values ∆S s and Ss for CB
and benzene are listed in Tables 1 and 2. Table 2 also
presents the entropy characteristics of CB converted
to 439 Ê.
ity Cp,ads
.
It has been shown13 that the dependence of qst on Γ
for the FI obeys the equation
It has been shown previously13 that, if the adsorption
isotherm is described by the Freundlich equation, the
differential entropy can be calculated from the formula
qst = q0 + RT 2n´(T)lnΓ,
(3)
where n´(T ) = dn´(T )/dT, q0 is a constant. According
to regression analysis, the variation of qst with Γ for both
compounds is described adequately by a logarithmic
equation and the regression pre-logarithmic factor coin-
cides almost exactly with that calculated from Eq. (3) for
CB (deviation 1.6%) and differs only slightly in the case
of benzene (8%).
–
–
^
S s = S s°(T ) – R[n(T ) + Tn´(T )]lnΓ.
(4)
It was proposed to use this expression as one of the
criteria that allow one to find out whether experimental
results obey the Freundlich equation. Yet another crite-
rion is the correspondence of the variation of qst vs. Γ to
Eq. (3). As can be seen from the foregoing, this criterion
is fulfilled.
The rather great qst values for CB and benzene point
to the possibility of chemisorption.
If the dependence of the entropy of the adsorption
phase on the amount adsorbed actually does satisfy
The heats of adsorption of CB are somewhat higher
than those for benzene (see Fig. 2), which is in line with
a higher polarity of CB (the dipole moment of the CB
molecule is 1.7 D). The small difference between the
heats may be due to the fact that the introduction of the
heteroatom gives rise to two opposite effects. On the one
hand, the adsorption interaction is enhanced due to the
higher dipole moment of the CB molecule, i.e., to
stronger electrostatic interaction with the potential field
of the adsorbent surface. In addition, the influence of
the proper heteroatom is also possible, for example, this
can give rise to the stronger two-center adsorption simi-
lar to the adsorption of CB on the hydroxylated surface
of rutile, described previously,14 or the interaction of the
Cl atom with the surface aluminum ions. On the other
hand, the negative inductive effect of the Cl atom
decreases the electron density on the aromatic ring and,
hence, makes the hydrogen bond between the surface
OH groups and the benzene ring π-electrons weaker
than that in the case of benzene. A similar effect has also
been found for the hydroxylated surface of rutile14
and ZnO.15
Table 1. Entropy characteristics of chlorobenzene adsorption at
508 Ê for various values of excessive adsorption (Γ)
–
–
–
–
Γ•107
–∆S s
–∆S theor
S s
S s°
–1
–1
–1
/mol g
J mol
K
3
6
9
12
15
18
21
24
127.4
122.9
120.3
118.6
117.2
116.0
115.0
114.2
97.5
96.7
96.9
95.6
96.2
95.3
95.6
96.1
322.7
320.7
320.1
318.1
318.2
317.0
317.0
317.2
279.6
279.5
280.1
278.9
279.7
279.0
279.4
280.0
Table 2. Entropy characteristics of benzene and chlorobenzene
adsorption at 439 Ê for various values of excessive adsorption (Γ)
Γ•107
/mol g
Benzene
Chlorobenzene
–1
–
–
–
–
–
–
–∆S s –∆S theor S s
–∆S s –∆S theor S s
Knowing qst, we can calculate the change in entropy
upon adsorption8
–1
–1
J mol
K
–
–
~
^
∆S s = S s – Sg = –qst/T,
3
6
9
12
15
18
21
24
40
80
149.0
141.1
136.5
133.2
130.6
128.5
126.8
125.2
119.4
111.4
100.7 239.6
162.3
116.7 287.8
115.3 284.4
115.1 283.0
113.6 280.5
114.0 280.3
112.9 278.7
113.0 278.3
113.4 278.3
99.8 240.2
98.2 240.5
97.5 240.8
97.0 240.9
96.6 241.1
96.2 241.3
95.9 241.4
94.8 241.8
93.2 242.4
158.5
156.3
154.9
153.7
152.7
151.9
151.2
—
~
where Sg is the entropy of the adsorbate in the gas
phase.* From the known Sg, the Ss value was found. All
–
~
the characteristics described above refer to the tempera-
^
~
^
ture T. The Sg°(T ) dependences were calculated from
~
the standard entropies Sg(298) and using the Ñp,g(T )
—
—
—
—
* The "bar" and "tilde" signs imply differential and molar aver-
age values, respectively.
—

Adsorption of chlorobenzene and benzene on γ-Al2O3 Russ.Chem.Bull., Int.Ed., Vol. 50, No. 1, January, 2001
71
–
Eq. (4), the Ss°(T ) value would not vary with Γ. The
We assume that the vibrational and rotational degrees of
freedom are retained intact upon adsorption. The de-
crease in entropy is represented by the relation21
–
^
S s°(T ) value for CB is really constant; the deviations are
random rather than regular and they are much smaller
than the above indicated inaccuracy (see Table 1). In the
case of benzene, the pre-logarithmic factor in Eq. (4)
~
–∆Stheor = Rln(Γs/c) + R[0.5 + ln(2πmkT/h2)0.5],
–
–
becomes equal to zero, and the equality Ss = Ss° is
where ñ is the adsorbate concentration in the equilibrium
gas phase, m is the mass of the adsorbate molecule, h is
the Planck constant, k is the Boltzmann constant, and Γs
is excessive adsorption per unit surface area of the
adsorbent.
expected to hold. In reality, insignificant monotonic
–
increase in entropy is observed. The change in the S s
value over the whole range studied was 2.6 J mol–1 K
,
–1
which is within the limits of experimental error. Hence,
–
^
S s°(T ) can formally be assumed to be constant and the
~
The ∆Stheor value is molar average. To pass to the
–
average S s value, equal to 241 J mol
K
—1, can be
—1
differential value, one should use the equation13
taken for benzene.
–
~
S s = Ss – R[n(T) + Tn´(T)],
Previously, it has been shown17 that the thermal
–
entropy (S therm) of several hydrocarbons adsorbed on a
which relates the molar average and differential entro-
pies in the case where the adsorption isotherm is de-
scribed by the Freundlich equation. Then
nonpolar homogeneous adsorbent (GTB) coincides with
their entropy in the liquid state (S °(liq)). It is of interest
~
to find out whether this regularity holds for adsorption
on alumina, which is a polar nonhomogeneous sorbent.
Proceeding from Eq. (4) and using the above-de-
scribed method,18 we can derive the following relation:
–
~
∆S theor = ∆S theor – R[n(T) + Tn´(T)].
–
The resulting ∆Stheor values for both benzene and CB
–
are smaller in magnitude than the ∆S s values determined
–
–
^
^
^
S therm = S s°(T ) – R[n(T ) + Tn´(T )]lnΓm,
experimentally (see Tables 1 and 2). Thus it follows that
the mobility of particles in the real adsorption layer is
restricted with respect to that predicted by the ideal two-
dimensional gas model.
where Γm is the adsorbed amount corresponding to a
monolayer coverage. It is fairly difficult to determine
unambiguously the Γm values19; therefore, the formal
procedure can be used.17 The molecular area of CB,
needed to calculate the monolayer adsorption, has been
assumed to be 0.465 nm2 (see Ref. 15). For benzene,
The loss of mobility with increase in the Γ value can
–
–
be characterized by the function D = |∆Ss| – |∆Stheor|.
Strictly speaking, the function D also reflects the change
in the adsorbent structure upon adsorption. However,
the coverages studied were low (∼0.001). If there exists
bond rigidity in the crystal lattice, it becomes obvious
that the change in the surface structure induced by
–
–
S therm = S s°; therefore, calculation of Γm was not
–
required. The Stherm value for CB at 508 Ê is equal to
301 J mol
241 J mol
–1
K
–1, while that for benzene at 439 Ê is
K
–1. These results coincide with the entro-
–1
adsorption would involve no more than 10 —10–4% of
–5
pies of CB and benzene in the liquid state at the
the total adsorbent surface. Hence, it can be considered
corresponding temperatures calculated from thermody-
that the contribution of the change in the adsorbent
–
–1
namic data10,16,20 (300 and 232 J mol
tively).
K
–1, respec-
entropy to the ∆Ss value would be negligibly small and
interpretation of the function D in terms of the mobility
The view on the similarity of properties of substances
in the liquid and adsorption phases follows from the
Polanyi potential theory,19 which postulates enhance-
ment of the intermolecular interactions in the field of
adsorption forces and compression of the adsorption
of the adsorption layer is justified.
As the coverage of the surface increases, the D value
decreases (Fig. 3). This is due to the fact that the
molecules adsorbed first on the most active sites of the
phase to a liquid-like state.
–1
–1
D/J mol
K
–
Yet another interpretation of the fact that the S therm
~
and S °(liq) coincide can be proposed without resorting
45
to the potential theory. Thermal entropy characterizes
the state of the adsorbate in the adsorption phase in
which its mobility is limited by the surface and by the
potential field of the adsorbent. Since the mobility of a
molecule in liquid is restricted by neighboring mol-
ecules, the state of a substance in the adsorption field is
close to the state of the liquid phase.
1
35
25
2
Some information concerning the mobility of mol-
3
ecules in the adsorption layer can be gained from com-
–
parison of the ∆Ss values calculated theoretically and
–1
found experimentally.21 Let us consider the simplest
model of an ideal two-dimensional gas in which one
degree of freedom of the forward motion has been lost.
0
5
10
15
Õ107/mol g
Fig. 3. The function D vs. excessive adsorption Γ for chloroben-
zene at 439 (1) and 508 K (3) and benzene at 439 Ê (2).

72
Russ.Chem.Bull., Int.Ed., Vol. 50, No. 1, January, 2001
Asnin et al.
Optimization in Chemistry and Chemical Technology], Vyssh.
shkola, Moscow, 1978, p. 31 (in Russian).
8. A. A. Lopatkin, Teoreticheskie osnovy fizicheskoi adsorbtsii
[Theoretical Foundations of Physical Adsorption], Izd-vo
MGU, Moscow, 1983, 344 pp. (in Russian).
9. G. W. Reklaitis, A. Ravindran, K. M. Ragsdell, Engineering
Optimization. Methods and Applications, J. Wiley and Sons,
New York—London—Sydney—Toronto, 1983.
10. Kratkii spravochnik fiziko-khimicheskikh velichin [Brief Hand-
book on Physicochemical Values], Eds. K. P. Mishchenko
and A. A. Ravdel´, Khimiya, Leningrad, 1967, 182 pp. (in
Russian).
11. A. A. Lopatkin and N. K. Shoniya, Zh. Fiz. Khim., 1999, 73,
1769 [Russ. J. Phys. Chem., 1999, 73 (Engl. Transl.)].
12. T. A. Rudnitskaya and A. A. Lopatkin, Zh. Fiz. Khim., 1997,
71, 535 [Russ. J. Phys. Chem., 1997, 71 (Engl. Transl.)].
13. L. D. Asnin, A. A. Fedorov, and Yu. S. Chekryshkin, Izv.
Akad. Nauk, Ser. Khim., 2000, 178 [Russ. Chem. Bull., Int.
Ed., 2000, 49, 175].
surface are bound to the adsorbent more strongly than
molecules adsorbed at greater coverages.
At T = 439 K, the decrease in the loss of molecular
mobility of benzene with an increase in the surface
coverage is more pronounced than that in the case of
CB. This implies that various types of fixation on the
surface are available for benzene. Conversely, in the case
of CB, as the very active sites are occupied, the adsor-
bate molecules acquire approximately equal opportuni-
ties for fixing on the surface. Evidently, adsorbed ben-
zene is more sensitive to the inhomogeneity of the
alumina surface than chlorobenzene.
The authors are grateful to N. E. Skryabina (Perm
State University) and R. M. Yakushev for assistance in
X-ray diffraction measurements and determination of
the specific surface area.
14. M. Nagao and Y. Suda, Langmuir, 1989, 5, 42.
15. M. Nagao and K. Matsuoka, J. Chem. Soc., Faraday Trans.
1, 1988, 84, 1277.
References
16. Kratkii spravochnik po khimii [Brief Handbook on Chemistry],
Nauk. dumka, Kiev, 1965, 836 pp. (in Russian).
17. A. A. Lopatkin and R. S. Petrova, Zh. Fiz. Khim., 1994, 68,
675 [Russ. J. Phys. Chem., 1994, 68 (Engl. Transl.)].
18. A. A. Lopatkin, Ros. Khim. Zhurn. [Russ. Chem. J.], 1998,
91 (in Russian).
1. A. A. Fedorov, Yu. S. Chekryshkin, and N. G. Shadrina,
Zh. Prikl. Khim., 1998, 71, 1828 [Russ. J. Appl. Chem., 1998,
71 (Engl. Transl.)].
2. P. E. Eberly, J. Phys. Chem., 1961, 65, 68.
3. A. A. Kubasov, I. V. Smirnova, and K. V. Topchieva, Kinet.
Katal., 1964, 5, 520 [Kinet. Catal., 1964, 5 (Engl. Transl.)].
4. E. Cremer and H. Huber, Angew. Chem., 1961, 73, 461.
5. B. C. Lippens and J. J. Steggerda, Physical and Chemical
Aspects of Adsorbents and Catalysts, Ed. B. G. Linsen, Aca-
demic Press, London—New York, 1970, p. 171.
6. A. V. Kiselev and Ya. I. Yashin, Gazo-adsorbtsionnaya
khromatografiya [Gas Solid Chromatography], Nauka, Mos-
cow, 1967, 256 pp. (in Russian).
19. S. J. Gregg and K. S. W. Sing, Adsorption, Surface Area and
Porosity, Academic Press, London—New York, 1982.
20. D. R. Stull, E. F. Westrum, and G. C. Sinke, The Chemical
Thermodynamics of Organic Compounds, J. Wiley and Sons,
New York—London—Sydney—Toronto, 1969.
21. A. A. Lopatkin, Zh. Fiz. Khim., 1997, 71, 916 [Russ. J. Phys.
Chem., 1997, 71 (Engl. Transl.)].
7. S. L. Akhnazarova and V. V. Kafarov, Optimizatsiya
eksperimenta v khimii i khimicheskoi tekhnologii [Experiment
Received February 18, 2000;
in revised form July 6, 2000