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Isotherm equation for water vapor adsorption by microporous carbonaceous adsorbents
Letters to the Editor
402
Isotherm equation for water vapor adsorption by microporous carbonaceous adsorbents (Received 19 March 1981) The qualitative difference in adsorption of the vapors of water and organic substances results from adsorption interactions of a different nature. In the case of organic substances adsorption is due to dispersion forces. Hydrogen bonds play the deteimining role for water adsorption. The development of concepts of water adsorption by nonporous and microporous carbonaceous adsorbents is described in the generalizing paper[l]. The main cause for water adsorption are the primary adsorption centres-oxygen surface compounds of a car~naceous adsorbent. They are capable of adding on water molecules by means of hydrogen bonds. Each water molecule adsorbed is a secondary adsorption centre, which is also capable of forming hydrogen bonds with other water molecules. If a0 is the number of primary adsorption centres and a is the adsorption value for the relative pressure h = p/p,, then the dynamic equilibrium condition will be expressed by K&,+@)(l
-ku)h
=K,ff.
a,,= A&
(11)
k = A&c.
(12)
By way of example , Fig. I gives the plots of water adsorption isotherms in a linear form for two active carbon samples according to Andreyeva’s experiments. The plot of Fig. 2 depicts the adsorption isotherms, The solid lines fit the calculated points (AC? no = 0.411mmol~g, c = 2.51, a, = 17.91mmoi/g; AC9 ~0= 0.076mmol/g, c = 1.54, a, = 27.98mmol~g: the experimen~l points are denoted by different symbols. The water vapor adsorption isotherm equation under review is applicable practically over the entire investigated range of equilibrium relative pressures from 0.1 to I.
(1)
The 1.h.s. of eqn (1) expresses the adsorption rate, which is proportional to the total number of adsorption centres uO+a and to the relative pressure h. The term 1- ka takes into account the decrease in the number of acting adsorption centres with an increase in filling. The desorption rate is proportional only to the adsorption value a. The parameter k is determined from the condition a = a, at h = I where a, is the limiting value of vapor adsorption. Denoting the kinetic constant ratio c = Q/K~, we obtain the expression (2) for the parameter k: k = I/a, - l/[c(ao+ a,)].
(2)
Fig. 1. AC7 0, AC9 q.
As a result the isotherm equation for water vapor adsorption on active carbon takes the form h = ai[cfao t n)(l - kiJ)l.
(31
This equation contains three parameters ao, c and 4, (or k), which can be determined from a single adsorption isotherm. According to Polyakov and Andreyeva eqn (3) can be written in L the form of a quadratic trinomial a/h = A, f A2a - Apa
(4)
where A, = cao; A2 = c(1 - o,k);
A, = ck.
(5)
To obtain a linear equation we introduce the function 2 = (alh - Q~hi)~(U - ~i) Then, on the basis of eqns (4) and (51,we Z
=
(61
get
(A, - A,u,) - A,a = & - Ala.
(71
The slope of a line constructed from expe~mental data is equal to the coefficient A* The other coefficients are determined from eqns (8) and (9) A2=5tAlai Al = ailhi - Azai + A,o,Z
(8) (9)
where Z. is the intercept made by the line on the ordinate. Using the factors At, A2 and A3 it is easy to calculate the parameters of the adsorption isotherm by eqns ~10~12). c = 0.5(A2+ .\/(Az2+4A,A3))
(W
Fii. 2. AC7 P, AC9 0.
403
Letters to the Editor In order to calculate the adsorption values from given relative pressures at known parameters aO, c and k we transform (3) into a quadratic equation a2 - [(I - a,k)/k - I/(ckh)]a If we denote the bracketed solution will be a =X
expression
- so/k = 0.
Ins&&e of Physical Chemistry USSR Academy of Sciences 117312 Moscow, U.S.S.R.
(16) M. M. DUBININ V. V. SERPINSKY
(14)
and only the plus sign in front of the radical has a physical meaning. For microporous carbonaceous adsorbents not subjected to special oxidation usually a0 < a,, and one can assume a0 t a, = a.. Then we obtain bv (12) k = (c - I)/(ca,)
h=al[c(o,+n)(l-~.9)].
(13)
of eqn (13), by 2x its
t d(X* t so/k)
and the adsorption isotherm equation becomes:
REFERENCES I. M. M. Dubinin, Carbon 18,355 (1980). 2. M. M. Dubinin, E. D. Zaverina and V. V. Serpinsky, J. Chem. Sot. (London), 1760 (1955).
(15)
OW-f223/81/05MO3-UZSOZ.~/0 @ 1981PergamonPressLtd.
Cahx~ Vol. 19. No. 5. pp. 403404, 1981 Printed in Great Britain.
High intensity and high energy carbon beam source (Received 6 March
The importance of atomic and molecular carbon species has been recognized in many fields for some time. In recent years, however, there has been increased interest in obtaining reaction rate data and heats of formation for the primary individual vapor components, i.e. C,, CZ, and CZ. This information is necessary in the further characterization of combustion processes and the vaporization of graphite. Various methods have been used for the production of atomic and molecular carbon vapors[l-71. These include photolysis of carbon suboxide[l], nuclear decay[2], high temperature ovens[3], microwave discharges[4], carbon arcs[5] and “front surface” laser vaporization[6,7]. Laser vaporization studies of carbon thus far have been a “front surface” phenomenon. (The laser beam is directed toward the front s&face of a thick graphite target.) Generally, the angle between the detector and the laser beam is -45 degrees. Carbon species up to C~C have been detected in this manner with the species Cl, CZ, and Cj being predominantly formed. It has been found that the ratios of the first three polymeric forms of carbon produced with front surface laser vaporization using laser pulsewidths of -4OOnsec agree with thermodynamic equilibrium results, such as those obtained using oven sources. In this letter we report the results of laser vaporization of thin graphite films. The films are prepared by vacuum deposition of graphite vapor on glass microscopic slides. The laser beam is always brought through the transparent glass slide and is incident on the side of the film in contact with the glass substrate (real surface vaporization). An important fact of the real surface vaporization with a short, Q-switched laser pulse is that the vapor cloud does not reach thermodynamic equilibrium[E]. This non-equilibrium feature is extremely desirable in the production of carbon sources because the concentration ratios of various carbon species become variable and controllable as a function of the degree of non-equilibrium of the source cloud. This carbon vapor source, therefore, offers great potential for the study of gas phase chemical kinetics and energy dependent reactive cross sections of individual carbon species. Our preliminary results do, indeed, show the nonequilibrium feature and the carbon species concentration ratios do not agree with the equilibrium data previously reported. A reasonably comprehensive description of the technique of “rear surface” laser vaporization is given elsewhere[9]. Briefly, a Q-switched ruby laser pulse (E - IJ/Pulse, FWHM - 75 nsec) is used to vaporize the graphite film deposited on transparent glass slides which are mounted inside a high vacuum chamber. The collumated laser beam is directed through a quartz window and
1981)
partially focused on the rear side of the target film by a 125 mm focal length lens. The lens-to-target distance is externally adjustable, allowing further variation in laser energy density at the target surface. A small spot of the film is rapidly released into the vapor phase by absorption of the laser radiation. The vapor cloud behaves like a high temperature gas bubble which freely expands against the substrate into a half sphere in the vacuum system. The transient non-equilibrium expansion is of an inertia dominated source type flow. Furthermore, the transition from a near continuum to free molecular flow happens so rapidly that the translational velocities of the beam particles become frozen in a very short distance downstream from the source. The fact that this distance is negligibly small compared with the distance from the detector to the target film allows the kinetic energy of the particles to be determined by the time-offlight method. Carbon beams are exacted from the vapor clouds by a series of collimated apertures which, in the present study, are situated on the laser beam axis. The experimental apparatus is shown schematically in Fig. 1. The beam detection system consists of an electron impact ionizer, quadrupole mass filter, and an electron multiplier tube. The resulting signal at the anode of the electron multiplier is amplified with a wide band operational amplifier and displayed on an oscilloscope. The stagnation temperature of the transient vapor cloud has not been measured directly. However, time-of-flight measurements of the velocity distribution in the beam allows the temperature to be determined according t3 a first order model[lO]. By analyzing the carbon time-of-flight spectrum, it is found that the distribution of energy in the carbon beams covers a range from 0.1 to IO eV. Determination of the absolute flux of the beam from the signals obtained from the mass spectrometer is a non-trivial task. However, given a measure of the total amount of material vaporized and with a knowledge of the angular distribution, it can be shown that the beam intensity is -IO*’ particles/str/sec. This intensity is at least an order of magnitude higher than what was achieved by conventional methods. For a given target film thickness, all the above mentioned beam parameters (e.g. intensity, kinetic energy and stagnation temperature) can be controlled and characterized by a single parameter, the laser energy density. Concentration measurements were performed with a ruby laser adjusted to deliver an energy density of -3.7 J/cm’ on a 0.3 pm thick graphite target. The incident angle of the laser beam was zero degrees from the target normal. Data were recorded by
402
Isotherm equation for water vapor adsorption by microporous carbonaceous adsorbents (Received 19 March 1981) The qualitative difference in adsorption of the vapors of water and organic substances results from adsorption interactions of a different nature. In the case of organic substances adsorption is due to dispersion forces. Hydrogen bonds play the deteimining role for water adsorption. The development of concepts of water adsorption by nonporous and microporous carbonaceous adsorbents is described in the generalizing paper[l]. The main cause for water adsorption are the primary adsorption centres-oxygen surface compounds of a car~naceous adsorbent. They are capable of adding on water molecules by means of hydrogen bonds. Each water molecule adsorbed is a secondary adsorption centre, which is also capable of forming hydrogen bonds with other water molecules. If a0 is the number of primary adsorption centres and a is the adsorption value for the relative pressure h = p/p,, then the dynamic equilibrium condition will be expressed by K&,+@)(l
-ku)h
=K,ff.
a,,= A&
(11)
k = A&c.
(12)
By way of example , Fig. I gives the plots of water adsorption isotherms in a linear form for two active carbon samples according to Andreyeva’s experiments. The plot of Fig. 2 depicts the adsorption isotherms, The solid lines fit the calculated points (AC? no = 0.411mmol~g, c = 2.51, a, = 17.91mmoi/g; AC9 ~0= 0.076mmol/g, c = 1.54, a, = 27.98mmol~g: the experimen~l points are denoted by different symbols. The water vapor adsorption isotherm equation under review is applicable practically over the entire investigated range of equilibrium relative pressures from 0.1 to I.
(1)
The 1.h.s. of eqn (1) expresses the adsorption rate, which is proportional to the total number of adsorption centres uO+a and to the relative pressure h. The term 1- ka takes into account the decrease in the number of acting adsorption centres with an increase in filling. The desorption rate is proportional only to the adsorption value a. The parameter k is determined from the condition a = a, at h = I where a, is the limiting value of vapor adsorption. Denoting the kinetic constant ratio c = Q/K~, we obtain the expression (2) for the parameter k: k = I/a, - l/[c(ao+ a,)].
(2)
Fig. 1. AC7 0, AC9 q.
As a result the isotherm equation for water vapor adsorption on active carbon takes the form h = ai[cfao t n)(l - kiJ)l.
(31
This equation contains three parameters ao, c and 4, (or k), which can be determined from a single adsorption isotherm. According to Polyakov and Andreyeva eqn (3) can be written in L the form of a quadratic trinomial a/h = A, f A2a - Apa
(4)
where A, = cao; A2 = c(1 - o,k);
A, = ck.
(5)
To obtain a linear equation we introduce the function 2 = (alh - Q~hi)~(U - ~i) Then, on the basis of eqns (4) and (51,we Z
=
(61
get
(A, - A,u,) - A,a = & - Ala.
(71
The slope of a line constructed from expe~mental data is equal to the coefficient A* The other coefficients are determined from eqns (8) and (9) A2=5tAlai Al = ailhi - Azai + A,o,Z
(8) (9)
where Z. is the intercept made by the line on the ordinate. Using the factors At, A2 and A3 it is easy to calculate the parameters of the adsorption isotherm by eqns ~10~12). c = 0.5(A2+ .\/(Az2+4A,A3))
(W
Fii. 2. AC7 P, AC9 0.
403
Letters to the Editor In order to calculate the adsorption values from given relative pressures at known parameters aO, c and k we transform (3) into a quadratic equation a2 - [(I - a,k)/k - I/(ckh)]a If we denote the bracketed solution will be a =X
expression
- so/k = 0.
Ins&&e of Physical Chemistry USSR Academy of Sciences 117312 Moscow, U.S.S.R.
(16) M. M. DUBININ V. V. SERPINSKY
(14)
and only the plus sign in front of the radical has a physical meaning. For microporous carbonaceous adsorbents not subjected to special oxidation usually a0 < a,, and one can assume a0 t a, = a.. Then we obtain bv (12) k = (c - I)/(ca,)
h=al[c(o,+n)(l-~.9)].
(13)
of eqn (13), by 2x its
t d(X* t so/k)
and the adsorption isotherm equation becomes:
REFERENCES I. M. M. Dubinin, Carbon 18,355 (1980). 2. M. M. Dubinin, E. D. Zaverina and V. V. Serpinsky, J. Chem. Sot. (London), 1760 (1955).
(15)
OW-f223/81/05MO3-UZSOZ.~/0 @ 1981PergamonPressLtd.
Cahx~ Vol. 19. No. 5. pp. 403404, 1981 Printed in Great Britain.
High intensity and high energy carbon beam source (Received 6 March
The importance of atomic and molecular carbon species has been recognized in many fields for some time. In recent years, however, there has been increased interest in obtaining reaction rate data and heats of formation for the primary individual vapor components, i.e. C,, CZ, and CZ. This information is necessary in the further characterization of combustion processes and the vaporization of graphite. Various methods have been used for the production of atomic and molecular carbon vapors[l-71. These include photolysis of carbon suboxide[l], nuclear decay[2], high temperature ovens[3], microwave discharges[4], carbon arcs[5] and “front surface” laser vaporization[6,7]. Laser vaporization studies of carbon thus far have been a “front surface” phenomenon. (The laser beam is directed toward the front s&face of a thick graphite target.) Generally, the angle between the detector and the laser beam is -45 degrees. Carbon species up to C~C have been detected in this manner with the species Cl, CZ, and Cj being predominantly formed. It has been found that the ratios of the first three polymeric forms of carbon produced with front surface laser vaporization using laser pulsewidths of -4OOnsec agree with thermodynamic equilibrium results, such as those obtained using oven sources. In this letter we report the results of laser vaporization of thin graphite films. The films are prepared by vacuum deposition of graphite vapor on glass microscopic slides. The laser beam is always brought through the transparent glass slide and is incident on the side of the film in contact with the glass substrate (real surface vaporization). An important fact of the real surface vaporization with a short, Q-switched laser pulse is that the vapor cloud does not reach thermodynamic equilibrium[E]. This non-equilibrium feature is extremely desirable in the production of carbon sources because the concentration ratios of various carbon species become variable and controllable as a function of the degree of non-equilibrium of the source cloud. This carbon vapor source, therefore, offers great potential for the study of gas phase chemical kinetics and energy dependent reactive cross sections of individual carbon species. Our preliminary results do, indeed, show the nonequilibrium feature and the carbon species concentration ratios do not agree with the equilibrium data previously reported. A reasonably comprehensive description of the technique of “rear surface” laser vaporization is given elsewhere[9]. Briefly, a Q-switched ruby laser pulse (E - IJ/Pulse, FWHM - 75 nsec) is used to vaporize the graphite film deposited on transparent glass slides which are mounted inside a high vacuum chamber. The collumated laser beam is directed through a quartz window and
1981)
partially focused on the rear side of the target film by a 125 mm focal length lens. The lens-to-target distance is externally adjustable, allowing further variation in laser energy density at the target surface. A small spot of the film is rapidly released into the vapor phase by absorption of the laser radiation. The vapor cloud behaves like a high temperature gas bubble which freely expands against the substrate into a half sphere in the vacuum system. The transient non-equilibrium expansion is of an inertia dominated source type flow. Furthermore, the transition from a near continuum to free molecular flow happens so rapidly that the translational velocities of the beam particles become frozen in a very short distance downstream from the source. The fact that this distance is negligibly small compared with the distance from the detector to the target film allows the kinetic energy of the particles to be determined by the time-offlight method. Carbon beams are exacted from the vapor clouds by a series of collimated apertures which, in the present study, are situated on the laser beam axis. The experimental apparatus is shown schematically in Fig. 1. The beam detection system consists of an electron impact ionizer, quadrupole mass filter, and an electron multiplier tube. The resulting signal at the anode of the electron multiplier is amplified with a wide band operational amplifier and displayed on an oscilloscope. The stagnation temperature of the transient vapor cloud has not been measured directly. However, time-of-flight measurements of the velocity distribution in the beam allows the temperature to be determined according t3 a first order model[lO]. By analyzing the carbon time-of-flight spectrum, it is found that the distribution of energy in the carbon beams covers a range from 0.1 to IO eV. Determination of the absolute flux of the beam from the signals obtained from the mass spectrometer is a non-trivial task. However, given a measure of the total amount of material vaporized and with a knowledge of the angular distribution, it can be shown that the beam intensity is -IO*’ particles/str/sec. This intensity is at least an order of magnitude higher than what was achieved by conventional methods. For a given target film thickness, all the above mentioned beam parameters (e.g. intensity, kinetic energy and stagnation temperature) can be controlled and characterized by a single parameter, the laser energy density. Concentration measurements were performed with a ruby laser adjusted to deliver an energy density of -3.7 J/cm’ on a 0.3 pm thick graphite target. The incident angle of the laser beam was zero degrees from the target normal. Data were recorded by