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Calculation of desorption energy distribution applied to temperature programmed H2O desorption from silicate glass surface
Vacuum/volume 37/numbers Printed in Great Britain
11 /l Z/pages 819 to 823/l
0042-207x/87$3.00+ Pergamon Journals
987
.oo Ltd
Calculation of desorption energy distribution applied to temperature programmed H,O desorption from silicate glass surface l-l Wittkopf. Democratic
Department Republic
of Chemistry,
Friedrich-Schiller-University,
DDR
6900 Jena
Steiger
3 Haus 3, German
received 20 June 1986
A method of calculating on an interation process silicate glass surfaces.
the desorption energy distribution from temperature programmed is proposed, checked by model calculations, and applied to H,O
Introduction
Thermal desorption spectra of H,O from silicate glasses show a complex structure indicating the heterogeneity of the glass surface. Many papers have been published concerning the interpretation of thermal desorption spectra from homogeneous surfaces as summarized in many reviews (see Menzel’, Yates’, Jiintgen and van Heck3), but not in the case of heterogeneous surfaces. The overall desorption rate R, of a heterogeneous surface with a continuous desorption energy distribution p (E) may be represented by E Rd(T,
m=X p(E).
t)=
s
R,(K
t,
~9.
dE
(1)
Lm
where R&T, t, E) represents the single site desorption of desorption energy E which follows the applied temperature-time scheme programme of the experiment and is usually calculated as
R,(T, t, E)= No ’ 7. exp( - E/RT) f ‘exp
exp( - E/RT)
-7’
L
s0
. dt
desorption desorption
data based spectra from
where the initial coverage vector N,( E,) gives an approximation for the energy sites distribution. We call A(T, t, Ei) the unit-desorption function from a site with the energy Ei under the applied temperature-time programme, because the function is related to the unit initial coverage. Equation (3) is the desorption analogue of the homotattic patch approximation in adsorption thermodynamics of heterogeneous surfaces, k is the number of energetically different surface sites. Following Carter’ the estimation of the energy distribution results in solving a linear equation system:
R(7;, tj)=No(Ei)
* A(~,
tj, Ei).
(4)
R(7;, tj) is the vector of overall desorption rates taken from an experimental desorption spectrum under k different T,-tj conditions. The matrix A(7;, tj, Ei) can be calculated from equation (2) for the k different 7;-tj conditions, if a series of k energy sites is preselected in an expected energy range. The preexponential factor 7 in equation (2) is assumed to be of the same value for all energy sites and is constant in the temperature range of the given experiment. From the N,(E,) vector we get the relative energy sites population as
1 (2)
for first order desorption. N,is the initial coverage of the surface and 7 is the preexponential factor. Other symbols have their usual meaning. As of the energy sites shown by Carter et d4, the estimation distribution in an analytical form is only possible for the exponential temperature-time programme. Otherwise we have to apply numeric approximations.
ffi=No(Ei)/No;
No=
i
No(Ei).
(5)
i=l
This relative energy sites population should approach the desorption energy distribution for very large numbers of energy sites: lim Hi = p(E).
k-a
Theoretical
analysis
The first useful attempt in this way was made by Carter’ replaced equation (1) by a sum:
R,=
i i=l
No(Ei)
A(T, t, Ei)
who
(3)
Carter5 applied this approximation for calculating the desorption energy sites distribution of an ion implanted glass by assuming first order desorption, and he obtained obviously good results. But, in general, there are some problems in following Carter’s approximation. Because of the sharp maximum of the desorption function 819
H Wittkopf:
Calculation
of desorption
energy distribution
(equation (2)) compared to the temperature range of interest. the matrix becomes singular in numeric treatment, if we do not choose the Eij, 7;- tj conditions in such a way that the maximum of the applied unit-desorption functions gives elements close to the main diagonal of the coefficient matrix. This can be arranged by using the relation between the maximum temperature r,, and the site energy E, which was deduced by Carter5 and Redhead’:
EiRTz
=7/p,,,
(6)
exp( - E/RT,).
[j, is the heating rate at maximum temperature: /j,= (?T!ir),.,,,. By means of equation (6) we can select k different temperatures so that each temperature r, corresponds to the maximum of the unit-desorption function from a surface site with energy ,5,. In this way we obtain a linear equation system equation (4) which can always be solved by means of common mathematical methods. But the resulting initial coverage vector N,(E,) is valid only in some simple cases. If we try to recalculate the desorption energy distribution from a desorption spectrum shown in Figure 1. calculated on the basis of the assumption of five different energy sites (Table l-first column), ;‘= IOr s-‘. linear temperature rise of 10 K mini’, N, = 1 mol, we will attain an incorrect solution. even if we provide the same energy sites in equation (4) (Table 1 -second column). This is a general problem of the inversion of a Fredholm integral equation of first kind. The inversion of equation (1) in order to get the energy sites distribution is an ‘ill posed’ problem if the kernel R&T, t, E) is smoother or more continuous with respect to the variables than RJT, t). as pointed out by Britten et ~1’. As this inversion is of
280
320
360
400
440
480
much interest in adsorption thermodynamics. various methods were used to solve this problem. Britten et rr1’ proposed a method based on a regularization technique which is also applicable to temperature-programmed desorption spectra. and they analysed CO desorption from oxidized graphite. The recalculated desorption spectrum is very similar to the experimental one and it proves the quality of this method. But Britten’s method is rather complicated (mathematical and numerical). thus we tried to find a simpler way in returning to equation (3). The purpose of this is the possibility of obtaining. the overall desorption rate of a heterogeneous surface by summing the unit-desorption functions A( r, t. E,) depending on the surface site energy E, and the applied temperatureetime programme. These functions are modified by the unknown initial site-coverage jY,(E,). if we assume constant ;‘. So we can fit an experimental desorption spectrum to the theoretical equation (3) in providing a set of energy sites within an expected range by varying the initial sites coverage. The resulting set of ,Y,,(E,) represents an approximation for the energy sites distribution. This problem can be solved with good results if we take the following conditions into account. (I) Each unit-desorption function .4(T. t. E,) gives its main contribution to the overall spectrum at the maximum temperature r,,,. The relation between r,,, and E, is given by equation (6). (2) The lowest desorption site energy gives its main contribution at the lowest temperature. (3) The expected energy range is limited by the applied temperature range. because f&, corresponds to r,,i,. and I?,,,,~ to Tn,dX.via equation (6). (4) The value for N,( E,) is only physically sensible if it is positive or zero. For a fitting procedure we have first to choose the energy range which can be expected according to condition (3). Thus we obtain an equidistant energy vector of k elements. From this energy vector we calculate via equation (6) the corresponding temperature vector. This method makes sure that the main contribution of the unit-desorption function A( T. t. E,) to the overall desorption spectrum is given at temperature T. Now we start with the lowest temperature of the temperature vector by fitting the initial coverages N,,, into the Rd( T. r) spectrum in an iteration process, The first steps are:
R,(T,)=N&4(T,,
T(K)
Figure I. Model desorptlon spectrum R,(T) calculated by using live different energy sites (see Table I--first column). ;‘= lOI SC’ linear temperature programme. heating rate: 10 K min I. A’!‘,, = I mol.
Rd(T2)=Nb;‘.
E,) A ( Tz, E, ) + Nj,;’ A ( T, , Ez )
RK)=Nb:‘+(T_v
E,)+N;;bUT,.
El)
+ .V;,‘<’ A ( T_,, E, ) Table I. Energy distribution provided for the model desorption spectrum. Figure I (first column), and the results of recalculation means of matrix inversion technique (second column)
by
Rd( T,)= 85 90 95 100 105 I10 115 120 125 130
0 11.1 0
12.2 0 11.1 0
44.4 0 11.1
i
I$,;
A(T,.
E;)
0.5 I I.0 I .2
26.9 13.6 9.2 9.9 3x.7 9.6 6.5
Nb;‘=
R‘,(T)-
1
Nhj’. .4(q.
I<, and the following
R,,( 7;)-
iteration
i
formula
E,)
1
[A(q.
E,)] ~’
(7)
is used:
“;;:m ” .4(T,, E;)
[.4(T.
E,]
‘.
,*jll (8)
820
H Wittkopf:
Calculation
of desorption
energy distribution
The upper index (x) gives the iteration step of N,&. After each iteration step we can check whether all N,,, values are physically sensible demanding Nc.20.
If we recalculate the desorption spectrum from this energy site distribution again, we will obtain the initial spectrum with deviations which are so small that they cannot be shown in contrast to Figure 1. So we conclude that our iteration process may also lead to a good approximation of experimental data. We have applied this procedure to some experimental thermal desorption spectra of water from silicate glasses. Figure 3 represents a series of desorption spectra recorded by a mass spectrometer (m/e= 18) where a linear temperature-time programme was applied to the glass samples in a vacuum system. The basic pressure was 10m4 Pa and the samples were taken from ground glass pieces (l-2 mm in diameter) with a total surface area of about l&20 cm’. Some details of the experimental arrangement are given by Munch and Wittkopf’, but no cooling below room temperature was applied in the present studies. The chemical composition of the glasses is roughly given in Table 2. No further pre-treatment of the samples was applied, but they were ground and stored under atmospheric conditions for two weeks for relaxation of mechanical stress. The glass samples show complex desorption spectra in the temperature range investigated from 300 to 800 K. This structure changes with the chemical composition. The increase of the
(9)
Otherwise negative Ng) values are taken as zero. So we attain a good convergence of the iteration process with the initial values Nbl’ from the first step, and the additional condition equation (9) in about 200 or 300 steps. We put this algorithm into a computer programme which can be run on a personal computer with no more than 128 kbyte, if we provide SO-100 energy steps. Results and discussion
To check the quality of this iteration process we applied it to the model desorption spectrum described above by providing 50 energy steps in the range from 80 to 145 kJ molt ‘. The result is shown in Figure 2. We get give groups of energies, that means each of the provided energy sites splits into a group of energies caused by the limited resolution of this method. But the population relation of these groups is the same as the one provided.
40
IO
O-
A90 II I
22 2 E,
I 3 II I
(kJ
444
I
I
I
600
700
em
T(K)
mol-‘1
Figure 3. H,O-desorption spectra from silicate glass samples, ground and stored 2 weeks under atmospheric conditions, normalized to 1 cm’ total surface area, linear temperature programme, heating rate= 10 K min-‘. The composition of the glass sample is given in Table 2.
Figure 2. Energy distribution calculated from the desorption spectrum, Figure 1, providing 50 energy steps in a range from 80 to 145 kJ molt i, y’= lOI so’, linear temperature programme, heating rate= 10 K mini.
Table 2. Main constituents
I 500
400
II I
of the samples,
Sample
Constituent Si02
I II III IV V VI
20 64 61 69 78 69
quantities
B,O,
given in mol %. Transformation
PbO
Na,O/K,O
35 23 10
10 4 8 11 18
19 6
10
temperature
BaO 55 10
at viscosity
ZnO
10 -
2
TV=1013 poise
T,= lOL3 (K) 900 830 695 710 700 815
821
H Wittkopf:
Calculation of desorption
energy distribution
;
2bO
237
E (kJ rnol-‘I 85'
I20
I60 E, (kJ mot-‘)
200
24C
I60
237
E (kJmoi_‘)
I
IhO
lb0 E (kJ mole’)
I
1 237
lb0
E,(kJ
mol-‘)
desorption rate at high temperature (above 7000 K ) is caused by the beginning of the glass transition region of the samples. which increases the water desorption from the bulk phase. So the range of surface desorption is limited bq the beginning of thi\ transition region and it is characteristic of each silicate glass. From these desorption spectra the energy distributions were calculated by providing SO energy steps in the range 85-245 kJ mol ‘, with ;I= IO’s ’ and the experimental temperature programme. The results are shown in Figure 4. In each case w’e obtain a wide variety of energy population which differs considerably with chemical composition in a similar way as the desorption spectra. The region above Ei= 200 kJ mol ’ ih influenced by the beginning of bulk phase desorption as discussed above, and it is not so characteristic of the glass surface. The first region up to E,=90 kJ molt ’ could not be detected by thermal desorption technique in a vacuum starting at room temperature. Conclusions
I60 E, (kJ mol.’
822
2i7
1
Comparing the energy distributions the following conclusions may be drawn. (1) The region from 00 to 110 kJ mol ’ seems to be ;I continuous distribution caused by H,O molecules adsorbed in ;I second or higher coordination sphere on primary adsorbed H,O molecules. (2) The region between I IO and 150 kJ mol ’ might bc characteristic of alkali ions in the glass network. while the energy region between 150 and 200 kJ rnol~~ ’ is due to divalent ions like Ba’+, Zn’+ or Pb’ I-‘urther studies are necessary for a detailed interpretation of the desorption spectra and energy distributions.
H Wittkapf: Calculation
of desorption
energy
distribution
References
’ D Menzel, Chemistry and Physics of Solid Surfaces IV (edited by R Vanselow and R Howe), p 389, Springer, Berlin (1982). ’ J T Yates, Jr, Meth Exp Phys, 22, 425 (1985). 3 H Jiintgen and K H van Heck, Fortschr Chem Forsch, 13, 601 (1970). 4 G Carter, P Bailey and D G Armour, Vacuum, 34, 797 (1984).
5G Carter, Vacuum, 12, 245 (1962). 6 P A Redhead, Vacuum, 12, 203 (1962). ’ J A Britten, B J Travis and L F Brown, Adsorption and Ion-Exchange ‘83, p 7, AIChE Symposium (1983). s U Miinch and H Wittkopf, Wiss Zeitschr FSU, Naturwiss Reihe, 33,95 (1984).
823
11 /l Z/pages 819 to 823/l
0042-207x/87$3.00+ Pergamon Journals
987
.oo Ltd
Calculation of desorption energy distribution applied to temperature programmed H,O desorption from silicate glass surface l-l Wittkopf. Democratic
Department Republic
of Chemistry,
Friedrich-Schiller-University,
DDR
6900 Jena
Steiger
3 Haus 3, German
received 20 June 1986
A method of calculating on an interation process silicate glass surfaces.
the desorption energy distribution from temperature programmed is proposed, checked by model calculations, and applied to H,O
Introduction
Thermal desorption spectra of H,O from silicate glasses show a complex structure indicating the heterogeneity of the glass surface. Many papers have been published concerning the interpretation of thermal desorption spectra from homogeneous surfaces as summarized in many reviews (see Menzel’, Yates’, Jiintgen and van Heck3), but not in the case of heterogeneous surfaces. The overall desorption rate R, of a heterogeneous surface with a continuous desorption energy distribution p (E) may be represented by E Rd(T,
m=X p(E).
t)=
s
R,(K
t,
~9.
dE
(1)
Lm
where R&T, t, E) represents the single site desorption of desorption energy E which follows the applied temperature-time scheme programme of the experiment and is usually calculated as
R,(T, t, E)= No ’ 7. exp( - E/RT) f ‘exp
exp( - E/RT)
-7’
L
s0
. dt
desorption desorption
data based spectra from
where the initial coverage vector N,( E,) gives an approximation for the energy sites distribution. We call A(T, t, Ei) the unit-desorption function from a site with the energy Ei under the applied temperature-time programme, because the function is related to the unit initial coverage. Equation (3) is the desorption analogue of the homotattic patch approximation in adsorption thermodynamics of heterogeneous surfaces, k is the number of energetically different surface sites. Following Carter’ the estimation of the energy distribution results in solving a linear equation system:
R(7;, tj)=No(Ei)
* A(~,
tj, Ei).
(4)
R(7;, tj) is the vector of overall desorption rates taken from an experimental desorption spectrum under k different T,-tj conditions. The matrix A(7;, tj, Ei) can be calculated from equation (2) for the k different 7;-tj conditions, if a series of k energy sites is preselected in an expected energy range. The preexponential factor 7 in equation (2) is assumed to be of the same value for all energy sites and is constant in the temperature range of the given experiment. From the N,(E,) vector we get the relative energy sites population as
1 (2)
for first order desorption. N,is the initial coverage of the surface and 7 is the preexponential factor. Other symbols have their usual meaning. As of the energy sites shown by Carter et d4, the estimation distribution in an analytical form is only possible for the exponential temperature-time programme. Otherwise we have to apply numeric approximations.
ffi=No(Ei)/No;
No=
i
No(Ei).
(5)
i=l
This relative energy sites population should approach the desorption energy distribution for very large numbers of energy sites: lim Hi = p(E).
k-a
Theoretical
analysis
The first useful attempt in this way was made by Carter’ replaced equation (1) by a sum:
R,=
i i=l
No(Ei)
A(T, t, Ei)
who
(3)
Carter5 applied this approximation for calculating the desorption energy sites distribution of an ion implanted glass by assuming first order desorption, and he obtained obviously good results. But, in general, there are some problems in following Carter’s approximation. Because of the sharp maximum of the desorption function 819
H Wittkopf:
Calculation
of desorption
energy distribution
(equation (2)) compared to the temperature range of interest. the matrix becomes singular in numeric treatment, if we do not choose the Eij, 7;- tj conditions in such a way that the maximum of the applied unit-desorption functions gives elements close to the main diagonal of the coefficient matrix. This can be arranged by using the relation between the maximum temperature r,, and the site energy E, which was deduced by Carter5 and Redhead’:
EiRTz
=7/p,,,
(6)
exp( - E/RT,).
[j, is the heating rate at maximum temperature: /j,= (?T!ir),.,,,. By means of equation (6) we can select k different temperatures so that each temperature r, corresponds to the maximum of the unit-desorption function from a surface site with energy ,5,. In this way we obtain a linear equation system equation (4) which can always be solved by means of common mathematical methods. But the resulting initial coverage vector N,(E,) is valid only in some simple cases. If we try to recalculate the desorption energy distribution from a desorption spectrum shown in Figure 1. calculated on the basis of the assumption of five different energy sites (Table l-first column), ;‘= IOr s-‘. linear temperature rise of 10 K mini’, N, = 1 mol, we will attain an incorrect solution. even if we provide the same energy sites in equation (4) (Table 1 -second column). This is a general problem of the inversion of a Fredholm integral equation of first kind. The inversion of equation (1) in order to get the energy sites distribution is an ‘ill posed’ problem if the kernel R&T, t, E) is smoother or more continuous with respect to the variables than RJT, t). as pointed out by Britten et ~1’. As this inversion is of
280
320
360
400
440
480
much interest in adsorption thermodynamics. various methods were used to solve this problem. Britten et rr1’ proposed a method based on a regularization technique which is also applicable to temperature-programmed desorption spectra. and they analysed CO desorption from oxidized graphite. The recalculated desorption spectrum is very similar to the experimental one and it proves the quality of this method. But Britten’s method is rather complicated (mathematical and numerical). thus we tried to find a simpler way in returning to equation (3). The purpose of this is the possibility of obtaining. the overall desorption rate of a heterogeneous surface by summing the unit-desorption functions A( r, t. E,) depending on the surface site energy E, and the applied temperatureetime programme. These functions are modified by the unknown initial site-coverage jY,(E,). if we assume constant ;‘. So we can fit an experimental desorption spectrum to the theoretical equation (3) in providing a set of energy sites within an expected range by varying the initial sites coverage. The resulting set of ,Y,,(E,) represents an approximation for the energy sites distribution. This problem can be solved with good results if we take the following conditions into account. (I) Each unit-desorption function .4(T. t. E,) gives its main contribution to the overall spectrum at the maximum temperature r,,,. The relation between r,,, and E, is given by equation (6). (2) The lowest desorption site energy gives its main contribution at the lowest temperature. (3) The expected energy range is limited by the applied temperature range. because f&, corresponds to r,,i,. and I?,,,,~ to Tn,dX.via equation (6). (4) The value for N,( E,) is only physically sensible if it is positive or zero. For a fitting procedure we have first to choose the energy range which can be expected according to condition (3). Thus we obtain an equidistant energy vector of k elements. From this energy vector we calculate via equation (6) the corresponding temperature vector. This method makes sure that the main contribution of the unit-desorption function A( T. t. E,) to the overall desorption spectrum is given at temperature T. Now we start with the lowest temperature of the temperature vector by fitting the initial coverages N,,, into the Rd( T. r) spectrum in an iteration process, The first steps are:
R,(T,)=N&4(T,,
T(K)
Figure I. Model desorptlon spectrum R,(T) calculated by using live different energy sites (see Table I--first column). ;‘= lOI SC’ linear temperature programme. heating rate: 10 K min I. A’!‘,, = I mol.
Rd(T2)=Nb;‘.
E,) A ( Tz, E, ) + Nj,;’ A ( T, , Ez )
RK)=Nb:‘+(T_v
E,)+N;;bUT,.
El)
+ .V;,‘<’ A ( T_,, E, ) Table I. Energy distribution provided for the model desorption spectrum. Figure I (first column), and the results of recalculation means of matrix inversion technique (second column)
by
Rd( T,)= 85 90 95 100 105 I10 115 120 125 130
0 11.1 0
12.2 0 11.1 0
44.4 0 11.1
i
I$,;
A(T,.
E;)
0.5 I I.0 I .2
26.9 13.6 9.2 9.9 3x.7 9.6 6.5
Nb;‘=
R‘,(T)-
1
Nhj’. .4(q.
I<, and the following
R,,( 7;)-
iteration
i
formula
E,)
1
[A(q.
E,)] ~’
(7)
is used:
“;;:m ” .4(T,, E;)
[.4(T.
E,]
‘.
,*jll (8)
820
H Wittkopf:
Calculation
of desorption
energy distribution
The upper index (x) gives the iteration step of N,&. After each iteration step we can check whether all N,,, values are physically sensible demanding Nc.20.
If we recalculate the desorption spectrum from this energy site distribution again, we will obtain the initial spectrum with deviations which are so small that they cannot be shown in contrast to Figure 1. So we conclude that our iteration process may also lead to a good approximation of experimental data. We have applied this procedure to some experimental thermal desorption spectra of water from silicate glasses. Figure 3 represents a series of desorption spectra recorded by a mass spectrometer (m/e= 18) where a linear temperature-time programme was applied to the glass samples in a vacuum system. The basic pressure was 10m4 Pa and the samples were taken from ground glass pieces (l-2 mm in diameter) with a total surface area of about l&20 cm’. Some details of the experimental arrangement are given by Munch and Wittkopf’, but no cooling below room temperature was applied in the present studies. The chemical composition of the glasses is roughly given in Table 2. No further pre-treatment of the samples was applied, but they were ground and stored under atmospheric conditions for two weeks for relaxation of mechanical stress. The glass samples show complex desorption spectra in the temperature range investigated from 300 to 800 K. This structure changes with the chemical composition. The increase of the
(9)
Otherwise negative Ng) values are taken as zero. So we attain a good convergence of the iteration process with the initial values Nbl’ from the first step, and the additional condition equation (9) in about 200 or 300 steps. We put this algorithm into a computer programme which can be run on a personal computer with no more than 128 kbyte, if we provide SO-100 energy steps. Results and discussion
To check the quality of this iteration process we applied it to the model desorption spectrum described above by providing 50 energy steps in the range from 80 to 145 kJ molt ‘. The result is shown in Figure 2. We get give groups of energies, that means each of the provided energy sites splits into a group of energies caused by the limited resolution of this method. But the population relation of these groups is the same as the one provided.
40
IO
O-
A90 II I
22 2 E,
I 3 II I
(kJ
444
I
I
I
600
700
em
T(K)
mol-‘1
Figure 3. H,O-desorption spectra from silicate glass samples, ground and stored 2 weeks under atmospheric conditions, normalized to 1 cm’ total surface area, linear temperature programme, heating rate= 10 K min-‘. The composition of the glass sample is given in Table 2.
Figure 2. Energy distribution calculated from the desorption spectrum, Figure 1, providing 50 energy steps in a range from 80 to 145 kJ molt i, y’= lOI so’, linear temperature programme, heating rate= 10 K mini.
Table 2. Main constituents
I 500
400
II I
of the samples,
Sample
Constituent Si02
I II III IV V VI
20 64 61 69 78 69
quantities
B,O,
given in mol %. Transformation
PbO
Na,O/K,O
35 23 10
10 4 8 11 18
19 6
10
temperature
BaO 55 10
at viscosity
ZnO
10 -
2
TV=1013 poise
T,= lOL3 (K) 900 830 695 710 700 815
821
H Wittkopf:
Calculation of desorption
energy distribution
;
2bO
237
E (kJ rnol-‘I 85'
I20
I60 E, (kJ mot-‘)
200
24C
I60
237
E (kJmoi_‘)
I
IhO
lb0 E (kJ mole’)
I
1 237
lb0
E,(kJ
mol-‘)
desorption rate at high temperature (above 7000 K ) is caused by the beginning of the glass transition region of the samples. which increases the water desorption from the bulk phase. So the range of surface desorption is limited bq the beginning of thi\ transition region and it is characteristic of each silicate glass. From these desorption spectra the energy distributions were calculated by providing SO energy steps in the range 85-245 kJ mol ‘, with ;I= IO’s ’ and the experimental temperature programme. The results are shown in Figure 4. In each case w’e obtain a wide variety of energy population which differs considerably with chemical composition in a similar way as the desorption spectra. The region above Ei= 200 kJ mol ’ ih influenced by the beginning of bulk phase desorption as discussed above, and it is not so characteristic of the glass surface. The first region up to E,=90 kJ molt ’ could not be detected by thermal desorption technique in a vacuum starting at room temperature. Conclusions
I60 E, (kJ mol.’
822
2i7
1
Comparing the energy distributions the following conclusions may be drawn. (1) The region from 00 to 110 kJ mol ’ seems to be ;I continuous distribution caused by H,O molecules adsorbed in ;I second or higher coordination sphere on primary adsorbed H,O molecules. (2) The region between I IO and 150 kJ mol ’ might bc characteristic of alkali ions in the glass network. while the energy region between 150 and 200 kJ rnol~~ ’ is due to divalent ions like Ba’+, Zn’+ or Pb’ I-‘urther studies are necessary for a detailed interpretation of the desorption spectra and energy distributions.
H Wittkapf: Calculation
of desorption
energy
distribution
References
’ D Menzel, Chemistry and Physics of Solid Surfaces IV (edited by R Vanselow and R Howe), p 389, Springer, Berlin (1982). ’ J T Yates, Jr, Meth Exp Phys, 22, 425 (1985). 3 H Jiintgen and K H van Heck, Fortschr Chem Forsch, 13, 601 (1970). 4 G Carter, P Bailey and D G Armour, Vacuum, 34, 797 (1984).
5G Carter, Vacuum, 12, 245 (1962). 6 P A Redhead, Vacuum, 12, 203 (1962). ’ J A Britten, B J Travis and L F Brown, Adsorption and Ion-Exchange ‘83, p 7, AIChE Symposium (1983). s U Miinch and H Wittkopf, Wiss Zeitschr FSU, Naturwiss Reihe, 33,95 (1984).
823