THOMAS BERNSTEIN, DIETER MICHEL, AND HARRY PFEIFER/ Carbon-13 NMR and Infrared Spectroscopic Investigations of Acetone Adsorbed on Silica Gel Surfaces

Carbon-13 NMR and Infrared Spectroscopic Investigations of
Acetone Adsorbed on Silica Gel Surfaces
THOMAS BERNSTEIN, DIETER MICHEL, AND HARRY PFEIFER
Karl-Marx-UniversitiJt, Sektion Physik, Linn~strafle 5. DDR-7010 Leipzig, German Democratic Republic
AND
PETER FINK
Friedrich-Schiller-Universiti~t, Sektion Chemie, Lessingstra[3e I0,
DDR-6900 Jena, German Democratic Republic
Received June 3, 1980; accepted January 6, 1981
Carbon-13 NMR and IR investigations were carried out for adsorption of acetone on partially
dehydroxylated and on methylated silica gel samples. The appreciable downfield shift for the
carbon-13 resonance line of the C = O group on partially dehydroxylated silica gel (ca. 9 ppm with
respect to adsorption on methylated silica gel at higher coverages) and the shift of the IR stretching
vibration band of the surface hydroxyl groups (A~on = 370 cm -I) are due to a strong interaction of the acetone molecules with the surface hydroxyl groups. The four IR bands observed
for the C = O stretching vibration of acetone adsorbed on partially dehydroxylated silica gel are
ascribed to interactions with geminal OH groups, with isolated (free) OH groups, with nonhydroxylic adsorption sites, and to the gaseous state. The number of interacting sites evaluated
from the NMR shifts was 1.4/nm~ and 0.3/nm~ for partially dehydroxylated and methylated silica
gel, respectively.
(i) characterize the interaction of acetone
molecules with surface sites of silica gel,
(ii) elucidate the role of the surface
hydroxyl groups by comparing the interaction of molecules with partially dehydroxylated and with methylated silica gel
surfaces, and
(iii) derive more quantitative conclusions
concerning the strength of the interaction
and the number of adsorption sites.
INTRODUCTION
The interaction of hydrocarbons with
silica-containing adsorbents and the characterization of the adsorption sites were discussed in numerous papers (1-4). Among
the different spectroscopic methods which
were applied in these studies, nuclear
magnetic resonance, and especially carbon-13 NMR spectroscopy (2), is a rather
new method and its combination with infrared spectroscopy seems to be of great importance for a deeper understanding of
adsorption phenomena.
In this work we combine the results of
carbon-13 high-resolution NMR and of infrared spectroscopic measurements in order to
MATERIALS AND METHODS
All measurements were performed at
room temperature. Carbon- 13 NMR spectra
were taken at 22.63 MHz using a Bruker
HX 90 Fourier transform spectrometer.
The shifts are referred to the shifts of
acetone molecules adsorbed on the methyl-
310
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Journal of Colloidand InterfaceScience, Vol.84, No. 2, December1981
NMR A N D IR O F A C E T O N E A D S O R B E D ON S I L I C A G E L
ated surface at higher coverages (4.30
statistical monolayers) in order to separate
the influence of bulk susceptibility of the
adsorbent and of intermolecular interactions between the adsorbed molecules. Positive shifts are to lower field. The experimental error is about ___0.5 ppm.
The infrared spectroscopic measurements
were carried out with a Zeiss UR 20 spectrometer. Thin tablets (o.d. 2 cm, weight
about 4-5 mg/cm2) were placed in a quartz
cell (with CaFz windows) and pretreated as
described below.
As adsorbates we used acetone p.a. grade
(VEB Laborchemie, Apolda, German Democratic Republic), acetone enriched with
about 40% carbon-13 nuclei in both positions and acetone enriched about 95% in the
CO group only (Stohler Isotope Chemicals, Innerberg, Switzerland). The adsorbent was Kieselgel according to Stahl
(Fa. Merck, Darmstadt, Federal Republic
of Germany) with a specific surface area
(BET, N2, 77 K) of 320 mZ/g,
The methylated specimens were prepared starting from silica gel which was
partially dehydroxylated at 570 and 1070 K
for NMR and IR samples, respectively. By
means of a treatment with hexamethyldisilazane at 470 K according to the following scheme (5)
~ S i O H + (CH3)~-Si-NH-Si(CH3)3
~ Si-O-Si-(CH3)3 + (CH3)3-Si-NH2,
~ S i O H + (CH3)3-Si-NH2 ~
~ Si-O-Si-(CH3)~ + NH3
the surface hydroxyl groups were substituted by trimethyl silyl groups which are
stable to hydrolysis at room temperature
and to thermal treatment in vacuo up to
720 K (6). The specific surface area of the
methylated samples was 250 m2/g and the
residual concentration of surface hydroxyl
groups about 0.1/nm 2.
The latter value was obtained from the
decrease of the extinction of the OH stretch-
311
ing vibration band after methylation by comparing with standard values for the unmodified silica gel.
For the carbon-13 NMR measurements
both hydroxylated and methylated samples were activated at 670 K before adsorption. For the IR measurements the
silica gel samples were pretreated at 1070 K
because at lower temperatures a broad absorption band due to bound hydroxyl
groups occurs which does not allow a sufficiently accurate study of the stretching
vibration of the free hydroxyl groups and
its perturbation by adsorbed molecules.
On the other hand these bound hydroxyl
groups do not show, with respect to free
OH groups, a preferent hydrogen bond
formation with adsorbed molecules (7, 8).
For NMR measurements the greater number of hydroxyl groups at a pretreatment
temperature of 670 K (5.50H/nm 2 as compared with 0.8 OH/nm 2 at a pretreatment
temperature of 1070 K) is essential in order
to obtain higher concentrations for the adsorbed molecules. The hydroxyl group concentrations were measured by means of 1H
NMR broad-line techniques (cf. Ref. (3))
and agree within the limits of experimental
error (_+ 15%) with the standard values.
RESULTS AND DISCUSSION
Carbon-13 NMR Investigations
Carbon-13 NMR chemical shifts for molecules adsorbed on normal and methylated
silica gels are listed in Table I. There is no
dependence of the resonance shifts on the
number of adsorbed molecules for the carbons of the methyl groups but a clear effect on the carbonylic carbon in both types
of silica gel (cf. also Fig. 1). The large
downfield shift of the latter carbon in the
case of the adsorption on partially dehydroxylated silica gel and the clear difference to the values obtained for methylated
silica gel indicate clearly the existence of
a strong interaction between the carbonyl
group of acetone and the surface hydroxyl
Journal of Colloid and Interface Science, Vol. 84, No. 2, December 1981
3 12
BERNSTEIN ET AL.
TABLEI
fast exchange
Coverage Dependence of 1~C NMR Shifts 8(C")) of
Adsorbed Acetone ((C(1)H3)2C(2)O) Relative to the
Shifts 6m(C")) for Adsorption on Methylated Silica Gel
(Sample with a Coverage of 4.30 Statistical Monolayers):
~ ( C (i)) = ~°bs(C(i)) -- ~m(C(i))
(ppm)
Coverage a
(statistical monolayers)
0.01
0.05
0.07
0.15
0.30
0.40
0.75
1.30
8(C (~))
8(C m )
8(C ~2))
-1.3
9.2
-0.7
4.6
4.1
3.9
--
-0.9
-1.5
--
8.3
-1.1
-1.3
7.5
--
2.50
4.30
--
--
--
-0.9
- 1.5
-0.8
6.8
5.8
-0.8
4.0
-0.7
-0.7
- 1.4
-0.0
2.6
0.0
0.0
-0.0
-0.1
-4.1
-0.3
-7.9
0.0
0.0
2.6
1.4
Liquid state
Gaseous state (30)
-
2.9
6AM.
[2]
8AM
+ kNI6--~--]2 - kN(~.--~-I
\SAM/
\SAM/
.
[3]
F r o m E q . [3] it f o l l o w s
8
_ _
kN + kNa
1 +
--
2kN
8AM
___
[41
--
2kN
F o r a s t r o n g c o m p l e x , i . e . , if t h e c o n d i t i o n
>> 1 is fulfilled, w e o b t a i n f r o m E q . [4]:
kN
a Surface area of the acetone molecule: 0.4 nm2.
-
8AM
g r o u p s . T h e r e s i d u a l d o w n f i e l d shift f o r t h e
carbonylic carbon on methylated samples
a r i s e s f r o m an i n t e r a c t i o n w i t h t h e r e s i d u a l
OH groups and a smaller number of nonhydroxylic centers (see below).
I t is p o s s i b l e to d e s c r i b e t h e e q u i l i b r i u m
among free molecules (M), free adsorption
s i t e s ( A ) , a n d t h e c o m p l e x e s (MA) b y t h e
equation
N
8)
8AM
8(C m )
NAM
F r o m E q s . [1] a n d [2] o n e finds
8_kNA(1
Methylated
silica gel
Silica gel
8-
+
2
_+
2N
[5]
~
"
A c c o r d i n g to Eq. [5], t h e o b s e r v e d r e s o n a n c e shift 8 r e m a i n s c o n s t a n t , 8 = 8AM, as
~(O~,)
8,0
6.C
k
M + A <-~--MA,
from which the relation
k =
4'CL
SAM
(N
-
NAM)(NA
--
NaM)
[1]
among the total number of adsorption
sites (NA),
the number of complexes
(NAM), a n d t h e t o t a l n u m b e r o f m o l e c u l e s
(N) follows.
I f 6 d e n o t e s t h e o b s e r v e d r e s o n a n c e shift
a n d 6AM t h e shift o f a m o l e c u l e on an
a d s o r p t i o n site, w e o b t a i n in t h e c a s e o f
Journal of Colloidand Interface Science, Vol.
84, No. 2, December 1981
2£
2.0
4.0
Covetocje
[m
staotnisotic(l~s]alyer
FIG. 1. Coverage dependence of x3C NMR shifts
8(0 2)) of the carbonylic carbon of acetone adsorbed
on partially dehydroxylated (Q) and methylated (×)
silica gel.
NMR AND IR OF ACETONE ADSORBED ON SILICA GEL
long as the total number of the adsorbed
molecules is less than the number NA of
sites (positive sign of Eq. [5]). If N > N~
we obtain a decrease of the observed
shift ~ with increasing number N of molecules (negative sign of Eq. [5]).
In our case, however, we do not observe such a behavior even for the lowest
coverages used. Consequently, we still find
free molecules although the adsorption sites
are not completely occupied. Therefore the
assumption of a strong complex as discussed above cannot be used and it is impossible to derive the resonance shift ~AM
of the complex by means of a simple direct
extrapolation of the observed shifts to zero
coverage. A more suitable form of Eq.
[3] is given by
~AM__kNa
8
+ 1 + __N
kNA
1 -
.
313
~A~
s~z'
~o
8
4
ppm
2
•
a)
2
6
4
8
SAM = I 0 ppm
10
N (I - S/SAM )
3AM
~-
0 ppm
SAM = 5 ppm
[6]
NA
o12
A plot of (~AM/~) over N(1-6/~AM) should
give a straight line with the slope N~ 1.
Therefore, in order to analyze the experimental shift 8 as a function of the number
of adsorbed molecules, the quantity ~AM has
to be chosen in such a way that a straight
line results. The problem is to find the smallest possible value 6AM by this trial-anderror procedure. For the solution of Eq.
[6] the method o f least squares is used
(cf. Fig. 2). Thus, the minimum error arises
for partially dehydroxylated specimens if
6aM is chosen to lie between 10 and 15 ppm.
The mean number of sites is 1.4 _+ 0.2/nmL
In the case of methylated samples the procedure leads ~AM = 7-- l0 ppm and the mean
number o f sites is 0.3 _+ 0.1/nm 2.
These values are in a reasonable agreement with the concentrations of surface
hydroxyl groups for our samples. It seems
to be unlikely that all hydroxyl groups can
interact with the molecules because of
sterical reasons. The computations reveal
that the resonance shifts 8AM are in both
cases ca. 10 ppm. Hence the adsorption
sites are of the same nature.
'
o'.4
'
&
'
&
'
i.~"
N(1-~/~AM)
Fm. 2. Plot of the resonance shifts according to
Eq. [6] for acetone adsorbed on partially dehydroxylated (a) and methylated (b) silica gel.
Consequently, the results support directly
the assumption o f a predominant interaction between acetone molecules and surface hydroxyl groups. Hence, especially for
the methylated samples with a distorted
surface structure, the total number of
adsorption sites consists of the small
amount of remaining hydroxyl groups (cf.
above) and some nonhydroxylic adsorption
sites (cf. the discussion of the IR results)
which additionally interact with adsorbate
molecules.
The values of the equilibrium constants k
derived from Eq. [6] are ca. 2 for both cases.
Unfortunately the error is rather large so
that possible small differences cannot be
seen.
Infrared Spectroscopic Investigations
Adsorption on partially dehydroxylated
silica gel. It is well known (1, 4, 9) that
Journal of Colloidand Interface Science, Vol. 84, No. 2, December 1981
314
BERNSTEIN ET AL.
acetone molecules adsorbed on silica gel
surfaces interact with surface hydroxyl
groups. This interaction leads to a decrease of the extinction of the stretching
vibration band of the free surface hydroxyl
groups (f'oH = 3748 cm -~) and to the occurrence of a broad band due to h y d r o x y l
groups interacting with acetone molecules.
This latter band is shifted by 330-395
cm -~ to lower wavenumbers for surface
coverages of about 0 = 1 statistical monolayers (9-18) and characterizes the hydrogen-bonding interaction between acetone
and the free silanol groups. The respective specific contribution to the interaction
energy is about 30 kJ/mole (19).
For our silica gel which was dehydroxylated at 1070 K, the wavenumbers
f'oa were shifted by 290 and 370 cm -1 for
very low and monolayer surface coverages,
respectively (cf. Table II). In the region of
the C ~ O stretching vibration of acetone
we observed four bands in d e p e n d e n c e on
the surface coverage (cf. Fig. 3): The band
at 1710 cm -~ with a shoulder at 1690 cm -~
occurs for a small number of adsorbed
TABLE H
Characteristic IR Wavenumbers for the Systems
Acetone/Partially Dehydroxylated Silica Gel (a) and
Acetone/Methylated Silica Gel (b)
a
Vapor pressure
of acetone
(Pa)
b
~c:=o
(era-')
~'oa
(era -1 )
f~c~--~-o
(era-')
1.3
x
102
1690 (shoulder)
1710
290
1710
2.7
x
102
1690 (shoulder)
1710
1735 (shoulder)
320
1710
1720
1735
6.6 x 102
1690 (shoulder)
1710
1735
340
1710 (shoulder)
1720
1735
10.6 x 102
1690 (shoulder)
1710
1720
1737
370
1720
1737
Journal of Colloid and Interface Science, Vol. 84, No. 2, December 1981
absor-
1710
k if1722:57
e~,~
)ressure[
172x~/~1757
1722
~1757
pressure
1064
951
665
665
>-66
1690
200
133
Lz~
~
19;o~ [o~-,;
I .t735
599
266
~7oo ~8oo 19oo~ ~:~-,]
FIG. 3. IR spectra of the Uc=o region of acetone
adsorbed on partially dehydroxylated (a) and methylated (b) silica gel in dependence on the adsorbate
pressure.
acetone molecules. With increasing coverage further bands appear at 1720 cm -1
and at 1735-1737 c m - L
As in Refs. (14, 20) the band at 1710 cm -1
is ascribed to adsorbed molecules which
are involved in hydrogen-bonding interaction with isolated hydroxyl groups, i.e.,
a so-called 1:1 interaction. The IR absorption at 1690 cm -1 revealed for all coverages
about the same small relative intensity with
respect to the band at 1710 cm -~ and disappeared if the total concentration of O H
groups is drastically reduced (e.g., by
methylation, see below). Hence the shoulder
at 1690 cm -1 cannot be related to an interaction with nonhydroxylic surface sites.
Furthermore, its assignment to the Vc=c
stretching vibration of the enol form of acetone can be rejected. The possibility that
the enol form might have a much higher
relative abundance in the adsorbed state
than for liquid acetone (where its total
amount is much less than 1%) is excluded because in this case the laC resonance
lines for the methyl carbons should be
shifted to lower frequencies with respect
to the liquid due to proton exchange between the keto and enol tautomers.
For partially dehydroxylated silica gels
the C = O stretching band at 1690 cm -~ is
ascribed (14, 20) to adsorption involving
NMR AND IR OF ACETONE ADSORBED ON SILICA GEL
hydrogen-bonding interaction between one
molecule and two hydroxyl groups. However, the n u m b e r of adjacent hydroxyl
groups interacting with each other is
negligibly small for samples dehydroxylated
at 1070 K. Besides the isolated hydroxyls
only geminal surface hydroxyl groups remain which might be responsible for the
shoulder at 1690 cm -1. The occurrence of
geminal O H groups has been checked recently by IR spectroscopy both for silica
gel (21) and for aerosil (22). Their relative
amount is about 10% for aerosil and less
than 20% for silica gel after dehydroxylation at 1070 K (6). This low concentration
is consistent with the small extinction of
the band at 1690 cm -1.
The IR spectra (Fig. 3a) show that acetone
molecules first o f all interact with hydroxyl
groups (up to 6.6 × 102 Pa). This can be
checked independently if we compare the
adsorption isotherm measured gravimetrically at 323 K (Fig. 4) with an adsorption
isotherm determined by IR spectroscopy
(the specimen in the infrared beam is exposed to a temperature of about 320 K).
The latter isotherm was evaluated from
the decrease of the extinction of the isolated O H groups with increasing acetone
pressure neglecting the small amount of
molecules interacting with geminal groups.
From a comparison of the two isotherms
we conclude that only above a pressure of
6.6 × 102 Pa the adsorption of acetone
molecules occurs on other sites than the surface h y d r o x y l groups. This is in agreement
with the appearance of the band at 1720
cm -1. Therefore together with the results for
methylated silica gel (see below), this band
is attributed to an interaction with nonhydroxylic adsorption sites on the surface.
The values of the w a v e n u m b e r for bands
occurring at the highest coverages (17351737 cm -1) are typical for acetone molecules in the gaseous state.
The other bands for adsorbed acetone
at 1370 ( ~ s y , C - - H ) , 1430 (Sasy,c-H), 2927, 2973,
and 3020 cm -~ (vc-H) belonging to sym-
315
Molecules
per nmz
o
1.4
1(
b
0.~
0.6
0,4
0.2
,;
~'o
io
2o
s;
vepour pressure
of acetone [Pa]
FIG. 4. Adsorption isotherms for partially dehydroxylated silica gel (pretreated at 1070 K) at 323 K;
(a) gravimetrical adsorption isotherm; (b) IR spectroscopically determined isotherm of the singular SiOH
groups interacting with acetone molecules.
metric and asymmetric bending vibrations
and to different C - H stretching vibrations
of the methyl group, respectively, deviate
only slightly from the corresponding values
in the gaseous state (1363, 1435, 2927, 2972,
and 3018 cm -1 (23)).
As is shown in Table II the shift A~oH
of the wavenumbers of interacting hydroxyls
increases from 290 to 370 cm -j with growing acetone coverage. M o r e o v e r the bandshape is asymmetric. An even higher value
for the shift (439 cm -1) in the case of a
statistical monolayer of acetone on aerosil
pretreated at 1070 K was reported by
Curthoys et al. (18). The augmentation of
the band shift with increasing coverage has
been found also for other adsorbates.
McDonald (24) explained this p h e n o m e n o n
for nitrogen adsorption on silica as due to
one nitrogen molecule interacting with several hydroxyl groups at low coverages. At
higher coverages a redistribution occurs; as
a result a bond is formed between each
molecule and a hydroxyl group which is
accompanied by an increase of the interJournal of Colloid and Interface Science, Vol. 84, No. 2, December 1981
316
BERNSTEIN
action energy for each hydroxyl group. In
the case of aromatic molecules the increase
in the band shift of the OH groups was
explained in terms of a closer interaction
or reorientation of the molecules with growing coverage (25).
Griffiths et al. (20) distinguished two
modes of adsorption of acetone from carbon
tetrachloride solution onto silica. The
weaker adsorption involves single hydrogen-bonding interaction between isolated hydroxyl groups and acetone and
leads to spectral shifts A~oa = 306 cm -1
and A~co = 15 cm -1 (solution: ~co = 1720
cm -~, adsorption: f'co = 1705 cm-0. The
stronger adsorption is characterized by
spectral shifts Af'on = 246 cm -~ and Af'co
= 30 cm -~. According to Ref. (20) the
doubling of the shift of the keto group supports the suggestion that each adsorbed
molecule is involved in hydrogen bonding
with two adjacent hydroxyl groups. This
interpretation applied to our system would
imply that at low coverages acetone
molecules should interact preferably with
geminal hydroxyl groups. The shift of the
band maximum would then be caused by an
increasing participation of isolated hydroxyl
groups involved in 1:1 interactions with
adsorbed acetone molecules. However, this
conclusion is inconsistent with the fact that
the extinction of the IR band at 1690 cm -1
increases proportionally to the extinction
of the band at 1710 cm -1 in that interval
of rising coverages where we observe the
increase of the shift Abort. Therefore, a
preferent adsorption of acetone molecules
at geminal hydroxyl groups must be excluded and the above explanation cannot
be applied to our system.
Asymmetric shapes of distorted OH
groups belonging to hydrogen-bonding
interactions of phenol with proton acceptors
in solution (certain carbonylic compounds
like ketones and chinones) were explained
by Dunken and Fritzsche (26, 27) in terms
of a superposition of two symmetric broad
IR bands of distorted OH groups. It could
Journal of Colloid and Interface Science, Vol. 84, No. 2, December 1981
ET AL.
be shown that the two components are due
to different spatial arrangements ("isomerism") of the hydrogen bond O - - H . . . . O~-C
(i.e., interaction of the proton of the hydroxyl group with the sp 2 orbitals of the
oxygen in the CO group and an interaction
with 7r orbitals of the CO group, respectively) and that they are not due to 1:1 and 1:2
hydrogen-bonding interactions between proton acceptor and one or two hydroxyl
groups, respectively. Similar conclusions
were drawn by Castagna et al. (28) and by
Conzi et al. (29). It is interesting to note
that the IR spectrum in Ref. (27) reveals
only one C~---O stretching band for the interacting molecules. Hence, the appearance of
two C = O bands for interacting acetone
molecules and the asymmetry observed for
the shifted O--H stretching vibration band
in the present work must not be correlated
necessarily with each other.
A d s o r p t i o n on rnethylated silica gel. For a
vapor pressure of about 1.3 x 10~ Pa only
a weak C~---O stretching band at 1710 cm -1
appears which is assigned to acetone
molecules adsorbed at residual surface
hydroxyl groups (3%). Increasing the
vapor pressure to only 2.7 × 102 Pa gives
rise to the bands at 1720-1722 cm -1 and
at 1735-1737 cm -1 which dominate with
growing coverage (cf. Table II and Fig. 3b).
From these results it follows that only a
very small number of acetone molecules
interacts with the residual hydroxyl groups
and that the overwhelming part is adsorbed
on nonhydroxylic adsorption sites (band at
1720-1722 cm-i). The wavenumbers for
the C - - H vibrations of the trimethylsilyl
groups change only insignificantly (2915
2920 cm -~, 2969---> 2972 cm-0 due to
acetone adsorption.
CONCLUSIONS
(i) Carbon-13 NMR spectra were studied
for acetone molecules adsorbed on partially
dehydroxylated silica gel (pretreatment
temperature 670 K) and methylated silica
NMR AND IR OF ACETONE ADSORBED ON SILICA GEL
gel surfaces. The appreciable downfield
shift for the carbon of the C : O group on
partially dehydroxylated surfaces is due to
hydrogen-bonding interactions with surface
hydroxyl groups.
(ii) These resonance shifts were interpreted on the basis of a simplified model
involving complex formation between acetone and surface hydroxyl groups. The
number of interacting sites evaluated directly from the NMR shifts is 1.4/nm 2 for
partially dehydroxylated silica gel (pretreated at 670 K) and 0.3/nm z for methylated
silica gel samples. The latter value is greater
than the number of residual surface hydroxyl groups. This points to a comparably
strong interaction with nonhydroxylic adsorption sites.
(iii) The four IR bands for the C ~ O
stretching vibration of acetone on unmodified silica gel surfaces (pretreated at 1070 K)
are ascribed to interactions with geminal
surface hydroxyl groups (1690 cm-1), with
isolated surface hydroxyl groups (1710
cm-1), with nonhydroxylic adsorption sites
(1720-1722 cm-1), and to the gaseous state
(1735-1737 cm-1).
(iv) The shift of the IR stretching vibration band of the hydroxyl groups involved in hydrogen-bonding interactions
increases with growing acetone pressure.
This fact is explained in terms of different
spatial arrangements of the hydrogen bond.
The resulting ~3C NMR shift is an average
value due to fast exchange of the molecules
in the several states.
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Journal of Colloid and Interface Science, Vol. 84, No. 2, December 1981