Infrared spectra of water. II : Dynamics of H2O(D2O)
molecules
Y. Maréchal
To cite this version:
Y. Maréchal. Infrared spectra of water. II : Dynamics of H2O(D2O) molecules. Journal de
Physique II, EDP Sciences, 1993, 3 (4), pp.557-571. <10.1051/jp2:1993151>. <jpa-00247854>
HAL Id: jpa-00247854
https://hal.archives-ouvertes.fr/jpa-00247854
Submitted on 1 Jan 1993
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Phys.
J.
II
France
(1993)
3
557-571
APRIL
1993,
PAGE
557
Classification
Physics
Abstracts
61.25E
spectra
Infrared
molecules
Y.
of
water.
II
Dynamics
:
of
H~O(D~O)
Mardchal
D£partement
d'Etudes
(Received
de
Recherche
Fondamentale
Nucl£aires,
85X,
F-38041
9
J992,
accepted
October
22
Matikre
la
sur
Grenoble
Cedex,
SESAM/PCM,
Condens£e,
Centre
France
J992)
December
Spectra of e" (imaginary
dielectric
constant) of water in the IR region,
obtained
as
previous article by using attenuated
total
reflection
(ATR) techniques, are analyzed.
Criteria
presented which allow us to define, on the basis of spectroscopical arguments only, the
are
low
e"(T~) and the high
e"(T~) on
which
temperature
temperature
spectrum
spectrum
any
5 °C to 80 °C, may be
decomposed.
These
spectrum at
temperature T, in the range
spectra
bands
(intramolecular
display novel
features
their v~
stretch) have shapes which
have
great
similarities
in both
the 8 band
(intramolecular
bend) of the high
spectra
temperature
spectrum
e"(T~), has a simple shape with no apparent
which
with a good
approximated,
structure,
may be
precision, by a Lorentzian
A
discussion
features
of the origin of these
reveals a new picture
curve.
of
molecular
level : it is made of H~O
molecules
which
either perform
rotations
of a
water
at a
vibrational
character
(librations)
around
their three
rotations
and
appear in e "(T~) or perform
axes
around
their C2 symmetry
diffusional
of the
axis z of a
(relaxational)
character.
H20
molecules
latter
e"(T~).
Their
reaches
=35fb
0°C
atm.)
and
in
concentration
(I
type
at
appear
90 fb at 100 °C (I atm.). They have
rotational
energies around z greater than the maximum of the
potential energy goveming this rotation.
Around
they perform
their other
librations
which
two
axes
qualitatively do not differ from those performed by molecules
appearing in e "(T~). The
estimated
correlation
time, or average time during which phase
of 8 vibrations
coherence
in these
molecules
is kept, falls in the
10~ ~~-10~ ~~ s, as
deduced
from the
Lorentzian
shape of the 8 band in
range
e"(TH). The analysis of these spectra also indicates that the « 8 + v~ » band borrows its intensity
from
in the
vibrational
potential.
term
v~ via a cubic
Abstract.
described
in
a
m
Introduction.
1.
is
Water
instance,
a
species
is
Of
electronic
one
structure
non-bonding
bonds
better
in
which
the
understand
as
which
how
many
paradoxes.
stable
Its
constituent
molecules.
Yet
it
molecule,
has
a
very
H~O,
for
particular
lying
consequences
: it has
as
many
orbitals.
This is at the origin of an extremely high density of Hvalence
makes it an exceptional liquid. A part of the paradox is that we certainly
this
exceptional density of H-bonds is at the origin of exceptional
which
orbitals
water,
exhibits
simplest and most
looks quite ordinary
but
has
far
558
JOURNAL
properties
bonds,
of
one
of
the
spectra
up to
parameters
cell,
have
we
preceding
H20
how
than
even
a liquid,
species
familiar
recently poorly
temperature
as
been
able
II
manage,
with
N°
complex liquid [2].
a
has
which
by
studied
been
these
H-
although
techniques, its IR
available
all
directional
numerous
or
and
upon
ATR
no
good quality
spectra
IR
of
which
water,
described
are
in
a
study their dependence
these
Let us
that ATR spectra in the IR region are spectra of bulk
two
stress
parameters.
upon
consists of making absorption on the
only which gets out of a
water,
evanescent
as it
wave
crystal. As this
extends
of the size of the wavelength,
that is,
evanescent
wave
over
a region
several
microns in our case,
ATR
spectra are spectra of a film of this thickness, with negligible
surface
effects
disappear at a distance of the order of I nm [4].
which
The aim of this article is to analyze these IR spectra of water, in view of getting
insight
some
the
disposition and dynamics of H~O molecules
in
One of the
into
main
results
water.
described
in I is that any
5 °C ~ T ~ 80 °C ; e" is the imaginary
dielectric
spectrum e"(T) (
of water) may be decomposed into any two
constant
spectra e "(To ) and e"(Ti) following the
equation :
[3] (which
article
will
e"(T)
In
these
mind
in
points
"(To)
e
equations we have not
the e"(T) represent
various
=
In
the
shall
we
a(T)
a
=
condition
that
choice
These
a
(T, 0,75 )
equations
These
The
(T)
the
all
=
(1)
P, but
wavenumbers
at
has
[8-10].
of a(T, To, Ti)
isosbectic
where
P
recognized
previously
been
with
T
To )]
(1
x
0.2
Ti )/(Ti
[(T
To
in
well
are
To is taken equal to 0 °C and Ti to 75 °C,
which
simply
article,
shall
a(T, To, Ti),
we
When
TOY (Ti
keep
shall
we
of several
presence
all
wavenumbers
the
(near infrared) bands
variations
considered,
the
[(T
to
e"(Ti)i
appear
points
isosbectic
such
approximation.
of the
the
rest
equation :
in
obeys
simplicity,
implies
for
and
ie"(To)
x
NIR
temperatures
suppose
then
of
quadratic
a
the
a(T, To, Ti)
explicited,
presence
[5-7] or 2 v~
of
range
I in
spectra. This form
the
which
spectra
The
bands
by
described
of
bands
e"(Ti).
Raman
v~
e"(To)
=
that
in
denoted
be
following)
4
paradox is that,
Another
systematic dependence of these spectra
H/D isotopic composition
reported. Using an
were
known
obtain
to
PHYSIQUE
molecules
if
water
most
were
such
[I]
water
keep
to
DE
which
write
II
(2)
composition, under the
H/D composition.
same
experimental
results.
suited
describe
well
to
special
and
e"(Ti)
have,
e"(To)
however,
no
whatever
the H/D isotopic
(I) and (2) are valid
e"(T) in equation (I) stand for spectra having the
of To
and Ti
corresponding
0 °C
=
and
temperatures
physical meaning.
H~O(D~O)
molecules
In
is
spectra
of
obtaining
water,
shall
view
in
75 °C
=
we
description
a
of
instead
of
these
the
take
spectra
e"(T~)
and
structure
as
a
dynamics
basis
for
of
the
e"(T~) which are the
high
respectively if phase
observed
low
and
which
would
be
temperatures
at very
spectra
very
reached.
These
could
be
experimentally
before
such
transitions
did not
temperatures
occur
defined
by
their
physical
meaning,
which
then
e"(T~),
have
e"(T~)
and
spectra
are
a
decomposition on the experimentally known spectra e "(To ) and e"(Ti ) (Eq. (I)), that is, by
a(T~, To, Ti ). With such a basis, we have :
their a(T~)
a(T~, To, Tj) and a(T~)
decomposition
of
spectra
e"(T)
with
(Eq. (I))
spectra
and
=
=
to
T
temperature
at
the
concentration
e"(T~)
given by
a
of
(T)
defect
«
=
=
a
e"(T~)
»
a
(T)
molecules,
(T, T~, T~)
=
la (T)
ie"(T~)
x
that is the
a
e"(T~)1
proportion
(T~)i/ ia(T~)
(3)
of
a
molecules
(T~)1
contributing
(4)
4
N°
Let
as
mention
us
article.
this
define
a
insufficient
will
that
has
pressure
described
in
to
of
arrangement
analysis,
this
Analysis
only depend
not
have
to
WATER
on
temperature
effect
an
II
OF
similar
559
to
also
T but
that
of
depends
pressure,
on
[I I].
temperature
As
spectra
dependence of a will not be considered in
Let us also note that the quadratic development of a(T) in equation (2) is of no use
(T~) and a (T~ ), and consequently e "(T~ ) and e "(T~ ), as this development is largely
for
extrapolations to very low and very high temperatures.
The problem,
which
I
article
discussed
be
does
a
shown
been
obtained
were
section
in
quantities. Once
be
performed
2.
SPECTRA
IR
will
2, I
this p
atm,
then
be to
in
e"(T~)
2, I
DETERMINATION.
into
several
The
has
bands
quantitative attempt
decomposition on a
to
which
will
allow
us
to
define
these
e"(T~) and e"(T~)
section 3a
dynamical
description
for
which
incorporates novel features
revealed
water,
of
various
bands
of
will
the
by
e"(T~).
and
Gaussian
in
criteria
find
spectroscopic analysis
a
subsequent
subsections.
In
defined
H~O(D~O) molecules
will be proposed.
of
I
at
analyze
Gaussian
decomposition of the
been proposed by
this
band
basis
is,
and
get
however,
band,
2 v~
and
Luck
picture
a
the
at
obtained
as
Ditter
in the
[8] and
of
water
at the
origin of a lack
region,
NIR
constituted
molecular
the
level.
flexibility
of
first
The
which
Some
the precision.
attempts to directly
from
high
of
Raman
bands
temperature
temperature
components
v~
experimental spectra have been later proposed [6, 12]. Such a procedure avoids decomposition
form. As
bands having a predetermined
described
previously (Eqs. (1)-(4)) IR spectroscopy
on
is particularly well adaptated to it, and, in order to define e "(T~) and e "(T~ ) we shall be able to
criteria
spectroscopic
only, discarding
thermodynamical
which
less
be
to
use
ones
seem
precise. The first criterion
which
shall
is
that
these
have
negative
It
spectra
parts.
we
use
no
implies a(T~)
l. I and a (T~
2, I for spectra of any isotopic composition.
With the latter
the
value
band
(Fig, I) of e"(T~) has
unfamiliar
dip at
nevertheless
quite
v~
an
3 150 cm~
which
makes it
unreasonable.
The
absence
of this dip requires a(T~)
l.7. We
furthermore
reasonably postulate that the decomposition of any
e"(T) on
spectrum
may
e"(T~) and e"(T~) is valid up to 100°C (we have
it up to
80°C). It implies
checked
a(T~)~ l.25 by extrapolating
T=100°C.
equation (2) up to
In
order
have
better
to
a
determined
value for this quantity,
Raman
which
appeal
exhibit
strongly
spectra
to
we
may
decreasing v~ (libration) bands when the temperature is raised [5]. It is then
reasonable
to
intensity
of
e"(T~
has
weak
that
the
band
in
the
equivalent
)
Raman
spectrum
a very
assume
v~
intensities
of v~ Raman
bands mainly originate from
which is equivalent to assuming that the
of these
lattice
molecules
which
The
concentration
water
appear in e"(T~) in IR spectra.
«
»,
intensities
of
bands
molecules
is I
-a(T)
(Eq.(3)).
Taking the
these
Raman
at
v~
proportional to 0.225 and 0.076 [5] respectively,
have
0 °C and Ti
75 °C to be
To
we
using equations (2) and (4) :
makes
it
hard
define
the
to
when
use
wishes
one
low
to
improve
and
~
~
~
=
=
[1
gives a(T~)
(and with any
1.5
It
2 700
cm~
up to
this
now
«
3
+
In
I,I
(I)
which
It
higher
be
may
undetected,
»
we
(the
have
negative
is
a
the
e"(T~)
due
some
to
which
and
bands
which
indicated
values
that
localized
fall
a(T~)
on
0.225/0.076
=
=
a
(T~)/[a(T~)
1].
(5)
adopt. Let us note that with this value
negative part in the region 2 350a
very
which
remained
small
dependence
of e"(T~)
temperature
introduces
negative values originating from a derivative of
dependence of the
of
(small)
to a
temperature
centers
in this region) in e"(T~).
value)
equivalently,
or,
(Ti)]
value
=
bandshape
v~
(To)]/[I
a
the
which
we
shall
has
should
weak
be
less
than
high frequency
side
0.6.
For
of the
v~
values
band
of
a(T~)
appear
less
than
which
can
560
PHYSIQUE
DE
JOURNAL
II
N°
4
~
Uj
~~
o
to
,,
I
+~~
,,
o
o
WRVENUMBER
Fig.
I.
a(T~, To, Tj)
bands
Spectra
1.25
of
e"(T~)
ordinary
(thick line), a(T~)
2.05
=
=
equation(I)
using
calculated
water
(thin line), To
0 °C
=
and
Tj
a(T~)=
with
75 °C.
Denominations
of
=
indicated.
are
with
hardly be justified,
even
dependence,
they are too
because
0.8 as the
choose
a(T~)
most
assumption
the
e"(T~)
that
has
a
hidden
temperature
bandshape. We shall
representative. An argument supporting the choice of this
value
will be given in section
2.3. As may be
in figure 2
variations
of a(T~) modify the
seen
intensity of the v~ band
without
changing its position and shape significantly.
In the following,
otherwise
indicated, to
unless
spectra E"(T~) and e"(T~) will correspond,
a(T~)
0.8 and a (T~)
1.5. The
value for a(T~) relies
quantitative
these
values
latter
on
for a(T~) is only the
It consequently
does
That
reasonable.
preclude
most
arguments.
not
choosing, if justified, other values. As will be seen these will, nevertheless,
modify our
not
conclusions
in a significant
With
these
values
find, using equation (4), that the
manner.
we
defect
represented
concentration
of
H~O
molecules,
by
their
e"(T~), at the
spectra
a
localized
to
come
from
a
derivative
=
=
temperature
of
fusion
=
T~
0 °C
=
is
:
a
(T~)
(6)
0.35
=
loo
concentration
of defect
molecules
at
same
way (Eq. (4)) the
a
equal to 0.89. The adoption of different
values
for a(T~)
lead
would
changes for these values,
especially for
a(100),
long as they stay
as
compatible with the absence of negative parts in e"(T~) and e"(T~).
In the
be
2.2
v~
These
BANDS.
extensively
studied
in
Raman
correspond
and
NIR
to
stretching
spectroscopies.
vibrations
One
novel
o-fi---O
point
appears
loo
to
found
°C is
no
within
the
which
have
in IR
to
significant
limits
been
spectra in
N°
4
IR
>
lU
SPECTRA
OF
WATER
II
561
562
PHYSIQUE
DE
JOURNAL
II
4
N°
=
Uj
m
to
d4
Dz
oJ
Fig.
v~
of
band
energies
conceming
bonded.
which
from
2.3
may be
that in
3
These
band
This
e"(T~)
striking
is
the
where
effect
feature
is
gas
it has
in
£H(?)
P~
with
P~
29
40
=
cm~
=
~,
cm~
P~
',
P~
206
=
e"(T~)
ordinary
correspond
which
phase). They
in
appears
drawn
are
found
exception
the shape of
point in this
noted
a
more
in
the
e"(T~)
have
637
where
and
cm
and
21
R~
marked
=
keeps
v~ in
article.
bending
vibration
scarcely studied up to
narrower
in
'
+
j(P
PH)/RHI~)
34
for
We
Lorentzian
have
=
IR
cm~
heavy
when
spectra
may
within
H~O
an
in
except
temperature
(Figs.
then
shapes
H-
are
different
now,
the
the
curvatures
much
not
are
water
of
which
in
the
bands
R~
is
lines
normal
position
variations
e"(T~)
3
cm~
Thin
for
molecules
small
they become
quantitative
manner
region P w 2 000 cm~
PH/"RH(i
cm~
to
been
H~O
that
=
=
of
the
resonances,
been
different
two
on
with
important
an
bands
are
in
e"(T~)
and
Fermi
to
which
spectra
[5].
raised
most
attributed
(the v~
situated
that,
remains
e"(T~),
BANDS.
Raman
where
vibrations
v~
nevertheless
It
molecule
some
bands
v~
e"(T~)
in
80cm~'
and
2 8
is
in
and
heavy
(thick
lines).
e"(T~) for ordinary
water
toward
lower
frequencies of 100 cm~ '
multiplied by 2 and shifted
for heavy
for e"(T~).
The
points the
Wavenumbers
water.
are
arrow
e"(T~) of heavy water.
3.
bands
4
see
of
the
5)
and
that
the
form
:
(7)
for
ordinary
water
and
water.
peak at a
somewhat
higher
wavenumber
cm~~ for heavy water) but exhibits
asymmetric
features
and is wider.
This tendency is not unexpected as,
when going to ice an
wider
even
band
with no
apparent peak at all j20]. We may suspect this 3 band in water to be
appears
composed of two bands, as clearly appears in the case of HDO
molecules
j19]. This is on the
limit
of detection,
however,
in our
of H~O and D~O
molecules.
present
case
The
3
band
(1650 cm~~
for
in
water
and
a
1210
N°
4
SPECTRA
IR
OF
WATER
II
563
m
to
d4
oJ
d
I
I4RVENUMBER
Fig.
e"(TL) (thick line)
4.
e"(T~)
line
This
3
v~
+
(Fig. 4j
band
»
we
an
e"(T~)
of
subtract
66
P
=
22
P
=
cm~
from
',
cm
water.
8
«
obtained
to
in
and
«
170
=
Gaussian
these
to
resulting 3 band, while P
quantities represent the rough
empirical
procedure.
by this
of the
625
=
e"(T~)
The
v~
will
cm~
be
98
«~
useful
~,
=
in
procedure
same
overtone
dotted
v~ » have
subtraction
e
bands.
«
is
then
cm~
section
is
better
~
is its
a
(T~ )
"
=
They
spectrum
represents
subtracted.
been
of the
The
thin
Lorentzian
curve
260
~.
the
also
Gaussian
two
of the
bands
for
3
form
:
/~
for
cm
overlaps
bandshape
and
v~
approximate
(8)
the
band
overtone
and
assign
«
knowledge,
simply
of
they
state
present
our
for
overlapping
these
bands.
The
resulting
integrated intensity P~, center of intensity
of the
3
first
v~
values
band.
»
then
may
We
second
and
bandshape
found
estimated
3 +
zero)
order
of
then
are
These
the
for the
In
characterization
rough
P)/«]~)/«
cm~
moment
of
overtone
an
the
best
simple empirical
simulation
represent
line in figure 4. Its
spectrum is drawn in dotted
normalized
P~ and width «~ P~ and «~ are respectively the
P~
The
water.
+
after
obtain
1/2[(P
cm
and
cm~
on
band
(exp
P
=
=
order
=
300
P
In
experimental
the
2 165
P
~,
special meaning
any
and
v~
spectrum
superimposed
is
ordinary
in
band
G(P)
with
the
is
arrow
ordinary
of
e"(T~).
from
3
e"(TH) (thin line)
(Eq. (8)) simulating 2
and
bands
by
marked
spectrum
(Eq. (7))
«
Gaussian
where
centered
e"(T~)
equal to
be
of
first
not
moments
measured
be
in
to
do
which
and
is
these
allowed
P~= 42cm~~,
of
moments
the
3
band
in
3.
applied to the
approximated by
C (P
P/2
=
«
cosh
of e"(T~)
empirical band
band
an
(w/2
[(P
P
heavy
in
)/«
of
the
water
form
(Fig. 5).
The
:
(9)
564
DE
JOURNAL
PHYSIQUE
II
N°
4
oJ
~
iii
ua
d4
m
oJ
.
'
''
I
Fig. 5.
e"(T~)
the
which
«
+
v~
»
subtracted
We
are
P~. As
e"(T~),
P~
3
have
the
The
P~
been
5.
are
with
this
criterion
a
P~ being
which
in
the
is
those
visible
we
may
it
retain
from
=
cm~
m
of
in
e"(T~),
on
the
looks
that,
=
moments
has
been
P~
and
definition
of
intensities
for
chosen
The
while
~.
comparable
is
is
reason
the
intensities
the
that
think
to
in
e"(T~)
of
they
that
3
bands
somewhat
H-bonds
this
in
effect
increases
is
e"(T~)
e"(T~) and
surprising
[22].
attributed
as
As
to
a
3
bands
H-bonds
an
accuracy
of lo
cm~ ~,
centers
are
in
by
some
found
e"(TL)
at
are
of
component
residual
frequency side of the dotted spectra
useless to go deeper into this analysis but,
low
within
differ
in
as
of
figures
a
4
and
conclusion
intensity
e"(T~) are the same.
width of 3 bands in e"(T~) is most
probably the
manifestation
of a
modulation
of
The
goveming the 3 vibrations by some low frequency
force
intermolecular
modes of
constant
molecule.
Good
candidates
for such
modes
3 in an H~O (D~O)
symmetry
same
as
are
O-O-O bending
which fall in the 50 cm~
region [17, 23]. Such a modulation
leaves
modes
[24].
integrated intensity of the band
unaltered
bands
is
arrow
e"(T~).
P~ of
strength
0.8.
cm~
first
baseline
constant
a
65
The
3.
an
[21],
Lorentzian
a
with
[3, 19]. It is then logical
environment
P~. This is
than
which
have
a(T~)
different
and
overlap
«~
~,
e"(T~)
and
a
P~ and
when
Fig. 5),
taking a(T~)
for
Gaussian
a
smaller
190
by the
e"(T~) and
smaller
than
in
affected
rough procedure
subsection
of this
when
varies
intensities
of
e"(T~)
in
between
of its
because
spectrum
~, P~
cm~
=
intensities
overtone
v~
With
33
hardly
wavenumbers
higher
certainly not weaker
the
(dotted
bands
3
same
centers
cm~
then
has
bands
these
band
slightly
this
intermediate
subtracted
not
3
that
see
is
represents
2 vL
somewhat
band
remaining
and
after
character
a
e"(T~) (thin line) of heavy water.
The
dotted
spectrum
marked by
(Eq. (9)) has been
subtracted.
The thin line
subtraction
of the
Lorentzian
(Eq. (7)) from e"(TH).
curve
line)
simulating
band
obtained
has
3
of the
lo
the
spectrum
the
(thick
e"(T~)
where
of 3
and
the
the
the
the
N°
IR
4
2.4
3
«
v~
+
ordinary
for
them
as
bands
v~ »
The
+
6 lo
and
water
3
«
These
BANDS.
»
bands
whose
heavy
for
cm~
Raman
or
II
maxima
e"(T~) fall around 2 150 cm~
ambiguity when assigning
some
in
is
There
water.
565
[13, 25], and it is the aim of this
spectra
subsection
discussed
in the
band has been
they are a 3 x v~
overtone
of ice [20]. An
attribution
is that
these
bands
have
similar
shapes,
argument against this
case
and particularly
comparable widths, in e"(T~) and in the spectrum of ice. The main but not
significant
differences
found in a
somewhat
larger intensity in ice accompanied by a shift of
are
50 cm~
situation
of v~ bands
whose
towards
higher
wavenumbers.
It does not
reflect
the
some
maxima
much
separated : they are found at 650-700 cm~~ in e"(T~) and at 850are
more
900 cm~
in the case of ice, which implies that the
maxima
of 3 x v~ differ by a quantity much
examine
to
it.
the
be
3
«
H-bonded
of
bands
to
experienced by
that
e"(T~)
between
v~
+
a
by
systems
the
linear
terms
[15, 24].
particular H~O
a
and
of
spectrum
ice.
however, so straightforward.
not,
anharmonicity such as
mechanical
is
»
of
consequence
the
3
mode
of
constant
'
cm~
attribution
The
cannot
v~
50
than
greater
possibility
OF
are
in IR
WATER
SPECTRA
in
The
molecule
is
reason
in
ice
that
in
v~,
the
usual
is
of
none
for
such
symmetry,
exists,
band
a
it
force
reasons
of
as
tetrahedral
a
such
where
symmetry
modulation
for
coordinates
the
For
a
as
three
the
has
representation
which
would
make
the
symmetry
a
completely symmetrical. A complementary
is
that
in
this
argument
this
band
would
would
correspond to a 00
11
get its intensity from the 3 band, and
case
transition,
while the 3 band
itself
lo
transition
(the set of bands 3
would
correspond to a 00
and « 3 + v~ » is in this
electronic
with
Franck-Condon
comparable to
bands
most
case
[24, 26] ). The center of intensity of this 3 band is then that of all 00
transitions
structures
n
1870cm~~
and
would
fall
ordinary
is
consequently
for
This
at
water.
not
common
a
1595cm~~
value [22],
especially
when
compared with that in the gas phase at
[27].
v~
librations
of
corresponding
this
molecule
potential
-
-
-
Furthermore
it
would
position
same
transition)
then
be
e"(T~)
in
by
hard
understand
to
e"(T~)
and
(Sect.
cm~~
how
2.3)
(00
bands
3
whereas
-
the
3
«
lo
transition)
+
band
v~»
is
fall
at
the
(00-11
appreciably less
e"(T~) than in e"(T~) (Fig. 5).
Another
possibility would be that that this « 3 + v~ » band is a
electrical
of «
consequence
anharmonicity»
(presence of
non-linear
in
vibrational
coordinates
in
dipolar
the
terms
moment). The
of qualitatively
similar
Raman
bands in
however,
makes
this
spectra,
presence
assumption
unlikely,
since
then
polarizability
derivatives,
instead
of
dipolar
moment
derivatives,
trigger
transitions.
The
novel
point conveyed by IR spectra is that the ratio of the
intensities
of
these
bands in e"(T~) and
3 + v~ »
e"(T~) is of the same
of magnitude as that of their
order
«
(Fig. 3). It strongly suggests that the « 3 + v~»
band
of a
is a
v~ bands
consequence
mechanical
anharmonicity appearing in the form of a cubic term (the lowest order
anharmonic
term) in the potential coupling the
coordinates
of the 3, v~ and v~ modes.
Such
of the
terms
are
those
responsible for
Fermi
[24, 26]. It implies that
this
nature
same
as
resonances
band
3 + v~
borrows
its intensity from v~ but that its position is mainly
defined
by the
«
position of
+ v~.
intense
is
shifted
loo
some
between
these
spectra
two
and
in
»
3.
Interpretation.
IR
spectra
are
[8, 9] and
NIR
water
compatible
Raman
molecules
molecules
at
possibility
to
»,
that
is
origin of
explain why
the
with
spectra
H20
the
now
molecules
e"(T~).
distances
This
typical
picture
standard
[5, 12, 17, 28-30]
which
are
description
of
a
of
describes
and
the
at
offers
tetrahedral
origin
the
which
water
water
as
a
e"(T~),
advantage of
ordering
of
of O
emerged
mixture
atoms
of
and
«
«
from
basic
defect
retaining
(as
found
»
the
in
566
ice)
kept
are
defect
in
molecules
molecules,
to
be
to
as
by X-ray
and
that
of
water
rather
from
and
deduced
DE
ensure
patches
form
experiments
thought
are
diffraction
shown
as
here
are
and
aggregate
to
water,
molecules
JOURNAL
bonded.
less
liquid,
a
rigidly
techniques
diffraction
neutron
is
N°
II
basic
as
molecules,
bonded
Raman
and
of
nature
These
from
region,
these
while
defect
these
defect
displays
however,
4
thought
are
deduced
as
spectroscopy,
spectrometry,
NIR
[31-35].
molecules
water
spectra [36] in the supercooled
The
usual
description of the
Raman
from
PHYSIQUE
some
particularly those
incompatibilities with novel features
revealed by IR
conceming v~ and 3 bands of e"(T~). I shall first discuss these incompatibilities, before proposing a
molecules
with
bands in e"(T~).
which is compatible
picture for these defect
new
H20(D20)
keeping
H-bond
been
described
molecules
molecules
have
Defect
strong
as
one
(of
the
nature
same
be
may
such
a
«
linking basic
[37, 38] or
H-bonds
as
bifurcated
H-bond
»
molecules)
water
even
broken
a
and
H-bond
weaker
one
which
difficulty
[8, 9]. The
H-bond
with
descriptions is that there is not one type of defects, but there are two which are
complementary and in equal number, as they are created in pairs, a point already noted [38]. In
order to
illustrate
this point let us think of a defect
consisting of one
molecule
Hstrong
bond and one
broken
H-bond.
Its
complementary
defect is an H20
molecule
establishing two
with its O-H
H-bonds
but accepting only one
H-bond
its two
lone-pairs.
strong »
groups
«
on
These
complementary
defects
contribute
would imply a (T) (Eq. (3))
cannot
to e"(T~), as this
be
less
than
0.5.
This is an
impossible
condition
satisfy since at Tj
75 °C (or
to
to
a(Ti )
I) it implies a(TH) + a (T~) ~ 2, using equation (4). As seen in section 2, I this cannot
be
with a(TL) and a(T~)
obtained
satisfying even the less
conditions
(
I,I
severe
0.6 and 1.25 ~ a (T~ ~ 2, I) which
for e "(T~ ) and e (T~ ) to display
a (T~)
are
necessary
negative parts.
no
complementary
defects
These
should
consequently
contribute
e"(T~). The presence of
to
«
»
=
=
~
"
~
of defects,
kinds
two
of
e"(TH)
the
same
and
is
band
band
3
bers
[22].
than
3
at
Furthermore
interchange
8"(TH) can
of
the
kinds
two
rejected
be
is in
would
on
the
contradiction
Similar
difficulties
with
arise
untenable,
is
is
then
expect
bands
3
spectra
as
the
3 band
give
consisting of one strong
while
complementary
defects
3 bands
higher
at
wavenum-
that
both
kinds
defects
of
defects
as
e"(T~)
in
in IR
seen
asymmetrical 3 bands [39]
H-bonds
give symmetrical
strong
which
what
assumption
The
wavenumber
give
we
e"(TL)
in
bands
with
contradiction
structure.
no
same
equivalent
two
is in
with
H-bond
weakened
have
which
however,
narrow
narrow
one
which
a
to
be
at
lower
wavenumbers
rapid
a
might explain the
Lorentzian
of 3 in
basis that it strongly depends on the
concentration
of defects,
a
e"(T~) (and also e"(T~)) being temperature independent.
is
not
defects,
of
with
what
found
in
section
2.3.
which
for
bands
v~
been
has
it is
which
e"(T~),
only, as
hard
how
understand
to
Finally
shape
bands
due
to
shapes similar (Sect. 2.2) to bands
as
originating from one kind of molecules
in e"(T~).
Another
difficulty of such a model is that it predicts v~
librational
bands
to
at
appear
significantly lower
in e"(T~) than in e"(T~). This
wavenumbers
does
what
be
not
to
seem
happens as this difference is of 100 cm~ ' only (Fig. 4), which is also visible as a shift of this
between
of « 3 + v~ » bands
order of magnitude
maxima
between
e"(T~ and e "(T~ (Fig. 3)
described
in the
literature
and is
small
shift only of these
bands
with
temperature
as
a
v~
kinds
two
of
molecules,
defect
in
have
[25, 40].
DYNAMICS
3, I
type of
one
bands
implies
The
most
of
that
the
molecules
some
basic
basic
of
exists
straightforward
and
vibrations,
to
fulfill
this
in
because
Furthermore
molecules.
way
appears
molecules
water
water
their
From
MOLECULES.
DEFECT
from
different
much
v~
OF
defect
in
some
these
discussion
e"(T~).
their
v~
the
coupled
requirements is
way
it
may be
defect
These
concluded
keep many
Lorentzian
shape of
bands
to
to
3,
has
suppose
a
that
cannot
features
their
diffusional
these
only
that
molecules
of
3
be
the
bands
character.
defect
H20
N°
molecules
(z is
whose
molecules
are
the
of
bisector
the
II
the
567
their
for
levels
energy
directions
in
O-H
two
WATER
OF
SPECTRA
IR
4
rotations
plane
of
axis
their
around
molecule)
the
above
are
z
the
consequently display a
and
character
keeping a vibrational
around
and
librations
their
other
(they still perform
their
rotations
around
for
two
x
axes
rotational
energies (around z) below this
have, on the contrary,
y). Basic
molecules
water
their
which is certainly a
around
three
librations
maximum
and
consequently perform
axes,
particularity of water. This description adopts the same physical basic picture as that proposed
maximum
of
diffusional
potential
the
character
goveming
energy
rotations
their
for
around
rotations
these
this
axis,
z
while
identification
of the
from it with the
somewhat
[41, 42]. It differs
molecules,
whereas
being responsible for the apparition of defect
attribution.
identify it as that of lower frequency with no particular
Robinson
and
coworkers
rotation
from the fact that for any H~O molecule
This particular
choice of the z axis
a
comes
rotational
potential unchanged, while it requires a rotation of
of w around
this axis
the
leaves
experiences,
considered
molecule
Furthermore
when the H20
around
the other
2 w
two
axes.
by
Robinson
rotation
in ice,
as
and
around
coworkers
as
z
of
environment
an
tetrahedral
the
symmetry,
force
for
constants
these
three
rotations
It implies
because of the linearity of H-bonds.
the
around equilibrium (zero rotation),
are
same
positions
in that
around their equilibrium
of the three potentials are the
that the
curvatures
same
the
potential
environment,
properties we deduce that, in a tetrahedral
From
these
two
case.
for
rotations
maxima
maximum
for a rotation of w/2 around z is much
lower than the potential
considered
longer
of
the
molecule
When the
environment
of w around
the other
two
no
axes.
periodicities
of
modified,
maxima
strongly
but
the
these
keeps a tetrahedral
symmetry,
may be
if
all,
the
majority
of
molecules,
change,
and
for
three
rotations
do not
the
the
not
great
than the
maxima
of the potentials
maximum
around z
remains
lower
of the potential
much
energies around z
with their
rotational
We may then have
molecules
around the other two
axes.
the
while the
rotations
around
above the
maximum
of the potential goveming this rotation,
other
two
We
and
character
for
spectra
the
these
easily
then
may
Raman
under
remain
axes
vibrational
the
:
the
IR
terms
when
in
realizes
one
that
describing
coordinates
corresponding
the
discrepancy
change only little
potentials,
retaining
thus
a
exhibit
between
IR
v~ bands
is
when
the
raised
temperature
that
apparent
bands
[25, 40],
while
bands
the
Raman
keeping their shapes and positions
understood
of
rotations.
two
understand
[43]
maxima
their
have
intensities
unchanged.
in
a
The
tetrahedral
rotations
z,
of
of
because
the
IR
v~
[5],
decrease
band
dipole moment
has
the parity.
These
the
symmetry
around
dramatically
which
behavior
may be
linear
no
bands
are
consequently not very sensitive to rotations
when
environment
longer
around z
the
even
no
keeps this
tetrahedral
symmetry (in the average it has this symmetry). They consequently do
such
rotations
altered, as when passing from basic
suffer an abrupt change when
water
not
are
molecules
defect
molecules.
They are consequently not very
sensitive
concentration
to
to the
of defect
molecules,
and display small changes only when the
This is not
temperature is varied.
for
Raman
where
polarizability
linear
in
describing
bands
has
coordinates
terms
true
v~
rotations
around z in a
tetrahedral
sensitive
symmetry and are consequently much
to the
more
concentration
3.2
so
defect
of
rotations
by three
fluidity
by
characterized
of
a
the
fact
character,
vibrational
bonds
preceding
that they
the
From
DISCUSSION.
much
molecules.
of
instead
four.
which
These
section
are
it appears
four-bonded
may also
molecules
that
but
basic
by
in principle be
certainly have
H20 molecules
fact
achieved
a
molecules
water
the
small
that
by
not
are
they experience
molecules
contribution
held
in
the
e"(T~) displays
as
similarities
with the IR
difference
is that they
spectrum of ice1 [20, 44]. The main
some
certainly form much less cyclic
of H~O molecules,
they may be
and in that
structures
sense
molecules
found in amorphous
solid
[45], where
closer
H-bonds
thought to be
to
water
are
JOURNAL
of
DE
water.
PHYSJQUE Jl
They
T
3,
have
N'4,
some
APRIL
1993
similarities
with
in
ice
23
JOURNAL
568
bent
more
are
molecules
consequently
rotations
between
5 °C
significant
the
around
description
At
on
strictly
likely to
in this
valid
in the
finite
[31-36].
size
of
axes
of
a
a
Defect
diffusional
4
molecules
They
perform
character.
liquid,
normal
range of
in the
valid
remain
region
higher
shorter
a
N°
which
axes.
temperatures
justified
remain
is
here
expected
mechanism
to
three
80 °C. It is
and
aggregates.
molecules
their
presented
description
The
II
which
have
diffusional
is
They may aggregate in clusters of
display rotations around their z
only part of the properties of molecules
in ice.
than
those
PHYSIQUE
DE
increase
is the
80 °C
than
of
range
investigated, that
supercooled region where
temperatures
deep
structuration
in
we
the
because
the
temperatures,
of
basic
validity
expect
water
of
this
concentration
of
display
cooperative properties, certainly becomes
and
may
more
more
broken
appreciable.
Such
certainly
H-bonds
in
-5
°C,
the
80°C,
in
present
are
range
)
also
in
e"(T~),
"(T~
and
but
quantity
sufficient
in
major
the
feature.
They
not
to
a
appear as
e
have been
detected in NIR spectra [10, 46, 47] which is a region where they can be
detected
H-bonds,
broken
with
to
much
a
which
v~
sensitivity
greater
vibrations
by
conventional
From
the magnitude
e"(T~ ) (Sect. 2.3) we
of
molecules.
this
(through
width
varying
form
of
energy
the effect
that
not
of
some
intensities
the
H-bonds
related
compared
as
to
molecules
which
their
intensities
and
be to
the
observed.
We
alter
may
widths.
widths
~
I~H
2
wr~
~~
and
« l (rapid
expressed in
modulation
P
condition
). We
of
instead
bands
Kubo's
"Tc
"
the
contrast,
these
in
such
effect
of
this
due
to
molecules.
bands
appear in
their
modify
which
bands
for
be
cannot
neighbour
on
of
it
as
dilution,
characteristic
using
write,
then
In
of
situated
by isotopic
are
band
3
responsible
are
instance),
for
vibrations
between
H~O
would
displacements
of 3,
the
time during which the
average
centered
«~ be the width (second
intermolecular
and
vibrations
of
or
rotations
constant
[3, 19]
of
bands
kept.
all
describing
curve
r~,
Let
intermolecular
force
transfers
time
is
freeze
these
of the
energy
environment
the
transfers
R~
where
broken
for
Lorentzian
molecules
could
we
the
correlation
the
defect
in
if
of
R~
estimate
derivative-like
but
centers,
width
the
modulation
a
vibrational
resonance
When
band
3
likely
It is
of
may
vibrations
of the 3
coherence
moment)
with
region,
IR
magnitude
of
order
one
H-bonds.
strong
the
than in the
smaller
be
may
vibrational
resonance
isotopic dilution, which
theory of lineshapes [48] :
is not
upon
(10)
~I~
the
factor
deduce
2
from
comes
w
As it is
the
reasonable
fact
that
expect
«~ are
w
R ~.
«~
where «~ is the width of the
band in e"(T~) which we have
order
to be of the
«~ « «~,
seen
of 3 R~ (Sect. 2.3) for both ordinary and heavy water,
deduce
that
has
value
falling
we
a
«~
between
and 3 R~.
From
these
values
deduce, using equation (10) with
extreme
R~
we
R~
m
35
»
to
cm~
10~ ~~/2
w
<
r~
10~ ~~/2
«
w
(in seconds).
(I1)
time is certainly too short to be
T~-type correlation
measured
by NMR experiments [2].
principle it falls into the possibilities of Raman
but
has apparently
spectroscopy,
been
not
using this technique. It corresponds to 8 making a small number of oscillations only
measured
before loosing phase
coherence.
It is likely to be in
diffusive
connected
to the
nature
someway
around z. The precise
of
rotations
mechanism
by which it is connected,
however,
remains
Finally, let us note that a Tj-type relaxation
unknown.
mechanism,
corresponding to a finite
This
In
lifetime
(
m
10~
«~(«~«
P~ (the
'~
1/(2 WRH) for the first
s) for this lifetime. We
R~)
center
to
of
obtain
the
a
band)
excited
think
state
in
3
Lorentzian
unchanged
when
give
would
likely to
shape,
which
it less
passing
occur
as
would
from
the
it
be
order
same
imply
would
hard
e"(T~)
to
to
of
a
correlate
e"(T~).
magnitude
much
smaller
with
a
N°
4.
Conclusion.
The
analysis
of IR
ratio,
noise
e"(T~)
using
obtained
spectra,
revealed
the
of e"(T~)
e"(T~)
the
band
shape
centered
the
at
same
features
e"(T~). The interpretation of these
dynamics of H~O(D~O or HDO)
molecules
mechanism
that proposed by
Robinson
and
as
and
Lorentzian
development.
its
in
molecules
whose
for
types
differ
from
while
rotations
are
the
for
be
the
such
molecules.
temperatures
central
arguments
our
as
their
symmetry
of
three
attributed
of
to
ATR
As
any
having
defect
axis
those
molecules
(
more
molecules
vibrational
a
have
a
in
appear
not
proposed earlier,
having broken or
5 °C
special
studies
molecules
does
it
water
precise
water
~
T
~
80 °C)
This
might,
vibrational
bands
role.
intramolecular
concem
have
we
spectra
our
from
basic
be
to
Basic
considered
play
the
pressures.
or
techniques,
bands.
libration
z
from
being
as
of
for
somewhat
able
a
of
spectroscopic
axes
z
the
differ
also
temperatures
range of
H-bonds
do not
to
seem
using
obtained
bands
however,
of
has
band
physical
same
called
are
previous
the
higher
at
case
although
have
intermonomer
In
weakened
that,
note
we
axis
This
character.
H-bonds.
strongly
not
the
special role
coworkers'
model.
These
properties
defect
molecules
which
thought
were
weakened
or
around
the
differs
which
are,
and
nature
liquid-like
and
us
not
from
starts
[41, 42] but
two
which
Robinson
Let
does
It
structure.
unsymmetrical
description
propose
a
to
us
coworkers
into
apparent
no
which
water
molecules
especially
strongly
which
allowed
in
good signal-toshapes
between
a
similar
the
as
(librations),
diffusional
however,
This
with
narrow
display
which
display
wavenumber
molecules
molecules.
conclusions
concems
those
broken
is
and
bands
v~
consequently adopted. We
dynamics of both kinds
perform
rotations
around
main
character
classifies
defect
and
what
are
It
techniques
ATR
features:
novel
569
II
WATER
OF
SPECTRA
IR
4
limited
were
conceming
results
invoked
to
P
m
650
cm
'
we
only part of these bands and have consequently been obliged to appeal to older spectra in
saw
the FIR region. Such
amenable
better quality using
and certainly
modem
to
spectra are
scarce
equipment which has made great progress. It will in particular be very useful to verify that the
decomposition
of
vibrations
follow
of
intermonomer
the
decomposition
that
same
as
intramonomer
bands
(Eqs. (I) and (2)), which is not a priori true, as parts of e"(T~) and
e"(T~) in the FIR region might display temperature
variations.
It will be the aim of subsequent
experiments to look at this point.
This
article
has been
devoted
analysis of the
variations
of IR spectra of
with
to the
water
In
forthcoming
articles
[19, 49] 1 shall analyze their
variations
with
deuterium
temperature.
concentration.
This
will
allow
the
determination
various
of
mechanical
such
parameters,
as
coupling energies or Fermi
energies of various
vibrations.
resonance
interest of obtaining precise IR spectra of water
Let us finally note that the
extends beyond that
of conveying
information
the
and dynamics of H20
molecules
in pure
structure
water,
on
as it
allow to apply IR
domain of aqueous
solutions, particularly the
spectroscopy to the vast
may
domain
of
molecular
biology, where IR spectroscopy has scarcely been used outside
narrow
spectral windows
where
does
absorb.
water
not
intra
and
intermolecular
Acknowledgments.
I
am
indebted
conceming
I
am
and
also
to
more
grateful
comments.
Professor
J. E.
particularly
to
Professor
Bertie,
article
W.
University
I of this
A. P.
Luck,
series
of
but
Alberta,
which
University
of
highly valuable
repercussions in
Marburg, for helpful
for
had
comments
this
article.
discussions
570
JOURNAL
DE
PHYSIQUE
II
N° 4
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