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Purely discrete Markovian frequency modulation in molten alkali perchlorates
Journal of
MOLECULAR STRUCTURE
Journal of Molecular Structure 349 (1995) 21-25
Purely discrete perchlorates
Markovian
frequency modulation
in molten alkali
S.A.Kirillov SONAR Research Centre for Biotechnological Systems, Prosp. Peremohy 52-2, 252057 Kiev-57, Ukraine
The vibrational
decay of the symmetric
stretching
v,(A)
mode of ClO;
anion
in fused 0.76 LiClO, - 0.24 KClO, mixture at 513 K was shown to be arisen from purely discrete Markovian frequency modulation process without any memory caused by ion-induced dipole attraction between the probe anion and adjacent cations. This process is collision-assisted and z,, , the modulation time, and TV,, , the time between cation-anion collisions in molten media, were found to be in close agreement. Several models for zec calculation were analysed, model was found to be the most suitable for molten salts.
and the Enskog
Studies of vibrational line contours provide investigators with valuable source of information concerning interparticle interactions and picosecond dynamics in molecular liquids [ 1, 21. If compare to commonly used molecular liquids, molten inorganic salts are systems formed by charged particles and involved extremely This leads to specific features in vibrational strong interparticle interactions. spectra of molten salts t.hat have been pursued extensively over the last decade, and the progress made has been summarized in several review articles [3 - 51. The purpose of this paper is to present an example of unusual frequency modulation process newly discovered in molten salts. Time dependent intermolecular interactions are known to change the instantaneous vibrational frequency and, in turn, to cause the broadening of the isot.ropic line contours. Such a process of frequency modulation depends on how the phase memory decays and leads to the correlation functions of vibrational dephasing of different forms. It. was shown very recently [6] that the correlation function of vibrational dephasing may be expressed in the most general way as -lnG(t)
= iV(2)$zi
where M(2)
(-1)” (t / Zo)3/k+nn+’ k.=,n!(3/k+n(2r)(3/k+?za+l)
is the vibrational
second moment,
0022-2860/95/$09.50 0 1995 Elsevier Science B.V. SSDI 0022-2860(95)08699-4
t is the time, and z,, is the
All rights reserved
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0 ‘I
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23
Fig. 1. The best fit (curve) to experimental G (t) (points) for molten perchlorate mixture.
0
.4
.8
1.2
TIME/
1.6
PS
The parameter r, may serve as an interesting probe for the dynamics of fluid when compared to some theoret.ical predictions. Its order of magnitude suggest,s that modulation events in melt lie within binary collision time domain. This justifies the use of the Enskog model cation-anion collisions in molten salt, r& = 4dN(nKT
[ ii]
to calculate
rBc , the time
between
,’ ‘&A)‘,“’
(2)
Here cr is the collision diameter, N is the number density of colliding particles u is their reduced mass, K is the Boltzmann constant and T the temperature.
and
In our estimates we used R(Li) = 0.68 A, R (K) = 1.33 A, R (ClO,) = 1.45 + 1 .I = 2.55 A where 1.45 A is the Cl-O bond length [ 121 and 1.1 A is intermolecular radius of oxygen [ 131; N was calculated using density data [ 141. This gives
rBc (K-ClO,)
= 1.3 ps, rBc (Li-ClO,)
= 0.29 ps. The results
obtained
agree well
with r, and show that collisions between lithium ion and anion may presumably be responsible for the frequency modulat,ion process. It is quite
appropriate
to mention
here that
previous
estimates
of
zBc were
found to be much lower than z0 [.5]. Several models were used for this purpose. Basing on the definitions of diffusion coefficient in the theory of Brownian motion (D = 02 / 6 rsc> aud in the kinetic and p the density) ret = po’ / 6 77 According
theory of gases (D = 77/p , 77 is the viscosity
one obtains (3)
.
to Ref. [ 1.51, in the case of molecular
rBc = (a - o)(n;u / 8 KT)“’ ,
liquids,
the best
zBc
are
(4)
24
where a is t.he mean distance between particles in a liquid. The obvious shortcoming of Eq. (3) is its underestimation of interactions in real fluids as, in fact, it approximates a liquid by an ideal (dense) gas. Eq. (4) seems to be more realistic since ideal-gas events are supposed to occur in a cell with rigid movable walls. Anyway, both equat.ions overestimate gas-like properties of real liquids. Moreover, in the case of binary melts, the definition of partial (which corresponds to collisions between anion and certain sort, of cations) requires some arbitrary assumptions.
ret
As an example one may compare rH, calculated for liquid potassium nitrate at 626 K using Eqs (21, (3) and (4) which were found as O.lS, 0.015 and 0.020 ps, respectively.
The values of p and 71 were taken from Ref.
[ 131. The characteristic
time of frequency
[ 171. For the perchlorate
ps, and by Eq.
Eq. (4) (2)
mixture
under investigation,
is hardly applicable.
or experimental
gives the most reasonable
r0 value.
results,
modulat,ion
Again,
= 2.32 A
in this salt is r, = 0.19 Eq.
(3)
gives
this is far from either
One may conclude
comparing
[ 161, R (NO,)
ps
rBc = 0.025 rsc estimat,ed
that the Enskog
to other models used to calculate
theory zBc.
REFERENCES 1. W.G.Rothschild, Dynamics of Molecular Liquids, Wiley, New York, 1984. 2. C.H.Wong, Spectroscopy of Condensed Media. Dynamics of Molecular Interactions, Academic Press, Orlando, 198.5. 3. S.A.Kirillov, in: A.N.Lazarev (ea.), Dynamic Properties of Molecules and Condensed Media (in Russian), Nauka, Leningrad, 1988, p. 190. 4. S.A.Kirillov, J. Mol. Liquids, 4.5 (1990) 7. 5. S.A.Kirillov, Khim. Fizika (Russ.), 11 (1992) 678. 6. S.A.Kirillov, Chem. Phys. Letters, 202 (1993) 459. 7. S.A.Kirillov, Chem. Phys. Letters, 200 (1992) 205. 8. S.A.Kirillov, G.A.Voyiatzis, G.M.Photiadis, and E.A.Pavlatou, Molec. Phys., (1994) submitted. 9. V.I.Snezhkov, S.A.Kirillov, and V.D.Prisiazhnyi, Opt. Spectrosc. (Russ.), 43 (1977) 991. IO. S.A.Kirillov and D.Tunega, Z. Naturforsch., 45a (1990) 14.5. 11. P.S.Dardi and R.I.Cukier, J. Chem. Phys, 89 (1988) 4145. 12. H.Siebert, Anwendungen in der Schwingungsspektroskopie in der anorganisches Chemie, Springer, Berlin, 1966. 13. A.R. Ubbelohde, Melting and Crystal Structure, Clarendon, Oxford, 196.5. 14. A.A.Farmakovskaya, Ph.D. thesis, Sverdlovsk, 1972. 15. F.J.Bartoli and T.A.Litovitz, J.Chem. Phys., 56 (1972) 413. 16. G.J.Janz, Molten Salt Handbook, Academic, New York, 1967. 17. T.Kato and T.Takenaka, Molec. Phys., 48 (1983) 1119.
MOLECULAR STRUCTURE
Journal of Molecular Structure 349 (1995) 21-25
Purely discrete perchlorates
Markovian
frequency modulation
in molten alkali
S.A.Kirillov SONAR Research Centre for Biotechnological Systems, Prosp. Peremohy 52-2, 252057 Kiev-57, Ukraine
The vibrational
decay of the symmetric
stretching
v,(A)
mode of ClO;
anion
in fused 0.76 LiClO, - 0.24 KClO, mixture at 513 K was shown to be arisen from purely discrete Markovian frequency modulation process without any memory caused by ion-induced dipole attraction between the probe anion and adjacent cations. This process is collision-assisted and z,, , the modulation time, and TV,, , the time between cation-anion collisions in molten media, were found to be in close agreement. Several models for zec calculation were analysed, model was found to be the most suitable for molten salts.
and the Enskog
Studies of vibrational line contours provide investigators with valuable source of information concerning interparticle interactions and picosecond dynamics in molecular liquids [ 1, 21. If compare to commonly used molecular liquids, molten inorganic salts are systems formed by charged particles and involved extremely This leads to specific features in vibrational strong interparticle interactions. spectra of molten salts t.hat have been pursued extensively over the last decade, and the progress made has been summarized in several review articles [3 - 51. The purpose of this paper is to present an example of unusual frequency modulation process newly discovered in molten salts. Time dependent intermolecular interactions are known to change the instantaneous vibrational frequency and, in turn, to cause the broadening of the isot.ropic line contours. Such a process of frequency modulation depends on how the phase memory decays and leads to the correlation functions of vibrational dephasing of different forms. It. was shown very recently [6] that the correlation function of vibrational dephasing may be expressed in the most general way as -lnG(t)
= iV(2)$zi
where M(2)
(-1)” (t / Zo)3/k+nn+’ k.=,n!(3/k+n(2r)(3/k+?za+l)
is the vibrational
second moment,
0022-2860/95/$09.50 0 1995 Elsevier Science B.V. SSDI 0022-2860(95)08699-4
t is the time, and z,, is the
All rights reserved
(I)
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aq?
ptn? (asea
‘( 1 >
*auI!J uo!Jelal.to:,
x) >
0 ‘I
uoyeqJn?Jad
23
Fig. 1. The best fit (curve) to experimental G (t) (points) for molten perchlorate mixture.
0
.4
.8
1.2
TIME/
1.6
PS
The parameter r, may serve as an interesting probe for the dynamics of fluid when compared to some theoret.ical predictions. Its order of magnitude suggest,s that modulation events in melt lie within binary collision time domain. This justifies the use of the Enskog model cation-anion collisions in molten salt, r& = 4dN(nKT
[ ii]
to calculate
rBc , the time
between
,’ ‘&A)‘,“’
(2)
Here cr is the collision diameter, N is the number density of colliding particles u is their reduced mass, K is the Boltzmann constant and T the temperature.
and
In our estimates we used R(Li) = 0.68 A, R (K) = 1.33 A, R (ClO,) = 1.45 + 1 .I = 2.55 A where 1.45 A is the Cl-O bond length [ 121 and 1.1 A is intermolecular radius of oxygen [ 131; N was calculated using density data [ 141. This gives
rBc (K-ClO,)
= 1.3 ps, rBc (Li-ClO,)
= 0.29 ps. The results
obtained
agree well
with r, and show that collisions between lithium ion and anion may presumably be responsible for the frequency modulat,ion process. It is quite
appropriate
to mention
here that
previous
estimates
of
zBc were
found to be much lower than z0 [.5]. Several models were used for this purpose. Basing on the definitions of diffusion coefficient in the theory of Brownian motion (D = 02 / 6 rsc> aud in the kinetic and p the density) ret = po’ / 6 77 According
theory of gases (D = 77/p , 77 is the viscosity
one obtains (3)
.
to Ref. [ 1.51, in the case of molecular
rBc = (a - o)(n;u / 8 KT)“’ ,
liquids,
the best
zBc
are
(4)
24
where a is t.he mean distance between particles in a liquid. The obvious shortcoming of Eq. (3) is its underestimation of interactions in real fluids as, in fact, it approximates a liquid by an ideal (dense) gas. Eq. (4) seems to be more realistic since ideal-gas events are supposed to occur in a cell with rigid movable walls. Anyway, both equat.ions overestimate gas-like properties of real liquids. Moreover, in the case of binary melts, the definition of partial (which corresponds to collisions between anion and certain sort, of cations) requires some arbitrary assumptions.
ret
As an example one may compare rH, calculated for liquid potassium nitrate at 626 K using Eqs (21, (3) and (4) which were found as O.lS, 0.015 and 0.020 ps, respectively.
The values of p and 71 were taken from Ref.
[ 131. The characteristic
time of frequency
[ 171. For the perchlorate
ps, and by Eq.
Eq. (4) (2)
mixture
under investigation,
is hardly applicable.
or experimental
gives the most reasonable
r0 value.
results,
modulat,ion
Again,
= 2.32 A
in this salt is r, = 0.19 Eq.
(3)
gives
this is far from either
One may conclude
comparing
[ 161, R (NO,)
ps
rBc = 0.025 rsc estimat,ed
that the Enskog
to other models used to calculate
theory zBc.
REFERENCES 1. W.G.Rothschild, Dynamics of Molecular Liquids, Wiley, New York, 1984. 2. C.H.Wong, Spectroscopy of Condensed Media. Dynamics of Molecular Interactions, Academic Press, Orlando, 198.5. 3. S.A.Kirillov, in: A.N.Lazarev (ea.), Dynamic Properties of Molecules and Condensed Media (in Russian), Nauka, Leningrad, 1988, p. 190. 4. S.A.Kirillov, J. Mol. Liquids, 4.5 (1990) 7. 5. S.A.Kirillov, Khim. Fizika (Russ.), 11 (1992) 678. 6. S.A.Kirillov, Chem. Phys. Letters, 202 (1993) 459. 7. S.A.Kirillov, Chem. Phys. Letters, 200 (1992) 205. 8. S.A.Kirillov, G.A.Voyiatzis, G.M.Photiadis, and E.A.Pavlatou, Molec. Phys., (1994) submitted. 9. V.I.Snezhkov, S.A.Kirillov, and V.D.Prisiazhnyi, Opt. Spectrosc. (Russ.), 43 (1977) 991. IO. S.A.Kirillov and D.Tunega, Z. Naturforsch., 45a (1990) 14.5. 11. P.S.Dardi and R.I.Cukier, J. Chem. Phys, 89 (1988) 4145. 12. H.Siebert, Anwendungen in der Schwingungsspektroskopie in der anorganisches Chemie, Springer, Berlin, 1966. 13. A.R. Ubbelohde, Melting and Crystal Structure, Clarendon, Oxford, 196.5. 14. A.A.Farmakovskaya, Ph.D. thesis, Sverdlovsk, 1972. 15. F.J.Bartoli and T.A.Litovitz, J.Chem. Phys., 56 (1972) 413. 16. G.J.Janz, Molten Salt Handbook, Academic, New York, 1967. 17. T.Kato and T.Takenaka, Molec. Phys., 48 (1983) 1119.