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Dynamics of liquid sulphur around the equilibrium polymerization transition
Physica A 201 (1993) 381-385 North-Holland SDI: 0378-4371(93)E0272-G
Dynamics of liquid sulphur around the equilibrium polymerization transition L. Des&esa,
R. Bellissent”,
P. Pfeuty”
and A.J.
Dianouxb
“Laboratoire Leon Brillouin (CEA-CNRS), CEN Saclay, 91191 Gif-sur-Yvette, blnstitut Laue Langevin, BP 156, 38042 Grenoble Cedex 9, France
France
Liquid sulphur has been known since the beginning of this century to show at a temperature T, = 160°C a liquid-liquid transition assumed to consist of the polymerization of S, rings into very long polymeric chains. A first neutron scattering study of the liquid local order enabled us to check this assumption at a microscopic level. Then, the vibrational density of states and local motions were studied by time-of-flight (TOF) inelastic neutron scattering as a function of temperature, below and above T,. Both the decrease of the modes characteristic of S, rings and the evolution of the quasielastic scattering with temperature are consistent with the picture of a polymer transition at T, followed by a ring-chain equilibrium.
1. The polymer transition of liquid sulphur At a temperature Tp = 160°C liquid sulphur exhibits a polymerization transition with an increase of several orders of magnitude in the viscosity. A wide range of both experimental [l] and theoretical [2] studies has led to assume the following mechanism. (i) Between 113 and 160°C sulphur is a molecular liquid, essentially made of S, rings. (ii) Above 160°C due to entropy maximization, the S, rings open to polymerize into very long S, chains; one can then define an equilibrium polymerization resulting in a mixture of rings and chains. A neutron scattering study of the liquid structure as a function of temperature has been performed in order to throw some light on the short range order features linked to this assumed polymerization transition. The pair correlation function of liquid sulphur has been determined below T,,, at 130 and 150°C and above Tp, at 170, 200, 250 and 300°C. The main results of this experiment are summarized in fig. 1. The pair correlation function, g(r), clearly shows that the intensities and the positions of the two first peaks, at 2.05 and 3.31 A respectively, remain unchanged throughout the whole temperature range. Moreover, these distances are identical to the 1st and 2nd neighbours distances of the S, rings of crystalline sulphur, indicating that the bond length and 0378-4371/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved
382
L. Des&es
et al. I Dynamics of liquid sulphur
q(r)
3
0
2
4
6
8
IO di)
Fig. 1. Pair correlation function g(r) of liquid sulphur below T, at 130 and 15O”C, and above T, at 170, 200, 250 and 300°C. Insert: Integral over the third peak of g(r) as a function of temperature.
covalent angle are retained at all temperatures. On the contrary the third peak, which corresponds to the 3rd and 4th neighbours distances, exhibits a strong decrease with temperature as the rings start to open and agglomerate into long polymeric chains. To get a more quantitative view of this local order evolution, we have integrated over the third peak the function g(r) - 1 so as to give the departure of g(r) from the random distribution expected for purely Gaussian chains (purely Gaussian chains liquid would yield only an extremely low g(r) third peak). In doing so, we could then deduce the proportion of sulfur atoms belonging to rings or chains as a function of temperature, assuming that the low temperature sulphur consists of rings only [3]. Our results, see the insert of fig. 1, are quite consistent with a macroscopical study of the high temperature liquid [4].
2. Dynamics of liquid sulphur In accordance with the description we reported in the first section, the polymerization transition should also manifest itself through important changes in the dynamics of liquid sulphur. Up to now, the vibrational dynamics had only been studied by Raman and IR spectroscopy [5], yielding mainly information on the low temperature (T < T,) molecular liquid. Therefore we have undertaken a dynamical study by using the IN6 TOF spectrometer at ILL in order to determine, for temperatures ranging from 125°C up to 4OO”C, the quasielastic scattering and the vibrational density of
L. Des&es
et al. I Dynamics of liquid sulphur
383
states (VDOS) of liquid sulphur. For comparison, similar measurements have been carried out on crystalline sulphur powder just below the melting point. The VDOS of liquid sulphur has been drawn in fig. 2. All the patterns exhibit a well-defined distribution of modes up to the higher temperature in the liquid state. The overall shape of this VDOS is fairly similar to that of the powder, even at the higher temperatures of the measurements. If we observe more closely the mode distribution we can first remark that, apart from some smoothing, there is almost no change in the VDOS upon melting; all the solid state modes remain present in the low temperature liquid, the intensities are the same as well. This strongly supports the idea that this low temperature liquid consists of a melt of S, rings with the same individual structure as the solid state rings. If we now look at the higher temperature behaviour of the liquid, we can easily discriminate 2 regions. (i) At energies
f’
Sulphur
T=
‘,,
“I,,,
x - Sulphur
I1
110°C
4k> 0
sb
Fig. 2.
w(meVI
Fig. 3.
Fig. 2. Vibrational density of states Z(w) of liquid and crystallized sulphur for various temperatures. Fig. 3. Parametrization of the quasielastic scattering by two Lorentzians for different temperatures and as a function of q. Z, and W, are the corresponding intensities and weights.
384
L. Des&es
et al. I Dynamics of liquid sulphur
higher than 20 meV, the main peaks are monotonically decreasing with temperature. Since all the corresponding modes have been assigned to S, rings by previous Raman studies [5,6], this behaviour is consistent with the temperature-dependent S, rings content of the liquid as determined in the first paragraph. (ii) At energies lower than 20 meV, the most obvious change is that the peak located around 18meV seems to broaden at 230°C and then to reappear at a slightly lower energy for higher temperatures. However, the main broad peak, around 5 meV, is almost unchanged at all temperatures, suggesting that rings and chains have a similar behaviour as far as long range interactions are concerned. Concerning the quasielastic part, the scattering function has been analyzed as the sum of 2 Lorentzian contributions. We have represented in fig. 3 the variation of the widths, W, and W,, and the integrated intensities, I, and Z,, as a function of the momentum transfer 4 for all temperatures. The wider one (around 0.4 meV) is almost indepenc$nt of the temperature and its intensity exhibits a unique peak around 1.8 8, . Its intensity seems to correspond to a fast local motion, presumably the reorientation of the S, molecules. The sharper one (0.01 to 0.1 meV range) is temperature-dependent and its mymenturn transfer behaviour shows a de Gennes narrowing at about 1.2 8, . The corresponding intensity h:s a fairly sharp structure with two well-defined peaks, at 1.2 and 1.75 A , for the lower temperatures. The higher 4 peak slowly vanishes with increasing temperature. Such a signature of a slow diffusive motion could correspond to the ring diffusion in the chain-ring equilibrium liquid.
3. Conclusion We have performed an inelastic neutron scattering experiment, using a TOF spectrometer, on liquid sulphur in a wide temperature range around the polymer transition. The VDOS spectrum we obtained shows up a fairly well-defined structure up to 500°C. However, we can observe a weakening of the frequencies corresponding to the S, molecules internal modes, while other frequencies are much less sensitive to the temperature. The quasielastic part also exhibits a fairly structured behaviour, even for the highest temperatures. These first observations on the dynamics of liquid sulphur are quite consistent with the idea of a liquid-liquid transition from a liquid of S, rings to a temperature-dependent dynamical equilibrium of rings and chains.
L. Des&es
et al.
I Dynamics of liquid sulphur
References [l] [2] [3] [4] [5] [6]
B. Meyer, Elemental Sulfur (Wiley, New York, 1965) p. 95. J.C. Wheeler, S.J. Kennedy and P. Pfeuty, Phys. Rev. Lett. 45 (1980) 1748. R. Bellissent, L. Descotes, F. Boue and P. Pfeuty, Phys. Rev. B 41 (1990) 4. J.C. Koh and W. Klement Jr., J. Phys. Chem. 74 (1970) 4280. K. Hattori and H. Kuwamina, J. Non-Cryst. Solids 59 (1983) 1063. P.D. Harvey and IS. Butler, J. Raman Spectrosc. 17 (1986) 4.
385
Dynamics of liquid sulphur around the equilibrium polymerization transition L. Des&esa,
R. Bellissent”,
P. Pfeuty”
and A.J.
Dianouxb
“Laboratoire Leon Brillouin (CEA-CNRS), CEN Saclay, 91191 Gif-sur-Yvette, blnstitut Laue Langevin, BP 156, 38042 Grenoble Cedex 9, France
France
Liquid sulphur has been known since the beginning of this century to show at a temperature T, = 160°C a liquid-liquid transition assumed to consist of the polymerization of S, rings into very long polymeric chains. A first neutron scattering study of the liquid local order enabled us to check this assumption at a microscopic level. Then, the vibrational density of states and local motions were studied by time-of-flight (TOF) inelastic neutron scattering as a function of temperature, below and above T,. Both the decrease of the modes characteristic of S, rings and the evolution of the quasielastic scattering with temperature are consistent with the picture of a polymer transition at T, followed by a ring-chain equilibrium.
1. The polymer transition of liquid sulphur At a temperature Tp = 160°C liquid sulphur exhibits a polymerization transition with an increase of several orders of magnitude in the viscosity. A wide range of both experimental [l] and theoretical [2] studies has led to assume the following mechanism. (i) Between 113 and 160°C sulphur is a molecular liquid, essentially made of S, rings. (ii) Above 160°C due to entropy maximization, the S, rings open to polymerize into very long S, chains; one can then define an equilibrium polymerization resulting in a mixture of rings and chains. A neutron scattering study of the liquid structure as a function of temperature has been performed in order to throw some light on the short range order features linked to this assumed polymerization transition. The pair correlation function of liquid sulphur has been determined below T,,, at 130 and 150°C and above Tp, at 170, 200, 250 and 300°C. The main results of this experiment are summarized in fig. 1. The pair correlation function, g(r), clearly shows that the intensities and the positions of the two first peaks, at 2.05 and 3.31 A respectively, remain unchanged throughout the whole temperature range. Moreover, these distances are identical to the 1st and 2nd neighbours distances of the S, rings of crystalline sulphur, indicating that the bond length and 0378-4371/93/$06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved
382
L. Des&es
et al. I Dynamics of liquid sulphur
q(r)
3
0
2
4
6
8
IO di)
Fig. 1. Pair correlation function g(r) of liquid sulphur below T, at 130 and 15O”C, and above T, at 170, 200, 250 and 300°C. Insert: Integral over the third peak of g(r) as a function of temperature.
covalent angle are retained at all temperatures. On the contrary the third peak, which corresponds to the 3rd and 4th neighbours distances, exhibits a strong decrease with temperature as the rings start to open and agglomerate into long polymeric chains. To get a more quantitative view of this local order evolution, we have integrated over the third peak the function g(r) - 1 so as to give the departure of g(r) from the random distribution expected for purely Gaussian chains (purely Gaussian chains liquid would yield only an extremely low g(r) third peak). In doing so, we could then deduce the proportion of sulfur atoms belonging to rings or chains as a function of temperature, assuming that the low temperature sulphur consists of rings only [3]. Our results, see the insert of fig. 1, are quite consistent with a macroscopical study of the high temperature liquid [4].
2. Dynamics of liquid sulphur In accordance with the description we reported in the first section, the polymerization transition should also manifest itself through important changes in the dynamics of liquid sulphur. Up to now, the vibrational dynamics had only been studied by Raman and IR spectroscopy [5], yielding mainly information on the low temperature (T < T,) molecular liquid. Therefore we have undertaken a dynamical study by using the IN6 TOF spectrometer at ILL in order to determine, for temperatures ranging from 125°C up to 4OO”C, the quasielastic scattering and the vibrational density of
L. Des&es
et al. I Dynamics of liquid sulphur
383
states (VDOS) of liquid sulphur. For comparison, similar measurements have been carried out on crystalline sulphur powder just below the melting point. The VDOS of liquid sulphur has been drawn in fig. 2. All the patterns exhibit a well-defined distribution of modes up to the higher temperature in the liquid state. The overall shape of this VDOS is fairly similar to that of the powder, even at the higher temperatures of the measurements. If we observe more closely the mode distribution we can first remark that, apart from some smoothing, there is almost no change in the VDOS upon melting; all the solid state modes remain present in the low temperature liquid, the intensities are the same as well. This strongly supports the idea that this low temperature liquid consists of a melt of S, rings with the same individual structure as the solid state rings. If we now look at the higher temperature behaviour of the liquid, we can easily discriminate 2 regions. (i) At energies
f’
Sulphur
T=
‘,,
“I,,,
x - Sulphur
I1
110°C
4k> 0
sb
Fig. 2.
w(meVI
Fig. 3.
Fig. 2. Vibrational density of states Z(w) of liquid and crystallized sulphur for various temperatures. Fig. 3. Parametrization of the quasielastic scattering by two Lorentzians for different temperatures and as a function of q. Z, and W, are the corresponding intensities and weights.
384
L. Des&es
et al. I Dynamics of liquid sulphur
higher than 20 meV, the main peaks are monotonically decreasing with temperature. Since all the corresponding modes have been assigned to S, rings by previous Raman studies [5,6], this behaviour is consistent with the temperature-dependent S, rings content of the liquid as determined in the first paragraph. (ii) At energies lower than 20 meV, the most obvious change is that the peak located around 18meV seems to broaden at 230°C and then to reappear at a slightly lower energy for higher temperatures. However, the main broad peak, around 5 meV, is almost unchanged at all temperatures, suggesting that rings and chains have a similar behaviour as far as long range interactions are concerned. Concerning the quasielastic part, the scattering function has been analyzed as the sum of 2 Lorentzian contributions. We have represented in fig. 3 the variation of the widths, W, and W,, and the integrated intensities, I, and Z,, as a function of the momentum transfer 4 for all temperatures. The wider one (around 0.4 meV) is almost indepenc$nt of the temperature and its intensity exhibits a unique peak around 1.8 8, . Its intensity seems to correspond to a fast local motion, presumably the reorientation of the S, molecules. The sharper one (0.01 to 0.1 meV range) is temperature-dependent and its mymenturn transfer behaviour shows a de Gennes narrowing at about 1.2 8, . The corresponding intensity h:s a fairly sharp structure with two well-defined peaks, at 1.2 and 1.75 A , for the lower temperatures. The higher 4 peak slowly vanishes with increasing temperature. Such a signature of a slow diffusive motion could correspond to the ring diffusion in the chain-ring equilibrium liquid.
3. Conclusion We have performed an inelastic neutron scattering experiment, using a TOF spectrometer, on liquid sulphur in a wide temperature range around the polymer transition. The VDOS spectrum we obtained shows up a fairly well-defined structure up to 500°C. However, we can observe a weakening of the frequencies corresponding to the S, molecules internal modes, while other frequencies are much less sensitive to the temperature. The quasielastic part also exhibits a fairly structured behaviour, even for the highest temperatures. These first observations on the dynamics of liquid sulphur are quite consistent with the idea of a liquid-liquid transition from a liquid of S, rings to a temperature-dependent dynamical equilibrium of rings and chains.
L. Des&es
et al.
I Dynamics of liquid sulphur
References [l] [2] [3] [4] [5] [6]
B. Meyer, Elemental Sulfur (Wiley, New York, 1965) p. 95. J.C. Wheeler, S.J. Kennedy and P. Pfeuty, Phys. Rev. Lett. 45 (1980) 1748. R. Bellissent, L. Descotes, F. Boue and P. Pfeuty, Phys. Rev. B 41 (1990) 4. J.C. Koh and W. Klement Jr., J. Phys. Chem. 74 (1970) 4280. K. Hattori and H. Kuwamina, J. Non-Cryst. Solids 59 (1983) 1063. P.D. Harvey and IS. Butler, J. Raman Spectrosc. 17 (1986) 4.
385