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Pressure Dependence of the Boson Peak of Glassy Glycerol Muhtar Ahart, Dilare Aihaiti, Russell J. Hemley, and Seiji Kojima J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b01993 • Publication Date (Web): 31 May 2017 Downloaded from http://pubs.acs.org on June 8, 2017

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The Journal of Physical Chemistry

Pressure dependence of the Boson peak of glassy glycerol

Muhtar Ahart1, Dilare Aihaiti2, Russell J. Hemley3, and Seiji Kojima4*

1

Geophysical Laboratory, Carnegie Institution of Washington Washington DC 20015, USA

2

College of Science, George Mason University, Fairfax, VA 22030, USA 3

Department of Civil and Environment Engineering

The George Washington University, Washington DC 20052, USA 4

Division of Materials Science, Faculty of Pure and Applied Sciences University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan *E-mail: [email protected]

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ACS Paragon Plus Environment


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Abstract The pressure dependence of the Boson peak (BP) of glycerol, including its behavior across the liquid-glass transition, has been studied under pressure using Raman scattering. A significant increase of the BP frequency was observed with pressure up to 11 GPa at room temperature. The pressure dependence of BP frequency νBP is proportional to (1+P/P0)1/3, where P and P0 are the pressure and a constant, respectively, the spectra are consistent with a soft potential model. The characteristic length of medium range order is close in size to a cyclic trimer of glycerol molecules, which is predicted as the medium range order of a BP vibration using molecular dynamics simulations. The pressure dependence of a characteristic length of medium range order is nearly constant. The pressure induced structural changes in glycerol can be understood in terms of the shrinkage of voids with cyclic trimers remaining up to at least 11 GPa. The pressure dependence of intermolecular O-H stretching mode indicates that the intermolecular hydrogen bond distance gradually decreases below the glass transition pressure of ~5 GPa, while it becomes nearly constant in the glassy state indicating the disappearance of the free volume in the dense glass.

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1. Introduction A Boson peak (BP) is a universal low-energy excitation in disordered materials in the frequency range of 10 ~ 100 cm-1 (0.3 ~ 3.0 THz) typically observed by Raman and neutron/x-ray inelastic scattering. BPs are attributed to the excess parts of vibrational density (VDOS) of states above Debye level, g(ν)/ν2, where g(ν) and ν are the distribution of VDOS and frequency, respectively. Such an excess is also observed as a peak in Cp/T3 at low temperatures around 10 K, where Cp and T are the heat capacity and temperature, respectively.1, 2 Considerable experimental work on BPs has been reported on various disordered systems by changes in composition and temperature. The origin of BPs has been discussed in terms of various physical models such as localized modes of nano-sized clusters,3 quasilocal vibrations of atoms in an anharmonic potential,4 the Ioffe-Regel crossover regime,5 spatial variation of the elastic moduli,6 and the counterpart of the acoustic van Hove singularities of crystals.7 However, the applicability of these models remain unclear. In general, changes in physical properties as a function of temperature or composition are much less than can be afforded by compression using modern high-pressure techniques which can now produce very high compressions on many materials. As a result, significantly larger changes in the BP are expected by varying pressure compared temperature for many systems, thereby providing important contraints on different theoretical models. For example, the application of pressure of 1.4 GPa to poly(isobutylene) causes the increase of density about 20 % and the boson peak frequency becomes twice.8 In silica glass, the BP peak frequency increases by more than a factor of three on compression to 30 GPa. 9, 10 Such large changes cannot occur in the temperature dependence. Therefore, the pressure induced drastic changes are very important to discuss the universality of Boson peak dynamics. Glycerol (propane-1,2,3-triol, C3H8O3) is a well-known glass forming material.11 It is also an important cryoprotectant because of its activity in maintaining the structure of biological macromolecules through preferential hydration.12 The temperature dependences of its physical properties have been extensively studied. Glycerol undergoes a liquid-glass transition Tg at ~190 K and ambient pressure. The fragility index of glycerol is m = 53 and is known as an intermediate liquid.13 The BP of glycerol has been clearly observed by Raman scattering at low temperatures,14 and later studied by inelastic neutron and x-ray scattering.15, 16

However, pressure dependence of its BP has apparently not been reported. Here we studied the BP under pressure of this organic glass-former using Raman scattering techniques.

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2. Experimental Methods Glycerol was loaded into a 50 μm thick stainless steel gasket with a 130 μm diameter hole was used as the sample chamber in a diamond anvil cell (DAC). Raman grade diamond anvils with a culet size of 300 μm were used with a symmetric DAC. A chip of ruby was loaded for pressure determination. All Raman spectra were measured using a Princeton Instruments Acton SP2300 spectrometer with a CCD and 532 nm solid-state diode excitation laser.17 The laser power used was about 7 mW before entering the DAC. An 1800BLZ grating was used and the Raman signal was measured in the backscattering geometry with an average collection time of 30 s at 295 K. The use of ultra-fine notch filters (Ondax Inc.) allowed measurements of spectra down to approximately 10 cm-1. We used a long working distance Mitutoyo 20X objective with a numerical aperture of 0.28, giving a spatial resolution of 1.14 μm for the Raman measurement.

3. Pressure dependence of the Boson peak The pressure dependence of the glass transition temperature dTg/dP of glycerol is positive, as for most glasses. However, it is much smaller than that of non-hydrogen bonded o-terphenyl, polyisobutene, and borate glass.18 In hydrogen-bonded liquids, the stronger the hydrogen bonding, the smaller is the effect of pressure on Tg. Lower molecular weight alcohols at ambient pressure (e.g., methanol and n-propanol with Tg = 98K) undergo a liquid-glass transition at Pg= 3 and 5 GPa, respectively.19-21 Glycerol undergoes such a transition at a pressure Pg of ~5 GPa at room temperature.22, 23 Recently, the sound velocity and density of glycerol under pressure through the transition were studied by Brillouin scattering.24 In the present study, the pressure dependence of Raman scattering spectra of glycerol between 10 and 4000 cm-1 was measured up to 11 GPa. The BP Raman intensity I(ν) is related to the imaginary part of Raman susceptibility χ”(ν) and the VDOS, g(ν) by the following equation. I = " + 1,

(1)

χ" / = / ,

(2)

where, n(ν) and CRam(ν) are the Bose-Einstein distribution function and the light-vibration coupling constant, respectively.25, 26 The frequency dependence of the BP has been examined for various glasses, and the following universal linear frequency behavior in the vicinity of νBP was reported.27 CRam(ν)∝ν /νBP + B,

(3)

where νBP and B are BP frequency and a constant, respectively. This frequency dependence 4


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of the observed νBP by Raman scattering is slightly higher than that obtained by neutron inelastic scattering, although the essential behavior is similar. To examine the excess part of VDOS g(ν)/ν2, the reduced Raman intensity IR(ν) is calculated from the observed intensity spectra. = / + 1

(4)

The pressure dependence of the low-frequency region of IR(ν) is shown in Fig. 1. The BP is clearly observed up to 11 GPa. In a study of the temperature dependence of the BP at ambient pressure, the peak was observed a few tens degrees above the glass transition temperature Tg ~190 K in the liquid state.14 The characteristic time scale of a BP excitation is in the THz range, which is much shorter than structural relaxation times even in a liquid state; thus the observation of a THz range, it is recognized as a glassy state. For the observation through the reported glass transition pressure Pg ~5 GPa.23, 28 The BP can be measured by Raman scattering. 3.1 Pressure dependence of Boson peak frequency The BP frequency νBP increases markedly with pressure (Fig. 1). Increasing of BP frequency under pressure is the common nature in organic and inorganic glasses.8, 9 Using a soft potential model, the pressure dependence of the BP frequency νBP is given by νBP(P)= νBP(0)(1+P/P0)1/3,

(5)

where P and P0 are pressure and a constant.29, 30 This equation well reproduces the pressure dependence of the PB frequency of silica glass up to 42 GPa (P0=0.44 GPa). 9 The peak frequency was determined by fitting with the formula of Malinovsky et al.31 The fitted curve for glycerol gives νBP(0) =30.1 cm-1 and P0=0.298 GPa (Fig. 2). The value of P0 can be compared to that of borate glass (0.29 GPa) 30 and silica glass (0.44 GPa); 30 however, we are unaware of values reported for organic glasses. The anharmonicity of a glass has been related to its fragility, relaxation time, and BP frequency. The BP mode Gruneisen parameter Γb is useful for characterizing behavior of the material.30 The BP Γb is given by Γ = 2

!

,

(6)

where V is volume. The Γb value obtained for glycerol is = 11.6, which is much smaller than Γb =36 of silica glass.30 The structural unit of silica glass is a SiO4 tetrahedron, while that of glycerol is a weakly hydrogen bonded cluster. The weaker bonds among structural units in a glass gives rise to increased anharmonicity. A correlation of the fragility with the Gruneisen parameters was found in lithium borate glasses,32 and the higher anharmonicity corresponds to higher fragility. The observed values of fragility in silica33 and glycerol,34 are 28 and 54, respectively. Although fragility is defined for liquid state, vibrational properties of glasses 5



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well below Tg correlate with the fragility value.33 Generally the network bonding becomes weaker, the fragility increases, therefore, the present result is consistent with the variation of fragility. 3.2 Pressure dependence of characteristic length The medium range ordered glasses are closely associated with both their structural relaxation and in low-frequency vibrational properties. Molecular dynamics simulations of glycerol indicate that the BP excitation is related to the normal mode of a cyclic trimer of glycerol molecules of about 9 Å in size.35 The correlation between a BP and a first diffraction peak (FSDP) in the static structure factor S(Q) determined by neutron and x-ray diffraction has been reported.36 In deuterated glycerol, the FSDP determined by neutron diffraction give Q1=1.4 Å-1.37 The value of glycerol determined by x-ray diffraction is in good agreement within experimental uncertainty.38 With the FSDP of Q1=1.4 Å-1, the characteristic length of the peak is, LFSDP=2π/Q1=4.5 Å. According to the localized mode model of a BP,3, 32 the characteristic length LBP determined from the νBP is given by LBP = VD/ νBP , where VD =(1/VL3+2/VT3)1/3 is Debye velocity determined by longitudinal sound velocity VL and transverse sound velocity VT. A similar relation was also derived from the Ioffe–Regel rule as the correlation length. Recently, the pressure dependence of VL was reported for glycerol.24 The value of VT is not reported in that study; we assume VT/VL =0.493 using the observed value of VT/VL for hydrogen-bonded ice.39 This value is comparable to the molecular dynamics liquid-state simulation of glycerol at 260 K; i.e., VT/VL = 0.45.40 We find that the pressure dependence of LBP is nearly constant (Fig. 3). The mean values of LBP =9.5 Å and LFSDP=4.5 Å are approximately equal to the outer and inner diameters of a cyclic trimer of glycerol molecules (Fig. 4). This observation indicates that the correlation length of cooperative vibration indicated by the BP is longer than that of the static cluster inferred from the FSDP in glycerol. The difference can be caused by the fact that the former includes the contribution of weakly hydrogen bonded molecules surrounding the cyclic trimer. As a result, the BP in glycerol has been attributed to the lowest frequency normal mode of vibration of a cyclic trimer as predicted by Uchino and Yoko.35 Recently, it has been reported that adding nano-sized molecules to glycerol induced the broadening of the α relaxation. 41 Notably, the size of these molecules is 11 Å,41 which is comparable with LBP=9.5 Å. Apparently, the effect of additions of molecules with size LBP can increase the α relaxation, Comparison of temperature or pressure dependence between the BP frequency and sound velocity has been examined in the context of elastic heterogeneity, and some difference was reported. In polycarbonate, the BP frequency decreased by a factor of 2 between 53 K and room temperature, while the sound velocity decreased only by 20%.42 In the pressure dependence of the BP frequency of 6


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poly(isobutylene), the BP frequency becomes twice at 1.5 GPa, while the sound velocity increases about 50%, and it is concluded that the BP variation under pressure cannot be explained by the elastic continuum transformation only.7 For some oxide glasses, the differences in the changes in BP frequency and sound velocity were also reported.43 However, nuclear inelastic scattering suggests that the main variations of BP on compression and pressure release, as well as quenching, follow expected variations of the elastic continuum; i.e., changes in the BP frequency follows variations of the sound velocity.44 The pressure dependence of the BP frequency of glycerol is similar to that of its longitudinal sound velocity, because the pressure dependence of LBP is nearly constant (Fig. 3). Within experimental uncertainties, the small temperature dependence of LBP is obtained using the observed values of BP14 and the longitudinal sound velocity. 44 45 The calculation of LBP is based on the assumption of a constant VT/VL ratio, because the transverse sound velocity in a glassy state is unknown.. Therefore, if this ratio depends on pressure, LBP changes and the BP variation under pressure cannot be explained by an elastic continuum transformation alone. 3.3 Scaling of Boson peak spectrum The lineshape of a BP is related to the distribution of vibrational density states (VDOS). It is known that the boson peak has rather universal spectral shape for many glass-forming systems.29, 31 As is common in BPs in polymer glasses, the shape of the peak appears to be essentially independent of pressure below 1.5 GPa.8, 45 Such a universal spectral shape was also observed in the composition dependence of binary glasses. In xLi2O-(1-x)B2O3 glasses, the νBP =24 cm-1 of pure borate glass increases about three times up to 79 cm-1 with the increase of the Li2O content x up to 0.28.32 However, the spectral shape of the BP remains the same at all x on the combined plot obtained by scaling the frequency on the frequency of the νBP for each composition. 29 According to the theoretical study on weakly interacting quasi-local harmonic vibrational (QLV) modes, the VDOS is independent of the actual value of the anharmonicity.42, 43 It is a universal function of frequency depending on a single parameter — the BP frequency νBP which is a function of interaction strength. Such remarkable increase in BP frequency and the scaling of BP spectra have been explained as resulting from an increase in concentration of QLV’s and consequently of their interaction. This supports also the idea of a universal shape of BPs predicted by Malinovsky and Sokolov.31 Such a universal shape of BPs was also predicted theoretically for the pressure dependence of the peaks.42 In poly(isobutylene), it was found that the shape of the boson peak remains unchanged even at such high compression up to 1.4 GPa. Therefore, it is useful to examine the universality of the lineshape of the BP in glycerol under pressure. Figure 5 shows scaled BP spectra at various pressures. The scaled spectra were well reproduced by the formula of Ref. 31. (Fig. 5a), indicate that the scaling holds under high 7



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pressure. A comparison between the low-temperature and high-pressure BP spectra is instructive. Figure 5(b) shows the spectrum of 10.2 GPa at 295 K and that of ambient pressure at 96 K. The reduced intensity is normalized and two frequency scales are scaled to adjust the peak position of two BPs. The BP line shapes are of BP spectra are very similar, while the intensity of BP intensity at high pressure shows the slightly higher values above νBP. According to the theoretical calculation, the BP intensity above νBP slightly increases as the anharmonicity increases. Molecular dynamics simulation of glycerol predict an increase in fragility under high pressure that is ascribed to a decrease in hydrogen bonding.46 Therefore, this slight difference may be thus be caused by the increase in anharmonicity,

4. Pressure dependence of intermolecular hydrogen bonding Measurements of the temperature/pressure dependence of the high-frequency vibrational modes gives new insights into the changes of structure such as configuration, deformation of molecules, and interatomic interactions, especially the O-H stretching band is very sensitive for the change of hydrogen bonds.47-49 The temperature dependence of the Raman spectrum in liquid and glassy glycerol reveals remarkable changes in the O-H stretching band.50-52 The results may be compared with structural changes in glycerol in liquid, glassy and crystalline states predicted by molecular dynamics simulations. 46, 53, 54 The pressure dependence of the high frequency Raman bands was also measured (Fig. 6). As the pressure increases the hardening of the peak frequency and the broadening of the bands were observed. Generally, the linewidths of bands in liquid and glassy states arise from damping and the distribution of mode frequencies, the distortion of molecular structure under high pressure. An interesting change in the temperature dependence of Raman scattering spectrum of glycerol is observed in the O-H stretching band around 3300-3600 cm-1 (Fig. 7).52 53 This band reflects the distance of the intermolecular hydrogen bond and its distribution.47, 49,49 According to the study of temperature dependence of the peak frequency of the O-H band related to the mean distance of the intermolecular hydrogen bond shows the clear change in the vicinity of a liquid-glass transition temperature. On cooling from a high-temperature liquid state, the interatomic hydrogen bond distance decreased markedly, while below Tg the decrease in distance lessens, because the free volume “holes” decreased gradually towards Tg and the change in distance almost stops.52 The O–H band frequency also shows a remarkable decrease up to the liquid-glass transition pressure, while in the glassy state the distance is nearly constant (Fig. 7). These observations indicate that the behavior of the intermolecular hydrogen bonds are similar for both temperature- and pressure-induced liquid-glass transitions. Another remarkable change is the symmetric and asymmetric C-H stretching mode at 2886 and 2946 cm-1, respectively, at 8


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ambient pressure.50, 51 As the pressure increases, the symmetric C-H stretching mode disappears or merges into the asymmetric mode. This suggests that the structure of the glycerol molecule becomes more symmetric under pressure.

5. Conclusions The Boson peaks (BPs) of glycerol studied under pressure using Raman scattering show a remarkable increase in BP frequency on compression. The pressure dependence of BP frequency νBP is proportional to a cubic root of pressure, (1+P/P0)1/3, and all the BP spectra at various pressures are well scaled. These two observations can be explained by the soft potential model. The pressure dependence of νBP can be explained by the elastic continuum transformation. The characteristic length of medium range order is close to the outer size of a cyclic trimer of glycerol molecules, which was predicted as the medium range order of BP vibration using molecular dynamical simulations. 35 The O-H stretching band shows the remarkable change near the glass transition pressure indicating the difference in the mean distance of the intermolecular hydrogen bond between liquid and glassy states. The pressure dependence of a characteristic length of medium range order is nearly constant. Thus, pressure-induced changes in glycerol up to 11 GPa can be essentially the shrinkage of voids and the persistence of cyclic trimers.

Acknowledgements This research was partially supported by EFree, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences under award DE-SC-0001057 (salary support for M.A.) and the facilities used at Carnegie were supported by the US Department of Energy/National Nuclear Security Administration (DE-NA-0002006, CDAC).

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frequencies investigated via molecular dynamics simulations. J. Chem. Phys. 2016, 144, 054502. (41) Gupta, S.; Fischer, J. K. H.; Lunkenheimer, P.; Loidl, A.; Novak, E.; Jalarvo, J. ; Ohl, M. Effect of adding nanometre-sized heterogeneities on the structural dynamics and the excess wing of a molecular glass former. Sci. Reports. 2016, 6, 35034. (42) Schroeder, J.; Wu, W. M.; Apkarian, J. L.; Lee, M.; Hwa, L.; Moynihan, C. T. Raman scattering and Boson peaks in glasses: temperature and pressure effects. J. Non-Cryst. Solids. 2004, 349, 88. (43) Buchenau, U.; Sch.; SchM.; Apkarian, J. L.; Lee, M.; Hwa, L. ; Moynihan, C. T. Rn scattering study of the vibration-relaxation crossover in amorphous polycarbonates. Phys. Rev. Lett. 1995, 73, 2344. (44) Monaco, A.; Chumakov, A. I.; Monaco, G.; Crichton, W. A.; Meyer, A.; Comez, L.; Fioretto, D.; Korecki, J.; Ruffer, R. Effect of densification on the density of vibrational states of glasses. Phys. Rev. Lett. 2006, 97, 135501. (45) Comez, L.; Fioretto, D.; Scarponi, F. ; Monaco, G. Density fluctuations in the intermediate glass-former glycerol: A Brillouin light scattering study. J. Chem. Phys. 2003, 119, 6032. (46) Root, L. J. ; Berne, B. J. Effect of pressure on hydrogen bonding in glycerol: A molecular dynamics investigation. J. Chem. Phys. 1997, 107, 4350. (47) Nakamoto, K.; Margoshes, M. ; Rundle, R. E. Stretching frequencies as a function of distances in hydrogen bonds. J. Am. Chem. Soc. 1950, 77, 6480-6486. (48) Hemley, R. J.; Chen, L. C. ; Mao, H. K. New transformations between crystalline and amorphous ice. Nature. 1989, 338, 638-640. 12


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Kollman, P. A. ; Allen, L. C. Theory of the hydrogen bond. Chem. Rev.

1972, 72, 283-303. (50) (51)

Mudalige, A.; Pemberton, J. E. Vib. Spectrosc. 2007, 45, 27. Mendelovici, E.; Frost, R. L. ; Kloprogge, T. Cryogenic Raman

spectroscopy of glycerol. J. Raman Spectrosc. 2000, 33, 1121-1126. (52) Kojima, S. Anomalous behaviour of the O-H stretching vibrational mode in the liquid-glass transition of glycerol. J. Mol. Strac. 1993, 294, 193-195. (53) Chelli, R.; Procacci, P.; Gardini, G.; Della Valle, R. G. ; Califano, S. Glycerol condensed phases Part I. A molecular dynamics study. Phys. Chem. Chem. Phys. 1999, 1, 871-877. (54) Chelli, R.; Procacci, P.; Gardini, G.; Della Valle, R. G. ; Califano, S. Glycerol condensed phases Part II.A molecular dynamics study of the conformational structure and hydrogen bonding. Phys. Chem. Chem. Phys. 1999, 1, 879-885.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure Captions

Figure 1. Pressure dependence of reduced low frequency Raman spectrum showers the Boson peak (295 K). Figure 2. Pressure dependence of the BP frequency. Figure 3. Pressure dependence of the characteristic length LBP. Figure 4. Schematic illustration of glycerol cyclic trimer and characteristic length LBP. The solid circle denotes that of FSDP, LFSDP ~4.5 Å, and the dotted circle denotes that of a Boson peak, LBP ~ 9.5 Å. Figure 5. Scaled BP intensity versus frequency for (a) various pressure where both reduced intensity and frequency are normalized, and (b) 10.2 GPa (295 K) and ambient pressure (96 K) where the reduced intensity is normalized and two frequency scales are scaled to adjust the peak positions of the BPs. Figure 6. Pressure dependence of high-frequency Raman scattering spectra under high pressure in the frequency range 2780-3560 cm-1. The Raman bands are labeled according to the assignments of Mendelovici et al.52 Figure 7. Pressure dependence of the O-H stretching band.

14


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Figures

Glycerol

2.5

χ"(ν)/ν{n(ν)+1} (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


295 K

2.0

0.3 GPa 0.9 GPa 1.8 GPa 3.0 GPa 5.5 GPa 10.2 GPa

1.5

1.0

0.5

Boson peak

0.0 50

100

150

200

250

-1

Frequency shift (cm ) Figure 1

15



120

Boson peak frequency (cm-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Glycerol 100 80 60 40 20 295 K 0 0

2

4

6

8

10

Pressure (GPa) Figure 2

16


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characteristic length (nm)

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2.0 Glycerol 1.5 Pg

1.0 0.5 0.0 0

2

4

6

8

10


17



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 4

18


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Glycerol

1.4

295 K

IR(ν)/IR(νBP)

1.2 1.0 0.8 0.6 10.2 GPa 5.5 GPa 3.0 GPa 1.8 GPa Malinovsky's function

0.4 0.2 0.0 0.5

1.0

(a)

1.5

ν/νBP

2.0

1.4

2.5

Glycerol

1.2

IR(ν)/IR(νBP)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.0 0.8 0.6 0.4 0.2

10.2 GPa at 296 K ambient pressure at 96 K

0.0 0.5

(b)

1.0

1.5

2.0

2.5

ν/νBP

Figure 5

19



2000

Raman intensity (arb. unit)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Glycerol

1500

10.7 GPa

1000

8.57 GPa 7.11 GPa 5.71 GPa 3.61 GPa

500

symmetric CH stretch

2.09 GPa 0.82 GPa

antisymmetric CH stretch

0 2800

0.0 GPa

OH stretch

3000

3200

3400

Frequency shift (cm-1)

Figure 6

20


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O-H mode frequency (cm-1)

Page 21 of 28

Glycerol

3340 3320 Pg

3300 3280 3260 0

2

4

6

8

10


21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1. Pressure dependence of reduced low frequency Raman spectrum showers the Boson peak (295 K). 197x233mm (72 x 72 DPI)


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Figure 2. Pressure dependence of the BP frequency. 204x168mm (72 x 72 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3. Pressure dependence of the characteristic length LBP. 224x179mm (72 x 72 DPI)


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Figure 4. Schematic illustration of glycerol cyclic trimer and characteristic length. The solid circle denotes that of LFSDP ~4.5 Å, and the dotted circle denotes that of a Boson peak, LBP ~ 9.5 Å. 178x143mm (72 x 72 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 5. Scaled BP intensity vs. frequency for (a) various pressure where both reduced intensity and frequency is normarized, and (b) 10.2 GPa at 295 K and ambient pressure at 96 K where the reduced intensity is normalized and two frequency scales are scaled to adjust the peak position of two BPs. 176x290mm (72 x 72 DPI)


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Figure 6. Pressure dependence of high-frequency Raman scattering spectra under high pressure in the frequency range 2780-3560 cm-1. The Raman bands are labeled according to the assignments of Mendelovici et al.52 226x167mm (72 x 72 DPI)



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 7. Pressure dependence of O-H stretching band. 208x154mm (72 x 72 DPI)


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Pressure Dependence of the Boson Peak of Glassy Glycerol - The

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