Structural and Dielectric Relaxations in Vitreous and Liquid State of

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Structural and Dielectric Relaxations in Vitreous and Liquid State of Monohydroxy Alcohol at High Pressure Igor Vladimirovich Danilov, Alexei A. Pronin, Elena Leonidovna Gromnitskaya, Mikhail V. Kondrin, Alexander Gennadievich Lyapin, and Vadim V. Brazhkin J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b05335 • Publication Date (Web): 02 Aug 2017 Downloaded from http://pubs.acs.org on August 2, 2017

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The Journal of Physical Chemistry

Structural and Dielectric Relaxations in Vitreous and Liquid State of Monohydroxy Alcohol at High Pressure I.V. Danilov,†,‡ A.A. Pronin,¶ E.L. Gromnitskaya,† M.V. Kondrin,∗,† A.G. Lyapin,†,‡ and V.V. Brazhkin† †Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow, 108840 Russia ‡Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, 141701 Russia ¶General Physics Institute, Russian Academy of Sciences, Moscow, 117942 Russia E-mail: [email protected]

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Abstract 2-ethyl-1-hexanol monoalcohol is a well-known molecular glassformer, which for a long time attracts attention of researchers. As in all other monohydroxy alcohols, its dielectric relaxation reveals two distinct relaxation processes attributed to the structural relaxation and another more intense process, which gives rise to a low-frequency Debye-like relaxation. In this monoalcohol, the frequency separation between these two processes reaches an extremely high value of three orders of magnitude, which makes this substance a rather convenient object for studies of mechanisms (supposedly common to all monoalcohols) leading to vitrification of this type of liquids. In this work, we apply two experimental techniques, dielectric spectroscopy and ultrasonic measurements (in both longitudinal and transverse polarizations) at high pressure, to study interference between different relaxation mechanisms occurring in this liquid, which could shed light on both structural and dielectric relaxation processes observed in a supercooled liquid and a glass state. Application of high pressure in this case leads to the simplification of the frequency spectrum of dielectric relaxation, where only one asymmetric feature is observed. Nonetheless, the maximum attenuation of the longitudinal wave in ultrasonic experiments at high pressure is observed at temperatures ≈ 50 K above the corresponding temperature for the transverse wave. This might indicate different mechanisms of structural relaxation in shear and bulk elasticities in this liquid.

Introduction Monohydroxy alcohol 2-ethyl-1-hexanol (C8 H18 O or 2E1H) is a well-known molecular glassformer, which for a long time attracts attention of researchers. 1–12 One of the particular features of the class of branched monoalcohols, where this substance belongs to is a significant discrepancy between characteristic relaxation times revealed by dielectric spectroscopy and frequency-resolved rheological techniques. Low-frequency shear viscosity measurements (in the frequency range ν = 10−3 − 103 Hz) demonstrated that this discrepancy can reach 2


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a record-breaking value 3,9 of three orders of magnitude. Such a discrepancy poses questions on the relevance of the current model of dielectric relaxation in normal and supercooled liquids where it is supposed to be caused by the reorientation of molecular dipoles (inherently connected with the geometry of the molecule) and the molecular dynamics determined by the shear viscosity of the liquid. This means that the dynamics of molecules revealed in the frequency-dependent shear viscosity and the dielectric spectroscopy experiments expected to produce results at least comparable in order of magnitude. Therefore, the experimentally observed large difference between them poses a serious problem that has to be addressed. The calorimetry study 4,13 demonstrated that the thermodynamic glassification temperature Tg ≈ 145 K almost coincides with the results obtained in the shear-viscosity study. 5 On the other hand, the dielectric spectroscopy measurements provide contradictory values depending on which one of several dielectric processes present in this liquid is taken into account. From the approximation of temperature evolution of the most intense low-frequency process (having a nearly Debye-like character), the “dielectric” glass-transition temperature Tg1 ≈ 155 K is obtained. Here, the “conventional” glassification temperature is defined as the temperature at which the characteristic frequency of the corresponding relaxation process is equal to ν0 = 10−3 Hz . The relaxation process with an almost Debye-like frequency dependence is always observed in monohydroxy alcohols and its origin is still under discussion. It is supposed that the “true” relaxation process (called α) caused by structural relaxation in the liquid corresponds to the second peak in the dielectric loss spectrum, which is located at a higher frequency and is almost an order of magnitude weaker (see Fig. 1a). Extrapolation of its temperature dependence in 2E1H yields the value Tg2 ≈ 145 K comparable to the structural and thermodynamic results. The widely accepted explanation of these anomalies 14 is based on the formation of supramolecular structures in liquid alcohols consisting of a few hydrogen bonded molecules aligned in chains or rings. This notion can be traced back to the classical works by Kirkwood 15 and Cole 16 and it was named “the transient-chain liquid model”. 17 Circumstantial evidence for this model came from the crystal structure of

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log10(ν /Hz) −2

0

6

4

1

1.4

2

0.5

1.2

a)

0.8 1 log10(ε ’)

←

log10(ε ’’ ) − 0.5 0

0.4

T=181 K

0

→ ν0 = 1.14

− 1.5 −1 − 0.5 log10(G ’/GPa) , log10(δt)

−1

0.6

→

− 0.8

←

β = 0.16

→

T=157 K

b) −2

− 1.6

log10(G ’’/GPa) − 1.4 − 1.2 −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

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−2

0

2

4

6

log10(ν /Hz)

Figure 1: Dielectric spectroscopy (a) and shear-mechanical spectra (b) data 5 for 2E1H at the ambient pressure and different temperatures. The temperatures were selected in such a way that the main relaxation frequency falls into the same frequency range 10 < ν0 < 100 Hz. The symbols and ◦ stand for the real and imaginary parts of the corresponding kinetic coefficient, respectively. Thin solid lines in panels a) and b) are empirical approximations of experimental data (see Supplementary Information for details). The dashed line in panel b) is the attenuation decrement of the transverse acoustic wave δt obtained by fitting the experimental shear response. The observed deviation of experimental data for G′ from the calculated one (visible in the low frequency range in panel b) previously 10 was attributed to the contribution from the Debye-like low-frequency process. 4


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solid simple alcohols (ethanol 18–20 and methanol 21–25 ), where these hydrogen bonded infinite molecular chains are the main structural motif, which is conserved even in the high-pressure crystal phases up to 10 GPa. The recent nuclear magnetic resonance (NMR) studies 17 in n-butanol revealed the existence of different dynamics of hydroxyl and alkyl groups of the alcohol molecule. It was found that the characteristic relaxation time τa of the alkyl group is almost equal to the structural relaxation time, while the characteristic relaxation time τOH of the hydroxyl end is an almost order of magnitude larger. This characteristic time τOH is turned out to be intermediate between the dielectric relaxation time (τD , which is about two orders of magnitude larger than the structural relaxation time) and τa . The ratio between τD and τOH on the one hand and the ratio between the amplitudes of Debye and α-relaxation processes (according to the Kirkwood law, it can be related to the ratio between the electric dipole moments along the supramolecular chain and normal to it) on the other hand produce the number of molecules in the chain N ≈ 10. Therefore, this model predicts that the main dielectric relaxation process is due to the oscillation of the dipole moment along the chain, so its reversal requires the flipping of hydrogen bonds of all N molecules comprising the chain. In turn, the α-process is caused by the fluctuations of the alkyl group of individual molecules in the plane normal to the chain, whose dynamics is determined by the fast structural relaxation. The subsequent NMR measurements on 2E1H corroborated this model 8 and gave the τOH value being up to an order of magnitude higher than the structural relaxation time. This observation might indicate the presence of longer hydrogen bonded chains in this alcohol (10 < N < 100). Measurements at high pressure could provide an additional insight into this problem, but such experiments are rather scarce because of their technical complexity. The dielectric spectroscopy measurements, carried out in the limited pressure range P < 1.6 GPa, demonstrated 26–30 that the application of high pressure above 0.6 GPa leads to merging two (Debye and α) relaxation processes into one asymmetric process with the intensity almost equal to that of the original Debye-like process. A similar distortion of the Debye relaxation process

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at high pressure was also observed in other simple alcohols (ethanol and methanol). 31,32 However, viscosity measurements at high pressure and room temperature 30 demonstrated difference between the dielectric relaxation time and structural relaxation time (deduced from viscosity data) under these P − T conditions in 2E1H. Therefore, even at high pressure (where only one dielectric relaxation process is observed), the difference between structural and electrical dipole relaxation processes still exists. The aim of this work is to collect more experimental information on the behavior of dielectric relaxation in 2E1H in a wider P −T range and to compare it to the elastic properties, probed by transverse and longitudinal acoustic waves. In this paper, we present the results of dielectric spectroscopy measurements at high pressure up to 4 GPa and ultrasonic study in the pressure range up to 1 GPa.

Experimental Results Dielectric spectroscopy The dielectric response of 2E1H in the pressure range 0.6 < P < 4.1 GPa can be quite satisfactorily fitted with the only one stretched relaxation function of the Cole-Davidson type (see Supplementary Information for details). Although an increase in the pressure leads to a systematic increase in the asymmetry and width of the relaxation function (it is reflected in a decrease in the stretching exponent β from 0.8 to 0.25, see Fig. 2 a ) but no definite changes in the frequency separation and/or the ratio of the high- and low-frequency dielectric process amplitudes can be detected. Although the high frequency relaxation process can be detected in the high pressure experiments as an additional spectral density in the high frequency wing of the main dielectric process in the imaginary part of dielectric response, but due to the limited frequency range and the limitation of the measurement device the precise pressure evolution of this secondary process can not be determined. Still at low pressures and low temperatures this feature can be fitted and the obtained characteristic frequencies 6


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are shouwn in Fig. 2. Our experiments demonstrates that this additional spectral density is well separated in the frequency range from the main dielectric relaxation and its amplitude is not enhanced with the pressure rising. So the “deformation” of the Debye-like dielectric relaxation process in this mono-hydroxy alcohol under high-pressure (which manifests itself in decrease of the stretching exponent β) should be attributed to some inherent feature of this liquid, which probably might be common to all other simple alcohols where such deformation of the almost Debye-like dielectric relaxation were observed too (e.g. ethanol and methanol 31,32 ). The temperature dependence of the characteristic frequency obtained for the main dielectric relaxation process can be well interpolated with the Waterton–Mauro (WM) 33,34 relation (see Fig. 2 b): log10 (ν0 ) − log10 (ν∞ ) =

A E exp( ) T T

(1)

The previous studies 32,35 demonstrated that the WM relation has many benefits in comparison to the more known Vogel–Fulcher–Tammann equation. Relation Eq. (1) catches a non-divergent character of the relaxation times, which is likely present in glasses, the more or less realistic values of fitting parameters (ν∞ and E), and, the last but not the least, the more robust fitting of experimental data collected in the limited temperature range. For example, the WM equation in simple alcohols yields the values ν∞ close to the dynamic crossover frequency and the values E (in a two-level glass system, this is equivalent to the energy difference between the energy levels) of several hundreds of Kelvin. However, if one is interested only in the composite parameters of a vitrification process such as the fragility index mp ≡ d log10 ν10 /d TTg |T =Tg (measure of deviation of relaxation time from the Arrhenius behavior) and the dielectric glass-transition temperature Tg , then both WM and VFT laws yield approximately similar results. Here only “dielectric” fragility index and glassification temperature are meant which are surely different from their“true” structural counterparts because of the discrepancy between the main dielectric relaxation and the α one. Nonetheless, this sort of quantification adopting “fragility” notion is still very useful 7



1/T, 1/K 0.004

0.005

0.006

β 0.4 0.6 0.8

1

0.003

6

α

α 4 0.0

log10(ν0 Hz)

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2

0.6 1.5 2.2

0 4.0

−2

4.25

0.003

0.004

0.005

0.006

1/T, 1/K

Figure 2: Temperature evolution of the characteristic frequency ν0 and parameter β along selected isobars (pressure values in GPa are shown near the corresponding curves). Similar symbols on both panels correspond to the same thermodynamic conditions. Thin lines are fits according to Eq. (1). The dashed curves designated as α are guide to eyes which traces the temperature evolution of secondary α features of the main dielectric relaxation at low pressures (P=0.0, 0.6 GPa).

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because it allows us compare our results with the previously reported one. Interesting to note that the parameter E in Eq. (1) plays the role of the “entropy activation energy”. 34 Simple comparison 36 of VFT and MW equations demonstrates that at temperatures well above glassification temperature E should be comparable to T0 parameter (“ideal glass temperature”) obtained from the VFT equation. Obviously T0 should be less than the conventional glassification temperature. In practice it turns out just the opposite and E parameter in 2E1H (see Table 1) or other molecular glassformers 32,35 is well above glassification temperature which we consider to be more realistic parametrization of the vitrification process. Our findings demonstrates (see Table 1) that E parameter also drastically increases with the pressure rising. There is an isothermal counterpart of Eq. (1) proposed long ago 37 following the ideas of the Waterton paper 33 and named the Shishkin equation after its author: 38,39

log10 (ν0 ) − log10 (ν∞ ) = C exp(D · P )

(2)

The point of this equation is the same as in Eq. (1); i.e., the “ideal glass” state (the glass with infinite relaxation time) cannot be obtained by fast compression of a liquid to finite pressures. There is not much of experimental evidence corroborating Eq. (2) because of a limited pressure range. In the original work, 37 this equation was proposed on the basis of measurements in the pressure range P < 0.5 GPa. Nonetheless, in our case it provides a more or less accurate interpolation of experimental data in a fairly wide pressure range (Fig. 3).

The pressure rising also increases the fragility index of 2E1H from 30 at the

ambient pressure (i.e., E21H is a quite “strong” glassformer in “dielectric” sense under normal conditions) to more than 90 at P > 4 GPa. This “strong-to-fragile” transition in the temperature behavior of the main dielectric relaxation generally corresponds to the previously observed trend 28,29 but the pressure dependence of mp in our work seems to be monotonic and gives somewhat lower values in the range P < 1.6 GPa than it was reported

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P, GPa 0

1

3

2

4

5

4

5

β

0.8 0.6 0.4 6 361.1 4

log10(ν /Hz)

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297.4 2

0

−2

0

1

2

3 P, GPa

Figure 3: Pressure evolution of the characteristic frequency ν0 and parameter β along the two isotherms (temperature values in Kelvin are shown near the corresponding curves). Similar symbols on both panels correspond to the same thermodynamic conditions. Thin lines are fits according to Eq. (2).

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P, GPa 0

1

3

2

5

4

mp

80 60 40

a)

6 350

3 0

300

−3 T, K

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250

200

b) 150 0

1

2

3

4

5

P, GPa

Figure 4: Pressure evolution of the fragility index mp (a) and the P − T diagram of relaxation times (b) revealed in 2E1H by dielectric spectroscopy and ultrasonic measurements. The open and gray symbols in panel a) correspond to the data obtained in this work and in the previous work, 28 respectively. The symbols in panel b) are extrapolated dielectric “glass-transition” temperatures (corresponding to the thermodynamic parameters where the characteristic relaxation frequency is ν0 = 10−3 Hz) and the smoothed curves are relaxation frequency levels (the log10 (ν0 , Hz) values, are shown near the curves). The symbols ♦ and correspond to the data from the isobaric and isothermal measurements in this work, respectively, and ◦ are the data from the paper. 26 The symbols × and ∗ designate the temperatures of shear rigidity loss and the position of attenuation maximum observed in ultrasonic measurements (at frequencies of 5 and 10 MHz, see Fig. 5). 11 ACS Paragon Plus Environment


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Table 1: Parameters of the Mauro-Waterton (Eq. (1)) and Shishkin (Eq. (2),the last two rows) equations in 2E1H at high pressures. Pg , GPa 0.0 0.6 1.5 2.2 4.0 4.25

Tg , K 152.4 207.7 245.5 272.6 336.1 349.9

∞ ) log10 ( νHz 17.7 10.5 9.28 9.3 8.5 7.3

3.31 4.94

297.4 361.1

11.9 7.6

mp E, K 30.13 221.82 44.7 690.3 51.5 1021.3 58.3 1289.3 91.9 2690.1 90.4 3064.1 D,GPa−1 0.35 0.6

A, K 910.3 129.2 55.20 34.06 1.40 0.65 C -4.81 -0.51

earlier. Such a difference can be caused by slightly different methods of calculation of this quantity. The “dielectric” glass-transition temperatures Tg (obtained by the extrapolation of dielectric relaxation time to 103 s) and fitted parameters of the WM equation are presented in Table 1. The smoothed version of dielectric relaxation times in P − T coordinates is also shown in Fig. 4b. It is worth mentioning that the pressure dependence of fragility index mp obtained from dielectric measurements of 2E1H also follows the general trend. In hydrogen bonded liquids, it increases with the pressure rising (similarly to glycerol 40,41 ) in contrast to purely van-der-Waals bonded liquids such as propylene carbonate 42 where it decreases with an increase in the pressure.

Ultrasonic measurements The result of ultrasonic measurements was quite unexpected because it was found that the relaxation times observed in the propagation of longitudinal and transverse waves have different values in the whole pressure range P < 0.5 GPa. It can be seen most clearly in the attenuation of acoustic waves (see Fig. 5 b) where the loss of a transverse signal (with a frequency of 5 MHz) and the maximum attenuation of the longitudinal acoustic wave (with a frequency of 10 MHz) are observed in different temperature ranges (spaced by more than 50 K). According to the Kramers–Kronig relation, the corresponding step-like features

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are also observed in the same temperature range on the respective velocities of acoustic waves (see Fig. 5 a). These features are due to the effect appearing when the frequency of structural relaxation (responsible for either the shear or bulk elasticity) coincides with the frequency of a probe acoustic wave (5–10 MHz): at higher temperatures the structural relaxation becomes faster (higher ν0 ) and the liquid itself consequently becomes less viscous. Therefore, the experiment demonstartes that the main absorption of longitudinal ultrasonic waves took place at higher temperatures (Fig. 5) than the loss of shear rigidity indicates the presence of another (slower than structural, responsible for shear elasticity) relaxation process, presumably caused by the relaxation of the bulk elastic modulus. The observed temperatures of shear rigidity loss and the maximum attenuation of longitudinal acoustic waves are shown in Fig. 4b. It is easily seen in this figure that the difference between these two temperatures is about 50 K and can hardly be accounted for by the probe frequency difference between transverse (5 MHz) and longitudinal (10 MHz) sound waves. The difference between relaxation times of longitudinal and transverse ultrasonic waves can serve as an indication of different mechanisms of structural relaxations probed by differently polarized sound waves. It is also worth mentioning that both bulk and shear moduli of 2E1H at low frequencies (ν < 10 kHz) demonstrated the same frequency dependence. 12 This contradiction can supposedly be attributed to different relaxation mechanisms revealed by different experimental techniques in the low- and high-frequency limits. From the speeds of sound, both elastic moduli can be calculated (Fig. 6). It can be concluded that the rather strong frequency dependence of the bulk modulus also leads to substantial decrease in the longitudinal sound velocity with increasing temperature. It is a rather uncommon phenomenon because the coincidence of the relaxation frequency with the frequency of an ultrasonic wave probe in some liquids (e.g., propylene carbonate 42 ) does not necessarily lead to substantial changes in the temperature dependence of the bulk modulus, and its temperature dependence remains more or less smooth. However, it should be mentioned that the two relaxation times at the room temperature were already observed

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Ultrasound velocity (km/s)

3.5

a)

3.0 2.5 2.0 1.5

0.1 GPa 0.25 GPa 0.5 GPa

0.1

Attenuation

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Longitudinal wave Transverse wave

0.01

b)

1E-3

100

125

150

175

200

225

250

275

300

Temperature (K) Figure 5: Speeds of sound (a) calculated from the raw experimental data and the attenuation coefficient (b) for the longitudinal (open symbols) and transverse (closed symbols) acoustic waves in 2E1H at different pressures (corresponding values are shown in the inset). Dashed lines are guide to eyes.

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in 2E1H in the frequency dependent longitudional sound attentuation measurements 2 which were ascribed to the different characteristic relaxation frequencies of the bulk and shear moduli. This difference leads to the different sound dispersion of transverse and longitudinal sound waves as schematically depicted in Graphical Abstract, where T0 – T2 corresponds to different temperature values. The same picture illustrates the sequence of relative dispersion events with temeperature rising. If the measurement frequency νprobe remains fixed (which is the case in the pulse ultrasonic technique) the temperature increase from the glassy state (T0 ) would result in sequentional loss of transverse sound wave (T1 corresponding to devitrification of the glass), then the dispersion anomaly in longitudinal sound waves (T2 so formally it takes place in the already supercooled liquid state) turns up and the last come the maximum of dielectric losses at even higher temperatures (> T2 , that is rather deep inside the supercooled liquid state). The infinite frequency elastic moduli can be revealed by the measurements in the glassy state of 2E1H (Fig. 7). At liquid nitrogen temperature in the whole pressure range (P < 1 GPa), the frequency of the ultrasonic probe wave is well above the relaxation frequency of glassy 2E1H; therefore, the obtained elastic moduli can be approximately equal to the G∞ or K∞ parameters. Their pressure dependencies are sufficiently smooth and monotonically increasing.

Discussion We argue that the ultrasonic measurements corroborated the notion of the intermediate relaxation time (corresponding to the parameter τOH related to flipping of hydrogen bonds in the transient-chain liquid model). We believe that the same time value is observed in the propagation of longitudinal acoustic waves. Indeed, as it was shown in the preceding sections, the temperature of shear rigidity loss is always lower than the temperature at which the maximum attenuation of longitudinal acoustic waves is observed. Therefore, the characteristic frequency of shear relaxation at any fixed temperature should be higher than that of

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8

0.1 GPa 0.25 GPa 0.5 GPa

Bulk modulus (GPa)

7 6 5 4 3

a)

2

3.0

Shear modulus (GPa)

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

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0.1 GPa 0.25 GPa 0.5 GPa

2.5 2.0 1.5

b) 1.0 100

125

150

175

200

225

250

275

300

Temperature (K) Figure 6: Temperature evolution of the bulk (a) and shear (b) elastic moduli in 2E1H at designated pressures.

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7 2.8 T=77 K

6.5

2.6

←

→

5.5

2.4

G, GPa

6 K, GPa

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


5 2.2 4.5 2 4 0

0.2

0.4

0.6

0.8

1

P, GPa

Figure 7: Pressure evolution of the bulk () and shear () elastic moduli in 2E1H along the isotherm at liquid nitrogen temperature.

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longitudinal relaxation (it is schematically depicted in Graphical Abstract). The relaxation of transverse acoustic waves is determined by the shear elastic modulus (see Supplementary materials for details); thus, its relaxation is determined by the same mechanism as the shear viscosity measured in the standard rheological experiments. In other words, this frequency is just the frequency of structural relaxation in liquid and glasses 1/τα . In its turn, the relaxation time of longitudinal acoustic waves is greater than the time τα , but it is always less than the dielectric relaxation time. This conclusion can be inferred from the already presented experimental data in 2E1H where the relaxation observed in longitudinal acoustic waves took place at lower temperatures (see Fig. 4 b) in comparison to the dielectric relaxation measured at the same frequency. We prefer the term dielectric relaxation instead of Debye relaxation, because its Debye-like character observed at the ambient pressure is lost at higher pressures; i.e., it is impossible to distinguish between Debye-like and structural α-relaxations only by their frequency dependence. Therefore, the relaxation time revealed by the experiments with longitudinal acoustic wave propagation is intermediate between dielectric and structural relaxation times. Within the transient-chain liquid model, it seems almost obvious that the bulk elastic properties of such a liquid should be determined by the elastic properties of these chains, which serve as (so to say) reinforcement elements of the whole structure. On the other hand, the shear viscosity of such media is determined by friction between these chains, which is determined in this model by the interchain forces (purely of the van der Waals character) caused by the transverse dipole moment normal to the chain axis. Therefore, difference in the nature and strength of the forces acting along the chains (hydrogen bonds) and normal to it (dipole–dipole interaction) explains the difference between the relaxation times observed in the transverse and longitudinal ultrasonic experiments. We should note that almost the same intermediate relaxation time in the purely shear rheological response in 2E1H was also observed in the work of Gainaru et al 10 (the tail of the corresponding process is also visible in Fig. 1 b). However, the amplitude of this process is much lower than that of shear one,

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so its appearance in this sort of rheological experiments might be caused by some nonlinear effects. This consideration is applicable to the supercooled liquid state where the relaxation time is sufficiently small. When this time becomes comparable to the typical time of measurements (by convention it is taken to be equal to 102 − 103 s), a glass transition occurs. It vividly manifests itself in the experiments where some static parameters are measured (such as the heat capacity, static viscosity, static conductivity), but in some circumstances, it is also observed as a small anomaly on the temperature (or pressure) dependence of a certain high-frequency parameter. We would like to mention the work by Kozhevnikov et al. 43 where the glass transition in quenched liquid selenium was observed as steps with a magnitude of ≈ 3% on the temperature dependencies of the transverse and longitudinal velocities of sound (with the probe frequency ν = 7 − 22 MHz). However, many factors influence the appearance of such anomalies, and among others the most prominent are characteristics of the relaxation process in the liquid. Since molecular dynamics in the glass state is significantly retarded and can be characterized by the fictive temperature (intermediate between the true thermodynamic temperature and the glassification temperature), the magnitude of possible relaxation of any physical coefficient in the glass state should be between its value at the glass-transition point and the value determined from the extrapolation of the (supercooled/)liquid dependence. Consequently, the maximum value of any high-frequency parameter is its value at the glass-transition point. For example, the maximum value of the speed of sound or the elastic moduli at the frequency of the probe wave νprobe = 107 Hz is R(νprobe /ν0 ) where ν0 = 10−3 − 10−2 Hz. Due to a rather weak frequency dependence of the elastic relaxation function (we should mention that β = 0.16 in 2E1H) and despite a very large frequency ratio νprobe /ν0 = 1010 , the largest possible “residual” amplitude of the relaxation process can be still substantial and 3% reported for selenium 43 might be realistic enough. However, in our experiments with 2E1H, we cannot detect any downturn on the real part of the sound propagation coefficients (speed of sound or elastic moduli). Some

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anomalies were still observed in the longitudinal sound attenuation coefficient, which in our opinion can be caused by these effects. Thus, ultrasonic measurements provide also some hints on the pressure evolution of the main dielectric relaxation process. Previously, it was supposed 26 that the distortion of the relaxation process at higher pressures is caused by merging Debye-like and α-relaxation processes, which was concluded from the decrease in the frequency gap between them at higher pressures. However, according to the ultrasonic measurements in the same pressure range P < 0.6 GPa, we have found that these two processes do not merge. An increase in the pressure up to 0.5 GPa leads to a decrease in the distance (in the temperature scale that remains almost invariant in the whole pressure range) between these two absorption features revealed in longitudinal and shear ultrasonic experiments. As it was mentioned previously these two absorption features correspond two different molecular dynamics caused by intraand interchain forces. So the difference between this two times demonstrates existence of hydrogen-bonded molecular chains with almost the same length in this liquid at high pressures. For this reason, we believe that the transformation of the dielectric relaxation process at higher pressures is caused by the distortion of the original Debye-like process rather than by its merging with the dielectric α relaxation.

Conclusions In this work, we have studied structural and dielectric relaxation processes in 2-ethyl-1hexanol, which is a well-known monoalcohol glassformer. Dielectric measurements demonstrate that at high pressure the main relaxation process (which has a Debye-like form at ambient pressure) transforms into general asymmetric process observed in many other molecular glassformers. Increase of pressure leads to further distortion of the main relaxation peak (which can be quantified by the decrease of the stretching exponent from approximately 1 at ambient pressure to 0.25 at P=4.2 GPa). Still under these condition additional spectral

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weight is still retained at the high-frequency wing of the main dielectric relaxation process so we can not conclude that the distortion of the main dielectric relaxation process is caused by the merging of the Debye- and α-relaxation. Ultrasonic measurements generally corroborate this conclusion and indicate that the relaxation time observed in the attenuation of the shear sound wave at the pressure range up to 0.5 GPa is considerably (2-3 orders of magnitude) smaller than the dielectric relaxation time. Investigating the attenuation of transverse and longitudinal acoustic waves, we have found that the relaxation of this monoalcohol at high pressure involves two characteristic relaxation times. The observed data were found to be compatible to the previously proposed model of “short hydrogen-bonded supramolecular chains”. The relaxation of longitudinal waves indicates that the elastic and dielectric properties of this alcohol at high pressure are mainly determined by the switching of hydrogen bonds along these chains.

Acknowledgement This work was supported by the Russian Science Foundation (grant no. 14-22-00093). The work of A.A.P. was supported by the Russian Foundation for Basic Research (grant no. 16-02-01120). We thank V.N. Ryzhov and M.G. Vasin for helpful discussions, A. Loidl and P. Lunkenheimer for bringing up this topic to our attention and R. Tyapayev for technical assistance.

Supporting Information Available An additional information on the experimental methods and the fitting procedures is available as Supporting Information in single PDF file.

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Graphical TOC Entry Dielectric Losses

Ultrasonic Dispersion log(ω)

Longit. T2

2πνprobe T0

T2 T1 ε″

Transv.

T1

T0 < T1 < T2

T0

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log(k)

Structural and Dielectric Relaxations in Vitreous and Liquid State of

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