Secondary Relaxation in Supercooled Liquid Propylene Glycol under

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Secondary Relaxation in Supercooled Liquid Propylene Glycol under Ultra-High Pressures Revealed by Dielectric Spectroscopy Measurements Mikhail V. Kondrin, Alexei A. Pronin, and Vadim V. Brazhkin J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b07328 • Publication Date (Web): 04 Sep 2018 Downloaded from http://pubs.acs.org on September 8, 2018

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The Journal of Physical Chemistry

Secondary Relaxation in Supercooled Liquid Propylene Glycol under Ultra-High Pressures Revealed by Dielectric Spectroscopy Measurements M.V.Kondrin,∗,† A. A. Pronin,‡ and V. V. Brazhkin† †Institute for High Pressure Physics, Russian Academy of Sciences, Troitsk, Moscow, 108840 Russia ‡General Physics Institute, Russian Academy of Sciences, Moscow, 117942 Russia E-mail: [email protected]

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The Journal of Physical Chemistry 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

Abstract 1-2-propanediol (propylene glycol) is a well-known glassformer, which easily vitrifies under wide range of cooling rates. An interesting feature of propylene glycol is that, similar to glycerol, it retains one-mode primary relaxation (slow α process) under a wide range of external P − T conditions. It was demonstrated that the emergence of secondary (β) relaxation requires the application of very high pressures P > 4.5 GPa. In this pressure range, the observation of secondary relaxation is partially obfuscated by the presence of strong decoupling of the static (ionic) conductivity and primary relaxation (the fractional Debye–Stokes–Einstein effect). However, secondary relaxation can be unambiguously extracted from experimental data by the correlation procedure of the imaginary and real parts of the dielectric response by means of Cole–Cole plots. This is the second (after glycerol) example of observation of Johari–Goldstein relaxation under ultra-high pressures P > 2 GPa.

Introduction The electric permittivity spectra of supercooled liquids exhibit several relaxation features, which are believed to be the key to achieve a better understanding of the glass transition. The most prominent of them is the structural relaxation (α) characterized by a strong dependence of the relaxation time on temperature and pressure, traced over a wide range of frequency. In addition, all glassformers demonstrate faster secondary or β-relaxation processes. They appear as a pronounced peak in dielectric loss spectra (type B systems) or as an excess wing on the high-frequency side of the structural relaxation (type A). Secondary relaxations named Johari–Goldstein 1 (JG) relaxation similarly to α-peak are caused by the motion of the molecules as a whole. They are believed to be the intrinsic properties of supercooled liquids but their microscopic origin is still questioned. JG relaxations should be distinguished from relaxations caused by intramolecular motions. The application of external pressure can help “separate” JG relaxation from the main relaxation and so to say converts type-A glassformers 2


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in type-B ones. However, the crossover pressure turns out prohibitively high in many cases (for glycerol, this pressure is P > 2.5 GPa). In this paper, we consider propylene glycol (PG) that is a well-known small molecular glassformer. 2,3 It is characterized by a high dielectric response consisting of the single α process, which does not split by the application of a moderate pressure P < 1 GPa. 4,5 For this reason, we believe that it is a good candidate to check whether application of higher pressures can influence its excess wing and lead to the emergence of pronounced secondary relaxation. The parameters characterizing the vitrification process of PG (glass-transition temperature, fragility index, etc.) at high pressure can be established too. Besides that, interesting information can be obtained regarding correlation between the static conductivity and characteristic frequency of α-relaxation. In the normal liquids, the most general relation between the ionic viscosity ηi and the ionic conductivity σ0 is the Nernst–Einstein law: σ0 1 = 2 ηi ne The substitution of Maxwell’s relation ηi = βG∞ /ν0 into this equation yields the Debye– Stokes–Einstein (DSE) equation for the conductivity σ0 /ν0 ≈ const , which is actually observed in experiments with simple molecular glassformers. 6 Deviations from this proportionality, where ν0 is associated with some charge relaxation process, are occasionally observed in supercooled liquids. Such deviations are commonly described by the phenomenological relation σ0 ∼ ν0s 0 < s < 1, which was named fractional DSE (fDSE) relation. 7–18 However, this effect is observed rather sporadically and the origin of the fDSE relation is unknown. It is interesting to compare results obtained for PG and for its two derivatives: glycerol and propylene carbonate (PC). Glycerol is a weakly hydrogen-bonded glassformer but its bonds are stronger than that of PG. Propylene carbonate is a van-der-Waals-bonded liquid. Influence of high pressure on hydrogene bonding is poorly studied subject. 19 It was shown previously that the application of pressures above 2.5 GPa leads to onset of distinct secondary

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relaxation in glycerol 20,21 and no transformation of the relaxation process was observed in PC 22 at pressures up to 4.2 GPa. So, one might expect an intermediate behavior for PG, which ultimately will be demonstrated in our paper.

Methods The samples of 99.5%-purity 1-2-propanediol were obtained from Acros Organics and were used as delivered. The high-pressure dielectric spectroscopy experiments were carried out in Toroid type anvils 23 in the P −T region P < 5.2 GPa and 150 K < T < 373 K. As a sensor, we used a plane capacitor made of copper plates separated by Teflon spacers (with a thickness of 0.1 − 0.2 mm) and 1.5-mm-diameter holes punched in them. Its typical empty capacitance was about 10 pF. The measurement capacitor was immersed in the liquid contained in a Teflon cell. Thus, the studied liquid also served as a pressure-transmitting medium. The signal from the capacitor was recorded by a Novocontrol-Alpha analyzer in the frequency range of 1 Hz – 2 MHz. The pressure and temperature sensors consisting of a manganin wire and a chromel–alumel thermocouple were also placed in the Teflon cell. The overall accuracies of determination of the pressure and temperature were better than 0.05 GPa and 0.1 K, respectively. In every experimental run, two or three isobars and isotherms were swept in a “stepwise” manner. That is, we first increased the pressure until the α-relaxation frequency became lower than the range of our measurements. After that, we started to heat our setup until this frequency became higher than our frequency range, etc. In the process of experiment, we took special care to prevent the transition of the sample to the glass state (which could be easily checked by the breakage of a manganin sensor). The rate of pressure and temperature variation was not strictly controlled but the typical rates can be estimated as 0.02 GPa/min and 0.5 K/min, respectively. Dielectric spectroscopy data presented in this paper were obtained in several runs of this type. The frequency-dependent complex dielectric response was obtained from the raw ca-

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pacitance C(ν) and conductivity σ(ν) (converted to unit length by multiplication with the appropriate geometric factor l/S, where l and S are the length and surface area of the capacitor, respectively): ε(ν) = ε′ + iε′′ =

σ(ν) C(ν) +i ε0 2πε0 ν

This response can be described by the general formula

ε(ν) = i

σ0 X + ∆εi Ri (ν/νi ) + ε∞ ν

(1)

All coefficients in this formula are real (and physically meaningful) values: σ0 is the static conductivity (in reduced values of the permittivity of free space ε0 ), ∆εi are the intensities of several relaxation processes Ri with characteristic frequencies νi contributing to the dielectric response and ε∞ is the dielectric constant at infinite frequency (in practice, this means the frequency at which the influence of all considered relaxation processes is negligible). Note that, due to the Kramers–Kronig relation, ∆εi are real constants that allows one to fit the real and imaginary parts of experimental data simultaneously. Throughout this paper, we adopt the Cole–Davidson function (due to its simplicity) for the description of the dielectric relaxation response: RCD (ν) =

1 (1 − iν/ν0 )β

(2)

As an example, the fit of this formula to the experimental data collected at P = 3.2 GPa is shown in Fig. 1.

Results The temperature evolution of the characteristic frequency and parameter β of the main relaxation process along several isobars in the pressure range P < 3.2 GPa is shown in Fig. 2. It should be noted that dielectric relaxation in this pressure range still retains its unimodal character and an increase in pressure results in the broadening of the relaxation 5



log10(ν Hz) 0

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log10(ε ″)

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0.5

0 300

T (K) 320 340

360

1.8 1.6 log10(ε ′)

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1.4 1.2 1 0.8 0

1

2

3

4

log10(ν Hz)

Figure 1: Fit of Eq. 1-2 to the dielectric spectroscopy data obtained at P = 3.2 GPa. The color of each curve specifies the temperature at which it was collected.

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process, which can be deduced from a decrease in the parameter β from ≈ 0.6 at ambient pressure to ≈ 0.2 at P = 3.2 GPa. The temperature dependence of the characteristic frequency obtained for the main dielectric relaxation process can be well interpolated by the Waterton–Mauro 24,25 relation (see Fig. 2 b): log10 (ν0 ) − log10 (ν∞ ) =

E A exp( ) T T

(3)

Previous studies 26,27 demonstrated that the Waterton–Mauro relation has many benefits in comparison to the more known Vogel–Fulcher–Tammann equation. Relation (3) 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. Both the Waterton–Mauro and Vogel–Fulcher–Tammann laws yield approximately similar results for the composite parameters of a vitrification process such as the fragility index mp ≡ d log10 ν10 /d TTg |T =Tg (measure of deviation of the relaxation time from the Arrhenius behavior) and the dielectric glass-transition temperature Tg (by convention, the temperature at which ν0 = 10−3 Hz). The “dielectric” glass-transition temperatures (obtained by the extrapolation of dielectric relaxation times to ν0 = 10−3 Hz) and fitted parameters in Eq. 3 are presented in Table 1, where the fragility index is related to the parameter A in Eq. 3 as mp = A/Tg exp(E/Tg )(1 + E/Tg ). Table 1: Glass-transition temperature Tg , fragility index mp , and the parameters log10 (ν∞ ) and E of the Waterton–Mauro equation (3) in propylene glycol at high pressures P , GPa 0.0 0.8 1.6 2.2 3.2

Tg , K 164.43 195.37 236.97 251.35 279.27

∞ log10 ( νHz ) 15.25 11.78 15.47 13.47 14.67

mp 42.47 42.77 47.94 47.32 51.27

E, K 382.6 565.2 615.1 722.14 810.1

The comparison of glass-transition temperatures Tg and fragility indices mp in PG, PC, 7



0.003

0.0035

1 , K−1 T 0.004 0.0045

0.005

0.0055

0.006

0.6

β

0.5 0.4

a)

0.3 6

b)

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log10(ν0 Hz)

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2

0

−2

0.003

0.0035

0.004

0.0045

0.005

0.0055

0.006

1 , K−1 T

Figure 2: Plots of the relaxation parameter β (see Eq. 2, panel a) and characteristic frequency ν0 (panel b) along several isobars P = (+)0, (◦) 0.8, () 1.6, (♦) 2.2, and (△) 3.2 GPa. Thin lines are fits by Eq. 3.

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1

3

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250

300

0

P, GPa 2

200

Tg , K

90

a)

70

80

b)

50

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mp

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


350

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0

1

2

3

4

P, GPa Figure 3: Parameters Tg (panel a) and mp (panel b) for () propylene glycol, (♦) PC, and (◦) glycerol. The data for PC and glycerol are taken from Refs. 21,22 Solid curves are guides to eye.

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and glycerol reveals an unambiguous trend depending on the strength of intermolecular forces (Fig. 3). All three molecules have the same hydrocarbon backbone consisting of three carbon atoms. As was already mentioned, PC is a purely van-der-Waals bonded liquid, and PG and glycerol are weakly hydrogen bonded ones, although hydrogen bonds in glycerol are stronger because it has three hydrogen bonds per molecule while PG has only two. Correspondingly, the weaker the bonds, the steeper the pressure dependence of the glasstransition temperature and the weaker the pressure dependence of the fragility index (in PC, it is negative). At higher pressures, qualitative changes in dielectric relaxation in PG took place and secondary relaxation emerged at pressures P > 4.5 GPa. This secondary relaxation manifests itself as a small hump in the high-frequency wing of the imaginary part of dielectric relaxation data collected along the 350-K isotherm (see Fig. 4). Due to the decoupling of the static conductivity and characteristic frequency of primary relaxation, the peak corresponding to the α-process is submerged under the low-frequency wing corresponding to ionic conductivity. This effect makes the emergence of secondary relaxation less evident but it can be detected by means of the Cole–Cole plot, i.e., the plot of the imaginary vs. real part of the dielectric response (see Fig. 5). Because amplitudes of primary and secondary relaxations are oder of magnitude different it is convenient to draw the Cole-Cole plots in slightly modified manner that is in double logarithmic scale which makes changes in high-frequency flank of dielectric response (corresponding to the lower left corner of the Cole-Cole plot) more spectacular. The comparison of isobaric data collected at P = 3.2 GPa (Fig. 5 a) and along the 350-K isotherm in the pressure range 2.2 GPa < P < 5.2 GPa (Fig. 5 b) clearly demonstrates a qualitative difference between them and obviously indicates that the secondary relaxation attains a significant amplitude at pressures P > 4.5 GPa. This pressure is significantly higher than the secondary relaxation onset pressure in glycerol (P = 2.5 GPa 21 ), which until now was a record-breaking value. We remind that similarly to PG glycerol has distinct secondary relaxation at high pressure (see Fig. 6 a) while in PC only one relaxation is observed upto

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log10(ν Hz) 0

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3 2.5 2.5 3 3.5 4 4.5 5

log10(ε ″)

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P (GPa) 1.5 1 0.5 0

2 1.8 1.6 log10(ε ′)

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1.4 1.2 1

0

1

2

3

4

5

6

log10(ν Hz)

Figure 4: Relaxation in propylene glycol along the 350-K isotherm at P = 2.2 − −5.2 GPa. The color of each curve specifies the pressure at which it was collected.

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a)

300

320

T (K) 340

360

log10(ε ″)

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b) 2.5 3 3.5 4 4.5 5

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P (GPa)

2 log10(ε ″)

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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1.5

1

0.5

0

1

1.2

1.4

1.6

1.8

2

log10(ε ′)

Figure 5: The Cole–Cole plots of dielectric relaxation (panel a) along the 3.2-GPa isobar at T = 295−375 K and (panel b) along the 350-K isotherm at P = 2.2−−5.2 GPa. Qualitative difference between the plots demonstrates the emergence of secondary β relaxation at T = 350 K and P > 4.5 GPa. The color of each curve specifies the pressure or temperature at which it was collected. 12


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a)

2

log10(ε ″)

1.5

1

0.5

300

310

0

320

330

T, K

1.2

1.4

1.6

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log10(ε ′)

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b)

− 0.5

log10(ε ″) 0 0.5

P, GPa 3.4 3.6 3.8

4

4.2

−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


1

1.2

1.4

1.6

1.8

log10(ε ′)

Figure 6: Correlation between the real and imaginary parts of the permittivity (the Cole– Cole plot) in glycerol (P = 4 GPa, T = 290 − 340 K, panel a) and PC (T = 410 K, P = 3.3 − 4.3 GPa, panel b). The color of each curve specifies the pressure or temperature at which it was collected. The data from Refs. 21,22 were used.

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4.2 GPa (see Fig. 6 b). In our opinion this difference is connected with the strength of the intermolecular forces present in the liquids: stronger the bonds the lower is the pressure where onset of the secondary relaxation is observed. It is conjectured that for PC even higher pressures should be applied (about 8 GPa or higher) to reveal the secondary relaxation. It is also interesting to note an enhancement of the fDSE effect in PG under high pressure, which leads to the decoupling of the static conductivity and frequency of primary relaxation mentioned above (see Fig. 1). The relation between the static conductivity and characteristic frequency in PG at ambient pressure is almost linear (typical Debye–Stokes–Einstein relation). However, nonlinear deviation occurs at higher pressures and a power law σ0 ∼ ν00.67 is observed at P = 3.2 GPa (fDSE, 7–18 Fig. 7). It should be noted that a similar behavior has already been detected in PG and its oligomers at high pressure. 4,5 However, the origin of these deviations is not well understood. Recently, it was found that an increase in pressure above a threshold value of 0.5 GPa results in a fractional relation between the static conductivity and viscosity in 2E1H 28 and PC 29 too, although the normal DSE is observed at ambient pressure in these glassformers. Recently, 29 it was proposed that a similar deviation from the DSE relation in PC at high pressure can be caused by the interference of some high-frequency process present in liquids 30–32 in the terahertz range. This additional relaxation process provides so to say a “shunting” mechanism of charge transfer, which appears at high pressures and low temperatures where the static conductivity ensured by the main relaxation process is too low.

Conclusions To summarize, we have established that the application of high pressure leads to the splitting of main α-relaxation in PG and appearance of secondary fast relaxation as a separate peak on the high-frequency side of the imaginary part of the α-process. Pressures at which this splitting takes place are higher than 4.5 GPa and are significantly higher than that for

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50

40

σ0 (kHz)

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


30

20

10

0

200

400

600

800

1000

1200

ν0 (kHz) Figure 7: Correlation between the static conductivity σ0 and characteristic frequency ν0 at P = 3.2 GPa. The nonlinear dependence is a result of the fDSE effect.

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glycerol (P > 2.5 GPa 21 ). There is a definite dependence of the secondary relaxation onset pressure on the strength of intermolecular forces in the sequence of glycerol, PG, and PC. The weaker the forces, the higher this pressure. For weakly van-der-Waals bonded PC, there are no traces of α-relaxation splitting up to the pressure P = 4.2 GPa. It is remarkable that the pressure-dependent glass-transition temperature and fragility index also significantly correlate with the type of intermolecular forces and their strength. The application of high pressure also leads to decoupling of the static conductivity and the characteristic relaxation frequency, which takes place at pressures above 3 GPa. As a result, we have observed a nonlinear relation between the static conductivity and characteristic frequency at high pressures, which can be described by the fDSE relation with an exponent of 0.67. The strong difference of this exponent at ambient (where it equals 1) and high pressures makes PG a convenient experimental object where microscopic mechanism of ionic transport responsible for the fDSE relation can be studied.

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).

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log10(ε ″) 1

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T=350 K P=2.2−5.2 GPa 0

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1.2

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log10(ε ′)

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Secondary Relaxation in Supercooled Liquid Propylene Glycol under

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