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Journal of Non-Crystalline Solids 353 (2007) 4273–4277 www.elsevier.com/locate/jnoncrysol

Effect of temperature and pressure on the structural (a-) and the true Johari–Goldstein (b-) relaxation in binary mixtures Khadra Kessairi a,b,*, Simone Capaccioli a,c, Daniele Prevosto Soheil Sharifi a, Pierangelo Rolla a,b

a,b

,

a

c

Dipartimento di Fisica, Universita` di Pisa, Largo Pontecorvo 3, I-56127 Pisa, Italy b CNR-INFM, POLYLAB, Largo Pontecorvo 3, I-56127 Pisa, Italy CNR-INFM, CRS SOFT, Dipartimento di Fisica, Piazzale Aldo Moro 4, I-00185 Roma, Italy Available online 1 October 2007

Abstract We investigated the microscopic origin of the excess wing through isothermal and isobaric dielectric relaxation measurements for the Quinaldine/tristyrene mixture. Our results show that the excess wing, characteristic of the high frequency side of the structural loss peak in neat Quinaldine, becomes a well resolved Johari–Goldstein secondary relaxation on mixing with the apolar tristyrene. Analyzing the temperature and pressure behavior of the two processes, a clear correlation has been found between the structural relaxation time, the Johari–Goldstein relaxation time and the dispersion of the structural relaxation (i.e. its Kohlrausch parameter). These results support the idea that the Johari–Goldstein relaxation acts as a precursor of the structural relaxation and therefore of the glass transition phenomenon.  2007 Elsevier B.V. All rights reserved. PACS: 64.70.Pf; 77.22.Gm Keywords: Dielectric properties, relaxation, electric modulus; Glass formation; Glass transition; Pressure effects; Viscosity and relaxation; Structural relaxation

1. Introduction An important aspect concerning the relaxation dynamics of glass forming materials is the investigation of the molecular origin of the secondary relaxation and its possible connection to the structural relaxation and thus to the glass transition phenomenon [1]. It is widely accepted that some secondary relaxations have an intra-molecular character and originate from the motion of part of the molecules almost decoupled from the rest, as for example some side groups in polymers [2]. Besides, in some other systems, the observed secondary relaxation reflects the * Corresponding author. Address: Dipartimento di Fisica, Universita` di Pisa, Largo Pontecorvo 3, I-56127 Pisa, Italy. Tel.: +39 050 2214322; fax: +39 050 2214333. E-mail address: [email protected] (K. Kessairi).

0022-3093/$ - see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.01.095

motion of the whole molecule (inter-molecular secondary relaxation). Binary mixtures of rigid polar molecules dissolved in apolar solvents are excellent systems to deepen the understanding of the molecular slowing down and of the origin of secondary relaxation in glassy systems [3–5]. In fact, 30 years ago Johari and Goldstein studied by means of dielectric spectroscopy the orientational dynamics of a rigid polar molecule (chloro-benzene) dissolved in an apolar solvent (decalin) [3]. The binary mixture showed in the glassy state the existence of a well resolved b-relaxation (called Johari–Goldstein relaxation (JG)), evidently not related to intra-molecular degrees of freedom but, on the contrary, to certain motions of essentially the entire molecule. Such (JG) b-relaxation process has been shown in several systems [4,6]. Some hints to distinguish (JG) from secondary process originating from intramolecular motion have been recently suggested [2,7]. Recently, it

K. Kessairi et al. / Journal of Non-Crystalline Solids 353 (2007) 4273–4277

turned out that the independent (primitive) relaxation time of the coupling model (CM), sp, is nearly the same as the (JG) b-relaxation time, sb, for a large number of glass forming systems [7]. At any temperature and pressure, sp is calculated by the CM equation n

sp ¼ ðtc Þ sa1n ;

ð1Þ

through the parameters sa and the value of the Kohlrausch-exponent, bKWW = (1  n), of the Kohlrausch–Williams–Watts (KWW) function /ðtÞ ¼ exp½ðt=sa Þ

1n

;

ð2Þ

used to reproduce the structural loss peak. In Eq. (1) tc  2 ps for molecular liquids. From the Eq. (1), the separation between sa and sp is given by log sa  log sp ¼ n log sa  n log tc

ð3Þ

and since sp  sb, the same result can be inferred about the separation between sa and sb, i.e. log sa  log sb ¼ n log sa  n log tc :

ð4Þ

The frequency separation of a and b loss peaks is strictly related to the coupling parameter, n (Eq. (4)). The coupling parameter, which is related to the broadness of the structural peak, is affected by the inter-molecular coupling. The greater is n, greater are the inter-molecular constraints leading to the many molecules dynamics. Broadband dielectric spectroscopy recently showed in binary mixtures of polar rigid molecules in apolar solvents with higher Tg [8] that the so-called ‘excess wing’ (EW), which is the characteristic of the neat system (where n is small) evolves in a well resolved b-relaxation. In this case the coupling parameter n becomes larger and so the time scale between the a-relaxation and b-relaxation increases (Eq. (4)) allowing in this way to resolve the b-peak. The emerging b-process can be considered of inter-molecular origin since it is related to the motion of the whole molecule [9]. Consistently, it is found to be strongly related to the structural a-relaxation [9]. In this work, we studied by means of dielectric spectroscopy a binary mixture of a rigid polar molecule (Quinaldine) dissolved in an apolar viscous solvents (tristyrene). The secondary dynamics of a pure system presents an excess wing, whereas its mixture with an apolar compound presents a separate secondary peak. Analyzing the temperature and pressure behavior of structural and secondary processes in the mixture, a clear correlation has been found between the two relaxation times and the dispersion of the a-relaxation. The results are rationalized in the framework of the coupling model (CM) [10]. 2. Experimental Quinaldine (Qn, molecular weight 143.19 g/mol), and Tristyrene (3Styr, molecular weight 370 g/mol, polydispersity 1) were used as received from Aldrich and Polymer Standards Service (PSS), respectively. Qn is a quite rigid

molecule with one main molecular dipole moment l of 3.8 D, whereas 3Styr has a much lower dipole moment of 0.2 D. Since the total relaxation strength is related to the square of the dipole moment (De / l2), the contribution of Qn molecules to the dielectric strength is expected to be more than two order of magnitudes larger than that of 3Styr. The glass transition of pure Qn and 3Styr systems are 180 K and 232 K, respectively. The complex dielectric constant e = e 0  ie00 was measured in the frequency range from 102 Hz up to 107 Hz at different isothermal and isobaric conditions using Novocontrol Alpha analyzer. The temperature at atmospheric pressure was varied from 100 and 320 K by means of a conditioned nitrogen flow cryostat. The high pressure experiment was carried out by means of an hydrostatic press and silicon oil as a pressure transmitting medium. A Teflon membrane prevented the oil to contact the dielectric cell. The temperature of the whole pressure chamber was controlled by a thermal jacket connected to a liquid circulator. 3. Results A comparison between the dielectric spectra of neat Qn system and of the mixture of concentration c = 10 wt% (c = wtQn/(wtQn + wt3St)) of Qn in 3Styr is shown in Fig. 1. Two spectra at different temperatures but with the same frequency of maximum of the a-loss peak have been selected. The loss spectrum of pure Qn is characterized by a narrow a-peak. On the high frequency tail of the latter we observe a loss contribution in excess that is usually called ‘excess wing’. When Qn is mixed with 3Styr, that has an higher Tg, the structural a-relaxation becomes broader and a well resolved secondary relaxation appears. As the polar molecules Qn are quite rigid and their molecular dipole is strongly coupled to the overall motion, no second-

0

10

β - relaxation n=0.53

-1

K*ε''

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EW

n=0.30 -2

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f[Hz] Fig. 1. Comparison of the dielectric loss spectra of 10 wt% Qn dissolved in 3Styr (Open stars, T = 230 K) and of pure Qn (filled squares, 188 K). Spectra with the same fmax of the a-relaxation have been selected. In both cases the continuous curves represent the KWW functions to fit the structural peak, with reported values of the coupling parameters n. The vertical arrows indicate the position of the JG secondary relaxation predicted by the coupling model (Eq. (1)).

K. Kessairi et al. / Journal of Non-Crystalline Solids 353 (2007) 4273–4277

ary relaxation due to intra-molecular degrees of freedom are expected. A similar result has been recently reported [8] for the rigid molecule picoline: neat picoline has a small n = 0.36 and shows an excess wing instead of a b-relaxation. When mixed with a higher Tg glass-formers such as tristyrene or OTP, at sufficiently high concentrations of the solvent molecules, the JG b-relaxation of picoline was resolved. The b-relaxation in the spectra of Fig. 1 as well as those of Ref. [8] appears to be peculiar of mixtures of rigid polar with apolar molecules. The coupling parameter, which is a measure of the deviation of the structural peak from the Debye relaxation, is n = 0.30 ± 0.03 for the pure Qn and n = 0.53 ± 0.02 for 10% Qn/3Styr (Fig. 1). Some selected dielectric relaxation spectra of the mixture Qn/3Styr (10 wt%) at different temperatures above and below Tg are shown in Fig. 2(a). A bimodal relaxation scenario is visible above Tg, with the a-relaxation loss peak, located at lower frequencies, being more intense and more strongly affected by cooling than the b-relaxation. Below Tg the b-process appears symmetric in shape and decreases in intensity on cooling. Near Tg, the two relaxations are

T 225K

P= 0.1 MPa

233K

-1

263K

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-2

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-3

10

ε"

(a) T= 238K

P

-1

60.1

30.3

0.1

-2

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380 MPa -3

10

(b) -2

10

both visible and well separated in the frequency scale, so that the a-loss peak can be separately well fitted by the Fourier transform of the KWW function (Eq. (2)) with n = 0.53, as shown by the dotted line in Fig. 2(a). The increase of pressure slows down the a-relaxation similarly to the decrease of temperature: the a-peak shifts to low frequencies and eventually the liquid is structurally arrested in a glassy state, without reaching its equilibrium configuration. Moreover, even the b-relaxation is sensitive to compression, both above and below the glass transition (Fig. 2(b)). The fit by the Fourier transform of the KWW function to the a-loss peak, shown by the dotted line in Fig. 2(b), gives a coupling parameter of n = 0.53, the same as in the case of the atmospheric pressure case. The dielectric spectra were well fitted in the whole temperature and pressure range by a superposition of Havriliak–Negami (for a-process) and Cole–Cole (for b-process) functions. In this way the contribution of each process has been singled out by a simple superposition fitting procedure [11] and the relaxation times of the single processes, sa,sb were obtained by (2pmm)1, where mm is the loss peak maximum frequency related to the a and b-relaxations peaks, respectively. The overall dynamics can be quantitatively represented by the relaxation map, i.e. the plot of the logarithm of relaxation times versus the reciprocal of temperature or versus pressure as shown in Fig. 3(a) and (b), respectively. Usually, the logarithm of sb in the glassy state exhibits a linear behavior with temperature, corresponding   Eb to the Arrhenius law sb ¼ s0 exp RT , as shown in Fig. 3. The activation energy in the glassy state is 62.5 ± 2 kJ mol1. In this case it is noteworthy that sb deviates from the glassy Arrhenius behavior on crossing the glass transition. On the other hand, the time sa of the co-operative arelaxation exhibits above Tg the typical non-linear behavior and its temperature dependence can be fitted by the Vogel–Fulcher–Tammann–Hesse (VFTH) equation sa = s0exp[B/(T  T0)], with the Vogel temperature T0 = 150 ± 1 K and B = 3860 ± 10 K. Concerning the pressure behavior for the isotherm at 238 K, a linear relations(P, T) = s(T, Patm)exp(P D V/(RT)) has been found for both sa in the supercooled regime (activation volume DVa = 242 ± 3 cm3/mol) and sb(DVb = 43.9 ± 0.6 cm3/ mol) in the glassy state.

173K

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4. Discussion -1

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f[Hz] Fig. 2. Selected dielectric loss spectra of 10% Qn/3Styr vs. frequency: (a) at different temperatures (from right to left: 263, 253, 248, 238, 233, 226, 203, 183, 173 K with P = 0.1 MPa, (b) at different pressure (from right left: 0.1, 15.6, 30.3, 50.2, 60.1, 80.2, 104.9, 200.8, 380.0 MPa with T = 238 K). In both panels the dotted lines represent KWW curves to fit the structural peak, with value of the coupling parameters, n = 0.53 and the continuous lines are HN fitting curves The vertical arrows indicate the position of the JG secondary relaxation predicted by the coupling model for: (a) P = 0.1 MPa, T = 233 K and T = 225 K; (b) T = 238 K, P = 30.3 MPa and P = 60.1 MPa).

Binary mixtures of polar rigid molecules in apolar solvent are excellent systems to study the ‘genuine’ JG secondary relaxation and its relation with the structural a-relaxation and therefore on the glass transition phenomenon. In fact, when a quite rigid molecules with only one strong dipole moment is dissolved in an apolar system, we can argue that the observed relaxation process reflect motions of the whole polar molecule. Qn satisfies the above characteristics since it is quite rigid and it has only one main molecular dipole related to the heterocyclic ring.

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Fig. 3. Logarithm of the experimentally determined relaxation time for the a-process (solid circles) and b-process (open stars) for 10 wt% Qn/3Styr, vs. (a) 1000/T, (b) Pressure (P). The continuous lines represent the VFTH equation for a-relaxation, and the Arrhenius behavior for the b-process (in the glassy state), the dotted lines indicate the separation between the structural a-relaxation and the secondary b-relaxation at (T ; P T g ).

For these reason we can say that the well resolved secondary b-relaxation can be identified as the ‘genuine’ JG relaxation, in the sense that it is a local and non-cooperative process but entailing the motion of the molecule (Qn) as a whole. Generally, the nature of the secondary b-relaxations can be identified by their dynamic properties, their dependence on pressure and temperature, their relation, if any, or lack of relation to the a-relaxation, and by the comparison of their sb to the independent relaxation time, sp, of the coupling model [1,12,13]. We calculated the primitive relaxation time sp by the co-operative relaxation time sa and the coupling parameter n (see Eq. (1)), as predicted by the CM. It is important to mention that concentration fluctuations, that usually broaden the structural peak in mixtures, in this case should be negligible due to the small concentration of the polar component. Consequently, the dispersion of the structural relaxation (the coupling parameter) can be used as a measure of many molecules interaction. The peak frequency of the primitive relaxation is in fair agreement with that of the JG secondary peak observed in the Qn/3Styr mixture (vertical arrow in Fig. 1). In the case of the pure Qn, the primitive relaxation is predicted in the region of the EW and this is in agreement with the interpretation that the excess wing would be a b-relaxation hidden under the a-peak. According to Eq. (3) for fixed value of sa, max, the separation of the JG peak must be larger for greater values of n. In fact, when we mixed the pure Qn with 3Styr, the structural a-relaxation becomes broader, due to the larger constraints imposed to the Qn molecules by the slower surrounding 3Styr molecules, and the coupling parameter changes from n = 0.30 ± 0.02 for pure Qn to n = 0.53 ± 0.02 for 10 wt% Qn/3Styr. Moreover, a well resolved secondary peak can be observed in dielectric spectra. (Fig. 1).

A test of the Eq. (3). for the JG relaxation with temperature and pressure dependence was done, and a good agreement was found for the calculated sp and sb as shown by the vertical arrows in the Fig. 2. At frequency of nearly 1 Hz, the coupling parameter n is the same at ambient pressure and T = 233K and at high pressure P = 30.3 MPa and T = 238 K and this means that the dispersion of the structural a-relaxation and its time scale separation with the secondary b-relaxation have to be considered simultaneously, as shown also by [14,15]. Moreover, according to the Eq. (3), sb should be constant if at different temperature and pressure conditions the frequency of the loss peak maximum of the structural a-relaxation and its dispersion are constant. In fact, the loss spectra at ambient pressure and T = 225 K, and that at highest pressure P = 60.1 MPa and T = 238 K which have the same sa and the same n = 0.53 have also the same sb, as shown by the vertical arrow and in which the frequency of the maximum of the JG – relaxation is around 6 · 104 Hz. It is generally agreed that sb has an Arrhenius temperature dependence in the glassy state but recently some deviations, more than the fit uncertainty, from this behavior were shown when the glass transition was crossed [8,16]. In such cases, as well as in our case (see Fig. 3), such deviation occurred far from the merging region, so that the mutual interference between the two processes could be neglected. Different scenarios for the a  b dynamics above Tg have been reported by Garwe and co-workers [17]: only extending our measurements to the high frequency and high temperature range will be possible to determine which kind of merging scenario addressed by Garwe is more appropriate for the mixture for 10 wt% Qn/3Styr. Anyway, the deviation of sb from the glassy state T-dependence is predicted by the CM, since sp cannot have an Arrhenius behavior according to Eq. (3) as sa has a VFT behavior

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above Tg. It is important to point out that a separation of almost seven decades between sa and sb exists for our system in the region where the deviation from the Arrhenius dependence of the glassy state occurs (see Fig. 3). This fact prevents from explaining the deviation from the Arrhenius behavior as apparent, only in terms of fitting procedure, as proposed in Ref. [18]. In fact, the two peaks in the spectra of our mixture are very well separated and their mutual interference would not be enough to shift the time scale sb observed in the relaxation map more than two decades to match the extrapolation of the Arrhenius behavior. It is important to mention that in systems similar to ours, a similar deviation from the Arrhenius behavior of the glassy state has been reported [8] also using the fitting procedure suggested in Ref. [18]. Moreover, also for the pressure dependence a change of dynamics between two nearly linear behaviors with different slopes is observed (Fig. 3(b)) at the glass transition. We believe that this effect is nothing but the pressure counterpart of what observed in the isobaric experiment. The activation volume of the b-process increases above Tg because of the larger free volume fluctuations present in the liquid state. All these results indicate that the JG relaxation, as expected, feels the change of thermodynamic conditions (volume, entropy, enthalpy) characterizing the glass transition. The strong relation between structural and JG relaxation is not only qualitative, but also quantitative: as predicted by CM [7], locating the glass transition line (Tg, Pg) for different isobaric and isothermal conditions at sa = 100 s, sb (Tg, Pg) is found to attain the same value (15 ls), irrespective of the fact that the conditions of temperature and of pressure are different. If the JG relaxation time scale is expected to be affected by pressure or volume and so could be influenced by the glass transition, it is not trivial that such a quantitative correlation exists between structural (a-) and secondary (JG) dynamics. 5. Conclusion In this paper we showed that in our system the excess wing is nothing but a JG process so close in the time scale to the a-process that its low frequency side is hidden beneath the a-peak. By mixing the polar rigid molecule with an apolar solvent characterized by an higher Tg, the separation between a- and JG-process is increased with increasing the relative fraction of the apolar solvent, so that the excess wing feature evolves in a well resolved b-peak.

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Analyzing the temperature and pressure behavior of the two processes for our mixture, a clear quantitative correlation has been found between the time scale separation of the a- and JG relaxation and the dispersion of the a-relaxation (i.e. its Kohlrausch bKWW parameter). The results can be rationalized in the framework of the coupling model (CM) [10]. An universal scenario appears, where temperature reduction and increase of pressure act in a similar way, slowing down the a-relaxation. Once sa(Ti, Pi) is determined, irrespective of Ti and Pi, a given dispersion parameter n = 1  bKWW is obtained, as shown in Ref. [14]. Then, as a consequence of Eq. (1), also a given the time scale sb of the JG relaxation is obtained. The whole dielectric response at long and short times is so fully determined by the time scale of structural relaxation and by its dispersion. Acknowledgement Financial support by MIUR-FIRB 2003 D.D.2186 grant RBNE03R78E is kindly acknowledged. References [1] K.L. Ngai, M. Paluch, J. Chem. Phys. 120 (2004) 857. [2] N.G. McCrum, B.E. Read, G. Williams, Anelastic and Dielectric Effects in Polymeric Solids, Wiley, New York, 1991. [3] G.P. Johari, M. Goldstein, J. Chem. Phys. 53 (1970) 2372. [4] G.P. Johari, M. Goldstein, J. Chem. Phys. 56 (1972) 4411. [5] M.F. Shears, G. Williams, J. Chem. Soc. Farad. Trans. II 69 (1973) 608; M.F. Shears, G. Williams, J. Chem. Soc. Farad. Trans. II 69 (1973) 1050. [6] Md. Shahin, S.S.N. Murthy, J. Chem. Phys. 122 (2005) 014507. [7] K.L. Ngai, J. Chem. Phys. 109 (1998) 6982. [8] T. Blochowicz, E.A. Ro¨ssler, Phys. Rev. Lett. 92 (2004) 225701. [9] S. Capaccioli, K.L. Ngai, J. Phys. Chem. B 109 (2005) 9727. [10] K.L. Ngai, J. Phys. Condens. Matter. 15 (2003) S1107. [11] D. Prevosto, S. Capaccioli, M. Lucchesi, P.A. Rolla, K.L. Ngai, J. Chem. Phys. 120 (2004) 4808. [12] K.L. Ngai, P. Lunkenheimer, C. Leo´n, U. Schneider, R. Brand, A. Loidl, J. Chem. Phys. 115 (2001) 1405. [13] K.L. Ngai, M. Paluch, J. Phys. Chem. B 107 (2003) 6865. [14] K.L. Ngai, R. Casalini, S. Capaccioli, M. Paluch, C.M. Roland, J. Phys. Chem. B 109 (2005) 17356. [15] S. Hensel-Bielowka, M. Paluch, J. Ziolo, C.M. Roland, J. Phys. Chem. B. 106 (2002) 12459. [16] O. van den Berg, M. Wubbenhorst, S.J. Picken, W.F. Jager, J. NonCryst. Solids 351 (2005) 2694. ¨ nhals, H. Lockwenz, M. Beiner, K. SchrO ¨ ter, E. [17] F. Garwe, A. SchO Donth, Macromolecules 29 (1996) 247. [18] R. Bergman, F. Alvarez, A. Alegrı´a, J. Colmenero, J. Chem. Phys. 109 (1998) 7546.