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Journal of Non-Crystalline Solids 353 (2007) 4313–4317 www.elsevier.com/locate/jnoncrysol

Effect of thermodynamic history on secondary relaxation in the glassy state S. Sharifi

a,*

, D. Prevosto

b

a,b

, S. Capaccioli

b,c

, M. Lucchesi

a,b

, M. Paluch

d

a PolyLab-CNR, Largo B. Pontecorvo 3, I-56127 Pisa, Italy Dipartimento di Fisica, Universita` di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy c CNR-INFM, CRS SOFT, Piazzale Aldo Moro 2, I-00185 Roma, Italy d Institute of Physics, Silesian University, Uniwersytecka 4, 40-007 Katowice, Poland

Available online 4 October 2007

Abstract We investigated by dielectric spectroscopy the effect that the thermodynamic history of a glass has on the secondary relaxation process. In particular we focused our attention to glassy states at the same conditions of temperature and pressure but reached with different combinations of variation of the external parameters. Our analysis shows that the effect of thermodynamic history on the relaxation frequency is related to the activation volume of the process: secondary processes with larger activation volume present a larger effect of the thermodynamic history. This demonstrates an important role of density in determining such behavior in glassy systems. Ó 2007 Elsevier B.V. All rights reserved. PACS: 77.22.Gm; 61.43.Fs; 05.70.a Keywords: Dielectric properties; Pressure effects; Thermodynamics; Secondary relaxation

1. Introduction The glassy state is a nonequilibrium state of materials [1]. As a consequence, the observed thermodynamic and relaxation properties slowly evolve with time because of the evolution of the molecular configuration towards a state with lower energy [2]. The relaxation strength, De, of the secondary process was observed to decrease [3,4] or to vary nonmonotonously [5,6] with time at fixed thermodynamic conditions in the glassy state. Another consequence of the nonequilibrium condition of glasses is that thermodynamic and relaxation properties show different values when measured in the glassy state at fixed thermodynamic condition subsequently to different vitrification histories [7–9]. For example, this was observed for the relaxation frequency of several secondary processes [3,10]

*

Corresponding author. Tel.: +39 050 2214322; fax: +39 050 2214333. E-mail address: sharifi@df.unipi.it (S. Sharifi).

0022-3093/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2007.03.044

consequently to cooling with different rates, or after vitrification combining different sequences of cooling and compression steps [11–13]. The reason why secondary processes are influenced by the thermodynamic history of the glass is not clear at all, and the microscopic mechanisms at the basis of such dependence are unknown. The situation is even more complicated since the molecular mechanisms at the basis of secondary process are not clear at all. Some secondary relaxations are interpreted in terms of small rotations of molecular subgroups decoupled from the whole molecule [14]. Another interpretation is that secondary processes originate from local, non-cooperative, reorientation of the whole molecule (Johari–Goldstein, JG, process) [15,16]. A route to distinguish JG and nonJG processes on the basis of their dynamic properties is reported on previous publications [16,17]. A greater sensitivity to the thermodynamic history is expected for secondary processes of JG type due to their intermolecular origin. In this work we present the study of the influence of the glass thermodynamic history on the secondary processes of

S. Sharifi et al. / Journal of Non-Crystalline Solids 353 (2007) 4313–4317

2. Experiment BMPC, (average molecular weight, MW = 296 g/mol, with Tg at ambient pressure 246 ± 1 K [18]) and PDE (MW = 346 g/mol, Tg at ambient pressure 295 ± 1 K [18]) were synthesised in the laboratory of Professor H. Sillescu and obtained from Dr Roland Bo¨hmer. PPGE (with MW = 345 g/mol, Tg = 258.4 ± 0.5 K [21]) was obtained from Aldrich, and PPG400 (MW = 400 g/mol, Tg = 191 ± 1 K [24]) was purchased from Fluka. Dielectric measurements were performed with a commercial analyzer. For measurements varying pressure, the sample was placed in a parallel plates capacitor that was placed in a pressure room. Pressure variations were generated by a manual pump and transmitted to the sample through silicon oil. The sample cell was properly insulated from the oil with Teflon. A liquid circulator allowed the control of temperature through the use of a thermal jacket wrapped around the pressure room, (353–233 K). Repeatability of measurements in the supercooled liquid state was checked assuring that the surrounding oil does not contaminate the sample, not even after that the sample was led at high pressure. 3. Results Representative dielectric loss spectra measured in the glassy state of BMPC are presented in Fig. 1. We can observe a peak, corresponding to the secondary relaxation, which slowly moves towards lower frequencies on increas-

260 K

Glass transition relaxation

10

-1

10

100 MPa 200 MPa

,,

four molecular glass formers, namely poly [(phenyl glycidyl ether)-co-formaldehyde] (PPGE), 1,18-bis (p methoxyphenyl) cyclohexane (BMPC), poly (propylene glycol) (PPG400) and phenolphthalein-dimethyl-ether (PDE). These systems are particularly suitable for such investigation because their quite compact molecular structure and since their secondary processes can be measured in favorable temperature and pressure conditions for our apparatus. Despite the compact molecular structure, all the systems present a complex relaxation scenario. Glassy PDE presents three different relaxation processes: a so called excess wing, and two secondary relaxations [18,19], that are interpreted in term of local motions of parts of the molecule [13,18,19]. Glassy PPGE shows two secondary processes, the slower being of JG type [20,21], and the faster probably related to local motion of the epoxy subunits. BMPC show two secondary relaxations in the glassy state whose molecular origin is not clear at all [19,22]. Finally, glassy PPG400 shows two secondary relaxations, the slower one was classified as JG type [23]. In this research, we will focus on the intramolecular process of PDE and BMPC (the slowest one) and PPG400, on the JG relaxation of PPGE. In such a way, we have the possibility of comparing the effect of thermodynamic history on secondary processes which are mainly of intermolecular origin (case of PPGE), as well as secondary processes of intramolecular origin (PDE, PPG400).

ε

4314

-2

300 MPa Secondary relaxation -1

10

0

1

10

10

2

10 ν (Hz)

3

10

4

10

5

10

Fig. 1. Isothermal loss spectra of BMPC at various pressures in the glassy state. Secondary peak slightly shifts with pressure towards lower frequencies. Empty squares represents the loss spectrum measured at 100 MPa corrected for the contribution of the a-peak.

ing pressure. The rise at low frequency is due to the tail of the a-relaxation peak. Representative spectra of the other systems can be found in Refs. [13,18,20–24]. The secondary relaxation was analyzed in terms of the symmetric Cole– Cole function. eðxÞ ¼ e1 þ

De 1 þ ðixsÞ

1a

:

ð1Þ

The analysis was performed with a home made fitting program written in Matlab, which uses two minimization routines based on the Gauss–Newton and the Nelder–Mead minimization methods. The a-parameter usually increases with increasing pressure or decreasing temperature, and the obtained values are in the range 0.4–0.6 for all the cases. The loss maximum frequency, mmax = 1/(2ps), was obtained by the parameter in Eq. (1) and studied as a function of pressure (Fig. 2(a)–(d)). The logarithmic of the maximum frequency increases linearly with pressure for all the investigated materials. The pressure counterpart of the temperature Arrhenius law, mmax(P) = m0 exp [DVP/ (kBT)], can describe this dependence where DV is the activation volume, kB the Boltzman constant, and m0 the relaxation frequency at ambient pressure, which can be described by m0(T) = KBT/(2ph)* exp[DS/(kB)]* exp[DH/ (kBT)] [26], where kBT/h is the Debye frequency, DS the activation entropy and DH the activation enthalpy. For studying the effect of thermodynamic history on secondary relaxations, we produced a glass at external pressure Pf and temperature Tf according to two thermodynamic paths (Fig. 3). In the first, starting from a temperature Ti above Tg, we isothermally pressurized the liquid to the final pressure Pf, and then we cooled it at constant pressure down to Tf (path A). In the second, we isobarically cooled down the system from Ti to Tf, then we isothermaly increased pressure to Pf (path B). The parameters characterizing the different paths for each system are reported in Table 1. The values of Ti are much higher than the glass transition temperature, in a range that the a-relaxation time is smaller than microsecond. The cooling rates at ambient and higher pressures were lower than 1 K/min and the rate of increasing pressure was lower than 10 MPa/min. Each system,

S. Sharifi et al. / Journal of Non-Crystalline Solids 353 (2007) 4313–4317

log(νmax)

a 3

4315

4

b 3 T=293 K

T=263 K

2

2

T=253 K

T=276 K

T=243 K

1 200

T=253 K

400

200

3

400

c

600

d

log(νmax)

7.28 2

7.24 T=260 K T=246

1

T=233 K

0

200

400

7.20

T=238 K 400

Pressure (MPa)

500

Pressure (MPa)

Fig. 2. Logarithmic of the maximum loss peak frequency as a function of pressure at different temperatures (as indicated in the figure) for (a) PPGE, (b) PDE, (c) BMPC and (d) PPG400. Error bars are smaller than symbols size.

Pressure (MPa)

(TfPf) Path A

Glass

Tg(P) Path B

Liquid (Ti , Pi)

Temperature [K] Fig. 3. Schematic representation of the thermodynamic paths used in the experiment to vitrify the systems. In experiments, the starting point (Ti, Pi) is in the liquid and the final point (Tf, Pf) in the glassy state.

Table 1 Parameters of the thermodynamic paths followed during vitrification Path A

PDE PPGE BMPC PPG400

Path B

Ti, Pi

Tf, Pf

Tg(P)

Ti, Pi

Tf, Pf

353 K 0.1 MPa 313 K 0.1 MPa 293 K 0.1 MPa 314 K 0.1 MPa

276 K 500 MPa 253 K 500 MPa 233 K 400 MPa 238 K 500 MPa

353 K 240 MPa 313 K 400 MPa 293 K 290 MPa 251 K 500 MPa

353 K 0.1 MPa 313 K 0.1 MPa 293 K 0.1 MPa 314 K 0.1 MPa

276 K 500 MPa 253 K 500 MPa 233 K 400 MPa 238 K 500 MPa

The values of Tg(P) are approximate and calculated according to the data reported in the cited references, glass transition temperature for path B is reported in Section 2.

with the exception of PPG400, was vitrified by compression along the path (A) and by cooling along the path (B). The values of temperature and pressure at which the systems were vitrified along path A were estimated according to unpublished data of PPG400 and the data reported in Refs. [13,20,22] for the other samples (Table1). The maximum error is around ±5%. Usually the glass transition temperature was determined from relaxation data assuming that the a-relaxation time at Tg is 100 s. In Fig. 4 the loss peaks measured subsequently the two paths are reported for the four systems. The spectra are vertically shifted in order to have the same value of the maximum loss. The used shift factor (SF) is reported in Fig. 4. The absolute values of dielectric loss cannot be easily compared due to the variation with pressure and temperature of the empty capacity of the cell. The various pathways yield different maximum frequencies for the peaks of PPGE and PDE, but not for BMPC and PPG400. In all systems where the secondary relaxation is affected by the thermodynamic history, the maximum frequency in glasses prepared along path A is lower than in glasses prepared along path B. 4. Discussion Density variations affect the secondary relaxation process in the investigated systems. In fact, the relaxation frequency decreases on increasing pressure at fixed temperature, which correspond to an increase of density (Fig. 2). The extent of the density effect on the secondary dynamics depends on the investigated system. If we assume

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S. Sharifi et al. / Journal of Non-Crystalline Solids 353 (2007) 4313–4317

a

PDE T=276 K P=500 MPa SF=1.15

b

ε

,,

PPGE T=253 K P=500 MPa SF=1.1 -2

10

ν max

0

1

10

-2

2

10

ν max

-3

10 3

10

1

4

10

c

BMPC T=233 K P=400 MPa SF=1.09

-1

10

3

2

10

10

ν max 4

10

10

10

d

PPG400 T=238 K P=500 MPa SF=1.09

ε

,,

10

ν max

ν max

ν max -3

10

-1

10

0

10

1

10

2

ν

10

3

3

10

4

10

10

5

6

10

ν

10

Fig. 4. Loss spectra of the secondary relaxation measured after vitrification along path A (triangles) and B (squares) for (a) PPGE, (b) PDE, (c) BMPC and (d) PPG400. The spectra measures after vitrification along path A are vertically shifted by shift factor (SF) to obtain the same value of maxima loss of those measured after vitrification along path B.

Table 2 Activation volume (1 ml/mol = 602.2 nm3), DV, calculated at the temperature Tf, activation energy, DE, activation enthalpy, DH, and activation entropy, DS (see Section 3 for details), calculated at P = 0.1 MPa

PDE PPGE BMPC PPG400

Tf (K)

DV (ml/ mol)

DE (kJ/ mol)

DS (J/mol/ K)

DH (kJ/ mol)

276 253 233 238

20.8 ± 0.9 19.8 ± 0.6 6.5 ± 0.4 3.1 ± 0.7

53.9 ± 0.9 53.0 ± 0.3 40.9 ± 0.2 28.1 ± 0.4

33.4 ± 0.7 37.6 ± 0.4 12.5 ± 0.3 20.9 ± 0.1

52 ± 2 57 ± 1 47.0 ± 0.4 29.5 ± 0.6

vitrification procedure. In order to quantitatively address this hypothesis density measurements should be necessary in connection to the dynamic ones. For example, dilatometric measurements should be performed together with dielectric ones. Also refractive index measurements could be used for monitoring density variation of the sample [25]. However, a rough quantitative analysis can be performed basing only on dynamics. The relative variation of the frequency of the maximum loss peak, Dmmax/mmax, as measured after paths A and B correlates with the activation volume in our systems (Fig. 5): the bigger is the activation volume, or in first approximation the larger is the

Activation entropy ΔS (J/mol/K) 5 1.0

Δνmax /νmax

similar values of the pressure dependence of the density, q, then the dependence on pressure of the logarithmic of mmax is related to that on density d log mmax/dP = (d log mmax/ dq)(dq/dP). Accordingly, secondary relaxation in PDE and PPGE are more sensitive to density (larger values for DV) than those in BMPC and PPG400 (Table 2). Systems vitrified along path A are compressed in the liquid state and then in the glassy state, whereas systems vitrified along the path B are compressed only in the glassy state (Fig. 3). We can expect that glasses prepared along path A have larger density than those prepared along path B. In fact, compressing is usually more effective in increasing the density than cooling and the compressibility of the liquid is larger than that of the glass. This hypothesis is consistent with the observed pressure dependence of the secondary relaxation (Fig. 3). In fact, in glassy PPGE and PDE with higher density (prepared along path A) the secondary relaxation is slower than in glasses with lower density (path B). We can suggest that density variation are at the basis of the observed dependence of relaxation frequency on the

10

15

20

25

30

35

40

35

40

PPG400 (T=238 K, P=500 MPa) BMPC (T=233 K, P=400 MPa) PPGE (T=253 K, P=500 MPa) PDE (T=276 K, P=500 MPa)

0.5

0.0 5

10

15

20

25

30

Activation volume ΔV (ml/mol) Fig. 5. Normalized difference between frequencies of maximum of secondary peaks in glasses prepared along paths A and B: closed symbols are plotted as a function of DV (lower x-axis), open symbols as a function of DS (upper x-axis). Lines are guides for eyes.

S. Sharifi et al. / Journal of Non-Crystalline Solids 353 (2007) 4313–4317

density dependence of the secondary process, the larger is the effect of thermodynamic history on the relaxation frequency of secondary processes. Even if the density plays a role in such scenario, we cannot exclude other contributions, as that of the complexity (intramolecular cooperativity) of the process. The degree of cooperativity is related to the activation entropy of the process, DS, which can be determined by fitting the temperature dependence of m0 according to the function reported in Section 3 [26]. The analysis of isobaric literature data (PPG400 [23], BMPC [22], PDE [18], PPGE [20]) evidenced that DS is larger for PDE and PPGE (Table 2). Roughly the values of DS is larger when DV is larger, then the trend observed between Dmmax/mmax and DV is valid also between Dmmax/ mmax and DS (Fig. 5). However, in details the relative magnitude of DS is exchanged respect to DV in the pairs PDE– PPGE and BMPC–PPG400. Interestingly, the increase of the degree of intramolecular cooperativity is accompanied by an increase of DS. The secondary process of PPGE, which is classified as JG process according to its dynamic properties [20], has smaller DV but larger DS values than that of PDE, which is not a JG process. Moreover, we can see that the increase of Dmmax/mmax as a function of DV is larger for more cooperative secondary process with respect to the less cooperative one. Finally, we note that the activation enthalpy and the activation energy (estimated by an Arrhenius fit of m0(T)) have similar trends of the formers parameters, but the values for the different materials are closer each other. An interpretation of the effect of thermodynamic history on relaxation properties was proposed in term of nanometric heterogeneity of the glass structure [5,6]. In this paper, we speculate that this interpretation can account for the presented results. Accordingly, the smaller relaxation frequency of the secondary relaxation in PDE and PPGE after vitrification along path A could be explained by a more homogeneous structure with respect to the glass obtained along path B [6]. This interpretation could also explain the lower dielectric strength observed after path A [6]. In order to verify such hypothesis a characterization of the structure of the glass is needed [26], which however is not available at this moment. Raman spectra or neutron scattering measurements after the different thermodynamic paths could be used to this scope. 5. Conclusions We investigated the effect that the thermodynamic path (pressure and temperature variations) followed in the vitrification procedure has on the secondary relaxation process, when measured in the glassy state at the same conditions of temperature and pressure. Secondary processes with larger activation volume are more dependent on the thermodynamic history. We argued an important role of density in

4317

determining such behavior in glassy systems, but volume measurements are necessary for more quantitative test. Further measurements are needed to investigate in greater detail if such dependence is influenced also by the degree of intramolecular cooperativity of the secondary process and by the spatial heterogeneity of the glass structure. Acknowledgments Financial support by MIUR-FIRB 2003 D.D.2186 Grant RBNE03R78E and by PRIN project ‘Aging, fluctuation and response in out-of-equilibrium glassy systems’ are kindly acknowledged. Financial support of the Committee for Scientific Research, Poland KBN, Grant No. 1P03B 075 28 is also gratefully acknowledged. References [1] C.A. Angell, Science 267 (1995) 1924. [2] L.C.E. Struik, Physical Aging in Amorphous Polymers and Other Materials, Elsevier, Amsterdam, 1978. [3] D. Prevosto, S. Capaccioli, M. Lucchesi, P.A. Rolla, K.L. Ngai, J. Chem. Phys. 120 (2004) 4808. [4] G.P. Johari, J. Chem. Phys. 77 (1982) 4619. [5] S. Etienne, L. David, E. Duval, A. Mermet, A. Wypych, G. Simeoni, Solid State Phen. 115 (2006) 99. [6] A. Wypych, E. Duval, G. Boiteux, J. Ulanski, L. David, A. Mermet, Polymer 46 (2005) 12523. [7] H.W. Bree, J. Heijboer, J. Polym. Sci. Polym. Ed. 12 (1974) 1857. [8] A.J. Kovacs, R.A. Stratton, J.D. Ferry, J. Phys. Chem. 67 (1963) 152. [9] J.E. McKinney, M. Goldstein, J. Res. Nat. Bur. Stand., Section A 78A (1974) 331. [10] N.B. Olsen, T. Christensen, J.C. Dyre, Phys. Rev. E 62 (2000) 4435. [11] A. Reiser, G. Kasper, S. Hunklinger, Phys. Rev. Lett. 92 (2004) 125701. [12] M. Paluch, S. Pawlus, S. Hensel-Bielowka, K. Kaminski, T. Psurek, S.J. Rzoska, J. Ziolo, C.M. Roland, Phys. Rev. B 72 (2005) 224205. [13] D. Prevosto, S. Capaccioli, M. Lucchesi, P.A. Rolla, M. Paluch, S. Pawlus, Phys. Rev. B 73 (2006) 104205. [14] N.G. McCrum, B.E. Read, G. Williams, Anelastic and Dielectric Effects in Polymeric Solids, Wiley, New York, 1967. [15] G.P. Johari, M. Goldstein, J. Chem. Phys. 53 (1970) 2372. [16] K.L. Ngai, J. Phys: Condens. Matter 15 (2003) S1107. [17] K.L. Ngai, M. Paluch, J. Chem. Phys. 120 (2004) 85. [18] S. Kahle, J. Gapinski, G. Hinze, A. Patkowski, G. Meier, J. Chem. Phys. 122 (2005) 074506. [19] S. Hensel-Bielowka, M. Paluch, Phys. Rev. Lett. 89 (2002) 025704. [20] D. Prevosto, S. Capaccioli, S. Sharifi, K. Kessairi, M. Lucchesi, J. Non-Cryst. Solids. (2007), in press. [21] S. Corezzi, M. Beiner, H. Huth, K. Schro¨ter, S. Capaccioli, R. Casalini, D. Fioretto, E. Donth, J. Chem. Phys. 117 (2002) 2435. [22] S. Hensel-Bielowka, J. Ziolo, M. Paluch, C.M. Roland, J. Chem. Phys. 117 (2002) 2317. [23] K. Grzybowska, A. Grzybowski, J. Ziolo, M. Paluch, S. Capaccioli, J. Chem. Phys. 125 (2006) 044904. [24] S. Capaccioli, R. Casalini, M. Lucchesi, G. Lovicu, D. Prevosto, D. Pisignano, G. Romano, P.A. Rolla, J. Non-Cryst. Solids. 307–310 (2002) 238. [25] C.G. Robertson, G.L. Wilkes, Polymer 39 (1998) 2129. [26] Howard W. Starkweather Jr., Macromolecules 23 (1990) 328.