J. Phys. Chem. B 1999, 103, 4071-4077
Equilibrium and Non-Equilibrium Type β-Relaxations:
D-Sorbitol
4071
versus o-Terphenyl
Hermann Wagner and Ranko Richert* Max-Planck-Institut fu¨r Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany ReceiVed: September 29, 1998; In Final Form: January 11, 1999
A previous observation, which indicated that the β-relaxation intensity of o-terphenyl is sensitive to the thermal history, is substantiated by dielectric relaxation experiments. Unlike the β-processes of other materials, only the quenched glassy state of o-terphenyl displays this secondary relaxation feature. The β-intensity is observed to decay gradually upon annealing and disappears altogether in the equilibrium liquid state at T > Tg. We compare the case of o-terphenyl with the concomitant signatures of D-sorbitol, which represents the more typical case of a glass-former which exhibits the slow β-process also in the liquid state including the R-βmerging scenario. We also present data of this R-β-merging for D-sorbitol confined to pores of 5 nm diameter, indicating that no longer-ranged correlations are involved in the secondary process.
Introduction The dielectric signature of structural relaxation in most glassforming liquids is a broad and asymmetric loss profile ′′(ω) if assessed in terms of the frequency domain dielectric function *(ω).1 Especially in the supercooled regime, the temperature dependence of the average relaxation time 〈τ〉 regarding this primary or R-relaxation is characterized by a more or less pronounced deviation from an Arrhenius type behavior with the tendency of 〈τ〉(T) to diverge according to the Vogel-FulcherTammann (VFT) equation,
log10(τ/s) ) A +
B T - To
(1)
at To . 0.1,2 At the glass-transition temperature Tg the relaxation time exceeds the time window set by the experiment, such that the structure is no longer capable of attaining the equilibrium condition in the glassy state at T < Tg. Although the longerranged structural relaxation is frozen for T < Tg, many disordered materials exhibit a secondary or slow β-relaxation.3-5 These processes of lower intensity differ phenomenologically from the R-process by their very broad but symmetric loss profile and by an Arrhenius such as temperature dependence.3-6 The important aspect that the occurrence of a β-relaxation does not require intramolecular degrees of freedom has been advanced by Johari using o-terphenyl as one of the many examples.3 Viewed on a relaxation map, -log(τ/s) versus 1/T, the trace of the β-process tends to merge into that of the R-process at a temperature denoted Tβ, at which the characteristic time scale is near 10-6 s.2,6 Above Tβ, only a single relaxation is preserved, which is reminescent of the R-process below Tβ. It has also been observed that Tβ coincides with the temperature TB, at which the VFT parameters of the primary relaxation change considerably.6 Simultaneously, at TB )Tβ the molecular dynamics begin to depart from the temperature dependence expected on the basis of configurational entropy Sc(T) via the theory of Adam and Gibbs.7 Regarding this merging regime of the two processes, evidence is being * Corresponding author. Fax: +49/6131/379100. E-mail: richert@ mpip-mainz.mpg.de.
accumulated that the secondary relaxations take over the entire intensity, while the R-process fades as the temperature is raised.4,5 Other observations in this field include the universal value of the activation energy EA ≈ 24 RTg,4 the apparent collapse of the activation energy EA ≈ 0 near Tg for D-sorbitol,8 and the counterintuitive trend of the permittivity ′ in the β-regime of o-terphenyl.9 Although a consistent picture capable of rationalzing all these diverse findings is still lacking, the β-relaxation is meanwhile recognized as an important aspect of the entire structural relaxation. Two fundamentally different pictures as regards the nature of the β-relaxation are being considered. In the first, each molecule contributes to the secondary process by a small and local librational motion. Second, there exist islands within the material whose relaxational character differs from the bulk by retaining motional degrees of freedom even well below Tg, while larger-scale relaxations are entirely frozen in the remaining material.10 A simple experimental discrimination between these two scenarios remains impossible for techniques which yield ensemble averaged or macroscopic information only. In a recent paper, we have demonstrated the spatially homogeneous occurrence of the β-relaxation in D-sorbitol using the technique of solvation dynamics for locally probing the dielectric properties.11 In the present work, we reinvestigate the dielectric relaxation of o-terphenyl with emphasis on the amplitude of the β-relaxation near and below Tg. Especially, the dependence of the β-peak on the preparation conditions of the glassy state is assessed experimentally by comparing the quenched glass with the effects of annealing at temperatures T < Tg. We thereby substantiate a previous 9,12 observation, where the β-process disappeared after annealing at T ) 234 K for 24 h. Consistent with this annealing effect, the present data indicate that no β-relaxation is observed in the equilibrium liquid state of o-terphenyl, which discriminates this case from the more typical glass-formers, where the β-intensity continues to increase for temperatures T > Tg. The data obtained for o-terphenyl is confronted with the case of D-sorbitol,8,13,14 which constitutes a representative example for those materials for which the β-process gains amplitude in the liquid state and merges into the R-relaxation trace. This R-β-merging scenario of D-sorbitol
10.1021/jp9838947 CCC: $18.00 © 1999 American Chemical Society Published on Web 03/19/1999
4072 J. Phys. Chem. B, Vol. 103, No. 20, 1999
Wagner and Richert
Figure 1. Drawing of the vacuum-sealed sample capacitor cell used for dielectric measurements on liquid samples. Housing and counter electrode are gold-plated invar steel parts; the insulating window is sapphire. The O-rings are required only for volatile liquids. The capacitor diameter is 18 mm, the electrode separation is ≈ 66 µm.
is shown to occur also if the material is geometrically confined to length scales of 5 nm using porous glasses, indicating that longer-ranged correlations are not involved in this regime of complex relaxation patterns.
Figure 2. Dielectric loss of o-terphenyl plotted as ′′(ω) versus log (f/Hz) for various temperatures. The lowest curve is recorded at T ) 178 K; the other curves refer to the temperatures 242-270 K in steps of 4 K, in the order of increasing peak frequency. The data are shown as measured at a density of 48 points per decade.
Experimental Technique The material o-terphenyl has been purified by recrystallization. The compound D-sorbitol (D-sorbit, D-glucitol, C6H14O6) has been purchased from Sigma Chemical Company (98%+) and is used as received. The material had to be heated to well above the melting temperature for a longer period of time in order to turn the sample entirely transparent. Otherwise, the sample remains opaque and the relaxation strength is reduced to approximately one-half of the value obtained for the entirely clear liquid material. Frequency-dependent dielectric permittivity and loss in terms of *(ω) ) ′(ω) - i′′(ω) have been measured using the frequency response analyzer Solartron SI-1260 equipped with a Mestec DM-1360 transimpedance amplifier. For D-sorbitol the frequencies ranged from f ) 10-2 Hz to f ) 107 Hz at 12 points per decade, while o-terphenyl was measured from f ) 1 Hz to f ) 106 Hz at a higher density of 48 points per decade. The measurements are evaluated relative to the signals of the empty capacitors, so that absolute values of the permittivity are obtained even without the exact knowledge of the geometrical capacity. The annealing effects of o-terphenyl have been studied using the 1 kHz precision bridge Andeen-Hagerling AH-2500. The sample capacitor consists of parallel plates of 18 mm L having a uniform separation of ≈ 66 µm. This cell is vacuumtight, its geometry is temperature-insensitive, and the electrode separation is defined without the need of spacer material between the electrodes. Figure 1 shows this capacitor, which turned out to be very useful for high-definition dielectric measurements on liquid and glassy samples. The shape of the upper electrode reduces electric stray field effects and allows for a sufficient material reservoir outside the electrode gap. The cell was temperature controlled by a Novocontrol Quatro nitrogen-gas cryostat to a relative accuracy of approximately (0.05 K. For the measurements concerning the geometrical confinement of D-sorbitol, we have employed a GelSil porous glass (GelTech) of 5 nm nominal pore diameter. According to a BET analysis supplied by GelTech, the sample is characterized by an actual pore diameter of 4.6 nm, a pore volume fraction of 0.68, and a surface area of 594 m2/g. A disk of this porous silica glass with 10 mm diameter and 300 µm thickness has been washed extensively in H2O2 and then dried at 200 °C in a vacuum in order to remove surface contaminations. Directly following this preparation, molten D-sorbitol is imbibed into the pores, and the excess amount of liquid is removed. The sample
Figure 3. Dielectric loss ′′(ω) of o-terphenyl scaled logarithmically versus log (f/Hz) for various temperatures. The curves refer to the temperatures T ) 178, 202, 226, 242, 246, 250, 254, 258, 262, and 266 K, in the order of increasing peak frequency. The corresponding steps are 24 K in the β-regime and 4 K in the R-regime. The lines obtained by sliding averages are meant as guides for clarity in the range ′′(ω) < 10-3.
is placed between spring-loaded brass electrodes of 10 mm diameter. The impedance measurements have been conducted as in the case of the bulk samples. Results The dielectric permittivity ′ and loss ′′ of o-terphenyl has been measured for a series of temperatures 170 K e T e 270 K. Figure 2 displays a selection of loss curves ′′(ω), showing the R-relaxation regime and one lower-temperature curve which displays the small and broad β-process. The temperature dependent loss at low amplitudes is shown in Figure 3 on a logarithmic ordinate scale, including only a selection of temperatures for clarity. These data have been measured in the sequence of increasing temperature after quenching the sample from 340 to 130 K. From these curves the frequency positions fmax of the loss maxima are derived and translated to peak relaxation times τmax using τmax ) (ωmax)-1 ) (2πfmax)-1. The resulting values for τmax and for the relaxation strength ∆ are compiled graphically in Figure 4. A VFT fit according to eq 1 as regards τmax(T) for the R-process of o-terphenyl yields A ) -22.1, B ) 1820 K, and To ) 168 K. For the β-relaxation we find A ) -12.35, B ) 1880 K, and To ) 0. The effects of annealing the initially quenched o-terphenyl sample have been monitored by recording the loss ′′(t) at a
Equilibrium and Non-Equilibrium Type β-Relaxations
Figure 4. Characteristic R- and β-relaxation parameters, -log(τmax/s) and ∆ versus 1/T, for o-terphenyl derived from the data of Figures 2 and 3. The lines in the activation plot are fits according to eq 1, with A ) -22.1, B ) 1820 K, and To ) 168 K for the R-process and A ) -12.35, B ) 1880 K, and To ) 0 for the β-process. The vertical dotted lines mark Tg ) 246 K.
Figure 5. Isothermal aging experiment for the initially quenched o-terphenyl glass at T ) 238 K. The aging effect is monitored in terms of the time-dependent dielectric loss ′′(t) measured at a fixed frquency of f ) 1 kHz. The inset shows ′′(T) for f ) 1 kHz for quenched o-terphenyl (dashed line) and after annealing at T ) 234 K for 24 h (solid line), which has erased the β-peak around T ≈ 205 K.9
fixed frequency of f ) 1 kHz as a function of waiting time. Figure 5 shows a representative annealing curve obtained isothermally at T ) 238 K. Altering the annealing temperature is found to affect the initial and final amplitude of ′′(t), but no systematic change of the time scale required to approach equilibrium could be detected. After annealing the glassy sample at T ) 234 K for 50 h, the β-peaks shown in Figures 2 and 3 are no longer resolved. A further observation after this efficient annealing is that the high-frequency wing of the R-peak becomes steeper, i.e., in a power law representation, ′′ ∝ ω-κ, the value of κ has increased by ≈10%. The dielectric properties of D-sorbitol in the range 200 K e T e 300 K are shown in Figure 6, which represents part of a larger data set published recently.11 For this polar material the absolute loss signals exceed those observed for o-terphenyl by orders of magnitude. Also, the relative contribution of the β-peak is unusually large for D-sorbitol. Because the R- and β-peaks are not well separated at higher temperatures, the parameters for the peak frequencies and relaxation strengths are obtained by fitting the data using the sum of two Havriliak-Negami 15
J. Phys. Chem. B, Vol. 103, No. 20, 1999 4073
Figure 6. Dielectric loss curves ′′(ω) of D-sorbitol as a function of temperature in the range 200 K e T e 300 K plotted in steps of 4 K.11 The low-frequency wings due to dc-conductivity are drawn as dotted lines.
Figure 7. Characteristic R- and β-relaxation parameters, -log (τmax/s) and ∆ versus 1/T, for D-sorbitol derived from the data of Figure 6. The open circles in the activation plot refer to the β-process of D-sorbitol confined to 5-nm pores. The lines in the activation plot are fits according to eq 1, with A ) -11.51, B ) 384 K, and To ) 239 K for the R-process, A ) -16.76, B ) 3122 K, and To ) 0 for the β-process, and A ) -14.87, B ) 2520 K, and To ) 0 for the confined β-process. The open diamonds indicate the sum ∆(T) ) ∆R + ∆β. The vertical dotted lines mark Tg ) 268 K.
(HN) type functions and including a term which accounts for dc-conductivity if required,
*(ω) ) ∞ +
∆R [1 + (iωτ1)R1]γ1
+
∆β
σdc i oω [1 + (iωτ2)R2]γ2 (2)
From such fits we derive the peak positions fmax for the two relaxations. The resulting values of ∆ and τmax as a function of temperature are depicted in Figure 7. It should be emphasized that eq 2 is meant to serve as a data reduction tool for extracting the peak frequencies and relaxation strengths, devoid of any physical implementations. For the VFT parameters as regards τmax(T) for the R-process of D-sorbitol, we find A ) -11.51, B ) 384 K, and To ) 239 K. For the β-relaxation at temperatures
4074 J. Phys. Chem. B, Vol. 103, No. 20, 1999
Wagner and Richert terms of F1/2 are similar, F1/2 )0.74 for o-terphenyl and F1/2 ) 0.70 for D-sorbitol, using the definition2
Tg F1/2 ) 2 - 1, τ(T1/2) ) 10-6 s, τ(Tg) ) 10+2 s T1/2
Figure 8. Dielectric loss curves ′′(ω) of D-sorbitol confined to porous glass with 5-nm nominal pore diameter. The curves are parametric in temperature in the range 200 K e T e 300 K plotted in steps of 4 K. The low-frequency wings due to dc-conductivity are drawn as dotted lines. The R-β-merging scenario of Figure 6 is qualitatively preserved under this geometrical confinement.
T < Tg, an Arrhenius law is observed, i.e., A ) -16.76, B ) 3122 K, and To ) 0, according to eq 1. The dielectric loss data of D-sorbitol confined to the pores of 5 nm diameter are shown in Figure 8 with the curves referring to c′′(ω) of the D-sorbitol/silica glass composite sample. According to the Maxwell-Wagner-Sillars theory, the composite dielectric function c*(ω) depends in a nonlinear fashion on the dielectric properties of the filler material, f*(ω), and of the silica glass matrix having m*(ω) ≈ 3,
/c (ω) ) (n + φ - n‚φ)‚/f (ω) + (1 - n - φ + n‚φ)‚/m(ω)
/m(ω)‚
(n - n‚φ)‚/f (ω) + (1 - n + n‚φ)‚/m(ω) (3)
where φ is the filler volume fraction and n is the depolarization factor with n ) 1/3 for spherical particles.16 For a polar filler such as D-sorbitol in a dielectrically inert matrix, a quantitative analysis requires determining f*(ω) on the basis of c*(ω) and m*(ω).17 Being interested mainly in the confinement effects associated with the β-relaxation, we can refrain from such a calculation because f*(ω) ≈ m*(ω) in the glassy state of D-sorbitol. In this special case, the Maxwell-Wagner equation reduces practically to a linear rescaling which corrects for the volume fraction of the filler. An analysis of the curves of Figure 8 along the lines of eq 2 reveals that the shape of the β-relaxation loss profiles is identical to the case of bulk D-sorbitol in the temperature regime T < Tg. The temperature dependence of the β-peak relaxation time τmax(T) is included in Figure 7 and again follows an Arrhenius law, A ) -14.87, B ) 2520 K, and To ) 0 in eq 1. Both shape and peak relaxation time of the β-relaxation in the glassy state of confined D-sorbitol are not affected by Maxwell-Wagner corrections. Discussion We start the discussion by comparing the relaxational phenomenology of the two present glass-forming materials. Using the kinetic criterion τg ) τ(Tg) ) 100 s, we arrive at glass transition temperatures Tg ) 246 K for o-terphenyl and Tg ) 268 K for D-sorbitol. The fragilities of these systems in
(4)
Common to both glass-formers is that the temperature dependence of the peak relaxation times τmax associated with the structural or R-relaxation is VFT-like, the loss profiles are asymmetrically broadened, and for T > Tg the total relaxation strength ∆ decreases according to the Boltzmann term of the ensemble averaged dipole orientation 〈cos θ〉 in the equilibrium state. In the glassy state well below Tg, both β-relaxations are subject to an Arrhenius type temperature dependence, their loss curves are symmetrically broadened, and ∆β displays no significant variation with temperature. The extrapolations of the Arrhenius curves, τmax(T), for the β-processes tend to intercept the trace of the R-process at a temperature Tβ, at which the structural relaxation times are near τmax(Tβ) ) 10-7 s, with Tβ ≈ 290 K for o-terphenyl and Tβ ≈ 335 K for D-sorbitol. Further examples which meet the above phenomenology can be found: 1,4-polybutadiene,9,18 poly(alkyl methacrylates),5 1-propanol,6 and toluene,4 to name a few. It is presumably the apparent universality of these β-relaxation scenarios which guides one to seek a common interpretation, irrespective of the specific glass-forming material. Within the literature it is common pratice to refer to the Johari-Goldstein (JG) type β-relaxation for all the above examples, mainly with the idea to discriminate these inherent secondary relaxations from side-group motions or similar effects of intramolecular degrees of freedom. Various models are being discussed for rationalizing the β-process phenomenology.10,19,20 One of them, the picture of “islands of mobility”, has been advanced by Johari.10 It assumes that the secondary relaxation is spatially confined to islands within the structurally arrested bulk material. The molecular mobility, and thus the dielectric activity, in such islands or defect states are high, whereas the volume fraction taken by these regions is relatively low. An alternative view is to assume that each relaxing unit involved in the primary relaxation also contributes to the secondary relaxation by subtle and more localized motions. In this latter picture, the occurrence of the β-relaxation is spatially homogeneous, while “islands of mobility” refer to spatial heterogeneity. In the present context, spatial homogeneity refers to the absence of nanoscopic or larger-length scales as regards the amplitude of the process rather than its relaxation time. In a recent paper,11 we have investigated the problem of spatial heterogeneity as regards the β-process of D-sorbitol using the solvation dynamics technique where the liquid of interest is doped with a phosphorescent dye at a low concentration. This method probes the local dielectric properties in the vicinity of chromophores by means of the time-dependent Stokes shifts. We observed that the local response sensitized by the chromophores was identical to the ensemble averaged result of a standard dielectric experiment. This led to the conclusion that the occurrence of the β-relaxation in D-sorbitol is spatially homogeneous in the above sense, and thereby incompatible with the picture of “islands of mobility” of considerable spatial extent.11 o-Terphenyl. The fragile glass-former o-terphenyl is one of many materials investigated by Johari in his original work on the secondary relaxations. Already there it has been observed that the thermal history affects the amplitude of the β-process, indicated by alteration in the β-intensity of order 10%.3 In a recent study of the sub-Tg dynamics of several organic glass-
Equilibrium and Non-Equilibrium Type β-Relaxations formers of low molecular weight, we have measured the dielectric loss ′′(T) at f ) 1 kHz for temperatures between 25 K and Tg.12 Those materials for which the quenched and annealed glassy states have been compared were salol, oterphenyl, and N-methyl--caprolactam. The most pronounced case was o-terphenyl, where we observed that the clearly visible β-process amplitude disappears after annealing the sample at T ) 234 K for 24 h. The cases of salol and N-methyl-caprolactam were subject to the analogous features, but with only slight indications of what might be a secondary process in the quenched glass. The high resolution required for visualizing these annealing effects confined these experiments to a fixed frequency of f ) 1 kHz, where a resolution of < 10-7 in tan(δ) is achieved. At that time, the following questions have remained unanswered: Does annealing shift the relaxation frequency away from f )1 kHz or does it depress the intensity of the β-process? What are the time scales of annealing effects? Does the sensitivity to the thermal history in the glassy state imply that the β-relaxation must be absent in the equilibrium liquid state for T > Tg? Our attempt to answer the above questions begins with a qualitative inspection of literature data on o-terphenyl reported by Johari and Goldstein 3 and by Wu and Nagel.21 In both cases the traces on the relaxation map, log(fmax/Hz) versus 1/T, end at Tg although the R- and β-peaks are still separated by as much as 4.5 decades in frequency. Recalling that the intensity ∆β tends to increase with temperature near Tg for many materials, one should expect that the β-peak is detectable if o-terphenyl parallels the behavior of other materials as regards the secondary relaxation. Within the limits of accuracy, the present τmax(T) results depicted in Figure 4 are compatible with those cited above. However, we observe additionally that the relaxation strength vanishes as we approach Tg. This feature is indicated by the ∆β(T) curve in Figure 4, obtained upon stepwise heating the quenched o-terphenyl sample at a rate of approximately 4 K/h. The onset temperature of this fading is near T ) 230 K. The result ∆β(T) discussed above cannot be considered timeinvariant. This is shown in Figure 5 where the loss ′′ at f ) 1 kHz and T ) 238 K ) Tg - 8 K is seen to depend on the waiting time on the scale of hours. The inset of Figure 5 indicates that only small changes in the absolute value of ′′(t) at f ) 1 kHz and T ) 238 K may be expected even if ∆β decays to zero. Repeating this annealing experiment ′′(t) for other temperatures, T ) 234 K and T ) 242 K, revealed no systematic trend of the time scale associated with ′′(t). However, the relaxation strength ∆β observed at sufficiently low temperatures, where annealing no longer occurs, does depend on the rate ∂T/∂t of the quench process. This signals that the fading of ∆β must become considerably faster at elevated temperatures, relative to the 5 h time scale observed at T ) 238 K. Most probably, it is precisely this equilibration time which leads to the decreasing ∆β(T) curve, because the acquisition time for a single temperature of the data set shown in Figure 3 was around 1 h. After efficient annealing (50 h at T ) 234 K), no indication of the β-process was observable within the present experimental limits, i.e., for temperatures T g 170 K and for frequencies f ) 1 Hz to f ) 106 Hz. From the above observations we conclude that the slow secondary relaxation of o-terphenyl is associated with excess molecular mobility featured only by the glassy state if prepared by quenching the liquid. We shall denote this case the G-type β-process, because it appears only in the glassy state, as opposed to the L-type as in D-sorbitol, which is also present in the liquid state. For the G-type β-relaxation, the “islands of mobility”
J. Phys. Chem. B, Vol. 103, No. 20, 1999 4075 picture might be appropriate, if one assumes that these defect states are not in thermodynamic equilibrium with the remaining liquid such that they disappear upon annealing. The lifetime of such defect states is not necessarily identical with the time scale of the primary structural relaxation. D-Sorbitol. Already a qualitative inspection of the β-relaxation scenarios, o-terphenyl in Figure 3 versus D-sorbitol in Figure 6, shows the different behavior above Tg. In the supercooled liquid state of D-sorbitol, the β-intensity increases rapidly with temperature on the account of the R-process. Thereby, D-sorbitol parallels the behavior of toluene 4 and of the series of poly(alkyl methacrylates).5 Thus far, no significant temporal decrease of the β-intensity has been observed for these L-type processes. The only thermal history effect observed by Olsen 8 concerns the peak position of the secondary loss profile, which shifts slightly near Tg. As is true for the extrapolated trace of τmax(T) for the β-relaxation of o-terphenyl, the R-β-merging occurs near structural relaxation times of order 10-6 s. For the β-relaxation of D-sorbitol, the trace of τmax(T) begins to deviate from the Arrhenius behavior in which the two relaxation peaks are no longer separated by a pronounced minimum. In this regime, the characteristic parameters of the two processes depend strongly on the model on which the fit functions are based. The independent sum of two HN peaks should be appropriate only for spatially distinct origins of the R- and β-relaxation. According to our recent solvation dynamics study of the secondary relaxation in D-sorbitol,11 we assume that the L-type β-contributions are spatially homogeneous, i.e., that every relaxing unit involved in the R-process contributes also to the β-process. In such a model, the primary structural relaxation affects the local motions responsible for the β-process unless they are well separated on the time scale, such that the local motion is confined to a practically static environment. A more reasonable approach to the total relaxation which accounts for these mutual “interactions” has been advanced by Williams.22 The prediction in terms of the normalized time domain correlation functions φ(t) reads
φ(t) ) a‚φR(t) + (1 - a)‚φR(t)‚φβ(t)
(5)
where φ(t) is the total correlation decay and φR(t) and φβ(t) are the contributions associated with the primary and secondary processes, respectively. For 1,4-polybutadiene Arbe et al.18 have demonstrated that eq 5 leads to more physical results regarding τR(T) and τβ(T) in the regime of merging than does eq 3. The majority of pure materials for which the β-relaxation has been investigated belongs to this L-type, e.g., D-sorbitol, toluene, polyalkyl methacrylates, 1-propanol, and 1,4-polybutadiene. Opposed to o-terphenyl, various observations point toward the L-type β-relaxation being a spatially homogeneous feature intrinsic in the motion of each relaxing unit. The assumption of the local character of the secondary relaxation implies that no longer-range correlations are involved in the β-process and is consistent with our result of the spatially homogeneous occurrence. With respect to the primary structural relaxation, such correlations are made responsible for the dimension of the cooperatively rearranging regions introduced by Adam and Gibbs7 and for the length scale of cooperativity deduced from experiments. This issue has been assessed experimentally employing nanoporous glasses.23,24 The basic idea behind such studies is that geometrical confinement induces a cutoff in the longest-possible-length scale relevant to the relaxation process. The pronounced β-intensity in D-sorbitol makes possible an analogous assessment, applied for the first
4076 J. Phys. Chem. B, Vol. 103, No. 20, 1999 time to a secondary process. The comparison between the loss curves for the bulk material, Figure 6, and those for the same glass-former but confined to pores of 5 nm diameter, Figure 8, clearly shows that the merging scenario remains qualitatively the same. We consider this to be experimental confirmation of the expectation that no spatial correlations in excess of several nanometers are involved in this regime of a complex bimodal decay of orientational correlation. For R-processes it is the rule that the loss profile becomes wider and more symmetric upon geometrical confinement to scales below ≈ 10 nm.25-27 In contrast, the shape of the β-process of D-sorbitol in the glassy state remains unaffected by the present 5 nm confinement, in accord with the assumption of a process that is spatially more localized than the R-response. As seen in Figure 7, the activation barrier of the β-process is altered by introducing a geometrical confinement. The activation parameter B of eq 1 (with To) 0) changes from 3122 K in the bulk to 2520 K in the confined case. Since Tg shifts by only a few K due to the 5 nm pores, this lowering of the activation barrier can also be expressed by a change from B ) 11.6 Tg to B ) 9.4 Tg upon confinement. Without a further detailed study of these confinement effects as a function of pore size, the origin of this change in activation energy remains unclear. One possibility is a different temperature-dependent density F(T) in nanopores relative to the bulk situation. Summary and Conclusions We have reinvestigated the dielectric signatures of the primary or R-relaxation and of the secondary or slow β-relaxation for the materials o-terphenyl and D-sorbitol, thereby focusing on systems where the β-process does not involve intramolecular degrees of freedom. Opposed to the well-known R-β-merging scenario in the supercooled liquid state of many glass-forming materials, we find evidence that the β-process of o-terphenyl is associated with molecular motion which is featured only in the quenched glassy state. This notion is derived from the observations that annealing at T < Tg is capable of efficiently suppressing the β-intensity and that the relaxation strength ∆β tends to zero upon approaching Tg from lower temperatures. The annealing effect appears to evolve on time scales longer than the average structural relaxation time. For discriminating between these differing β-relaxation scenarios, we refer to the o-terphenyl case as G-type, because it exists only in the glassy state, and to the other cases such as D-sorbitol as L-type, because here the β-process is most pronounced in the liquid state. Although o-terphenyl is often quoted as a typical example for a β-relaxation, it rather appears as an exception as regards the secondary relaxation in the liquid state. The question remains why the G- and L-type secondary relaxations are phenomenologically very similar in several ways at temperatures below Tg, although they differ strongly in the regime T > Tg. As noted above, the β-features also common to o-terphenyl are (i) the Arrhenius behavior 3-6 of the peak β-relaxation time τmax(T); (ii) the scaling of the activation parameter B ∝ Tg;4 and (iii) the extrapolated interception with the R-trace at the demarcation temperature Tβ.6 We emphasize again that for many glass-formers it has been found that the temperature dependence τmax(T) of the primary relaxation changes qualitatively at TB ) Tβ and that τmax(T) begins to depart from the configurational entropy Sc(T) at T ) TB.2 Also, TB ) Tβ coincides with other characteristic scaling temperatures.2 Although the R-β-merging scenario near T ) Tβ is still to be clarified, the above notions underline the importance of the time scale τmax(Tβ), which is around 10-6 s for most materials.
Wagner and Richert Current models which recognize the relevance of these observations are the “top of the landscape” view supported by Angell 2 and the relation of the β-process to the primitive relaxation time of the primary relaxation advanced by Ngai.19 It is generally accepted, and supported by the present findings regarding the β-relaxation in nanoporous confinement, that secondary relaxations are local processes. A consequence is that their lack of cooperative aspects of motion gives rise to the Arrhenius behavior instead of the VFT law observed for the R-process. In the glassy state of matter, such local modes are confined to the cage structure of neighboring molecules, which is static on the time scale of the β-relaxation. Without going into details, we note that an increasing confinement of supercooled liquids leads to more symmetrically broadened loss peaks of the R-relaxation 25-27 and also results in the tendency of τR(T) to approach the Arrhenius behavior.28,29 In other words, a severely confined R-relaxation becomes reminiscent of the β-process phenomenology. With the aim of improving the understanding of slow β-relaxations, we have presented some partly provocative ideas rather than stressing the quantitative aspects. The classification into G-type and L-type β-processes suggests to allow for different physical mechanisms being responsible for what appears as a universal behavior of localized molecular modes. For these small-scale motions associated with the β-relaxation, the molecular structure and chemistry might be more important than realized thus far. In view of the instability of the G-type β-relaxation of o-terphenyl, it seems possible that materials for which no β-relaxation has yet been observed would simply have to be quenched faster in order to give rise to a β-peak. Such experiments and a more systematic study of the cooling rate dependence might shed new light on this active field of research. Acknowledgment. We are grateful to C. A. Angell and K. L. Ngai for stimulating discussions. We thank F. Kremer for slicing the porous glasses and for the access to ref 28 prior to publication. Financial support by the Deutsche Forschungsgemeinschaft (SFB 262) and the Fonds der Chemischen Industrie is gratefully acknowledged. References and Notes (1) Ediger, M. D.; Angell, C. A.; Nagel, S. R. J. Phys. Chem. 1996, 100, 13200. (2) Richert, R.; Angell, C. A. J. Chem. Phys. 1998, 108, 9016. (3) Johari, G. P.; Goldstein, M. J. Chem. Phys. 1970, 53, 2372; 1971, 55, 4245. (4) Kudlik, A.; Tschirwitz, C.; Benkhof, S.; Blochowicz, T.; Ro¨ssler, E. Europhys. Lett. 1997, 40, 649. (5) Kahle, S.; Korus, J.; Hempel, E.; Unger, R.; Ho¨ring, S.; Schro¨ter, K.; Donth, E. Macromol. 1997, 30, 7214. (6) Hansen, C.; Stickel, F.; Berger, T.; Richert, R.; Fischer, E. W. J. Chem. Phys. 1997, 107, 1086. (7) Adam, G.; Gibbs, J. H. J. Chem. Phys. 1965, 43, 139. (8) Olsen, N. B. J. Non-Cryst. Solids 1998, 235-237, 399. (9) Hansen, C.; Richert, R. Acta Polymer. 1997, 48, 484. (10) Cavaille, J. Y.; Perez, J.; Johari, G. P. Phys. ReV. B 1989, 39, 2411. (11) Wagner, H.; Richert, R. J. Non-Cryst. Solids 1998, 242, 19. (12) Hansen, C.; Richert, R. J. Phys.: Condens. Matter 1997, 9, 9661. (13) Angell, C. A.; Smith, D. L. J. Phys. Chem. 1982, 86, 6, 3845. (14) Nozaki, R.; Suzuki, D.; Ozawa, S.; Shiozaki, Y. J. Non-Cryst. Solids 1998, 235-237, 393. (15) Havriliak, S.; Negami, S. J. Polym. Sci., Part C: Polym. Symp. 1966, 14, 89. (16) Sillars, R. W. J. Inst. Electron. Eng. 1937, 80, 378. (17) Yan, X.; Streck, C.; Richert, R. Mater. Res. Soc. Symp. Proc. 1997, 464, 33. (18) Arbe, A.; Richter, D.; Colmenero, J.; Farago, B. Phys. ReV. E 1996, 54, 3853. (19) Ngai, K. L. Phys. ReV. E 1998, 57, 7346.
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