Dynamics of glass-forming liquids. III. Comparing the dielectric α- and β-relaxation of 1-propanol and o-terphenylC. Hansen, F. Stickel, T. Berger, R. Richert, and E. W. Fischer Citation: J. Chem. Phys. 107, 1086 (1997); doi: 10.1063/1.474456 View online: http://dx.doi.org/10.1063/1.474456 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v107/i4 Published by the AIP Publishing LLC. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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Dynamics of glass-forming liquids. III. Comparing the dielectrica- and b-relaxation of 1-propanol and o -terphenyl

C. Hansen, F. Stickel, T. Berger, R. Richert, and E. W. FischerMax-Planck-Institut fu¨r Polymerforschung, Ackermannweg 10, 55128 Mainz, Germany

~Received 27 January 1997; accepted 16 April 1997!

We have measured the dielectric relaxation of the glass-former 1-propanol for temperatures between65 and 350 K in the frequency range 1022 to 2•1010 Hz and the photon correlation spectro-scopy decays nearTg . Attributing the strong Debye-type process of 1-propanol to distinct-OH group effects leaves two faster processes related to the structural relaxation which canbe identified as a-relaxation and Johari–Goldstein typeb-relaxation characteristic ofnonhydrogen-bonding supercooled liquids. From the temperature dependent relaxation timest(T) regarding the three distinct loss peaks, we can specify ana-b-bifurcation temperatureTb , which coincides with characteristic qualitative changes in thet(T) behavior, as also observedfor ortho-terphenyl and other glass-forming liquids. This assignment is confirmed by the correla-tion times derived from incoherent quasielastic light-scattering data obtained from thesimultaneously measured photon-correlation spectroscopy. ©1997 American Institute of Physics.@S0021-9606~97!50728-8#

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INTRODUCTION

Glass-forming materials are capable of combiningdisordered liquidlike state with the relatively slow molecudynamics if cooled below their melting temperature in tcase that crystallization does not occur. In this supercoostate a quasiuniversal behavior is often found as regardstemperature dependence of some characteristic relaxatime and the temporal pattern by which equilibrium is rstored after a small perturbation.1–4 Further cooling belowthe glass transition temperatureTg leads to the glassy state iwhich the system is no longer capable of equilibrating witha time window given by experimental conditions. The epirical laws commonly cited in this context are thVogel–Fulcher–Tammann5 ~VFT! temperature dependencof the form

log~t!5A1B/~T2T0!, ~1!

whereA, B, andT0 are constants with respect to tempeture, and witht tending to diverge asT approaches the Vogel temperatureT0.0. The special case ofT050 restoressimple activated behavior expressed by the Arrhenius lAlso, the wide spectrum of conceptually different relaxatiexperiments used to characterize the molecular motion insupercooled state of matter often comply with the stretcexponential or Kohlrausch–Williams–Watts6,7 ~KWW! de-cay law, which reads:

f~ t !5f0•exp@2~ t/tKWW!b#. ~2!

In this expressiontKWW is a characteristic time constant, anb, in the range 0,b<1, delineates the degree of nonexpnentiality. The particular valueb51 describes a simple exponential or Debye-type pattern. The dispersive KWW dein the time domain is complemented in the frequency domby the Havriliak–Negami8 ~HN! function commonly used tofit dielectric relaxation data. In the HN function of the for

1086 J. Chem. Phys. 107 (4), 22 July 1997 0021-9606/97

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the dielectric constants in the limits of high and low frquency are respectively denoted«` and «s , andtHN againsets a characteristic time scale. The shape parametersa andg in the range 0,a, a•g<1 quantify the symmetric andasymmetric broadening of the loss peak relative to Debehavior witha5g51.

For a significant number of glass-forming materials theexists a correlation between the KWW dispersion paramb and the fragility9 of the material,10 where the latter prop-erty relates to the deviation of the VFT law from the Arrheius case, T050, in an Angell plot11 scaled aslog@t(T)/t(Tg)# versusTg /T. A prominent example for dis-obeying these VFT and KWW ‘‘universalities’’ is1-propanol, because it seems to combine the temperaturependence of a more fragile liquid with a KWW dispersioparameterb51, i.e., the predominent dielectric relaxationpurely exponential.12 Without referring to ab-process, theentire dielectric function of 1-propanol well above the glatransition is commonly described by three processes,13–15

«* ~v!5«`1(i51

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@11~ ivt i !a i#g i

, ~4!

with a15g151 andt1.t2.t3 , i.e., with the slowest pro-cess, 1, being a Debye relaxation and with a contributD«1 , which takes.90% of the total relaxation strengtD«5(D« i .

In addition to the structural ora-process addresseabove, many glass-forming materials exhibit a further dieltrically activeb-process of the Johari–Goldstein16 ~JG! type,i.e., one which is not related to the motion of subunits psessing degrees of freedom that are significantly decoufrom those of the molecule as a whole. These local relaxacomponents are known to follow an Arrhenius-type tempe

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1087Hansen et al.: Dynamics of glass-forming liquids. III

ture dependence, which tends to merge into that ofa-process at relaxation times around 1ms.17 Viewed fromthe high-temperature side, the structural relaxation thusfurcates atT5Tb into the remainder of thea-process and afasterb-process, which is not affected by the glass transitregarding its dynamical behavior nearTg .

In the present work we show that thea-b-bifurcationtemperatureTb observed for a series of glass-forming marials coincides with a characteristic temperatureTB , derivedfrom a detailed analysis of the variation of the relaxatitime with temperature using the derivatives of log~t! withrespect toT. As a common feature of supercooled simpliquids, a data presentation of the form@] log(t/s)/](1/T)]21/2 versusT linearizes a VFT dependence18 andclearly indicates a transition atTB upon lowering thetemperature,19 at which the dynamics changes fromVFT(T.TB)

to a different VFT(T.TB)or from a VFT to a

non-VFT behavior. This result ofTB5Tb is paralleled by thebehavior of 1-propanol, if process 2 is assigned to the sttural a-process and a further fast process is assumed toflect theb-relaxation. Unlike the previous observations rgarding peak III, this b-process becomes increasingseparated from the other peaks upon cooling towards sciently low temperatures. Therefore, apart from the stroDebye peak at lower frequencies, 1-propanol can be unstood as a typical glass-forming material. This identificatof peak II with thea-relaxation is confirmed by photoncorrelation spectroscopy performed simultaneously withelectric measurements and by the comparison with viscomechanical relaxation, and Brillouin light-scattering data.

EXPERIMENTS

Dielectric relaxation experiments were performed in tfrequency domain in order to quantify the complex dielectfunction «* (v)5«8(v)2 i«9(v) in the frequency range1022 to 2•1010 Hz. For this range four different systems aused: a frequency response analyzer~Solartron FRA-1260,1022 to 106 Hz!, an impedance analyzer~HP-4192A, 102 to107 Hz!, a coaxial line reflectometer~HP-4191A, 106 to109 Hz!, and a network analyzer~HP-8510E, 5•107 to 2•1010 Hz!. For frequencies from 1022 to 107 Hz a discsample geometry is used, for measurements between 106 and109 Hz a coaxial arrangement with the sample capacmounted as part of the inner conductor is employed, andrange above 109 Hz is covered by a network analyzer evalating both reflection and transmission signals. The frequeoverlap of the three measurement regimes is sufficienobtain reliablefmax(T) data in the entire range from 1022 to1010 Hz. The sample temperature has been controlled btemperature controller~Quatro, Novocontrol! using a heatedN2 gas stream. Independently, we measure the sampleperature with a Pt-100 sensor at a relative accuracy of bethan60.05 K. The liquid 1-propanol~nPOH! has been measured in the entire range stated above, whereas bis-methphenyl-cyclohexane~BMPC! was not investigated abov

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109 Hz. Due to its low relaxation strength, ortho-terphen~OTP! has been studied dielectrically only for frequenciesto 106 Hz.

The low-temperature data for 1-propanol in the ran65 K<T<121 K has been measured with the gain-phatechnique for frequencies 1021 Hz< f<106 Hz employing aSolartron 1260 analyzer combined with a dielectric interfa~Mestec, DM 1360!. The sample cell consists of two braselectrodes of 12 mmB mounted on sapphire plates whicare embedded in a massive brass block so that the elecseparation is 200mm. The data are measured relative to tgeometric capacityCgeo;5 pF so that the precise value oCgeo is irrelevant for obtaining absolute«* (v) values. Thevariation ofCgeo with temperature has been experimentaconfirmed not to exceeddC/dT'180 aF/K in the range 20to 300 K. The residual dielectric loss of the evacuatsample capacitor has been checked with a 1 kHz impedancebridge ~Andeen-Hagerling, AH-2500!, resulting intand<2•1026. The vacuum tight sample cell is mounted othe final stage of a closed cycle helium refrigerator~LeyboldRDK 10-320! equipped with silicon-diode sensors and teperature controlled to within630 mK ~Lake Shore Mod.330!.

The photon-correlation spectroscopy~PCS! setup con-sists of an Ar-ion laser (l5514.5 nm) operated at 700 mWa N2 continuous flow low-temperature cryostat~Oxford, CF-1204!, and a digital-t-correlator~ALV-5000, Langen, FRG!.The data were acquired in VV geometry using a precisdust free 10 mmB Pyrex-glass cell filled with the purifiedand filtered~Millipore, 0.22 mm! liquid nPOH sample. Theglass cell is equipped with two 635 mm platinum electrodesat a distance of;1 mm in order to measure the dielectrrelaxation simultaneously to the PCS data. Thefmax valuesfrom this dielectric data have been used to exactly matchtemperature scale of the PCS experiment to that of the ohigh resolution dielectric measurements described above

RESULTS

As a characteristic and well known feature of supcooled liquids, we observe that the dielectric loss«9(v) isgenerally broadened with respect to simple Debye behavApart from the common excess loss at frequencies whv•t@1, this dispersion can numerically be well accountfor by using the HN formula in Eq.~3!. Due to the presenceof charged impurities a dc-conductivity contributionsdc hasto be accounted for, so that we actually used the fit funct

«9~v!5sdc/v•«02Im@«* HN~v!#, ~5!

where Im@ # denotes the imaginary part of«* . For delineat-ing the temperature dependence of a relaxation time orquency we face the problem of selecting a particular and wdefined frequency out of the distribution of event timwhose width vanishes only in the Debye case. We chosfocus on the frequencyfmax, at which«9 shows a maximum.This value is easily obtained from the HN fit parameteusing20

, No. 4, 22 July 1997

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1088 Hansen et al.: Dynamics of glass-forming liquids. III

fmax5~2ptHN!21•sin1/a~ap/~212g!!

•sin21/a~agp/~212g!!. ~6!

Although fmax5vmax/2p51/2ptmax is a rather arbitraryquantity within the probability density of finding a certarelaxation frequency, it is well suited for unambiguously dlineating the temperature dependence of dynamprocesses.19

Figure 1 displays the dielectric relaxation data of nPOin terms of«9 versus log10( f /Hz) for the lower temperaturebetween 120.8 and 64.8 K and in the range 0.1 Hz to 1 MApart from the strong Debye peak, the data indicate tsmaller processes following different temperature depdences. These data have been subject to an HN analysicording to Eqs.~4! and~5!. Figure 2 shows the nPOH data119.7 K, together with the entire fit and the three individufit curves. As far as being observable in the presentquency range, the strong loss peak is of Debye charawhereas the two other processes at higher frequenciessignificantly broadened.

Following Eq.~6!, fmax is derived from the fit parametera, g, andtHN for the three peaks, in the following denotedII, and III in the order from low to high peak frequencieThe results forfmax as a function of temperature are graphcally compiled in Fig. 3. Analogous data for the van dWaals type glass-forming liquids orthoterphenyl~OTP! andbis-methoxy-phenyl-cyclohexane~BMPC! are depicted inFigs. 4 and 5, respectively.

The photon-correlation spectroscopy data for nPOHtially yield the intensity autocorrelation functionG(2)(q,t)

FIG. 1. Experimental dielectric loss«9 results for nPOH in the temperaturrange 120.8 K>T>64.8 K in steps of 2 K and in the order from upper tolower curves. Three distinct contributions, I, II, and III, are observed, whonly peak I resembles a Debye type process.

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5^I (q,t)•I (q,0)&. Following common practice, the Siegerelation21

g~2!~q,t !5F11 fU^E~q,t !•E* ~q,0!&

^uE~q,0!u2& U2G ~7!

is used to express theg(2)(q,t) result in terms of the fieldautocorrelation function G(1)(q,t)5^E(q,t)•E* (q,0)&,where f is a factor that depends on the coherence condiset by the experiment. The corresponding data analysissumes a KWW pattern forg(1)(q,t), whose parameters aroptimized such that a good fit forg(2)(q,t) is obtained viaEq. ~7!. In order to have values that are comparable todielectric frequency domain results«9(v), the KWW fitsreflecting theg(1)(q,t) data are numerically transformed vtheir relaxation time distribution into the equivalent frquency domain representationx9(v) by a method describedin detail22 elsewhere. From these susceptibility spectracharacteristic frequenciesfmax(T) are evaluated, where thtemperature assignment for the PCS experiment is achieby matching the dielectric loss spectra from the two setuA representative PCS curve in terms of itsx9(v) for T5119.7 K is displayed in Fig. 2. The fourfmax(T) data pointsinferred from the photon correlation spectroscopy for nPOin the range 105.7 K<T<119.7 K are included in Fig. 3.

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FIG. 2. Dielectric loss«9[x9 for nPOH measured atT5119.7 K~squares!.The solid curve represents the fit to the data according to Eq.~4!, the dashedcurves are the individual contributions with the following parameters: pI: D«566.25, a51, g51, tHN52.84•1022 s; peak II:D«52.45, a51,g50.35, tHN55.30•1024 s; peak III: D«50.67, a50.57, g50.92, tHN53.88•1026 s. The PCS curve~crosses! is a susceptibility representation othe actual KWW type time domain result obtained for the same temperaT5119.7 K and is shifted arbitrarily on the log(x9) ordinate scale.

, No. 4, 22 July 1997

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1089Hansen et al.: Dynamics of glass-forming liquids. III

DISCUSSION

In the context of classifying glass-forming materialsterms of ‘‘strong’’ and ‘‘fragile’’ systems,11 the most promi-nent exception is 1-propanol, because its main dielectric ctribution combines a Debye-type relaxation pattern wmarked deviations from an Arrhenius like temperaturependence of the relaxation time constant. This unusualcurrence of a strong Debye-type feature and further distdielectric processes in nPOH has been well documensince the work of Davidson and Cole.13–15 The aim of un-derstanding these features, which can also be observeother primary alcohols of higher molecular weight,15 has ledto numerous studies and to a number of different picturesrationalizing the experimental findings.17,23–27In the follow-ing it shall be demonstrated on the basis of the presenttailed reinvestigation that nPOH displays the characteribehavior of a low molecular weight glass-forming liquid,peak II is regarded as structural ora-process, while peak IIIresembles the features typical for a Johari–Goldstein typ16

b-process.We begin the discussion with a series of more qualitat

observations. In Fig. 1 it is seen that peaks I and IIsimultaneously shifted outside the experimental frequewindow as the temperature is lowered from;120 to

FIG. 3. Temperature dependence of the peak frequencyfmax for nPOH,defined by the conditionx9( fmax)5xmax9 , and of the viscosityh. The opensymbols refer to the dielectric results (x5 fmax/Hz) for peak I ~h!, peakII ~s!, and peak III~n!. The dashed line is an Arrhenius fit to the peIII relaxation data, log10( fmax/Hz)512.921032K/T. The solid symbolsrefer to light-scattering data (x5 fmax/Hz), the present PCS data~L!and unpublished~Ref. 35! Brillouin results ~,!. The solid line followingfmax(T) of peak II indicates the temperature dependent inverse visco(x5k•h21/Poise21) of nPOH taken from literature results~Refs. 42–45!,whereh21(T) is shifted by a constant log10(k)58.3 to match the mechanical retardation~Refs. 23, 28! data point~1!. Tb'138 K marks the bifurca-tion temperature regarding peaks II and III.

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;100 K. In contrast, peak III persists in residing within thrange 1021 Hz< f<106 Hz at much lower temperaturesFigure 3 parallels this observation in more detail: Peaks III remain constantly separated by approximately 2 decadethe entire rangefmax(T),107 Hz, whereas the curves are nlonger parallel forfmax(T).107 Hz. Consequently, the viscosityh(T) can follow the temperature dependence of onpeak I or peak II, not both. As shown in Fig. 3, the courseh21(T) complies well with that offmax(T) for peak II, butwould significantly deviate from the peak I curve abo;200 K. More precisely,fmax(T) for peak I andh

21(T) aresubject to distinct apparent activation energies at elevatemperatures,19 so that these data sets do not only differ byshift factor regardingh21. Together with the present detailed observations that the inverse viscosityh21(T) andfmax(T) for the process II are highly linked quantities overwide temperature range, this notion already points towapeak II being the signature of thea-relaxation.

The drawback of viscosity data is the ambiguity regaing the required shift factor inhs5G`•ts , ts being theshear relaxation time, for a comparison with dielectric ‘‘rlaxation’’ times tD . A further complication arises from thenotion thattD actually refers to a retardation time when otained from«* (v) data. For the viscosity data in Fig. 3 thdilemma can be resolved by the use of the measuredchanical relaxation data reported by Litovitz28,29 and

ty

FIG. 4. Temperature dependence of the peak frequencyfmax for OTP, de-fined by the conditionx9( fmax)5xmax9 , and of the viscosityh. The opensymbols refer to the dielectric results (x5 fmax/Hz) for thea-process~s!and for theb-process~n!, with theb-relaxation data taken from the literature ~Ref. 16!. The dashed line is an Arrhenius fit to theb-relaxation data,log10( fmax/Hz)515.222543K/T. The solid line represents literature da~Refs. 46–51! on the viscosity (x5k•h21/Poise21) of OTP with log10(k)58.0. The diamonds refer to PCS data~Ref. 52! and the triangles represenBrillouin light-scattering data~Refs. 53, 54! (x5 fmax/Hz), both taken fromthe literature.Tb'290 K marks the bifurcation temperature regarding thea-andb-peaks.

, No. 4, 22 July 1997

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1090 Hansen et al.: Dynamics of glass-forming liquids. III

Angell23 for n-propanol. The result of this study is that thratio of the dielectric~peak I! to the mechanical retardatiotime is 160, or 2.2 decades atT5143 K ~included as1 inFig. 3!. This value is employed to determine the absolposition of theh(T) data on the log10( fmax/Hz) ordinatescale in Fig. 3. Therefore, the mechanical retardation timcoincide with the dielectric retardation times of peak II toremarkable degree of accuracy. An analogous offset betwmechanical and main dielectric~peak I! retardation times hasbeen observed for another primary alcohol, pentanol.30 Itshould be realized that for nonhydrogen-bonding liquidsratio of the main dielectric~a-process! to the mechanicaretardation time is of the order of 3 or less.28,29

Further evidence for the peak assignment stems fromshape analysis of the distinct loss contributions outlinedFig. 2. As a representative example we focus on thespectrum«9(v) obtained forT5119.7 K and the resultingHN shape parametersa andg, which, respectively, quantifythe symmetric and asymmetric broadening of«9(v) on thelog(v) scale. The results for the individual peaks area5g51 ~Debye type! for peak I,a51, g50.35~Cole–Davidsontype31! for peak II, anda50.57, g50.92 ~'Cole–Coletype31! for peak III. Therefore, peak II is mainly asymmetrcally broadened, while peak III has a symmetric appearaThe HN shape parametersa andg for peak II are well rep-resented by a KWW exponentb50.56 if cast into the timedomain equivalent decay. A quantitative approach to colating the temperature dependence of the average relaxtime ^t& with the stretched or KWW exponentb at the glass

FIG. 5. Temperature dependence of the dielectric peak frequencyfmax forBMPC, defined by the condition«9( fmax)5«max9 . The open symbols refer tothe dielectric results for thea-~s! andb-process~n!. The dashed lines area VFT fit to thea-relaxation forT.Tb , log10( fmax/Hz)513.4–504K/(T2219 K), and an Arrhenius fit to theb-relaxation data, log10( fmax/Hz)513.222615K/T. Tb'270 K marks the bifurcation temperature regardithea- andb-relaxation.

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transition Tg , uses the fragility indexm defined bym5d log^t&/d(Tg /T) at T5Tg , whereTg is given here by thecondition ^t&(T5Tg)5100 s.12 The observed correlationbetweenm andb for over 70 glass formers can be expressby m'250(630)2320•b. The data pairm529 andb51~with respect to peak I! for nPOH is well outside the usuam(b) trace.12 However, referring to peak II withb(Tg)'0.60 andm'35 gives rise to coordinates (m,b) which aretypically observed for polymers and network type glaformers. This fragility argument, together with the notiothat susceptibility spectra of structural relaxations are moften asymmetrically broadened, as is peak II, again argin favor of relating peak II rather than peak I to thea-processof nPOH.

Quasielastic light-scattering experiments, photocorrelation spectroscopy, as well as Brillouin scatterimethods, probe the fluctuations of the dielectric ten«(q,t) in the hydrodynamic limit.21 The geometry of theexperiment, VV, VH, or unpolarized, delineates which coponents of the tensor contribute most significantly to thecay of the field autocorrelation function. For the VV casethe PCS experiment on nPOH it can be expected thatresultg(2)(q,t) mainly reflects the density–density correltions, whose characteristic time scale has been observematch the dielectric relaxation times within60.5 decades inmany cases.32–34Figure 2 includes ax9(v) spectrum basedon theg(2)(q,t) result for nPOH. In order to eliminate anpossible offset between the temperature scales of the dietric and PCS experiment, the temperature assignment ofPCS data relies on the dielectricfmax values measured in thlight-scattering cell simultaneously to acquiring the photocorrelation data. However, this supplementary dielecmeasurement is not of sufficient accuracy to resolve peakand III as shown in Figs. 1 and Fig. 2. Due to the wescattering intensity of nPOH the precise form of the Px9(v) spectrum is not well resolved. However, Fig. 2 cleaindicates that the dielectric peak I is not coupled to densfluctuations, whereas peak II matches the frequency posiof the PCS data. The data in Fig. 3 confirm this latter cocidence for different temperatures nearTg from the presentexperiment as well as for the high-temperature range asrived from Brillouin scattering data.35 Note that in contrast toviscosity data, light-scattering results are comparable todielectric times on absolute scales, i.e., no arbitrary shift ftor is involved. The overlap between the time scales ofdielectric process II and those of the density autocorreladecay, together with the comparison with the viscosity dastrongly argues in favor of interpreting peak II in termsthe structural relaxation.

It is worthwhile noting that based on the viscosity alight-scattering data, peak I appears to be decoupled fromstructural processes in nPOH, although it carries appromately 96% of the entire dielectric relaxation strengthD«.From the present experimental study no physical picturederlying the process I can be deduced. However, it has bdemonstrated that the model of a single dipole of consmomentm, which is assumed rotationally blocked for som

, No. 4, 22 July 1997

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1091Hansen et al.: Dynamics of glass-forming liquids. III

residence time in the associated or hydrogen-bonded stain qualitative accord with the experimental findings falcohols.25 For low values of the association probability, thcorresponding calculations predict a strong Debye-type pcess, reflecting the residence time, which can be longerthe orientational correlation time of the dipole. Without ging into details, it could be rationalized in this manner thno structural dynamics is observed at the time scale of pcess I.

We now turn to the process of peak III, which diffequalitatively from peaks I and II by displaying a wide balmost symmetric Cole–Cole type31 relaxation time disper-sion and a relaxation strengthD« II(T), which increases withtemperature together with an Arrhenius-like variation of tcharacteristic relaxation time with temperature. The loss pfiles «9(v) are shown in Figs. 1 and 2 and the temperatdependence offmax is seen in Fig. 3. The dashed line in Fi3 shows an Arrhenius fit forfmax(T) of peak III, based on thelow-temperature data where peaks II and III are well serated. According to this activation plot, the coursefmax(T) for peak III appears to merge into that of peak II abifurcation temperature denotedTb , with Tb'138 K fornPOH. Near and aboveTb , this third process can no longebe discriminated unambiguously from the loss componenpeak II, although a high frequency shoulder in«9(v) re-mains visible. The existence of a fast process subjectsymmetric relaxation time dispersion, to an increasing fution D«(T), and to an Arrhenius-like temperature depedence, which merges into thea-process at higher temperatures, is a common feature of glass-forming liquids termb-relaxation.2–4 Figure 4 shows the equivalent behavior fthe van der Waals type glass-former OTP withTb'290 K,where thea- andb-processes of OTP are analogous toresults for peaks II and III of nPOH in Fig. 3. As a furthexample, where the dielectrica-relaxation data are availablalso aboveTb'270 K, we show the identical scenario foBMPC. Note that theb-relaxation of BMPC shown here habeen denotedg-process in a previous study,36 and a furthersecondary relaxation can be observed around 109 Hz.

In previous papers, the quantitiesd log(x)/dT,d log(x)/d(1/T), and d2 log(x)/dT2 regarding experimentadielectric relaxation (x5 fmax/Hz) or other dynamic datahave been demonstrated to constitute powerful tools in oto obtain a detailed insight into the precise variation ocharacteristic relaxation time with temperature.18 This tech-nique is somewhat similar to evaluating the apparent acttion energyEA(T) for non-Arrhenius systems.

37 Especially,casting the fmax(T) data into a plot scaled a@d log10( fmax/Hz)/dT#21/2 versus T or scaled as@2d log10( fmax/Hz)/d(1/T)#

21/2 versus 1/T linearizes aVFT-type temperature dependence, and in the latter casArrhenius behavior appears as a horizontal line. For a seof glass-forming liquids, including nPOH, it has been shoin detail that the common application of a VFT law for thtemperature range just aboveTg is often inappropriate.

18,19Incontrast, the dynamics obeys a VFT law to a very highcuracy above a certain temperatureTB , where the dynamicsis many orders of magnitude faster than atTg . Using the

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derivative of log(fmax/Hz) with respect to temperaturegives rise to a clear cut temperatureTB , at which a quali-tative change in the temperature dependence appearsimilar truncation of the dynamical behavior into distinlow- and high-temperature VFT regimes has been poinout already by Barlow, Lamb, and Matheson.38 The plots of@2d log10( fmax/Hz)/d(1/T)]

21/2 versus 1/T are shown inFigs. 6 and 7 for the viscosity and dielectric data of OTP aBMPC, respectively.39 The resulting values forTB are TB'290 K for OTP andTB'270 K for BMPC, while TB5140 K for nPOH has been determined previously.19Withinthe accuracy of determining these values, we thereforeTB5Tb for the alcohol nPOH as well as for the aprotic liquids OTP and BMPC. Although only these three exampare shown here, we have confirmed the coincidence ofTBandTb for other materials, e.g., 1-butanol. From this obsvation we conclude that the bifurcation of thea-processat temperaturesT.Tb into the remainder of thea-relaxa-tion and theb-relaxation forT,Tb is accompanied by aqualitative change of the characteristica-relaxation timescale as a function of temperature atTB5Tb . The positionof TB andTb on the temperature scale is often such thatrelaxation time scale atTB is within the range 1025 to1027 s (4< log10( fmax/Hz)<6).19 Note that theb-processmust not necessarily carry sufficient dielectric strength toobservable and that intramolecular modes might be coup

FIG. 6. Temperature dependence offmax for the dielectrica-process and ofthe viscosity of OTP plotted as@2d log10(x)/d(1/T)#

21/2 ~in units ofK21/2! versus 1/T. The dielectric data~x5 fmax/Hz, open circles! are iden-tical to the results shown in Fig. 4, but scaled such that a VFT dependappears as a linear function in this plot. The crosses are literature re~Refs. 46–51! for the viscosity (x5h21/Poise21). TB'290 K marks thetemperature where thefmax data begin to deviate from the VFT fit~solidline! valid for T.TB , log10(h

21/Poise21)53.02200K/(T2250 K).Above a second characteristic temperatureTA'455 K the viscosity datafollow an Arrhenius law, log10(h

21/Poise21)54.22980K/T.

, No. 4, 22 July 1997

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1092 Hansen et al.: Dynamics of glass-forming liquids. III

to the librational motion of the entire molecule.Since the peaks II and III of nPOH are no exception

regards the ruleTB5Tb , it can be concluded that peak III ithe signature of ab-relaxation in nPOH. Note that process Iof nPOH would extrapolate tofmax of process I only at fre-quencies in excess of 1010 Hz. The independence of this rulon the chemical constitution of the liquid points towarthese secondary processes being related toJohari–Goldstein16,17~JG! type effect, instead of being baseon the motion of particular subunits of the molecub-relaxations attributed to the JG process are found to meinto thea-relaxation at temperaturesT.Tg , where the re-laxation time is around 1ms,16,17as also found presently. Ouobservation of a qualitative change in the course offmax(T) atTb concurs well with the idea of the JG-typeb-relaxation,indicating librational modes of the molecular motion, whialso govern the structural relaxation. Therefore, the dielecloss profile at the bifurcation pointTb is likely not to besimply the sum of thea- andb-contribution.40 Other second-ary relaxation processes associated with the motion ofticular subgroups of the constituent molecules are alsonotedb-relaxations. As true for the JG-typeb-process, othersecondary relaxations also display Arrhenius-like tempeture dependences, as well as a symmetric relaxationdispersion, presumably due to the common property of thprocesses being highly local, i.e., they do not involve larscale cooperative motion of adjacent units. On the othand, the dynamics of side groups should depend morethe chemical constitution and are thus not expected to fol

FIG. 7. Temperature dependence offmax for the dielectrica-process ofBMPC plotted as@2d log10( fmax/Hz)/d(1/T)#

21/2 ~in units of K1/2! versus1/T. The dielectric data~s! are identical to the results shown in Fig. 5, bscaled such that a VFT dependence appears as a linear function in thisTB'270 K marks the temperature where thefmax data begin to deviate fromthe VFT fit ~solid line! valid for T.TB , log10( fmax/Hz)513.42504K/(T2219 K).

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the universal relation to thea-process as discussed above fthe JGb-process.

In the above series of arguments we have employed Oas a reference glass-forming material, whose propertiesqualitatively paralleled by a series of other chemically dferent liquids. OTP is well investigated, so that lighscattering data are available for both the low and high teperatures. The dielectric measurements on OTP doexceed frequencies of 106 Hz, but the dynamical propertieat higher temperatures are documented by precise viscodata. The BMPC results are also considered here in ordedemonstrate that the same conclusions apply when regardielectric data only, i.e., without invoking results from diferent experimental methods. Most important is that OTPprototypical liquid for displaying ab-process that originatefrom the same permanent dipole that also gives rise toa-relaxation.16 The parallel features of thea- andb-processes of OTP and of nPOH~peaks II and III! can besummarized as follows. Thea-relaxations are asymmetrically broadened as regards their loss profile«9(logv), withthe relaxation strengthsD« decreasing with increasing temperature, roughly according to the well knownm2/3kT con-tribution. Theb-relaxations are subject to a more symmetbroadening and their relaxation strengths decrease astemperature is lowered, which can be rationalized bysubsequent freezing of the molecules participating inb-process. For both materials, the temperature dependenfmax(T) or h21(T) can be divided into three distinct regimeTg,TB,TA,Tb , whereTb denotes the boiling temperature. In the rangeTB to TA , fmax(T) and other dynamicaquantities obey a ‘‘high-temperature’’ VFT law to a higdegree of accuracy. The rangeT,TB is characterized eitheby a deviation from the above VFT behavior or by a trantion to a further ‘‘low-temperature’’ VFT curve. AboveTA , an Arrhenius behavior is observed with an activatienergyEA that is similar for different dynamical processes.is important to recall that the above characterizationfmax(T) or h21(T) holds for a wide spectrum of chemicalldifferent glass-forming materials.19 A clear exception fromthis rule is seen for the Debye peak I of nPOH, by displayan activation energy aboveTA that is a factor of 1.4 belowthat of the viscosity. This particular feature is paralleledthe entire series of alcohols from methanol to 1-octanol,which EA(h)/EA( fmax)51.4060.03 has been found.19

SUMMARY AND CONCLUSIONS

We have reinvestigated and analyzed the dielectric prerties of 1-propanol, especially in the range of low tempetures, where the smallest process appears as a well sepaloss peak and can be identified as a secondary relaxaThe resulting data for the parametersfmax(T), a, g, andD«(T) related to the three distinct processes are compawith the equivalent properties derived from light-scatteriexperiments and viscosity data, and with other glass-formmaterials. Based solely on the dielectric relaxation behavthe two small peaks, II and III, of nPOH are reminiscentthe dynamics typical for a glass-forming material regard

lot.

, No. 4, 22 July 1997

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1093Hansen et al.: Dynamics of glass-forming liquids. III

the temperature dependent characteristic relaxation freqcies as well as symmetry, widths, and amplitudes of theprofiles. Moreover, peak II is the only process in nPOH tis paralleled by viscosity, mechanical relaxation, and ligscattering data. Therefore, the present data are not comible with the assumption41 of peak II resembling a typicahigh frequency component of the peak I relaxation. Assiing peak II to the signature of structural relaxationa-process, and peak III to a Johari–Goldstein tyb-relaxation removes any qualitative differences betweendynamical behavior of nPOH and other nonhydrogebonding liquids, e.g., OTP and BMPC, as long as peaknPOH is ignored. The latter notion is especially emphasiby observing the coincidence of thea-b-bifurcation tempera-ture Tb with qualitative changes in the course offmax(T) atT5TB , which occurs equally in all three liquids presentunder study. In contrast to typicala-processes, it is alsoshown that the dominating slowest peak, I, possessescounterpart signals in the quantities directly related to strtural relaxation like viscosity and density fluctuations. Espcially noteworthy is the absence of any signature of peakthe density autocorrelation function probed by photocorrelation spectroscopy and the strikingly different activtion energies regarding the dielectricfmax(T) andh21(T) attemperatures aboveTA .

ACKNOWLEDGMENTS

We thank B. Strube for the unpublished Brillouin lighscattering data on 1-propanol. Financial support by the Dsche Forschungsgemeinschaft~Sonderforschungsbereic262! is gratefully acknowledged.

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