PHYSICAL REVIEW B VOLUME 57, NUMBER 22 I ruNE 19!

Comparison of the structural and orientational glass-transition dynamics in ethanol

M. A. MillerDepartment of Physics and Astronomy and Center for Fundamenta.l Materials Research, Michigan State lJniversity,

East lansing, Michigan 48824

M. Jimenez-RuizDepartment of Physics and Astronomy and Center for Fundafiental Mateials Research, Michigan Smte [Jnfuersity,

East Lans;ng, Michigon 48824and Instituto de Esttuctura de la Materia, Consejo Superior de Investigaciones Ciefiirtca, Serrano 123, E-28006 Madid, Spain

F. J. BermejoInstituto de Estructura de la Materia, Consejo Supeior de Investigaciones Cientifica, Serrano 123, E-28006 Madrid, Spain

Norman O. BirgeDepartment of Physics ahd Astrohom! @nd Center for Fundafiental Materiak Research, Michigan State llniversity, East ktnsing,

Michigan 48824(Received I December 1997)

The dynamics of the supercooledliquid and rotator-phase crystal of the same matedal, ethanol, are com-pared from measurements of the complex dielectric susceptibility. The relaxation times for the two phases are

very close and appear to cross at 96 K, the tempemture coresponding both to the structuml glass transition ofthe supercooled liquid and to the orientational glass transition of the rotato. phase. Above 96 K, the relaxationtime of the supercooled liquid decreases faster than that of the rotator phase, presumably due to the liberationof additional ftanslational degrees of freedom in the fomer. The dielectric results, coupled with recent specific-heat measurcments of the two phases, suggest that the rotational degrees of freedom provide the domilantcontribution to structural relaxation near the glass tansition, while flow processes provide a smaller contribu-tion. [S0163- 1 829(98)00726-7]

The dynamics of glass-forming liquids has been exten-sively studied dudng recent years from both the theoreticaland experimental points of view.l The dominant dynamicalprocess governing the behavior of a glass-forming material isrefefed to as the arelaxation. and is identified as a stuctumlrelaxation. From an experimental point of view, the a relax-ation displays some universal features: a depa ure ftomDebyelike behavior and a rapid increase in the relaxationtime with decreasing temperature, The relaxation times (7)have non-Arrhenius temperature dependence and can typically be parametuized by means of the empirical Vogel-Tamman-Fulcher 1aw.2 Recent studiesl have identified suchuniversalities in the glassy behavior of a class of materialsknown as orientationally disordered crystals (ODC's), whosemolecular centers of mass possess long-range periodicity, yetretain orientational degrees of freedom.4 In ccrnparison totn:e structu(al glasses, which are disordered both translation-ally and rotationally, the ffanslational order of ODC's repre-sents a significant reduction in the total number of degrees offreedom available to the material. This reduction of struc-tural complexity should facilitate theoreticai modeling, andthus ODC'S are of great interest as model glass-forming sys-tems. The remark;bie similarity in behavior of some ODC'sand supercooled iiqui<is near the glass tansition sugge;tsthat a direct way of experimentally addressing the most re[-evant phenor[ena of so-called "glassy behavior" is io studya single polymorpt'ic system that disrrlays glassy behavio; irrtwo structurally dissimilar phaies.

It has been known for two decadess that ethanot(CrH5OH) exhibits interesting phase polymorphism, and ap-pears to be quite unique in that it can be made to assume avadety of phases simply by varying the temperature in acontrolled manner. The fully disordered liquid phase trans-forms into a skuctural gtass (SG) upon rapid cooling. Theorientationally disordered crystalline phase transfofins froma rotator phase (RP) to an orientational glass (OG) uponcooling at a moderate rate. Finally, the stable, orientationallyordered crystal is produced either by very slow cooling ofthe liquid or by annealing the RP or supercooled liquid. Re-cent x-ray. neutron-diffraction, and Raman-spectroscopico /

studies have confirmed the existence of an orientationalglasslike hansition in the RP crystal at nearly the same tem-perature (fs:97 K) obseryed for the supercooled liqui.d-to-structural glass kansitic[. The close similarity of high-frequency dynamical behavior in the orientational-glass andstructural-glass phases has been established by neutlon time-of-flight spechoscopy and low-temperature specific-heatmeasurements.8 These properties, combined with the factthat the RP crystal can be readily prepared irom the struc-tural glass, suggest that ethano[ provides a unique opportu-nity to investigate and compare the relaxation dynamics ofboth phases near their respective glass transitions. Such acon4rarison may help to clarify the role of transiational andrrtational degrees of freedom iu the dynamieal response of amaterial approaching the giass transition.

We tr.'re rneasured the complex dielectric suscepti"Liiily(6:e'*ie") :f the supercoole$-liquid and rctator-crysteJ

I ruNE 1998-rI

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RI3 978 MILLER, IIMENEZ-RUIZ, BERMEJO, AND BIRGE 57

phases of ethanol near their respective glass transitions. Wefind that the dielecaic relaxation in both the supercooled-liquid (SCL) and RP crystal is nonexponential, and that pa-rameters characterizing the relaxation (e.g., degree of non-Debyeness and average relaxation time) can be approximatedusing a Cole-Davisone fitting function. For a given tempera-turc, comparison of the dielectric response in each phase

indicates a steeper temperature dependence of the averagerelaxation time in the SCL relative to that of the RP crystal,and the relaxation times of both phases are nearly equal at7:96 K.

Preparing ethanol in the supercooledJiquid and rotator-crystaiphase foltows an established protocol.6 Rapid coolingof the liquid at a rate greater than 6 K/min bypasses crystal-lization at Tu:159K,to and allows entry into thesupercooled-liquid regime. Continuing to cool at the pre-scribed rate leads to the structural-glass ftansition at f8:97K. The RP crystal (body-centered-cubic, lattice con-stant a:5.37 A) is then fomed by warming and annealingin the temperature range 102-110 K. The exact temperatureand annealing time required for conversion to the RP crystaldepends on the warming rate, as well as the initial coolingrate into the glassy state.s

Measurement of the frequency- and temperature-dependent complex dielectric susceptibility was carried outusing a sealed coaxial capacitor identical in design to thatused in our previous work.' Two different measurementschemes were employed depending on the frequency rangeunder consideration. In the range I mHz to 10 kHz, the in-phase and out-of-phase currents through the capacitor weremeasured usirg a Stanford SR850 Dual Phase Lock-in Am-plifier in conjunction with a Stanford SR570 Current-to-Voltage Amplifier. For frequencies of I kHz to 10 MHz, a

Hewlett-Packard 4192A Impedance Analyzer was used in astandard four-terminal pair configuration to measure the ca-pacitance and conductance of the sample. Data obtainedfiom the two methods are in excellent agreement where theyoverlap.

Sample material consisted of 200-proof, dehydrated ethylalcohol (ethanol) obtained from Quantum Chemical Com-pany of Tuscola, Illinois. To avoid contamination with watervapor, fi[ing of the capacitor was carried out at room tem-perature in a dry-nitrogen atmosphere. The sample cell wasthen frozen, evacuated of remaining nitrogen gas, and sealed.

The sample cell was then mounted inside a nested cryocanar:rangement described elsewhere.3 Finally, the entire cryo-can assembly was immersed in a double-walled glass Dewar.This design provided control of the sample temperature towithin 0.05 K over the range 4-300 K, and minimized theoccuffence of temperature gradients across the sample,

Figures 1(a) and 1(b) show our data for the reat (e') andimaginary (e") parts of the dielectric susceptibility for thesupercooled liquid as a function of frequency for tempera-

tures of 96, 98, and 100 K. Figures 2(a) and 2(b) show thecorresponding data taken in the RP crystal at temperatures of96, 98, 100, 102, lO4, 106, 108, and 110 K. Although theglass-tansition temperature is usually quoted as T":97 K,we emphasize that all our data are taken in the metastableequilibrium SCL and RP, respectively. The data at 96 K, inparticular, were observed not to change over more than t h,

indicatirg that no structural relaxation was taking place. Ob-

1O-3 1O2 1On 100 10! 'tG 103

Frequency (Hz)

FIG. l. (a) e' and (b) e" vs frequency for temperatures of 96(O), 98 (l), and 100 K (I) in the supercooled-liquid phase ofethanol. Solid lines are fits to the Cole-Davidson function.

taining data over a broad temperature range in the SCL phase

was hindered by the fact that time-dependent transitions tothe RP crystal occur above 102 K. Thus, in order to broadenthe range of liquid-phase data, additional measurements were

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FIG. 2. (a) e' and (b) e" vs frequency for temperatues of 96(a),98 (r), 100 (v), 102 (A), 104 (o), 106 ( ), 108 (tr), and

110 K (l ) in the rctator-crystal phase ofethanol. Solid lircs are fltsto the Cole-Davidson function.

5',1 COMPARISON OF THE STRUCTURAL AND . . .

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FIG. 4. Plot of the Cole-Davidson exponent a vs tempemturefor both the supercooledJiquid (L) and rotator-crystal (O) phases.Both phases exhibit increasingly non-Debye behavior as the glasstransition is approached, a common characteristic of many glass-

forming materials.

taken on warming from the SG, and the data in Fig. 2 wereverified to be reproducible on warming from the OG.

Figure 5 shows the temperature dependence of the meanrelaxation time in both the RP crystal and SCL phases. Thesolid lines are fits to the Vogel-Tamman-Fulcher (VTF)equation2 giYen by

r: ro explAl(T-Tr)). (2)

Here, 16 is an attempt time and f0 is the Vogel temperatureat which the relaxation time diverges. Results of the VTF

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FIG. 3. (a) e' and (b) e" vs frequency for temperatures of 164(O), 173 (O), and 181 K (A) in the liquid phase of ethanol. Solidlines are nts to the Cole-Davidson function plus a term of the formoa"lot in e" due to dc conductivity.

made in the temperature range 164-181 K. Figures 3(a) and3(b) show the high-temperature liquid-phase data, where thecontribution of dc conductivity to the response at low fre-quencies is readily apparent.

The solid lines passing through the data in Figs. 1-3 arefits to the Cole-Davidson fitting forme given by

a( ro): e- * (e6 - e -)t(1- i@torceD)", (l)

where a:2rf .It is well known that ntting relaxation datawith empirical forms such as the Cole-Davidson orKohlraush-Witliams-Watts functionrr does not accuratelydescribe the relaxation at all frequencies. In particular, atfrequencies higher thall two decades or so above the peak,the data typically obey a shallow power-law dependence ex-tendjng to very high frequency.12 ll Nevenheless. the Cole-Davidson form can be used in the main peak region to pro-vide estimates of parameters characterizing the dynamicalresponse such as the mean relaxation time (z: U@t), anda, the degree of departure from a Debye-govemed relaxationprocess ( a: 1).

Figure 4 shows the temperature dependence of the widthparameter a for both the SCL and RP crystal. Both phases

display a characteristic feature common to many glass-forming materials. namely. a decrease oI a with temperatureindicating deviation from idealized Debye behavior.r FiguresI and 2 show that the rotational contribution to the staticssceptibility, e0-6-, is similar in the two phases, indicat-ing that the molecules undergo complete rotatio in the 3CLas they do in the RP crystal. A surprising feature of the datain Figs. 1 and 2 is the decrease in es- e- at low temperature.This cannot be due to partial crystallization of the sampledudng the measurement because the data in Fig. 1 were

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FIG. 5. The mean relaxation time rvs inverse temperatue forthe liquid and supercooledJiquid (A) and rotator-crystal (O) phases

of ethanol. The relaxation times cross at 96 K, near the glass-tansition temperature.

Rl3 979

Rl3 980 MILLER, JIMENEZ-RI'IZ BERMEJO, AND BIRGE 5',7

Parameter A To ao

TABLE I. VTF fit paramete$ ofthe mean relaxation time in the

RP crystal and SCL phases of ethanol.crease in the specific heat of approximately 3i J mol-l K-1.Presumably the exka 9 J mol-r K I in the SCL specific heat

not preseni in the RP crystal coresponds to danslationaldegrees of freedom. These results suggest that the rotationaldegrees of freedom are the dominant contributor to structuralrelaxation processes near the glass transition in both the RPcrystal and SCL, and that flow processes such as mass dif-fusion associated with transtational degrees of freedom in the

SCL contribute to a lesser extent.In conclusion, we have used dielectric specfioscoPy to

compare the dynamical response of the SCL and RP crystalphases of ethanol. we find that the orientational-glass tran-sition in RP crystal exhibits all the characteristics observedin the structural-glass transition: an increasingly non-Debyerelaxation and faster-than-Arrhenius behavior in the relax-ation time as the glass transition is approached. Comparisonof the relaxation time behavior above 96 K displays the ef-fect of the additional translational freedom available to the

liquid resulting in faster molecular reorientation in the SCLrelative to the RP crystal for a given temperature. The dielec-tric data indicate that rotational motion is the dominant dy-namical process governing the glass transition in both SCLand RP crystal ethanol. Thus, the construction of a minimalmodel utilizing restricted degrees of freedom now appears

relevant to the behavior of real materials. A model such as

that explored by Renner, Lowen, and Barratr5 involving hard

needles on an fcc lattice, should be simple enough to allow adetailed numerical and analytical treatment.

we are grateful to s. R. Nagel and D. L. Price for theirrole in establishing this collaboration. F.J.B. and M.J.R. ac-

knowledge suppod from DGICYT Grant (Spain) No. PB95-0075-c03-01.

SCLRP crystal

fitting for each phase arc listed ir Tabte I. The mean relax-

ation times in the two phases are nearly equal at T:96K,and display a temperature-dependent shift toward a longeraverage relaxation time in the RP crystal phase relative to the

SCL with increasing temperature. This manifests itself ex-pedmentalty as a pronounced shift of the RP crystal relax-ation peak toward lower frequency relative to the relaxationpeak in the SCL at the same temperature. This behavior can

be explained by considering the degrees of freedom availableto the materiat in passing through the glass transition in each

phase. The OG-rRP transition involves the liberation ofpurely rotational degrees of freedom, while the SG--+SCL

hansition involves liberation of both rotational Qnd hansla-

tional degrees of freedom. As the temperature increases

above 96 K, the additional ffanslational freedom present inthe SCL provides the constituent molecules with a less re-

strictive local environment, leading to increasingly shorter

relaxation times in the SCL relative to the RP crystal for a

given temperature. Recenl specific-heat measurements5 l4

performed on both the SCL and RP crystal near their respec-

tive glass transitions support this argument: the OG--+RP

crystal transition involves an increase of about

22! mol tK-t and the SG--SCL transition involves an in-

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