Molecular Glasses with High Fictive Temperatures for Energy

J. Phys. Chem. B 2002, 106, 1069-1080

1069

Molecular Glasses with High Fictive Temperatures for Energy Landscape Evaluations V. Velikov, S. Borick, and C. A. Angell* Department of Chemistry and Biochemistry, Arizona State UniVersity, Tempe, Arizona 85287-1604 ReceiVed: May 24, 2001; In Final Form: NoVember 8, 2001

With an interest in obtaining data on laboratory glass samples to compare with simulated glasses produced by molecular dynamics computer simulations, we have explored, using calorimetric techniques, the fictive temperatures that can be obtained using different laboratory quenching methods. We describe some useful analytical methods for characterizing quenched samples and, in the process, demonstrate a modified graphical treatment of DSC data that directly yields the m fragility index (“steepness” index) and permits the assembly of enthalpy relaxation data on different liquids in a fragility plot. Using these methods, we provide evidence for the trapping of high-Tg molecular glasses at fictive temperatures up to 1.16Tg and show that fictive temperatures up to and even beyond the crossover temperature for fragile glass formers should be possible using refined electrospray and fiber-spinning techniques. We discuss the relation of the low-T/Tg enthalpy relaxation, found in all hyperquenched glasses, to topographic features of the energy landscape for glassforming liquids.

Introduction Goldstein1

Following the seminal contributions of and Stillinger,2 the development of an appropriate collective-coordinates treatment of glass-forming liquid properties is attracting increasing attention.3-11 In this quest, the computational method of molecular dynamics (MD) and its adjunct, instantaneous normalmode (INM) analysis have been a focus of activity, and characterization of the energy landscapes appropriate to liquids of different character is advancing rapidly. A general problem for these studies, however, arises from computational limitations. The glasses obtained and characterized in computer experiments are almost invariably in structural states of such high energy (and such short relaxation time) that their laboratory equivalents do not exist.12 Because there is a limit to the rate at which this computational problem will be overcome, a more effective means of redressing the gap between computational and experimental samples might be to develop, or systematically to apply, laboratory methods for producing glasses on the same time scales as apply in simulations. Simulations now routinely extend to the nanosecond time scale,13 and in isolated cases,14 liquids have been simulated for as long as 1 µs. The normal glass transition temperature Tg,10 determined using 10-K/min scans, is the temperature at which the structural relaxation time reaches ∼100 s. Then, for a fragile liquid such as o-terphenyl, the temperature at which a 10-ns simulation is successfully completed (meaning that the simulation has extended over at least 10 times the liquid’s relaxation time of 1 ns15) will fall at 1.2-1.25 Tg. For an intermediate liquid such as glycerol, on the other hand, the ratio Tg(sim)/Tg10 will be 1.4-1.6. These figures should be borne in mind for comparison with the results of the present studies and of previous studies reanalyzed in this work. Quite apart from the need to improve comparisons with the simulation results, there is a need to make more effective experimental separations of the important degrees of freedom in the liquid state problem. For instance, we have recently provided evidence that the difference between so-called strong

and fragile behavior in liquids might be largely determined by the vibrational density of states (DOS)16,17 and, in particular, is determined by how the DOS changes with the packing of the particles at increasing thermal excitation above Tg. To clarify this picture, there is an urgent need for methods of producing glassy samples in these high-enthalpy configurations so that the vibrational characteristics of the excited configurational states can be determined under conditions in which there is no centerof-mass diffusion, in which displacements can be approximated as harmonic. A third reason for seeking to trap very high energy states of viscous liquids for detailed low temperature study is the unresolved origin of the bifurcation of relaxation functions of fragile liquids into R and β (or primary and secondary) branches.18 This occurs at a temperature that corresponds19 to the temperature assigned to the critical temperature Tc of mode coupling theory,20 which has also been called the crossover temperature, Tx, by a number of workers.21-24 At this temperature, conjugate gradient quenching studies of MD configurations, performed to obtain information on the structure of the energy landscape at different excitation levels,4 have found an abrupt change of character in the basin shape. This is a matter of fundamental interest, and it is desirable to obtain laboratory examples of liquids trapped in structural states typical of this region, for detailed characterization. In this paper, we examine, calorimetrically, the products of different cooling and quenching procedures and develop calorimetric methods for assessing the states of glasses obtained using different fast cooling procedures. Our particular interest has been in obtaining high-fictive-temperature molecular (van der Waals) liquids, as the most detailed simulation studies have been made on van der Waals liquids (mixed LJ4,6-10) and the most fragile (nonpolymeric) liquids studied to date have been molecular in nature.17,18 The formation of glasses by rapid quenching has been widely researched,24-32 particularly in the field of metallic glass studies,26-32 and some of these studies will be considered further

10.1021/jp012001z CCC: $22.00 © 2002 American Chemical Society Published on Web 01/05/2002

1070 J. Phys. Chem. B, Vol. 106, No. 5, 2002 below. Whereas such studies have been directed mainly at the bypassing of crystallization, and have become less common since bulk metallic glass formers were discovered,28 some have specifically addressed the magnitude and subsequent relaxation of the frozen-in enthalpy.25,30 In the neutron scattering investigations of melt-spun metallic glasses by Suck,31,32 the relaxation of the frozen-in states was monitored through the changes in the density of vibrational states with which it is associated. These studies, however, were performed on systems that appear, from a review of related systems,33 to lie in the intermediate to strong class of liquid behavior. Such liquids have a simpler behavior than fragile liquids: an R-β bifurcation often can not be observed, and a crossover in temperature dependence at Tc is not obvious as it is for fragile liquids, so a single set of VFT equation parameters can fit the data over the whole viscosity range down to the glass transition. It might be expected that the most interesting behavior will be obtained with systems of fragile character. Not only are the fragile liquids those in which the R-β bifurcation is most clearly seen, but they are also those that provide the clearest evidence for heterogeneous dynamics.18 Although there have been many studies of high-quench-rate glass formation in the fibering of such fragile systems as molten fluorides,34 so far, no efforts have been made to characterize their enthalpies and structures relative to those of the normal-rate-cooled glasses.35 Thus, there is a data gap for high-fictive-temperature fragile glass formers that we are initiating efforts, here, to close. Configurational Energy and Fictive Temperature Assessments. The trapped-in energy of a quenched glass can be determined unambiguously by calorimetry. The evolution of heat is measured as the quenched-in structure relaxes toward its normal state at the standard glass transition temperature. Because the energy landscape is defined by the potential energy of the state points as functions of Cartesian particle coordinates,1-3 an energy level on the landscape relative to that of a glass produced at a standard rate can be assigned directly from the calorimetric results. Using differential scanning calorimetry, the energy evaluation is achieved by integrating the excess negative contribution to the upscan heat capacity curve relative to a standard upscan heat capacity curve for the same material. The “standard upscan” in this paper is one that is recorded at a heating rate of 20 K/min on a sample that was first cooled at the same rate from above Tg to well below Tg and then upscanned immediately. The evaluation of the fictive temperature (which is the trapping temperature discussed above) of such glasses has been described in detail by such authors as Moynihan36 and Hodge.37 The graphical procedure for a case with typical molecular glass former heat capacity behavior is illustrated in Figure 1a. The fictive temperature is defined as the temperature at which the rate of change of a function with temperature, extrapolated from below and above the glass transition, must undergo a stepwise change to satisfy the physical condition of continuity of that function. This construct appears to have met only limited acceptance as a way of assigning an unequivocal characteristic temperature to the vitrification process. It has been overlooked in favor of simpler visual geometrical constructs,38 such as the extrapolated onset of the glass transition or the midpoint glass transition. These latter approaches are practical from the point of view of ease of evaluation but are often subjective and difficult to reproduce. They can also be influenced by the effects of instrumental time constants. In a recent study,39 we examined several of the possible metrhods of defining the glass transition by scanning calorimetry and have shown that, for a given choice

Velikov et al. of cooling rate -Q (with heating rate Q), three of them agree to better than 1 °C for a variety of glass formers of both fragile and intermediate character. The three are (1) the fictive temperature defined by the Figure 1a construction, TFQ,S; (2) the midpoint glass transition temperature recorded upon cooling Tg,mid(Q-), which has also been called the midpoint “ergodicitybreaking” (EB) temperature,40 and; (3) the onset glass transition temperature, based on the temperature of intersection of the glass heat capacity with the line of steepest apparent Cp change in the transformation range, using heating scans of same-ratecooled samples, Tg,onset(Q-fQ+). This has also been called the “ergodicity-making” (EM) onset temperature.40 Most data in the molecular liquid literature are reported for this method. Therefore, these three definitions can be used interchangeably, whereas others such as the midpoint heating definition favored by the polymer community38 should be relegated to the role of secondary characteristic temperatures. Of the above three definitions, the second is the simplest in the sense that it is independent of thermal history beyond the downscan rate. However, for the case of extremely fast quench histories, the more rigorous characterization of the ergodicity breaking process represented by TFQ evaluated by the Figure 1b construction relating it to the standard fictive temperature of Figure 1b, is indispensable. This is because the other two definitions are almost impossible to realize (record) experimentally. The construction that we use in this study to obtain TF36,37 for glasses of nonstandard quenches is shown in Figure 1b. It consists of mapping the enthalpy-time behavior of the fastquenched glass, upon reheating to the liquid state, onto that of the standard glass defined above in such a way that the first law of thermodynamics is satisfied for the supercooled liquid. Some development of evaluation methods is given in the Experiments and Methods section. Fast Quenching Techniques. To obtain high cooling rates, it is necessary to reduce the dimensions of the sample under study to values that are small with respect to the thermal diffusion length that controls the rate at which thermal energy can flow out of the system and to transfer heat rapidly across the sample surface. In the melt spinning of glasses, the film of metal being cooled is reduced to a fraction of a millimeter in thickness during the cooling process. The cooling rates estimated for melt-spun glasses are on the order of 106 K/s.26-30 (We quote hyperquench rates in units of K/s for consistency with the literature, but DSC scan rates are reported in K/min). Higher cooling rates can, in principle, be obtained by cooling the ribbons from both sides by use of twin roller techniques; 41,42 by reducing the sample size in additional dimensions, e.g., by quenching threads and droplets; and also by laser melting of very thin samples that are already in atomic contact with good heat sinks.43 As early as 1935, Tammann and Elbrachter44 were spraying micron size droplets onto cold plates to vitrify such inorganic liquids as PbCl2. More recently, Mayer24 described the quenching of micron-sized aerosol droplets of water that were accelerated to hypersonic velocities before being splatted onto a 77-K cold plate. It is possible to obtain submicron droplets by electrostatically driven spraying techniques.45,46 However the collection and manipulation of such particles can become a major problem, as found in the present study. They tend to disperse across any available surfaces, as well as into the atmosphere. An alternative is to change the liquid character slightly so that fibers of nanoscopic dimensions are formed.47 To form fibers, it is necessary for the liquid to have at least some polymeric character to damp out the capillary waves that otherwise cause droplets

Molecular Glasses with High Fictive Temperatures

J. Phys. Chem. B, Vol. 106, No. 5, 2002 1071

Figure 1. (a) Differential scanning calorimeter upscan of glass formed from typical fragile liquid, showing construction defining the fictive temperature, as in ref 36 and its coincidence with Tg onset. (b) Representative scan of very fast-quenched (cooling rate Q2) glass sample from same liquid, showing the relation of the enthalpy recovery exotherm to the (higher) fictive temperature of the glass.This is a schematic to make obvious the principles involved in obtaining the fictive temperature of the rapidly quenched glass from its “excess heat capacity”. The overshoots characteristic of the normal scans (seen in panel (a)) have been suppressed for this purpose.

to form via a Raleigh instability.48 It has been a major simplification in our study that the main material of study is prepared in long fine threads of highly hydrophobic character. The latter is important to avoid rapid contamination of the highsurface-area material by environmental water. It is also a major advantage if the material has a very high glass transition so that the frozen-in state can be largely retained at room temperature for subsequent evaluation. In the following sections, we describe initial, and only partially successful, work with electrospun droplet samples of the model fragile molecular liquid glass former ortho-terphenyl (OTP) (Tg below ambient) and a more successful study of glassy fibers of a high-Tg relative of OTP, which is a synthetic pitch (details below). The direct measurement by DSC of the relaxation of the excess enthalpy frozen in during ultrafast

vitrification is presented and compared with available literature data on ultrafast-quenched metallic glasses. Some unexpected difficulties encountered with the generally inert pitch samples are discussed. Figure 2 shows the viscosities of the materials of the present study measured in the temperature range 520-675 K49-51 and compares them with the viscosity of tri-R-naphthyl benzene (TRNB) which is the largest organic molecule for which the temperature dependence of viscosity (fragility) has been fully characterized.52-54 The OTP data are also from ref 52, except for some very high-temperature data obtained by Arzimanoglou in this laboratory.53 The thick dashed lines are plots of the bestfit Vogel-Fulcher-Tammann (VFT) equation, where fitting was limited to the high-temperature data in the cases of OTP and TRNB for comparison with the available data on the pitch

1072 J. Phys. Chem. B, Vol. 106, No. 5, 2002

Velikov et al. Experiments and Methods

Figure 2. Arrhenius plots of viscosities of three liquids related to the present study. The lowest-Tg liquid, curve A, is o-terphenyl (OTP) of fragility m ) 76.5 according to the definition in refs 55 and 56. The data are from ref 52. The middle liquid is tri-R-naphthyl benzene, the largest aromatic molecular species for which accurate viscosity data over the whole range are available.54 The third liquid is the molten pitch for which less extensive data are available from different sources.49-51 In each case, the 10-K/min calorimetric onset Tg (which we show elsewhere to be the same as the fictive temperature and the midpoint-cooling Tg) is shown. Best fits through the highest temperature data points to the Vogel-Fulcher-Tammann equation are shown as full lines which emphasize the failure of such fits to predict Tg in all cases.

sample. The arrows show the values of Tg measured by differential scanning calorimetry in all three cases. It can be seen that the VFT fits to the high-temperature (low-viscosity) data lead, in all cases, to a great mismatch in the low-temperature data for the viscosity, which is clearly less than 1012 Pa s (1013 Poise) at the calorimetric Tg. The viscosity behavior of the pitch is in a series relation with those of the smaller (seven- and threering) molecular glass formers TRNB and OTP. The fragility of TRNB is known to be fairly high, 66 on the m scale55,56 (based on ac heat capacity data). The value obtained directly from the slope of the plot in Figure 3 [by m ) Tg-1 d(log η)/d(1/T)] is 69.5. This is somewhat less than the value for OTP, which is listed as m ) 81 in ref 56 and is 76.5 according to the data in Figure 2. From these comparisons, the pitch, whose quenching behavior we will study, seems established as a moderately fragile liquid. It has the additional favorable properties for this type of investigation that were mentioned above. Unfortunately, it also has the disadvantage of being a complicated multicomponent mixture of (highmolecular-weight) aromatic molecules of which an example is given in Figure 4. Our results must therefore be seen as preliminary pointers to a more detailed investigation on specially synthesized single-component versions of this type of high-Tg material that we plan for future work.

Materials. ortho-Terphenyl (OTP) (99%, Aldrich) for calibration runs and analytical methods developments was sealed in aluminum DSC pans and scanned a 20 K/min after a variety of controlled cooling runs up to the maximum value of 80 K/min. One run was also performed on the sample after cooling at the maximum rate possible in the DSC (uncontrolled). For electrospray quenching, a sample was melted in an in-houseassembled electrospray apparatus.57 Initially the electrostatically charged jet of droplets was sprayed into liquid nitrogen, but attempts to collect the quenched powders met with no success. Later, the jet was targeted directly into a liquid-nitrogen-cooled DSC sample pan. After sample collection, the unsealed pan was cold-transferred into the DSC sample holder for immediate scanning from -170 °C to 10-15 °C above the glass transition.7 The great difficulty of performing these low-temperature sample manipulations while avoiding atmospheric water incorporation led to our early abandonment of work on OTP. Instead, the high-molecular-weight polyaromatic substitute described in the previous section was used, so that all manipulations could be made at ambient temperature without loss of the quenched-in state in advance of scanning. This was the highestTg material of aromatic character (and hence high-temperature stability) that we could obtain. It was adopted for its high Tg and availability in melt-spun form, at the expense of sample purity. This material is a synthetic hydrocarbon pitch designated ARA-24, manufactured by Mitsubishi Gas Chemical Company, Inc. and obtained from the Air Force Materials Laboratory in Dayton, OH. It has a softening point between 210 and 260 °C (ASTM method D-3104). The molecular structure is indicated in Figure 3, where it is compared with structures typical of other pitches. ARA-24 is used as a precursor in the production of graphite nodules (for electrochemical cell anodes and cathodes) and carbon fibers (for structural reinforcement applications). Unlike coal-tar and petroleum-based pitches, it is derived from naphthalene and alkylnaphthalene and is essentially an oligomer of polynaphthalene with some high-molecular-weight aromatic ladder-polycyclized portions of the molecule, as indicated in Figure 2. The particular rodlike structure of the molecule makes it, at processing temperatures, essentially a thermotropic liquidcrystalline melt, thus the designation “100% mesophase” given by the manufacturer. We obtained melt-spun fibers of this material from Prof. D. Renneker of the Institute of Polymer Science at the University of Akron (Akron, OH). The fibers cool in air during flight by a combination of collision-exchange with air molecules across and radiation from the enormous surface area that is created when the submicron fibers form. The fibers are collected in air and compacted, and then a small amount is sealed into an aluminum DSC pan for thermal evaluation. Samples of the asreceived pitch, which were in the form of pellets that had cooled rapidly by contact with a water-cooled metal surface, were also studied for comparison. Physical Characterization. Viscosity data for the pitch, obtained in refs 49 and 50 using standard equipment and methods,49-51 are shown in Figure 2 in comparison with the data for OTP and T-R-NB. All thermal characterization was carried out using a PerkinElmer model DSC-7 differential scanning calorimeter. Work on the glassy pitch samples was done in ambient mode with the DSC head’s coldfinger immersed in an ice-water cooling bath. Work on the OTP samples was done in subambient mode with a liquid nitrogen cooling bath. Temperature calibration of the DSC was done by the 2-point method with (a) cyclopentane



Figure 3. Structures of o-terphenyl (OTP) and tri-R-naphthyl benzene (TRNB) and representative structures of two different types of pitches, one from coal tar and the other (studied in this work) from a naphthalene polymerization process (Mitsubishi Chemical ARA-24). The sample studied contains a distribution of such complex molecules. The pitch studied in this work is the synthetic material ARA-24 from Mitsubishi Chemicals.

Figure 4. (a) DSC upscans at the (standard) heating rate, 20 K/min, of two o-terphenyl OTP glasses formed at different cooling rates, -20 and -Q K/min, which is the maximum rate permitted by the instrument. The upper scan is called the standard scan. (b) (Right-hand ordinate) Difference between the two curves of part a shown as curve A. This can be called the excess heat capacity curve and appears as a positive quantity. Its integral gives the excess enthalpy of the quenched glass. Curve B is the difference between the standard scan and the 20-K/min upscan following the fastest controlled-temperature downscan permitted by the DSC instrument, which is -73 K/min. Curve C is obtained by taking the difference between a cooling scan at -10 K/min, less than the standard value, and the standard scan, and of course, it shows a negative displacement. The difference areas (excess enthalpies) are used to obtain the fictive temperatures that are plotted in Figure 5.

and indium as the standard materials in subambient mode of work and (b) indium and lead for the above ambient work. Heat flow calibration of the DSC was carried out using the melting enthalpy of the indium standard. A variety of scan rates were

employed, with higher scanning rates of 20 and 40 K/min being used for smaller samples, as well for specific heat values away from the glass transition. Heating rates of 20 K/min were used as standard in the fictive temperature determinations, based on


Velikov et al.

Figure 5. Scaled Arrhenius plot of the cooling rate for glasses formed at -Q K/min vs the resulting fictive temperature. The scaling parameters are the standard cooling rate (QS ) -20 K/min) and fictive temperature TFS of the standard glass, formed by Q0 cooling. The slope of this plot gives the m fragility index directly. The obtained value 77 is to be compared with the value of 76 obtained from the activation energy for viscosity at Tg in Figure 2 using m ) Ea/2.303RT and the value of 81 obtained from dielectric relaxation data.56 The vertical dashed line is drawn at the scaled fictive temperature of the sample of maximum DSC cooling rate (TFQ/TFS ) 1.104), hyperquenched OTP, which is assessed in the inset (see below). The quench rate for this sample can therefore be obtained as Q ) 105QS, which is 2 × 106 K/min or 6.6 × 104 K/s. The inset shows the definition of the fictive temperature22,23 for the standard scan and the fictive temperature for the hyperquenched OTP glass. The latter is assessed from the upscan exotherm enthalpy, which is obtained from the excess heat capacity curve displayed in Figures 1(b) and 4. As seen in the inset, the fictive temperature of the standard scan coincides (to within 0.2 K) with the glass transition temperature defined by the Cp-onset criterion.36,39

measurement of the release of the frozen-in enthalpy. Scans of 10 K/min were used in some heat capacity evaluations. Samples of pitch fiber with weights between 2.5 and 10.3 mg were sealed in aluminum pans. The weights of the empty and sealed pans were measured to within 0.01 mg, and the sample weight was obtained from the difference. The sample weight for the fiber samples was limited by the ability to compact the fibers into small flakes and the packing efficiency of these flakes. The data were exported in text format by the software operating the DSC and plotted and analyzed externally. Analytical Methods. Here we show, using data for oterphenyl, how the familiar DSC scans can be converted into difference curves from which the fictive temperatures can be quickly assessed. Then, we show how the fictive temperatures can be used (a) to obtain directly an m fragility (steepness index) for the liquid when the cooling rates are all known or (b) to determine an unknown cooling rate when the m value for the substance is already known. Figure 4 shows the DSC heating scans, at 20 K/min, of an OTP sample with the following thermal histories: (a) The sample is “rate-cooled” at 20 K/min through the glass transition (-Q ) -20 K/min) and then, without any annealing, scanned up at +20 K/min to the liquid state above Tg. This down-up sequence is called the “standard scan” and the fictive temperature obtained is the standard value TFS. (b) The sample is “quenched” in the DSC, i.e., cooled at the fastest cooling rate achievable in the DSC in this temperature range and then, without any annealing, scanned up at 20 K/min. Figure 4 also shows, on the right axis (which is twice the LHS scale), the difference between the standard scan and some nonstandard scans with both faster and slower cooling rates.

Curve A is the difference between the standard scan and the DSC-quenched sample, i.e., the difference between the two scans of part a. The area under the difference scan gives the value of the excess frozen-in enthalpy of the quenched sample relative to that of the standard sample, characterized by the standard scan and having the fictive temperature TF0. The value of the enthalpy difference in this case is 1.9 J/g Curve B is the difference between the 20-K/min rate-cooled scan and that for a sample cooled at 73 K/min, the maximum controlled rate of cooling that we could obtain. The excess frozen-in enthalpy for this thermal history of the glass is, of course, still positive, but it is less than in the case of the sample quenched in the DSC (difference curve A). When the cooling rate is lower than the scanning rate, as in the case of scan C, which was cooled at 10 K/min, the difference is negative. This reflects the fact that, at the end of cooling (the beginning of the upscan), the sample has a lower enthalpy value than the standard rate-cooled sample. The area under the difference curve for the DSC-quenched sample (curve A of Figure 4) is used to obtain a fictive temperature, with the Figure 1(b) procedure. The value is found to be 265.1 K, 18.7 K above the standard TF (TFS obtained for the -20/+20 cool/heat history). To convert this TF value to an effective quench rate, we must first obtain a calibration plot. We use the calculated relative excess frozen-in enthalpies from the scans of known cooling rates to construct the plot of log(Q/QS) vs TFS/TF shown in Figure 5. This is an alternative version of the usual plot for determining the activation energy for enthalpy relaxation near the glass transition.36 In the present version, the slope is actually the fragility index m,55,56 and the activation energy can be calculated


Figure 6. Raw data for electrospray-quenched OTP, showing initial 20-K/min upscan and immediately succeeding 20-K/min upscan after 20-K/min rate cooling.

by multiplying m by RTFS ln(10). A peculiar feature of this representation of the kinetic nature of the calorimetric glass transition is that the other constant in this linear plot also equals m. All lines, arising from liquids of different fragilities mi, pass through the point (1, 0) (which refers to the particular glassy state chosen as the standard or reference glass) and have negative slopes of value m. From the data of this study, we derive a value of m for OTP of 77. This is identical, within uncertainties, to the value of 76.5 derived from the viscosity data of Figure 2, and close to the literature value of 81 (cited in ref 56), which is derived from specific heat spectroscopy data. Note that relaxation data for a variety of liquids can be assembled on this same plot. Because they share a common point at the reference value, the plot will be the enthalpy relaxation time equivalent of the common fragility plot. In this case the relaxing quantity that classifies the liquids between strong and fragile is the fundamental quantity used in the description of the energy landscape itself. Such a plot has advantages that we will exploit in future work. Using this plot, with the reference cooling rate QS of 20 K/min (and with some assurance from Figure 2 that an Arrhenius slope for the relaxation time is a good approximation for some distance above Tg), we can now deduce the cooling rates of unknown samples from their measured excess enthalpies. For instance, for the sample quenched in the DSC (Figure 4, curve A), we obtained the fictive temperature of 247.0 K, implying TF ) 1.014TFS. Using this value to find the x coordinate in Figure 5 for the quenched sample (marked by the dashed vertical line), we obtain the value of Q, the cooling rate experienced by the sample during the quench. From the intercept logQ/QF ) 1.09, we obtain Q ) 247 K/min, which, from prior experience and observation, accords well with the expected maximum cooling rate of this particular DSC apparatus for subambient cooling with a liquid nitrogen filled tank (manufacturer quotes 300 K/min). Thus, we establish this particular type of fragility plot as a calibration curve for converting experimentally recorded relaxation enthalpies to the corresponding fictive temperatures and cooling rates. We now use this as a tool to analyze the data on the electrosprayed OTP sample. Results In Figure 6, we show the 20-K/min upscan for the electrosprayed OTP sample and compare it with the subsequent +20 K/min scan after cooling from above Tg at -20 K/min. The latter is completely normal and comparable to the -20/+20


Figure 7. Excess heat capacity of hyperquenched glass compared with curves from Figure 4 for lower cooling rates. Note very low-temperature onset of exothermic release of trapped-in enthalpy.

scan of Figure 4. This indicates that the pen upswing after passing Tg on the initial scan is due to the proximity of the ice melting point and to the fact that the open sample pan from the electrospray sampling process was heavily contaminated with condensed moisture. Hence, the post-Tg behavior is to be ignored, and the behavior in the vicinity of Tg is to be treated with caution. The presence of a strong exotherm, however, is certain. When an adjustment of the slope of the hyperquenched sample scan is made so that the coincidence at low temperature is maintained but the difference at the end of the glass transition is eliminated, the difference scan obtained from the Figure 6 data bears a systematic relation near Tg to those of the slower quenches seen in Figure 4b. The relation is shown in Figure 7. This comparison shows the major effect of very fast quenchingsan effect that has been seen in previous studies on other glass formers (to be discussed below) but that is now seen for the first time for a fragile example. Whereas the (quantitatively uncertain) behavior of the excess heat capacity in the vicinity of Tg is a continuation of the Figure 4 trend, the development of a broad peak with a maximum around -60 °C and the very much earlier start (approximately -100 °C) of the enthalpy recovery, are striking distinctions. The very early onset of relaxation, and the broad low-temperature peak in the excess heat capacity have both been seen in previous studies of fast-quenched glass samples.25,30 As discussed later, they contain information on the depth and distribution of the traps in configuration space at the higher levels on the energy landscape. From the excess heat value obtained by integration, we derive, via the Figure 1(b) construction (see Figure 5 inset), a fictive temperature for the electrosprayed sample of 1.076TFS. Using the Figure 5 calibration plot, we find that this result corresponds to a Q/QS value of 105.4, or a quench rate of ∼105 K/s. Although this result suffers from uncertainty because of the adjustments needed for the initial scan in Figure 6, it is comparable to values from other droplet quenching techniques.24 When improvements currently in progress with the method of collecting quenched droplets are completed, the quench rate obtained will be determined more reliably and the rate will also be increased. Meanwhile, sealed-sample studies on melt-spun pitch fibers of much higher Tg values provide needed comparisons. Figure 8 shows the calorimetric behavior of the as-supplied pitch fiber material. The upper curves marked A and B are representative of the heat capacity of the initial scans of two


Velikov et al.

Figure 8. Calorimetric behavior of two as-received ARA-24 pitch bulk samples. Initial scans show a substantial exotherm despite the fact that the sample was cooled without quenching, which was unexpected. The scan with the reduced exothermic effect is for a sample sealed in the pan under a nitrogen blanket to avoid a significant exothermic contribution from trapped air oxidation of the pitch. The upper scan is therefore the only one relevant to the present application. The lower section of the figure shows the difference between the initial and immediate rescan, called the excess heat capacity of the initial scan. The fictive temperatures obtained from the integrals of the excess heat capacity by the method of Figure 1b are marked on the upper curves with question marks, for reasons explained in text. These data pointed up the trapped air oxidation problem, which became more marked in the study of melt-spun (high-surface-area) pitch presented in Figure 9.

bulk samples the histories of which will be explained in the discussion below. Immediate repeat scans consistently show that the “jump” in the heat capacity through the glass transition is small relative to the glassy value, as in the cases of many polymeric glass-forming materials in comparison with, for instance, OTP (Figure 4). The difference between the rate-cooled repeat scan (reheated at the same rate as cooled) and the initial scan gives the difference scan, which, until now, has described the relaxation of the excess enthalpy. The area under the curve gives the value of the excess enthalpy immediately before the beginning of the upscan, and from this value, a fictive temperaturesthe effective glass transition temperature for the particular thermal history of the samplesis calculated according to the construction in Figure 1B. The fictive temperatures so obtained are marked in Figure 8 with question marks, because for curve A in particular, the value is unexpectedly high. Some other source of enthalpy release was indicated, either physical resulting from highpressure extrusion effects or chemical. That it is chemical rather than physical in origin is indicated by the difference between samples A and B, which differed only in that sample B was sealed in its pan under a nitrogen blanket. This suggests that air oxidation even in the vicinity of Tg, might be a source of enthalpy release that would then cause fictive temperatures deduced from the data to be spurious. The problem is emphasized in the subsequent study of the fibers in which the surface available for oxidation is much greater, making the effect much more sudden. In Figure 9, we show the initial scan and the rescan of two samples of the melt-spun fibers prepared from the same grade pitch. Here, sample D was sealed in its pan under dry nitrogen. The initial scan labeled C is displaced down by 0.5 J/(g K) for clarity of presentation. The difference scans are plotted below. The maximum temperature in the initial scan was not allowed to go above 240 °C, the top of the glass-liquid transformation range of the bulk material, to avoid any artifacts from the collapse of the fibers and reduction in the surface area. The

Figure 9. Initial scan and rescan of two samples of melt-spun ARA24 pitch, the sample C pan being sealed in the open and the sample D being sealed in a dry-nitrogen-filled box. The difference in the excess heat capacities is shown in the lower part of the figure. The sharp exotherm seen in the case of sample C is assigned to reaction with air oxygen sealed into the pan. This reaction also explains the difference between the initial scans of bulk samples A and B seen in Figure 8. Only the data of sample D are considered further in Figure 10.

rescanned fibers show the same low temperature behavior as the as-spun fibers and the same glass transition temperature range as the bulk sample. The initial scan in the case of the sample labeled C shows a very pronounced exothermic peak, which would imply an exceptionally high fictive temperature by the Figure 1B construction. It is much stronger than in the case of sample D or the case of the exotherms for the bulk material samples in Figure 8. This uncharacteristic peak, together with the quite unexpected fictive temperature implied by the total enthalpy release in the unquenched bulk sample sealed under air, confirms a nonrelaxational origin for the sharp component of the Figure 9 exotherm. Indeed, a search of the literature on these materials reveals58 that these pitch materials will react with oxygen to



TABLE 1. glass

preparation

OTP mesophase pitch (s.#D) Zr100-XCuX Pd77.5Cu6Si16.5 Pd77.5Cu6Si16.5 Pd48Ni32P20 Na2O-CaO-SiO2 glass (NBS710)

Q ref (K/s)

Tg (K)

∆Cp(Tg)

∆H

droplet fiber

- ∼105 ?

splat quench bulk quench ribbon spinning ribbon spinning fiber drawing

60 ? 680-760 4-5 cal/(mol K) 50-100 cal/mol 30 ∼103 636 ∼2 cal/(mol K)c 105-135 cal/mol 30 ∼106 636 ∼2 cal/(mol K)c 190 cal/mol 30 ∼106 585 ∼2 cal/(mol K)c 250 cal/mol 25 1473a

246.4 456

0.49 J/(g K) 0.17 J/(g K)

8.5 J/g 11.3 J/g

TF (K) 265.1 528 varies with X 689-704 731 685

a From quoted VFT parameters B and T according to the relation m ) 16 + 590B/[T ln(10)].66 0 0 of the liquid-glass heat capacity difference according to the authors.

cross-link the aromatic molecules and that this is a technical advantage of the Mitsubishi material for graphite fiber production. Such a chemical effect explains the difference between samples sealed under air and under nitrogen. The area difference corresponds well with estimates of the enthalpy of oxidation that would be permitted by the small amount of oxygen sealed into the pan, of course, seen only in the initial scan. Using only the data for the nitrogen-protected sample, we find by the Figure 1b construction, the more reasonable fictive temperature listed in Table 1. The value found, 1.16Tg, is comparable to values deduced for some hyperquenched metallic glasses discussed in the next section. It should be regarded with some caution and treated as an upper bound. It is also to be seen as an encouragement to extend this type of investigation to other high-Tg fragile liquids. Discussion It is of interest to compare the results obtained for the two molecular liquids of this work with those from previous studies on other systems. Most previous work on rapid quenching was performed on metallic glasses and was driven by the shortage of alternative methods of forming them. We examine two of the cases in which a conscious effort was made to characterize the frozen-in state obtained calorimetrically and the more recent case of a model silicate glass studied by Huang and Gupta.25, In none of these early cases was the method of the present paper applied to the observations, so neither fictive temperatures nor cooling rates have been obtained from the products of the quenched materials themselves. (Frequently, these are estimated using other routes.)59 The two metallic glass cases we consider are (i) the study on Zr-Cu glassy alloys prepared by Giessen and co-workers60 and (ii) the earlier study of Pd-Ni-P and Pd-Cu-P glasses by Chen and Coleman.30 The former was based on splat-cooled materials, and the latter employed centrifugal melt spinning, which is considered faster. Chen and Coleman estimated their cooling rates to be on the order of 106 K/s. The results of Kearns et al.60 are presented qualitatively by the authors, with rough estimated values of parameters such as (1) ∆Trelax, which is the observed temperature interval in which Cp(t) shows a negative (exothermic) deviation from the value for an annealed sample; (2) ∆Cp,relax, the magnitude of this deviation; (3) ∆Cp(Tg), which is the heat capacity step change at Tg and has the value 4-5 cal/(mol K); and (4) a rough estimate of the total frozen-in enthalpy relaxation ∆Hrelax, which was 50-100 cal/mol. Adding their range of quoted values of Tg, we obtain, by using the most simple approximate equation for the fictive temperature

TF(Q) ) TFS + ∆Hrelax(Q)/∆Cp(Tg)

b

∆TF ) TF - Tg (K) 18.7 72 10-25 53-68 95 100

TF/Tg

fragility m value

1.076 1.16

77a 70a

1.013-1.033 1.11 1.15 1.17

35-40b 52 52 41 20a

From a compilation in ref 33. c Average value

a range of possible values of TF(Q) and a corresponding range of values for TF(Q)/TFS. The results are presented in Table 1. The values of ∆TF ) 10-25 K and TF/Tg ) 1.013-1.033 obtained in this way are small compared to those evaluated in the present and earlier works. Assuming adequate calorimetry, it appears that splat quenching is not very effective, particularly as the Zr-Cu glasses are quite strong in character.33 The data of Chen and Coleman30 are much more detailed and systematic. Their method of data presentation is similar to ourssplotting both the heat capacity scans and the exothermic difference peaks that represent the relaxation of the frozen-in excess enthalpy. From their tabulated data (using only the experimental data, free of their model assumptions), we arrive at the TFS values, calculated by the approximate equation listed above, shown in Table 1. They are comparable to the results of the present study. In particular, the value of the ratio TF/TgS, 1.11-1.17, is close to or above the value obtained by us for the pitch fibers, namely, 1.16. For equivalent quenches, a larger value could be expected on the basis of the lower fragility of these metallic glasses. A significant observation of both metallic glass studies is the very wide range of detectable enthalpy relaxation. It starts some 100 K below Tg in the case of the merely fast-quenched Zr-Cu alloys of Kearns et al. and almost 200-275 K below Tg in the case of the ultrafast-quenched metal-metalloid glasses of Chen and Coleman. The case studied by Huang and Gupta25 is clearer because the base glass is one of the industry standards and is extremely well-characterized (NBS-710, soda lime silica glass). The quenching was achieved in the standard glass fibering process, and the fine fibers are known to be subjected to cooling rates on the order of 105 K/s (see also ref 59). To compare the behaviors of metallic and silicate glasses with that of our molecular glasses, we construct a Tg-scaled plot showing the dependence on temperature of the excess enthalpy release rate dHex/dT (i.e., our excess heat capacity plot of Figure 4) and present the data in Figure 10. Figure 10 shows that, relative to Tg, the enthalpy relaxation commences at the lowest temperature,

Molecular Glasses with High Fictive Temperatures for Energy

Recommend Documents