18550
J. Phys. Chem. 1996, 100, 18550-18553
Glass and Crystal Formation in Binary Aromatic Mixtures: A Mechanism for Reducing Spin-Lattice Relaxation Times Wei Wang, Ronald J. Pugmire,* and David M. Grant* Departments of Chemistry and Chemical and Fuel Engineering, UniVersity of Utah, Salt Lake City, Utah 84112 ReceiVed: July 25, 1996X
The phase diagram constructed from differential scanning calorimetry data indicates that the binary mixture of dibenzofuran (DBF) and hexamethylbenzene (HMB) forms a simple eutectic system. Comparative studies of proton T1 values for the annealed and quenched samples show the annealed material can be best described as a two-phase mixed crystals, while a rapidly quenched sample is a combination of a metastable one-phase glass and two-phase mixed crystals. It is found that glass formation is the key to the T1 reduction of DBF in the HMB doping technique reported previously. The interesting trends in the T1 and the relative spin population of DBF is explained with the competition between glass formation and crystalline phase separation.
Introduction Structures and properties of a composite material are important topics in material science and technology. An important example is the study of the miscibility and compatibility of polymer blends by various physical techniques including solidstate NMR.1 However, the compatibility of small organic molecules in solid mixtures has not been extensively studied, although they represent well-defined model systems and information about their miscibility certainly would contribute to a better understanding of larger and more complex polymeric blends. We reported recently2 that for organic mixtures, a compound with short proton spin-lattice relaxation times (T1 ) could shorten, by 2 orders of magnitude, the very long T1 in an aromatic compound. Due to improved intermolecular proton spin diffusion, such relaxation agent doping allows many previously inaccessible rigid-lattice aromatic compounds to be studied by this proton-enhanced 13C solid-state method. These improvements, used with the 2D magic angle turning (MAT) experiment,3 provide for the first time the principal values of the chemical shift tensors in this class of compounds. Such three-dimensional anisotropic chemical shifts yield additional chemical insight into the molecular4 and electronic structures.5 Although this doping technique had been shown to be highly beneficial, the detailed relaxation mechanism remained unclear. A common belief, for example, is that the solid binary mixture must be a solution in order to achieve the intimate molecular mixing that facilitates efficient intermolecular spin diffusion. In the present work, it is shown that metastable glass formation may play a key role in the proton T1 reduction of rigid aromatic molecules. Experimental Section Preparation of Samples. Dibenzofuran (DBF) was obtained from Aldrich (99+%), and hexamethylbenzene (HMB) from Kodak (99%). Both were used as received. Weighed samples of DBF and HMB are mechanically mixed in a Pyrex test tube to give various mole ratios and then submerged into a large oil bath maintained at 175 °C. When a clear miscible liquid melt is obtained after heating for a short period of time, the hot melt is briefly vortexed to maximize sample dispersion. To cool the hot homogeneous liquid solution slowly, the heating element X
Abstract published in AdVance ACS Abstracts, October 1, 1996.
S0022-3654(96)02270-8 CCC: $12.00
of the oil bath was simply turned off, and the bath and sample allowed to cool with a typical rate of approximately 0.021 °C/ s. To cool the hot liquid solution quickly, the hot melt was poured onto a heavy copper plate in thermal equilibrium with liquid nitrogen. To anneal the quenched sample, the solid blends are first kept at 80 °C for 6.5 h and then cooled to the ambient temperature at a rate of 0.007 °C/s. DSC Measurement. A Shimadzu DSC-50 differential scanning calorimeter, DSC, was used to determine the temperature of fusion for various DBF-HMB solid mixtures. A typical sample was 3 mg, and scanning was over the range 25-180 °C with a heating rate of 0.167 °C/s. NMR Spectroscopy. All of the NMR relaxation measurements were carried out on a CMX-100 spectrometer (13C Larmor frequency of 25.152 MHz), equipped with an Otsuka Electronic’s (Fort Collins, CO) 7.5 mm 13C/1H double-tuned probe with a γB2 of 62.5 kHz. The proton T1’s of DBF were measured via the 13C detected CP/MAS comb-pulses-saturationrecovery pulse sequence. Since a measurement of the proton T1 on a given sample usually takes about 12 h to complete, the order of the delay time, τ, was randomly scrambled and experiments were interleaved to minimize the influences of short-term fluctuations and long-term drifting of certain variables (e.g., temperature, magnetic field, RF gain, etc.), that could affect the 13C resonance intensities. Results and Discussion Equilibrium Phase Diagram. The fusion temperatures on the heating curves were used to construct the phase diagram shown in Figure 1. It is observed that the equilibrium phase diagram of a binary DBF-HMB mixture is a eutectic system with a polymorphic transition of solid HMB at 114 °C. The eutectic temperature at 72 °C is constant for all compositions of the binary mixture. The eutectic point appears in the vicinity of χHMB ) 0.25-0.28. There are no detectable one-phase areas near either the pure DBF or HMB vertical lines. Thus, the binary system would appear to be a simple eutectic system without appreciable formation of solid solutions. To understand the phase behavior of the binary aromatic hydrocarbon mixture on cooling from a completely miscible and homogeneous melt, it is instructive to follow three isocomposition lines (1, 2, and 3 in Figure 1) for two kinetic scenarios: slow cooling and fast cooling. Slow Cooling. Line 1 has a mole ratio (DBF:HMB) of 7:1, i.e., χHMB ) 0.125. At point a, DBF and HMB form a © 1996 American Chemical Society
Binary Aromatic Mixtures
Figure 1. Equilibrium phase diagram of a DBF-HMB binary system as measured by DSC. TDBF and THMB are the melting points of DBF and HMB, respectively. TE is the eutectic temperature, and TP is the polymorphic transition temperature of HMB.
homogeneous, one-phase liquid melt. On slow cooling to point b, DBF begins to crystalize and the liquid becomes more concentrated in HMB. At this point the system is in a solidliquid, two-phase equilibrium. Further cooling yields more DBF crystals, and the composition of the liquid follows the DBF liquidus line until it reaches point f, the eutectic point, where the first crystal of HMB forms. The three phases (the pure DBF crystal, the liquid melt, and the pure HMB crystal) coexist together at this point. The remaining degree of freedom at this point is the pressure. When the temperature is lowered below the eutectic temperature, all HMB and DBF solidify to form an ordered, two-phase mixture of the two crystals. The overall mole fraction of HMB is, of course, at the initial 0.125 value for the mixed crystals. Line 2 starts at point e, with the homogeneous binary liquid with a composition of χHMB ) 0.25. On cooling to the point f, at or near the eutectic point, both DBF and HMB start to crystallize out of the liquid solution simultaneously, again creating the coexisting three-phase system. Note that the liquid should be most viscous at the eutectic point since it is the lowest temperature obtainable for any liquid state in this system. On further cooling to point g, only the heterogeneous two-phase mixture of crystals of DBF and HMB exists, with an overall composition of χHMB ) 0.25. Line 3 is similar to line 1, except on reaching point i, it is now the high-temperature form II of the HMB crystal that precipitates from the liquid solution. On further cooling to point j, the lower temperature crystals, HMB I, begin to form at the expense of HMB II, and the liquid solution has followed the liquidus line to the peritectic triple point. Further cooling deposits only HMB I and the melt moves on to the eutectic point. Fast Cooling (Quenching). Line 2 is first examined in the limit of fast cooling. As the temperature suddenly drops to point f and below, DBF and HMB tend to crystalize separately from the liquid solution, but with rapid cooling at this temperature, the higher viscosity hinders the diffusion needed to obtain pure crystals.6 Thus, while nucleation of pure crystals still continues to occur, the crystal growth slows to be comparable with the process of freezing out of a disordered, amorphous glass. This glass coexists in a metastable condition with the two mixed crystals. In an idealized, extremely fast cooling experiment, only a 100% single-phase metastable binary glass would form.
J. Phys. Chem., Vol. 100, No. 47, 1996 18551
Figure 2. Modeling the proton T1. The open circles are the experimental magnetization, while the solid line is the single-exponential fit and the dotted line is the double-exponential fit.
For a cooling rate of 100 °C/s achieved in this work, however, the competition between separation by crystallization and glass formation makes the final solid mass a mixture of a binary glass and two pure crystals. Note, at the eutectic composition, glass formation tends to maximize while crystallization is less dominant. Corresponding arguments can be made for line 1 and 3 at quenching, with the resultant solid mass also consisting of binary glass plus mixed crystals. The portions of mixed crystals relative to glass are higher both for lines 1 and 3 than for 2, due to the increased tendency of pure crystal formation at these compositions. NMR Data Reduction. A DBF molecule has four chemically inequivalent protons and six chemically inequivalent carbons. However, a CP/MAS spectrum resolves only four carbon lines (of relative intensity 1:2:2:1); the two middle lines are each doubly degenerate pairs of carbon lines.2 The intensity of each 13C resonance line is plotted vs the variable delay τ specified in Figure 2 to give the typical growth curve shown in Figure 2. To extract the proton T1 values, the data were fit by both a single-exponential (eq 1) and a double-exponential (eq 2) model:
M(τ) ) M∞[1 - exp(-τ/T1)] + Mres1
(1)
M(τ) ) M∞A[1 - exp(-τ/T1A)] + M∞B[1 - exp(-τT1B)] + Mres2 (2) where M(τ) is the proton-enhanced 13C magnetization at a given τ. Equation 2 is designed to characterize two linearly independent terms involving spin ensembles A and B. M∞A is the equilibrium magnetization of the A spin with a characteristic spin-lattice relaxation time constant T1A; similarly, M∞B and T1B are the corresponding values for spin B. The fitting procedure for the A and B spins produced the best-fit proton T1’s (which are the weighted average of all the proton relaxation time constants arising from the A and B spin ensembles) and their relative population fractions M∞A/(M∞A + M∞B) and M∞B/ (M∞A + M∞B). The residual values Mres1 and Mres2 measure the difference between the data and predicted values for the respective single- and double-exponential relaxation models. The double-exponential model applies only for quench-doped mixtures. The sum of the squares, ΣM2res, measures the success of the overall fit in either model. For the quenched mixtures, it is
18552 J. Phys. Chem., Vol. 100, No. 47, 1996
Wang et al. TABLE 1: Effect of Annealing on T1 (s) of the Quenched Samples pure DBF
χHMB ) 0.125
χHMB ) 0.250
χHMB ) 0.500
26.3 ( 5.5 31.1 ( 6.7 28.9 ( 6.9 quenched short T1a 370 ( 55 490 ( 39 long T1a 1542 ( 63 545 ( 63 annealed and 1542 ( 63 871 ( 27 839 ( 40 861 ( 14 slowly cooled
Figure 3. (a) Two proton T1’s of quenched DBF in HMB are obtained from fitting the experimental relaxation data using a double-exponential model. (b) Relative spin populations of DBF obtained by fitting the experimental relaxation data using the double exponential model. In both curves the open circles apply to the short T1 component that may be associated with DBF in the glass. Conversely, the filled circles denote the long T1 component associated with DBF in the mixed-crystal portion of the samples.
found that the experimental relaxation curves are fit much better by a double-exponential model than by a single-exponential model (e.g., the sum of squared residual in Figure 2 was 17.6 for the double-exponential model vs 313 for the singleexponential model). The four 13C detected proton T1’s are then weight averaged to yield a single-proton T1 for spin A and B, respectively. NMR Relaxation Data on the Quench-Doped Mixtures. In light of the above discussions of the phase diagram given in Figure 1, it is easy to understand the proton spin-lattice relaxation profile as a function of χHMB, shown in Figure 3. For pure DBF, the relaxation data can be best fit with a single long relaxation time (T1 ) 1542 ( 63 s at 2.35 T)5 that reflects both a rigid-lattice structure and the absence of any intrinsic relaxation centers. On doping DBF with HMB, a new spin population emerges with a very short proton T1 for DBF. This new spin population is attributed to the homogeneous glass phase with a frozen liquid-like amorphous structure. The average distance between the nuclear spins in the respective DBF and HMB molecules is much shorter in the single phase glass than in a mixture of the two pure crystals. These shorter distances make proton spin diffusion7 much more efficient in the glass phase, resulting in a much shorter proton T1 of DBF spins. The long T1 spin population of DBF, attributable to the two-phase mixed crystal, has a longer T1 compared with the glass phase due to its crystalline nature. However, the T1 value for the mixed crystal is still shorter by a factor of 2 or 3 compared with the pure DBF, indicating that doping introduces HMB crystallites into the vicinity of DBF crystallites. The average separation in the mixture of finely divided crystals, although larger than that of the glass, is short enough to allow some intercrystalline spin diffusion to occur, albeit with considerably reduced efficiency compared to that in a metastable glass. As the composition of the mixture moves from pure DBF toward the eutectic point, the proton T1 value for the DBF spins
in the glass phase remains constant (Figure 3a) but its relative population climbs from 0% at the pure DBF to 31% near the eutectic point where χHMB is about 0.25 (Figure 3b). This observation is consistent with the proposal that glass formation is the easiest in the vicinity of the eutectic points. A 5-fold reduction, though smaller than that of the glass, is also noted in the proton T1 value of DBF spins in the mixed-crystalline phase when compared with the T1 value of the pure DBF; nonetheless the population of DBF decreases from 100% in the neat compound to 69% around the eutectic point. As samples with compositions in the vicinity of the eutectic point have the most favorable composition for glass formation, it is not surprising that the highest signal-to-noise ratio of the DBF spectra2 occurs around this same 3:1 DBF:HMB composition. The signal intensity measures the population of observable spins. With a pulse recycling delay of 80 s, only the spins from the glass phase contributed to the DBF signal. The mixedcrystal phase, although dominating the total spin population, is saturated by the RF pulses and does not contribute to the intensity of the carbon signals arising from the glass phase at short delay times. As the delay time is increased a contribution from the mixed-crystal phase becomes apparent as noted in ref 2. Above the peritectic composition appearing at about χHMB ) 0.45, the HMB II crystals precipitate rapidly from the melt. This competing process decreases the availability of HMB before the DBF-HMB glass can form and the relative amount of the long T1 component has a population of about 80% (Figure 3b). Below the peritectic point but above the eutectic point, the amount of glass, or short T1 component, increases accordingly as the composition moves from right to left toward the eutectic point (Figure 3b). A relatively unchanged value for the shorter T1 population of DBF indicates that the glass phase has essentially the same overall composition even though the overall DBF composition changes dramatically over this range. Effect of Annealing on Quenched Samples. To reduce the T1 effectively, one needs to rely on the favorable kinetics of glass formation. It is observed that both short and long T1 values in quenched samples vary according to their compositions (Table 1). This demonstrates that glass formation and smaller crystal domain size depend on the sample composition. When rapidly quenched, solid mixtures are subjected to annealing at 80 °C and subsequently cooled slowly, one observes that the annealed mixture can no longer be described by the double-exponential model. Instead, the single-exponential relaxation is sufficient once again to describe the proton T1, and the characteristic T1 values fall within 857 ( 27 over the range of samples with χHMB equal to 0.125, 0.250, and 0.500. Annealing of rapidly cooled samples destroys the glass phase and allows smaller crystal domains to grow toward the size found at thermodynamic equilibrium. Therefore, the previous two spin populations associated with the combined glass and mixed crystal system convert into the mixed crystal system with a single constant T1 as a function of χHMB. The single T1 values of either the slowly cooled and/or the annealed mixture are uniform across a wide range of compositions. The equilibrium phase diagram (Figure 1) dictates that no stable solid solution will form at these three compositions (χHMB ) 0.125, 0.250, 0.500). Hence, the
Binary Aromatic Mixtures uniformly single T1 values suggest that the slowly cooled and the annealed samples are both two-phase mixed crystals, rather than one-phase solid solution. It also suggests that intercrystalline spin diffusion in the mixed crystals exists between finely divided particles, and its effect is to reduce the proton T1 by a factor of 2. The annealing process provides a clear description of possible relaxation mechanisms, important in relaxation doping techniques, from either a solid solution or from glass formation. Although both solid solutions and glasses share some common features, e.g., they are both one-phase and homogeneous in their physical properties,8 and they both may have variable compositions, they do differ in the following ways. A substitutional solid solution implies long range ordering of the lattice sites, i.e., an AxB1-x solid solution has a lattice array of a B crystal, and at each lattice point, the chance of finding an A is given by the subscript x. Solid solutions are somewhat similar to a stoichiometric cocrystal but differ from such cocrystals in that x may vary over a narrow range. The formation of a substitutional solid solution usually requires the crystal lattice structure of pure A and pure B to be similar,9 a condition not satisfied in the DBF-HMB binary system.10 Finally such solid solutions are thermodynamically stable and have an identifiable one-phase region in an equilibrium phase diagram. By contrast, a glass does not imply any lattice ordering; it is an amorphous array, more like a typical liquid, in which only short-range ordering is found. A glass is thermodynamically metastable and will be destroyed by annealing, which increases the longrange order. Since it is usually rare to find a dopant with similar crystal structure as the molecule of interest, one seldom encounters a binary substitutional solid solution. Admittedly, such systems would provide a very effective way to reduce T1. The study of this particular binary system allows us to formulate a strategy for selecting a suitable relaxation doping agent. First, the dopant must have a short T1 and a higher melting point than the compound to be doped. The high melting point of a dopant pushes the eutectic point away from the dopant toward the pure compound of interest. Fortunately this minimizes the dilution effect of the dopant and preserves the signal intensity of the compound of interest. Second, one may locate the eutectic composition from an equilibrium phase diagram and the glass formation is maximized near this eutectic point. Third, the eutectic melt should be quenched as rapidly as possible to maximize glass formation. Conclusion The equilibrium phase diagram of the DBF-HMB binary system provides an explanation of the solid-state NMR relaxation data of a quenched binary mixture of DBF and HMB. It
J. Phys. Chem., Vol. 100, No. 47, 1996 18553 is found that metastable glass formation becomes the key to the T1 reduction of DBF in the HMB doping technique. The somewhat unusual but interesting T1 and relative spin population curves may be explained with a hypothesis of competition between glass formation and crystal phase separation. As the composition of the mixture gets closer to the eutectic point, it becomes easier for the glass to form, and therefore a larger glass spin population is observed with uniformly shorter T1 values. Accordingly, as one approaches the eutectic point, it becomes more difficult for the individual crystal to grow, thereby partially blocking the phase separation. The mixed crystals exhibit a reduced T1 and lower population. Such relaxation data demonstrate that solid-state NMR can characterize intermolecular interactions in composite materials for distances comparable to the spin diffusion length of a few nanometers. Acknowledgment. We would like to thank Dr. Craig Young for a generous loan of the Shimadzu DSC-50 used in this work. W.W. is appreciative of Prof. Ying Wang for an early introduction to phase phenomena. This work is supported by PETC in the Department of Energy under the Consortium for Fossil Fuel Liquefaction No. DE-FC22-93PC93053 and by the Office of Basic Energy Science of DOE under Grant DE-FG0294ER14452. References and Notes (1) For example: (a) White, J. L.; Mirau, P. Macromolecules 1993, 26, 3049. (b) Caravatti, P.; Neuenschwander, P.; Ernst, R. R. Macromolecules 1985, 18, 119. (c) McBrierty, V. J.; Douglass, D. C.; Kwei, T. K. Macromolecules 1978, 11, 1265. (2) Wang, W.; Hu, J. Z.; Alderman, D. W.; Pugmire, R. J.; Grant, D. M. Solid State NMR 1995, 5, 257. (3) (a) Gan, Z. J. Am. Chem. Soc. 1992, 114, 8307. (b) Hu, J. Z.; Wang, W.; Liu, F.; Solum, M.; Alderman, D. W.; Pugmire, R. J.; Grant, D. M. J. Magn. Reson. A 1995, 113, 210. (4) Wang, W.; Phung, C. G.; Alderman, D. W.; Pugmire, R. J.; Grant, D. M. J. Am. Chem. Soc. 1995, 117, 11984. (5) Wang, W.; Alderman, D. W.; Facelli, J. C.; Pugmire, R. J.; Grant, D. M., manuscript in preparation. (6) Murthy, S. S. N.; Kumar, D. J. Chem. Soc., Faraday Trans. 1993, 89, 2423. (7) Bloembergen, N. Physica, 1949, 15, 386. Abragam, A. The Principles of Nuclear Magnetism; Clarendon Press: 1961. (8) Homogeneous or heterogeneous physical properties are relative depending on the scale of the physical interactions. In this work, the major gauge of the scale is the proton spin diffusion length. Short T1 values in DBF indicate that DBF and HMB mix intimately for intermolecular distances at the nanometer scale. This dimension approximates the mean proton diffusion length for this system within an order of magnitude. (9) Kitaigorodsky, A. I. Molecular Crystal and Molecules; Academic Press: New York, 1973. (10) (a) Brockway, L. O.; Robertson, J. M. J. Chem. Soc. 1939, 1324. (b) Banerjee, A. Acta. Crystallogr. 1973, B29, 2070.
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