Molar Volumes of Ethylcyclohexane and Butyronitrile Glasses

Aug 6, 2013 - ABSTRACT: Molar volumes (Vm) of vapor-deposited ethylcyclohexane. (ECH) and butyronitrile (BN, sometimes called butanenitrile) glasses ...
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Molar Volumes of Ethylcyclohexane and Butyronitrile Glasses Resulting from Vapor Deposition: Dependence on Deposition Temperature and Comparison to Alkylbenzenes Hideyuki Nakayama, Kio Omori, Katsunobu Ino-u-e, and Kikujiro Ishii* Department of Chemistry, Gakushuin University, 1-5-1 Mejiro, Toshimaku, Tokyo 171-8588, Japan S Supporting Information *

ABSTRACT: Molar volumes (Vm) of vapor-deposited ethylcyclohexane (ECH) and butyronitrile (BN, sometimes called butanenitrile) glasses were studied as a function of deposition temperature (Td). ECH glasses deposited at Td sufficiently below their glass-transition temperature (Tg) exhibited changes in Vm on heating similarly to alkylbenzenes. At Td close to Tg, ECH formed dense glasses as alkylbenzenes do, although these glasses were only slightly more dense than its supercooled liquid (SCL) states at the same temperatures. For BN, no indication of the formation of dense glasses was observed even at Td close to Tg, and the variations in Vm with the temperature elevation were different from those of alkylbenzenes. Analysis of the initial Vm of the deposited glasses of different compounds demonstrated that its Td-dependence was well correlated with the steepness index (m) of the corresponding SCL. Quantum-chemical calculations concerning dimer formation by the studied compounds showed that the hydrogen bond between a C−H bond in the alkyl group and π-electrons in the phenyl ring stabilizes the alkylbenzene dimers, suggesting the possibility of the dense glass formation and large m of these compounds. The small m value of BN was also discussed on the basis of the calculation results.

1. INTRODUCTION Vapor-deposition is a potentially useful method of generating functional molecular films in a wide variety of material preparation processes.1 Several molecular glasses prepared by vapor deposition have recently attracted significant interest, since their properties differ from those of glasses prepared by the standard liquid-quenching method. Both indomethacin (IMC) and tris-naphthylbenzene (TNB) have been reported to form glasses with a lower enthalpy than liquid-quenched glasses following vapor deposition at temperatures approximately 15% below their glass transition temperatures (Tg).2,3 Toluene (TL), ethylbenzene (EB),4−7 nifedipine, felodipine, and phenobarbital8 have also been reported to form low-enthalpy glasses by vapor deposition at temperatures slightly lower than the Tg of each compound. Such glasses are sometimes called ultrastable glasses (USG), because ordinary glasses typically require thousands to millions of years to transform into the corresponding physical structure as the result of standard aging processes.9 We have studied the properties of vapor-deposited glasses of TL, EB, propylbenzene (PB) ,and iso-propylbenzene (IPB),and found by analyzing the laser-light interference in the resulting film samples that the molar volume (Vm) of the glasses immediately after the vapor deposition strongly depends on the deposition temperature (Td).10,11 Interestingly, glasses of EB, PB ,and IPB deposited at temperatures in the vicinity of 0.9Tg had Vm values below those expected for the supercooled liquid (SCL) state of each compound at the same temperature.11,12 We consider that the formation of such dense glasses may © 2013 American Chemical Society

involve some molecular processes which are similar to those associated with the formation of USG characterized by low enthalpy. However, it is still not clear whether USG and dense glasses can both be regarded as belonging to a common class of materials. Chen and Richert have investigated the fragility and other physical properties of the SCL states of organic compounds which are capable of forming USG by vapor-deposition.13 They noted that the SCL state of a USG-forming compound exhibits a temperature-dependent relaxation time (τ) which does not correspond to the Vogel−Fulcher−Tammann (VFT) expression:14−16 log τ = A + B /(T − T0)

(1)

Chen and Richert assumed the existence of a turnover temperature (TB) which separates the temperature-dependent relaxation behavior of an SCL into two temperature regions, each of which may be described by a VFT expression. According to their work, calculations involving τ values acquired below TB allow more accurate estimation of Tg and the parameter m. The latter variable has been termed either the “steepness index” or the “fragility index” and is defined as Received: April 29, 2013 Revised: August 5, 2013 Published: August 6, 2013 10311

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Table 1. Experimentally Derived and Calculated Parameters of Compounds Included in This Study: Tg of Samples Prepared at the Lowest Td (Parentheses), Tg Obtained by Thermal Methods for Liquid-Quenched Samples, the Relative Ti (see text), the Steepness Index m, and the Intermolecular Interaction Energy ΔE of the Dimer Tg/K (Td/K)

compounds toluene (TL) ethylbenzene (EB) propylbenzene (PB) isopropylbenzene (IPB) ethylcyclohexane (ECH) butyronitrile (BN) a

116.3 (78.1) 116.2 (77.6) 125.7 (78.2) 129.4 (78.1) 103.7 (72.7) 99.7 (74.7)

Tg/K (liquid quenched) a

117 115a 122c 126d 104.5e 97f

Ti/Tg (Td,min) 0.79 0.85 0.86 0.86 0.93 1.00

ΔE/kJ mol−1

m b

104.4 97.5b 74.5b 77.6b 57.2b 56.4g

−21.3 −19.7 −26.0 −21.6 −12.7 −23.3

Reference 50. bReference 13. cReference 51. dReference 52. eReference 19. fReference 23. gReference 28.

m=

incidence angle of 60°, and variations in the intensity of the reflected light as well as Raman spectra were acquired. Samples were made to a thickness of approximately 10 μm at a deposition rate of about 0.2 μm min−1 by monitoring the laser interference resulting from the sample. After the cessation of vapor deposition, the sample temperature was raised at a constant rate of 0.28 K min−1. All of these processes were performed in a vacuum chamber with a base pressure of approximately 10−7 Pa. In this article, we focus on changes in the reflected laser light during these trials rather than the Raman spectra which we obtained. 2.2. Analysis of Reflected Light Intensity. We have reported previously that changes in Vm of vapor-deposited glass or liquid samples can be estimated by analyzing their laser light interference fringe. The description of the analysis method was originally given in ref 30 and supplemented in refs 11 and 12. In the present work, we essentially employ the same technique to analyze the structural evolution of ECH and BN samples. We therefore made the following three assumptions in this study as in our previous work: (i) the uniaxial volume change occurs normal to the substrate,30 (ii) there is an isotropic refractive index31 although optical properties of compounds with anisotropic molecular shapes may be anisotropic to some extent even in the glassy state of a highly disordered structure,1,32,33 and (iii) the constant molar refraction may be defined using the Lorentz−Lorenz equation.34 In this article, however, we modify the manner in which the Vm data are expressed, since it has been shown that SCLs formed from vapor-deposited glasses via glass transition are sometimes in nonequilibrium states.12 We therefore estimated the practical changes in Vm of samples using the following process. As a first step, we selected a reference temperature at which samples of each compound were believed to have completed their glass transition into SCLs. Temperatures of 108.0 and 103.0 K were chosen as reference values for ECH and BN, respectively. In order to estimate the refractive index (n0) and molar volume (Vm,0) at the reference temperature, we measured the temperature dependence of the refractive index (n) for ECH and BN over the temperature range from 167 to 300 K (see the Supporting Information). At a wavelength of 514.5 nm, the following results were obtained: n = 1.5761−4.746 × 10−4 T for ECH and n = 1.5232−4.642 × 10−4 T for BN. By extrapolating these relationships to lower temperatures, and assuming constant molar refractions,37 values of n0 = 1.5247 and Vm,0 = 121.74 cm3/mol were estimated for ECH, and values of n0 = 1.4754 and Vm,0 = 73.77 cm3/mol were found for BN. We subsequently determined the refractive index shift (Δn) which results in one cycle of movement of the state point on the interference fringe.30 The resulting values were −0.036 and

d log10⟨τ ⟩ d(Tg /T )

T = Tg

(2)

where ⟨τ⟩ is the average relaxation time. Ethylcyclohexane (ECH) is a typical glass-forming compound. Its relaxation behavior has recently been extensively studied19−22 and was contrasted with those of several USGforming compounds.13 In the discussion of ref 13, Chen and Richert suggested that ECH does not form USG on the basis of our unpublished data of the Vm values of vapor-deposited ECH glasses. As we mentioned previously, it is still not clear whether USG and dense glasses can both be regarded as belonging to a common class of materials. We thus report in the present article our experimental data regarding the Td dependence of the Vm of ECH glasses. We also report similar data for vapor-deposited glasses of butyronitrile (BN) which exhibits excess enthalpy in glass states and was studied in pioneering works on vapordeposited molecular glasses.23−25 In addition, we discuss the factors which appear to be essential to the formation of dense glasses on the basis of quantum chemical calculations. Several studies have been reported to date regarding glass formation by BN in addition to refs 23−25. Schiener and coworkers studied the dielectric relaxation of BN and discussed its fragility.26 We reported its crystal structure and compared its Raman spectra in different states in relation to the coexistence of trans and gauche molecular conformations27 (note that BN is referred to as butanenitrile in this reference according to the IUPAC recommendations, as opposed to the more conventional name butyronitrile). In addition, Ito and co-workers have recently reported the solvent response and dielectric relaxation of supercooled BN.28 We also briefly discussed the turnover of the temperature dependence of the wavenumber of a Raman band of BN at the glass transition.29 13,17,18

2. EXPERIMENTS, ANALYSES, AND QUANTUM-CHEMICAL CALCULATIONS 2.1. Sample Preparation and Measurement of Reflected Light Intensity. Glass samples were prepared at a constant Td in the same manner as in our previous studies.11,12,30 Reagent-grade ECH (Sigma-Aldrich) and BN (Tokyo Chemical Industry) were used after purification by distillation and fractional crystallization. The compounds were vaporized and deposited on a gold-coated copper substrate which was mounted on a coldfinger cooled with cold helium gas. The substrate temperature was measured via an Au/Fechromel thermocouple inserted into the copper block. Throughout the entire vapor deposition process, as well as during subsequent experiments at elevated temperatures, laser light (514.5 nm, 30 mW) was directed at the sample at an 10312

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−0.026, respectively, for ECH and BN samples approximately 10 μm thick. The parameter n was then estimated, according to eq 3, using a sufficiently large number of state points on the reflection fringe and calculating Vm at each state point.

n = n0 + Δn(δ /2π )

(3)

Here δ is the phase difference on the interference fringe from the reference temperature. Note that eq 3 allows only an approximation of the change in n, and therefore the resulting values of Vm should be considered only semiquantitative in terms of accuracy. Finally, we converted each Vm into a relative value normalized to the value of Vm which the sample prepared at the lowest Td exhibited at its Tg.35 The values of Tg of samples prepared at such Td are given in Table 1, along with Tg determined by thermal methods for liquid-quenched samples. The true Vm of each sample at the reference temperature was possibly different from the Vm estimated using the above process, depending on the degree of nonequilibrium of the SCL state at the reference temperature.12 However, the variation of Vm with temperature, as summarized by the normalized values displayed in Figure 2, is sufficiently accurate to allow a discussion in this article of the changes in Vm in the region below the reference temperature. 2.3. Quantum-Chemical Calculations of Dimer Formation. To further investigate molecular aggregation in the glass and SCL states of these compounds, we performed quantum-chemical calculations concerning the structure and energy of their corresponding dimers using the Gaussian 09 software package36 on an HPC-5000 computer (HPC Systems Co.) at the MP2/6-311++G(d,p) level. During these calculations, we corrected for basis set superposition error (BSSE) using the counterpoise method.37,38

Figure 1. Variations, on heating, in laser light intensity reflected from (a−c) ECH and (d−f) BN samples deposited at temperatures indicated in each plot. The symbols G, L, and C represent glass, supercooled liquid, and crystal states. Open squares and circles designate the location of Tr (see text) and Tg.

structural relaxation in the glass. The one exception occurred in the case of ECH glass deposited at 98.2 K, in which rapid expansion accompanied the transition from gradual thermal expansion to structural relaxation (see also Figure 2), a phenomenon which is discussed below. The open circle in each panel indicates the Tg, at which point rapid change in the light interference associated with structural relaxation in the glassy state transformed into a more gradual change due to thermal expansion of the SCL.

3. RESULTS AND DISCUSSION 3.1. Intensity Evolution of Reflected Laser Light due to Temperature Elevation of Samples. Figure 1 presents plots showing typical variations in reflected light intensity of ECH and BN films as the temperature is increased at a constant rate. The Td of each sample is indicated within its respective plot. We have previously investigated the causes of similar intensity variations observed in the case of aklylbenzene films generated by vapor deposition.11,12,30 When the sample is transparent, changes in its reflected light intensity result from movement of the state point on the interference fringe due to changes in both the thickness and refractive index of the sample. Conversely, a reduction in the reflection intensity is observed when the sample exhibits light scattering. All of the vapor-deposited samples studied to date demonstrated pronounced laser light scattering on being heated to the temperature at which crystallization takes place. In addition, some EB, PB, and IPB samples deposited at low values of Td also exhibited transient light scattering in the midtemperature region while in their SCL states. We attribute this scattering to the appearance of structural inhomogeneity accompanying relaxation from one SCL state to another.39,40 Based on patterns in the reflected light intensity variations observed for a variety of vapor-deposited samples, we were able to assign physical states to the specimens studied in the present work. These states are indicated by G (glass), L (SCL), and C (crystal) in each plot in Figure 1. The empty squares on the plot in each panel indicates the temperature (Tr) at which the gradual thermal expansion of the glass turned into a rapid volume change (primarily associated with shrinkage) due to

Figure 2. Variations, on heating, in the relative volumes of (a) ECH and (b) BN samples produced at different Td which are indicated on the plots. Horizontal axis represents the temperature normalized to the Tg of a sample prepared at the lowest Td (see Table 1). Vertical axis represents the Vm normalized by the Vm of the same sample at its Tg. Dashed lines indicate extrapolation of the changes in Vm in the liquid state normalized in the same manner. 10313

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3.2. Structural Changes of ECH and BN Samples Associated with Temperature Elevation. It is helpful to examine first Figure 1b, which plots the intensity evolution of an ECH sample deposited at 82.9 K. Between 83 and approximately 96 K (the Tr value for this sample marked by an empty square), the state point exhibited a gradual forward movement on the interference fringe, indicating steady thermal expansion. At Tr, the movement of the state point was reversed, which demonstrates the onset of relatively rapid shrinkage. At about 106 K (open circle, Tg), the movement of the state point again reversed and a second phase of gradual thermal expansion began. It is therefore considered that the sample transformed into the SCL state at 106 K, and eventually crystallized over the range of 130−134 K, during which it exhibited a rapid decrease in reflection intensity. Essentially similar changes in light reflection were observed for ECH samples deposited at 73.0 and 98.2 K, although there were some differences in the details. In the case of the 73.0 K sample (Figure 1c), the intensity exhibited a complicated change within the temperature region associated with the SCL state, suggesting the appearance of a degree of optical inhomogeneity, similar to that exhibited by EB, PB, and IPB samples deposited at low values of Td,11,39,41 although not as pronounced. It therefore appears that, to some extent, this sample retained in the SCL state a memory of the highly disordered structure formed when it was deposited at a Td significantly below its Tg. Conversely, in the case of the ECH sample deposited at 98.2 K (Figure 1a), the gradual thermal expansion in the glass state changed at the Tr of about 105 K into a rapid expansion linked with structural relaxation. It was then immediately followed by another gradual expansion of the SCL state at the material’s Tg value of approximately 106 K. The behavior exhibited by this sample of ECH glass, deposited at a Td equal to approximately 0.92Tg, is similar to the behavior shown by dense glasses of alkylbenzenes deposited at temperatures in the region of 0.9Tg.10−12 We observed very similar variations in light reflection for BN samples deposited at different Td values. The samples deposited at 74.9 and 85.2 K (Figure 1f,e) demonstrated changes with temperature very much like the changes seen for ECH deposited at 73.0 and 82.9 K (Figure 1c,1b), respectively. The BN specimen deposited at 95.1 K (Figure 1d), however, does appear to behave differently from the ECH samples, in that it exhibits an abrupt intensity change soon after the start of the temperature elevation. This change is attributed to structural relaxation accompanied by volume shrinkage since this sample, at its Tg value of 101 K, shows a reversal of the state point movement associated with gradual thermal expansion in the SCL state. 3.3. Analyses of Molar-Volume Changes of ECH and BN Samples. Based on the evolution of light reflection summarized in Figure 1, we estimated the changes in Vm associated with heating of ECH and BN samples prepared at different Td, with the results presented in Figure 2. The vertical axis of Figure 2 indicates the relative volume of each sample normalized to the Vm of a sample deposited at the lowest Td, while the horizontal axis is the temperature normalized to the Tg of the compound when prepared at the lowest Td (see Table 1). The dashed line in each plot indicates the temperature dependence of the Vm of liquid ECH or BN extrapolated into the SCL region and normalized in the same manner. We wish

to stress that the reliability of these analytical results is limited by the assumptions described in section 2.2. In general, the relationship of the Vm of ECH (Figure 2a) with temperature is similar to the behavior exhibited by alkylbenzenes.11 Hereafter, we use the term “excess volume” to refer to the difference between the Vm of the glass and that of the SCL state at the same temperature. The excess volume of the as-deposited glass becomes larger as Td is lowered and the glasses deposited at low Td values exhibit thermal expansion more or less up to the Tr of each sample. It should be noted here that the behaviors of the samples deposited at 97.7, 98.2, and 100.1 K indicate that ECH forms glasses slightly more dense than its SCL at the same temperature when Td is very close to Tg. In a private communication to Richert13 in August 2011, Ishii mentioned that ECH did not form the same dense glasses as were observed in the cases of EB and some related compounds. However, based on our recent results, this statement may be amended by noting that ECH is capable of forming glasses slightly more dense than its SCL at Td values very close to its Tg, but the resulting change in density is essentially insignificant compared with the density changes of EB and related materials. It should be also pointed out that Tg of the slightly more dense glasses of ECH are not higher than that of the less dense glass deposited at 93.2 K. This behavior is different from those observed for alkylbenzenes.11 In addition, the differences between Tr and Tg of the slightly more dense glasses of ECH are appreciably larger as compared with the corresponding differences observed for alkylbenzenes.11 These facts suggest the weakness of the intermolecular conformation which made the density of the ECH glass slightly smaller than that of its SCL. The variations in Vm observed in the case of BN samples deposited at different Td values (Figure 2b) are quite different from those observed for ECH and alkylbenzenes. The BN samples show either a narrow or essentially nonexistent temperature range associated with thermal expansion in the glassy state. During the vapor deposition of BN at lower Td values, we observed that the samples had a tendency to become less transparent, indicating significant inhomogeneity in the refractive index on the spatial scale comparable to the laser wavelength. This level of inhomogeneity in a sample is believed to induce structural relaxation concurrent with a slight elevation in temperature. As a result, the Vm plots of almost all samples, as seen in Figure 2b, roughly converge into a single curve as the temperature approaches Tg. 3.4. Deposition-Temperature Dependencies of Tg and Tr. As described in section 3.1, we determined the Tg of each sample, on the basis of reflected light intensity variations, as the temperature at which structural relaxation in the glass is complete and thermal expansion in the SCL state begins. We have found that Tg values derived in this manner roughly agree with values determined from calorimetry, as shown in Table 1. However, it should be noted that our values of Tg depend on the rate of temperature elevation as well as on Td. Using EB as an example, we previously estimated that, at a temperature rise rate of 0.28 K/min, the apparent Tg was approximately 1 K higher than is measured when using a slower rate.30 Therefore, a small allowance should be made for differences between our Tg values and those determined by other methods. It is thought that our Tg values exhibit a dependence on Td likely because of differences in the degree of disorder associated with different Td values.11 10314

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expansion in the glass state. Figure 3 also demonstrates that the difference between Tr and Tg increases in order of EB, ECH, and BN, suggesting that the molecular arrangements of the vapor-deposited glasses of these compounds are increasingly less stable on thermal agitation in this order. 3.5. Td-Dependence of the Vm of As-Deposited Glasses. Figure 4 plots the relative Vm of as-deposited glasses

As an aid to understanding the dependence of the apparent Tg on Td, Figure 3 plots the Tg and Tr of each ECH and BN

Figure 4. Td dependencies of the relative Vm of as-deposited glasses. Volume data for TL, EB, PB, and IPB are taken from ref 11, and data concerning their liquid states are from ref 42. The vertical axis is the same as that in Figure 2. The horizontal axis represents Td in the same manner as in Figure 3 and also represents the temperature of the corresponding SCLs as in Figure 2.

of the various compounds studied in this work as a function of Td. The abscissa is the same as in Figure 3, while the ordinate is the same as in Figure 2. The ECH and BN data are the initial values of relative Vm for each sample shown in Figure 2, and the alkylbenzene data are the same as those reported in our previous paper.11 The solid lines represent the estimated Td dependence of each compound’s initial Vm in the lower or mid Td region, while dashed lines represent the temperature dependences of the Vm values estimated for each compound as an SCL (see the Supporting Information and ref 42). For all compounds, the Vm values of the glasses prepared at temperatures sufficiently below Tg are larger than those expected for the compound’s SCL at the same temperature, meaning that such glasses possess a degree of excess volume which is dependent on Td. The solid line for each compound intersects with the dashed line representing the extrapolation of the relative Vm of its SCL, and we denote the temperature at this intersection as the relative Ti. In the case of BN, the relative Ti is almost unity, suggesting that vapor-deposition of BN does not produce glasses with densities greater than that of the corresponding liquid-quenched glasses at any value of Td. It is interesting to observe that the relative Ti of ECH is slightly less than unity, while the Ti values of the alkylbenzenes are significantly below unity. The solid lines in Figure 4 associated with those compounds which have smaller values of Ti tend to go down to the dense side across the dashed lines of the SCLs. Therefore, if the Ti of a compound is small, the temperature region over which that compound may potentially form dense glasses can be expected to be wide. Figure 4 implies that the Vm of a glass fabricated at Ti could have the same Vm as the corresponding SCL, but the structure of the glass at Ti may be different from that of the SCL in the equilibrium state.9 It should be pointed out here that the dashed lines in Figure 4, which are extensions of the temperature dependencies of the Vm values of the SCLs, are similar to the lines which represent the temperature dependencies of the enthalpy or entropy of

Figure 3. Td dependencies of the Tr (open squares) and Tg (open circles) of (a) EB, (b) ECH, and (c) BN. EB data are taken from ref 11. The horizontal axis represents Td normalized to the Tg of the sample deposited at the lowest Td for each compound. The vertical axis represents Tr or Tg normalized in the same manner.

sample as a function of Td. The corresponding data for EB are also reproduced in this figure.11 Both the ordinate and abscissa of Figure 3 present temperature normalized to the Tg of the sample deposited at the lowest Td for that compound. Hereafter, we refer to the normalized Td value as the relative Td. Both the Tg and Tr of EB show maxima at relative Td values in the region from 0.85 to 0.9, which is similar to the other alkylbenzene glasses.11 Tr indicates the onset temperature of the structural relaxation heading toward glass transition and is considered to manifest the stiffness of the samples against thermal agitation. On the other hand, Tg of our glass samples is considered to be affected by the structural changes and/or local temperature changes in the relaxation process before arriving at Tg, and the quantitative discussion of the height of the bump seen in Figure 3 for the relative Tg is difficult. By comparing the results of EB and ECH in Figure 3, it is noticed that Tr of EB shows a maximum at the relative Td values of approximately 0.9 while almost no maximum is seen in the corresponding plot of ECH. This difference in the Td-dependences of Tr of EB and ECH might indicate that ECH glasses do not attain even with Td close to Tg the special stabilization similar to that assumed for EB glasses deposited at the relative Td around 0.9. In contrast to EB and ECH, the Tg of BN is essentially constant irrespective of the relative Td. This indicates that BN does not form a specific molecular packing even when the glass is deposited at Td close to its Tg. In contrast, the Tr of BN shows a monotonic decrease with decreasing relative Td, as a result of the very narrow temperature interval of its thermal 10315

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SCLs in the temperature region below Tg.43,44 Therefore, if the relative Ti of a compound is significantly less than unity, the compound has the ability to form, by vapor deposition, glasses with lower energies on the potential energy landscape relative to an ordinary glass that deviates from equilibrium upon cooling to the region below Tg.9 3.6. Correlations between the Behaviors of VaporDeposited Glasses and Supercooled Liquids. It has been pointed out that the SCL of molecular compounds such as TL or EB shows a steep increase in relaxation time as their temperatures approach their Tg.13 We therefore plotted in Figure 5 the relative Ti values of the compounds studied herein

Figure 6. Conformations of the TL, EB, PB, IPB, ECH, and BN dimers as optimized by ab initio calculations. The intermolecular interaction energy values of each dimer are given in Table 1.

Figure 5. Correlation between m and Ti (see text). Numerical values of these same data are given in Table 1. The vertical axis is normalized in the same manner as in Figure 3. The dashed line is presented solely as a visual guide.

alky group interacts with the π electrons of the phenyl ring in the partner molecule. This is a weak version45 of the hydrogen bonding seen in water or a wide variety of organic compounds. For three of the four alkylbenzenes (the exception being IPB), two sets of hydrogen bonds are formed almost symmetrically and appear to contribute significantly to ΔE. In the case of IPB, we have not yet identified a stable conformation in which two sets of hydrogen bonds are formed and so the ΔE of the IPB dimer displayed in Figure 6 is less than that of the PB dimer. In the dimer formation of ECH, neither a hydrogen bond nor a strong electrostatic interaction is expected, and thus only weak dispersion forces may be dominant. Accordingly, the ΔE for the ECH dimer is the smallest among the dimers studied here, and the magnitude of this parameter thus allows a rough estimation of magnitude of the dispersion interactions in the four alkylbenzene dimers, since the number of electrons in ECH is comparable to the number of electrons in these alkylbenzenes. The result of the ΔE calculation associated with formation of the BN dimer was the most remarkable. Since BN has significantly fewer electrons than the other compounds in Table 1, the fairly large value of ΔE for the BN dimer obviously results from the electrostatic interaction between the large dipole moments of BN molecules. This result raises the issue of why, with regard to the formation of dense molecular glasses, the behaviors of the BN glasses are so different from those of alkylbenzene glasses when they have such similar ΔE values. The possible reasons for this phenomenon are discussed in subsequent sections. One might have a question to what extent such calculations on the formation of isolated dimers are meaningful, since the actual glasses may contain interactions among many molecules. As an answer to such questions, the following facts may be recalled. The crystal structures have been known for BN27 and TL.46,47 The local molecular packing similar to that obtained in our calculations exists in the BN crystal. Interestingly, for TL,

against their steepness index, m. The m values used here were determined from the temperature dependence of the dielectric relaxation times of SCLs near the glass transition of each compound13,28 and are summarized in Table 1 along with Tg and Ti values. The dashed line in Figure 5 is included solely as a visual guide, although it does suggest a correlation between Ti and m, such that compounds with higher m values tend to have an enhanced ability to form dense glasses through vapor deposition. Both IMC and TNB are typical of compounds which form stable glasses and so may be used to examine the relationship between Ti and m. The m values of these compounds have been estimated to be 82.8 and 86.0,13 respectively, and so, from Figure 5, their Ti can be estimated at approximately 0.85, which is in agreement with the Td at which the stable glasses of these compound are formed.2,3 It should be noted, however, that Ti represents the lower limit at which anomalously dense glasses may be formed by vapor deposition and we have in fact found that EB, for which m is larger than IMC or TNB, forms its most dense glass in the Td region around 0.9Tg.10,11 3.7. Results of Quantum-Chemical Calculations. It is important to understand why some compounds form anomalously dense glasses by vapor deposition while many others do not. To improve our understanding, it is helpful to study the molecular aggregation of the compounds included in this work. To this end, we performed quantum-chemical calculations concerning the formation of dimers from these compounds, using the Gaussian 09 software package. The stable dimer conformations thus obtained are shown in Figure 6, and the intermolecular interaction energy, ΔE, of each dimer, which is the difference between the total energy of the dimer and the sum of the energies of the component molecules, is listed in Table 1. The conformation feature common to alkylbenzene dimers is that one of the hydrogen atoms in the 10316

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such a molecular packing exists in the stable crystal,46 while it does not exist in the metastable crystal.47 Thus, such calculations on the dimer formation are useful as an initial guide to understanding the molecular aggregation in the dense glasses. 3.8. Compounds Forming Dense Glasses by Vapor Deposition. As a preliminary step, it is helpful to summarize the properties and behaviors of the glasses formed by vapor deposition of ECH and BN, neither of which form especially dense glasses. For both compounds, the excess volume of the as-deposited glass was observed to increase as Td was lowered. At values of Td very close to Tg, ECH forms glasses slightly more dense than its SCL at the same temperature, while there is no evidence that BN forms high-density glass at all. During heating following vapor deposition, ECH glasses initially exhibit thermal expansion over a limited temperature range and then undergo either shrinkage or expansion, depending on the value of Td, as the result of structural relaxation preceding the glass transition. Conversely, BN glasses first show a slight thermal expansion over a very narrow temperature interval, after which all samples undergo gradual shrinkage due to structural relaxation regardless of the Td at which they were formed. Finally, Ti, which represents the temperature at the intersection between the Td dependence of the initial Vm of the glasses at the deposition and the temperature dependence of the Vm of the corresponding SCLs, was slightly lower than Tg for ECH but almost coincides with Tg in the case of BN. The differences between the behaviors of ECH and BN as summarized above are relatively minor, compared to the very different behaviors exhibited by the alkylbenzenes, which form remarkably dense glasses. The appreciable difference between the behaviors of these two groups of compounds is clearly seen in Figures 4 and 5, in which it is evident that the compounds which form high density glasses tend to possess a high steepness index and low relative Ti. Chen and Richert13 analyzed the temperature dependence of the relaxation time of SCL in detail. They noted that the dielectric relaxation behavior of ECH differed from those of the USG forming compounds which had larger m values than that of ECH. In the present article, we compared the Ti value of ECH with those of alkylbenzenes in Figure 5 by arranging Ti as a function of m, where we adopted the m value of each compound reported by Chen and Richert.13 We found a weak correlation between Ti and m among the compounds containing ECH and alkylbenzenes, the latter having the ability to form dense glasses as we have reported so far. Therefore, Figure 5 might reflect some relation between USG and dense glasses. However, we are still not sure that USG and dense glasses can be regarded as belonging to a common class of materials. Therefore, investigation into the relation between these kinds of glasses should be pursued. The existence of USG has been suggested mainly on the basis of thermal and kinetic properties, while that of dense glasses has been suggested on the basis of molar volume estimation. Recently, Ediger and coworkers have studied the optical properties of IMC32 and TNB33 for which the formation of USG has been reported. On the other hand, Rodriquez and co-workers4,5 and Schick and co-workers7 studied thermal properties of TL and EB for which the possible formation of dense glasses has been reported. We also made thermal studies on EB.6,48 We consider at present that we should examine a wide variety of compounds which form USG or dense glasses from various viewpoints.

In the early stages of the study of molecular glasses, Angell suggested that fragile liquids, which are liquids having large m values, have a high density of minima on the potential energy landscape drawn along the configuration coordinate of the system.44 It is difficult to imagine a substantial structure of a liquid comprising a very large number of molecules. However, it is helpful to recall that the alkylbenzene compounds which form dense glasses tend to be out of equilibrium even in the SCL state attained through the glass transition.11,12 We believe that the ability to achieve locally allowed intermolecular conformations with specific stabilities might make the energy landscape of the system rich in the fine structures and tend to force the system out of equilibrium. The hydrogen bonds associated with the formation of alkylbenzene dimers could play such a role in making the m values of these compounds large and in the formation of their anomalously dense glasses. Finally, we wish to comment on the apparently paradoxical observation that the steepness index of BN is much smaller than the indexes of the alkylbenzenes, even though its ΔE value (representing the stability of its dimer) is approximately equal to the alkylbenzene ΔE values. In considering this issue, we recall that the dimer formation in the liquid state of acetonitrile, which has a cyano group in its molecule as in BN, has been suggested on the basis of the far-infrared spectroscopy49 and that such formation of local structures in a liquid is considered to be enhanced as the temperature is lowered. We thus propose that the electric dipole moment of the BN cyano group is so large that the dimer bound by two cyano groups behaves as if it were a single nonpolar molecule having two short hydrocarbon chains and a small core made of cyano moieties.

4. CONCLUSION The variations with Td of the Vm of ECH and BN glasses generated by vapor deposition were studied based on the laserlight interference of film samples, in order to obtain a better understanding of such materials. Based on comparisons with previously reported results for alkylbenzenes, it was found that the formation of dense glasses by vapor deposition is not a common property of all glass-forming compounds. An analysis of the excess volume included in glass samples deposited at lower or mid Td values showed that Ti, the estimated low temperature limit for the formation of a dense glass by vapor deposition, is lowered as the steepness index of the corresponding SCL, m, increases. The results of quantumchemical calculations concerning the formation of dimers in these compounds indicated that the dimer must possess a large stabilization energy, ΔE, if it is to form a dense glass. The results also suggest that some specificity in the local molecular conformations is required in order for the SCL to have a sufficiently large value of m such that it is capable of forming dense glasses. As an example, BN does not form dense glasses even though its calculated ΔE is comparable to those of the alkylbenzenes which do form dense glasses. We suggest that this occurs because the intermolecular static interactions between BN molecules are so strong that the dimer behaves as a nonpolar single molecule.

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ASSOCIATED CONTENT

S Supporting Information *

Description of the measurements of refractive indices of ECH and BN at low temperatures (with two figures) and description of the assumption of optical isotropy of vapor-deposited glass 10317

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samples. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81-3-3986-0221. Notes

The authors declare no competing financial interest.

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