Phase and Glass Transitions Observed by Adiabatic Calorimetry of

Publication Date (Web): September 2, 2013 ... Heat capacities of crystalline p-tert-butylcalix[4]arene·toluene host–guest compound were measured in...
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Phase and Glass Transitions Observed by Adiabatic Calorimetry of Host p-tert-Butylcalix[4]arene and Guest Toluene Inclusion Crystal, Suggesting the Progress of the Combined Order−Disorder Process of the Host−Guest Molecules Kouhei Ueda*,† and Masaharu Oguni Department of Chemistry, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo 152-8551, Japan ABSTRACT: Heat capacities of crystalline p-tert-butylcalix[4]arene·toluene host−guest compound were measured in a temperature range between 3 K and 345 K by adiabatic calorimetry. The crystal showed one second-order phase transition at 256.4 K accompanied by wide heat-capacity tails on both the high and low temperature sides and two first-order phase transitions with heat-capacity peaks at 127 K and 139 K. The total entropy of a sequence of the phase transitions was assessed experimentally to be 47 J K−1 mol−1, indicating that the number of allowed distinguishable molecular configurations is over 100 in the high-temperature disordered state. Many such distinguishable configurations are understood to be produced by a special intermolecular interaction of C−H···(π-electron) bonds formed between p-tert-butylcalix[4]arene and toluene molecules, and the transitions were interpreted as originating from orientational order−disorder of both the guest toluene molecule and the tert-butyl groups of host arene in their combination.

1. INTRODUCTION The structure of a molecular-assembled system is maintained through weak inter- and intramolecular forces such as hydrogen bonds and van der Waals force. The hydrogen-bond energy is ordinarily larger than the van der Waals force typically represented by dispersion force, in their contributions to determine the microscopic structural configurations of the relevant groups of organic compounds. C−H···(π-electron) interaction is a kind of hydrogen bond formed between a hydrogen atom chemically bonded with a carbon atom and π electrons. The interaction is important in that its strength is intermediate between that of the hydrogen bond of O−H···O or N−H···N and van der Waals force; the energy has been estimated to be a few kJ mol−1,1,2 and plural interactions are often existent in a bundle so as to contribute strongly to determination of the structural configuration of a molecular assembly. The latter event occurs because the π-electron orbital is not located at a special small site but extends in many cases over many atoms within an organic compound, for example, on a phenyl ring.1−4 Thus, much attention has been recently paid to the C−H···(π-electron) interaction as an important interand intramolecular force to explain the structure and functional mechanism of molecular-assembled systems and supramolecules.3,4 The attention to the systems comes from industrial as well as scientific importance, for example, organocatalytic reactions in molecular cages, molecule storage, and drug delivery.5−10 Calixarene and its derivatives have a conic molecular structure and can include a certain molecule in this conic © 2013 American Chemical Society

void which functions as a cage for the host−guest type supramolecule.8,11−14 This type of supramolecule can be considered as a model system for studying how the interand intramolecular forces function to assemble the host and any guest molecule because the guest molecule bonds with the host cage through the intermolecular forces and changes its site or orientation if many close-in-magnitude potential minima are present. p-tert-Butylcalix[4]arene (BC4A) is an extensively studied compound as a host supramolecule of inclusion compounds.8,11−13,15−20 BC4A can include a molecule of many species in the void of the conic cage which is composed of four phenol planes bridged by four methylene (−CH2−) groups at their ortho-positions; each phenol ring possesses further a tert-butyl group located at the para-position (see Figure 1). In the cases of a certain larger guest molecule such as benzene, toluene, and some benzene derivatives, host−guest crystals, in which the host:guest molecular ratio is 1:1 or 2:1, are formed.8,11−14 With toluene as the guest, a 1:1 crystal can be prepared from the toluene solution, and also a 2:1 crystal can be formed from the 1:1 crystal by evaporating, at high temperatures, half of the toluene molecules in association with a change in the packing structure of the host BC4A molecules.8 These crystals are thermally stable so that the toluene molecule can be kept in the void even above the boiling temperature of liquid toluene. The structure and dynamic properties of the 1:1 Received: May 8, 2013 Revised: August 5, 2013 Published: September 2, 2013 11836

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lines in the X-ray diffraction, however, there exists a possibility that the phenyl plane of the toluene molecule is ordered at a special orientation in the lowest-temperature phase with space group Pc. The transition enthalpy reported by DSC leads about 1.2 J K−1 mol−1 for the transition entropy; namely, the number of allowed distinguishable configurations for the inclusion compound BC4A·T is smaller than two even in the hightemperature phase, which is inconsistent with the above structural results. It is not yet clear how the two kinds of disorders described above are correlated with each other and progress with increasing temperature: Considering that the interrelation between the positions of host BC4A and guest toluene molecules is determined mainly by the C−H···(π-electron) interactions between the C−H of alkyl groups and the π electrons of phenyl rings, the two kinds of disorders must be strongly correlated. Clarification of the dynamic and static features of the compound is helpful for understanding and designing the mechanism of the catalytic reaction and molecule storage of supramolecular assemblies. Heat-capacity measurements by adiabatic calorimetry are adequate for disclosing features of the phase transition and of the molecular dynamics. In this study, heat capacities and dielectric relaxation times for the crystalline BC4A·T 1:1 host−guest compound were derived in the temperature ranges of 3 K to 345 K and 50 K to 300 K, respectively, and we found a sequence of phase transitions and a glass transition as a freezing-in phenomenon of the configurational change of molecules on the way to their orientational ordering in the low-temperature tail of the phase transitions.

Figure 1. One of the structures found in the inclusion compound of host p-tert-butylcalix[4]arene and guest toluene molecules.11−13

p-tert-butylcalix[4]arene·toluene (BC4A·T) crystal have been extensively studied experimentally and theoretically.8,11−13,15−20 In crystalline BC4A·T, the guest toluene molecule is placed in unique directions and positions based on the intermolecular interactions as follows: the methyl group of toluene is located toward the top of the BC4A conic cage, and the toluene phenyl ring lies between tert-butyl groups as shown in Figure 1.11−13 This implies that the position and orientation of the toluene molecule are determined by the C−H···(π-electron) interactions formed between the C−H of host tert-butyl groups and π electrons of the toluene phenyl ring and between the C−H of the toluene methyl group and π electrons of the BC4A phenyl rings.12 So far, structural studies have shown two kinds of disorders to exist at room temperature.11,13,15−17 One is based on the toluene molecular plane being nonparallel to the principal axis of the BC4A molecule. Considering that the crystal structure was reported to possess a space group of P4/n, the toluene molecule must be disordered among four positions or orientations. The other kind of disorder comes from the rotational angle of each tert-butyl group; namely, the angular position of a set of three methyl groups is disordered between two places without considering the orientation of the hydrogen atoms in each methyl group. The occupancy ratio of the two angles in the latter disorder of the tert-butyl group has been reported to be 77:23 by Andreeti11 and 50:50 by Enright et al.13 Both kinds of disorder are known from NMR measurements to be in equilibrium dynamically between the allowed configurations at room temperature.15−17 According to the results from solid-state 13C NMR spectroscopy, the crystal structure changes from that with a 4-fold rotational symmetry at room temperature to that with a 2-fold one at low temperatures.15−17 This structural change was interpreted as indicating the presence of a phase transition originating from the orientational order−disorder of the guest toluene molecule in the cage. The phase-transition temperature was determined to be 248 K, as the temperature at which a splitting in the 13C NMR spectrum appeared.15−17 A thermal anomaly was also observed by DSC to occur at this temperature, and the phase-transition enthalpy was estimated to be 0.3 kJ mol−1.15 The space group of the low-temperature crystal structure has been determined to be P2/n.13 The four tert-butyl groups of the BC4A molecule were understood to be ordered at a fixed rotational-angle site and also the guest toluene molecule to be ordered at sites with a 2-fold rotational symmetry. Taking into consideration that the space groups P2/ n and Pc reveal the same extinction rule for their Bragg-peak

2. EXPERIMENTAL SECTION 2.1. Sample Preparation. BC4A was purchased from Wako Pure Chemical Industries Ltd. Crystalline BC4A·T 1:1 compound was obtained from the toluene solution by cooling it slowly and purified by repeating the recrystallization processes three times. 2.2. Calorimetric Measurement. The purified BC4A·T polycrystalline sample was loaded into a calorimeter cell, and the cell was sealed tightly with an indium gasket under an atmosphere of helium gas. The mass of the sample used was 6.501 g. Heat capacities were measured in a temperature range of 3 K to 345 K with an adiabatic calorimeter by the intermittent heating method reported previously; namely, energy input into the calorimeter cell and thermometry at equilibrium without the input were repeated alternately under adiabatic conditions.21−23 The average heating rate for measurements is around 0.1 K min−1, and the period for each thermometry is about 10 min. Considering that the quantity of the sample used in the present measurements is small as compared with that used in the calibration of the calorimeter,21 the inaccuracy and imprecision of the heat capacity data derived are expected to be ±0.4% and ±0.1%, respectively. When a glass transition or a first-order phase transition is revealed, the sample ordinarily shows spontaneous heat-release or -absorption effects as its enthalpy change toward the equilibrium state. The effects are detected as an increase or decrease, respectively, in the temperature of the calorimeter cell during the thermometry periods. The spontaneous enthalpyrelaxation rate is equated to the slope dT/dt of the temperature change as follows: 11837

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temperature of toluene used as solvent for the recrystallization is 180 K, we can state that the anomalies are the attributes inherent to the BC4A·T crystal. Three anomalies at 127 K, 139 K, and 255 K, exhibiting heat-capacity peaks, are interpreted as due to phase transitions. Observed at around 79 K is a heatcapacity jump, and the anomaly is understood as due to a glass transition, as mentioned later. The temperature of the phase transition around 255 K was determined to be Ttrs = 256.4 K, at which the heat capacity showed the sharpest change in its temperature dependence. This transition corresponds to that reported as ascribed to the order−disorder process of the guest toluene molecule within the host BC4A molecule.15 To derive the anomalous part of the heat capacities due to the phase transitions, we attempted, by using the heat capacity values observed in the ranges of 58−76 K and above 310 K, to estimate the normal part, i.e., baseline, of the heat capacities without the transitions. In the low-temperature range, no contribution from the transitions was assumed to exist based on the presence of a glass transition around 79 K. Above 310 K, because the contribution originating from a short-range order relevant to the 256.4 K transition is inevitably involved in the observed heat capacities, the observed values were fitted with a polynomial function including a Bethe high-temperatureapproximation term, B/T2, in which B was left as a fitting parameter. The derived polynomial function is as follows:

(1)

where n and Cgross are the quantity of the sample used and the gross heat-capacity composed of the contributions of the sample and the calorimeter cell, respectively. The heat-release or -absorption effects are observed when the characteristic time of any phenomenon is in the range of 102 to 106 s under our measurement conditions. For example, in a glass-transition temperature (Tg) region, the characteristic time, named as relaxation time, for the configurations of molecules to attain their equilibrium Boltzmann distribution crosses this calorimetric time range when the sample is cooled or heated. If the sample was cooled rapidly through the temperature region, the molecular configurations in the sample must be frozen in a high enthalpic state, and if cooled slowly, it must be in a low enthalpic state. When these samples are heated for the measurements, the former sample would reveal a heat-release effect and the latter a heat-absorption effect in the thermometry periods as the respective equilibrium states around the Tg are approached, as described later. 2.3. Dielectric Relaxation Measurement. Dielectric relaxation spectroscopy was applied to the BC4A·T polycrystal at some frequency values between 1 Hz and 1 MHz in a temperature range from 50 K to 300 K. A Solartron type-1260 impedance analyzer was used for the measurements with help from a Solartron type-1296 signal buster interface. The sample in pellet form was prepared by pressing the powdery crystalline sample with a force of 10 MPa under vacuum. The diameter of the pellet was 10 mm, and the thickness was 0.5 mm. The pellet was sandwiched between two electrodes of gold-coated copper plates. No silver paste was used because its solvent might enter the pellet sample.

Cp(normal)/J K−1 mol−1 = −8.12 × 10−9T 4 + 5.21 × 10−6T 3 − 1.53 × 10−3T 2 + 3.55 × T + 10.8

(2)

and represented by a solid line in Figure 2. B was determined to be 1.14 × 106 J K mol−1. Figure 3a shows the obtained anomalous part of the heat capacities due to the phase transitions. Figure 3b shows the spontaneous enthalpy-relaxation rates observed during the thermometry periods from 115 K up to 345 K. Two endothermic peaks were found at 127 K and 139 K, indicating that the two lower-in-temperature phase transitions are of the first order. The enthalpies and entropies of the two transitions were estimated to be ΔtrsHm(128 K) = 0.51 kJ mol−1, ΔtrsSm(128 K) = 4.0 J K−1 mol−1, ΔtrsHm(139 K) = 0.37 kJ mol−1, and ΔtrsSm(139 K) = 2.7 J K−1 mol−1. On the other hand, the heat capacity peak at 255 K was accompanied by no endothermic behavior, and therefore the transition was interpreted to be of the second order. The total enthalpy ΔtrsHm(tot) and entropy ΔtrsSm(tot) of the three transitions were calculated from the anomalous part in Figure 3a as 10.4 kJ mol−1 and 47 J K−1 mol−1, respectively. In this calculation, it was assumed that the anomalous heat capacities below the glass-transition temperature of 79 K are given by ΔCm(T)/(J K−1 mol−1) = 6.07 × 10−2(T/K); the contributions to the transition enthalpy and entropy were evaluated as ΔtrsHm(345 K) = 4.7 J K−1 mol−1, respectively. Figure 4 shows the entropy ΔtrsSm(T) due to the order−disorder phase transitions as a function of temperature. A heat capacity jump of about 5 J K−1 mol−1 was observed at around 79 K. Such a jump has been observed characteristically of a glass transition, namely, a freezing-in phenomenon of molecular rearrangement in the low-temperature tail of phase transition in crystals.23−26 The presence of a jump and the

3. RESULTS 3.1. Heat-Capacity and Enthalpy-Relaxation Behaviors of Crystalline BC4A·T. Figure 2 shows the molar heat capacities obtained for BC4A·T at constant pressure. Four anomalies were observed at around 79 K, 127 K, 139 K, and 255 K on the heat capacity curve. Considering that the fusion

Figure 2. Heat capacities of crystalline p-tert-butylcalix[4]arene· toluene (BC4A·T). A solid line represents the baseline for the anomalous part of the heat capacities due to a sequence of phase transitions. 11838

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Figure 3. Anomalous part of heat capacities due to a sequence of phase transitions (a) and spontaneous endothermic-drift rates associated with the transitions (b): The heat capacities were derived by subtracting the baseline values, represented by the solid line in Figure 2, from the values observed experimentally. The anomalous part above 345 K, drawn with a solid line, was estimated by considering the contribution expressed by a B/T2 term. No endothermic effect around 256.4 K indicates that the transition with Tc = 256.4 K is of a second-order type.

Figure 5. Heat capacities (a) and spontaneous enthalpy-relaxation rates (b) around a glass transition: open circle, sample precooled rapidly; solid circle, sample precooled slowly. Dotted lines represent tangent lines to the heat capacity curves below and above the glass transition. Solid lines are guides for eyes.

feature characteristic of glass transitions.22−26 The glasstransition temperature, by adiabatic calorimetry, was determined to be Tg = 79 K at which the slowly precooled sample revealed the maximum endothermic effect on heating (see Figure 5b) and at which the relaxation time becomes 1 ks.22−26 The relaxation time τ and the activation energy ΔEa for the molecular rearrangement are equated, assuming the process is a classical one, by the following Arrhenius equation:22−26 τ = τ0 exp{ΔEa /(RT )}

(3)

where τ0 is the relaxation time extrapolated to the hightemperature limit, ordinarily taking a value of 10−12−10−16 s and corresponding roughly to the frequency of molecular vibrations.22−26 Substituting Tg = 79 K, τ = 1 ks, τ0 = 10−14 s for simplicity, and gas constant R, into this equation gives the activation energy for the molecular rearrangement, ΔEa = 25 kJ mol−1. Below the Tg, the relevant molecular rearrangement is frozen in the nonequilibrium state with the configurational disorder remaining, namely, with the residual entropy mentioned above as the contribution to the transition entropy. 3.2. Dielectric Relaxation Behavior of Crystalline BC4A·T. Figure 6 shows temperature dependence of the dielectric loss for crystalline BC4A·T at some constant values of frequency f. One peak was observed at any frequency. These peak-temperatures correspond to those at which the relaxation time τ of a certain molecular rearrangement to change the orientation of a dipole moment crosses 1/2πf.27−31 The relaxation times determined by the dielectric measurements and that determined as the Tg by the above calorimetry are plotted with open circles and a closed circle in Figure 7 as an Arrhenius expression. The solid line is the line fitted, by a leastsquares method, to the dielectric relaxation times with eq 3; ΔEa was determined as 25.2 kJ mol−1 and τ0 as 2.7 × 10−14 s. The results are consistent with the presence of the calorimetric glass transition mentioned above and indicate that the molecular rearrangement processes observed by calorimetry and dielectric measurements are the same.

Figure 4. Temperature evolution of the transiton entropy ΔtrsSm (T) due to a sequence of phase transitions. A horizontal straight line below the glass trasntion temperature represents the frozen-in residual entropy described in the text.

associated appearance of spontaneous enthalpy-relaxation rates around 80 K are shown in Figure 5a and 5b, respectively. The measurements were executed for the two samples precooled at different speeds beforehand; one was cooled at a high speed of −10 K min−1 and the other at a low speed of −25 mK min−1 below 115 K. The average heating speeds for the measurements were about 0.1 K min−1 in between the two, high and low, precooling speeds. An exothermic enthalpy-relaxation effect was observed in the sample precooled rapidly, and, on the other hand, an endothermic effect was observed in the sample precooled slowly. This hysteretic relaxation phenomenon is the 11839

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residual entropy due to the glass transition was included in the value as stated above. The value corresponds to R ln(290), indicating that over 100 molecular arrangements are allowed as distinguishable in the disordered state at the infinitely high temperature extrapolated, and is larger by 30% than the fusion entropy of pure toluene. Taking into consideration that the number of the distinguishable arrangements permissible to a guest toluene molecule in the BC4A·T cage was limited to a few or a few tens as observed by diffraction measurements,11,13 this largeness of the entropy implies that the disorder includes not only the orientation/position of a toluene molecule but also that of a BC4A frame. We should consider the disorder of the phase transitions as composed of two components; i.e., disorder of the BC4A frame and disorder of the toluene arrangement. First, we consider the disorder potentially happening in the configuration of the BC4A molecule. In reality, according to the crystal structure determined at room temperature,11,13 the disorder occurs concerning the rotational angle in the tert-butyl group on each phenol ring of BC4A; two distinguishable angles were found to be permissible. The symmetry of the crystal structure of BC4A·T reportedly belongs to space group P4/n with orientational/positional disorder of the principal axis of toluene molecule and orientational disorder of the tert-butyl group. The 4-fold rotational symmetry axis is located on the principal axis of the BC4A molecule. The structural analysis left it undetermined whether the four tert-butyl groups within the BC4A molecule rotate correlatively or not. In the correlative situation the contribution from the tert-butyl groups to the transition entropy is evaluated as R ln(2), and in the latter the contribution as R ln(24). The latter situation fits well to explain the transition entropy obtained experimentally. Next, we consider disorder of the toluene molecule. Without taking into consideration the hydrogen-atom positions of methyl group, toluene is a planar molecule with a 2-fold rotational symmetry axis as the principal type. The symmetry group is lower than the high-temperature structure space group P4/n. Thus, the toluene molecule must be dynamically disordered among some positions to fulfill the presence of a 4-fold rotational symmetry axis for the BC4A·T complex. In addition to this, the principal axis of the toluene molecule has been suggested experimentally and theoretically to be tilted from the 4-fold axis of the complex as illustrated in Figure 8a1.13,16,17,19 This means that at least four equivalent stable orientations/positions must be present for the toluene molecule at high temperatures as drawn with four arrows in Figure 8a-2. Thus, the contribution to the transition entropy from the disorder due to the tilt direction of toluene is evaluated as R ln(4). Another disorder was reported from crystal-structural analyses to be present concerning the orientation of toluene molecule. The methyl group of toluene is located in the top portion of the BC4A conic cage as shown in Figure 1.11−13 Calculation also indicated the same host−guest relative position as the most stable.19 On the other hand, careful NMR measurement suggested the presence of a small fraction of toluene molecules with the methyl group in the bottom portion of the conic cage as drawn in the right-hand side of Figure 8b, even in the low-temperature phase; 5% at 115 K by 2H NMR and 10% at 150 K by 13C NMR.16,17 These two NMR results are interpreted as indicating the presence of two permissible orientational states of toluene molecule concerning the location of methyl group. The temperature dependence of the occupation fractions at the two temperatures implies an energy

Figure 6. Temperature dependence of dielectric loss in crystalline BC4A·T: cross mark, 3.16 Hz; diamond, 31.6 Hz; square, 316 Hz; triangle, 3.16 kHz.

Figure 7. Arrhenius plot of the relaxation times for BC4A·T crystal: closed circle, glass-transition temperature determined by adiabatic calorimetry; open circle, data derived by dielectric measurements. A solid line represents the straight one fitted to the dielectric-relaxation time data by a least-squares method.

4. DISCUSSION 4.1. Molecular-Configurational Disorder Considered Based on the Heat Capacities of Phase Transitions. The whole phase transitions are interpreted to be of an order− disorder type as were indicated previously by structural and NMR studies.12,15−17 The transition entropy of the type can be roughly described by the Boltzmann equation: ΔtrsSm = R ln(WII/WI)

(4)

where WI and WII are the numbers of distinguishable microscopic, configurational states allowed in the low-temperature ordered and high-temperature disordered states, respectively. In general, it is reasonable to assume that WI = 1 at 0 K. In this study, the total transition entropy was estimated experimentally to be 47 J K−1 mol−1, where the 11840

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⎛ ΔE ⎞2 CS = Rg0g1(g0 + g1)−2 ⎜ S ⎟ ⎝ kBT ⎠

In deriving above the high-temperature heat-capacity tail of the phase transitions, the Bethe high-temperature approximation was utilized as representing the short-range order in the disordering process. The parameter B was obtained to be 1.14 × 106 J K mol−1 by the fitting. There are two kinds of components contributing to the short-range-order: one is the orientation about the top or bottom locations of methyl group of the toluene molecule and the other is the two possible rotation angles of each tert-butyl group. Here, the interrelation among four tert-butyl groups was treated as independent. Thus, the B term can be written as B = CS,d + 4 × CS,r where CS,d is the Schottky anomaly due to the toluene molecule and CS,r is that due to each tert-butyl group. From the low temperature 13C NMR measurements, the energy difference ΔES between the two locations of methyl group of toluene was estimated above to be 2.8 kJ mol−1 by assuming the Boltzmann distribution, which was almost equal to a theoretically calculated value.16,17,19 After subtraction of the contribution from the toluene molecule, the energy difference ΔES between the two angles of the tert-butyl group was derived as 2.7 kJ mol−1. From the estimated ΔES, the population ratio of the two permissible angles for each tert-butyl group was calculated to be 75:25 at room temperature by using its Boltzmann distribution; it is compared with 77:23 by Andreeti11 and 50:50 by Enright et al.13 4.2. Thermal Characters of a Commensurate−Incommensurate−(Supercommensurate) Phase Sequence for the Transitions. Phase transitions of a commensurate− incommensurate−(supercommensurate) type have been observed to show characteristic properties.32−34 No heatabsorption effect was observed around the transition at 256.4 K, and a reasonably clear heat-capacity jump was observed. These indicate that the transition is of a second-order type as found as a character of (normal-commensurate)-to-incommensurate phase transitions.32−34 On the other hand, the transitions at 127 K and 139 K exhibit definite heat-absorption effects as well as sharp heat-capacity peaks. These are in accord with the characters of incommensurate-to-(supercommensurate) phase transitions due to stepwise lock-in features.32−34 Gray and coworkers pointed out the extent of the ordering−disordering changes even during single-crystal X-ray diffraction measurement in the low-temperature phase of BC4A·T,13 which is consistent with the existence of an incommensurate nature in the low-temperature phase of BC4A·T, because the situation of the pinning effects relaxes toward more stable states in any incommensurate phase. Thus, the transitions observed in the present BC4A·T crystal are implied to be of a commensurate− incommensurate−(supercommensurate) phase sequence concerning the order−disorder of BC4A and toluene molecules and show lock-in phenomena in the two steps. 4.3. Glass-Transition Phenomenon in the LowTemperature Tail of the Phase Transitions. A glass transition was observed calorimetrically as the classical relaxation phenomenon in which the characteristic time becomes 1 ks at 79 K. The calorimetric and dielectric relaxation times, as plotted in Figure 7, are well expressed by one Arrhenius equation. This fact implies that the two measurements detect the same molecular rearrangement process and therefore that the process attributed to the glass transition is

Figure 8. Schematic illustration of the location of guest toluene molecule with a tilt angle ϕ depicted with exaggeration for clarity (a1), four possible orientation directions depicted with solid arrows in the 4-fold-rotational-symmetric BC4A cage (a-2), and two possible orientations for the methyl group of toluene, namely top or bottom portions within the void of the conic BC4A host cage (b).

splitting of 2.8 kJ mol−1 between the two states assuming their Boltzmann distribution. This disorder should be also included for explaining the transition mechanism. Its contribution to the transition entropy is evaluated as R ln(2). The total transition entropy is thus composed, from the above consideration, of three components: disorder of the orientation angle of the tert-butyl group, disorder of orientation of the principal axis of toluene molecule around the 4-fold rotational symmetry axis of BC4A, and disorder of orientation about the top or bottom locations of the methyl group of the toluene molecule. WII is then written as the product of three contributions: WII = 24 × 4 × 2 = 128. ΔtrsSm(tot) is evaluated as 40.3 J K−1 mol−1 which accords in the order of magnitude with the value obtained experimentally. The realization of many such stable positions/orientations of the toluene molecule and of the two possible rotational angles of the tert-butyl groups would be connected, as stated above, with the presence of the C−H···(π-electron) interactions formed between the C−H of host tert-butyl groups and π electrons of the toluene phenyl ring and between the C−H of the toluene methyl group and π electrons of BC4A phenyl rings.12 The energy difference between the tert-butyl rotation angles in the ground and excited states can be derived from the anomalous heat capacities remaining as a short-range order, by using the expression for a Schottky anomaly in its hightemperature limit. The Schottky heat capacity CS is expressed by the following equation: ⎛ g ⎞⎛ ΔE ⎞2 exp(ΔES/kBT ) CS = R ⎜⎜ 0 ⎟⎟⎜ S ⎟ 2 ⎝ g1 ⎠⎝ kBT ⎠ [1 + (g0/g1)exp(ΔES/kBT )]

(6)

(5)

where g0, g1, and ΔES represent the degeneracies of the ground and excited states and the energy difference between the two states, respectively. In the high-temperature limit, it can be approximated by the following equation: 11841

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The Journal of Physical Chemistry B

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accompanied by a change in the orientation of a dipole moment. As mentioned above, there are three modes of rearrangement motions of molecules. The reorientation of tertbutyl groups brings no or a little change in a dipole moment so that it cannot be the origin of the glass transition. The reorientation, as shown in Figure 8b, of the toluene molecule can be the candidate for the origin. Considering the occupancyfraction ratio between the two orientations at 115 K and 150 K,16,17 only a little contribution is evaluated to the Cp jump at 79 K; the contribution ΔCp = 5 J K−1 mol−1. This means that the mode of rearrangement is not the main origin of the glass transition, although the mode is understood to contribute to the dielectric loss in the temperature range measured. The remaining mode is switching the tilt angle of the principal axis of toluene within the BC4A cage as the tilt directions are shown with arrows in Figure 8a-2.15−17 The switching of the tilt angle brings a change in the orientation of the dipole moment present with toluene. Considering that the rearrangement process breaks some C−H···(π-electron) interactions with a few tens kJ mol−1 which functions as a potential barrier against its progress, there is a high possibility that the process is the origin for the glass transition.

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CONCLUSION In this study, we carried out precise heat-capacity measurements of a crystalline BC4A·T host−guest compound by adiabatic calorimetry and observed a second-order phasetransition at 256.4 K accompanied by first-order lock-in transitions in two steps and a glass transition. The total entropy of the phase transitions was experimentally estimated to be 47 J K−1 mol−1. It indicates that over 100 molecular configurations are present as distinguishable in the hightemperature disordered phase. Many such configurations were interpreted to be composed of three components of disorder: orientations of the tert-butyl group, locations of the toluene molecule fulfilling the presence of the 4-fold rotational symmetry of BC4A, and up-side-down orientations of the toluene molecule within the BC4A cage. It was suggested that the disorders in the positions and directions of the toluene molecule are created and stabilized by C−H···(π-electron) intermolecular interactions; the energy of each interaction is a few kJ mol−1. This C−H···(π-electron) interaction is slightly larger than the van der Waals interaction as dipole−dipole interactions of many kinds and is expected to be formed with different angles and between many combinations of C−H hydrogen atoms and π electrons simultaneously.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +81-48-462-4661. Tel: +8148-462-9410. Present Address †

RIKEN, 2-1, Hirosawa, Wako-shi, Saitama 351-0198, Japan.

Notes

The authors declare no competing financial interest. E-mail: [email protected].

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REFERENCES

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dx.doi.org/10.1021/jp404561b | J. Phys. Chem. B 2013, 117, 11836−11842