New Static Apparatus for Vapor Pressure Measurements: Reconciled

Article pubs.acs.org/jced

New Static Apparatus for Vapor Pressure Measurements: Reconciled Thermophysical Data for Benzophenone Vojtěch Štejfa, Michal Fulem,* Květoslav Růzǐ čka, and Pavel Morávek Department of Physical Chemistry, University of Chemistry and Technology, Prague, Technická 5, CZ-166 28 Prague 6, Czech Republic S Supporting Information *

ABSTRACT: A newly developed static apparatus, capable of measuring the vapor pressure in the temperature range 273− 368 K and in the pressure range 0.1−1333 Pa, is presented. The apparatus was calibrated by measuring the vapor pressure of recommended reference materials, naphthalene, n-decane, and ferrocene, and thoroughly tested. Subsequently, new vapor pressure data for benzophenone were measured in the temperature range 293−365 K with the aim to establish revised thermophysical data for this compound. Although benzophenone is another material recommended as the reference material for sublimation pressure and enthalpy measurements, the published sublimation thermodynamic data show a significant spread, and the recommendation was made with reservations which involved a reported metastable crystalline phase. We clarify this point based on reviewing the literature reporting the phase behavior and crystallographic studies and an extensive study on the polymorphic behavior of benzophenone performed in the present work. These findings are put in context with the studies reporting thermodynamic properties in which the authors were not aware of polymorphic behavior of benzophenone. The experimental data on vapor pressure for benzophenone were supplemented by ideal-gas heat capacities calculated by combining statistical thermodynamics and density functional theory (DFT) calculations. Calculated ideal-gas heat capacities and critically assessed experimental data on vapor pressure, condensed phase heat capacities, and sublimation enthalpies were subsequently treated simultaneously to obtain a consistent description of vaporization and sublimation thermodynamic properties of benzophenone.

1. INTRODUCTION A series of increasingly improved static apparatuses for vapor pressure measurements has been constructed over the past years in our laboratory.1−4 In this work, a newly designed apparatus capable of measuring vapor pressure in the temperature range 273−368 K and in the pressure range 0.1−1333 Pa is described and thoroughly calibrated and tested by the measurements of recommended reference materials, naphthalene, n-decane, and ferrocene. After a careful calibration of the experimental setup including the evaluation of the measurement uncertainties, new vapor pressure measurements along with an extensive study on phase behavior of benzophenone and the calculation of ideal-gas thermodynamic properties by combining the statistical thermodynamics and density functional theory (DFT) calculations were undertaken with the aim to develop recommended sublimation thermodynamic properties for benzophenone. Even though benzophenone is recommended as the reference material for sublimation pressure and enthalpy measurements,5−8 the literature data for both properties do not show an agreement expected for the material used to calibrate experimental equipment. In addition, the recommendation was made with reservations concerning a possible formation of metastable crystalline phase. It seems that © XXXX American Chemical Society

a long history of the phase behavior and crystallographic studies performed on benzophenone clearly indicating a formation of metastable crystalline phase9,10 was overlooked in works reporting thermodynamic properties. In this work, we briefly summarize current knowledge on the polymorphic behavior of benzophenone and discuss it in regard to the suitability of benzophenone as a calibrant for the measurement of sublimation thermodynamic properties. Subsequently, recommended thermodynamic data for both sublimation and vaporization equilibria were developed by a multiproperty simultaneous correlation of vapor pressure and ideal-gas heat capacity data obtained in this work combined with critically assessed literature values on vapor pressure, condensed phase heat capacities, and calorimetrically determined sublimation enthalpies. Received: June 24, 2016 Accepted: August 15, 2016

A

DOI: 10.1021/acs.jced.6b00523 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 1. Sample Descriptions chemical name

CAS RN

source

initial mole fraction purity

naphthalene n-decane ferrocene benzophenone

91-20-3 124-18-5 102-54-5 119-61-9

Aldrich Fluka Aldrich Aldrich

>0.99

zone refining

purification method

0.998

vacuum sublimation

final mole fraction purity

analysis method

1.0000a 0.9997 0.9998 1.0000a

GCb GCb GCb GCb

a

Mole fraction of impurities is below the detection limit of the GC analysis estimated to be x = 0.0001. bGas−liquid chromatography (chromatograph Hewlett−Packard 6890 equipped with a column HP-1, length 25 m, film thickness 0.52 μm, diameter 0.30 mm, and FID detector). The average was of at least two determinations.

Figure 1. Scheme of the apparatus STAT 8.

2. EXPERIMENTAL SECTION 2.1. Materials. The description of the samples used in this work including their purity, methods of purification, and purity analysis is listed in Table 1. 2.2. Static Apparatus for Vapor-Pressure Measurements. A newly developed apparatus for vapor pressure measurements, internally denoted as STAT8, is schematically shown in Figure 1. It is constructed of stainless steel internally electrochemically polished tubing with DN 16 CF and VCR connections and all-metal, pneumatically operated, angle valves VAT series 57 (VAT Vacuumvalves AG, Switzerland) for ultrahigh vacuum. The pressure is measured by a capacitance diaphragm absolute gauge (CDG) Barocel 659 (Edwards, UK) with a measuring upper limit of 1333 Pa. The temperature of the pressure sensors is kept at T = 396 K by an internal temperature controller. The calibration of CDG at 396 K was performed by the manufacturer at 11 equally spaced pressures from 0 to 1333 Pa by comparison to the transfer standard with a maximum relative deviation of 0.10%. The pressure gauge is connected to a stainless steel container with the measured material placed in a homemade air thermostat that allows adjustment of the sample temperature using thermoelectric elements in the temperature range from 273 K up to 373 K with stability better than 0.01 K. The sample

temperature is measured by a secondary reference thermistor silicon-bead probe Hart 5611A (Fluke, USA) in a four-wire connection. The calibration of the thermistor was performed by comparison with a thermometrics temperature standard (Amphenol ES215) by the manufacturer and was traceable to ITS-90 and NIST. The uncertainty in the sample temperature measurement is estimated to be less than 0.01 K. A self-heat error is minimized by duplicating the conditions of calibration; i.e., the resistance measurements are performed with the same source current of 10 μA as during the calibration. The tubing between the cell and the pressure gauges is placed in an insulated box thermostatted at a temperature higher than that of the sample in order to avoid the condensation of its vapor. The box is thermostatted by using air convection forced by means of a ventilator and is controlled to ±0.1 K. The vacuum pump used to evacuate the system between the measuring cycles is a turbomolecular pump EXT70H (Edwards, UK). The primary vacuum is ensured by a scroll vacuum pump Edwards XDS5 (Edwards, UK). The use of these vacuum pumps assures an oil-free pumping that significantly decreases the adsorption of measured samples caused by oil film that is formed when rotary and/or diffusion pumps are used. A cold trap cooled down to 230 K by a B



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thermoelectric cooler is placed between the measuring system and the turbomolecular pump. Prior to measurement of vapor pressure, the apparatus is checked for tightness by MKS PICO helium leak detector (MKS Instruments, USA). The apparatus is evacuated between individual measurement cycles to a pressure of about 10−6 Pa. A computer using the Agilent VEE program monitors the temperature and pressure of the sample and controls the measuring procedure (temperature and valve control). 2.3. Calorimetrical Measurements. Three calorimeters, TA DSC Q1000 (TA Instruments, USA), PE DSC 8500 (PerkinElmer, USA), and Setaram μDSC IIIa (Setaram, France, Tian−Calvet calorimeter), were used to investigate the phase behavior of benzophenone. A thorough temperature and enthalpy calibration of the calorimeters using the reference materials (water, gallium, naphthalene, indium, and tin) was performed prior to the phase behavior measurements of benzophenone. The heat capacities of crystalline β-form (metastable phase) were measured using the PE DSC 8500 calorimeter and StepScan method with a step of 2 K and heating rate 2 K·min−1. The data were evaluated in a standard three-run procedure (sample, blank, and sapphire) using our own code as the software Pyris 11 provided by PE does not offer this option.

Figure 2. Calibration data for STAT8 apparatus: deviations of pressure measured by CDG (pCDG) from recommended vapor pressure values (prec). Red ×, naphthalene (prec2); blue □, n-decane (prec11); green ▲, ferrocene (prec12); , calibration master curve; ---, derived combined expanded uncertainty of vapor pressure measurements using STAT8 apparatus, Uc(p) = 0.01p + 0.05 Pa. The data plotted in this figure can be found in Table S1 in the Supporting Information.

defined uncertainty interval, and it can be described as a function of the measured pressure:

3. RESULTS AND DISCUSSION 3.1. Calibration Results. The apparatus STAT8 was calibrated by measuring the vapor pressure of three reference materials, naphthalene, n-decane, and ferrocene, over the whole working range of the apparatus, i.e., in the pressure range 0.1− 1333 Pa and temperature range 273−368 K. The vapor pressure measurements of the reference materials were performed by varying the temperature at random to detect systematic errors caused by insufficient degassing of measured samples. The experiments were carried out repeatedly at selected temperatures. A full automation of the STAT8 apparatus allowed us to perform a high number of measuring cycles, which typically led to the lowering of the measured pressure. When the pressure decrease was negligible, the sample was considered completely degassed, and the final set of data was recorded, typically after completing tens of measuring cycles at selected temperatures. At least three experimental points were obtained for each temperature. The obtained CDG readings pCDG of vapor pressure as a function of temperature listed in Table S1 were compared to the recommended vapor pressure data prec for naphthalene,2 n-decane,11 and ferrocene.12 Despite a significantly different volatility of the reference materials (i.e., the calibration measurements covered different pressure and temperature intervals), the deviations of pCDG from prec for all of the reference materials showed a systematic positive values that could be described by a single function (a calibration master curve) over the whole working range of the apparatus. This indicates both the internal consistency of the calibration measurements and the recommended values. The calibration results are shown in Figure 2. The combined expanded uncertainty of vapor pressure measurements Uc(p) (0.95 level of confidence, k = 2) using the STAT8 apparatus was estimated based on the deviations of experimental data points from the recommended vapor pressure values after the correction using the derived calibration master curve. Uc(p) was set so that the deviations of 97.5% of experimental vapor pressure points from the recommended values lied within the

Uc(p /Pa) = 0.01p /Pa + 0.05

(1)

3.2. Phase Behavior Studies of Benzophenone. The use of benzophenone as a reference material for sublimation pressure and enthalpy measurement was questioned due to a possible formation of a metastable crystalline phase.5 The thermodynamic studies performed by adiabatic calorimetry attempting to clarify this point report only an instability in the melting region7 or suggest that the metastable phase is not formed if the crystals are obtained by cooling the liquid phase and might be formed only by recrystallization from a solvent.13 It seems that the authors7,13 overlooked a series of studies on the polymorphic behavior of benzophenone dating back to the 19th century and reports of the formation of the metastable form already in 18719,10 (benzophenone is claimed to be the first organic compound identified as polymorphic10). The overview of the phase behavior studies and attempts to obtain the structural parameters of the metastable phase are presented in the paper by Kutzke et al.,10 and thus only most important findings are repeated here. Benzophenone is known to crystallize from a supercooled melt in (at least) two monotropically related polymorphic formsin a stable αform (Tfus ≈ 321 K, orthorhombic crystal system, space group P212121 with a = 10.281, b = 12.123, c = 7.987 Å at 293 K) and in a metastable β-form (Tfus ≈ 298 K, monoclinic crystal system, space group C2/c with a = 16.232, b = 8.163, c = 16.362 Å, α = β = 90°, γ = 112.94° at 293 K).10 As discussed in detail in the section 3.3.4, benzophenone molecules adopt preferentially a twisted conformation with C2 symmetry and thus form two conformational enantiomers. As observed by Kutzke et al.,10 the stable α-form is enantiomorphous, while the metastable β-form is racemic. During the monotropic phase transition from the metastable β-form to the stable α-form, half of the molecules switch their configuration to form their mirror image. Kutzke et al.10 also determined the molecular structure and concluded the molecular parameters in both crystalline phases are almost identical with two exceptions: (i) the dihedral angle between two phenyl rings is 54.4° in α-form and 64.5° in C



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β-form and (ii) the central bond angle in the carbonyl group is 121.4° in α-form and 118.9° in β-form. Regarding the preparation of the metastable β-phase, it is suggested that β-form can be obtained by supercooling the melt to the temperatures in the range 238−250 K.10,14 The formation of α-form is favored above this temperature range while below 203 K the supercooled melt transforms to the glassy phase. The pretreatment of the melt is reported not to affect the selectivity of crystallization. The liquid benzophenone is also known to supercool easily well below its fusion temperature Tfus (by more than 120 K below Tfus of α-form15) allowing measurements to be made in both the solid and liquid phases in the same temperature interval. In this work, special attention regarding the correct identification of the measured phases was paid during the vapor measurements. Furthermore, an extensive study on the phase behavior of benzophenone was conducted using three calorimeters with samples possessing various thermal histories and masses ranging from 0.005 to 0.7 g. 3.2.1. Vapor Pressure Measurements Using the STAT8 Apparatus. The vapor pressure measurements were performed over the temperature range 293−364 K with the initial mass of the sample of about 2 g. The sample was first melted in the STAT8 apparatus to speed up the degassing process. No solidification was detected down to 293 K, and the vapor pressure measurements on the liquid phase were carried out in the temperature range 293−364 K. Subsequently, the sample was solidified by cooling with dry ice. The vapor pressure data measured in the temperature range 293−321 K did not show any evidence of a phase transition. The solid sample used for vapor pressure measurements was analyzed by DSC (Figure 3)

the sample with masses ranging from 0.005 to 0.7 g were carried out using the three calorimeters available in our laboratoryTA DSC Q1000, PE DSC 8500, and Setaram μDSC IIIa. Typical thermograms obtained when the melt was cooled down to 183 or 223 K and subsequently heated are shown in Figure 3. The obtained phase change temperatures and enthalpies are listed and compared with the literature values in Table 2. The calorimetric studies of the phase behavior of benzophenone resulted in the following observations: (i) cooling the sample down to 183 K lead to the formation of the glassy state with a glass temperature transition Tg occurring at (212 ± 1) K, in good agreement with the literature values (see Table 2), (ii) the metastable β-form was obtained by a cold crystallization (not during the cooling process) in the temperature range 241−253 K which agrees with the previous studies reporting the favorable temperature conditions for the nucleation of the β-form in the range 238− 248 K10 or 240−250 K,14 (iii) monotropic spontaneous transition from the metastable β-form to the stable α-form occurred typically in the temperature range 281−297 K predominantly for the grinded samples when the melt was not exposed to higher temperatures (not above approximately 333 K) while heating the melt of the grinded sample to higher temperatures (up to 393 K) prevented the transformation of β to α-form and only the fusion of the β-form was observed on the DSC thermogram, (iv) the transition of β to the α-form was not observed for the samples which had not been grinded prior to experiments regardless the temperature of the pretreatment of the melt, i.e., the behavior was the same as for the grinded samples heated to higher temperatures, and (v) cooling the samples of larger masses (about 0.5−0.7 g) down to about 258 K lead to the crystallization of the α-form or preservation of the subcooled liquid (small sample amounts of about 10 mg never solidified at these conditions). At this point, we do not fully understand the impact of grinding of the polycrystalline sample prior to experiments and the impact of the temperature of the melt pretreatment on the phase behavior, which in contradiction to the literature findings seems to affect the selectivity of crystallization. A more detailed study using various analytical techniques such the vibrational circular dichroism spectroscopy has therefore been initiated in attempt to clarify this behavior and is planned to be published separately. To complete the picture on the phase behavior of benzophenone, we note that a formation of another metastable modification denoted as γform was reported by Davidova et al.14,16 with the transition temperature between the γ- and β-form, Tγ−β, at 295.4 K. In several of our calorimetrical experiments, a small shoulder appeared on the fusion peak of the β-form (see Figure 3), i.e., in the vicinity of the reported Tγ−β. The use of slower heating rates did not lead to the peak separations. In few experiments, an analogous shoulder was also observed on the fusion peak of the α-form. Therefore, we are inclined to interpret this phenomenon as a result of the premelting effect rather than a phase transition confirming the existence of the γ-form. As our calorimetric measurements do not provide a strong evidence for the existence of the γ-form, we keep all the further discussion and data treatment only for two clearly identified crystalline phases in the studied temperature range 183 −321 K, i.e., metastable β-form and stable α-form. 3.3. Vapor Pressure and Thermophysical Data for Benzophenone. This section describes the procedure of developing revised recommended sublimation and vaporization thermodynamic data for benzophenone by multiproperty

Figure 3. Phase behavior of benzophenone. , sample taken from the STAT8 apparatus after the vapor pressure measurements in the solid phase; red , nongrinded sample (the same thermogram was obtained for the grinded sample whose melt was heated up to 393 K); green , grinded sample.

yielding Tfus = (321.3 ± 0.3) K. The vapor pressure curves for crystal−vapor and liquid−vapor equilibria intersect at the triple point temperature (320.7 ± 0.5) K which is close to the normal fusion temperature of α-form (see Table 2). The analysis presented above clearly indicates that the vapor pressure measurements were performed on the stable α-form. 3.2.2. Calorimetric Experiments. To explore further the phase behavior of benzophenone, an extensive calorimetric study using various temperature programs and the treatment of D



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Table 2. Phase Transition Temperatures and Enthalpies of Benzophenonea b

this work de Kruif et al.7 Chirico et al.13 Hanaya et al.23 Neumann and Völker42,c Davydova et al.14,16

Tα→l/K

ΔlαH0m/kJ·mol−1

Tβ→l/K

ΔlβH0m/kJ·mol−1

Tg/K

321.3 ± 0.3 321.03 ± 0.05 321.19 321.28 ± 0.01 321.15 324

18.6 ± 0.3 18.19 ± 0.05 18.606 ± 0.018 18.47 ± 0.02 16.74

298.3 ± 0.3

14.5 ± 0.3

212 ± 1

299.25 301

13.8

207 ± 1 211.7

Only literature sources reporting the fusion temperature and enthalpy of α-form with low uncertainty and/or those reporting also fusion temperature and enthalpy of β-form are listed. bThe values are determined based on the multiple determinations using the TA DSC Q1000 and PE DSC 8500 at p = (100 ± 5) kPa. The quoted uncertainties are combined expanded uncertainties (0.95 level of confidence). cCalculated from the vapor pressure data reported by the authors. a

experience with the sublimation and vaporization enthalpies measured by Morawetz which typically showed a good agreement with other reliable literature sources and good consistency with the related thermodynamic properties for multiple compounds previously studied in our laboratory. 3.3.3. Condensed Phase Heat Capacities and Calorimetric Sublimation Enthalpies. The heat capacities of liquid and crystalline α-form measured by adiabatic calorimetry in two laboratories13,23 show an excellent agreement. The values from these two literature sources were averaged and used in the SimCor method. The formation of the metastable crystalline βform was not observed in refs 13 and 23. As to our knowledge the heat capacities of crystalline β-form were not reported in the literature, we attempted to obtain these data in the frame of this work. In our laboratory, the Tian−Calvet calorimeter Setaram μDSC IIIa is typically used to measure heat capacities with the combined expanded uncertainties (0.95 level of confidence) Uc(Cp) = 0.01Cp (this is significantly less than the uncertainty of heat capacity measurements reachable by heatflux DSC calorimeters). As described in the section 3.2.2, we were not able to obtain the β-form using the Setaram μDSC IIIa calorimeter. At the same time, the heat capacity measurements of the β-form using DSC calorimeters were also not successful at the initial stage of the project. Therefore, we opted for an indirect determination of the difference between heat capacities of β and α-form, ΔαβCp,m, based on the temperature dependence of enthalpies of spontaneous transition from β-form to α-form, ΔαβHm, obtained during the phase behavior studies (see Figure S1). Assuming ΔαβHm to be a linear function of temperature, a constant value of ΔαβCp,m ≈ −10 J· K−1·mol−1 was derived over the temperature interval in which ΔαβHm were observed, i.e., 253−297 K. The cold crystallization enthalpies suffered from large discrepancies (see Figure S1) and were not included in the estimation of ΔαβCp,m. At the later stage of the project, we succeeded to measure the heat capacity of βform, Cβp,m, using the power-compensated calorimeter PE DSC 8500. The results are presented in Table 5. The heat capacities for both α-form and liquid phases measured in the same experiment were in agreement with the adiabatic values13,23 within 2%, which is assumed to be the uncertainty of Cβp,m values. Despite a higher uncertainty of the measurement, we can clearly see the negative ΔαβCp,m ≈ −(6 ± 2) J·K−1·mol−1 over the temperature interval 253−297 K which is in a reasonable agreement with the ΔαβCp,m determined indirectly. 3.3.4. Ideal-Gas Thermodynamic Properties. The thermodynamic properties in the ideal-gas state were calculated by statistical thermodynamics using the rigid rotor−harmonic oscillator (RRHO) approximation with correction for internal rotations using the one-dimensional hindered rotor model (1-D

simultaneous treatment of vapor pressure and related thermal data (SimCor method). The SimCor method was described in detail in ref 11 (for the reader’s convenience, a detailed description of the SimCor method is also presented in the Supporting Information) and was used in our laboratory to develop recommended vapor pressure and thermophysical data for several groups of crystalline and liquid compounds (see for example ref 17 and references therein). The following subsections (3.3.1−3.3.4) summarize the input data needed for the SimCor method obtained either in this work or by critical assessment of the literature data. The recommended vapor pressure equations and thermophysical data for both sublimation and vaporization equilibria are presented in the subsection 3.3.5. 3.3.1. Vapor Pressure. The experimental vapor pressure data obtained in this work are given in Table 3. The literature data listed in Table 4 were first critically assessed using the arc representation,18 which allowed us to reject obvious outliers. Afterward, the consistency of the vapor pressure data with related thermal properties was tested. The selected vapor pressure data used in the SimCor method (section 3.3.5) are given in bold in Table 4. 3.3.2. Calorimetric Vaporization and Sublimation Enthalpies. No calorimetrically determined vaporization enthalpies were found in the literature. The sublimation enthalpy was calorimetrically measured at 298.15 K by Morawetz 19 (ΔgcrHm(298.15 K) = (94.21 ± 0.33) kJ·mol−1), by Sabbah20 (ΔgcrHm(298.15 K) = (92.0 ± 0.7) kJ·mol−1, adopted from ref 5), and by Sabbah and Laffitte21 (ΔgcrHm(298.15 K) = 84.39 kJ· mol−1). We note that we corrected the value reported by Morawetz19 for a misprint. The value ΔgcrHm(298.15 K) = (93.35 ± 0.33) kJ·mol−1 can be found in compendia and databases, such as refs 5 and 22. By a closer inspection of Table 1 in ref 19 reporting the experimental results on determination of sublimation enthalpies for a set of compounds, one can see that the value given for the sublimation enthalpy of benzophenone is equal to the enthalpy change only in the main calorimeter, while for other compounds in the study the final value of the sublimation enthalpy is obtained as the sum of the contributions of the enthalpy changes in the main and auxiliary calorimeters. In the case of benzophenone, the contribution from the auxiliary calorimeter amounts to 0.85 kJ·mol−1. We added this contribution to the enthalpy change measured in the main calorimeter to obtain the value of the sublimation enthalpy of benzophenone ΔgcrHm(298.15 K) = (94.21 ± 0.33) kJ·mol−1. Only the corrected value reported by Morawetz19 was used in the SimCor method as the other two determinations originating from the laboratory20,21 show a significant discrepancy. The selection is also based on our E



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Table 3. Experimental Vapor Pressures of Benzophenonea T/K

pb/Pa

Δpc/Pa

293.11 293.11 293.11 298.48 298.48 298.48 302.13 302.13 302.14 307.46 307.48 307.48 312.77 312.78 312.78 318.05 318.05 318.05 323.33 323.33 323.33 328.52 328.52 328.52 333.79 333.79 333.79 338.90 338.90 338.90 344.09 344.09 344.09 349.19 349.19 349.19 354.35 354.35 354.35 359.40 359.40 359.40 364.47 364.47 364.48

Liquid 0.081 0.084 0.085 0.153 0.157 0.158 0.217 0.221 0.217 0.382 0.376 0.380 0.631 0.635 0.637 1.035 1.036 1.039 1.658 1.660 1.661 2.576 2.580 2.583 3.974 3.975 3.979 5.953 5.954 5.968 8.882 8.890 8.894 12.90 12.91 12.93 18.64 18.65 18.66 26.28 26.29 26.31 36.73 36.73 36.72

−0.006 −0.003 −0.001 −0.001 0.003 0.004 −0.008 −0.004 −0.008 −0.001 −0.008 −0.004 −0.007 −0.004 −0.002 −0.003 −0.002 0.001 0.001 0.003 0.004 −0.002 0.002 0.005 0.002 0.003 0.007 0.007 0.008 0.022 0.055 0.063 0.067 0.07 0.08 0.10 0.14 0.15 0.16 0.15 0.16 0.18 0.20 0.20 0.17

T/K

pb/Pa

The conformational properties of systems containing a multiaryl substituted central atom or planar framework were frequently studied due to their specific helical stereochemistry.26−29 These compounds are known to adopt socalled helical (propeller) conformations and to exhibit axial chirality. Analogously, the preferred conformation of benzophenone with minimum energy is helical (also known as twisted) possessing C2 symmetry and aryl rings twisted out of the central carbonyl plane in opposite directions by θ1 = θ2 ≈ 30°. The enantiomerization between P and M enantiomers might occur, in principle, via three possible pathways: (i) zeroring flip (conrotatory route), (ii) one-ring flip (disrotatory route), and (iii) two-ring flip (conrotatory route).27 The onering flip route is recognized to be the most energetically favorable rotational mechanism passing through the saddle point conformation in which one ring is orthogonal to and the other coplanar with the central carbonyl plane (θ1 = 0°, θ2 = 90°). The zero ring flip pathway passes through a planar transition state (θ1 = θ2 = 0°) or almost a planar conformation with a significantly higher energy. The two-ring flip route leads to a perpendicular conformation (θ1 = θ2 = 90°) which was reported to be more energetically favorable than a planar transition state.26 In this work, the conformational analysis performed at the B3LYP/6-311+G(d,p) level of theory confirmed the twisted conformer possessing C2 symmetry with θ1 = θ2 = 28.7° as the energetically most favored conformation (the energy of C1 symmetry twisted conformer optimized without symmetry restrictions was 0.1 kJ·mol−1 lower which is negligible compared with the uncertainty of the B3LYP method). The C2 symmetry twisted conformer displayed in Figure 4 was used for the calculation of vibrational frequencies and as an initial structure for PE scans. The Cartesian coordinates of the optimized geometry of the twisted conformer along with other molecular parameters such as the principal moments of inertia are given in Table S2 in the Supporting Information. The comparison of molecular geometry with crystallographic data presented in Table 6 shows that the molecular structure of the optimized twisted conformer is very similar to that found in the crystalline α-phase. The C2V symmetry planar conformer with relative energy of 27.9 kJ·mol−1 (32 kJ·mol−1 in30) compared to the twisted conformer was also successfully optimized. Two imaginary frequencies obtained for this structure nevertheless indicate that it is an unstable stationary point on the PE surface. A relaxed scan of PE of the phenyl rotation over full 360° range required for the application of the 1-D HR model exhibited discontinuities (see Figure S2 in the Supporting Information). Previously reported PE scans of phenyl rotation did not show this phenomenon due to either employing rigid scans (some molecular coordinates were kept frozen during the phenyl rotation) or lower level of theories (ab initio STO-3G or semiempirical MNDO methods).26 A 2-D scan of PE with 10° step was therefore performed to explain this behavior (see Figure 5). It clearly showed that the location of saddle point corresponding to the gable conformation (Cs symmetry, θ1 = −θ2 = 28.7°) caused the mentioned discontinuity on the 1-D relaxed PE scan. The energy barrier in the saddle point (24.2 kJ·mol−1) was in good agreement when obtained as the minimum on the Cs symmetry line and from several relaxed scans with one phenyl distortion fixed close to its natural position in the twisted conformer. The discussed part of energy scan can be linked to the zero-ring flip rotational mechanism suggesting that the optimal trajectory passes through the gable

Δpc/Pa

Crystalline (α-form) 293.08 0.042 −0.004 293.09 0.046 0.000 293.10 0.041 −0.004 296.29 0.068 −0.002 296.29 0.069 −0.001 296.30 0.067 −0.003 298.44 0.092 0.000 298.44 0.093 0.001 298.45 0.090 −0.002 300.55 0.124 0.004 300.56 0.118 −0.003 300.56 0.119 −0.001 303.20 0.168 0.000 303.22 0.166 −0.003 303.25 0.165 −0.004 306.93 0.263 −0.002 306.93 0.265 0.000 306.93 0.267 0.001 309.05 0.338 −0.004 309.05 0.340 −0.002 309.05 0.345 0.003 311.10 0.431 −0.005 311.10 0.434 −0.002 311.10 0.435 −0.001 314.30 0.629 −0.004 314.30 0.632 −0.001 314.30 0.635 0.002 317.33 0.891 −0.002 317.34 0.892 −0.002 317.34 0.899 0.005 319.40 1.130 0.004 319.41 1.128 0.001 319.41 1.131 0.004 320.42 1.256 −0.005 320.42 1.265 0.004 320.42 1.267 0.006 320.95 1.353 0.016 320.95 1.356 0.019 320.95 1.362 0.025

a

The standard uncertainty in the sample temperature measurements is u(T) = 0.01 K and combined expanded uncertainty (0.95 level of confidence, k = 2) in the vapor pressure measurements is Uc(p) = 0.01p + 0.05 Pa. bValues are reported with one digit more than is justified by the experimental uncertainty to avoid round-off errors in calculations based on these results. cΔp/Pa = (p − pcalc)/Pa, where pcalc is calculated from the Cox equation, eq 2, with parameters given in Table 7.

HR).24 Molecular geometry optimizations, vibrational frequencies calculations, and relaxed scans of potential energy (PE) were performed using the density functional theory (DFT) at the B3LYP/6-311+G(d,p) level of theory with the Gaussian 09 software.25 F



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Table 4. Overview of the Literature Vapor Pressure Data for Benzophenonea,b Nc

reference

(Tmin − Tmax)/ K

Neumann and Völker42

11

285−299

Volmer and Kirchoff44 Neumann and Völker42 Nitta and Seki45 Serpinski et al.46 Aihara47 Wood48 (as cited in TDE49) Přibilová and Pouchlý50 van Ginkel et al.51 de Kruif and van Ginkel8 de Kruif and van Ginkel8 de Kruif et al.7 Verevkin52 Monte et al.43

9 19 S 10 8 7 3 26 S S 26 6 40

273−321 289−315 308−nosp. 293−315 293−312 303−317 298−318 294−319 297−317 297−317 306−321 299−320 310−321

Jaquerod and Wassmer53 Finck and Wilhelm54 Neumann and Völker42 Dreisbach and Shrader55 Nitta and Seki45 Serpinski et al.46 DePablo56 de Kruif et al.7 Steele et al.39,g Steele et al.39 Monte et al.43

50 51 22 8 S 3 4 25 12 22 46

530−576 575−582 290−328 474−579 nosp. − 329 328−338 329−344 323−386 355−455 443−623 308−385

(pmin − pmax)/ Pa

mole fraction purity

Crystalline Phase (β-form) 0.025−0.15 nosp.f Crystalline Phase (α-form) 0.0027−1.43 nosp. 0.027−0.65 nosp. nosp. nosp. 0.048−1.40 nosp. 0.050−0.44 nosp. 0.15−0.85 nosp. 0.095−0.93 nosp. 0.057−1.07 nosp. 0.076−0.84 nosp. 0.076−0.86 nosp. 0.23−1.35 nosp. 0.088−1.05 0.9999 0.39−1.31 0.9999 Liquid Phase 33330−95992 nosp. 93451−106594 nosp. 0.063−2.40 nosp. 6287−101325 0.9986 nosp. nosp. 2.56−5.47 nosp. 3.15−9.53 nosp. 1.57−132.7 nosp. 19.7−3223 0.998 2000−232020 0.998 0.41−129 0.9999

u(T)d/ K

u(p)e/ Pa

method

0.2

1.5%

effusion

nosp. 0.2 nosp. nosp. nosp. nosp. 0.02 nosp. 0.1 0.1 0.01 0.1 0.01

nosp. 1.5% nosp. nosp. nosp. nosp. nosp. nosp. nosp. nosp. nosp. nosp. 0.01 + 0.0025 p

effusion effusion effusion effusion viscosity gauge effusion effusion effusion effusion (mass) effusion (torsion) static saturation static

0.04 0.03 0.2 nosp. nosp. nosp. 0.05 0.01 0.001 0.001 0.01

nosp. nosp. 1.5% 7 nosp. nosp. 5% nosp. 0.2 + 0.00015p 100 Pa were included in the SimCor method.

Table 5. Heat Capacitiesa of β-form of Benzophenone in J· K−1·mol−1 T/K

Cβp,m

T/K

Cβp,m

T/K

Cβp,m

214.2 218.1 222.1 226.1 230.1 234.1 238.0

168.8 171.5 174.4 176.9 179.8 181.4 183.6

242.0 246.0 250.0 254.0 258.0 262.1 266.1

187.8 191.3 193.4 196.9 198.8 201.9 204.7

270.1 274.1 278.1 282.1 286.1 290.1 294.1

207.6 209.9 213.5 215.6 218.8 221.5 224.0

a

Measured using the PE DSC 8500 calorimeter and step method at p = (100 ± 5) kPa. The standard uncertainty of the temperature is u(T) = 0.3 K, and the combined expanded uncertainty of the heat capacity is estimated to be Uc(Cp,m) = 0.02 Cp,m (0.95 level of confidence). Mean values of two determinations are given in the table.

Figure 4. Optimized molecular structure of twisted conformer of benzophenone with C2 symmetry (at the DFT B3LYP/6-311+G(d,p) level of theory).

rather than the planar conformation (see the route “b” in Figure 5). The one-ring flip mechanism can be linked to the second part of the trajectory passing through transition state where one ring is orthogonal to and the other coplanar with the central carbonyl plane (Cs symmetry, θ1 = 0°, θ2 = 90°, see the route “a” in Figure 5). The energy barrier of one-ring flip mechanism is 11.4 kJ·mol−1 (9.7 kJ·mol−126) and can easily be obtained using the relaxed PE scan. The two-ring flip route would pass through the perpendicular conformation (C2V symmetry, θ1 = θ2 = 90°), which is the global maximum on the PE surface (see route “c” in Figure 5). The calculations at

the DFT B3LYP/6-311+G(d,p) level of theory thus indicate that this rotational mechanism is highly unfavorable which is in contradiction to the analyses performed based on the calculations at lower levels of theory26 or molecular mechanics calculations.27 The final PE profile of phenyl rotation was composed from the zero-ring and one-ring flip rotational mechanisms in a way to avoid the discontinuity and fulfill the following considerations: (i) PE profile must have a 2-fold symmetry (the same as the phenyl top), (ii) PE must exhibit four energetically equal G



Article

Table 6. Characteristic Angles of Molecular Structure of Benzophenone

dihedral angle between phenyl rings carbonyl angle 1−7−9 dihedral 8−7−9−10a dihedral 8−7−1−2a

isolated molecule (this workb)

isolated molecule (literature)

α crystalline form (stable)

β crystalline form (metastable)

55.5 120.1 28.7 28.7

78.657 119.5,30 119.557 3230 2830

54.4,10 54,57 5658 123.5,10 123.1,57 119.6,27 12258 26.4,10 31,27 29.458 29.1,10 30,27 30.958

64.310 117.110 27.010 41.210

a

Indirect determinations are not listed. Four indirect determinations of dihedral angle 8−7−9−10 = 8−7−1−2 in the liquid phase summarized by Volovšek et al.35 suggest the values in the range 30−42°. bBased on the optimized molecular geometry of the C2 symmetry twisted conformer obtained at the DFT B3LYP/6-311+G(d,p) level of theory.

0.9618 (wavenumbers >2000 cm−1). The calculated vibrational frequencies are listed in Table S3 in the Supporting Information. Experimental vibrational frequencies of benzophenone were found in several papers.30,34−37 The complete set of assigned frequencies was presented by Volovšek et al.35 (with the help of molecular mechanics calculations). The agreement with scaled vibrational frequencies calculated in this work at the DFT B3LYP/6-311+G(d,p) level of theory can be considered satisfactory except the three lowest frequencies (see Table S3 in the Supporting Information). DFT B3LYP/6-311+G(d,p) calculations yielded 90, 61, and 42 cm−1 compared to 144, 105, and 86 cm−1 reported by Volovšek et al.35 The two lowest vibrational modes were visually determined to correspond to the phenyl top rotations and were therefore excluded from the vibrational partition function and treated using the 1-D HR model as described above. Nevertheless, the difference of 54 cm−1 in the third lowest frequency lead to an error of 0.9% in the standard ideal-gas entropy at 298.15 K, Sg0 m (298.15 K), reflecting the sensitivity of the entropy to the low frequencies. The calculated ideal-gas heat capacities and standard idealgas entropies at p = 0.1 MPa are listed in Table 7. Table S4 in the Supporting Information lists the ideal-gas thermodynamic properties and the contributions of internal rotations to the thermodynamic properties as obtained using the 1-D HR scheme in a wider temperature range 100−1000 K. We note that due to the existence of two enantiomers the contribution of R ln(2) arising due to the mixing entropy was included in the standard ideal-gas entropies (the existence of two enantiomers has no impact on the ideal-gas heat capacities). While no literature data on the ideal-gas heat capacities were found for comparison, four third law entropy values at 298.15 K could be calculated based on the calorimetrical data for undercooled liquid and α crystalline phase13,23 combined with the phase change entropy calculated from the Cox equation, eq 2, with the parameters listed in Table 8. All of the values are in the −1 −1 range Sg0 which is in m (298.15 K) = (444.4 ± 0.4) J·K ·mol satisfactory agreement with our theoretical value Sg0 m (298.15 K) = (447.5 ± 3) J·K−1·mol−1. 3.3.5. Recommended Vapor Pressure and Thermophysical Data Developed by the SimCor Method. The SimCor method (for details, see the section 1 in the Supporting Information) was used to correlate the selected literature vapor pressure (bold in Table 4) along with those determined in this work (Table 3), the selected calorimetric sublimation enthalpies (discussed in the section 3.3.2), and condensed phase heat capacities (section 3.3.3), and the ideal-gas heat capacities calculated in this work (Table 7). The nonideal behavior of the vapor phase was described using the second virial coefficient estimated by the method of Tsonopoulos38 using the additional term derived for ketones. The following data were used: critical parameters Tc = 830 K and pc = 3.352 MPa,39 dipole moment μ

Figure 5. 2-D scan of potential energy of phenyl rotations. Red , pathway of potential energy profile of phenyl rotation used in the calculations of ideal-gas thermodynamic properties (see Figure S2); magenta , Cs symmetry line (main diagonal); blue , C2 symmetry line (antidiagonal). Transition states: a, one-ring flip route; b, zeroring flip route; c, two-ring flip (along the C2 symmetry line). Color scale represents energy in kJ·mol−1.

minima corresponding to the twisted C2 symmetry conformer (two for P enantiomer and two for M enantiomer), and (iii) PE must exhibit two energy barriers for the one-ring flip mechanism and two energy barriers for the zero-ring flip mechanism alternating periodically. The final PE profile of phenyl rotation can be seen in Figure S2 in the Supporting Information. The determined heights of energy barriers and the Fourier expansion coefficients used to fit the PE profile are listed in Table S2 in the Supporting Information. The contributions of internal rotations of phenyl tops to thermodynamic properties were calculated using the 1-D HR scheme, which further requires the reduced moments of inertia Ir for internal rotations, the internal symmetry numbers, and the identification and exclusion of the torsional modes from the vibrational contribution to the partition function. The reduced moments of inertia Ir for internal rotations were calculated according to Pitzer and Gwinn31 from the optimized molecular parameters. The energy levels of hindered internal rotations were obtained by solving a one-dimensional Schrödinger equation using our code performing the FGH method32 and solving the eigenvalues problem by the QZ algorithm. The vibrational contributions to the ideal-gas thermodynamic properties were computed using the HO approximation using the fundamental frequencies calculated at the DFT B3LYP/6-311+G(d,p) level of theory which were scaled by frequency-dependent scaling factors recommended for sp2 structures33by 0.9808 (wavenumbers

New Static Apparatus for Vapor Pressure Measurements: Reconciled

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