Thermodynamic properties of caffeine: reconciliation of available experimental data

J. Chem. Thermodynamics 40 (2008) 1661–1665 Thermodynamic properties of caffeine: Reconciliation of availableexperimental data Vladimir N. Emel’yanenko, Sergey P. Verevkin * Department of Physical Chemistry, University of Rostock, Hermannstrasse 14, D-18051 Rostock, Germany Molar enthalpies of sublimation of two crystal forms of caffeine were obtained from the temperature dependence of the vapour pressure measured by the transpiration method. A large number of primary experimental results on the temperature dependences of vapour pressure and phase transitions have been collected from the literature and have been treated in a uniform manner in order to derive sublima- tion enthalpies of caffeine at T = 298.15 K. This collection together with the new experimental resultsreported here has helped to resolve contradictions in the available sublimation enthalpies data and to recommend a consistent and reliable set of sublimation and formation enthalpies for both crystal forms under study. Ab initio calculations of the gaseous molar enthalpy of formation of caffeine have been per- formed using the G3MP2 method and the results are in excellent agreement with the selected experi- Ó 2008 Elsevier Ltd. All rights reserved.
the help of additional experimental measurements. Additionalsupport for the measured values comes from ab initio calculations We have commenced studies on the thermochemical proper- of gaseous molar enthalpy of formation of caffeine using the ties of purine-like compounds with the aim of enlarging insight into the energetics of nucleic acids. Caffeine is a compound ofconsiderable industrial and environmental significance. Caffeine is a relatively simple model compound, which is useful in under-standing the structure–energy relationships of nucleic acids. Ther- modynamic properties of caffeine have been extensively studied. However, thermochemical data on caffeine are in apparent A sample of anhydrous caffeine obtained as the a-phase mate- disarray (see A very careful thermochemical study (com- rial (CAS registry number 58-08-2) was obtained from Sigma bustion calorimetry and DSC) of two anhydrous polymorphs of (USP grade). It was further purified by fractional sublimation at caffeine has been recently published in this journal Several T = 383 K and at reduced pressure. The purity analyses were per- months later, another thermochemical study of caffeine ap- formed using a gas chromatograph (GC) with a flame ionisation peared in the same journal, where the reported combustion en- detector. A HP-5 capillary column (stationary phase cross-linked thalpy of the a-phase of caffeine differs by about 20 kJ Á molÀ1.
5% PH ME silicone) was used in all our experiments. The column Since 1979, vapour pressure and enthalpies of sublimation of caf- was 30 m long, had an inside diameter of 0.32 mm , and a film feine polymorphs have been measured using diverse methods.
thickness of 0.25 lm. The flow rate of the carrier gas (nitrogen) We have carefully collected the primary experimental results on was maintained at 7.2 dm3 Á hÀ1. The starting temperature for the temperature dependence of vapour pressure and phase transi- the GC was 323 K for the first 180 s, followed by heating to tions available in the literature (see ). Analy- T = 523 K at the rate of 10 K Á minÀ1. No impurities greater than sis of the primary experimental data reveals that the sublimation 0.02 mass per cent were detected in the sample used in this enthalpies of the caffeine spread over 11 kJ Á molÀ1 for the a-poly- morph, and over 4 kJ Á molÀ1 for the b-polymorph. The purpose ofthis paper is to resolve the existing disagreement between the 2.2. Vapour pressure measurements of caffeine available values of the sublimation enthalpies of caffeine, with Vapour pressure and enthalpies of sublimation, Dg H feine polymorphs were determined using the method of transpira- * Corresponding author. Tel.: +49 381 498 6508; fax: +49 381 498 6502.
tion in a saturated nitrogen stream. About 0.5 g of the sample 0021-9614/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jct.2008.07.002 V.N. Emel’yanenko, S.P. Verevkin / J. Chem. Thermodynamics 40 (2008) 1661–1665 Compilation of data on enthalpies of sublimation Dg H Standard ab initio molecular orbital calculations were per- formed with the Gaussian 03 Rev. 04 series of programs . Ener- gies were obtained at the G3MP2 level of theory. The G3 theory is a procedure for calculating the energies of molecules containing atoms of the first and second rows of the periodic chart based on ab initio molecular orbital theory. A modification of G3 theory that uses reduced orders of Moller–Plesset perturbation theory is the G3(MP2) theory This method saves considerable computa- tional time compared to G3 theory with some loss in accuracy, but is much more accurate than G2MP2 theory. For all the species in-cluded in this study, full geometry optimisations were carried out at the HF/6-31G(d) level. The corresponding harmonic vibra- tional frequencies were evaluated at the same level of theory to Vapour pressures available in the literature were treated using equations confirm that the optimised structures found correspond to the po- in order to evaluate enthalpy of vaporization at T = 298.15 K, in the same way asour own results in tential energy minima and to allow the evaluation of the corre-sponding zero-point vibrational energies, ZPE, and the thermalcorrections at T = 298 K. The ZPE values were scaled by the empir- ical factor 0.8929. All the minima found at the HF/6-31G(d) level Compilation of the data available for the solid phase transition, DtransHm, and the were again fully re-optimised at the MP2(FULL)/6-31G(d) level.
The G3MP2 theory uses geometries from second-order perturba- tion theory and scaled zero-point energies from Hartry–Fock the- ory followed by a series of single-point energy calculations at the MP2(Full), QCISD(T), and MP2/GTMP2Large levels of theory (for details see reference The enthalpy value of the compound studied at T = 298 K was evaluated according to the standard ther- Caffeine was found to display a low-temperature a-polymorph modification at room temperature with the trigonal crystal struc- a Techniques: DTA, Du Pont 990 Thermal Analyzer; MCB, differential heat flux ture At T = 414 K, the a-polymorph of caffeine transforms into calorimeter MCB; TE, torsion effusion method; DSC, differential scanning calorim- a b-crystal phase and remains in this phase until the melting etry; SC, solution calorimetry; CC, combustion calorimetry; T, transpiration.
b Taken into account for the calculation of the average enthalpy of the phase transition (3.8 ± 0.3) kJ.molÀ1.
c Average enthalpy of fusion (21.4 ± 0.6) kJ Á molÀ1 was calculated from the data 3.1. Vapour pressure and sublimation enthalpies Vapour pressures of caffeine polymorphs measured in this work and those from the literature were treated with equations was mixed with glass beads and placed in a thermostated U-shaped tube having a length of 20 cm and a diameter of 0.5 cm. Glass beads with a diameter of 1 mm provide a surface large enough for rapid (vapour + solid) equilibration. At constant temperature (±0.1 K), a nitrogen stream was passed through the U-tube and the transported amount of material was collected in p , required for the correction of the sublima- a cooling trap. The flow rate of the nitrogen stream was measured tion enthalpies, have been derived according to a procedure devel- using a soap bubble flow meter and was optimised in order to oped by Chickos and Acree The following values: Dg C reach the saturation equilibrium of the transporting gas at each temperature under study. The transported material was collected 40:8 J Á KÀ1 Á molÀ1 for the b-phase have been used in this in a special cold trap and the amount of condensed product was p ¼ 95:3 J Á KÀ1 Á molÀ1, required for adjust- determined by weighing (±0.0001 g). The saturation vapour pres- ing the vaporization enthalpy (see was calculated using the group contribution method of Chickos and Acree . In order of the product collected within a definite period of time. Assuming to assess the uncertainty of the sublimation enthalpy, the experi- that Dalton’s law of partial pressures applied to the nitrogen mental data were approximated with the linear equation stream saturated with the substance i of interest is valid, values lnðpsatÞ ¼ f ðTÀ1Þ using the method of least squares. The uncertainty of psat were calculated using the equation in the enthalpy of sublimation was assumed to be identical with the average deviation of the experimental lnðpsatÞ values from this linear correlation. The experimental results for sublimation enthal- where R = 8.314472 J Á KÀ1 Á molÀ1, mi is the mass of the transported pies, and parameters a and b according to equation are listed in compound, Mi is the molar mass of the compound, and Vi is its vol- In order to ensure complete phase conversion to the ume contribution to the gaseous phase. VN2 is the volume of the car- b-phase during the transpiration measurements, the sample was rier gas and Ta is the temperature of the soap bubble meter. The firstly heated to T = 434.5 K and was kept at this temperature for volume of the carrier gas, VN2, was determined from the flow rate about 30 min. The vapour pressure experiments were conse- quently done from the higher to lower temperatures.
V.N. Emel’yanenko, S.P. Verevkin / J. Chem. Thermodynamics 40 (2008) 1661–1665 m ð298:15 KÞ ¼ ð108:1 Æ 1:1Þ=ðkJ Á molÀ1 Þ lnðp=PaÞ ¼ 307:56 À 116102:54 Á ðT=KÞ À 26:8 ln m ð298:15 KÞ ¼ ð104:2 Æ 3:6Þ=ðkJ Á molÀ1 Þ lnðp=PaÞ ¼ 313:26 À 116335:98 Á ðT=KÞ À 40:8 ln a Temperature of saturation.
b Mass of transferred sample, condensed at T = 293 K.
c Volume of nitrogen, used to transfer the mass m of the sample.
d Vapour pressure at temperature T, calculated from m and the residual vapour pressure at T= 293 K.
The temperature dependence of the vapour pressure for the so- lid caffeine is presented in . As can be seen, our vapour pressures are in a good agreement with the results measured bythe static method and by the Knudsen effusion method .
Vapour pressures reported by Griesser et al. lie systematically above the data available, most probably due to an error in the cal-ibration. Vapour pressures measured using the effusion method are somewhat below the available data, however, the trend seemsto be correct.
The sublimation enthalpy of the b-phase of caffeine derived in m ð298:15 KÞ ¼ ð104:2 Æ 3:6Þ kJ Á molÀ1, is definitely lower than those from Griesser et al. Dg H kJ Á molÀ1 from Bothe and Cammenga even taking into ac- count the large uncertainty of our results. It was not possible forus to determine the sublimation enthalpy of the b-phase of caffeine by the transpiration method more precisely, because of the very re-stricted temperature range from (420 to 434) K, which was at the The set of available sublimation enthalpies of the a-phase of caffeine also shows a large spread in values, from (106 to117) kJ Á molÀ1 (see ). There are two values from and FIGURE 1. Plot of vapour pressure measurements against reciprocal temperature from close to the level of 117 kJ Á molÀ1 and there are also for caffeine: ‘d’ – this work; ‘s’ – a-phase ; ‘+’ – b-phase ; ‘N’ – a-phase ;‘h’ – a-phase ; ‘M’ – b-phase ; ‘j’ – liquid phase ; ‘}’ – a-phase . The two values (and this work]) close to the level of 106 kJ Á molÀ1.
dotted lines indicate the temperatures of the phase transitions.
Which value of sublimation enthalpy is preferred? 3.2. Consistency tests of the experimental results py of phase transition of caffeine obtained by calorimetry Since a significant discrepancy in the available experimental sublimation enthalpy results collected in has been found,additional arguments to support the reliability of our new mea- As can be seen from the DSC results for the phase transition 3.2.1. Internal consistency of sublimation enthalpies and the enthalpy DtransHm(a ? b) from different sources are very consistent and the average value of (3.8 ± 0.3) kJ Á molÀ1 was calculated from these A valuable test of the internal consistency of the experimental results. Comparing the latter value with the enthalpy of phase tran- data of sublimation enthalpies for the a- and b-phase measured sition calculated using equation from the difference of Dg H in this work (see is the comparison with the enthal- (for the a and b phases) measured in this work (see ): V.N. Emel’yanenko, S.P. Verevkin / J. Chem. Thermodynamics 40 (2008) 1661–1665 DtransHm(a ? b) = 108.1–104.2 = (3.9 ± 3.8) kJ Á molÀ1. This estimate that has been proven to be consistent with the phase transition does not differ from the results measured by calorimetry (see enthalpy measured by DSC (see ). The values are in close ). Hence, in this way, our results for the sublimation enthalpies of agreement with the value DtransHm(a ? b) = (2.0 ± 0.3) kJ Á molÀ1, the a- and b-phase seem to be consistent. Similar treatment of measured using a solution calorimeter . Surprisingly, the the sublimations enthalpies measured by Bothe and Cammenga most recent value, Df H ðcrÞ ¼ ðÀ322:2 Æ 4:8Þ kJ Á molÀ1 for the a-phase of caffeine measured by Dong et al. by using (5.2 ± 0.9) kJ Á molÀ1 and those from Griesser et al. : Dtrans macro-combustion calorimetry is about 20 kJ Á molÀ1 less negative Hm(a ? b) = 116.6–108.5 = (8.1 ± 0.5) kJ Á molÀ1. Our results as well than the results from Pinto and Diogo . We do not have any as those from Bothe and Cammenga are internally consistent; disagreement between these data sets remains apparent.
sample by Dong et al. was contaminated with the b-phase, thedisagreement could be only within (2 to 5) kJ Á molÀ1 as shown 3.2.2. Internal consistency of sublimation enthalpies adjusted to the above. We shall try to resolve this contradiction with the help of our new values of sublimation enthalpies and high-level ab initio An additional argument to support the experimental results measured in this work is to consider the following thermochemicalcycle: 3.2.4. Experimental enthalpies of formation of caffeine in the gaseousphase Values of sublimation enthalpies of caffeine, derived in this work, have been checked for internal consistency. These values(see can now be used for further calculation of the stan- mðT fusÞ in equation was obtained by adjusting the enthalpy of vaporization measured by a static manometer (see For this purpose, we selected first the enthalpies of formation from Tav = 516.5 K to Tfus = 509 K. The value DgH ðcrÞ of for a- and b-phase of caffeine reported by Pinto and equation is the average of the available literature data (see Diogo and the resulting values of the standard molar enthalpies mðT fusÞ ¼ ð97:1 Æ 0:9Þ kJ Á molÀ1 compared with the similar adjustments of our new sublimation modynamic properties of a-phase) and Df H ðgÞ ¼ ðÀ236:4 Æ 4:3Þ enthalpies (according to equation for the b-phase of kJ Á molÀ1 (from the thermodynamic properties of b-phase). The very good agreement between these values is again further evi-dence of the internal consistency of the results selected in this work. However, the absolute value of the gaseous enthalpy of for- mation of caffeine still remains questionable. An additional possi-bility to test the consistency of the selected data is the comparison of the experimental gaseous enthalpy of formation ofcaffeine with the value calculated using quantum chemical calcu- For the adjustment of the sublimation enthalpy for the a-phase of lations. Such a test could be performed in the manner we sug- caffeine, the phase transition DtransHm(a ? b) = (3.8 ± 0.3) kJ Á molÀ1 at Ttrans = 414 K (see ) should be additionally taken into ac-count and it should also be adjusted to Tfus. The adjustment forthe a-phase of caffeine is as follows: 3.2.5. Enthalpy of formation of caffeine in the gaseous phase: quantumchemical calculations The ab initio molecular orbital methods used for the calculation p  ðT av À T fusÞ À DtransHmða ! bÞ of the enthalpy of formation of caffeine have not been yet reported in the literature. We have calculated using the G3MP2, a total en- ¼ 105:7 À 0:0268  ð509 À 388Þ À 3:8 þ 0:0014  ergy at T = 0 K, E0 = À679.383314 Hartree and enthalpy at T = 298.15 K, H298 = À679.369094 Hartree. In standard Gaussian-n the- ories, theoretical standard enthalpies of formation, Df H ðgÞ, are calculated through atomization reactions . Using this proce- As can be seen, results which have been obtained according to dure we have obtained for caffeine Df H ðgÞ ¼ À235:5kJ Á molÀ1.
equations are in excellent agreement. This fact provides Thus, the theoretical enthalpy of formation of caffeine is in excel- the additional evidence for the internal consistency of the experi- lent agreement with the experimental values derived from com- mental results determined in this work.
bustion experiments by Pinto and Diogo and enthalpies ofsublimation measured in this work. Hence, with the help of this 3.2.3. Experimental enthalpies of formation of caffeine in the theoretical result we are able to resolve the uncertainty in the available thermochemical data on caffeine.
The values of enthalpies of sublimation Dg H are required to obtain gaseous enthalpies of formation, Df H ðgÞ, of organic compounds, provided that their enthalpies of formationin the condensed phase, Df H (cr), are known. Standard molar This investigation was undertaken to establish a consistent set enthalpies of formation Df H ðcrÞ ¼ ðÀ345:1 Æ 2:3Þ kJ Á molÀ1 for of vapour pressures, sublimation, and formation enthalpies of caf- the a-phase and Df H ðcrÞ ¼ ðÀ340:6 Æ 2:3Þ kJ Á molÀ1 for the b- feine. We collected from the literature a large number of primary phase of caffeine were measured by Pinto and Diogo by experimental results and treated them uniformly in order to derive micro-combustion calorimetry. The difference between these val- T = 298.15 K. The data sets on phase transitions were checked for internal consistency. This collection together with the new exper- transHmða ! bÞ ¼ Df H ; ðcrb-phaseÞ À D imental results and theoretical calculations reported here has helped to resolve contradictions in the available thermochemical V.N. Emel’yanenko, S.P. Verevkin / J. Chem. Thermodynamics 40 (2008) 1661–1665 data and to recommend consistent and reliable sublimation and [6] S.S. Pinto, H.P. Diogo, J. Chem. Thermodyn. 38 (2006) 1515.
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