Phase Change Enthalpies and Entropies of Liquid Crystals William E. Acree, Jr.a… Department of Chemistry, University of North Texas, Denton, Texas 76203 James S. Chickosb… Department of Chemistry and Biochemistry, University of Missouri-St. Louis, St. Louis, Missouri 63121 ͑Received 11 February 2004; revised manuscript received 1 August 2004; accepted 7 September 2004; published online 17 July 2006͒ The thermochemical behavior of more than 3000 organic compounds known to form liquid crystals is reported along with references to the original literature. A group addi- tivity approach used to estimate total phase change entropies of organic molecules ap- plied to 627 of these liquid crystals is found to significantly overestimate their total phase change entropies. Comparison of experimental and estimated values also show significant scatter relative to database compounds. The origins of these discrepancies are discussed in terms of a model used to explain liquid crystal formation. © 2006 American Institute of Physics. ͓DOI: 10.1063/1.1901689͔ Key words: fusion enthalpy; fusion entropy; liquid crystals; liquid crystal compendium; phase transitions; total phase change entropy. Contents List of Tables 1. ⌬Tiso Contributions to 0 Stpce by the hydrocarbon portion of acyclic and aromatic molecules....... 1053 1. Introduction................................ 1052 2. Contributions of acyclic functional groups used 1.1. Phase Change Enthalpies................. 1052 T in estimating ⌬ isoS of liquid crystals; 2. Phase Change Entropies...................... 1053 0 tpce functional groups dependent on the substitution 2.1. Estimation of Total Phase Change Entropy... 1053 patterns. .................... 1053 2.2. ⌬Tiso Some Estimations of 0 Stpce of Liquid 3. Contributions of the remaining acyclic functional Crystals............................... 1055 ⌬Tiso groups used in estimating 0 Stpce of liquid 2.2.1. 1,2,13,14-Tetrahydroxytetradecane.... 1055 crystals................................... 1054 2.2.2. 4-Butylcyclohexyl 4. Contributions of the cyclic hydrocarbon portions 4-methoxycinnamate................ 1055 of the molecule............................. 1054 2.2.3. Diphenyl 4,4Ј-biphenyldicarboxylate.. 1055 5. Contributions of the cyclic functional groups 2.2.4. bis͑4-Heptyloxyphenyl͒ ⌬Tiso used in estimating 0 Stpce of liquid crystals. 1055 2,5-thiophenedicarboxylate.......... 1056 6. Application of group additivity toward the 2.2.5. Benzene hexa-nonanoate............ 1056 ⌬Tiso estimation of 0 Stpce of liquid crystals........ 1056 2.3. Statistics of the Correlations of Total Phase 7. A series of compounds including liquid crystals Change Entropy......................... 1056 whose heat capacity and phase transitions of the 2.3.1. Database Compounds............... 1056 crystalline phase have been studied over most 2.3.2. ⌬Tiso of the experimentally accessible region. ........ 1059 Calculations of 0 Stpce for Liquid Crystals.......................... 1057 8. Some examples of compounds forming liquid ⌬Tiso crystals upon supercooling the melt............ 1062 3. A Discussion of Stpce for Liquid Crystals. 1058 0 9. Group values for estimating heat capacities of 4. A Discussion of T , T and T for Liquid fus cld iso solids at Tϭ298K.......................... 1063 Crystals................................... 1060 10. Abbreviations and notations used in Table 11. 1064 5. Why Do Liquid Crystals Form?............... 1062 11. The solid-liquid phase change properties of 6. A Compendium of the Thermochemical liquid crystals.............................. 1065 Behavior of Liquid Crystals................... 1064 12. References for Table 11...................... 1323 7. Acknowledgment........................... 1330 8. References................................. 1330 List of Figures ͒ 1. A comparison of the experimental and calculated a Electronic mail: [email protected] b͒Electronic mail: [email protected]; corresponding author. total phase change entropies of 2637 compounds.. 1056 © 2006 American Institute of Physics. 2. A comparison of calculated and experimental Õ Õ Õ Õ Õ 0047-2689 2006 35„3… 1051 280 $40.001051 J. Phys. Chem. Ref. Data, Vol. 35, No. 3, 2006 1052 W. E. ACREE, JR. AND J. S. CHICKOS ⌬Tiso tween anisotropic solids that are rigidly and uniquely ar- 0 Stpce for 627 liquid crystals............... 1057 3. A histogram of the distribution of errors in ranged in a lattice with very little mobility, plastic crystals ⌬TisoS (exp)Ϫ⌬TisoS (calc) for 2637 that flow under stress and usually characterized by rotational 0 tpce 0 tpce motion within a lattice, and isotropic liquids characterized by compounds used in deriving and validating group parameters for estimating total phase free rotational and translational motion. If the forces of in- change entropies............................ 1057 teraction are sufficiently strong, a more limited form of self- 4. A histogram of the distribution of errors in association can also be detected in the gas phase, as exem- T T plified by the dimerization observed with some carboxylic ⌬ isoS (exp)Ϫ⌬ isoS (calc) for liquid crystals.. 1058 0 tpce 0 tpce acids. 5. A plot of the difference between experimental Of all the techniques used to study liquid crystals, thermal and calculated ⌬TisoS as a function of the 0 tpce analysis, while perhaps not the most sensitive, provides a number of carbon atoms..................... 1058 quantitative measure of the magnitude of the interactions re- 6. A plot of the entropy of the benzene sponsible for self-assembly. A study of the thermal behavior hexa-n-alkanoates as a function of the number exhibited by liquid crystals may also provide insight into the of carbon atoms............................ 1059 associative behavior of other molecules that behave noniso- 7. A comparison of the melting and clearing tropically but do not form liquid crystals. This study reports temperatures of the odd thiocholesteryl the thermal behavior of some 3000ϩ liquid crystals and n-alkanoates............................... 1060 compares the total molar phase change entropy (⌬TisoS ) 8. A comparison of the melting and clearing 0 tpce temperatures of the even thiocholesteryl of a representative number of them to the total molar phase n-alkanoates............................... 1060 change entropy of substances that are believed to melt to 9. A comparison of the melting and clearing isotropic liquids. In view of the large number of compounds temperatures of the alkyl in the database, the calculated and experimental total molar 4Ј-methoxybiphenyl-4-carboxylates.. ......... 1061 phase change entropy of some 667 entries on approximately 600 different compounds were compared. Compounds were selected to include a variety of functional groups and struc- 1. Introduction tures. In order to simplify the calculations, members of ho- mologous series were frequently chosen. If the compounds Since their first discovery back in 1888, interest in the selected included multiple independent determinations of properties and practical applications of liquid crystals has their thermal properties, all entries for the compound were 1,2 increased dramatically. General acceptance of liquid crys- included in the analysis. tals as a distinct phase of matter was slow, occurring some 30 Throughout this article, Tfus , Tcld , and Tiso are used to years since they were first reported. Liquid crystalline behav- distinguish between slightly different events and conditions. ior is found among numerous classes of compounds that in- The temperature, Tfus, refers to the temperature at which a clude biphenyls, cholesterol esters, soaps, lipids, polymers, solid is converted to either an isotropic liquid or to a liquid and elastomers. More than 76 000 compounds have been 3͑a͒–͑c͒ crystal. Tcld is used to refer to the clearing temperature if the identified as exhibiting liquid crystalline behavior. This isotropic liquid is converted to the liquid crystal by super- paper will review the total phase change enthalpies and en- cooling the isotropic liquid below Tfus ; Tcld may be observed tropies of the more than 3000 compounds whose condensed experimentally at the temperature the supercooled liquid be- phase thermochemical properties have been studied. comes cloudy. The term T has been used to refer to tem- Unlike most small molecules that behave isotropically iso peratures at which the liquid becomes isotropic above T . upon liquefaction, many molecules that are highly non- fus The relationship between these terms is defined as follows: spherical in shape, exhibit marked self-assembly in the liquid T ϽT рT . phase that persists even upon continued heating. Cylindrical cld fus iso rod, disk, and banana shaped molecular structures are among 1.1. Phase Change Enthalpies those most frequently encountered exhibiting this behavior. Loss of self-assembly can occur in stages and can be moni- An examination of the phase change enthalpies of liquid tored by changes in a variety of physical properties. In some crystals reveals that these substances exhibit several thermal cases, liquid crystalline behavior is observed, only upon su- transitions that can be detected. For most substances, the percooling of the melt. In these instances, the melting of the largest enthalpic change occurs upon conversion of the solid solid first produces an isotropic liquid; self-association is ob- to a nematic or smectic phase. In a few cases, some highly ͑ served upon supercooling below the melting temperature. Al- substituted anthraquinones for example, see C124H216O18 , ͒ though