 H s (298 K) =  H v (298 K) +  H fus (298 K) We have discussed methods to estimate  H v (298 K); are there any ways to estimate  H fus (298 K) or  H fus (T fus ) ? Walden’s Rule:  H fus (T fus ) / T fus = 54.4 J mol -1 K -1

Figure. Fusion enthalpies as a function of the number of methylene groups of the n-alkanes.

Figure. Total phase change enthalpy of the n-alkanes as a function of the number of methylene groups.

Figure. Total phase change entropy of the n-alkanes as a function of the number of methylene groups.

Fusion enthalpies as a function of the number of methylene groups (N) of the n-alkanes.  H fus (T fus ) = (2929±178)N - (3281±13006); r 2 = Total phase change enthalpies as a function of the number of methylene groups (N) of the n-alkanes.  H fus (T fus ) = (3552±80)N + (972±5868); r 2 = Total phase change entropy as a function of the number of methylene groups (N) of the n-alkanes.  S fus (T fus ) = (9.027±0.25)N + (45.1±18.44); r 2 =

Table. Contributions by the hydrocarbon portion of acyclic and aromatic molecules Acyclic and Aromatic Carbon Groups Group Value G i, Group Coefficient C i J. mol -1. K -1 primary sp 3 C CH secondary sp 3 C>CH a tertiary sp 3 C-CH< quaternary sp 3 C>C< secondary sp 2 C=CH tertiary sp 2 C=CH quaternary sp 2 C=C(R) tertiary sp CH-C  14.9 quaternary sp C-C  -2.8 aromatic tertiary sp 2 C=C a H- 7.4 quaternary aromatic sp 2 C adjacent to an sp 3 atom=C a (R) peripheral quaternary aromatic sp 2 C adjacent to an sp 2 atom=C a (R) internal quaternary aromatic sp 2 C adjacent to an sp 2 atom=C a (R) a The group coefficient of 1.31 for is applied only when the number of consecutive methylene groups equals or exceeds the sum of the remaining groups; R: any alkyl or aryl group unless specified otherwise

Estimations of acyclic and aromatic hydrocarbons Examples: ethylbenzene:  H fus (T fus ) = 9.16 kJ mol -1 ; T fus = K octylbenzene:  H fus (T fus ) = kJ mol -1 ; T fus = K 4-methyl-1-pentene:  H fus (T fus ) = 4.93 kJ mol -1 ; T fus = K

Table. Functional groups dependent on the substitution patterns Functional Groups Group Value (G k ) Group Coefficient (C k ) J/(mol -1 K -1 ) Total number of functional groups in the molecule: k; G k k = chlorine R-Cl fluorines on an sp 3 CR-CF 2 -R hydroxyl group R-OH carboxylic acid R-C(=O)OH R: any alkyl or aryl group unless specified otherwise;

Table. Contributions of the remaining functional groups Functional Groups a Abbreviated Structure Group Value (G k ) a, J/(mol -1 K -1 ) bromine R-Br17.5 fluorine on an sp 2 carbonR 2 -CHF19.5 fluorine on an aromatic carbon=CF fluorines on an sp 3 carbonCF 3 -R fluorine on an sp 3 carbonR-CF-(R) fluorine in perfluorinated compounds b C n F 2n one fluorine on a ring carbon -CHF-; 17.4 two fluorines on a ring carbon-CF 2 -[17.5] iodineR-I19.4 phenol =C-(OH)-20.3 ether R-O-R4.71 aldehydeR-CH(=O)21.5 ketone R-C(=O)-R4.6 ester R-C(=O)O-R7.7 aromatic heterocyclic amine =N-[10.9] acyclic sp 2 nitrogen =N-[-1.8] tertiary amineR-N(R 2 )-22.2 secondary amineR-NH-R-5.3 primary amineR-NH nitro group R-NO

Table. Contributions of the remaining functional groups Functional Groups a Abbreviated Structure Group Value (G k ) a, J/(mol -1 K -1 ) azoxy nitrogenN=N(  O)-[6.8] nitrile R-C  N17.7 isocyanideR-NC[17.5] tertiary amidesR-C(=O)NR secondary amides R-C(=O)NH-R1.5 primary amide R-CONH N,N-dialkylformamideHC(=O)NR 2 [6.9] sulfidesR-S-R2.1 disulfides R-SS-R9.6 thiols R-SH23.0 a R: any alkyl or aryl group unless specified otherwise; values in brackets are tentative assignments; all group coefficients can be assumed to be 1; the functional groups are in bold;

Estimations of acyclic and aromatic hydrocarbon derivatives Examples: 3-heptanone:  H fus (T fus ) = kJ mol -1 ; T fus = 236 K p-  -cumylphenol:  H fus (T fus ) = kJ mol -1 ; T fus = K 2,3,4,5-tetrachlorobiphenyl:  H fus (T fus ) = 25.2 kJ mol -1 ; T fus = K

Estimations of cyclic hydrocarbons

Examples: cyclohexylbenzene:  H fus (T fus ) = 15.3 kJ mol -1 ; T fus = K adamantane:  H fus (T fus ) = 10.9 kJ mol -1 ; T fus = K;  H tran (T trans ) = 3.38; T trans = K fluorene:  H fus (T fus ) = kJ mol -1 ; T fus = K

Estimations of cyclic hydrocarbon derivatives C 27 H 46 O cholesterol  H fus (T fus ) = kJ mol -1 ; T fus = K;  H tran (T trans ) = 2.5; T trans = K

Estimate  S tpce (T fus ) of dibenzothiophene T fus  H fus (T fus ) 21.6 kJ mol -1 Estimate  S tpce (T fus ) of C 11 H 16 N 4 O 2 8-butyltheophylline T fus  H fus (T fus ) 32.3 kJ mol -1 theophylline

 -D-glucose T fus =432.2 K  fus H m = 34.3 kJ mol -1 l-menthol T fus =316.2 K  fus H m = kJ mol -1

1-chlorodibenzodioxin T fus = K  fus H m = 23.2 kJ mol -1 phenazine T fus = K  fus H m = kJ mol -1

Octyl methacrylate T fus = K  fus H m = 24.9 kJ mol -1 2-n-propy1-5-(4-bromophenyl)thiophene T fus = K  fus H m = 15.7 kJ mol -1

How good are these parameters at estimating  S tpce (T fus )? Fig. A comparison of the experimental and calculated total phase change entropies of 2637 compounds. The area between the two lines represents  2 .

Fig. A histogram of the distribution of errors in (exp) - (calc) for the database compounds of Fig. 1. Each interval represents one standard deviation (15.3 J. mol -1. K -1 ).

Applications of Group Values Used to Calculate  S tpce (T fus ) Although polymers are not completely crystalline, they can be made highly crystalline and they have a melting temperature associated with their melting. The degree of crystallinity can be determine by X-Ray crystallography.

Estimated Total Phase Change Entropy for Some Polymers

Table. Molar Transition Enthalpies (kJ mol -1 ) and Entropies (J mol -1 K -1 ) of Select Amphiphilic Semiperfluorinated-Semiper- hydrogenated Diblock and Triblock Organic Compounds a T(K)  H pce  S pce  S tpce 0.6  S tcpe  S tcpe  H tpce  H tpce exptcalcd calcd exptcalcd UNSUBSTITUTED DIBLOCK MOLECULES C 16 H 9 F 25 F 3 C(CF 2 ) 11 (CH 2 ) 4 H C 16 H 13 F 21 F 3 C(CF 2 ) 9 (CH 2 ) 6 H C 16 H 17 F 17 F 3 C(CF 2 ) 7 (CH 2 ) 8 H C 17 H 21 F 15 (CF 3 ) 2 CF(CF 2 ) 4 (CH 2 ) 10 H

T(K)  H pce  S pce  S tpce 0.6  S tcpe  S tcpe  H tpce  H tpce exptcalcd calcd exptcalcd C 18 H 13 F 25 F 3 C(CF 2 ) 11 (CH 2 ) 6 H C 18 H 21 F 17 F 3 C(CF 2 ) 7 (CH 2 ) 10 H C 19 H 21 F 19 (CF 3 ) 2 CF(CF 2 ) 6 (CH 2 ) 10 H C 20 H 17 F 25 F 3 C(CF 2 ) 11 (CH 2 ) 8 H C 20 H 21 F 21 F 3 C(CF 2 ) 9 (CH 2 ) 10 H

Figure. A comparison of calculated and experimental total phase change entropies for the partially fluorinated amphiphilic compounds.