Are there any ways to estimate melting points? What do melting points measure? “Melting is a function of the detailed structure of the crystalline state, and that diverse laws of melting must be looked for because of the diversity of the crystal structure” -Alfred Ubbelohde, “Melting and Crystal Structure” 1965.

Figure. Melting temperatures of the even n-alkanes versus the number of methylene groups, circles; experimental data

Figure. Melting points of the odd alkanes versus the number of methylene groups; circles: experimental data

Figure. The correlation between the function 1/[1-T f (n)/T f (  )] and the number of methylene groups, n, for the even n-alkanes.

Figure.The correlation between the function 1/[1-T f (n)/T f (  )] and the number of methylene groups for the odd n-alkanes.

Figure. Melting temperatures of the odd 1-alkenes, n-alkylbenzenes, n-carboxylic acids, N- (2-hydroxyethyl)alkanamides and 1,  -dicarboxylic acids versus the number of methylene groups, circles, squares triangles and hexagons: experimental data; lines: calculated results.

Conclusions drawn from the n-alkane results: The melting point of an alkane is not a group property. 2.The odd and even members of the series should be segregated. 3.The melting point of any long chain approaches the melting point of polyethylene. Since the nature of what is attached to the end of the polyethylene is not crucial to the properties of the polymer produced, we surmised that the mp behavior observed in n-alkanes should apply to any homologous series. 4.The first few members of the series usually deviate from the observed hyperbolic behavior.

T fus = T f (  )*[1- 1/(mn + b)]

Table. Melting-structure correlations of series related to polyethylene: parents with T f <411.3 K. a Homologous Series Parent Compound T f /K S m b r 2  /K n T Parent A.Hydrocarbons n-alkanes b butane e propane 85.2 o alkenes c 1-pentene e butene 87.8 o methylalkanes c 2-methylpentane e methylbutane o methylalkanes c 3-methylhexane e methylheptane o methylalkanes c 4-methylheptane e methyldecane d o methylalkanes e 5-methyldecane d e methylnonane o

2,3-dimethylalkanes c 2,3-dimethyldecane d e ,3-dimethylheptane 156 o ,4-dimethylalkanes c 2,4-dimethylundecane d e ,4-dimethyldecane d o ,4,6-trimethylalkanes e 2,4,6-trimethyltridecane d e ,4,6-trimethyldodecane d o n-alkylcyclopentanes f propylcyclopentane e ethylcyclopentane o n-alkylcyclohexanes f propylcyclohexane e ethylcyclohexane o n-alkylbenzenes c propylbenzene e ethylbenzene 178 o alkylnaphthalenes g 1-propylnaphthalene e ethylnaphthalene o alkylnaphthalenes g 2-propylnaphthalene e ethylnaphthalene o Alkynes f 1-pentyne e butyne o

B. Cycloalkanes m b r 2  /K n T Cycloalkanes h

Figure. Melting temperatures of the cycloalkanes versus the number of methylene groups. Both even and odd members are included.

C.Functionalized Alkanes Homologous Series Parent Compound T f /K S m b r 2  /K n T 1-alkanols i propanol147.2e ethanol143.2o alkanols j 2-nonanol d 184.7e butanol158.5o alkanethiols c 1-ethanethiol125.9o methyl alkanoates k methyl hexanoate202.2e methyl propanoate185.2o alkyl ethanoates c propyl ethanoate178.2e ethyl ethanoate189.6o ethyl alkanoates i ethyl butanoate172.4e

n -alkanal c butanal176.8e propanal193.2o n-alkanoic acids j butanoic acid268.5e propanoic acid253.5 o chloroalkanes c 1-chloropropane150.2 e chloroethane137.2 o fluoroalkanes c 1-fluorotridecane d e fluoroethane130o bromoalkanes f 1-bromopropane163.2 e bromoethane154.6o iodoalkanes f 1-iodopropane171.9 e iodoethane162.1o cyanoalkanes c 1-cyanopropane161.3 e cyanoethane180.3o ,2-dihydroxyalkanes c 1,2-hexanediol318.2o N-methylamino-alkanes c methyl-n-butylamine198.2o

1-N,N-dimethyl-aminoalkanes c dimethyl-n-ethylamine133.2o alkanones c 2-pentanone195.2e butanone 186.2o alkyl phenyl ketones k acetophenone293.2o F-[CF 2 ] 12 -[CH 2 ] n -H h F-[CF2] 12 -[CH 2 ] 2 -H344.2e N-methyl alkanamides l N-methylbutanamide268e N-methylpropanamide230.2o hydroxyethyl- alkanamides l N-(2-hydroxyethyl)hexanamide 319.2e N-(2-hydroxyethyl)pentanamide d 305.2o p-chlorophenacyl alkanoates l p-chlorophenacyl butanoate 328.2e p-chlorophenacyl propionate371.4o N-octadecyl alkanamides m N-octadecyl butanamide349.7e

n-alkanamides n butanamide389.2e propanamide356.2o alkyl 4-nitrobenzoates o propyl 4-nitrobenzoate 308.2e ethyl 4-nitrobenzoate 330.2o n-alkyl 3,5-dinitrobenzoates o ethyl 3,5-dinitrobenzoate 367.2o ,  dihydroxyalkanes c 1,2-dihydroxyethane260.2e ,3-dihydroxypropane246.2o N-(  -naphthyl)alkanamides m N-(  -naphthyl) hexanamide 380.2e N-(  -naphthyl) pentanamide 385.2o ,  -alkanedioic acids k 1,5-undecanedioic acid d 378o

D.Symmetrically Substituted Derivatives q sym dialkyl ether c,p diethyl ether e sym n-alkanoic acid anhydrides p,q butanoic anhydride e propanoic anhydride o sym di-n-alkyl sulfides r diethyl sulfide o sym N,N-dialkylamines c diethylamine 181 e dipropylamine o sym-tri-n-alkylamines c triethylamine o

sym-1,2,3-glycerol tri-alkanoate s  form 304.8e  form  ' form

Figure. Experimental melting points of the three polymorphic forms of symmetric glycerol trialkanoates ranging from decanoate to eicosanoate. Molecular packing in each series series is very similar.

If homologous series related to polethylene converge to the mp of polyethylene, what about other series converging to other polymers?

Figure.Experimental melting points as a function of the number of repeat units, circles: perfluoro-n-alkanes; squares: H[OCH 2 CH 2 ] n OH; triangles: C 2 H 5 CO-[NH(CH 2 ) 5 CO] n -NHC 3 H 7.

Figure. A plot of 1/(1 – mp(n)/mp  ) versus the number of CF 2 groups. The melting point of Teflon is 605 K.

Table.Melting-structure correlations of series related to other polymers Parent Compound T f /K S m b r 2  /K n T n-perfluoroalkanes Teflon (T f 605 K) perfluorobutane 164 e  perfluoropropane o  PolyethersPolyoxyethylene (T f 342 K) H[OCH 2 CH 2 ] 2 OH e  4.78 H[OCH 2 CH 2 ]OH o  5.28 PolyamidesNylon-6 (T f 533 K) H[NH(CH 2 ) 5 CO] 2 OH e  0.85 HNH(CH 2 ) 5 COOH o 

What if the melting temperature of the parent is greater than 411 K?

Figure 6.Experimental melting or smetic/nematic  isotropic transition temperatures for the odd series of 4-alkoxy-3-fluorobenzoic acids, trans-4’-n-alkoxy-3-chlorocinnamic acids, 6-alkoxy-2-naphthoic acids, and the even series of 8-alkyltheophyllines; symbols: experimental data; lines: calculated results.

Figure. Melting temperatures of the dialkylarsinic acids (odd series)

Figure. A plot of [1/(1- T  /T(n)] vs n for the dialkylarsinic acids. A value of 380 K was used for T .

Ascending hyperbola T fus = T f (  )*[1- 1/(mn + b)] Descending hyperbola T fus = T f (  )/[1- 1/(mn + b)]

Some of the compounds that show descending behavior relative to the parent show liquid crystalline behavior. For these compounds, which temperature correlates with the melting temperature of members of the series that do not form liquid crystals?

nematic Liquid Crystals

Figure. Circles: melting temperatures or temperatures at which the trans-4-n-alkoxy-3- chlorocinnamic acids becomes isotropic; squares are melting temperatures for compounds forming liquid crystals; triangles: smectic to nematic transitions

Figure. A plot of 1/[1-T(  )/T(n)] versus the number of methylene groups for trans-4-n-alkoxy-3- chlorocinnamic acids. The solid circles represent melting temperatures, the solid squares represent nematic to isotropic transitions, the circles represent smectic to nematic transitions and the squares represent from nematic to isotropic transitions. The temperatures at which the liquids become isotropic appear to correlate best. A value of 380 K was used for T(  ).

Why do the first few members of the series usually deviate from the observed hyperbolic behavior?

Why do homologous series exhibit melting points that behave in a hyperbolic fashion?

Figure. Total phase change enthalpies of the n-alkanes.

Figure. Total phase change entropies of the n-alkanes

Figure. Total phase change enthalpies of the dialkyl arsenic acids as a function of the size of the alkyl group.

Figure. Total phase change entropies of the dialkyl arsenic acids as a function of the size of the alkyl group.

Fusion Enthalpies N- Alkanes  tpce H(T f )/J. mol -1 = (3725  38)n - (1838  7500); (37 data points) r 2 = Di-n-alkylarsinic acids  tpce H(T f )/J. mol -1 = 2 (3348  66) n + (9512  2800); (17 data points) r 2 =

Total Phase Change Entropies (Fusion Entropies)  tpce S(T f ) = (A s )n + (B s ) J. mol -1. K -1 N-Alkanes  tpce S(T f ) = (9.3)n + (35.2) J. mol -1. K -1 ; Di-n-alkylarsinic Acids  tpce S(T f ) = 2(9.3)n + (11.2) J. mol -1. K -1 ;

 G =  H - T f  S ; at T f, :  G = 0 T f =  tpce H/  tpce S = (A H n + B H )/(A S n + B S ); N-Alkanes T f =  tpce H(T f ) = (3725)n - (1838)  tpce S(T f ) (9.3)n + (35.2) Di-n-alkylarsinic Acids T f =  tpce H(T f ) = 2 (3348)n+ (9512)  tpce S(T f ) 2(9.3)n + (11.2)

Figure. The melting point behavior of the even n-alkanes and the dialkylarsinic acids of formula [CH 3 (CH 2 ) n ] 2 AsOH when calculated as a ratio of the total phase change enthalpy to the total phase change entropy. Both were estimated by group additivity.

Figure. The distribution of errors based on the use of three experimental data points to estimate the melting behavior of each series for 995 compounds.