Adventures in Thermochemistry Estimation of Melting Temperatures James S. Chickos* Department of Chemistry and Biochemistry University of Missouri-St. Louis Louis MO Soulard Market Mardi Gras

The melting temperature of a crystalline material is a fundamental physical property. A number of studies have shown the the melting temperature of linear molecules is not an additive property. The dependence on structure particularly as applied to polymers has been developed by Flory and others. Flory, P. J. Thermodynamics of Crystallization of High Polymers, IV. J. Chem. Phys. 1949, 17, 223. Flory, P. J.; Vrij, A. Melting points of linear chain homologues. The normal paraffin hydrocarbons. J. Am. Chem. Soc. 1963, 85, Wunderlich, B.; Czornyj, G. A study of equilibrium melting of polyethylene. Macromolecules 1977, 10, 906. Buckley, C. P.; Kovacs, A. J. Melting behavior of low molecular weight poly(ethylene oxide fractions. I. Extended chain crystals. Prog. Colloid Polym. Sci. 1975, 58, 44. Mandelkern, L.; Stack, G. N. Equilibrium melting temperature of long chain molecules. Macromolecules 1984, 1, 871 and references cited. Chickos, J. S. Nichols, G. Simple Relationships for the Estimation of Melting Temperatures of Homolgous Series. J. Chem. Eng. Data 2001, 46,

The development of a general protocol has proven elusive and continues to be a problem. August (Photo: U.S. Geological Survey) August (Photo: US Geological Survey). Muir Glacier, Glacier Bay National Park and Preserve, Alaska

Number of methylene groups, n T f (n) Melting temperatures of the even n-alkanes versus the number of methylene groups Question: How does the melting temperature of polyethylene compare? Melting temperature of polyethylene = 413 K; Polyethylene behaves as a member of the even series.

Melting points of the odd alkanes versus the number of methylene groups; circles: experimental data Melting temperatures of the odd n-alkanes also appear to approach 413 K. Polyethylene appears to be common to both series. T f (n) Number of methylene groups, n Odd n-Alkanes Polyethylene behaves as a member of the odd series as well.

Melting temperatures from top to bottom (both even and odd series represented): 1,  -dicarboxylic acids, even N-(2-hydroxyethyl)- alkanamides, even n-carboxylic acids, odd n-alkylbenzenes, odd 1-alkenes, odd versus the number of methylene groups.

Why do the first few members of the series deviate from all the rest and why is there a difference between the odd and even members of the series?

TetracosaneEicosane The even n-alkanes pack similarly How can one take advantage of the hyperbolic melting behavior exhibited by these homologous series?

Even n-Alkanes The correlation between 1/[1-T f (n)/T f (  )] and the number of CH 2 groups for the even n-alkanes. The terms T f (n) and T f (  ) represent the melting temperature of the compound with n CH 2 groups and the melting point of polyethylene, 411 K, respectively 1/[1-T f (n)/T f (  )] Number of CH 2 groups, n Even n-Alkanes

1/[1-T f (n)/T f (  )] The correlation between the function 1/[1-T f (n)/T f (  )] and the number of CH 2 groups for the odd n- alkanes using T f (  ) = 411 K. Odd n-Alkanes

The linear correlation observed between between 1/[1-T f (n)/T f (  )] and the number of CH 2 groups, n, provided the following analytical expression which was used to fit the data using a non-linear least squares program: T f (n) = T f (  )*[1- 1/(mn + b)] m = slope; b = intercept n = number of carbons In all, melting temperature data was found and fit for over 50 homologous series containing a variety of functional groups and substitution patterns converging to to polyethylene in the limit. The deviation of the first few members of the series was explained in terms of packing in the solid state.

Melting points of the odd alkanes versus the number of methylene groups; circles: experimental data, line: calculated results. Source of Data: Brandrup, J.; Immergut, E. H. (ed) Polymer Handbook, 3 rd Ed. Wiley: NY and many others.

A comparison of the melting points of the even (  ) and odd (  ) n-alkanes

Packing in the crystal lattice for the first few members of the series are dominated by the functional group. As the tail gets longer, the hydrocarbon tail dominates the packing

d the first member of the series

Utility of the Method If melting points of three or more of the series are available, and a plot of 1/[1-Tf (n)/Tf (  )] is linear, it is possible to predict the melting temperatures of the remaining members of the series.

Melting points of the cycloalkanes versus the number of methylene groups. Both even and odd members are included. Melting Points of the Cycloalkanes

What about homologous series related to other polymers?

A plot of 1/[1-Tf (n)/Tf (  )] versus the number of CF 2 groups (even series). The melting point of Teflon is 605 K. Perfluorinated Alkanes

circles: perfluoro-n-alkanes: T fus (  ) = 605 K squares: H[OCH 2 CH 2 ] n OH: T fus (  ) = 342 K triangles: C 2 H 5 CO- [NH(CH 2 ) 5 CO] n -NHC 3 H 7.: T fus (  ) = 533 K Experimental melting points as a function of the number of repeat units

What about series with parent compounds that melt above 411 K?

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: drawn to identify different series

Summary Ascending hyperbola A plot of 1/[1-T /T (  )] vs n, the number of repeat units results in a linear relationship and T = T(  )*[1- 1/(mn + b)]

Descending hyperbola A plot of 1/[1-T(  )/T)] vs n, the number of repeat units, results in a linear relationship and T= T (  )/[1- 1/(mn + b)] Summary

Melting temperatures of the dialkylarsinic acids (odd series)

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

Melting temperatures of the dialkylarsinic acids (odd series)

trans-4’-n-alkoxy-3- chlorocinnamic acids, 6-alkoxy-2-naphthoic acids, and the even series of 8- alkyltheophyllines; symbols: experimental data; lines: calculated using a value of 380 K for T(  ).

n-alkanes dialkyl arsinic acids n-alkanes dialkyl arsinic acids K 360 K n →  ; T f → A H /A S

Many of the compounds that show a decreasing melting temperature with increasing number of repeat units form liquid crystals. Since liquid crystals can show several transition on route from crystal to isotropic liquid. Which if any of these transitions can be fit to T= T (  )/[1- 1/(mn + b)]?

T  = 380 K Do not form liquid crystals

.

Fusion Temperatures and Total Phase Change Entropy Liquid Crystals

Compounds for the Most Part That Do Not Form Liquid Crystals

Possible reasons for overestimating ∆S tpce 1.The existence of undetected solid-solid phase transition at low temperatures 2.Larger heat capacity of the liquid/solid phase relative to normal substances Sorai, M.; Asanina, S.; Destrade, C; Tinh, N. H. Liq. Cryst., 7, Why is the total phase change entropy of liquid crystals over estimated?

crystal → isotropic liquid liquid crystal Entropy Change from T = 15 to 385 K

Why do liquid crystal form?

The total entropy change from T = 15 to 285 K (clearing point) of both compounds that do and do not form liquid crystals appear to correlate ∆S tpce for those compounds melting not forming liquid crystals are reasonably reproduced The suggests a larger heat capacity of the solid and/or the liquid phase relative to normal substances for those members forming liquid crystals. Most liquid crystals have a two very different structural components; a rigid cyclic component (head group) and a more flexible tail. For short tails the head group dominates the packing in the crystal. For long tails, on their way to polyethylene, the tail dominates. In between, neither group dominates, resulting in a high density of low energy states, especially with regards to the tail. The result is often a liquid crystal.

■ clearing temperature’ ● melting temperature

Chickos, J. S.; Nichols, G. Simple Relationships for the Estimation of Melting Temperatures of Homologous Series. J. Chem. Eng. Data 2001, 46, 562. Acree, W. E. Jr. Chickos, J. S. Phase Change Enthalpies and Entropies of Liquid Crystals. J. Phys. Chem. Ref. Data 2006, 35, 1051 and references cited References

Acknowledgements Nichols, G. Acree, W. E. Jr.