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Adventures in Thermochemistry. Estimation of Melting Temperatures. James S. Chickos* Department of Chemistry and Biochemistry University of Missouri-St. Louis Louis MO 63121 E-mail: jsc@umsl.edu. Soulard Market Mardi Gras. The melting temperature of a crystalline

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slide1

Adventures in Thermochemistry

Estimation of Melting Temperatures

James S. Chickos*

Department of Chemistry and Biochemistry

University of Missouri-St. Louis

Louis MO 63121

E-mail: jsc@umsl.edu

Soulard Market

Mardi Gras

slide2

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, 3548.

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. Data2001, 46, 562-573.

slide3

The development of a general protocol has proven elusive and continues to be a problem.

August 1941. (Photo: U.S. Geological Survey)

August 2004. (Photo: US

Geological Survey).

Muir Glacier, Glacier Bay National

Park and Preserve, Alaska

slide4

Melting temperatures of the even n-alkanes versus the number of methylene groups

Question: How does the melting temperature of polyethylene compare?

Tf(n)

Melting temperature of polyethylene = 413 K;

Polyethylene behaves as a member of the even series.

Number of methylene groups, n

Number of methylene groups, n

slide5

Odd n-Alkanes

Melting temperatures of the odd n-alkanes also appear to approach 413 K.

Polyethylene appears to be common to both series.

Tf(n)

Polyethylene behaves as a member of the odd series as well.

Number of methylene groups, n

Melting points of the odd alkanes versus the number

of methylene groups; circles: experimental data

slide6

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.

slide7

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?

slide8

How can one take advantage of the hyperbolic melting behavior exhibited by these homologous series?

The even n-alkanes pack similarly

Tetracosane Eicosane

slide9

Even n-Alkanes

Even n-Alkanes

The correlation between 1/[1-Tf (n)/Tf ()] and the number of CH2groups for the even n-alkanes.

The terms Tf (n) and Tf () represent the melting temperature of the compound with n CH2 groups and the melting point of polyethylene, 411 K, respectively

1/[1-Tf (n)/Tf ()]

Number of CH2 groups, n

slide10

Odd n-Alkanes

The correlation between the function

1/[1-Tf (n)/Tf ()]and the number of CH2groups for the odd n-alkanes using Tf () =

411 K.

1/[1-Tf (n)/Tf ()]

slide11

Thelinear correlation observed between between 1/[1-Tf (n)/Tf ()]

and the number of CH2 groups, n, provided the following analytical expression which was used to fit the data using a non-linear least squares program:

Tf (n) = Tf()*[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 polyethylenein the limit.

The deviation of the first few members of the series was explained in terms of packing in the solid state.

slide12

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, 3rd Ed. Wiley: NY. 1967 and many others.

slide14

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

slide17

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.

slide18

Melting Points of the Cycloalkanes

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

slide21

Perfluorinated Alkanes

A plot of 1/[1-Tf (n)/Tf ()] versus the number of CF2 groups (even series). The melting point of Teflon is 605 K.

slide22

Experimental melting points as a function of the number of repeat units

circles: perfluoro-n-alkanes:

Tfus() = 605 K

squares: H[OCH2CH2]nOH:

Tfus () = 342 K

triangles: C2H5CO-[NH(CH2)5CO]n-NHC3H7.:

Tfus() = 533 K

slide24

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

slide25

Summary

Ascending hyperbola

A plot of1/[1-T /T ()] vs n,

the number of repeat units

results in a linear relationship

and

T = T()*[1- 1/(mn + b)]

slide26

Summary

Descending hyperbola

A plot of1/[1-T()/T)] vs n,

the number of repeat units,

results in a linear relationship

and T= T ()/[1- 1/(mn + b)]

slide28

1/[1- T(n)/T(n)]

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

slide30

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().

slide32

400.5 K

360 K

n → ; Tf → AH/AS

n-alkanes

dialkyl arsinic acids

n-alkanes

dialkyl arsinic acids

slide33

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)]?

slide34

T = 380 K

Do not form liquid crystals

slide38

Why is the total phase change entropy of liquid crystals over estimated?

Possible reasons for overestimating ∆Stpce

  • The existence of undetected solid-solid phase transition at low temperatures
  • Larger heat capacity of the liquid/solid phase relative to normal substances

Sorai, M.; Asanina, S.; Destrade, C; Tinh, N. H. Liq. Cryst., 7, 163-180 1990.

slide40

Entropy Change from T = 15 to 385 K

crystal → isotropic liquid

liquid crystal

liquid crystal

liquid crystal

crystal → isotropic liquid

crystal → isotropic liquid

slide42

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

∆Stpce 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.

slide43

■ clearing temperature’

● melting temperature

slide44

References

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. Data2006, 35, 1051 and references cited

slide45

Acknowledgements

Nichols, G.

Acree, W. E. Jr.