Adventures in Thermochemistry

Estimation of Melting Temperatures

James S. Chickos*Department of Chemistry and

BiochemistryUniversity of Missouri-St. Louis

Louis MO 63121E-mail: jsc@umsl.edu

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, 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. Data 2001, 46, 562-573.

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

Number of methylene groups, n

0 100 200 300 400 500

50

100

150

200

250

300

350

400

450

Number of methylene groups, n

Tf(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

0 10 20 30 40 50 60 70 80 90 100

50

100

150

200

250

300

350

400

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

Polyethylene appears to be common to both series.

Tf(n)

Number of methylene groups, n

Odd n-Alkanes

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

number of methylene groups, n

0 5 10 15 20 25 30 35 40

Tf

/ K

50

100

150

200

250

300

350

400

450

1-alkenesn-alkylbenzenescarboxylic acidsN-(2-hydroxyethyl)alkanamides1,-dicarboxylic acidscalculated

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.

number of methylene groups, n

0 5 10 15 20 25 30 35 40

Tf

/ K

50

100

150

200

250

300

350

400

450

1-alkenesn-alkylbenzenescarboxylic acidsN-(2-hydroxyethyl)alkanamides1,-dicarboxylic acidscalculated

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?

Tetracosane Eicosane

The even n-alkanes pack similarly

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

Even n-Alkanes

0 100 200 300 400 500

0

10

20

30

40

50

60

70

80The correlation between 1/[1-Tf (n)/Tf ()] and the

number of CH2 groups 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

)/T

f (

)]

Number of CH2 groups, n

Even n-Alkanes

Number of methylene groups, n

0 10 20 30 40 50 60 70 80

0

2

4

6

8

10

12

14

1/[1

-Tf (

n)/T

f (

)]

The correlation between the function 1/[1-Tf (n)/Tf ()] and

the number of CH2 groups for the odd n-alkanes using Tf () =

411 K.

Odd n-Alkanes

The linear 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 polyethylene in the limit.

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

Number of methylene groups, n

0 10 20 30 40 50 60 70 80

Ex

per

imen

tal

mel

tin

g p

oin

t, K

50

100

150

200

250

300

350

400

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.

0 20 40 60 80 100

50

100

150

200

250

300

350

400

450

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

number of methylene groups, n

0 5 10 15 20 25 30 35 40

Tf

/ K

50

100

150

200

250

300

350

400

450

1-alkenesn-alkylbenzenescarboxylic acidsN-(2-hydroxyethyl)alkanamides1,-dicarboxylic acidscalculated

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

CH2 CH CH2 CH2 CH2 CH3

CH3

CH3CH2 CH CH2 CH2 CH3

CH3

CH3

e o

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.

Number of methylene groups, n

0 50 100 150 200 250 300 350

Mel

ting

poin

t, K

100

150

200

250

300

350

400

450

Experimental melting pointCalculated melting point

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

Melting Points of the Cycloalkanes

HC

CH2

CH2

O

O C

C

O

O

(CH2)nCH3

(CH2)nCH3

O C(CH2)nCH3

O

What about homologous series related to other polymers?

Number of CF2 groups, n

0 5 10 15 20 25

1/(1

- m

p(n)

/mp

0

1

2

3

4

5

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

Perfluorinated Alkanes

number of repeat units, n

0 10 20 30 40 50

Tf (

n)/

K

100

150

200

250

300

350

400

450

500

Tf ; n = number of CF2

Tf ; n = number of -(CH2CH2O)-

Tf ; n = number of -(NH(CH2)5CO)-

calculated

circles: perfluoro-n-alkanes:

Tfus() = 605 K

squares: H[OCH2CH2]nOH:

Tfus () = 342 K

triangles: C2H5CO-

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

Tfus() = 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?

number of methylene groups, n

0 2 4 6 8 10 12 14 16 18

Tf

or

Ttr /

K

360

380

400

420

440

460

480

500

520

540

560

4-n-alkoxy-3-fluorobenzoic acidtrans 4'-n-alkoxy-3-chlorocinnamic acid6-n-alkoxy-2-naphthoic acid8-n-alkyltheophylline

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

0 100 200 300 400 500

50

100

150

200

250

300

350

400

450

Summary

Ascending hyperbolaA plot of 1/[1-T /T ()] vs n,the number of repeat unitsresults in a linear relationship

and

T = T()*[1- 1/(mn + b)]

0 50 100 150 200 250 300

480

500

520

540

560

580

600

620

640

660

680

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

Number of methylene groups

0 2 4 6 8 10 12 14 16 18

Mel

tin

g te

mp

erat

ure

/ K

390

395

400

405

410

415

420

Melting temperatures of the dialkylarsinic acids (odd series)

0 2 4 6 8 10 12 14 16 18

10

15

20

25

30

35

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) ]

Number of methylene groups

0 2 4 6 8 10 12 14 16 18

Mel

tin

g te

mp

erat

ure

/ K

390

395

400

405

410

415

420

Melting temperatures of the dialkylarsinic acids (odd series)

number of methylene groups, n

0 2 4 6 8 10 12 14 16 18

Tf

or

Ttr /

K

350

400

450

500

550

6004-n-alkoxy-3-fluorobenzoic acidtrans 4'-n-alkoxy-3-chlorocinnamic acid6-n-alkoxy-2-naphthoic acid8-n-alkyltheophyllinecalculated

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

400.5 K

360 K

n → ; Tf → AH/AS

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 ∆Stpce

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, 163-180 1990.

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

crystal → isotropic liquid

crystal → isotropic liquid

crystal → isotropic liquid

liquid crystal

liquid crystal

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

∆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.

■ 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.