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.
450
400
350
Tf(exp)/ K
300
250
200
150
100
50
0
100
200
300
400
500
number of methylene groups, n
Figure . Melting temperatures of the even n-alkanes versus the number of
methylene groups, circles; experimental data
400
Experimental melting point, K
350
300
250
200
150
100
50
0
10
20
30
40
50
60
70
80
Number of methylene groups, n
Figure. Melting points of the odd alkanes versus the number of
methylene groups; circles: experimental data
80
70
80
60
70
60
40
50
30
20
1/[1-Tf (n)/Tf (
1/[1-Tf (n)/Tf (
50
40
30
10
20
0
10
0
0
100
200
300
400
500
number of methylene groups, n
0
100
200
300
400
500
number of methylene groups, n
Figure. The correlation between the function 1/[1-Tf (n)/Tf ()] and the
number of methylene groups, n, for the even n-alkanes.
14
12
1/(1-mp(n)/mp)
10
8
6
4
2
0
0
10
20
30
40
50
60
70
80
Number of methylene groups, n
Figure. The correlation between the function 1/[1-Tf (n)/Tf ()] and the
number of methylene groups for the odd n-alkanes.
450
400
350
Tf / K
300
250
1-alkenes
n-alkylbenzenes
carboxylic acids
N-(2-hydroxyethyl)alkanamides
1,-dicarboxylic acids
calculated
200
150
100
50
0
5
10
15
20
25
30
35
40
number of methylene groups, n
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.
Tfus = Tf ()*[1- 1/(mn + b)]
Table. Melting-structure correlations of series related to polyethylene: parents with Tf <411.3 K.a
Homologous Series Parent Compound Tf /K
S
m
b
r2
/K
nT
Parent
A.
Hydrocarbons
n-alkanesb
1-alkenesc
2-methylalkanesc
3-methylalkanesc
4-methylalkanesc
5-methylalkanese
butane
134.9
e
0.161
1.153
0.989
2.0
53
propane
85.2
o
0.172
0.948
0.994
3.5
24
1-pentene
107.9
e
0.170
0.856
0.999
7.2
9
1-butene
87.8
o
0.164
0.925
0.998
2.4
8
2-methylpentane 119.6
e
0.155
0.951
0.993
5.5
10
2-methylbutane 113.4
o
0.144
1.18
0.998
2.1
9
3-methylhexane 100.2
e
0.145
0.981
0.984
4.8
6
3-methylheptane 152.7
o
0.129
1.19
0.996
2.4
7
4-methylheptane 152.2
e
0.125
1.29
0.998
1.5
6
4-methyldecaned 195.7
o
0.128
1.23
0.995
2.1
7
5-methyldecaned 183.2
e
0.121
1.24
0.995
1.9
7
5-methylnonane 186.7
o
0.113
1.41
0.996
2.0
6
2,3-dimethylalkanesc 2,3-dimethyldecaned
0.989
4.0
5
0.15
0.884 0.991
7.4
6
e
0.136
1.13
0.992
2.6
5
o
0.128
1.16
0.997 2.0
6
2,4,6-trimethylalkanese 2,4,6-trimethyltridecaned 171.2 e
0.151
0.781
0.962 7.5
4
2,4,6-trimethyldodecaned 161.2 o
0.114
1.04
0.957 7.8
4
8
2,3-dimethylheptane
183.7
e
0.155
156
o
2,4-dimethylalkanesc 2,4-dimethylundecaned 197.7
2,4-dimethyldecaned
n-alkylcyclopentanesf propylcyclopentane
183.2
0.898
155.8
e
0.155
1.23
0.999
ethylcyclopentane
134.7
o
0.155
1.17
0.999 1.6
8
propylcyclohexane
178.3
e
0.165
1.45
0.999 0.6
7
ethylcyclohexane
161.4
o
0.164
1.47
0.999 4.1
9
propylbenzene
173.6
e
0.166
1.21
0.999
1.4
8
ethylbenzene
178
o
0.164
1.23
0.999 3.4
10
1-propylnaphthalene 263.2
e
0.190
1.67
0.997 1.4
4
1-ethylnaphthalene
259.3
o
0.171
1.77
0.998 6.7
6
2-alkylnaphthalenesg 2-propylnaphthalene 270.2
e
0.131
2.29
0.955 3.5
5
n-alkylcyclohexanesf
n-alkylbenzenesc
1-alkylnaphthalenesg
Alkynesf
0.6
2-ethylnaphthalene
265.7
o
0.149
2.15
0.987 6.8
6
1-pentyne
167.5
e
0.172
1.15
0.999
0.7
9
1-butyne
147.5
o
0.180
0.993
0.999 2.0
9
B.
Cycloalkanes
Cycloalkanesh
m
b
r2
0.188
1.18
0.856
/K
21
nT
46
420
400
380
Tf / K
360
experimental data
calculated
340
320
300
280
0
50
100
150
200
250
300
350
Number of methylene groups, n
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 Tf /K
1-alkanolsi
S
m
b
r2
/K
nT
propanol
147.2
e
0.239
0.968
0.998
1.9
18
ethanol
143.2
o
0.244
0.953
0.999
4.0
15
2-nonanold
184.7
e
0.257
0.87
0.992
3.1
6
2-butanol
158.5
o
0.244
1.22
0.999
1.1
9
1-alkanethiolsc 1-ethanethiol 125.9
o
0.153
1.12
0.998
2.6
8
2-alkanolsj
methyl alkanoatesk
methyl hexanoate
202.2
e
0.179
1.30
0.995
2.6
17
methyl propanoate
185.2
o
0.167
1.26
0.991
4.1
11
propyl ethanoate
178.2
e
0.161
1.22
0.999
3.1
8
ethyl ethanoate
189.6
o
0.155
1.28
0.999
7.2
9
172.4
e
0.166
1.28
0.999
1.4
18
alkyl ethanoatesc
ethyl alkanoatesi
ethyl butanoate
n-alkanalc
butanal
176.8
e
0.159
1.77
0.982
7.4
propanal
193.2
o
0.183
1.24
0.945
8.1
8
butanoic acid
268.5
e
0.270
1.72
0.998
1.2
18
propanoic acid
253.5
o
0.265
1.44
0.999
1.0
15
1-chloropropane
150.2
e
0.160
1.07
0.997
2.4
8
chloroethane
137.2
o
0.166
0.941
0.999
6.5
9
1-fluorotridecaned 276.2
e
0.183
0.839
0.999
0.3
4
1-fluoroethane
130
o
0.171
0.846
0.999
7.3
9
1-bromopropane
163.2
e
0.164
1.15
0.999
0.9
9
bromoethane
154.6
o
0.159
1.04
0.999
4.9
11
1-iodopropane
171.9
e
0.172
1.21
0.999
2.4
18
iodoethane
162.1
o
0.168
1.10
0.999
3.0
19
1-cyanopropane
161.3
e
0.203
1.03
0.999
1.1
8
cyanoethane
180.3
o
0.191
1.09
0.998
2.9
9
1,2-dihydroxyalkanesc 1,2-hexanediol 318.2
o
0.336
2.18
0.995
5.2
7
o
0.164
1.55
0.994
2.2
8
n-alkanoic acidsj
1-chloroalkanesc
1-fluoroalkanesc
1-bromoalkanesf
1-iodoalkanes f
1-cyanoalkanesc
7
1-N-methylamino-alkanesc
methyl-n-butylamine
198.2
1-N,N-dimethyl-aminoalkanesc
dimethyl-n-ethylamine
133.2
o
0.165
0.774
0.999
0.3
7
2-pentanone
195.2
e
0.220
1.51
0.999
0.7
7
2-butanone
186.2
o
0.220
1.51
0.999
1.9
8
293.2
o
0.213
2.44
0.995
0.8
5
344.2
e
0.172
5.93
0.920
1.5
9
N-methylbutanamide
268
e
0.461
1.37
0.999
0.8
7
N-methylpropanamide
230.2
o
0.435
1.13
0.999
0.6
7
319.2
e
0.435
2.93
0.967
2.1
6
N-(2-hydroxyethyl)pentanamided 305.2
o
0.639
1.71
0.993
1.4
5
p-chlorophenacyl butanoate 328.2
e
0.288
3.27
0.953
6.0
6
p-chlorophenacyl propionate 371.4
o
0.231
4.05
0.809
8.8
7
e
0.257
5.49
0.981
1.3
7
2-alkanonesc
alkyl phenyl ketonesk acetophenone
F-[CF2]12-[CH2]n-Hh
F-[CF2]12-[CH2]2-H
N-methyl alkanamidesl
2-hydroxyethyl- alkanamidesl
N-(2-hydroxyethyl)hexanamide
p-chlorophenacyl alkanoatesl
N-octadecyl alkanamidesm
N-octadecyl butanamide
349.7
n-alkanamidesn
butanamide
propanamide
389.2
356.2
e
o
0.226
0.238
9.93
8.61
0.706
0.732
3.5
5.0
12
7
propyl 4-nitrobenzoate
308.2
e
0.162
2.22
0.995
3.0
7
ethyl 4-nitrobenzoate
330.2
o
0.213
1.94
0.984
6.9
9
367.2
o
0.035
5.13
0.566
2.7
8
1,2-dihydroxyethane
260.2
e
0.421
1.87
0.988
1.9
8
1,3-dihydroxypropane
246.2
o
0.476
0.25
0.993
8.1
6
N-(-naphthyl) hexanamide 380.2
e
0.400
9.07
0.970
1.2
6
N-(-naphthyl) pentanamide 385.2
o
0.356
9.28
0.998
3.2
3
o
0.730
9.30
0.925
1.9
8
alkyl 4-nitrobenzoateso
n-alkyl 3,5-dinitrobenzoateso
ethyl 3,5-dinitrobenzoate
1, dihydroxyalkanesc
N-(-naphthyl)alkanamidesm
1,-alkanedioic acidsk
1,5-undecanedioic acidd
378
D.
Symmetrically Substituted Derivativesq
sym dialkyl etherc,p
diethyl ether
157.2
e
0.135
0.932
0.999
1.7
4
butanoic anhydride 198.2
e
0.319
1.05
0.999
1.4
10
propanoic anhydride 228.2
o
0.221
2.25
0.980
23.8
5
171.2
o 0.292
1.01
0.998
1.4
6
diethylamine
181
e
0.298
1.14
0.913
10.2
8
dipropylamine
210.2
o 0.320
1.08
0.999
0.9
8
158.5
o 0.249
0.655
0.998
1.6
7
sym n-alkanoic acid anhydridesp,q
sym di-n-alkyl sulfidesr
diethyl sulfide
sym N,N-dialkylaminesc
sym-tri-n-alkylaminesc
triethylamine
sym-1,2,3-glycerol tri-alkanoates
 form
304.8
 form
' form
e
0.296
1.50
0.999
0.5
7
261.7
0.272
0.598
0.999
1.1
7
290.0
0.263
1.31
0.999
0.8
7
380
360
340
Tf / K
320
300
calculated value
form
' form
 form
280
260
240
6
8
10
12
14
16
18
20
22
Number of methylene groups, n
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?
500
450
400
Tf / K
350
300
250
Tf ; n = number of CF2
200
Tf ; n = number of -(CH2CH2O)Tf ; n = number of -(NH(CH2)5CO)calculated
150
100
0
10
20
30
40
50
number of repeat units, n
Figure. Experimental melting points as a function of the number of repeat
units, circles: perfluoro-n-alkanes; squares: H[OCH2CH2]nOH; triangles:
C2H5CO-[NH(CH2)5CO]n-NHC3H7.
5
1/(1 - mp(n)/mp
4
3
2
1
0
0
5
10
15
20
25
Number of CF2 groups, n
Figure. A plot of 1/(1 – mp(n)/mp) versus the number of CF2 groups.
The melting point of Teflon is 605 K.
Table.
Melting-structure correlations of series related to other polymers
Parent Compound
Tf /K
n-perfluoroalkanes
S
m
r2
b
/K
nT
Teflon (Tf 605 K)
perfluorobutane
164
e
0.159
0.768
0.999
1.3
6
perfluoropropane
125.5 o
0.140
0.855
0.920
14.3
4
Polyethers
Polyoxyethylene (Tf 342 K)
H[OCH2CH2]2OH
267.2 e
0.407
3.36
0.884
4.7
8
H[OCH2CH2]OH
260.6 o
0.554
2.34
0.953
5.2
8
Polyamides
Nylon-6 (Tf 533 K)
H[NH(CH2)5CO]2OH 471.2 e
0.089
10.0
0.650
0.8
5
HNH(CH2)5COOH
0.046
9.9
0.599
1.6
10
479.2 o
What if the melting temperature of the parent is
greater than 411 K?
560
4-n-alkoxy-3-fluorobenzoic acid
trans 4'-n-alkoxy-3-chlorocinnamic acid
6-n-alkoxy-2-naphthoic acid
8-n-alkyltheophylline
calculated
540
520
500
Tf or Ttr / K
480
460
440
420
400
380
360
0
2
4
6
8
10
12
number of methylene groups, n
14
16
18
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)
420
Melting temperature / K
415
410
405
400
395
390
0
2
4
6
8
10
12
Number of methylene groups
14
16
18
35
[1/(1- Tn)]
30
25
20
15
10
0
2
4
6
8
10
12
14
16
18
Number of repeat units
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
Tfus = Tf ()*[1- 1/(mn + b)]
Descending hyperbola
Tfus = Tf ()/[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?
Liquid Crystals
nematic
500
Number of repeat units
480
460
440
420
400
380
0
2
4
6
8
10
12
14
16
18
Transition temperatures
Figure. Circles: melting temperatures or temperatures at which the trans-4-n-alkoxy-3chlorocinnamic acids becomes isotropic; squares are melting temperatures for compounds
forming liquid crystals; triangles: smectic to nematic transitions
50
melting temperature
nematic to isotropic
smectic to nematic
solid to smectic
calculated
1/[1-380/T(n)]
40
30
20
10
0
0
2
4
6
8
10
12
14
16
18
number of methylene groups, n
Figure. A plot of 1/[1-T()/T(n)] versus the number of methylene groups for trans-4-n-alkoxy-3chlorocinnamic 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?
-1
8
e
+
5
7
e
+
5
6
e
+
5
5
e
+
5
4
e
+
5
3
e
+
5
Totalphsecangthlpy,kJmo
2
e
+
5
1
e
+
5
0
e
+
0
0
5
0
1
0
0
1
5
0
N
u
m
b
e
r
o
f
m
e
t
h
y
l
e
n
e
g
r
o
u
p
s
,
n
Figure. Total phase change enthalpies of the n-alkanes.
2
0
0
Totalphsecangtropy,Jml
-1 K -1
2
0
0
0
1
8
0
0
1
6
0
0
1
4
0
0
1
2
0
0
1
0
0
0
8
0
0
6
0
0
4
0
0
2
0
0
0
0
5
0
1
0
0
1
5
0
N
u
m
b
e
r
o
f
m
e
t
h
y
l
e
n
e
g
r
o
u
p
s
,
n
Figure. Total phase change entropies of the n-alkanes
2
0
0
140
Total phase change enthalpy/ kJ mol
-1
120
100
80
60
40
20
0
0
2
4
6
8
10
12
14
16
18
20
Number of alkyl groups on a chain
Figure. Total phase change enthalpies of the dialkyl arsenic
acids as a function of the size of the alkyl group.
350
-1
Total phase change entropy/ J mol K
-1
300
250
200
150
100
50
0
0
2
4
6
8
10
12
14
16
18
20
Number of methylene groups per alkyl chain
Figure. Total phase change entropies of the dialkyl arsenic acids
as a function of the size of the alkyl group.
Fusion Enthalpies
N- Alkanes
tpceH(Tf)/J.mol-1 = (372538)n - (18387500); (37 data
points)
r2 = 0.9964
Di-n-alkylarsinic acids
tpceH(Tf)/J.mol-1 = 2 (334866) n + (95122800); (17 data
points)
r2 = 0.9941
Total Phase Change Entropies (Fusion Entropies)
tpceS(Tf ) = (As)n + (Bs) J.mol-1.K-1
N-Alkanes
tpceS(Tf ) = (9.3)n + (35.2) J.mol-1. K-1;
Di-n-alkylarsinic Acids
tpceS(Tf ) = 2(9.3)n + (11.2) J.mol-1. K-1;
G = H - Tf S ; at Tf , : G = 0
Tf = tpceH/tpceS = (AHn + BH)/(ASn + BS);
N-Alkanes
Tf =
tpceH(Tf)
tpceS(Tf )
=
(3725)n - (1838)
(9.3)n + (35.2)
Di-n-alkylarsinic Acids
Tf =
tpceH(Tf)
tpceS(Tf )
=
2 (3348)n+ (9512)
2(9.3)n + (11.2)
500
450
400
350
Tf / K
300
250
even n-alkanes
dialkylarsinic acids
200
150
100
50
0
20
40
60
80
100 120 140 160 180
n, even number of methylene groups
Figure. The melting point behavior of the even n-alkanes and the dialkylarsinic acids of
formula [CH3(CH2)n]2AsOH when calculated as a ratio of the total phase change
enthalpy to the total phase change entropy. Both were estimated by group additivity.
300
250
Number of entries
200
150
100
50
0
-60
-40
-20
0
20
40
60
Tf (exp) - Tf (calcd) /K
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.