Are there any ways to estimate melting points?

1
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.  
2
Figure . Melting temperatures of the even
n-alkanes versus the number of methylene groups,
circles experimental data
3
Figure. Melting points of the odd alkanes
versus the number of methylene groups circles
experimental data
4
Figure. The correlation between the function
1/1-Tf (n)/Tf (?) and the number of methylene
groups, n, for the even n-alkanes.
5
Figure. The correlation between the function
1/1-Tf (n)/Tf (?) and the number of methylene
groups for the odd n-alkanes.
6
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.
7
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.
8
Tfus Tf (?)1- 1/(mn b)
9
Table. Melting-structure correlations of series
related to polyethylene parents with Tf lt411.3
K.a Homologous Series Parent Compound Tf /K
S m b r2 ??/K
nT  Parent A. Hydrocarbons n-alkanesb 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-alkenesc 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-methylalkanesc
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-methylalkanesc 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-methylalkanesc 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-methylalkanese 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
10
2,3-dimethylalkanesc 2,3-dimethyldecaned
183.7 e 0.155 0.898 0.989
4.0 5   2,3-dimethylheptane 156
o 0.15 0.884 0.991 7.4
6 2,4-dimethylalkanesc 2,4-dimethylundecane
d 197.7 e 0.136 1.13 0.992
2.6 5   2,4-dimethyldecaned
183.2 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 n-alkylcyclopenta
nesf propylcyclopentane 155.8 e
0.155 1.23 0.999 0.6 8  
ethylcyclopentane 134.7 o
0.155 1.17 0.999 1.6
8 n-alkylcyclohexanesf 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 n-alkylbenzenesc
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-alkylnaphthalenesg 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  
2-ethylnaphthalene 265.7 o 0.149
2.15 0.987 6.8 6 Alkynesf
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
11
B. Cycloalkanes m b r2
??/K nT Cycloalkanesh 0.188 1.18 0.856 21 4
6  
12
Figure. Melting temperatures of the
cycloalkanes versus the number of methylene
groups. Both even and odd members are included.
13

• Functionalized Alkanes
• Homologous Series
• Parent Compound Tf /K S m b
  r2 ??/K nT
• 1-alkanolsi propanol 147.2 e 0.239 0.96
  8 0.998 1.9 18
•   ethanol 143.2 o 0.244 0.953 0.9
  99 4.0 15
• 2-alkanolsj 2-nonanold 184.7 e 0.257 0.8
  7 0.992 3.1 6
•   2-butanol 158.5 o 0.244 1.22 0.9
  99 1.1 9
• 1-alkanethiolsc 1-ethanethiol 125.9 o 0.153 1.12 0
  .998 2.6 8
• 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 1
  1
• alkyl ethanoatesc
• 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
• ethyl alkanoatesi
• ethyl butanoate 172.4 e 0.166 1.28 0.999 1.4 18

14
n-alkanalc butanal 176.8 e 0.159
1.77 0.982 7.4
7   propanal 193.2 o 0.183 1.24
0.945 8.1 8 n-alkanoic
acidsj 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-chloroalkanesc 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-fluoroalkanesc 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-bromoalkanesf 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-iodoalkanes f 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-cyanoalkanesc 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 1-N-methylamino-alkanesc  
methyl-n-butylamine 198.2 o 0.164
1.55 0.994 2.2 8
15
1-N,N-dimethyl-aminoalkanesc  
dimethyl-n-ethylamine 133.2 o 0.165
0.774 0.999 0.3
7 2-alkanonesc 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 alkyl phenyl
ketonesk acetophenone 293.2 o 0.213
2.44 0.995 0.8
5 F-CF212-CH2n-Hh F-CF212-CH22-H 344.2 e
0.172 5.93 0.920
1.5 9 N-methyl alkanamidesl  N-methylbuta
namide 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 2-hydroxyethyl- alkanamidesl
N-(2-hydroxyethyl)hexanamide 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 alkanoatesl p-chlorophena
cyl 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 N-octadecyl alkanamidesm N-octadecyl
butanamide 349.7 e 0.257 5.49
0.981 1.3 7
16
n-alkanamidesn butanamide 389.2 e 0.226
9.93 0.706 3.5 12 propanamide 356.2 o
0.238 8.61 0.732 5.0 7 alkyl
4-nitrobenzoateso 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 n-alkyl
3,5-dinitrobenzoateso ethyl 3,5-dinitrobenzoate
367.2 o 0.035 5.13 0.566 2.7
8 1,? dihydroxyalkanesc 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)alkana
midesm 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 1,?-alkanedioic acidsk 1,5-undecanedioic
acidd 378 o 0.730 9.30 0.925
1.9 8
17
D. Symmetrically Substituted Derivativesq sym
dialkyl etherc,p diethyl ether
157.2 e 0.135 0.932 0.999 1.7 4 sym
n-alkanoic acid anhydridesp,q   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 sym di-n-alkyl
sulfidesr diethyl sulfide
171.2 o 0.292 1.01 0.998 1.4 6 sym
N,N-dialkylaminesc
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 sym-t
ri-n-alkylaminesc triethylamine
158.5 o 0.249 0.655 0.998 1.6 7
18
sym-1,2,3-glycerol tri-alkanoates ? form
304.8 e 0.296 1.50 0.999 0.5 7 ? form  
261.7 0.272 0.598 0.999 1.1 7 ?' form
  290.0 0.263 1.31 0.999 0.8  7  
19
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.
20
If homologous series related to polethylene
converge to the mp of polyethylene, what about
other series converging to other polymers?
21
Figure. Experimental melting points as a function
of the number of repeat units, circles
perfluoro-n-alkanes squares HOCH2CH2nOH
triangles C2H5CO-NH(CH2)5COn-NHC3H7.
22
Figure. A plot of 1/(1 mp(n)/mp?) versus the
number of CF2 groups. The melting point of
Teflon is 605 K.
23
Table. Melting-structure correlations of series
related to other polymers Parent Compound Tf
/K S m b r2
??/K nT n-perfluoroalkanes
  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 Polyoxyet
hylene (Tf 342 K) HOCH2CH22OH 267.2
e 0.407 3.36 0.884 ?4.7 8  HOCH2CH2OH
260.6 o 0.554 2.34 0.953 ?5.2 8   Polyamides Ny
lon-6 (Tf 533 K) HNH(CH2)5CO2OH 471.2
e 0.089 10.0 0.650 ?0.8 5 HNH(CH2)5COOH
479.2 o 0.046 9.9 0.599 ?1.6 10
24
What if the melting temperature of the parent is
greater than 411 K?
25
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.
26
Figure. Melting temperatures of the
dialkylarsinic acids (odd series)
27
Figure. A plot of 1/(1- T?/T(n) vs n for the
dialkylarsinic acids. A value of 380 K was used
for T?.
28
Ascending hyperbola Tfus Tf (?)1- 1/(mn
b) Descending hyperbola Tfus Tf (?)/1-
1/(mn b)
29
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?
30
Liquid Crystals
nematic
31
Figure. Circles melting temperatures or
temperatures at which the trans-4-n-alkoxy-3-chlor
ocinnamic acids becomes isotropic squares are
melting temperatures for compounds forming liquid
crystals triangles smectic to nematic
transitions
32
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(?).
33
Why do the first few members of the series
usually deviate from the observed hyperbolic
behavior?
34
Why do homologous series exhibit melting points
that behave in a hyperbolic fashion?
35
Figure. Total phase change enthalpies of the
n-alkanes.
36
Figure. Total phase change entropies of the
n-alkanes
37
Figure. Total phase change enthalpies of the
dialkyl arsenic acids as a function of the size
of the alkyl group.
38
Figure. Total phase change entropies of the
dialkyl arsenic acids as a function of the size
of the alkyl group.
39
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
40
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
41
?G ?H - Tf ?S at Tf , ?G 0 Tf
?tpceH/?tpceS (AHn BH)/(ASn
BS) N-Alkanes Tf ?tpceH(Tf)
(3725)n - (1838) ?tpceS(Tf ) (9.3)n
(35.2) Di-n-alkylarsinic Acids Tf
?tpceH(Tf) 2 (3348)n (9512) ?tpceS(Tf )
2(9.3)n (11.2)
42
Figure. The melting point behavior of the even
n-alkanes and the dialkylarsinic acids of formula
CH3(CH2)n2AsOH when calculated as a ratio of
the total phase change enthalpy to the total
phase change entropy. Both were estimated by
group additivity.
43

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.