are there any ways to estimate melting points? what do melting points measure? “melting is a...
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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.
number of methylene groups, n
0 100 200 300 400 500
Tf(
exp)
/ K
50
100
150
200
250
300
350
400
450
Figure . Melting temperatures of the even n-alkanes versus the number of methylene groups, circles; experimental data
Number of methylene groups, n
0 10 20 30 40 50 60 70 80
Exp
erim
enta
l m
elti
ng p
oint
, K
50
100
150
200
250
300
350
400
Figure. Melting points of the odd alkanes versus the number of methylene groups; circles: experimental data
number of methylene groups, n
0 100 200 300 400 500
1/[
1-T
f (n
)/Tf (
0
10
20
30
40
50
60
70
80
number of methylene groups, n
0 100 200 300 400 500
1/[1
-Tf (
n)/T
f (
0
10
20
30
40
50
60
70
80
Figure. The correlation between the function 1/[1-Tf (n)/Tf ()] and the
number of methylene groups, n, for the even n-alkanes.
Number of methylene groups, n
0 10 20 30 40 50 60 70 80
1/(
1-m
p(n
)/m
p )
0
2
4
6
8
10
12
14
Figure. The correlation between the function 1/[1-Tf (n)/Tf ()] and the
number of methylene groups for the 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
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 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
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-dimethylundecaned 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-alkylcyclopentanesf 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
B. Cycloalkanes
m b r2 /K nT
Cycloalkanesh 0.188 1.18 0.856 21 46
Number of methylene groups, n
0 50 100 150 200 250 300 350
Tf
/ K
280
300
320
340
360
380
400
420
experimental datacalculated
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 S m b r2 /K
nT
1-alkanolsi 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-alkanolsj 2-nonanold 184.7 e 0.257 0.87 0.992 3.1 6
2-butanol158.5 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
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
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
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
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-[CF2]12-[CH2]n-Hh
F-[CF2]12-[CH2]2-H344.2 e 0.172 5.93 0.920 1.5 9
N-methyl alkanamidesl
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
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-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
N-octadecyl alkanamidesm
N-octadecyl butanamide 349.7 e 0.257 5.49 0.981 1.3 7
n-alkanamidesn butanamide 389.2 e 0.226 9.93 0.706 3.5 12propanamide 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)alkanamidesm
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
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-tri-n-alkylaminesc
triethylamine 158.5 o 0.249 0.655 0.998 1.6 7
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
Number of methylene groups, n
6 8 10 12 14 16 18 20 22
Tf
/ K
240
260
280
300
320
340
360
380
calculated valueform' form form
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?
number of repeat units, n
0 10 20 30 40 50
Tf
/ 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
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.
Number of CF2 groups, n
0 5 10 15 20 25
1/(1
- m
p(n)
/mp
0
1
2
3
4
5
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 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 0.92014.3 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 479.2 o 0.046 9.9 0.599 1.6 10
What if the melting temperature of the parent is greater than 411 K?
number of methylene groups, n
0 2 4 6 8 10 12 14 16 18
T f o
r Ttr /
K
360
380
400
420
440
460
480
500
520
540
5604-n-alkoxy-3-fluorobenzoic acidtrans 4'-n-alkoxy-3-chlorocinnamic acid6-n-alkoxy-2-naphthoic acid8-n-alkyltheophyllinecalculated
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.
Number of methylene groups
0 2 4 6 8 10 12 14 16 18
Mel
tin
g t
emp
erat
ure
/ K
390
395
400
405
410
415
420
Figure. Melting temperatures of the dialkylarsinic acids (odd series)
Number of repeat units
0 2 4 6 8 10 12 14 16 18
[1/(
1- T
n)]
10
15
20
25
30
35
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?
nematic
Liquid Crystals
Transition temperatures
0 2 4 6 8 10 12 14 16 18
Nu
mb
er o
f re
pea
t un
its
380
400
420
440
460
480
500
Figure. Circles: melting temperatures or temperatures at which the trans-4-n-alkoxy-3-chlorocinnamic acids becomes isotropic; squares are melting temperatures for compounds forming liquid crystals; triangles: smectic to nematic transitions
number of methylene groups, n
0 2 4 6 8 10 12 14 16 18
1/[
1-3
80
/T(n
)]
0
10
20
30
40
50
melting temperaturenematic to isotropicsmectic to nematicsolid to smecticcalculated
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().
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?
Number of methylene groups, n
0 50 100 150 200
Tot
al p
hase
cha
nge
enth
alpy
, kJ
mol
-1
0e+0
1e+5
2e+5
3e+5
4e+5
5e+5
6e+5
7e+5
8e+5
Figure. Total phase change enthalpies of the n-alkanes.
Number of methylene groups, n
0 50 100 150 200
Tot
al p
hase
cha
nge
entr
opy,
J m
ol-1
K-1
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Figure. Total phase change entropies of the n-alkanes
Number of alkyl groups on a chain
0 2 4 6 8 10 12 14 16 18 20
Tot
al p
hase
cha
nge
enth
alpy
/ kJ
mol
-1
0
20
40
60
80
100
120
140
Figure. Total phase change enthalpies of the dialkyl arsenic acids as a function of the size of the alkyl group.
Number of methylene groups per alkyl chain
0 2 4 6 8 10 12 14 16 18 20
Tot
al p
hase
cha
nge
entr
opy/
J m
ol-1
K-1
0
50
100
150
200
250
300
350
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 = (372538)n - (18387500); (37 data
points)
r2 = 0.9964
Di-n-alkylarsinic acids
tpceH(Tf)/J.mol-1 = 2 (334866) n + (95122800); (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) = (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)
n, even number of methylene groups
0 20 40 60 80 100 120 140 160 180
T f / K
50
100
150
200
250
300
350
400
450
500
even n-alkanesdialkylarsinic acids
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.
Tf (exp) - Tf (calcd) /K
-60 -40 -20 0 20 40 60
Num
ber
of e
ntri
es
0
50
100
150
200
250
300
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.