Liquid Crystals

1
Liquid Crystals Recall that the total phase
change entropy of semi-perfluorinated compounds
were considerably less than the values estimated.
Many of these materials form liquid crystals.
2
Table. Molar Transition Enthalpies (kJ mol-1) and
Entropies (J mol-1 K-1) of Select Amphiphilic
Semiperfluorinated-Semiper-hydrogenated Diblock
and Triblock Organic Compoundsa T(K) ?Hpce ?Spce
?Stpce 0.6?Stcpe ?Stcpe ?Htpce ?Htpce expt
calcd calcd expt calcd UNSUBSTITUTED
DIBLOCK MOLECULES C16H9F25 F3C(CF2)11(CH2)4H 14
7.0 0.7 5 314.0 1.4 4 349.0 21.0 61 69.4 57.
1 93.6 23.1 19.9 C16H13F21 F3C(CF2)9(CH2)6H
306.0 4.2 14 318.0 16.9 53 67 61.6
100.9 21.1 19.6 C16H17F17 F3C(CF2)7(CH2)8H
301.2 9.5 31.6 303.2 5.7 18.8 50.3 90.2 147.9
15.2 27.3 C17H21F15 (CF3)2CF(CF2)4(CH2)10H 220
.0 3 13.6 261.0 18 69.0 82.6 84.6
138.6 21.0 18.9
3
T(K) ?Hpce ?Spce ?Stpce 0.6?Stcpe ?Stcpe ?Htp
ce ?Htpce expt calcd calcd
expt calcd C18H13F25 F3C(CF2)11(CH2)6H 164.0
0.5 1 316.0 3.5 11 357.0 23.4 65.5 79.7 65.7
107.8 27.4 23.5 C18H21F17 F3C(CF2)7(CH2)10H 2
88.0 3.5 12 308.0 20.2 65 77.7 86.8
142.3 23.7 26.9 C19H21F19 (CF3)2CF(CF2)6(CH2)1
0H 274.0 1 3.6 298.0 25 83.9 87.5 84.6
138.6 26 22.1 C20H17F25 F3C(CF2)11(CH2)8H 192.
0 2.4 12.5 329.0 6.4 19.5 361.0 23.7 65.7 97.6
74.7 122 32.5 26.9 C20H21F21 F3C(CF2)9(CH2)10H
317.0 4.0 12 337.0 24.4 72 85 78.9
129.3 28.4 26.6
4
Figure. A comparison of calculated and
experimental total phase change entropies for the
partially fluorinated amphiphilic compounds.
5
?Stcpe(calcd) (0.648?0.06) ?Stcpe expt
(30.1?13.5) r2 0.6525
6
Liquid Crystals
Since their first discovery back in 1888,
interest in the properties and practical
applications of liquid crystals has increased
dramatically.1,2 General acceptance of liquid
crystals as a distinct phase of matter was slow,
occurring some 30 years since they were first
reported. Liquid crystalline behavior is found
among numerous classes of compounds that include
biphenyls, cholesterol esters, soaps, lipids,
polymers and elastomers. More than 76000
compounds have been identified as exhibiting
liquid crystalline behavior.
7
Between 1850 and 1888, researchers found that
several materials behaved strangely at
temperatures near their melting points. It was
observed that the optical properties of these
materials changed discontinously with increasing
temperatures. W. Heintz, for example, reported in
1850 that stearin melted from a solid to a cloudy
liquid at 52C, changed at 58C to an opaque and
at 62.5C to a clear liquid. Others reported
observing blue colors when cholesterol esters
were cooled. Biologists observed anisotropic
optical behavior in "liquid" biological
materials, a behavior usually expected only in
the crystal phase.
8
In 1888, an Austrian botanist named Friedrich
Reinitzer, interested in the biological function
of cholesterol in plants, was looking at the
melting behaviour of an organic substance related
to cholesterol. (The chemical structure of
cholesterol was still unknown. Today we know that
the observed substance was cholesteryl benzoate).
He observed, as W. Heintz did with stearin 38
years before, that the substance melted to a
cloudy liquid at 145.5C and became a clear
liquid at 178.5C. He repeated an earlier
observation which showed that upon cooling the
clear liquid, a brief appearance of blue color
could be seen at the transition temperature, and
that a blue violet color appeared just before
crystallization from http//www.lci.kent.edu/lc_h
istory.html
9
An examination of the phase change enthalpies of
liquid crystals reveals that these substances
exhibit several thermal transitions that can be
detected. For most substances, the largest
enthalpic change occurs upon conversion of the
solid to a nematic or smectic phase. DSC is a
common way of studying the thermal behavior of
liquid crystals
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In the most popular DSC design, two pans sit on a
pair of identically positioned platforms
connected to a furnace by a common heat flow
path. In one pan, you put your sample. The other
one is the reference pan. You place an MT cell.
You then program the computer to turn on the
furnace to heat the two pans at a specific rate,
usually something like 5oC per minute. If heat is
adsorbed or emitted, the power supplied to
maintain a constant temperature is measured.
12
Figure. DSC trace of a typical compounds
exhibiting liquid crystal formation.
13
Schlieren texture of a nematic film with surface
point defects (boojums). This picture was taken
under a polarization microscope with polarizer
and analyzer crossed. From every point defect
emerge four dark brushes. For these directions
the director is parallel either to the polarizer
or to the analyzer. The colors are newton colors
of thin films and depend on the thickness of the
sample. Point defects can only exist in pairs.
One can see two types of boojuns with "opposite
sign of topological charge" one type with yellow
and red brushes, the other kind not that
colorful. The difference in appearance is due to
different core structures for these defects of
different "charge".
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15
T gt230 ºC
16
230 gt T gt 195 ºC
17
195 gt T gt 165 ºC
18
165 gt T gt 140 ºC
19
140 gt T gt 85 ºC
20
85 gt T gt mp ºC
21
C14H30O4 CH2OHCHOH(CH2)10CHOHCH2OH
?tpceSm(exp) 131.3 J mol-1.K-1 ?tpceSm (calc)
176.6 J mol-1.K-1 ?tpceSm(calc)
2(7.1)2(16.4)(0.6)2(1.7)(13.1)10(1.31)(7.1)
C20H28O3 ?tpceSm(exp) 82.7 J mol-1.K-1
?tpceSm (calc) 107.9 J mol-1.K-1 (calc)
217.637.133.433.72(-14.7) 5.30.75 5.3
47.42(-7.5)7.7 4.7
22
Fig. A comparison of the experimental and
calculated total phase change entropies of 2637
compounds. The area between the two lines
represents ?2 ?.
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Fig. A comparison of calculated and experimental
values for 627 liquid crystals. The solid line
represents the equation obtained by a linear
regression analysis and the area within the two
dotted lines represents anticipated values of
falling within ?2? based on the evaluations of
database compounds.
25
Fig. A histogram of the distribution of errors in
(exp) - (calc) for liquid crystals. Each
interval represents one standard deviation (15.3
J. mol-1.K-1). Six compounds has errors equal to
or larger than -30 ?.
26

• Possible reasons responsible for both the scatter
  and overestimations observed in Fig. 3.
• Some residual molecular association exists at the
  clearing temperature.
• Attenuation in phase change entropies is
  compensated at some temperature by increases in
  the heat capacity of the crystal.
• Polymorphism may also play a role.
• The solid phase may not possess total
  crystallinity. Studies on polymeric materials
  have shown that the measured enthalpies of fusion
  depend on the degree of crystallinity.
• Occurrence of undetected solid-solid phase
  transitions at low temperatures is certainly a
  possibility.

27
Table. A series of compound including liquid
crystals whose heat capacity and phase
transitions of the crystalline phase have been
studied over most of the experimentally
accessible regiona Transition T/K ?pceHm
?pceSm ?tpceSm (exp) ?tpceSm
(estimated) So (385 K) C36H54O12 benzene
hexa-n-pentanoate Sol/Sol 173.1
8.8 50.83 Sol/Sol 313.2 15.3 48.85 Sol/Liq 379.5
30.3 79.84 183.5 234.6
1629.9 C42H66O12 benzene
hexa-n-hexanoate Sol/Sol 251.6 25.67 102.0 Sol/S
ol 291.5 12.27 42.1 Sol/Sol 348.3 16.26
46.7 Sol/Liq 368.7 33.50 90.9 281.7
277 1877.1 C48H78O12 benzene
hexa-n-heptanoate Sol/Sol 129 1.1
8.5 Sol/Meso 353.8 32.2 91.1 Meso/Liq 359.3 21.5
59.9 159.5 319.8 2114.4
C54H90O12 benzene hexa-n-octanoate Sol/Sol 301.9
49.0 164.0 Sol/Meso 355.1 46.1 129.8 Meso/Liq 3
57.1 19.2 53.8 347.6 362.4 2361.3
  C60H102O12 benzene hexa-n-nonanoate Sol/Sol
248.3 19.4 78.13 Sol/Sol 278.3 4.9
17.60 Sol/Liq 353.1 69.2 195.98 291.7
405 2597.8 Liq/Meso 350 NA  
C66H114O12 benzene hexa-n-decanoate Sol/Sol 330.
8 75.7 228.9 Sol/Liq 360.9 91.8 254.3
483.2 448 2861.5   aCp measurements
of the solid from approximately 15 K to the
isotropic liquid at 385 K.
28
Recall that
So ?pceH/T
?fusH/Tfus
So evaluated from 15 K to 385 K

1. M. Sorai, K. Tsuji, H. Suga and S. Seki, Mol.
   Cryst. Liq. Cryst., 80, 33-58 (1980).
2. M. Sorai and H. Suga, Mol. Cryst. Liq. Cryst.,
   73, 47-69 (1981).12. M. Sorai, H. Yoshioka and H.
   Suga, Mol. Cryst. Liq. Cryst., 84, 39-54 (1982).
3. S. Asahina and M. Sorai, J. Chem. Thermodyn., 35,
   649-666 (2003).
4. S. Asahina, and M. Sorai, Liq Cryst., 28,
   1085-1092 (2001).

29

Fig. A plot of the entropy of the benzene
hexa-n-alkanoates at T 385 K as a function of
the number of carbon atoms.
30
The pentanoate, hexanoate and decanoate do not
form liquid crystals. The nonanoate does so only
on supercooling the isotropic liquid below the
melting temperature. Both the heptanoate and
octanoate form liquid crystals. Agreement between
estimated and experimental total phase change
entropies is within the noise level expected for
these estimations for the pentanoate, hexanoate,
octanoate and decanoate. Values for the
heptanoate and nonanoate are clearly
overestimated. Even for the octanoate, although
the two values are within experimental
uncertainty, the calculated value is somewhat
larger.
31

• Conclusions
• Deviations not due to residual molecular
  association existing at the clearing temperature.
• Effects due to polymorphism not likely.
• The solid phase is crystalline.
• Undetected phase transitions are not responsible.
• Attenuation in phase change entropies is
  compensated at some temperatures by abnormal
  increases in the heat capacity of the crystal.

32
Definition of Tfus, Tclr and Tiso for Liquid
Crystals Tfus melting temperature Tclr
temperature at which the liquid crystal clears
for some samples, this could below Tfus if the
sample supercools Tiso temperature at which
the liquid crystal becomes isotropic for most
compounds also equal to Tclr Tiso Tiso
max(?)1- 1/(mN b) for increasing Tf (n)
Tiso Tiso min/ 1- 1/(mN b) for decreasing
Tf (n)
33
Question How do the melting temperatures of
liquid crystals compare to the melting
temperatures of analogous compounds that do not
form liquid crystals?
34
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
35
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(?).
36
Tfus (n) 317/ 1- 1/((0.564)n 5.133)
r2 0.6586 Tiso (n) 234/ 1- 1/((0.0238)n
2.528) r2 0.9661
Fig. A comparison of the melting and clearing
temperatures of the thiocholesteryl n-alkanoates
(odd series) circles melting temperatures
squares clearing temperatures. The first and
third compounds in the series do not form liquid
crystals.16
37
Tfus (n) 259/ 1- 1/((0.0745)n 3.065)
r2 0.7508 Tiso (n) 328/ 1- 1/((0.4185)n
5.436) r2 0.9931
Fig. A comparison of the melting and clearing
temperatures of the thiocholesteryl n-alkanoates
(even series) circles melting temperatures
squares clearing temperatures
38
It appears that the melting temperature
correlates best with the temperature at which the
liquid crystals become isotropic. This means
that the temperature at which the solid melts is
lowered as a result of formation of the smectic
or nematic phase. Why is there a melting point
lowering? Why do impure materials melt lower than
pure materials?
39
Tiso Tiso min/ 1- 1/(mN b) for decreasing
Tf (n)
Tfus (n) 317/ 1- 1/((0.564)n 5.133) r2
0.6586 Tiso (n) 234/ 1- 1/((0.0238)n
2.528) r2 0.9661
Tfus (n) 259/ 1- 1/((0.0745)n 3.065)
r2 0.7508 Tiso (n) 328/ 1- 1/((0.4185)n
5.436) r2 0.9931
Question How was Tiso min determined for each
of these series?
40
Ans 1/1- Tiso min/T(n) was plotted against n
using Tiso min, as a variable. The best value of
Tiso min was chosen on the basis of a non-linear
least squares program.
41
Binary phase diagram
mp
100 A 0 A 0 B
100B

42
Packing of the solid in series that form liquid
crystals is affected much like the presence of an
impurity.
43
What happens when the descending portion of the
Tiso is reached?
44
A portion of the melting behavior expected of a
homologous series after the minimum is reached.
The members of the series exhibiting liquid
crystalline behavior occur on the descending
portion of the curve. Liquid crystalline behavior
appears to cease before the minimum. Once the
minimum is reached, the melting temperatures are
predicted to increase gradually to T 411 K.
Fig. A comparison of the melting and clearing
temperatures of the alkyl 4-methoxybiphenyl-4-car
boxylates (odd series) circles melting
temperatures squares clearing temperatures. The
first two and last entries do not form liquid
crystals.
45
Why Do Compounds Form Liquid Crystals?
46
Table Group values for estimating heat
capacities of solids at T 298 K
GroupValuesab GroupValuesabHydrocarbon
Groups ?(c) ?(c) primary sp3 C
36.6 tertiary aromatic sp2 C 17.5 secondary sp3
C 26.9 quaternary aromatic sp2 C
8.5 tertiary sp3 C 9.0 internal
quaternary aromatic sp2 C 9.1quaternary sp3 C
-4.98 cyclic secondary sp3 C
24.6 secondary sp2 C 46.0 cyclic
tertiary sp3 C 11.7 tertiary sp2 C
21.4 cyclic quaternary sp3 C 6.1 quaternary
sp2 C 6.86 cyclic tertiary sp2
C 15.9 tertiary sp C 23.9 cyclic
quaternary sp2 C 4.73 quaternary sp C
15.2
47
Functional Groups  alcohols, phenols 23.5
cyclic ether 9.71fluorine 24.8 isocyanate
52.7 chlorine 28.7 nitro group
56.1bromine 32.4 thiols
51.9 nitrile 42.3 primary sp3 N
21.6carboxylic acid 53.1 secondary sp3 N
-0.29 aldehyde 84.5 tertiary sp3 N
31.5 ketones 28.0 tertiary sp2 N
10.7 cyclic ketones 34.3 cyclic secondary
sp3 N 23.9ester 40.3 cyclic tertiary sp3
N 1.21lactone 45.2 cyclic tertiary sp2
N 13.9 ether 49.8 sulfides 116cyclic
sulfides 18.2
48
Simple dialkyl ethers and n-alkanes do not form
liquid crystals. In addition, their heat
capacities at T 298.15 K are generally well
modeled by the group values listed in the
previous tables. Why is it that dialkyl ethers
and n-alkanes do not form liquid crystals and why
are the Cp(c) values for these molecules at
various temperatures less than the values found
for compounds forming liquid crystals? Recall
that ?tpceSm (exp) lt ?tpceSm (estimated)
but that Sm(total) appears to be a linear
function in homologous series.
49
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.
50
The fact that the first few members of the series
deviate from the remaining members is explained
as a result of a change in packing from one
dominated by the functional group or head group
to one dominated by the chain. In liquid
crystals, this deviation is exaggerated. However,
if the packing is dominated by the head group,
then the alkyl chains will be packed loosely and
their contribution to the heat capacity will be
even larger than their normally high value. Why
would the contribution of Cp of a loosely packed
group be greater than for a more tightly packed
group?
51
Empirical Justification
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Theoretical Perspective
_ _ _ _ _ _

_ _ _ _ - -
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As a crystal is heated, more thermal motion will
be concentrated in the alkyl chains and less in
the rigid component. At some point the thermal
energy will be enough to disrupt the alkyl chains
so they become fluid, before all the attractive
forces associated with the head group are
overcome As a consequence, the tails are fluid
while the heads retain some degree of order. The
hydrophobic and hydrophillic interactions then
are responsible for the nature of the order
obtained. Whether a compound forms a liquid
crystal is likely to be a delicate balance
between how evenly or unevenly thermal motion is
distributed within the crystal.