Bistable phase behavior and kinetics of nonisothermal mesophase formation in a chiral side chain polymethacrylate

Article abstract of DOI:10.1021/ma047631o

Nonisothermal kinetics of smectic phase formation in a chiral liquid crystalline (LC) azodye polymer is studied. The Ozawa exponent value of n 2.5 is estimated for narrow polymer fractions with M_w/M _n 1.3-1.6 but a temerature-depende

Full text of DOI:10.1021/ma047631o

Macromolecules 2005, 38, 2729-2738
2729
Bistable Phase Behavior and Kinetics of Nonisothermal Mesophase
Formation in a Chiral Side Chain Polymethacrylate
Mikhail Kozlovsky,*,† Berndt-J. Jungnickel,‡ and Helmut Ehrenberg§
Institute of Macromolecular Chemistry, Darmstadt University of Technology, Darmstadt, Germany;
German Institute for Polymers (DKI), Darmstadt, Germany; and Institute of Material Science,
Darmstadt University of Technology, Darmstadt, Germany
Received November 17, 2004; Revised Manuscript Received January 23, 2005
ABSTRACT: Nonisothermal kinetics of smectic phase formation in a chiral liquid crystalline (LC) azodye
polymer is studied. The Ozawa exponent value of n ∼ 2.5 is estimated for narrow polymer fractions with
Mw/Mn ∼ 1.3-1.6 but a temerature-dependent value, 0.5 < n < 1.2, for the raw polymer of Mw/Mn ∼ 2.6.
The effect of molar mass on mesomorphism is studied, and the dependence of melting temperature on
subsequent heating from the rate of previous cooling, r, is theoretically explained. The narrow fractions
show a “bistable” phase behavior forming conventional Sm A phase on slow cooling, r < 1 K/min, but
another (probably a highly twisted TGB A*) mesophase on fast cooling, r > 1 K/min. A theoretical model
for such a behavior is suggested, and the structure of the two phases is studied by SAXS. The applicability
of the Kissinger approach to estimation of activation energy for TGB A* phase formation is discussed.
I. Introduction
polymer heating/cooling at a constant rate. The Ozawa
equation is written as
The isothermal crystallization of polymers is well
described1,2 and is usually interpreted in terms of the
Avrami approach. The theory developed by Mel Avrami
as early as in the 1940s3,4 considers a tiny nuclei of a
new phase continuously created or existing within the
old phase. There is a time-dependent probability of
nuclei activation for their growth, and not yet activated
nuclei start to grow later or will be swallowed by the
growing phase.
1 - ê(T) ) exp(-Φ(T)rn)
(2)
where r is the cooling rate, Φ(T) is called the cooling
function of the process, and the Ozawa exponent, n,
depends again on the domain growth and nucleation
mechanism. Similar to the Avrami plot, the Ozawa plots
in coordinates ln{-[1 - ln ê(T)]} vs ln(r/K min-1) should
show a series of parallel straight lines, thus correspond-
ing to an “isokinetic” mode of phase transformation. To
date, the Ozawa analysis is widely used to decribe
nonisothermal crystallization of industrial polymers.17-20
In this work, we have used the Ozawa approach to
study the mesophase formation in a chiral side chain
azo dye polymethacrylate, P8*NN
The Avrami equation
1 - ê(t) ) exp(-Btk)
(1)
describes growth of the volume part of the new phase,
ê, as a function of time, t. For a given substance and
crystal habit, there is an “isokinetic range” of temper-
atures and concentrations throughout which the kinetics
of phase transformation in the characteristic time scale
remains unchanged. The original theory yields integer
k values from 1 (linear growth of crystal nuclei) through
2 (two-dimensional growth) to 3 and 4 for spherical
crystallization, depending on the mode and dimension-
ality of nucleation. The Avrami analysis was success-
fully applied to the crystallization of polymers from LC
phases,5-8 to the growth of mesophases from isotropic
polymer melts,9-13 and to phase transition between
polymer LC phases as well.14,15
Isothermal studies are however possible only when
the phase transformation rate is much larger than
thermal response of the measuring system. Moreover,
it does not apply to practical processes such as industrial
synthesis or device fabrication which proceed under
nonisothermal conditions. For that case, Ozawa16 has
extended the Avrami approach to the situation of
for both raw polymer and its narrow fractions of
different molar mass. The recently synthesized polymer
is distinguished for high photooptical response being a
promising holographic media. Thus, e.g., a phase holo-
graphic gitter written in a P8*NN film by circularly
polarized laser beam shows diffraction efficiency as high
as 35% and more.21
The mesophase of the polymer, as formed by sponta-
neous cooling from above the phase transition, appears
optically isotropic and transparent for the wavelength
range λ > 500 nm but possesses a hidden layered
(smectic) structure. On the other hand, an ambiguous
mesomorphism has been observed for P8*NN so that
its optical appearance as an LC glass depends critically
on cooling rate. For that reason, the kinetics of me-
sophase formation in the polymer and the effect of molar
† Institute of Macromolecular Chemistry, Darmstadt University
of Technology.
‡ German Institute for Polymers.
§ Institute of Material Science, Darmstadt University of Tech-
nology.
10.1021/ma047631o CCC: $30.25 © 2005 American Chemical Society
Published on Web 03/08/2005

2730 Kozlovsky et al.
Macromolecules, Vol. 38, No. 7, 2005
Figure 1. Synthesis of the monomer M8*NN.
ethyl acetate 4:1 mixture and the second time with 10% ethyl
acetate in hexane. The goal product after removal of the
solvent in vacuo appears as a cherry viscous oil. Recrystalli-
zation from hexane at -18 °C gives an orange solid with
melting point below ambient temperature. Yield: 11.9. g (33
mmol, 75%).
mass distribution as treated in this paper are of great
importance.
II. Experimental Section
1. Synthesis of the Monomer. The monomer M8*NBN
was synthesized according to the scheme in Figure 1.
p-11-Bromoundecanoyloxy-p′-2-(S)-octyloxyazoben-
zene. 19.1 g (33 mmol) of p-2-(S)-octyloxy-p′-hydroxyazoben-
zene, and 5 mL (3.7 g, 36 mmol) of triethylamine were
dissolved in 100 mL of dry ether, and the solution of 12 g (42
mmol) of ω-bromoundecanoyl chloride in 50 mL of ether was
added dropwise (immediate precepitation of triethylammo-
nium chloride observed). The reaction media was stirred
overnight, then washed with water, diluted HCl, and water
again, and dried over CaCl2. The solvent was evaporated in
vacuo, and the residue was chromatographed on silica (toluene)
and recrystallized from ether to hexane, giving the goal ester
as egg-yellow plates. Yield: 9.0 g (15.6 mmol, 50%); mp 81
°C. 1H NMR (ppm): 7.88 (d+d, 4H), 7.21 (d, 2H), and 6.98 (d,
2H) aromatic; 4.46 (m, 1H) -O-C*H(CH3)C6H13; 3.45 (t, 2H)
Br-CH2-CH2-; 2.58 (t, 2H) -CH2-CH2-COO-; 0.9-1.9
aliphatic.
p-[2-(S)-Octyloxy]nitrobenzene. The R(+)-2-octanol (10
g, 76.8 mmol), p-nitrophenol (11 g, 79 mmol), and diisopropyl
azodicarboxylate (16 mL, 79 mmol) were dissolved in 350 mL
of ether and cooled in a water-ice bath for 0.5 h, and then
the solution of the triphenylphosphine in 50 mL of ether was
added dropwise during 5 min with stirring. The mixture was
stirred at room temperature overnight, the precepitate filterred
off, and the solvent removed. Since removal of the ether
induced further precipitation, the procedure was repeated five
times with 3-4 h intervals, giving a total of 21.8 g of
crystalline solid. The solvent was then removed, the rest
chromatographed on silica (toluene), and the first fraction
collected as a viscous yellowish oil.
Yield: 17.1 g (68 mmol, 90%). [R]D ) -7.4° (0.01 mg/mL in
methylene chloride). 1H NMR (ppm): 8.19 (d, 2H) and 6.92
(d, 2H) aromatic, 4.48 (hx, 1H) -O-C*H(CH3)-C6H13, 1.78 (m,
1H) and 1.65 (m, 1H) -O-C*H(CH3)-CH2-C5H11, 1.2-1.5
aliphatic including 1.36 (d, 1H) -O-C*H(CH3)-C6H13, and
0.91 (t, 3H) -O-C*H(CH3)-C5H10-CH3.
p-2-(S)-Octyloxyaniline. 65 g (0.29 mol) of SnCl2 was
suspended in ethanol, 14.3 g (57 mmol) of the p-2-(S)-
octyloxynitrobenzene added, and the mixture refluxed under
nitrogen for 1 h. After cooling, the reaction mixture was poured
into ice water. The solution pH was turned slightly basic (7-
8) by addition of solid K2CO3. The product was extracted with
ether, washed with brine, and dried with anhydrous MgSO4.
The solvent was distilled off, and from 12.1 g of crude product,
the aniline was distilled at reduced pressure as a yellow oil;
bp 132-134 °C at 5 mmHg. Yield: 11.1 g (50 mmol, 88%).
p-2(S)-Octyloxy-p′-hydroxyazobenzene. 9.6 g (43 mmol)
of p-2-(S)-octyloxyaniline was dissolved in 40 mL of ethanol,
40 mL of 6 N HCl added, the ethanol removed under vacuum
at 40 °C, and the rest left overnight at +4 °C. An ivory solid
crystallized over the acid aqueous solution. The solid was
powdered, cooled to 0 °C in an ice-salt bath, and an additional
20 mL of HCl added; the solution of 2.9 g (42 mmol) of NaNO2
in 20 mL of water was added dropwise with stirring, keeping
the temperature not above +5 °C (solution 1).
Phenol (4.0 g, 42 mmol) was dissolved in 100 mL of 2 N
NaOH and cooled to 0 °C in an ice-salt bath (solution 2). Then
solution 1 was added dropwise with stirring, keeping the
temperature not above +5 °C. After all solution 1 added, the
mixture was stirred overnight at room temperature. The
reaction media was then extracted with 4 × 200 mL of ether,
washed with water, and dried over MgSO4. The rest after
evaporation of ether was chromatographed on silica twice, the
first time changing the eluant from pure toluene to a toluene-
p-11-Methacryloyloxyundecanoyloxy-p′-2-(S)-octyloxy-
azobenzene. 6.5 g (11.2 mmol) of the bromo precursor was
dissolved in 50 mL of freshly distilled 1,3-dimethylimidazoli-
dinone-2, and 3 g (24 mmol) of powdered potassium methacry-
late was added. The mixture was stirred at room temperature
for 24 h and then poured into 300 mL of ice water, filtered,
dissolved in ether, washed with water, and dried over CaCl2.
The solvent was removed, and the rest was chromatographed,
changing eluent from the toluene-hexane 1:1 mixture through
pure toluene to the toluene-ethyl acetate 19:1 mixture. The
product recrystallized from methanol (mp 44.5 °C), but the
monomer can be supercooled and crystallizes at arbitrary
temperature, as e.g. 34 °C under shear flow. Yield: 4.5 (7.7
1
mmol, 70%). H NMR (ppm): 7.9 (d+d, 4H), 7.2 (d, 2H), and
7.0 (d, 2H) aromatic; 6.1 (s, 1H) and 5. (s, 1H) CH2dC(CH3)-
COO-; 4.5 (m, 1H) -O-C*H(CH3)C6H13; 4.2 (t, 2H) OOC-
CH2-CH2-; 2.6 (t, 2H) -CH2-CH2-COO-; 1.9 (s, 3H) CH2d
C(CH3)-COO-; 0.9-1.7 aliphatic.
2. Polymerization and Fraction Separation. The chiral
methacrylic azo dye polymer P8*NN was prepared by radical
polymerization of its monomer in solution, as follows. The
monomer (4.0 g, 6.9 mmol) and AIBN (40 mg, 0.24 mmol) were
dissolved in 40 mL of toluene, bubbled 0.5 h with Ar, and then
ampule closed and kept at 60 °C for 65 h. Then the solution
was diluted with toluene to 100 mL, and 45 mL of methanol
was added. The turbid liquid was heated until complete
clearing and let stay overnight at room temperature. The
mother liquid was carefully decanted, and the sediment
(bottom layer) was dried in vacuo, giving fraction I. The
procedure was repeated with the mother liquid six times more
by adding 10 mL of methanol, each time giving fractions II-

Macromolecules, Vol. 38, No. 7, 2005
Chiral Side Chain Polymethacrylate 2731
Table 1. Molar Mass Parameters for the P8*NN Fractions
av molar
mass, Mw
av deg of
dispersion ratio,
D ) Mw/Mn
polymer
(104 g/mol) polymerization, pw
fraction I
9.29
5.45
4.02
3.05
2.33
1.66
1.1
160
94
69
53
40
28
19
50
2.04
1.56
1.41
1.36
1.28
1.21
1.17
2.63
fraction II
fraction III
fraction IV
fraction V
fraction VI
fraction VII
raw polymer
2.9
VII, respectively. The nonfractioned raw polymer sample was
obtained by a separate polymerization of 0.3 g of monomer;
the sample was three times reprecipitated from toluene to
methanol and six times washed with boiling methanol.
Molar masses and dispersion ratios for the polymer fractions
are listed in Table 1.
3. Measurements. The molar mass of the polymer fractions
was estimated by size exclusion chromatography (SEC) in THF
solution using PMMA as standard.
DSC curves were taken using Perkin-Elmer DSC-2C equip-
ment calibrated with indium standard. The transition tem-
peratures were estimated on heating as DSC peak maximum
but on cooling as crossing of baseline with tangent of the
ascendent peak wing. The values estimated in this way have
been shown to correlate in a best way with the transition
temperatures observed by polarization microscopy (for the
birefringent phase state, Sm A).
Figure 2. Optical appearance of a P8*NN, fraction I film
cooled at different rates: (a) daylight, no polarizers; (b) crossed
polarizers.
X-ray diffraction profiles within the whole range (0.9° < 2Θ
< 29°) from 1 mm diameter capillary samples were recorded
on a STOE four-circle diffractometer with graphite monochro-
matized Cu KR radiation, λ ) 1.54 Å, but precise SAXS
measurements (0.6° < 2Θ < 10°) with Co KR radiation, λ )
1.7902 Å. Two-dimensional X-ray diffraction data have been
collected from an isolated fiber (18 µm diameter), using the
single-crystal diffractometer Xcalibur from Oxford Diffraction.
Mo KR radiation was monochromatized by a pyrolytic (002)
graphite crystal, and data were recorded by the sapphire CCD
detector for a sample-to-detector distance of 6 cm. 180 frames
were collected in æ-scan mode in steps of 1° with the rotation
axis parallel to the fiber and perpendicular to the incident
beam.
Figure 3. One-dimensional X-ray scattering profiles from
P8*NN fraction I at room temperature: 1, in the turbid phase
state (Sm A, cooled 0.3 K/min); 2, in the transparent phase
(probably TGB A*, cooled 10 K/min). Insert: small-angle
scattering range, on a logarithmic scale.
Polymer films and X-ray samples with predetermined
thermal history were prepared using the STC200/HS400
programmable heating stage (INSTEC).
III. Results and Discussion
1. Bistable Phase Behavior. It is well-known that
the phase transition behavior of crystallizable polymers
can be affected by thermal history. Thus, e.g., melting
temperature grows roughly linearly with the tempera-
ture of previous isothermal crystallization,22 as ex-
pressed by an evaluation procedure derived by Hoffman
and Weeks.23 The effect is of significant importance
especially for LC polymers (LCPs) which can form a
variety of mesophases between crystal or glass and
isotropic liquid melt. We have already reported some
cases when thermal pretreatment and particularly
cooling rate change phase behavior of an LCP not just
quantitatively (transition temperature) but also quali-
tatively (sequence of mesophases).15,24
All the P8*NN fractions I-VII show a prominent
difference in optical appearance if cooled from above the
transition point fast (10 K/min) or slowly (1 K/min).
When cooled fast, the polymer film at ambient temper-
ature is transparent and optically isotropic. Contrarily,
slow cooling results in films that are both birefringent
and turbid, as illustrated in Figure 2 for an about 20
µm thick film of fraction I with the highest molar mass.
A careful study of thermal behavior of the raw P8*NN
has shown the same bistable phase behavior as for its
fractions but at much lower critical cooling rates, r: the
polymer film can also form a “turbid” Sm A texture but
after cooling not faster than 0.3 K/min only.
Identification of the both mesophases and elucidation
of structural difference between those is of great im-
portance for the work. On the other hand, a detailed
discussion on that topic is far beyond the goals and the
scope of our paper, which is devoted mostly to the
kinetics of mesophase formation. For that reason, we
will discuss the obtained structural data shortly pre-
senting the basic results, and a detailed structural study
of the polymer will be published elsewhere.
One-dimensional X-ray scattering profiles from the
two mesophases are shown in Figure 3, and the data
on scattering reflections are summarized in Table 2. It
is worth noticing that the presented results correspond
to the same sample at the same temperature but after
different thermal pretreatment. Both mesophases show
a set of three SAXS peaks which more or less correspond
to three reflection orders from a single lattice.

2732 Kozlovsky et al.
Macromolecules, Vol. 38, No. 7, 2005
Table 2. Reflection Positions for P8*NN (Fraction I) in Two Different Phase States (25 °C)
small-angle reflections
wide-angle reflection
width of the WAXS reflection
mesophase
d1 ( 1.5 (Å)
d2 ( 1.0 (Å)
d3 ( 0.5 (Å)
D ( 0.01 (Å)
fwhmD ( 0.05 (deg)
SmA
TGBA*
61.8
64.8
30.3
33.0
19.6
20.2
4.47
4.32
4.54
4.82
The data indicate a minor but significant diference
in a smectic layer organization of the two phases. The
“turbid” mesophase of P8*NN is characterized by some-
what more ordered and more compact layer packing, as
evidenced by smaller d1 spacing value and by narrower
wide angle scattering halo (fwhmD values). The width
of the wide angle peak is nevertheless much higher than
would be characteristic for more ordered smectic phases,
such as Sm B.
in mesogenic groups. Also, enantiomeric copolymers
composed of the two optically isomeric monomers do
form the “transparent” phase up to a certain value of
enantiomeric excess only, while racemic copolymers
form the conventional Sm A phase instead.
The only structural model which can explain the
whole combination of the experimental data remains to
date an extra short pitch TGB (twist grain boundary)
phase, namely TGB A*.
Generally, microscopic observations and X-ray data
support the smectic A structure of the “turbid phase”.
The calculated length of the mesogenic group is about
37.3 Å (the corresponding molecular model is shown in
the Supporting Information, Figure S1). Therefore, a
bilayer packing of mesogens can be suggested with
overlapping of neighboring layers up to aromatic cores
(shown schematically in Supporting Information, Figure
S2). An alternative model of a bilayer Sm C* structure
with a tilt angle of about 30° is excluded by absence of
any ferroelectric properties in the substance.
The nature of the “transparent” mesophase is less
clear. It should possess a similar type of Sm A ordering
but be more defective. At the same time, the lack of
visually observed birefringence should be somehow
explained.
For conventional liquid crystals, the absence of bire-
fringence in a particular direction can be observed in
specially prepared oriented monodomain samples only
but not in bulk, nor in spheric drops at an arbitrary
direction, as for P8*NN. We should comment first that
such a visually isotropic mesophase with a hidden
smectic ordering was never observed by nonchiral
polymers of a similar structure, as e.g. LC poly-
(meth)acrylates with azobenzene photochromic side
chains.11,25-28 On the other hand, we have reported
similar mesophases for numerous chiral homopolymers
(polymethacrylates, polysiloxanes)29-32 and their co-
polymers with nonchiral azodye comonomers.24,33,34 The
detailed study of the “transparent smectic mesophase”
is presented in our recent paper;32 here we will sum-
marize them briefly.
It is well-known that a uniform helical twisting in a
smectic A phase composed of chiral molecules is forbid-
den by symmetry rules. To overcome the frustration,
small Sm A blocks in the TGB phase form a discontinu-
ous helical superstructure via a three-dimensional lat-
tice of screw disclinations penetrating the whole phase.36
A sketch of the TGB A phase is shown in the Supporting
Information (Figure S3). The TGB phases in low molar
mass liquid crystals appear in a short temperature
range above the Sm A phase, and they are birefringent
and can show selective reflection of visible light.37 In
contrast, the “transparent smectic” phase of chiral
polymers show a remarkable stability over temperature
and can be frozen in glass. In this connection we should
mention the early publications of Freidzon et al.38 on
cholesterol-containing poly(meth)acrylates which reveal
a helical twisting along with the selective light reflection
in the Sm A phase, also in a broad temperature range.
Stabilization of the TGB-like stucture by the polymer
main chain penetrating the screw defect system might
be the reason for such a thermal behavior. However,
we have reported earlier a TGB A* f Sm A transition
in chiral azo dye copolymers which can be observed at
low cooling rates only, r < 1 K/min.24
For the particular case of the “transparent smectic”
mesophase, an extra-short helical pitch of ∼250 nm or
less has been suggested, so that all structural elements
of the phase are smaller in dimensions than wavelength
of visible light. Hence, neither birefringence nor light
scattering at domain boarders can be observed visually
even for 15-30 µm thick films, as used for microscopic
observations.
(i) The smectic ordering in the mesophase is evidenced
by DSC data, X-ray measurements, and broad-line NMR
spectra.
The exact TGB A* structure for P8*NN fractions can
be hardly proven experimentally. It has been reported36
that any reliable and convincing information on the
TGB A* phase can be obtained only by high-resolution
X-ray scans from well-aligned samples. Generally,
orientation of LC polymers is a complicated experimen-
tal task, as compared with orientation of low molar mass
liquid crystals. For the particular case of P8*NN, the
orientation cannot be produced by extremely slow
cooling in a magnetic field, while another phase state
(Sm A) will be formed instead. We have tried to orient
a thin polymer fiber by drawing it from the isotropic
melt above the phase transition. Such a 18 nm thick
fiber shows a remarkable birefringence (Supporting
Information, Figure S4), but no splitting of the outer
X-ray reflection (Supporting Information, Figure S5),
probably to insufficient orientation.
(ii) For colorless chiral LC polymers, the presence of
a short-pitch helical superstructure is proven by UV
absorption and, more importantly, by UV reflection
spectra in thin films and also by circular dichroism (CD)
and by optical rotatory dichroism (ORD) spectra. The
helical pitch is estimated to be as short as 240-250 nm,
i.e., out of the visible wavelength range. For azo dye
copolymers, any measurements above are impossible
because of strong absorption of the photochromic moi-
eties.
(iii) AFM profiles of a free polymer surface also give
evidence of a two-dimensional periodic structure with
a ∼0.25 µm spacing. Worth noticing is that such a profile
has been measured for an azo dye chiral copolymer.35
(iv) Chirality is critical for the formation of such a
mesophase. Thus, the sign of optical rotation corre-
sponds to the absolute configuration of chiral centers
To summarize, the short pitch TGB A* structure for
the “transparent smectic” mesophase of P8*NN is not
proven conclusively yet remains the most probable one.

Macromolecules, Vol. 38, No. 7, 2005
Chiral Side Chain Polymethacrylate 2733
Figure 5. Phase transition temperatures on heating (Tm, 2),
and on cooling (Tc, 1,) and melting enthalpies, ∆Hm (9), for
the P8*NN fractions (open symbols) and raw polymer (closed
symbols), vs average molar mass, Mw.
Figure 4. DSC scans from P8*NN fractions, normalized to
sample weight: (a) second heating; (b) second cooling.
Figure 6. SEC profile from raw P8*N and its fractions II and
The X-ray data of Figure 3 and Table 2 also confirm
some “deteriorated Sm A” structure of the phase. For
that reason, we suggest the given structure for the
“transparent phase state” of P8*NN fractions.
V.
be hardly explained by a broader dispersion ratio only,
D ) 2.6 for the raw polymer vs D ) 2.04 for fraction I,
but rather by the presence of small amounts of the
monomer in the raw P8*NN, as indicated by original
GPC-SEC data shown in Figure 6. At the same time,
the transition enthalpy, ∆Hm, shows no influence of
molar mass value at all.
When cooling the sample at different rates, the DSC
peak shifts toward lower temperatures with increasing
rate, r, as illustrated by Figure 7 for fraction II. The
dependence of the peak maximum position on cooling
rate is however qualitatively the same for raw P8*NN
and all the fractions (some examples shown in Figure
8a). We should note here that estimation of the transi-
tion enthalpy from DSC curves for slow cooling is rather
complicated, since improper adjustment of the baseline
leads to high experimental errors. Nevertheless, rough
evaluation shows that the ∆Hm value is independent of
the cooling rate, as shown in Figure 9 for the particular
example of fraction IV.
2. Nonisothermal Mesophase Formation. DSC
curves from the P8*NN fractions are shown in Figure
4. The second heating/cooling scan at 10 K/min was
chosen to represent the thermal behavior since heating
above the transition point, Tm, erases any effect of
previous thermal treatment (all the subsequent heating/
cooling scans without any annealing show the same
curve). It can be clearly seen that the phase transition
for the raw polymer occurs in a broad temperature range
and about 15-20 K lower than for its fractions with
narrower molar mass distribution.
The transition temperatures for the polymer fractions
on heating, Tm, and on cooling, Tc, are plotted against
the average molar mass, Mw, in Figure 5 along with the
transition enthalpies, ∆Hm. For the sake of comparison,
also data for the raw polymer are shown. The data of
Figure 4 show that both Tm and Tc values become
independent of the molar mass starting from the aver-
age degree of polymerization, pw ∼ 30. Thus, fraction
VII can be considered rather as an oligomer but all other
fractions as true polymers. At the same time, the raw
polymer shows about 20 K lower transition temperature
on heating, as compared with fraction IV of similar
molar mass, Mw ∼ 3 × 104 g/mol. A less pronounced but
nevertheless remarkable difference of about 10 K is
observed also for the cooling scan. Such a difference can
As seen from Figure 4, the DSC peak for the raw
polymer is much broader than for the fractions. To
quantify that, we can define the transition interval as
difference between temperatures corresponding to con-
version rates of 10% and 90%, correspondingly
∆T10/90 ) Tê)10 - Tê)90

2734 Kozlovsky et al.
Macromolecules, Vol. 38, No. 7, 2005
Figure 9. Transition enthalpy on cooling, Tc for P8*NN
fraction IV, vs cooling rate.
Figure 7. DSC scans from P8*NN, fraction II, at different
cooling rates.
Figure 10. Development of the short pitch TGB A* me-
sophase in raw P8*NN (a) and its fraction V (b) vs temperature
on cooling at different coooling rates.
Figure 8. Transition temperature on cooling, Tc (a), and phase
transition interval, ∆T10/90 (b), for raw P8*NN and its fractions,
vs cooling rate.
the value appears to be the same for both fractions, II
and V (as e.g. 2.5 K for the standard cooling rate of 10
K/min) but an order of magnitude higher for the
nonfractioned polymer (15 K, correspondingly), as shown
in Figure 8b. This may have the same origin as the
strong deviation in the transition temperatures them-
selves, i.e., the presence of small amounts of the
monomer.
For the detailed kinetic studies, fractions II and V
were chosen along with the raw polymer. The phase
transformation rate, ê(t), is calculated by integration of
the DSC curves upon temperature, as shown in Figure
10 for the raw P8*NN sample and fraction V.
shows qualitatively similar behavior). There are how-
ever certain experimental problems in plotting the data
of Figure 9 in Ozawa coordinates, ln{-[1 - ln ê(T)]} -
ln(r/K min-1). First, the experimental error in ê values
grows drastically, as cooling rate decreases. Second, the
Ozawa value, ln{-[1 - ln ê(T)]}, is especially sensitive
to proper choice of the baseline position. For that reason,
only the middle part of the ê(T) curves in Figure 10 (0.05
< ê < 0.95) can be used for further calculations. Also,
the narrow temperature ranges of the transition, as
observed for polymer fractions (Figure 8b) do not overlap
enough (Figure 10b), to allow the Ozawa analysis in the
whole range of cooling rates, r, measured, in contrast
to the raw polymer.
The Ozawa plot for raw P8*NN is presented in Figure
11a and that for its fraction V in Figure 11b (fraction II

Macromolecules, Vol. 38, No. 7, 2005
Chiral Side Chain Polymethacrylate 2735
Figure 12. DSC curves on heating at 10 K/min from raw
P8*NN (a) and its fraction II (b) cooled previously at different
rates.
Figure 11. Ozawa plots for the kinetics of mesophase
formation in raw P8*NN (a) and its fraction II (b) at different
temperatures.
Qualitatively, the data of Figure 12 can be easily
explained by larger domain size for lower cooling rates,
similar to crystallization and subsequent melting of
crystallizable polymers.22 However, quantitatively the
effect of cooling rate seems to be more complicated.
When Tm values plotted against logarithm of the rate
of previous cooling, r, the data fall to a single straight
line for the raw P8*NN (Figure 13a) but not for narrow
fractions II and V (Figure 13b) where a kink is observed
at r ∼ 1 K/min. The latter value corresponds to the
critical cooling rate for the crossover from a TGB film
to a Sm A one, as observed in the thermooptical
experiment (Figure 2).
The linear correlation between Tmax and ln r can be
explained as follows. Hoffman and Weeks23 have shown
that that a linear relation holds between crystallization
temperature, Tc, and temperature of subsequent melt-
ing, Tm: Tm ) cTc. Ozawa16 assumes that ln Φ(T) ∼ T
and ln Φ(T) ∼ aT + b. Caze´ et al.39 have shown that
then Tc ∼ ln r and Tc ) n/a ln r. Combining this yields
Tm ∼ ln r and Tm ) cn/a ln r as indicated by Figure
13a. A kink in Figure 13b may then indicate a sudden
change in n, a change in c (which can be shown to
depend on interfacial energies and nuclei size), or a
change in a at that r. It will be shown below that n does
not change and that consequently growth and nucle-
ation dimensions remain unchanged. The parameters
c and a will however change with transition from the
TGB to Sm A mesophase formation.
Taking that in mind, we can conclude that the
polymer fractions behave in any case according to the
Ozawa theory (Figure 11b). In contrast, the kinetic data
for the raw polymer (Figure 11a) fall to straight lines
in Ozawa coordinates only at high temperatures and
high cooling rates; the lower the temperature, the higher
is cooling rate value, r, where deviation from the
straight line begins. The considerations above justify
however the neglection of the measuring points at lower
cooling rates as not representative, and the remaining
points allow again a satisfactory Ozawa analysis.
Before doing that, however, we should return to the
utmost example of the different phase growth at fast
and slow cooling of the polymer, namely the bistable
phase behavior (as discussed in the previous section).
Influence of the cooling rate on the phase condition of
P8*N can be observed also by DSC. Figure 12 presents
DSC scans from raw P8*NN (a) and its fraction II (b)
at standard heating rate of r ) 10 K/min but after the
sample having been cooled at different rates. As seen
from the figure, the transition point on subsequent
heating, Tm, shifts to higher temperatures as the cooling
rate decreases.
For the raw polymer, also a threshold at ∼25 °C can
be much better observed at the lowest rates of previous
cooling. Neither polarization microscopic observation
nor X-ray studies show any changes in the polymer film
at that temperature, however. For that reason, we
would suggest the threshold indicating rather partial
devitrification of the polymer than a Sm A-TGB A*
phase transition. The detailed structural studies are in
progress and will be published elsewhere.
Such a bifurcation in the phase behavior of P8*NN
could be explained by Figure 14. A metastable TGB A*
phase would be energetically less preferred than the

2736 Kozlovsky et al.
Macromolecules, Vol. 38, No. 7, 2005
Figure 15. Ozawa exponent values, nTGB (a), and cooling
function, ΦTGB(T) (b), for raw P8*N and fractions II and V, vs
temperature.
Figure 13. Transition temperature on heating, Tm, for the
raw P8*NN (a) and its fractions II and V (b) cooled previously
at different rates, vs the cooling rate.
Interpretation of these figures in terms of nucleation
and growth dimensions20 is however ambiguous since
Cheng and Wunderlich40 have shown that low values
of n may hint at nonlinear growth or at a nonnegligible
volume fraction of nuclei. In fact, since there is no
obvious reason for a change of nucleation and growth
dimensions with temperature (except possibly those
associated with the transition TGB A* f Sm A), the
temperature dependence of n and its small values most
probably indicate a temperature-dependent nonlinearity
of growth.
Usually, activation energy of the phase formation in
polymers is estimated using the Kissinger equation41
EA
r(Tmax) ) cTmax2 exp -
(3)
[
]
RTmax
Figure 14. Energy diagram for the bistable phase behavior
of P8*NN.
where R is universal gas constant, c is a preexponential
factor, and Tmax is the DSC peak maximum (as shown
in Figure 6a), corresponding to the highest phase
transformation rate. The activation energy here is
energy required to transport next mesogenic side chains
to the growing domain surface.
conventional Sm A* phase but requires a lower activa-
TGB
SmA
tion energy barrier to be overcome, EA
< EA
.
From our data, only the faster process, namely Iso f
TGB A*, can be evaluated and interpreted in terms of
Ozawa equation, eq 2. The corresponding Ozawa expo-
nent values, nTGB, and cooling functions, ΦTGB(T), for
raw P8*N and fractions II and V are shown in Figure
15. As seen from the Figures 11 and 15, the exponent
values for both polymer fractions are almost indepen-
dent of temperature, nTGB ∼ 2. In contrast, the slope of
However, the corresponding Kissinger plots (Figure
16) deviate from the straight lines for both raw P8*NN
and its fractions II and V, thus confirming that the
mesophase formation in P8*NN cannot be described
within a simple Kissinger model.
Note that the sign of the activation energy is negative
due to the positive slope of the graphs. In the available
literature, that sign problem has always not been
the straight lines changes monotoneously from nTGB
)
0.6 at 37 °C to nTGB ) 1.2 at 32 °C for the raw material.

Macromolecules, Vol. 38, No. 7, 2005
Chiral Side Chain Polymethacrylate 2737
for narrow polymer fractions but at much slower cooling,
r ) 0.3 K/min, for the raw polymer. A theoretical model
for the effect of “bistable phase behavior” has been
suggested as the metastable TGB A* phase being
energetically less preferred than the conventional Sm
A* phase but requiring a lower activation energy barrier
to be overcome, EATGB < EASmA. The model is supported
with structural SAXS study of the both mesophases for
same polymer sample at the same temperature but
obtained with different cooling rates.
The cooling rate, r, affects strongly the transition
point on subsequent heating, Tm. A linear dependence,
Tm ∼ ln r, has been observed and explained theoretically
for the raw polymer. In contrast, narrow polymer
fractions show a kink at r ∼ 1 K/min corresponding to
the crossover above.
Finally, the suggested theoretical model for the
“bistable phase behavior” is well confirmed by estima-
tion of the activation energy of mesophase nuclei
growth, EATGB and EASmA, as determined by a Kissinger
analysis.
Figure 16. Kissinger plots for estimation of activation energy
of the TGBA* phase formation.
considered, with a few exceptions.42,43 Again, this makes
the evaluation ambiguous. Assumed that the sign
problem is of negligible importance and the slope yields
TGB
the activation energy of TGBA* phase nucleation, EA
Acknowledgment. We are grateful to Dr. H. Pasch
and Mr. Ch. Brinkman (DKI, Darmstadt) for the GPC-
SEC measurements and to Mr. M. Roth (TU Darmstadt)
for his assistance in DSC measurements. The work was
supported by Deutsche Forschungsgemeinschaft (Projects
Re 923/8 and Ha 782/74).
TGB
in Figure 14, we could suggest that the EA
value is
not constant but depends on Tmax, i.e., by virtue of
Figure 8a, on the cooling rate. That means that rapid
cooling would yield a lower activation energy for the
creation of the TGBA* phase. This would be consistent
with the experimental finding and the sketch of Figure
14. By reducing the cooling rate, the activation energy
increases and finally approaches that for the transition
to the Sm A phase which then grows. This argumenta-
tion would support the experimental findings and the
diagram in Figure 14.
Finally, some speculations could be made about the
nucleation in the polymer (following the sketch in Figure
14). The first nucleation phase should be similar for both
Sm A and TGB A* phases, i.e., formation of small
smectic blocks, about 10 nm in size, i.e., 20-30 me-
sogenic groups side by side (Supporting Information,
Figure S3). When reaching that critical length, there
would be a bifurcation point: either the nondisturbed
Sm A domain grows further (but that requires a higher
activation energy to overcome noncentrosymmetric ster-
ic repulsion), or a kink appears, giving rise to the
growing screw disclination.
Supporting Information Available: Figures showing
molecular model of mesogenic side chain in P8*NN (S1),
suggested model for local Sm A packing of mesogenic side
chains in P8*NN (S2), sketch of the twist grain boundary
phase (S3), microphotograph of fiber drawn from P8*NN
fraction 1 (S4), and 2D WAXS pattern from the fiber (S5). This
material is available free of charge via the Internet at http://
pubs.acs.org.
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