Effect of alkyl chain length of alcohols on cholesteric uniaxial to cholesteric biaxial phase transitions in a potassium laurate/alcohol/potassium sulfate/water/brucine lyotropic mixture: Evidence of a first-order phase transition

Article abstract of DOI:10.1021/jp310981d

Lyotropic cholesteric liquid crystalline phases were prepared by doping the quaternary mixture of potassium laurate (KL)/potassium sulfate (K ₂SO₄)/alcohol (n-OH)/water with the chiral agent brucine. Different long-chain alcohols whose alkyl chains (n) vary from 8 (1-octanol) to 16 (1-hexadecanol) were used. The cholesteric uniaxial to cholesteric biaxial phase transitions were investigated by measuring the birefringences via polarizing optical microscopy, and the phase diagram was constructed as a function of the alkyl chain length of the alcohols. Alcohols with 9 a?? n a?? 12 presented the three cholesteric phases (cholesteric discotic - Ch _D, cholesteric biaxial - Ch_B, and cholesteric calamitic - Ch_C). The Ch_D-to-Ch_B transition was shown to be continuous, with a bare correlation length bigger than the typical micellar dimensions. Mixtures with n = 8 and n = 13 showed a first-order phase transition between the Ch_D and the Ch_C phases, without the presence of the Ch_B phase in between. These results are interpreted in terms of the nanosegregation of the alcohol molecules in the micelles with respect to the main amphiphiles molecules. ? 2012 American Chemical Society.

Full text of DOI:10.1021/jp310981d

Article
pubs.acs.org/JPCB
Effect of Alkyl Chain Length of Alcohols on Cholesteric Uniaxial to
Cholesteric Biaxial Phase Transitions in a Potassium Laurate/Alcohol/
Potassium Sulfate/Water/Brucine Lyotropic Mixture: Evidence of a
First-Order Phase Transition
Dennys Reis,† Erol Akpinar,‡ and Antonio Martins Figueiredo Neto*,†
̂
†Instituto de Física, Universidade de Sao Paulo, P.O. Box 66318, 05314-970, Sao Paulo, Sao Paulo, Brazil
̃
̃
̃
‡Department of Chemistry, Arts and Sciences Faculty, Abant Izzet Baysal University, P.O. Box 14280, Golkoy, Bolu, Turkey
ABSTRACT: Lyotropic cholesteric liquid crystalline phases
were prepared by doping the quaternary mixture of potassium
laurate (KL)/potassium sulfate (K2SO4)/alcohol (n−OH)/
water with the chiral agent brucine. Different long-chain
alcohols whose alkyl chains (n) vary from 8 (1-octanol) to 16
(1-hexadecanol) were used. The cholesteric uniaxial to
cholesteric biaxial phase transitions were investigated by measuring the birefringences via polarizing optical microscopy, and
the phase diagram was constructed as a function of the alkyl chain length of the alcohols. Alcohols with 9 ≤ n ≤ 12 presented the
three cholesteric phases (cholesteric discoticChD, cholesteric biaxialChB, and cholesteric calamiticChC). The ChD-to-ChB
transition was shown to be continuous, with a bare correlation length bigger than the typical micellar dimensions. Mixtures with n
= 8 and n = 13 showed a first-order phase transition between the ChD and the ChC phases, without the presence of the ChB phase
in between. These results are interpreted in terms of the nanosegregation of the alcohol molecules in the micelles with respect to
the main amphiphiles molecules.
concentration of the main amphiphile17 and on the shape
INTRODUCTION
■
anisotropy of the micelles.18 The bigger the concentration of
Lyotropic biaxial nematic phase (NB) is an intermediate phase
the chiral agent and/or the shape anisotropy of the micelles, the
between uniaxial discotic (ND) and uniaxial calamitic (NC)
smaller the cholesteric pitch.
nematic phases.1−3 The phase transitions between the uniaxial
Cholesteric-to-cholesteric phase transitions in the lyotropic
and biaxial phases are of second order, well-described within a
mixture of sodium decyl sulfate/decanol/water/brucine sulfate
mean-field approach.2
heptahydrate were discussed by Yu and Saupe.19 The phase
Cholesteric lyotropic phases (also named lyocholesterics)
diagrams of lyotropic mixtures with the three cholesteric phases
can be obtained by doping the lyotropic mixture, presenting the
nematic phase, with chiral agents.4−6 Similarly to the nematic
present some features that differ from those of mixtures with
phases, three types of cholesteric lyotropics were identified:6
the three nematic phases. Examples of phase diagrams, where
the three cholesteric phases are present, are given in refs 6, 20,
cholesteric biaxial (ChB), cholesteric discotic (ChD), and
and 21. In all these phase diagrams, the ChB phase domain is
cholesteric calamitic (ChC). The labels refer to the original
located in between the ChD and the ChC domains. To the best
nematic phase cholesterized by the addition of the chiral agent.
of our knowledge, a direct transition between the ChD and the
These phases can be produced by three ways: (i) addition of
chiral dopant molecule such as brucine sulfate to the achiral
nematic phase composed of amphiphilic molecules, e.g.,
potassium laurate (KL) and other additives (salt, water, and/
ChC was not experimentally reported.
Experimentally, the ChD−ChB phase transition was shown to
be continuous,22 differently from the ND−NB transition, with
correlation length ξ ≈ 12 nm, which coincides with the typical
or cosurfactant like another amphiphilic molecule or 1-
alcohol),7−11 (ii) directly using L- or D-enantiomer of a racemic
dimensions of the micelles in lyocholesterics. This modification
on the behavior of the phase transition was attributed to the
(DL-form) amphiphilic molecule, for example, L-alaninehydro-
chloride dodecylester,12−14 and (iii) using chiral solvents.15 The
first two ways are widely used to produce lyotropic cholesteric
phases by several research groups, and the last one is not so
common.
The structure of lyocholesterics was shown to be formed by
micelles organized in a helical arrangement keeping, locally, the
pseudolamellar ordering observed in lyotropic nematics.16 The
pitch of the cholesteric structure (P) depends on the relative
molar concentration of the chiral agent (cm), with respect to the
chiral elastic field present in cholesteric phases.
From the theoretical point of view, Brand and Pleiner23
invoked symmetry reasons to conclude that the ChD/C−ChB
transitions should be of first order or continuous, discarding the
second-order phase transition. However, there is not in the
Received: November 6, 2012
Revised: December 14, 2012
Published: December 27, 2012
© 2012 American Chemical Society
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Table 1. Molar Fractions (X) of Each Component in the Lyotropic Cholesteric Mixtures
a
b
mixture
alcohol
XKL
XK SO
Xalcohol
XH O
Xbrucine
cholesteric phase
ΔTB (°C)
2
4
2
n8
OcOH
0.0382
0.0382
0.0382
0.0382
0.0382
0.0382
0.0382
0.0382
0.0382
0.0060
0.0060
0.0060
0.0060
0.0060
0.0060
0.0060
0.0060
0.0060
0.0114
0.0114
0.0114
0.0114
0.0114
0.0114
0.0114
0.0114
0.0114
0.9434
0.9434
0.9434
0.9433
0.9433
0.9434
0.9433
0.9433
0.9434
0.0010
0.0010
0.0010
0.0010
0.0010
0.0010
0.0010
0.0010
0.0010
ChC, ChD
ChB, ChD
ChC, ChB, ChD
ChC, ChB, ChD
ChC, ChB, ChD
ChC, ChD
ChC
n9
NonOH
DeOH
>9.4
5.2
n10
n11
n12
n13
n14
n15
n16
UnDeOH
DDeOH
TDeOH
TeDeOH
PDeOH
HDeOH
3.7
2.5
ChC
ChC
a
b
The lowest working temperature was 5.0 °C. ΔTB corresponds to the cholesteric biaxial temperature range.
literature an experimental report of a first-order phase transition
between cholesteric phases. As pointed out before, lyotropic
cholesterics have two degrees of freedom which may be worked
out to explore the behavior of the phase transition: the intensity
of the chiral elastic field, controlled by the amount of chiral
agent present in the mixture, and the shape anisotropy of the
micelles which will be organized in the helical structure,
controlled by the types of the surfactant and cosurfactant in the
mixture. Usually, experimentalists employ the first approach,
keeping the same basic mixture and increasing the amount of
chiral dopant, giving rise to the phase diagrams already referred.
Less frequent is the investigation of the effect of the micellar
shape anisotropy in the phase transition behavior, keeping
constant the amount of chiral dopant and changing the type
and relative concentration of surfactant and cosurfactant.
Recently, we discussed the effect of different cosurfactants in
the uniaxial-to-biaxial phase transition in lyotropic mixtures
presenting the NB phase.24,25 Some of these mixtures presented
high values of the optical birefringence that could indicate the
existence of more anisometric micelles and/or a nano-
segregation of the cosurfactant in the micelles. These effects
could be explored to investigate the nature of lyocholesteric
mixtures obtained by adding chiral dopants to those lyotropic
mixtures presenting the uniaxial and biaxial nematic phases.
In this study, we investigated the effect of the alkyl chain
length of the long-chain 1-alcohols (n−OH) on the phase
diagram and phase transitions of lyocholesterics mixtures. For
this purpose, we used the quaternary lyotropic mixtures of
potassium laurate (KL)/K2SO4/n−OH/H2O,24,25 which
present the three nematic phases, and introduced brucine as
the chiral agent. Different cholesteric mixtures were prepared
with the cosurfactant varying from 1-octanol to 1-hexadecanol,
keeping all the components concentrations (in mole fractions)
constant. Polarizing optical microscopy and measurements of
the optical birefringences were used to identify the mesophases
and study the phase transitions.22
ferrofluid (less than 1 μL in about 2.5 mL of the mixture) was
used to improve the alignment of the mixture subjected to an
external magnetic field of about 0.9 kG. We have checked that,
at this small concentration, no detectable changes in the
transition temperatures and birefringences were observed,
within our accuracy. With the ferrofluid doping, the time
necessary to obtain a well-oriented sample decreases from days
to hours.
The details of the preparation of the lyotropic quaternary
mixtures of KL/K2SO4/alcohol/H2O, which presented the
nematic phases, were discussed elsewhere.24,25 The alcohols in
the mixtures were changed from octanol (OcOH) to
hexadecanol (HDeOH), keeping the mole fractions of all
constituents constant (Table 1).
For texture investigation, pitch, and birefringences measure-
ments, lyotropic samples were encapsulated in 0.2 mm thick
microslides. A Leitz Ortoplan-Pol microscope (with mono-
chromatic light, λ = 546 nm) and a temperature-controlled
device for the sample were employed in the experiments. To
prevent water loss, both ends of the microslides were closed
with special glue on which UV-light was applied to polymerize
it. Microslides were put into a heating stage (Instec) to identify
the phases and determine the transition temperatures. The
stage was thermally insulated in such a way that the
temperature was controlled with an accuracy of 0.01 °C.
The birefringences of the ChD and ChB phases were
measured following a procedure similar to the one described
in ref 22. Shortly, the microslide filled with the sample was put
⃗
in the heating stage and a magnetic field (|B| = 0.9 kG) was
applied to the sample, in the plane of the microscope stage. The
laboratory frame of reference is defined as follows: the x-axis is
parallel to the magnetic field direction; the z-axis is parallel to
the light beam; the y-axis is the third orthogonal axis of the
frame. The ChD and ChB orient with the helical axis parallel to
⃗
B. The well-aligned cholesteric fingerprint texture with stripes
(ChD) was obtained after keeping the samples in the magnetic
field for about 6 h. Starting from the ChD phase, the
temperature was changed step by step until the next phase
(ChB or ChC). At each stabilized temperature, pictures were
taken with a digital CCD camera keeping constant the light
intensity of the microscope illuminator as well as all the
parameters of the camera (zoom, focal length, f-number, and
shutter speed). The light intensity was measured from the
intensities of the pixels in different positions along the stripes of
the fingerprint texture in the ChB or ChD phases using the
software ImageJ from NIH Image. It is important to notice that
the ChC has the helical structure unwound in the presence of
the magnetic field.
EXPERIMENTAL SECTION
■
Potassium laurate was synthesized in our laboratory by
neutralization of lauric acid (Merck) with potassium hydroxide
(Merck). Following the neutralization, it was recrystallized
several times from absolute ethanol. Long-chain alcohols, 1-
octanol (OcOH), 1-nonanol (NonOH), 1-decanol (DeOH), 1-
undecanol (UndeOH), 1-dodecanol (DDeOH), 1-tridecanol
(TDeOH), 1-tetradecanol (TeDeOH), 1-pentadecanol
(PDeOH), and 1-hexadecanol (HDeOH), and brucine were
commercially available from Merck and Sigma with purity
>99%. The salt K2SO4 and water-based ferrofluid were obtained
from Fischer and Ferrotec, respectively. A small amount of
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RESULTS AND DISCUSSION
■
Phase Diagram. The textures were identified under
polarizing optical microscope. Samples in the ChD phase
were kept in the magnetic field until well-aligned cholesteric
stripes were observed, i.e., stripes mostly perfectly aligned
parallel to each other and perpendicular to the magnetic field.
In all the mixtures investigated, when the three cholesteric
phases are present, the ChD phase domain is located at higher
temperatures with respect to the ChB and ChC phase domains.
Then, the cholesteric uniaxial to cholesteric biaxial phase
transition temperatures were determined precisely by carefully
changing the temperature of the samples. As a working
example, let us analyze the case of a mixture that presented the
three cholesteric phases. In the ChD phase, dark regions were
observed between the bright cholesteric stripes, Figure 1a.
Figure 2. Phase diagram of KL/K2SO4/alcohol/H2O/brucine
mixtures, which was constructed by plotting the phase transition
temperatures vs the alkyl chain length of the alcohols. The labels 2P,
MP, I, and C correspond to two-phase (one of them is isotropic) and
multiphase (one of them is isotropic) regions, isotropic, and crystalline
phase, respectively. Solid and dashed lines are only guides for the eyes.
Figure 1. Textures from the mixture n9. (a) ChD phase, T = 20.00 °C;
(b) ChB phase, T = 12.50 °C. The labels P and A refer to the polarizer
and analyzer, respectively. The magnetic field is oriented along the x-
axis at 45° from the polarizer.
These regions correspond to the director oriented parallel to
the light propagation direction, perpendicular to the plane of
the analyzer and polarizer of the microscope. They correspond
to the cholesteric planes homeotropically oriented. Decreasing
the temperature, near the vicinity of the ChD-to-ChB transition,
light starts to be transmitted by the sample at these previously
black regions (Figure 1b). This means that, at the ChB phase,
the two optical axes that spin around the helical axis are not in a
homeotropic orientation. Details about the determination of
this transition temperature will be given in the following.
Further decreasing the temperature sample transits to the ChC
phase, and as the magnetic field is present, the helical axis is
unwound and a planar texture (with the director oriented
parallel to the magnetic field) is observed. Pleiner and Brand
predicted the existence of defects with singular cores in the ChB
phase.26
Figure 3. Textures from the mixture n13. (a) ChD phase, T = 46.70 °C;
(b) coexistence between ChD and ChC phases, T = 45.35 °C; (c)
coexistence between ChD and ChC phases, T = 43.50 °C. The labels P
and A refer to the polarizer and analyzer. The magnetic field is
oriented along the x-axis.
After all phase transition temperatures were obtained, they
were used to construct the surface of the phase diagram shown
in Figure 2, as a function of the alkyl chain length of the
alcohol. Two important results can be seen in Figure 2, as the
alkyl chain length of the alcohols increases: (i) the cholesteric
uniaxial to cholesteric biaxial phase transition is shifted to the
higher temperatures; (ii) the cholesteric biaxial domain got
smaller. These results are similar to our previous observations
with the mixtures of KL/K2SO4/alcohol/H2O, presenting the
three nematic phases, with different long-chain alcohols.25
A remarkable aspect of this phase diagram is the direct ChD-
to-ChC phase transition without passing through the ChB phase,
observed in mixtures with n8 (the shortest) and n13 (the
longest) alcohols. Figure 3 shows the textures of the mixture
with n13, observed under the microscope in three different
temperatures. Figure 3a corresponds to the ChD phase with the
homeotropic black stripes. Decreasing the temperature,
coexistence between the ChD and the ChC is observed. Figure
3b shows the original ChD texture, now with droplets of the
ChC being formed on it. Decreasing more the temperature, still
in the coexistence phase domain, some homeotropic regions
(from the ChD) are present, together with planar regions (from
the unwound ChC)Figure 3c. Decreasing more the temper-
ature the entire sample transits to the ChC phase, showing a
homogeneous planar texture. As pointed out in the
Introduction section, this direct transition was not exper-
imentally reported before, although theoretically predicted.23
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These aspects will be discussed in the following. Mixtures
whose composition had alcohol with more than 13 carbons in
the chain provided only ChC phase.
Table 2. Birefringence (Δn), Pitch (P), Ratios between
Landau Coefficients, and Bare Correlation Length (ξ0) of the
Cholesteric Mixtures
Scalar Order Parameter and the Landau Coefficients.
The free-energy density (F) of the cholesteric phase, in the
vicinity of the uniaxial-to-biaxial transition, may be written
as21,22
103
109 c/a0
mixture (Δn 0.2)
P
2.0 (μm) b/a0 (K)
(cm2 K)
ξ0 (nm)
n8
1.3
3.4
3.2
3.6
3.4
2.0
84.2
n9
62.2
67.3
8.1 0.7
2.9 0.2
3.6 0.3
5.1 0.4
1.2 0.2
1.2 0.3
0.7 0.5
2.7 1.2
20
20
15
30
2
3
5
6
n10
n11
n12
n13
1
2
1
4
F = a(T)ς2 + bς4 − cq2ς
65.6
(1)
93.1
where ς is the scalar order parameter of the biaxial phase, q =
2π/P, a(T) = a0(T − Tc), a0, b, c are the Landau coefficients,
and Tc is the cholesteric uniaxial-to-biaxial transition temper-
ature. Minimization of eq 1 with respect to ς gives an
expression that relates the scalar biaxial order parameter with T
and q: cq2 = a0(T − Tc)ς + bς3. The asymptotic behaviors of ς2
as a function of T are ς = 0 in the ChD phase and ς2 = −(a0/
b)(T − Tc) in the ChB phase. From the experimental point of
view, the scalar order parameter may be obtained by measuring
the optical birefringences of the sample. We define the optical
birefringences as Δn = n3 − n2 and δn = n2 − n1, where the
labels 1, 2, and 3 refer to a frame which spins along the helical
structure, with the 1-axis parallel to the x-axis. In the
homeotropic regions of the oriented ChD texture, the 3-axis
(representing the director direction) is parallel to the z-axis of
the laboratory frame. In this condition δn = 0 and Δn ≠ 0.
When the sample transits to the ChB phase, both birefringences
are different from zero. In a first-order approach, the biaxial
scalar order parameter may be written as ς ∼ δn/Δn.22 To
measure Δn we took pictures of a well-oriented sample in the
ChD phase close to the ChD−ChB phase transition temperature,
plotted the light intensity (I) along the x-axis, and compared
with the equation22
186.2
temperature, around the ChD−ChB transition temperature, for
each sample, and the values were substituted into the
equation22
I = I0 sin2[(πD/λ)δn]
(3)
Figure 5 shows the plots of ς2 as a function of the temperature
for all the samples investigated and the fits of the equation
I = I0 sin2[(πD/λ)Δn sin2(qx)]
(2)
where I0 is the maximum intensity of the stripes, D is the
sample thickness, and the homeotropic regions were set as the
background of the pattern. Figure 4 shows a typical result of I
as a function of x in the ChD phase. The values Δn of each
sample are given in Table 2.
Figure 5. Squared biaxial order parameter as a function of the
temperature for the different mixtures with the different alcohols. Solid
lines are fits of the equation obtained by the minimization of the free-
energy density F with respect to ς, taking into account the asymptotic
behaviors, to the experimental data.
To obtain we measured the light intensity in the
homeotropic regions of the pattern as a function of the
obtained by the minimization of the free-energy density F with
respect to ς, taking into account the asymptotic behaviors. The
parameters obtained from these fits are presented in Table 2.
Assuming that the Landau coefficient c has the same order of
magnitude of the typical Frank elastic constant (K) of the
cholesteric phase,22 we can write the bare correlation length of
the biaxial order parameter as ξ0 ∼ [c/(|a0|Tc)]1/2. The values of
ξ0 for the mixtures are given in Table 2.
Samples n9, n10, n11, and n12 presented an interesting behavior
of ς2 as a function of the temperature in the vicinity of Tc,
where a rounding off connects the two asymptotic behaviors.
This characteristic is due to the presence of the elastic chiral
field that imposes a chirality-induced biaxiality in the ChD
phase. The rounding off is more pronounced in samples n9 and
n12.
The ratio c/a0 informs about the chirality-induced biaxiality
in the ChD phase and, in our experiment, has the order of
magnitude of ∼10−9 cm2 K. This order of magnitude agrees
with the estimations of K/a0 ∼ 3 × 10−9 cm2 K from data
available in the literature for the magnetically induced biaxiality
in the uniaxial discotic nematic to biaxial nematic phase
Figure 4. Normalized light intensity measured as a function of the
distance x from a homeotropic stripe, along the magnetic field
direction. Sample n11 in the ChD phase, T = 31.00 °C. The solid line is
the plot of eq 3.
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transition.27,28 Comparing this ratio with other cholesteric
mixtures, our values are about 1 order of magnitude bigger than
that obtained with the mixtures of KL/DeOH/H2O, with the
chiral agents brucine sulfate heptahydrate (BSH), 1-N-lauroyl
potassium alaninate, and d-octanol,22 and 2 orders of
magnitude smaller than that obtained with the mixture of
KL/decylammonium chloride/water/BSH.21 The bare correla-
tion length (ξ0) calculated in our experiment also agrees with
that evaluated by light-scattering measurements in lyotropic
nematics,29 being larger than the typical micellar dimensions
(of the order of 10 nm). This result suggests that the structural
changes responsible for the transition occurs in a length scale
bigger than the micellar dimensions, supporting the intrinsically
biaxial micelle (IBM) model.30,31 The IBM assumes that in
lyotropic mixtures with a surfactant and a cosurfactant,
presenting the uniaxial and biaxial phases, micelles are
intrinsically biaxial (orthorhombic symmetry) and orientational
fluctuations are responsible for the phase transitions. In the case
of the cholesteric phases, obtained by the doping of originally
nematic phases with chiral molecules, no drastic modifications
of the micelles are expected. The elastic chiral field arranges the
correlation volumes in a helical structure in length scales of the
order of 102 μm. This elastic field, however, changes the
character of the transition, from the second order, in the case of
the nematics, to continuous in the case of some of the
cholesterics investigated in the present work. The other
theoretically predicted possibility, the first-order transition,
was observed in mixtures n8 and n13.
Role of the Alcohol Chain Length. In order to
understand the role of the alkyl chain length of the alcohol in
the cholesteric phases and phase transitions, we have to
consider how alcohol molecules are located in the micelles. The
neutron contrast studies with the mixture KL/DeOH/H2O
indicated that the DeOH molecules are preferentially located in
the flattest surface of the micelle, rather than in their rims.32
This result tells us that the surfactant and alcohol molecules are
not homogeneously distributed in the micelle, implying a
molecular segregation. However, this segregation may be more
or less pronounced, depending on the alcohol (or cosurfactant)
chain length. This aspect was already discussed in the case of
lyotropic mixtures with the three nematic phases, with different
alcohols.25 Let us summarize the main conclusions of this study
where the main surfactant was the KL (nKL = 11 carbons in the
chain33) and different alcohols, with number of carbons in the
alkyl chain (n) varying from 8 to 16, were used to prepare the
lyotropic mixtures. According to the IBM model, the
orthorhombic local symmetry of the micelles is the same in
the three nematic phases, and orientational fluctuations of them
lead to the macroscopic nature of the two uniaxial and the
biaxial nematic phase. These orientational fluctuations depend
on the shape anisotropy of the micelles, which change as a
function of the temperature, relative concentration of the
different compounds of the mixture, and the relation between
the chain length of the main amphiphile and that of the alcohol.
The chain length of the main amphiphile defines the micellar
double layer and the pseudolamellar ordering observed in
lyonematics (and on lyocholesterics). Just to help the
understanding, let us assume that the micelle may be (instantly)
sketched as a parallelepiped of dimensions A′, B′, C′, with A′ >
B′ > C′, where the dimensions A′, B′ form the largest micellar
flat surface, and C′ represents the bilayer. Our results lead to
the conclusion that alcohol molecules segregate in different
ways, depending on the value of n with respect to nKL. For n >
n
KL alcohol molecules accumulate more in the flattest surface of
the micelles (favoring the discotic nematic phaseA′, B′
plane), whereas for n > nKL alcohol molecules accumulate
preferentially in the curved surfaces of the micelle (favoring the
calamitic nematic phase). The same behavior is observed in our
present experimental phase diagram with the cholesteric phases
(Figure 2). Taking into account only the mixtures that present
the three cholesteric phases, increasing the alcohol chain length
leads to an increase of the ChC phase domain and a decrease of
the ChB and ChD domains (Figure 6). This result suggests that
Figure 6. Temperature ranges of the (a) ChD, (b) ChB, and (c) ChC
phases as a function of the number of carbons on the alcohol alkyl
chain.
long-chain alcohols (n > nKL) tend to pack preferentially in the
rims, probably due to steric reasons since it is easy to
accommodate longer molecules on this part of micelles,
increasing the shape anisotropy of the micelles in the sense
that they become more elongated (for instance, increasing
more A′ with respect to B′). This shape anisotropy favors the
orientational fluctuations which gives rise to the NC and,
consequently, the ChC phase (Figure 2). On the other hand,
small-chain alcohols may be more easily incorporated in the
flattest surface of micelles, favoring the cholesteric discotic
phase (Figure 2).
In the case of the cholesteric phases, it can be expected that,
depending on the nature of the chiral dopant, they can be
placed in the micelle differently. For instance, a small chiral
dopant, like L-mandelic acid, may be located between the head
groups of the surfactant molecules existing on the large micelle
surfaces and/or in the rims of the micelles. However, relatively
large chiral dopants, like brucine, should be located differently.
The brucine molecule has two different parts: one (part 1)
consists of the planar benzene ring to which two ether groups
(−OCH3) are bound; the other (part 2) is a little bit complex
part which is not as planar as part 1 (Figure 7).
Figure 7. Molecular structure of brucine.
If we consider it in 3D in space, part 2 is bulkier than part 1.
When this chiral dopant is added to our quaternary mixtures of
KL/K2SO4/alcohol/H2O, the nonpolar part of the brucine is
expected to pack inside the micelle, in the KL double layer.
This packing leads to an increase of this typical micellar
dimension (C′), which, according to the IBM model, favors the
orientational fluctuations that give rise to the ChC phase. In the
present experiment, as the molar fraction of brucine is the same
in all the mixtures investigated, we may consider that the
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amplitude of the chiral elastic field remains the same for all the
samples investigated. What changes with the different alcohols
used is the elastic medium that will be cholesterized by the
dopant. The value of the pitch of the cholesteric structure may
be seen as a measurement of the efficiency of the elastic chiral
field to establish the helical arrangement. The smaller the pitch,
more efficient is the elastic chiral field. It was previously shown
that 1/P is proportional to the concentration of the chiral agent
and to the micellar shape anisotropy.17,18
Our results indicate that as the number of carbon atoms in
the alcohol chain differs more with respect to that of the main
amphiphile (nKL = 11), the bigger the pitch. In the IBM
framework, this indicates less anisometric micelles and,
consequently, for the same chiral agent concentration, a higher
value of the pitch (Figure 8).
of the alkyl chain length of the alcohol, keeping constant the
mole fraction of all the mixture constituents. The mixtures with
the number of carbon atoms n = 9, 10, 11, and 12, i.e., with 9 <
nKL < 12, where nKL is the number of carbons of the KL,
presented the three cholesteric phases. As the alkyl chain length
of the alcohols increases the cholesteric uniaxial to cholesteric
biaxial phase transitions is shifted to the higher temperatures,
and the cholesteric biaxial domain got smaller. Measurements
of the biaxial order parameter in the vicinity of the transition
ChD-to-ChB revealed that this transition is continuous. The
chiral elastic field imposes a chirality-induced biaxiality in the
ChD phase. The order of magnitude of this chirality-induced
biaxiality in the ChD phase agrees with the estimations for the
magnetically induced biaxiality in the uniaxial discotic nematic
to biaxial nematic phase transition. The bare correlation length
calculated agrees with that evaluated by light-scattering
measurements in lyotropic nematics, being larger than the
typical micellar dimensions. This result suggests that the
structural changes responsible for the transitions occur in a
length scale bigger than the micellar dimensions, supporting the
IBM model. Mixtures with alcohols of n = 8 and n = 13 carbon
atoms presented a first-order phase transition between the ChD-
to-ChC. This result was interpreted as a consequence of the
nanosegregation of the alcohol molecules in the micelles with
respect to the main amphiphile molecules (KL).
AUTHOR INFORMATION
Corresponding Author
*E-mail: afigueiredo@if.usp.br.
■
Notes
The authors declare no competing financial interest.
Figure 8. Pitch of the ChD phase as a function of the number of
carbons in the alcohol alkyl chain. The molar fraction of brucine is
kept constant. The dashed line is only a guide for the eyes.
ACKNOWLEDGMENTS
■
We thank the Scientific and Technological Research Council of
̈
Turkey (TUBITAK), the National Institute of Science and
As pointed out before, the existence of a first-order transition
between the ChD and ChC phases is remarkable. The
temperature ranges of the phase coexistence domains are
about 5 and 3 °C for mixtures n8 and n13, respectively. The
existence of the ChB phase between the two uniaxial phases
seems to be strongly dependent on the shape anisotropy of the
micelles. In the case of the mixture n13, due to that the length of
the alcohol molecule is bigger than that of the KL, it seems
reasonable to assume that the alcohol molecules preferentially
accumulate in the micellar rims. This segregation should
increase one of the micellar dimensions, for instance, A′.
Changes in the temperature may modify the nanosegregation of
the alcohol molecules in the rims. Increasing the temperature
may promote a more homogeneous distribution of the alcohol
in the rims, implying in a more symmetric micelle (A′ ≈ B′).
This new geometry favors the orientational fluctuations
characteristics of the discotic phase. The micellar shape
anisotropy that allows the existence of the biaxial phase is not
achieved. A similar process may occur in the case of mixtures
with n8, now with the alcohol molecules accumulating
preferentially in the flattest surface of the micelles. This picture
certainly must be investigated in more details by using
complementary techniques as, e.g., NMR and contrast neutron
scattering experiments.
Technology on Complex Fluids (INCT-FCx), CNPq, and
FAPESP from Brazil for supporting this study.
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