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Soft MatterView Article OnlineView Journal

This article can be cited before page numbers have been issued, to do this please use: A. Gradišek, T. Apih, V. Domenici, V.Novotna and P. Sebastiao, Soft Matter, 2013, DOI: 10.1039/C3SM51625C.

Molecular Dynamics in a Blue Phase Liquid Crystal: A 1H Fast Field-Cycling NMR Relaxometry Study†

Anton Gradisek,a‡ Tomaz Apih,ab Valentina Domenici,c, Vladimira Novotna,d and Pedro Jose Se-bastiaoe

Received Xth XXXXXXXXXX 20XX, Accepted Xth XXXXXXXXX 20XXFirst published on the web Xth XXXXXXXXXX 200XDOI: 10.1039/b000000x

Liquid crystals exhibiting Blue Phases (BP) have been in focus of academic and commercial research interest in the last years due

to their highly interesting properties in the fields of optics and photonics. In order to better understand the properties of the BP, it

is important to study molecular dynamics in these phases, including molecular rotations/reorientations, diffusion, and collective

motions. Here, we present the first study of molecular dynamics in a BP system by means of 1H fast field-cycling relaxometry.

The investigated sample was a lactate derivative, containing two chiral centers, called 10BBL, exhibiting BP, TGBA*, TGBC*,

and SmC* phases stable in rather large temperature ranges. Molecular dynamics was investigated by means of analyzing the

temperature- and frequency-dependencies of spin-lattice relaxation. We compare the dynamics in the TGB phases with the one

in the BP and with the TGB phases investigated in previous works.

1 Introduction

The interest in Blue Phase Liquid Crystals (BPLCs) is re-

flected in an increasing number of publications in the re-

cent years, focusing first on prototypes in the fields of optics,

photonics and lasing applications based on BPLCs1–4. Blue

Phases (BP) are a group of mesophases occurring by decreas-

ing the temperature from the isotropic to helicoidal phases,

such as cholesteric (or chiral nematic) and twist grain bound-

ary (TGB) phases, in highly chiral liquid crystals5–8. So far,

three types of BP have been discovered and characterized by

complementary techniques, in thermotropic liquid crystals,

namely BP I, BP II and BP III. All of them are optically

isotropic and the determination of their structure has proven

to be a challenging task, due to the presence of an isotropic

3D distribution of LC molecules. One of the first properties

encountered by Reinitzer in 1888, who first observed Blue

Phases, is the optical reflectance of blue-violet light9. Later

† Electronic Supplementary Information (ESI) available. See DOI:

10.1039/b000000x/a Jozef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia.b EN-FIST Centre of Excellence, Dunajska 156, SI-1000 Ljubljana, Slovenia.c Dipartimento di Chimica e Chimica Industriale, via Risorgimento 35, 56126Pisa, Italy.d Institute of Physics, Academy of Sciences of the Czech Republic, Na Slo-vance 2, 182 21 Prague, Czech Republic.e Department of Physics, Instituto Superior Tecnico, University of Lisbon,Av. Rovisco Pais, 1049-001 Lisbon, Portugal; Centro de Fısica da MateriaCondensada, Av. Prof. Gama Pinto 2, 1649-003 Lisbon, Portugal; E-mail:pedro.jose.sebastiao@ist.utl.pt.‡ Present address: Korea Basic Science Institute, 169-148 Gwahak-ro,

Yuseong-gu, Daejeon 305-806, Korea.

on, it has been realized that these reflected blue colors are re-

lated to the helical pitch typical of Blue phases, which is usu-

ally in the range of the wavelength of visible light10. Depend-

ing on the order of appearance by increasing the temperature,

the blue phases were called BP I, BP II and BP III. BP I and

BP II have a cubic symmetry, whereas BP III has the same

symmetry as the isotropic phase. In particular, BP I is body-

centered cubic and BP II is simple cubic8. As demonstrated by

Stegemeyer et al. 11, the cubic lattices of the BP I and BP II are

actually lattices of ”line defects”, arising from the energy min-

imization of these highly chiral systems. An accepted picture

of BP I and BP II structures recurs to the concept of a 3D dis-

tribution of ”double-twist tubes”, made of molecules arranged

in doubled helices (see for instance the structure of the BP II

in Figure 1).12–14 The BP III structure is more amorphous than

that of BP I and BP II, by not exhibiting a long-range transla-

tional order, and there are evidences that it can be described as

an amorphous network of disclination lines15.

The Blue Phases are found in compounds that present, at

lower temperatures, other chiral phases such as the cholesteric

(N*) and the twist grain boundary (TGB) (”frustrated”)

phases’6. These last mesophases are characterized not only

by helical arrangement of molecules, but also by the posi-

tional ordering, typical of smectic phases. Of particular in-

terest are the phenomena occurring at the Blue Phase – TGB

phase transition, which is less common than the Blue Phase

– N* phase transition16,17. In the recent years, many efforts

have been dedicated to synthesize new liquid crystalline sys-

tems18 having blue phases stable in a wider temperature range

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Fig. 1 (Color online) Schematic picture of the cubic lattice of the

BP II phase and double twisted arrangement of LC molecules.

than usually found for other compounds where blue phases

are observed over just a few degrees6,7. The desire to stabilize

the BP phases has also led to synthesis of polymer stabilized

blue phases19 and other more exotic LC systems, which are

very promising for technological applications18,20. In this re-

spect, the understanding of the molecular origin of the optical,

electro-optical and other physical properties is important in or-

der to better design new BPLCs. The electro-optical response

of BP, for instance, is related to the molecular mobility and

to the typical motions responsible of the relaxation,21–23 as

recently observed from dielectric studies21. 1H NMR relax-

ometry is a perfect experimental tool to investigate dynamic

processes and their typical frequency ranges24–27. A proper

analysis of both temperature dependence of longitudinal re-

laxation times (T1) and their frequency dispersions, in terms of

different molecular and collective motions demonstrated to be

highly informative for several liquid crystalline systems.28–33

In this paper, we report a detailed proton NMR relaxation

study on a liquid crystal containing two biphenyls connected

by an ester group and a chiral chain with two chiral centres,

with the four-phenyl-ring molecular core laterally substituted

by chlorine atoms and a lactic acid unit in the chiral molecular

chain. This compound, named 10BBL for short, belongs to

a series of new systems33, which exhibit twist grain boundary

(TGB) phases, such as TGBA* and TGBC*, in a wide temper-

ature range, followed by the chiral ferroelectric smectic phase

(SmC*) at lower temperatures . Most of these nBBL liquid

crystals also exhibit a Blue phase at high temperatures, right

below the isotropic phase, and the decision to focus on the

10BBL sample is related to the fact that its Blue phase is sta-

ble in a wider temperature range. Here, we report a detailed

analysis of 1H NMR relaxation times, T1, their dispersions as

a function of frequency and T-dependence within the differ-

ent mesophases in terms of molecular motions typical of each

phase. To the best of our knowledge, this is the first 1H NMR

relaxometry study on the molecular dynamics in a LC Blue

phase.

2 Experimental

2.1 Material

The molecular structure of 10BBL is presented in Figure 2.

The sample was synthesized as reported in ref.33. The level of

purity of the sample was checked by HPLC chromatography

and liquid state 1H NMR and it is about 100% pure, as de-

tected by HPLC. The temperature transitions of 10BBL sam-

ple have been determined by DSC and polarizing microscopy

on cooling the sample from the isotropic phase to the crys-

talline phase as reported in Table 1. The transitions between

the isotropic (Iso) to BP II and from BP II to TGBA phases

have been clearly determined as first order from the appear-

ance of distinct DSC peaks both on cooling and heating the

sample. The nature of the two TGB phases was clarified from

X-ray and dielectric spectroscopy. The tilt angle and spon-

taneous polarization trends in the TGBC* and SmC* phases

were also determined33.

ClCl

O

OO

O

O

H

O

OH

**

Fig. 2 Molecular structure of the chiral liquid crystal 10BBL.

2.2 NMR methods

The relaxation dispersions in each of the phases were acquired

using the Fast Field Cycling NMR relaxometer SPINMAS-

TER FFC-2000 (Stelar s.l.r.). Around 500 mg of the sam-

ple was used for the measurement. The proton longitudi-

nal spin-lattice relaxation time T1 was measured in the fre-

quency range from 18 MHz to 5 kHz. Above 5 MHz, the

non-prepolarized (NPS) pulse sequence was used for relax-

ation measurements, while below that frequency a prepolar-

ized (PPS) pulse sequence was used. The prepolarization and

acquisition frequencies were 18 and 9.25 MHz, respectively.

A 6.5 μs proton 90◦ pulse was used. All other parameters were

optimized according to each experiment. Temperature was

controlled with a standard gas flow system with a precision of

±0.1◦. Before the beginning of the measurements, the sam-

ple was heated well above the BP-ISO transition and slowly

(with a cooling rate below 0.2 K/min) cooled to the temper-

ature range of the investigated phase. In a separate cooling

run, temperature dependencies of T1 were measured at 1 MHz

and 40 kHz. In addition, the temperature dependency of pro-

ton T1 was measured at the Larmor frequency ν = γB/(2π) of

100 MHz over a wide temperature range using a home-build

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Table 1 10BBL temperature transitions and phase transition enthalpies as determined by differential scanning calorimetry (DSC) at second

cooling and at a cooling rate of 10◦/min. 33

T/◦CCr

53←−−−−−+3.6

SmC*99←−−−−−−

TGBC*108←−−−−−

-0.20TGBA*

118←−−−−−-0.12

BP122←−−−−−

-0.01Iso

ΔH/kJmol−1

spectrometer and an Oxford superconducting magnet. The in-

version recovery pulse sequence with a 2.2 μs 90◦ pulse was

used.

2.3 Experimental Results

104

105

106

107

108

νL(Hz)

100

101

102

103

T1-1

(s-1

)

10BBL

T=393 K, BPT=386 K, TGBA*T=376 K, TGBC*T=353 K, SmC*T=333 K, SmC*

Fig. 3 Experimental spin-lattice relaxation results obtained as a

function of Larmor frequency in all mesophases of the chiral liquid

crystal 10BBL.

A selection of the experimental spin-lattice relaxation re-

sults is presented in Figure 3 and Figure 4. The T−11 disper-

sions in Figure 3 were obtained in the BP at T = 393 K, in the

TGBA* phase at T = 386 K, in the TGBC* phase at T = 376

K, and in the SmC* phase at T = 353 K and T = 333 K, re-

spectively. As it can be observed, the T−11 dispersion profiles

obtained for the TGBC* and SmC* are clearly different from

those obtained for the BP and TGBA* phases. In contrast, the

T−11 dispersion profiles in the BP and TGBA* phases seem

quite similar. Perhaps the most prominent difference lies in

the the fact that (T−11 )BP > (T−1

1 )T GBA∗ for frequencies above

∼ 200 kHz and (T−11 )BP < (T−1

1 )T GBA∗ for lower frequencies.

In Figure 4, T−11 temperature profiles are presented for dif-

ferent Larmor frequencies. The T−11 (T ) obtained at 100 MHz

presents a maximum for T ∼ 360 K and is completely different

from those obtained at 1 MHz and at 40 kHz. No discontinu-

ities are observed at the mesophases transition temperatures.

340 350 360 370 380 390 400T(K)

0

100

200

300

400

500

T1-1

(s-1

)

10BBL

340 350 360 370 380 390 400T(K)

0

0.5

1

1.5

2

2.5

3

3.5

T1-1

(s-1

)

SmC* TGBC*

TG

BA

*

BP

100MHz40kHz

1MHz

SmC* TGBC* BP

TG

BA

*

Iso

Iso

Fig. 4 10BBL experimental spin-lattice relaxation results obtained

as a function of temperature for a three selected Larmor frequencies.

The T−11 results were also obtained in the isotropic phase

of 10BBL but since the frequency dependence and tempera-

ture profiles analysis will not provide critical information re-

garding the interpretation of the proton spin-lattice relaxation

in the mesophases they will be presented only in the Elec-

tronic Supplementary Information. In fact, the magnetiza-

tion decay observed at 100 MHz was found to present three

relaxation components (associated to the methyl, methylene,

and aromatic 1H spin sub-systems) what was also detected for

another chiral LC compound exhibiting TGBA* and TGBC*

phases31. As it was not possible to resolve the magnetiza-

tion decay in terms of those three components for all Larmor

frequencies, only the spin-lattice relaxation results obtained

for the 10BBL mesophases are analyzed. Moreover, the T−11

temperature dependency in the BP at low frequencies was not

reliably obtained in comparison with the frequency sweep per-

formed at fixed temperatures in that phase; for this reason

those T−11 (T ) values were not included in the data analysis.

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3 Analysis and Discussion

3.1 Relaxation models.

The T−11 frequency and temperature dependencies can be an-

alyzed quantitatively in terms of relaxation models that take

into account the effect of the different types of molecular mo-

tions in the modulation of the proton spin-spin dipolar interac-

tions and thus the spin-lattice relaxation. Due to the fact that

proton dipolar spin interactions can be either intra- or inter-molecular, for liquid crystals of rod-like molecules, molecular

rotations/reorientations (R), translational self-diffusion (SD),

and collective motions (CM), have been proved to be effective

motions that affect the spin-lattice relaxation24,26–29,31.

When analyzing proton spin-lattice relaxation profiles that

include low frequency data it is often required to consider

additional relaxation contributions that depend on the spe-

cific nature of the mesophase being studied. In the case

of chiral liquid crystals presenting cholesteric and TGB

phases, a specific relaxation contribution associated to the

rotations/reorientations mediated by the translation displace-

ments (RMTD) along the helical axis has been proposed29,31.

Additionally, in the case of smectic C phases tilt direction fluc-

tuations (TDF) have been considered34.

Provided that molecular motions have distinct characteris-

tic correlation times and/or are statistically independent, the

relaxation model used to analyze the T−11 (T,ν) experimental

results consists of a sum of all motional contributions, neglect-

ing the contribution of any cross terms. The general equation

is(1

T1

)=

(1

T1

)SD

+

(1

T1

)CM

+

(1

T1

)R

+

(1

T1

)RMTD

, (1)

where each term refers to an individual relaxation mechanism.

Although 10BBL has basically a linear molecular structure

(see Figure 2), the two flexible ends have a completely dif-

ferent structure. Therefore, the relaxation model used for the

R contribution is described here by a sum of two Bloember-

gen, Purcell, and Pound (BPP) relaxation equations, with four

fitting parameters: two correlation times, τR1,2 and two pre-

factors AR1,235

(T−1

1

)R=

2

∑i=1

ARi

[τRi

1+4π2ν2 τ2Ri+

4τRi

1+16π2 ν2 τ2Ri

]. (2)

The relaxation mechanism associated with molecular trans-

lational self-diffusion in smectic A and C phases has been suc-

cessfully described by the Vilfan and Zumer’s model

(T−1

1

)SD=

9

8

( μ0

4π

)2

γ4h2 nτD⊥d3

QSmA

(2πντD⊥ ,

⟨r2⊥⟩

d2,

D0‖

D0⊥

),

(3)

where D0‖/D0

⊥ is the ratio for the self-diffusion coefficients

of the perfectly ordered phase (S = 1), and⟨r2⊥⟩= 4τD⊥D⊥.

d is the diameter of the molecule and n is the spin density.

Eq 3 can only be calculated numerically36. τD⊥ is the mean

square jump time associated with the translational diffusion

process. QSmA(

2πντD⊥ ,⟨r2⊥⟩/d2,D0

‖/D0⊥)

is a dimension-

less function that has to be calculated numerically36.

To the authors knowledge, no specific relaxation model to

describe the spin-lattice relaxation by translational diffusion

in Blue phases has been developed yet. Due to the fact that

Blue phases present locally nematic order, the model devel-

oped by Zumer and Vilfan for the spin-lattice relaxation in

the nematic phase was used37. This model has an expres-

sion similar to that of eq. 3 with a dimensionless function

QN(

2πντD⊥ ,⟨r2⊥⟩/d2,D0

‖/D0⊥)

that has to be calculated nu-

merically.

The collective motions (CM) observed in nematic and

smectic A and C phases are related with order director fluc-

tuations that occur in the liquid crystalline medium and are

characterized by different distributions of fluctuation modes

with amplitudes and damping times related to the anisotropic

viscoelastic properties of the compounds38. Depending on the

mesophases, director fluctuations with three-fold wave mode

components qx, qy, and qz, in the case of nematic phases, and

director fluctuations with two-fold wave mode components qx,

qy, in the case of smectic A phases, have been systematically

observed in calamitic and tetrapode liquid crystals27. The for-

mer are know as order director fluctuations, ODF, the latter

are usually referred to as layer undulations, LU. In the case of

smectic C phases not only LU were reported but also in-plane

fluctuations of the c-director, TDF, (e.g. azimuthal fluctua-

tions of the tilt direction in the smectic C layers)34. In general

terms, the relaxation model for the collective motions can be

summarized in the compact form

(T−1

1

)(CM,k)=

ACM,k

(2πν)k

[f CM

(νCmax

ν

)−

f CM,k(νCmin

ν

)],

(4)

where f CM,k(x) are the cut-off functions27,38, and ACM is the

prefactor that reflects the strength of the CM mechanism. For

CM≡ODF and CM≡TDF, k = 1/2, and T−11 dispersions show

a square-root trend as a function of the Larmor frequency as

initially proposed for nematics by Pincus et al. 39 and later ex-

perimentally verified by many authors27,38,40. When referring

to layer undulations, CM≡LU, then k = 1. The prefactor ACM

and the cut-off frequencies, νCmax and νCmin depend on the

inter-spin distances and angles, on the temperature, on the

nematic order parameter, and on the visco-elastic properties

of the compounds. The cut-off functions f CM(x) depend on

the particular phase structure but they produce the same type

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of effect on the T−11 low and high frequency limits, that is

to level-off T−11 (ν) for frequencies below νCmin and to force

T−11 ∼ ν−2 for ν larger that νCmax.

With respect to the rotations/reorientations mediated by the

molecular translation displacements in the direction of the

cholesteric helical axis or across the TGB grain-boundaries

the model was proposed by Vilfan et al. 41, depending on the

value of the helical pitch, p, and on the translational diffusion

coefficient:

(T−1

1

)RMT D= ARMT D

2τRMT D

1+16π2ν2τ2RMT D

(5)

with τRMT D = p2/(16π2D). The pre-factor ARMT D depends

on an average effective inter-proton distance. The molecular

reorientational diffusion process was initially referred to for

the BP by Samulski et al.42.

The correlation times τR1, τR2, τD⊥ , and τRMT D are usually

temperature-dependent and are described by Arrhenius-laws

of the type

τ = τTre f exp(

ER−1(T−1 −T−1re f )

), (6)

where τTre f is the value obtained for the reference temperature

Tre f , E is the activation energy, and R 8.31JK−1mol−1.

The ALU , AODF , and AT DF , pre-factors in eq 4 depend on

temperature both directly and indirectly through the visco-

elastic and nematic order parameter temperature dependen-

cies. Both linear and quadratic temperature dependencies

have been previously successfully used to model the ACM fac-

tors28,29

3.2 Model fits

The spin-lattice relaxation model from eq 1 was fitted simulta-

neously to all experimental data in each mesophase taking into

account both T−11 frequency and temperature dependencies. In

addition, a global fit was performed including the experimen-

tal results obtained for all mesophases. The analysis of the

experimental results required a global fit target since T−11 (T )

do not show discontinuities at the transition temperatures be-

tween mesophases. Therefore, some of the model fitting pa-

rameters must be the same for all mesophases. However, in

view of the specific structure of each individual mesophase,

the collective models used to fit the intermediate and/or low

frequency T−11 dispersion profiles must be different.

The best model fit curves to the experimental results are pre-

sented in Figure 5 and Figure 6. The model fitting parameters

obtained in a global fit using a generalized least-square min-

imization procedure25 are presented in Table 2. Additional

output details of the global fitting procedure is presented in

the Supporting Information. In Figure 7, a 3D plot is shown,

where different surfaces corresponding to each T−11 contribu-

tion as functions of the Larmor frequency and of the temper-

ature are shown. This figure summarizes the more detailed

plots of Figure 5 and Figure 6. Figure 8 presents the contour

plot obtained from the global model fit to the experimental re-

sults. As it can be observed, there are clearly different temper-

ature and frequency regions where the contribution of individ-

ual relaxation mechanisms are dominant. In particular RMTD

is seen in the low frequency region of the FFC frequency range

and for the higher-temperature mesophases (BP and TGBA*).

In the Blue phase, it can be noticed that the ODF contribution

is in-between the SD and the RMTD contributions.

0

100

200

300

400

500

T1-1

(s-1

)

R1

10BBL, νL(40 kHz)

R2

SD

LU

SmC* TGBC* TG

BA

*

BP

TDF

RMTD

R1

R2SD

TG

BA

*

BP

TGBC*SmC*

10BBL, νL(100 MHz)

SD

R1

R2LU TDF ODF

BP

TG

BA

*

TGBC*SmC*

10BBL, νL(1 MHz)

a)Iso

Iso

Iso

0

20

40

60

80

100

T-1

(s-1

)

b)

340 350 360 370 380 390 400T(K)

0

1

2

3

T1-1

(s-1

)

c)

Fig. 6 (Color online) Best model fits to the 10BBL experimental

spin-lattice relaxation temperature dependent results, for three

selected Lamor frequences of 100 MHz, 1 MHz, and 40 kHz.

As it can be observed, the relaxation model given by eq 1

fits quite well both T−11 dispersions and temperature depen-

dencies. The global fit was obtained considering that both

SD and rotations/reorientations are thermally activated and the

same activation energies were used when fitting the experi-

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104

105

106

107

108

νL(Hz)

100

101

102

103

T1-1

(s-1

)

a) 10BBL, T=393 K, BP

R2

RMTD

SD

ODF

104

105

106

107

108

νL(Hz)

100

101

102

103

T1-1

(s-1

)

b) 10BBL, T=386 K, TGBA*

R2

RMTD

SD

LU

104

105

106

107

108

νL(Hz)

100

101

102

103

T1-1

(s-1

)

c) 10BBL, T=376 K, TGBC*

R2

RMTD

SD

R1

LU

104

105

106

107

108

νL(Hz)

100

101

102

103

T1-1

(s-1

)

d) 10BBL, T=353 K, SmC*

R2

SD

R1

LU

TDF

Fig. 5 (Color online) Best global model fit results of the 10BBL experimental spin-lattice relaxation dispersion results obtained for a few

selected temperatures, as explained in the text: a) T=393 K, blue phase b) T=368 K, TGBA*, c) T=376 K, TGBC* and d) T=353 K, SmC*.

mental results in the four mesophases of 10BBL (in the case of

ED the value in the BP was 10% smaller than the one consid-

ered for the other mesophases). From the analysis of Figure 5

and Figure 6 it can be clearly seen that for each temperature

and frequency range, there is a particular relaxation mecha-

nism that has the largest contribution to T−11 in that region.

Except for the BP, the T−11 in the high frequency range

(∼ 20 − 100MHz) is essentially dominated by the local ro-

tations/reorientations. In the case of intermediate frequencies

(∼ 0.1−1MHz), translational self-diffusion is the most effec-

tive relaxation mechanism in all mesophases. At low frequen-

cies (< 10kHz), the spin-lattice relaxation is dominated either

by the relaxation mechanisms associated with collective mo-

tions or by the mechanism associated with the rotations medi-

ated by self-diffusion. The cross line in the (νL, T ) space be-

tween domains where (T−11 )A >(T−1

1 )B and (T−11 )A <(T−1

1 )Bfor relaxation mechanisms A and B is better observed in the

contour plot in Figure 8 and in the 3D plot of Figure 7.

The dominant contribution of rotations/reorientations

(T−11 )R obtained from the sum (T−1

1 )R1 + (T−11 )R2 in the

high frequency range over the other relaxation mechanisms is

clearly observed in Figure 6c where the different T−11 model

fitting curves are presented for the frequency of 100 MHz. In

fact, all the other contributions are negligible at 100 MHz – ex-

cept (T−11 )SD that has a reduced contribution in the BP model

fit.

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Fig. 7 (Color online) 3D plots of the model fit surfaces using the

fitting parameters obtained form the model fits to the experimental

T−11 results. The almost-transparent surface represents the sum of

all T−11 contributions. White lines represent the lines of constant

T−11 values

It is interesting to note that the T−11 temperature dependence

in the BP at 100 MHz is well described by the thermally acti-

vated relaxation mechanisms (T−11 )R1 +(T−1

1 )R2 +(T−11 )SD,

as it can be observed in Figure 6. However, at 1 MHz it

is clear that the temperature dependence is described mainly

by (T−11 )ODF as it increases with increasing temperature like

T−11 , while (T−1

1 )R1, (T−11 )R2, and (T−1

1 )SD present the oppo-

site temperature behavior. Therefore, although both BP and

TGBA* T−11 dispersion profiles are similar (see Figure 3), the

nature of the relaxation mechanisms and their relative contri-

butions to the spin-lattice relaxation is different in view of the

different mesophases’ structures. In the frequency range 100

kHz – 6 MHz T−11 is mainly described by (T−1

1 )ODF. (T−11 )SD

has a relevant contribution in a reduce frequency range 6 –

25 MHz. The value of d ∼ 5.6× 10−10 m obtained from the

fit of the BP data seems to reflect the less ordered state of

the 10BBL molecular chains in this mesophase. The value is

slightly larger than that found for the low temperature, more

ordered, 10BBL mesophases. At low frequencies (T−11 )RMTD

becomes predominant, revealing the characteristic chiral na-

ture of this mesophase with a short helical pitch. It is interest-

ing to note the relative importance of these rotations mediated

by the translational diffusion in comparison with either col-

lective motions or translational self-diffusion to the relaxation

process, revealed in the present study.

The T−11 dispersion in the TGBA* phase, in Figure 5, is

well explained by the dominating (T−11 )SD relaxation con-

tribution in the intermediate frequency region between 100

Fig. 8 (Color online) Contour plot presenting the predominant

relaxation mechanism as a function of frequency and temperature.

In white are represented lines of constant T−11 .

kHz and 20 MHz, as it was observed for other TGBA*

mesophases31,43. At low frequencies, the T−11 dispersion is

dominated by (T−11 )RMTD with the contribution of layer undu-

lations.

The description of the T−11 dispersion profile and tempera-

ture dependence in the TGBC* phase (see Figure 5 and Fig-

ure 6) is very similar to that of TGBA*. The relative contri-

butions of the relaxation mechanisms to T−11 in the 10BBL

TGBC* phase is slightly different from the ones found for the

TGBC* phases of the HZL /7*31. In-plane tilt direction fluctu-

ations are not detected in the 10BBL TGBC* phase in contrast

with the TGBC∗1 phase of HZL 7/*31. This might be related

with the fact that the 10BBL core with four phenyl rings is

larger that the molecular core of HZL 7/*, the former being

less flexible and less favorable to fluctuations of tilt direction

in the smectic C layers.

In the case of the SmC* phase (see Figure 5d) it is clear

that the molecular dynamics at low frequencies cannot be ex-

plained by the same relaxation mechanisms as in the TGB

phases since the (T−11 )RMTD contribution is no longer required

to interpret the experimental results. In fact, since the heli-

cal pitch in the SmC* is expected to be larger than the one

in the TGBC* phase, it will correspond to a larger τRMT D –

thus shifting the (T−11 )RMTD contribution to Larmor frequen-

cies below the fast field-cycling frequency range. (T−11 )LU

becomes the dominant relaxation mechanism below 10 kHz.

This description of T−11 was also found for SmC* phases of

other liquid crystals34,44. The contribution of in-plane tilt di-

rection fluctuations (T−11 )TDF is a minor model fit correction

that improves the overall quality of the global fit under the as-

sumption that the thermally activated relaxation mechanisms

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Table 2 Model parameters obtained from the best fits of eq 1 to the experimental T−11 results in the blue phase, TGBA*, TGBC*, and SmC*

phases of 10BBL. Index CM refers to the type of collective motions observed in the BP (CM ≡ ODF) and SmC* (CM ≡ T DF) phases.

AR1 = 4.2×108 s−2, AR2 = 8.8×108 s−2, d 5×10−10 m (5.6×10−10 m in BP), n 6.8×1028 m−3. The low cut-off frequencies could not

be precisely determined and only a upper limit of 5 kHz was estimated. ER1 68kJmol−1, ER2 41kJmol−1, ED 65kJmol−1

( 55kJmol−1 in the BP). For the BP AODF −20+1.0×103(T −Tre f ), for the TGBA*

ALU 775×103 −52×103(T −Tre f )+9×103(T −Tre f )2, for the TGBC* ALU 931×103 +14×103(T −Tre f )+9×103(T −Tre f )

2, and

for the SmC* AODF 2.4×103 −3.2×103(T −Tre f ) and ALU 1836×103 +151×103(T −Tre f )+6×103(T −Tre f )2

Phase BP TGBA* TGBC* SmC*

T (K) 393 386 376 353 333

τR1 (10−09s) 0.71±0.05 1.0±0.1 1.6±0.4 5.8±3.2 20±13

τR2 (10−10s) 1.8±0.1 2.3±0.1 3.2±0.1 7.3±0.3 16±2

τD (10−9s) 3.1±0.2 4.8±0.2 8.3±0.2 33±1 132±13

τRMT D (10−5s) 1.6±0.8 2.8±0.8 15±2 – –

ACM(104s−3/2) ∼ 1.5 – – ∼ 0.77 ∼ 1.4ALU (106s−2) – ∼ 1.1 ∼ 0.93 ∼ 1.6 ∼ 6.4ARMT D (107s−2) ∼ 3.1 ∼ 4.3 ∼ 2.1 – –

νCmax,ODF (107Hz) ∼ 1 – – – –

νCmax,LU (107Hz) – ∼ 5 ∼ 5 ∼ 5 ∼ 5

νCmax,T DF (107Hz) – – – ∼ 1 ∼ 1

have the same activations energies in all mesophases.

The overall description of the T−11 dispersions and temper-

ature dependencies, in all mesophases, in terms of the relative

contributions of the relaxation mechanisms is perhaps better

realized when observing the 3D plots of Figure 7. It is pos-

sible to observe that, depending on the temperature-frequency

region, one or another relaxation mechanism is predominant

over the others. In the T−11 model (eq 1) the change of the

collective motions from nematic order director fluctuations

to layer-undulations might produce discontinuities at phase

transitions BP-TGBA* and TGBC*-SmC*. Also, the RMTD

contribution may present discontinuities due to the change of

the helical pitch and/or self-diffusion coefficients, as a conse-

quence of different structure of the individual phases.

4 Conclusions

A molecular dynamics study by proton spin-lattice relaxom-

etry in the mesophases of the chiral liquid crystal 10BBL is

presented. The 1H spin-lattice relaxation time was measured

over a broad range of Larmor frequencies at different temper-

atures in all 10BBL mesophases and as a function of temper-

ature for a few selected Larmor frequencies. The experimen-

tal results were analyzed in terms of a T−11 relaxation models

that considered the most relevant relaxation mechanisms phys-

ically compatible with the mesophases’ structures of 10BBL.

In addition to the common rotations/reorientations and trans-

lational self-diffusion relaxation mechanism usually found to

contribute to the proton spin-lattice relaxation, the relaxation

mechanisms associated with collective motions were consid-

ered in the particular type of structure of each mesophase,

namely: order director fluctuations or layer undulations. Ad-

ditionally, the relaxation modulated by rotations mediated by

the translational displacements associated with the particular

helical structures found in the blue phase and in the TGB

phases, characterized by short pitches, was also included in

the T−11 model.

From the model fit performed simultaneously to the

T−11 (ν , T ) experimental results, taking into account the global

least-square minimization target that considered all T−11 re-

sults, it was possible to conclude that rotations/reorientations

and translational self-diffusion dominate the spin-lattice relax-

ation rate in the high and intermediate frequency ranges above

100 kHz, with exception of the BP spin-lattice relaxation rate.

In the BP, order director fluctuations are predominant between

∼ 50 kHz and 2 MHz. Otherwise, collective motions are rele-

vant only in the low frequency regime, below 100 kHz.

For all 10BBL mesophases, the T−11 dispersion above 50

MHz is dominated by rotations/reorientations as observed for

most nematic, TGB, smectic A, C, and C* phases of other

liquid crystals.

The T−11 results presented here, obtained for the first time

in a Blue phase, made possible to conclude that the specific

diffusion/rotation process along the helical axis in the 10BBL

BP and TGB phases is very important for frequencies below

∼ 50 kHz in the case of the BP and TGBA* and for lower fre-

quencies also in the case of the TGBC* phase. In the smectic

C* phase, this specific relaxation mechanism is not observed.

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Acknowledgments

This work was partly supported by the ”Fast Field-Cycling

NMR relaxometry study of chiral and non-chiral nematic liq-

uid crystals” bilateral project Slovenia-Portugal. V.D. thanks

the Centre of Excellence NAMASTE (Ljubljana) for the finan-

cial support as visitor professor. Authors thank V. Hamplova

and M. Kaspar (Prague) for providing the 10BBL sample. V.

D. and V. N. thank the project ASCR M100101204 for partial

support.

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Textual abstract for the Contents pages:

”1H NMR relaxometry study of the molecular dynamics in Blue, TGBA*,

TGBC* and SmC phases of chiral liquid crystal compound”

θθ

(TOC figure)

Contents1 Introduction 1

2 Experimental 22.1 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.2 NMR methods . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . 3

3 Analysis and Discussion 43.1 Relaxation models. . . . . . . . . . . . . . . . . . . . . . . . 4

3.2 Model fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4 Conclusions 8

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