Dielectric study of the liquid crystal compound octylcyanobiphenyl (8CB) using time domain spectroscopy

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Dielectric study of the liquid crystal compound octylcyanobiphenyl (8CB) using time domain

spectroscopy

T.K. Bose, R. Chahine, M. Merabet, J. Thoen

To cite this version:

T.K. Bose, R. Chahine, M. Merabet, J. Thoen. Dielectric study of the liquid crystal compound octyl-

cyanobiphenyl (8CB) using time domain spectroscopy. Journal de Physique, 1984, 45 (8), pp.1329-

1336. �10.1051/jphys:019840045080132900�. �jpa-00209871�

Dielectric study ^{of the} liquid crystal compound octylcyanobiphenyl (8CB) using time domain spectroscopy

T. K. Bose (*), R. Chahine (*), ^{M. Merabet} (*) ^{and J. Thoen} (**) (*) Groupe ^{de recherche en} diélectriques, Département ^de Physique,

Université du Québec ^à Trois-Rivières, C.P. 500 Trois-Rivières, Québec, ^{Canada G9A 5H7} (**) Laboratorium voor Molekuulfysika, Katholieke Universiteit Leuven,

Celestijnenlaan ²⁰⁰ D, ³⁰³⁰ Leuven, Belgium

(Reçu ^le 20 janvier ^1984, accepté le 24 avril 1984)

Résumé. 2014 La technique ^de spectroscopie ^{dans le domaine du} temps (SDT) ^est appliquée pour la première ^{fois à}

l’étude des propriétés diélectriques ^{de cristaux} liquides. ^{Nous mesurons la} permittivité complexe ^de l’octylcya- nobiphenyl (8CB) ^et comparons les résultats ^{avec ceux} de la littérature obtenus _{par les} méthodes fréquentielles ^en régime permanent ^{Nous montrons} également qu’il ^est possible de définir différents domaines de relaxation à

partir des résultats obtenus _par la technique SDT, ^en effectuant des approximations successives des fonctions de distribution des temps de relaxation.

Abstract. 2014 Time domain spectroscopy (TDS) ^is introduced for the first time to study ^the complex permittivity ^of liquid crystals. Measurements have been carried out for octylcyanobiphenyl (8CB) ^and the results are compared

with literature data obtained by conventional steady-state ^{methods in the} frequency ^domain. It is also shown that the TDS results enable one to calculate successive approximations ^{for the} relaxation time distribution func-

tions, ^{which can be used to} distinguish among different domains.

Classification

Physics ^Abstracts

61.30G - 77.40

64.70M

1. Introduction.

Time domain spectroscopy (TDS) ^was first intro- duced to the study of dielectric properties ^around

1969 [1, 2]. Although the earlier results were more

qualitative [3, 4] ^than quantitative, ^recent develop-

ments [5-11] ^{in data} acquisition, processing ^and

reduction of system ^{errors have} improved ^{the TDS} technique ^{to the} point ^where its accuracy probably

surpasses the traditional frequency domain methods.

The superiority ^{of TDS over the} established dielectric

steady-state ^{methods is due to} the fact that with this

technique ^{one can} obtain the complex permittivity

of a substance over a wide frequency range (100 kHz

to 10 GHz) ^{with a} single measurement

Valuable information on the characteristic _pro-

perties ^of liquid crystals ^{can be} derived from dielectric measurements [12, 13]. ^{In most cases the available} experimental ^{results were} obtained for rather low fre-

quencies (mainly ^{in the} kHz-range), giving only

information on the static permittivity. Measurements of the complex permittivity ^for frequencies ^above

10 MHz (the limiting frequency ^{for radio} frequency bridges) ^are relatively ^rare. Although measurements of dielectric permittivity ^at higher frequencies ^have

been reported ^{in the} literature, they ^exist only ^{for a}

limited number of frequencies [14-21]. During ^the

last _years an important ^{effort was made} by ^{a research}

group in Lille (France) ^{to cover the whole} frequency

range between 1 Hz and 26 GHz [22-27]. ^{In their} experimental setup ^three types ^of measuring ^{cells and}

five different measuring systems ^{are used} [27]. Although part ^{of the} measurements (for frequencies ^between

1 GHz and 18 GHz) ^have largely ^{been automated} [27], covering ^{the entire} frequency range remains time-

consuming.

In many liquid crystals, dielectric relaxation phe-

nomena occur in the Megahertz and the low Giga-

hertz _range. This is exactly ^the range which can be covered in a single measurement with the present

possibilities ^{of the TDS} techniques. ^{In this} article,

we shall present for the first time the application ^of

TDS to the study ^{of the} dielectric properties ^{of a} liquid crystalline material, octylcyanobiphenyl (8CB).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019840045080132900

1330

2. Basic principles ^{of TDS} measurements.

A basic TDS system ^is composed ^{of three} major

elements : a fast rising tunnel-diode pulse generator,

a wide-band sampling oscilloscope, ^{and a data-} acquisition system (Fig. 1). ^A step voltage pulse produced by the tunnel diode generator ^{with a} maximum repetition ^{rate of 100 kHz,} propagates along ^{a coaxial} line until it reaches the dielectric

sample, ^{where a} part ^{of the} signal ^{is reflected and the}

rest transmitted in the dielectric.

It is possible ^{to determine the} dielectric properties

of a substance by analysing only the first reflected [28]

or transmitted signal [29]. However, ^{the TDS} confi-

guration best suited for precision permittivity ^measu-

rements over a wide frequency range is the total reflection from a thin sample ^{with an} open ^or 50 Q termination [30-33].

Although ^the experimental measurements in a

TDS system ^are obtained in the time domain, ^subs-

tantial difficulties are encountered in extracting ^the

desired _response function 0(t) ^of the dielectric from the reflected signal. ^{A careful} comparison ^has

shown [30] ^{that the} analysis of the results is simpler,

more precise and broadband if they ^{are converted to}

the frequency ^domain.

In the case of the single reflection method, ^there

exists a simple relation in the frequency ^domain connecting the Fourier transforms R( jw) ^and VoUw)

of the reflected voltage r(t) and the incident voltage

vo(t).

It is given by :

where the complex reflection coefficient p* is related to the complex permittivity ^s* by

and

where and s" ^are respectively the real and imaginary parts ^{of s*. As} vo(t) ^and r(t) ^{are difficult to define in an} analytical form, ^{one can obtain} p* ^from equation (1) by using ^{numerical Fourier} transforms for R( jw)

and Yo( jw).

Fig. ^1.

^Basic diagram ^{of a TDS} system.

The analysis ^{based on} the total reflection configura-

tion for an open termination (Fig. 2) ^{is more} complex

but gives ^more satisfactory ^{results. For a thin dielectric} sample ^{with an} open termination, ^the complex ^die-

lectric permittivity ^is given by

where x ⁼ jWdB*1/2/C. ^{In this} expression ^{c =} 1/(Lc Cc)1/2 ^{is the} speed ^of light ^and Cr are, respec-

tively, ^the geometric capacitance ^and inductance _per unit length of the line and d is the length of the dielectric

sample. Equation (4), ^which gives ^{absolute values for}

the complex permittivity, ^{has been} successfully ^used

for moderately ^to strongly polar liquids (Es > 10) [31, 33]. ^{In the case of} weakly polar liquids, the accuracy of the measured transients is usually ^{not sufficient}

for a reliable determination of the absolute 8* values.

In this case it is more appropriate ^{to use the difference}

method [34, 35]. ^{It is based on} the difference between the reflection r.(t) ^{from a standard} dielectric of known permittivity 81 and the reflection r(t) ^{from the}

unknown dielectric of permittivity ^{B*. The difference}

is then given by [35] :

with f ^{= x coth x. One can take full} advantage ^of

this method by chosing ^a standard dielectric with a

real frequency independent 8:. ^{From an} experimental point ^{of view a} very suitable choice is air and as such,

9* ^{can be} replaced by ¹ and is is also 1 for air. The

major advantage ^{in this case is} essentially ^that vo(t) - rs (t ) ^reaches equilibrium ^{faster than} vo(t) ^{+ r(t ) and as a} consequence experimental ^trun-

cation (due ^to the finite time window) ^of the denomi- nator in equation (4) ^{can be avoided} [34, 35].

Fig. ^2.

Schematic behaviour of the time dependence ^of

the incident voltage v,(t) ^{and the} signal r(t) reflected from the

sample ^{for the total} reflection method

3. Experimental

Measurements were taken using ^a Hewlett-Pac- kard 181 TDR system. ^The experimental setup ^for the total reflection measurements is shown in figure ^4.

The basic setup ^{includes a} tunnel-diode pulse gene- rator (1105 A/I 106 B) ^{with a} repetition ^{rate of about} 105/s ^{and a} rise time of less than 20 _ps, a two channel broad-band (dc-18 GHz) sampling amplifier type 1811 A with remote feedthrough sampling ^head type ¹⁴³⁰ C, ^{and a} display memory oscilloscope type ^{181 A. In} conjunction with the basic TDR system,

we used a Nuclear Data system ^for data acquisition

and processing. ^The sample ^{cell is a} short section of a

standard 7 mm APC precision ^{50 Q} coaxial airline.

The length ^{of the} sample is determined by the electri-

cal length of the inner conductor of the cell. Its calibra- tion by using ^{known alcohols} (ethanol ^and butanol) gives ^a length ^{of 6.36 mm.} The dielectric sample ^is placed ^{between two} conductors of the coaxial line with inner radius of 1.5 mm and outer radius of 3.5 mm.

The correction of various experimental ^{errors such}

as slow asymmetric ^{drift of} the incident pulse, noise, jitter ^and unwanted reflections arising from disconti- nuities have been discussed in detail elsewhere [34, 36].

The 8CB material was obtained from BDH (Poole, Dorset, U.K.) and used without further purification.

The temperature ^{of the} sample ^was controlled within 0.3 OC by ^{means of an Inreco} temperature ^{test chamber.}

No magnetic ^{field was used to} orient the sample, but,

as will be shown further, ^the measurements in the nematic phase clearly indicate that the results corres-

pond ^to 8 g ^which proves that a uniform alignment

was obtained by ^{surface effects.}

For time domain spectroscopy ^8CB posed ^some

unusual experimental problems. Although this cyano-

compound ^{has a} relatively high permittivity ^{for a} liquid crystal, from the dielectric point ^of view, ^howe-

ver, it is a moderately polar liquid ^{but with a} relatively

low relaxation frequency. With its Eo ~ 9 it is situated at the lower limit for the method determining ^abso-

lute 8* values ^on the basis of equation (4).

On the other hand its permittivity ^{is too} high ^to

take full advantage of the difference method based ^on

equation (5). Furthermore, given the low relaxation

frequency, ^{one has to deal} effectively with truncation effects caused by the finite time window of the TDS.

One can derive the static permittivity 80 from equa- tion (4) in the limit cv -> 0 :

Thus ₈₀ is directly proportional ^{to the} integral ^to

infinite time of the difference curve vo(t) - ^{r(t) (i.e.}

the area between the curves of figure 2). ^{In order to} get

accurate results for s values at very low frequencies

the integrand ^should represent ^the complete response.

Fig. ^3.

Transient records for the total reflection method

(see ^Sect. 2). r(t) is the reflected voltage ^{from the} sample ^and rs(t) is the air reflected voltage. Note that the signals ^have

been inverted and that rit) ^{has the same decay as the inci-}

dent voltage vo(t).

Fig. ^4.

^Block diagram ^{for the} synchronized-successive- sampling ^method

Thus ideally ^one would desire _very long ^{TDS time}

windows in the experiment. ^{This is, however, for the}

case of 8CB in particular, ^not compatible ^{with the} requirement ^{of a} sufficiently ^{strong reflected} signal.

A stronger signal ^can be obtained by increasing ^the

cell length. ^But that reduces the high frequency ^limit.

In order to cover the whole frequency range of interest for 8CB with a single measurement, ^{we had to} compro- mise on an optimum length (6.36 mm) ^{of the cell.}

Under these conditions we could get ^{a maximum} time window T of about 7 ns free of spurious ^reflec-

tions. We were thus able to cover the difference curve

down to 5-6 % ^{of its} original ^value (see Fig. 5). ^This

is somewhat above the usually acceptable ^{level of 1 to}

2 % with faster relaxation times or lower static permit-

tivities [36]. ^To approximate the contribution of the

remaining ^{area for t} > T we added ^an exponential

tail to the difference curve, which at long times varies

1332

Fig. ^5.

Typical transient record for 8CB. r(t) ^{is the} signal

reflected from the 8CB sample ^and rs(t) ^{is the air reflected} signal.

as exp( - t/tc)’ where T, is the time constant for

charging ^the sample with static permittivity so and

length d through the resistance of the tunnel diode

pulse generator. ^{In order to avoid the additional} complication ^of extrapolating ^{also the sum curve,} v(0) ⁺ r(t), ^we used, however, equation (5) ^{with air}

as the standard material and as such c: ^{= 1 and} fs ^{= 1 and} Vo ⁼ exp(jco ² d/c) R,. ^We have tested the extrapolation procedure by starting ^{at different} points ^{between 6 ns and 7 ns} and found in all cases

very good ^internal consistency ^{and also} very good

agreement ^{with accurate low} frequency ^{results for}

so [37]. ^This gives confidence that the extrapolation procedure ^{is reliable.}

4. Results and discussions.

We have measured the dielectric properties ^{of 8CB}

over a large temperature range in the isotropic phase

as well as for a few temperatures in the nematic phase.

Figure ⁶ gives ^s’ and 8" results as a function of the

frequency f ⁼ w/2 n for three temperatures ^{of the} range coyered by ^the experiment ^{in the} isotropic phase. ^{T =} 41.5 °C is less than 1 °C above the ^nema- tic (N) ^to isotropic (I) phase transition temperature

TNI ^{= 40.8 °C. In} figure ^{7 the} corresponding ^Cole-

Cole plots ^are given for the results of figure ^{6. Results}

for e(w) ^and s"(co) ^{in the nematic} phase ^{at T = 37.3 °C}

are given ⁱⁿ figures ^{8 and 9. A} comparison ^{is made with}

the data (obtained with classical steady-state ^methods

in the frequency domain) ^{of Druon} and Wacrenier [23, 25] ^{for T =} 37 °C in the N-phase ^{as well as for}

T ⁼ 45 °C in the isotropic phase.

From figures 6 and 8 it can clearly ^{be seen that the}

100 kHz results are well below the dielectric relaxation

Fig. ^6.

^The frequency dependence ^{of the} real and ima-

ginary part ^{of the} complex permittivity (Eq. (3)) ^{for three}

temperatures ^{in the} isotropic phase ^{of 8CB.}

Fig. ^7.

^Cole-Cole plots ^{for the} e’(w) ^and 8"(m) data in the

isotropic phase of 8CB for the same three temperatures ^as in figure ^6.

frequencies ^{in the} MHz-range. Our TDS values for 8’ at that frequency ^are practically ^{the same as} the so values calculated by ^{means of} equation (6). ^In figure ¹⁰

we have compared ^our co results with accurate low

frequency data for 8CB [37]. ^{For most} temperatures the deviations are smaller than 2 %. ^{Our two data} points ^{in the} N-phase ^are in very good agreement ^with the static 81 data. This shows that the director was

oriented perpendicular ^{to the electric field direction}

even though ^{we did not use a} magnetic field. Thus surface effects alone were sufficient to obtain a uni-

formly ^oriented sample.

The comparison ⁱⁿ figure 8 with the data of Druon and Wacrenier [23, 25] ^{shows an overall} agreement between both sets of data. Some discrepancies ^are, however, visible in the Cole-Cole plots ^of figure ^9.

The differences seem to be most pronounced ^{in the} low-frequency region.

In figure ^{7 it can be seen that the Cole-Cole} plots

deviate from a semicircle at the high-frequency ^side

(small ^8’ values). ^The deviations from a semicircle are

even more pronounced ⁱⁿ figure ^{9 for} B!(ro) ^{in the}

Fig. ^8.

Comparison ^{between our} TDS results (dots) ^and

conventional steady-state ^data (pluses) by ^{Druon and}

Wacrenier (Refs. [23, 25]) for e’ and e" in the isotropic phase (at ^T

⁴⁵ °C) ^{and for} e’ and El ^{in the nematic} phase (at ^T

^37.3 oQ.

nematic phase ^{at T =} 37.3 °C. This skewed arc

situation, which indicates a distribution of relaxa- tion times, is often described by the Cole-Davidson

equation ^{for the} complex permittivity [38]. ^{The Cole-}

Davidson equation ^{assumes a} continuous distribution of relaxation times. As will be shown later, different relaxation domains are clearly present ^{in our data.}

Although it would be quite possible ^{to obtain reaso-} nably good fits with the Cole-Davidson equation,

the results would be of limited use because of the presence of several relaxation domains.

It can be clearly ^{seen from} figure ^{6 for the} isotropic phase ^that the relaxation frequency fR, corresponding

to the absorption maximum, decreases with decreasing temperature. ^The temperature dependence ^{of the}

relaxation frequency ^is usually ^described by ^{an Arrhe-}

nius type of relation [38] :

For the relatively unimportant temperature depen-

dence outside the exponential, ^one usually ^has

Fig. ^9.

^Cole-Cole plots ^{for the data} displayed ⁱⁿ figure ^8.

Dots are our TDS results and the pluses ^{are data} by ^Druon

and Wacrenier (Refs. [23, 25]).

Fig. ^10.

Comparison between results from different

sources for the static dielectric permittivity ^{of 8CB. The}

data by Thoen and Menu are from reference [37] ^{and the}

data by Druon and Wacrenier ^are from references [23]

and [25].

1334

m = 0 or m = 1. A is a constant, k ^{is the Boltzmann}

2

constant and E ^{is an} activation energy. ^We have fitted our fR data in the isotropic phase ^with equa- tion (7). For fR the maximum value for e(w) ^was

chosen. For the case m

0, ^{we obtain A}

2.42 ^x 1012 Hz and E

0.31 eV. For m

1/2, ^we get A ^{= 8.12 x 1010 Hz K -1/2 and E = 0.29 eV.}

Both fits are of nearly equal quality. The solid line

through ^our experimental data for the isotropic phase

in figure ¹¹ represents ^{the case m = 0. In} figure ¹¹ experimental fR values for 8CB from other ^sources have also been displayed ^Our average E ^{value of}

0.30 eV is lower than the value of 0.42 eV obtained by

Parneix [27] ^{for four} compounds ^of the nCB series

(n ^{from 4 to} 8). ^{Our value} is, however, ⁱⁿ quite good

agreement with the value of 0.27 eV of Davies et al. [16]

for 7CB.

It can be shown [38] ^that successively ^better approxi-

mations for the logarithmic distribution function of relaxation times G(ln z) ^{can be obtained from} 8"(cv), E’(w) and their derivatives with respect ^{to In w. The}

following expressions [38] ^are of interest to us here :

Fig. ^11.

Temperature dependence ^of the relaxation fre-

quency fR for 8CB. The solid line represents ^{a fit with} equation (7) ^{for our} TDS data in the isotropic phase. ^The

results of Druon and Wacrenier are from references [23]

and [25], and the results by Ratna and Shashidhar are

from references [39].

Go ^is usually ^{called the} normalized loss function. If

sufficiently detailed and accurate s’(co) ^and s"(co)

results over a large frequency range ^are available, looking ^{at these} higher derivatives _may also be a

valuable procedure ^to separate the different relaxation times in case of superposition. ^{This was} recently

demonstrated by ^Zeller [40] ^for measurements (up ^to

100 MHz) ^of 8)(cv) in the nematic phase ^of binary

mixtures of pentylcyanobiphenyl (5CB) ^and pentyl- cyanoterphenyl (5CT). ^{From the} calculation of G05 Gland G2 for these mixtures it was possible ^{to deter-}

mine two dominant relaxation times, which could be ascribed to the reorientation around a short molecu- lar axis of each type of molecule in the mixture.

Since from TDS one has in principle ^continuous

information available over the entire frequency range

(100 ^kHz-10 GHz), the above procedure ^{should be}

very useful in determining ^{different relaxation} regimes. ^{We have} applied this method to our TDS results for 8CB. In figure ^{12 the} quantities Gog G1 ^and G2 (defined ⁱⁿ Eqs. (8-10)) ^are plotted ^{as a} function of

frequency ^{for two} temperatures ^{in the} isotropic phase.

Fig. ^12.

Frequency dependence ^{of the} quantities Go, Gi

and G2 ^{defined in} equations (8-10) ^{for two} temperatures ⁱⁿ

the isotropic phase.

In figure ^{13 the same} quantities ^{for the} perpendicular

component ^{of the} complex permittivity et ^{are given}

for two temperatures in the nematic phase. ^{It can be}

seen very clearly ⁱⁿ figure ^{13 that} peaks appear for the higher derivatives, indicating ^the superposition ^of

different relaxation domains. For T

37.3 °C in

figure 13, three different relaxation domains seem to emerge from the Gland G2 ^results. The lowest one

at f1 = ^{50 MHz, a second} one f2 -- ^{200 MHz and a}

third one around f3 -- 800 MHz. The same sequence is present for the results at T = 40.5°C also in figure ^13.

The value of f1 has, however, ^{decreased to 43} MHz,

while f2 and f3 ^remain unchanged. Also in the isotropic phase only f1 ^shows temperature dependence, ^while f2 ^and f3 ^{as far as} observable remain constant. In both figures 12 and 13 the highest relaxation domain is rather poorly resolved because of substantial scatter in the calculated G1 ^and G2 ^{values. It can at the}

moment not be excluded that in the _range between 0.5 and 4 GHz more than one weak relaxation domain

might ^be present. ^The frequency dependence ^for 8* ^{of 5CB,} 7CB and 8CB (the ^data by ^{Druon and}

Wacrenier [23, 25] displayed ⁱⁿ Figs. ^{8 and} 9) ^have recently ^been discussed in detail by Wacrenier, ^Druon

and Lippens [26]. By ^a completely different numerical method [41] the distributed domain was decomposed

into elementary Debye type ^{domains. For} the data of 8CB at 37 °C three elementary ^{domains at 12.9 MHz,}

69.7 MHz and 370 MHz were obtained. The strongest relaxation mechanism at 69.7 MHz is quite ^{close to} our f1 ^{value. The 370 MHz value could possibly be}

considered as an average value between our f2 ^and f3 frequencies. ^{For the} relaxation frequency ^at

12.9 MHz which, according ^to Wacrenier et al. [26],

should arise from collective movements of the mole-

cules, ^{there is no evidence} present in the TDS data

(see Fig. 13). ^To clarify ^this point, additional TDS measurements with large time windows and _very well

aligned samples ^{are needed.} The relaxation frequency fi ^for 8 g in the nematic phase ^can be ascribed [13]

to the reorientation of the longitudinal component ^of the dipole ^moment of the 8CB molecule at a constant latitude with respect ^{to the} nematic director. The relaxation mechanism at high-frequencies ^{is most} likely ^{related to} intramolecular movements [26].

5. Summary and conclusions.

In this _paper, for the first time, results of an inves-

tigation by ^means of time domain spectroscopy (TDS) of the dielectric properties ^{of a} liquid crystal compound ^are presented. Valuable results could be obtained in a single measurement over a large ^fre-

quency range (100 ^kHz-4 GHz). Measurements were

carried ^out for octylcyanobiphenyl (8CB) ^{in the} isotropic phase between 70 °C and the nematic to

isotropic phase transition temperature ^{at 40.8 °C.}

Fig. ^13.

Frequency dependence ^{of the} quantities Go, G1 1

and G2 ^{defined in} equations (8-10), ^but restricted to the per-

pendicular components s’i and E" of the complex permittivity

for two temperatures ^{in the nematic} phase.

Results for the perpendicular component 8! ^{of the} complex permittivity ^were also obtained in the nema-

tic phase. Our results for the large dipole reorientation relaxation phenomena ^{in 8CB are in} qualitative

agreement ^with previous ^results by conventional

steady-state methods in the frequency ^domain [23, 25].

Because of the continuous information available in TDS over the entire frequency range, numerical differentiation techniques ^{allowed us to} separate ^diffe-

rent relaxation domains. Since TDS enables ^{one to} obtain information over a large frequency range,

rapidly ^{and at intervals as small as one} desires, ^{it is}

our opinion that this method is ideally ^{suited to}

make detailed studies of the influence of external _para- meters (like ^e.g. temperature, pressure and ^concentra-

tion) ^{on the} different relaxation domains in liquid

crystals.

1336

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