HAL Id: jpa-00249631
https://hal.archives-ouvertes.fr/jpa-00249631
Submitted on 1 Jan 1997
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Temperature Dependence of Light Transmittance in Polymer Dispersed Liquid Crystals
F. Bloisi, C. Ruocchio, L. Vicari
To cite this version:
F. Bloisi, C. Ruocchio, L. Vicari. Temperature Dependence of Light Transmittance in Polymer Dispersed Liquid Crystals. Journal de Physique III, EDP Sciences, 1997, 7 (5), pp.1097-1102.
�10.1051/jp3:1997178�. �jpa-00249631�
Temperature Dependence of Light Transmittance in Polymer Dispersed Liquid Crystals
F. Bloisi (*), C. Ruocchio and L. Vicari
Istituto Nazionale per la Fisica della Materia Dipartimento di Scienze Fisiche, Universith di Napoh "Federico II" Piazzale V. Tecchio, 80, 80125 Napoh, Italy
(Received 17 April 1996, accepted 29 Jauuary 1997)
PACS 61.30.Gd Orientational order of liquid crystals; electric and magnetic field effects
on order
PACS.42.25.Fx Diffraction and scattering
PACS 42 65.Pc Optical bistability, multistability and switching PACS.64 70.Md Transitions
in liquid crystals
Abstract. Polymer Dispersed Liquid Crystals (PDLC) are composite materials made of a
dispersion of liquid crystal droplets in a polymeric matrix When the liquid crystal is in the nematic phase, droplets appear as optically anisotropic spheres and the material is opaque white
Sample transmittance is a function of the temperature. If the liquid crystal refractive index in the isotropic phase is equal to the one of the polymer, after the nematic-isotropic transition the material is transparent. We present a mathematical model of the dependence of the sample
transmittance versus the temperature We show the model accuracy by comparison with new
experimental data.
1. Introduction
A typical Polymer Dispersed Liquid Crystals (PDLC) electro-optic device is made by a disper-
sion of liquid crystal microdroplets in a polymeric film. In the present paper we consider the
case of a liquid crystal in the nematic phase having bipolar molecular orientation inside each
droplet, since it is the more interesting for the majority of applications. Each droplet appears
as an optically uniaxial sphere, but the whole sample appears to be isotropic since droplets are randomly oriented. The refractive index mismatch between droplets and surrounding medium produces a strong light scattering when droplet size is close to visible light wavelength. Sam- ple scattering, and therefore sample transmittance, is usually controlled by the application of
an electric or a magnetic field, since the field aligns the liquid crystal molecules inside each
droplet and so that, with a careful choice of polymer refractive index, the index mismatch can be reduced to zero. In this situation the device becomes perfectly transparent, for a normally impinging light beam.
The switching from a translucent to a transparent state can also be induced by heating the sample if the refractive index of the polymeric binder is equal to the refractive index of the
(*) Author for correspondence (e-mail. bloisi@na.infn.it)
Q Les (ditions de Physique 1997
1098 JOURNAL DE PHYSIQUE III N°5
y
N~
o
i~~ )
z
Fig. 1. Reference frame- the z-axis is in the direction of the impinging beam (wavevector k) and the optical electric field Eopt is in the ~-direction. The sample surface is in the ~y plane. lid is the
director of a generic droplet
liquid crystal in the isotropic phase. The whole material transparency is a function of the tem-
perature since the refractive indexes of the liquid crystal are temperature dependent. Besides the fundamental interest in the study of the light scattering dependence on the temperature, this phenomenon can be of great interest for several purposes ranging from temperature sensors to photoaddressed displays. In this paper we present a model able to evaluate the influence of
temperature variations on the light transmission in a PDLC. We show also new experimental
results. Comparison between theoretical and experimental results demonstrates the accuracy of the model.
2. The Model
We assume that there is no light absorption either in the polymer or in the liquid crystal: the
light transmission is therefore controlled by the light scattering on the liquid crystal droplets.
Following the Anomalous Diffraction Approach (ADA) scattering theory [ii, for a droplet of radius R, the scattering cross section for a single droplet is:
8y~3j~4 y~« j~) 2 y~* 2
ad (~,§7) #
~
~~ l COS~§7 + ~° l Sin~
§7 II
~ ~P ~P
where (see Fig. 1) d and ~J give the orientation of the droplet director fld, I gives the
prop-
agation direction of impinging beam, I is the impinging beam wavelength, np is the polymer
refractive index, n]~ and n]~ are the effective (ordinary and extraordinary) droplet refractive indices:
'lie (d) " ~~~~~~ 12~)
jn(~Sin~ d + n(~COS~ d
ma " ndo (2b)
and ndo and nde are the ordinary and extraordinary droplet refracti,~e indices. We have com-
puted their expressions in a previous paper [2], for a different application, in the case of bipolar
droplet configuration:
~~~ /) (n] ]~~d~ )(n] + 2n)) ~~~~
~~° ~~° ~
~
' le ~~~ ~~~~~ ~~~
~~~~
where F (6,m) is the complete elliptic integral of the first kind, no and ne are the liquid crystal refractive indices and the droplet order parameter Sd is defined as [3]
Sd "
1~2 (f~d'fi)) (4)
droplet
where the average is taken over each droplet, P2 lx) is the second order Legendre polynomial
and fi is the nematic director (i.e. the direction of the symmetry axes of the molecule averaged
over thermal fluctuations) and gives the "direction" of the liquid crystal molecules. The droplet director id is the nematic director fi averaged over the droplet and gives the "direction" of each liquid crystal droplet. Thus the physical significance of the droplet order parameter is that it is a measure of the degree of orientational order of the nematic liquid crystal into each droplet.
The sample transmission ratio can now be written as:
~ =Tjexp(-Nvasds) (5)
IO
where IO is the impinging beam intensity, ds is the sample thickness, Nv is the number of
droplets per unit volume, as
= (ad)sampje is the average scattering cross section and TF is the Fresnel transmission coefficient [4j at air-glass interface (glass and polymer have been assumed to have the same refractive index np), for normal incidence
TF =
~~~
~
(6) (np + 1)
Since no field is applied the distribution function of the droplet directors is uniform with respect to both d and ~J; therefore as can be computed by integrating ad over the whole solid angle and dividing by 47r. This can be done once we observe that under the condition (nde ndo) /ndo « 1 we can expand n[~ in terms of (nde ndo), getting at the first order:
n)~ ci ndo + (nde ndo)sin~ d. (7)
Substituting into equation ii) and integrating we have
a~ = ~f~)~ '~~~
~°)~ ('~P
'~d° ~ ~ '~P
~'~d°
+
~~ l(~)
nP ride ado 3 nde ndo 105
where nde and ndo are given by equations (3).
3. Temperature Dependence
Using equations (8) and (3) we can express the sample scattering cross section as a function as = as ii, R, np, ne, no, Sd). Excluding the wavelength I, all other quantities are affected by
the sample temperature T.
1100 JOURNAL DE PHYSIQUE III N°5
Nevertheless in the following we will make the assumption of constant Sdi this means that the molecular director distribution inside the droplet is supposed to be unaltered by sample heating. This approximation is inadequate if a quasi-static electric field is applied to the
sample [5]. In such case, the director configuration depends on the equilibrium between the torque due to the electric field and the torque due to the elastic forces, mainly inside the bulk of the droplets. Since only elastic torque is influenced by temperature, the director distribution is changed by temperature variations. In the present experiment, however, there is no applied
electric field, so that the director distribution is due to the balance between two elastic effects:
the ordering bulk effect and the surface induced distortion effect. Both bulk and surface effects lower with the elastic constant decrease due to temperature rise. Up-to-day we have
no informations about experimental or theoretical results of this problem for planar tangential anchoring. A study [6] performed for droplets with homeotropic surface anchoring (giving
radial or axial droplet configuration) has shown that significative distribution changes occur only in a range of few Kelvin from the Nematic-Isotropic transition temperature. On the basis of this consideration we assume that the molecular director distribution inside the droplet is
unaltered while heating the sample.
The temperature dependence of the refractive indexes is due to variations of the density
and of the order parameter of the material. Here we will neglect the density changes of the materials since we are mainly interested in the heating induced PDLC switching from
translucent to transparent state, i.e. in the variations of the optical properties of the sample
when its temperature changes from a value below to a value above the liquid crystal nematic-
isotropic transition temperature TNI It is convenient to write the refractive indexes of the
liquid crystal in term of the dielectric permittivity at optical frequencv
~l
" ?opt + )/h£opt j9a)
n( = iopt /h£opt (9b)
3
because [7] the average electric permittivity zopt is independent on the order parameter, while the dielectric anisotropy can be written as
/~£opt = ~h£]pts (lo)
where S is the usual molecular order parameter defined as
S
- 1~2 (fi 'i (ii)
is the molecular axis and fi is the nematic director. It has been shown [8] that
S = 11 0.98T)°~~ (12)
is an universal function of the reduced temperature
T = Tl ~~ (13)
where T is the temperature, V is the volume and TM and Vi are their values at the Nematic- Isotropic transition. The constant values of Iopt and Ae]~~ can be easily computed by the knowledge of ne and no for any given value of the temperature.
Since we neglect the density changes of the materials we will also assume that the polymer
refractive index np and the droplet radius R are constant.
BS TO
laser ~ ~l
beam
,
~ ,
,
' D~ ~~~~~~~~~~~~~~'LI
---,
Fig. 2 Experimental setup. C: Chopper, BS Beam Splitter, Di, D2: photodiode detectors, TO.
Thermostatic Oven, S. Sample, LI. Lock-In amplifier. Laser beam is produced by a 0.5 mW HeNe
laser.
.8
n
ne
i.ti
.4
20 30 40 50 T(°C) 60
Fig. 3. Ordinary and extraordinary refractive indices us temperature, given by equations (9).
4. Experimental Results and Discussion
PDLC material is achieved by Polymerization Induced Phase Separation (PIPS) the liquid crystal is dissolved in the prepolymer followed by polymerization [9] method. Sample compo- sition, by weight is: 33% of liquid crystal (E7 by BDH), 25.6% EPON 815 (by Shell Chemical
Company), 7.9% MK107 (by Wilmington Chemical Corporation), 29.7% Capcure 3-800 (by
Diamond Shamrock), 3.7% B-component (by BOSTIK). The solution is mixed, centrifuged and sandwiched between glass plates. Sample thickness is 20 ~m. Curing is performed at 60 °C for about 24 hours. Droplets diameter is of the order of1 ~m. At 20 °C the sample is opaque
(translucent).
Experimental setup is depicted in Figure 2. The probe beam is from a 5 mW He-Ne laser
(wavelength 1
= 632.8 nm) and impinges orthogonally on the sample. A photodiode (Di) is
used to measure the transmitted intensity, with a Chopper (C) and Lock-In (LI) configuration,
to reduce noise and background signal. A Beam Splitter (BS) is used to send a reference beam to a second photodiode (D2) in order to check beam stability. The Sample (S) is placed inside
a Thermostatic Oven (TO) and is measured using a Pt-100 thermoresistance. The liquid
crystal's refractive indexes at 20 °C are no
= 1.51 and ne
= 1.74, while the polymer's one is np = 1.54. The nematic to isotropic transition temperature is TM = 54.5 °C. In Figure 3 we
report the refractive indexes uerms the temperature as given by equations (9).
1102 JOURNAL DE PHYSIQUE III N°5
1.00
~hwem -Them.
~hoem
0.75
o.50
0.25
T(°cj o.oo
20 30 40 50 60 70 80
Fig. 4 Experimental values of the sample transmission ratio vs. temperature for two different samples are compared with values given by the model presented in the text (solid line).
In Figure 4 we report the sample transmission ratio uersw the temperature. Solid line represent the theoretical results while experimental results are shown by circles and errors are within circle size. How it can be seen, our model is quite accurate both in the nematic and in the isotropic phases. Just in a range of few degrees around the N-I transition, theory appears
not adequate to the phenomenon description. We attribute this failure to the hypothesis of
constant droplet order parameter that does not hold during the transition. Further work is
required to improve the model applicability to the transition.
Acknowledgments
We acknowledge the technical aids of A. Maggio, S. Avallone and S. Marrazzo
References
iii Zumer S., Light scattering from nematic droplets: Anomalous diffraction approach., Phys.
Rev. A 37 (1988) 4006.
[2] Basile F., Bloisi F., Vicari L. and Simoni F., Optical phase shift of polymer dispersed liquid crystals, Phys. Rev. E 48 (1993) 432.
[3] Kelly J-R- and PalRy-Muhoray P., The optical response of polymer dispersed liquid crys- tals, Mol. Cryst. Liq. Crgst. 243 (1994) il.
[4] Born M. and Wolf E., Principles of optics (Pergamon, 1980).
[5j Bloisi F., Ruocchio C., Terrecuso P. and Vicari L., PDLC: influence of droplet order parameter in light transmittance, Opt. Comm~n (1996) in press.
[6] Erdmann J-H-, Zumer S. and Doane J-W-, Configuration Transition in Nematic Liquid Crystal Confined to a Small Spherical Cavity, Phys. Rev. Lett 64 (1990) 1907-1910.
[7] de Jeu W-H-, Physical properties of liquid crystalline materials (Gordon & Breach Science Publishers, flew York, 1979).
[8] de Gennes P-G- and Prost J., The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993).
[9] West J-L-, Phase separation of liquid crystals in polymers, Mol. Cryst. Liq. Cryst. Inc.
Nonhn. Opt. 157 (1988) 427-441.
