HAL Id: jpa-00247647
https://hal.archives-ouvertes.fr/jpa-00247647
Submitted on 1 Jan 1992
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.
Twist viscosity coefficient of a dilute solution of the main-chain mesogenic polymer in a nematic solvent : an
estimation of the anisotropy and the rotational relaxation time of polymer chains
Evgeniy Pashkovsky, Tamara Litvina
To cite this version:
Evgeniy Pashkovsky, Tamara Litvina. Twist viscosity coefficient of a dilute solution of the main- chain mesogenic polymer in a nematic solvent : an estimation of the anisotropy and the rotational relaxation time of polymer chains. Journal de Physique II, EDP Sciences, 1992, 2 (3), pp.521-528.
�10.1051/jp2:1992146�. �jpa-00247647�
J. Phys. II France 2 (1992> 521-528 MARCH 1992, PAGE 521
Classification
Physics Abstracts
61.30G 61.40K 62.10
Twist viscosity coefficient of a dilute solution of the main-chain
mesogenic polymer in a nematic solvent : an estimation of the
anisotropy and the rotational relaxation time of polymer chains
Evgeniy E. Pashkovsky and Tamara G. Litvina
Institute of Macromolecular Compounds, Academy of Sciences of the U-S-S-R-, Bolshoi pr. 31, St. Petersburg 199004, Russia
(Received 22 July 1991, accepted 15 November199I>
AbstracL The dynamics of Freederiks transition at bend deformation in the magnetic field was used to study the visco-elastic properties of a dilute solution of mesogenic main-chain polymer in a low molecular weight nematic liquid crystal pentylcyanobiphenyl (SCB>. Analysis of obtained data based on Brochard's theory for polymer chains in the nematic environment provided the
temperature dependences for the anisotropy R,/R~ of chains (where R, and R~ are dimensions parallel and perpendicular to the nematic director> and for the rotational relaxation time of chains r~. The value of Rj/R~ decreased with temperature from 1.85 to 1.75 and r~ decreased according
to the Arrhenius law.
1. Introduction.
In recent years the behavior of polymer chains in the nematic environment was the subject of both theoretic and experimental investigations. One of the means of detecting the anisotropy
of polymer coils is the measurement of the twist viscosity coefficient of polymer solutions in a nematic solvent. The twist viscosity coefficient for both side-chain and main-chain mesogenic polymer solutions in a low molecular weight nematic solvent was measured by the study of the
dynamics of Freederiks transition [1-5]. This parameter is very sensitive to the presence of
anisotropic polymer chains even for dilute solutions. According to the Brochard theory [6], the twist viscosity coefficient of these solutions depends on both the anisotropy of form and
the rotational relaxation time of a polymer coil. Therefore, the determination of the
anisotropy of a polymer chain in the nematic solution by measuring the twist viscosity
coefficient is a very delicate procedure as it involves the use of some simplifying assumptions conceming the type of the temperature dependence of the rotational relaxation time [1, 3].
In this article we present the method of separating the contributions of the rotational relaxation time and chain anisotropy to the twist viscosity coefficient of a nematic solution by taking into account the backflow effect for Freederiks transition at bend deformation in the
magnetic field. Before discussing our experimental results we will consider the theoretical basis of our measurements and calculations.
522 JOURNAL DE PHYSIQUE lI N° 3
2. Theoretical basis.
The viscosity of isotropic liquids is very sensitive to the presence of a small amount of the
polymer because polymer chains occupy a large volume fraction. The well-known dumbbell model for isotropic systems predicts the increase in viscosity with polymer concentration
61~ = (CkT/N ) r/6
=
(CA IN ) R~/6, (1)
where C is the number of monomers per volume unit, k is the Boltzmann constant,
T is the temperature of solution,
r and A are the relaxation time and the friction coefficient of
a chain respectively, N is the degree of polymerization and R is the radius of gyration of a
chain.
Brochard adapted the dumbbell model to the case when a low molecular weight solvent is a nematic liquid crystal [6]. In nematic solvents the polymer coil becomes anisotropic, and the
description of a chain involves two size parameters R,j and R~ (parallel and perpendicular to the nematic axis) (I). Furthermore, the friction force is also anisotropic, and two friction
coefficients or two relaxation times associated with chain motions parallel and perpendicular
to the nematic director are necessary for the description of the dynamic behavior of a chain :
Since there are different types of flow in the nematic liquid corresponding to different types of relative orientation of the director, the velocity and the velocity gradient, the addition of
polymer chains will produce the increase of three Miesowitch's coefficients and of the twist
viscosity coefficient yi.
1~ = (C kT/N ) r~ (R jllR( (3 )
&1~~ = (CkT/N ) r~(R )/Rj)) (4)
&1~~ =
(C/2N A~ R( (5)
&yi = (CkT/N ) r~(R( -Ri)~/Rj)R)
,
(6)
where r~ is the rotational relaxation time of a chain. The value of yi may be easily measured
by the method based on the observation of the Freederiks transition dynamics [7]. The
increment &y~ depends on relaxation time r~ and dimensions Rjj and R~. Hence the
determination of contributions connected with dynamic (r~) and geometric (Rj and
R~) properties of a polymer chain dissolved in the nematic liquid should be carried out
separately. The separation of these contributions to the twist viscosity coefficient of the nematic solution may be achieved by measuring not only the twist viscosity coefficient, but also one of Miesovitch's coefficients of a solution (for example 1~1). Dividing equation (6) on
(3) and solving obtained quadratic equation, we have for the R~/Rjj ratio : (R(/Rj/)
=
I ± (&y~/&1~~)~'~, (7)
where signs « + » or « » correspond to oblate (R~ ~ Rj) or prolate (R~ < Rj) forms of a chain along the nematic axis, respectively.
Therefore, it is possible to obtain the R~/Rj ratio if the increments &y, and
&1~~ are known. Furthermore, the rotational relaxation time can be estimated from
equation (3) if the ratio R~/Rjj is obtained.
(I) For an isotropic coil R,~
=
R)
=
R~/3.
N° 3 POLYMER IN NEMATIC SOLVENT 523
3. Experimental.
The measurement of the twist viscosity coefficient y~ and Miesovitch's coefficient
1~~ was carried out by using the theory of Freederiks transition dynamics [7] for bend
deformation.
At large values of reduced magnetic field h
= H/H~ (where H~ is the threshold value
corresponding to the appearance of bend deformation) the twist viscosity coefficient decreases markedly as a result of the backflow effect. The decrease in effective viscosity yf(h as a function of h is predicted in [7] and depends on parameter A
= a j/y~ 1~1, where a~ is one of Leslie's coefficients :
where y/(0) is the twist viscosity coefficient measured at relaxation in zero field
(h
= 0) and X is the number related to the wave vector of the distortion k : X
=
kd/2, d is the thickness of the nematic slab. In figure I, the increase in to/t (to/t
= yf (0)/yf (h ) as a function of the applied field h is presented for pentylcyanobiphenyl (SCB) and for a polymer
solution (see below). Time constants t and to corresponding to the reorientation of the director were obtained by measuring time intervals between the first two fringes of the
conoscopic pattem that moves with respect to the conoscope axis [7]. The numerical solution of equations (8) and (9) provides the determination of the parameter A by using the fitting
procedure for data presented in figure I which gives dependences of t/to on h for the polymer
solution and the pure solvent at the temperature T
=
21 °C.
fIf /
O /y
»"
2 Zv'
~$
j t
2 3
Fig. I. Dependences of t/t ratio on the reduced magnetic field h for pure SCB (o) and the solution of PDFOB in SCB 16). Solid and broken lines correspond to A
= 0.842 and A
= 0.736 respectively.
In order to check the accuracy of our results we have compared values of A obtained in our
experiment with those obtained by combination of data of H. Kneppe et al. [8, 9] for the twist
viscosity measurements in the rotating magnetic field and for Miesovitch's coefficients of SCB. Figure 2 shows a comparison between the values of the parameter A calculated from [8, 9] and measured in this study. One can see that values of A obtained in our study agree
well with those calculated from [8, 9]. The small difference between our and literature data
can be ascribed to the difference of methods used in [9] and in our work because the authors of [9] noted that deviations in the absolute values of the twist viscosity coefficient from that
obtained in earlier measurements were observed in their study.
524 JOURNAL DE PHYSIQUE II N° 3
~_
4
48
~
~ x
x
17
~
o.6
T- Tni it)
g ,2 g -4 o
Fig. 2. Dependences of the parameter A versus T T~, for SCB (o) and the solution of PDFOB in SCB (/L). Points (x) were calculated from [8, 9].
The twist viscosity coefficient yi was obtained from the equation y~
= yf(0)/(1 A/6),
and y/ (0) was measured at relaxation in zero field : yf (0
=
2 X
a
to H) (where
Xa is the anisotropy of diamagnetic susceptibility).
The procedure of measuring of to and H~ with high accuracy was described in detail in [7].
The values of l~i were calculated by taking into account the relationship between
yi, a~ and «~ (yi
= a~ a~) and the data for the ratio a~la~ calculated from [8, 9]. The
value of «~la~ varies from 0.049 to 0.065 in the temperature range
12.5 < T T~~ < 3.5 K for pure SCB. We assumed that the behavior of the a~la~ ratio
was similar for both SCB and polymer solution at T T~~ < 3.5 K. This assumption seems
to be reasonable far from the clearing temperature for a dilute solution. Therefore, we restricted our calculations by the condition T T~~ < 3.5 K.
Homeotropic orientation was obtained by the treatment of glass plates in a 9b solution of
cetylpiridiniumchloride in alkohol. The cell thickness was 80-100 ~m.
We studied SCB commercially produced in the U.S.S.R. (clearing temperature 33.5 °C)
without further purification and a dilute solution of the main-chain thermotropic liquid- crystalline poly(decamethylene-fumaroyl-bis-(4-oxybenzoate) (PDFOB) in SCB
HO (CH~) to-j ~P-COO-<H~CH-COO-4~-COO- (CH~ )~o-OOC-)~(CH~)~OOH
,
(where ~P are phenylene rings). The synthesis of PDFOB and the molecular weight
determination are described in [10, 11]. The sample with M~ = 4 320 was used in this study. It
is known from [12] that for polymer samples with fl~= 3900-20000 the value of
polydispersity lies in the interval flw/M~
= 2.2 2.0. Therefore we can expect that for our
sample flw/fl~
< 2.2. This value of polydispersity is not negligible, however one can use the data obtained for polydisperse sample to estimate average values of Rjj/R~ and r~, because
individual polymer molecules contribute independently to the viscosity in dilute solutions [13]. Therefore, the values of y~ and 61~, in equations (3) and (6) are determined as a sum of
contributions of individual molecules and we can conclude that viscosity averaged values of
Rj/R~ and r~ are obtained for the solution of polydisperse polymer sample.
Melting and isotropization temperatures, obtained for PDFOB sample in bulk by DSC, (DSM-3, « Bioinstrument », Puschino, U.S.S.R.) were 130 and156 °C respectively. Obser-
vations performed with polarizing microscope with hot-stage «Boetius » (VEB Analitik)
show birefringent texture at T
= 130 -156 °C. However we did not observe thread-like or
N° 3 POLYMER IN NEMATIC SOLVENT 525
schlieren textures specific for the nematic phase, probably, because of the high viscosity of an
anisotropic polymer melt.
Brochard's theory describes the behavior of polymer molecules in the dilute regime. This
regime realizes when chains behave independently in the solution. Therefore equations (3)- (6) predict the linear increase in viscosity coefficients of dilute solutions with polymer
concentration C. For PDFOB sample with fl~=4320 in SCB the dependence of
y~ on C is linear at C
< 4 weight fb [4]. Hence, the polymer solution with C
= 1.01 wt.fb for the same sample was prepared. The solution was obtained by mixing the components at T
= 130 °C for I hour.
The homogeneity of solution was checked by microscopic and conoscopic observations and
was confirmed by good quality of conoscopic patterns. The clearing point of the solution was the same as that for pure solvent. The homeotropic geometry provides the determination of
K~/x~ and yf (0)/Xa ratios. The values of Xa were taken from [14] and it was assumed that the values of Xa coincided for SCB and for the dilute solution.
4. Results and discussion.
The dependences of the elastic constants on temperature for both SCB and the polymer
solution are shown in figure 3. The values of K~ for SCB are consistent with the results for K~ obtained by a combination of K~/K~ ratio [15] and the value of K~ [16] but are smaller than
those obtained for K~ by Karat and Madhusudana [17]. There is a discrepancy between the results of elastic constant measurements in the literature due to different factors. In our case,
we were interested in the relative effect of polymer chains on the elastic properties and
viscosity of solution. The value ofK~ is only slightly higher for polymer solution than for pure
solvent. This fact can be explained by a low concentration of the polymer in solution
(C =1.013 wt.9b). Furthermore, according to both theoretical and experimental investi-
gations [18, 19], the effect of semiflexible polymer chains on K~ is not very pronounced.
In our previous article, we have shown that there was no appreciable effect of concentration
of PDFOB on the twist elastic constant K~ for a polymer solution in hydroquinone-bis-
geptyloxybenzoate up to relatively high concentration (C
=
10 fb) [20].
The effect of polymer molecules on the twist viscosity of a dilute solution is higher than on the elastic constant K~. Figure 4 gives the temperature dependences of the twist viscosity
coefficients for SCB and for polymer solution. The relative increment of the twist viscosity
coefficient is about 30 fb for our solution at T T~,
=
12.5 K. This value is rather high as
compared with the same value for solutions of the side-chain mesogenic polymer with the
degree of polymerization N
= 130 [21]. In our case N
= 8.7, therefore one can expect a large anisotropy of polymer chains Rjj/R~ for PDFOB.
We determined the Rj,/R~ ratio by measuring the parameter A and twist viscosity
Yi (see experimental Sect.). The values of A for the polymer solution, presented in figure I,
are smaller than for a pure nematic solvent. The value of A is sensitive to the anisotropy of
viscosity and the order parameter of the liquid crystal. For well-ordered lyotropic polymer liquid crystals, A is about [22]. The higher the parameter A, the more pronounced the backflow effect. The decrease in A for solution is consistent with the idea of suppression of
the backflow effect by adding linear molecules of PDFOB to the nematic solvent. It is
interesting to note that adding comb-like polymer chains to SCB produces no effect on the parameter A [21]. Therefore, one can assume that the dynamics of linear chains in a nematic solvent differs from that for comb-like chains.
The Rj,/R~ ratio was calculated according to equation (7). The results for the Rj/R~ ratio
are shown in figure 5 as a function of temperature. The temperature range in calculations was limited by the condition T T~~ < 3.5 K, as noted in the experimental section.
526 JOURNAL DE PHYSIQUE II N° 3
n .«/~ ill)
oz
" f~~.~~
i§
x
~
0,f
~
~- Gi f~ ~ ~w/ ~i)
-f4 -/2 -J -4 a -/p -g -4 a
Fig. 3. Fig. 4.
Fig. 3. Elastic constant K~ versus T T~, for SCB (o) and the solution of PDFOB in SCB (A>.
Symbols (a) and (x) correspond to values taken from references [15, 16] and [17] respectively.
Fig. 4. Values of the twist viscosity yi versus T T~~ for SCB (o) and the polymer solution IA),
~~~i
~-<-
~
T- Tm f~ )
-?2 -8 -4 a
Fig. 5. Dependence of the axial ratio Rj/R~ of a chain versus T T~,.
It is surprising that the value of Rjj/R~ changes very slowly with temperature and Rjj/R~ < 1.85. This value indicates that linear chains in the nematic solvent are not rod-like.
This conclusion is also supported by the study of molecular weight dependences of the twist
viscosity coefficient for linear chains in a nematic solvent [23].
The rotational relaxation time r~ was calculated from equation (3). Figure 6 gives the temperature dependence of the rotational relaxation time of a chain. The value of r~ changes with temperature according to the Arrhenius law with activation energy W
=
7 893 ± 159 K : r~ exp(7 893/n. This value is higher than the activation energy
characterizing the temperature dependence of the twist viscosity coefficient for a pure solvent SCB : yi Xa exp (5 455/n. We have shown that W
=
5 570 ± 87 K for the rotational relaxation time of comb-like polyacrylate chains with cyanobiphenyl mesogenic side groups [21]. This value is very close to the activation energy for the twist viscosity coefficient of SCB.
Mattoussi et al. [2] have also obtained the data for dilute solutions of comb-like mesogenic polymers in a nematic solvent. They have shown that the temperature dependences for both the twist viscosity y of a pure solvent and the chain rotational relaxation time were described
by the same value of the activation energy W. This fact was accepted a priori in [I] for side-
N° 3 POLYMER IN NEMATIC SOLVENT 527
j-la? (~)
6
2 ~~~/ ))
-/2 -g -4 o
Fig. 6. Dependence of the rotational relaxation time r~ on the reduced temperature T T~,.
chain mesogenic polymers. Such a suggestion may be incorrect for linear mesogenic polymers
as follows from our data. The difference in the behavior of linear and comb-like chains can be
related to the more complex mechanism of rotational relaxation of linear chains in the
nematic environment.
5. Conclusion.
The experimental study of the dilute solution of PDFOB in the nematic liquid crystal SCB shows the strong effect of polymer molecules on the twist viscosity and a weaker one on bend elastic constant. It should be noted that even for highly concentrated (C ~ 20 wt.fb) solutions
of the aromatic polyester DDA-9 in p = azoxyanisole (PAA), studied by Gilli, Sixou and
Blumstein [24], the increase in bend elastic constant is negligible with respect to the increase in twist viscosity.
The determination of the parameter A which is connected with the backflow effect at bend deformation provides the value of Miesovitch's coefficient for the solution. This procedure gives the possibility to evaluate both the anisotropy of polymer chains in the nematic solution
and the rotational relaxation time of a chain.
The ratio characterizing anisotropy of polymer molecules Rjj/R~ changes from 1.75 to 1.85 in the temperature range T T~~ =
(- 3.5) (- 12.5 K). This result agrees with the model calculations of Rjj/R~ at isotropic-nematic transition for worm-like chain without hairpins given by d'Allest et al. [25]. However the value of Rj/R~ obtained in their study by Small-
Angle Neutron Scattering for DDA-9 polymer molecules dissolved in PAA is higher (Rj/R~ =5 for chains with M~=6000) than that obtained in our experiment. This discrepancy may be caused by the difference in the polymer/solvent nematic interaction :
DDA-9 has mesogenic cores chemically similar to PAA molecules, whereas chemical
structure of PDFOB units differs strongly from SCB molecules. Furthermore this difference
may arise from the different inherent chain flexibilities for PDFOB and DAA-9 (ester
linkage, connecting mesogenic cores with decamethylene spacer, are oriented in opposite
directions in PDFOB and DDA-9 molecules). Therefore, it might be interesting to study the influence of both polymer-nematic solvent interaction and inherent chain flexibility on the behaviour of polymer molecules in a nematic environment.
In the near future, we will study nematic solutions of comb-like chains in nematic solvents in order to compare their behavior with that for linear chains. Furthermore, it would be
interesting to check the effect of a decrease of the parameter A by using different polymer-
