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Temperature dependences of the twist viscosity coefficient for solutions of comb-like mesogenic polymer
in a nematic solvent : estimation of the anisotropy and rotational relaxation time of chains
Evgeniy Pashkovsky, Tamara Litvina, Sergei Kostromin, Valery Shibaev
To cite this version:
Evgeniy Pashkovsky, Tamara Litvina, Sergei Kostromin, Valery Shibaev. Temperature dependences of the twist viscosity coefficient for solutions of comb-like mesogenic polymer in a nematic solvent : estimation of the anisotropy and rotational relaxation time of chains. Journal de Physique II, EDP Sciences, 1992, 2 (8), pp.1577-1587. �10.1051/jp2:1992223�. �jpa-00247753�
Classification Physics Abstracts
61.30G 61.40K 62.10
Temperature dependences of the twist viscosity coefficient for solutions of comb-like mesogenic polymer in a nematic
solvent : estimation of the anisotropy and rotational relaxation
time of chains
Evgeniy E.Pashkovsky (I), Tamara G.Litvina (I), Sergei G.Kostromin (2) and
Valery P. Shibaev (~)
II) Institute of Macromolecular Compounds of the Russian Academy of Sciences, Bolshoi 31, St.-Petersburg, 199004, Russia
(2) Chemical Department, Moscow State University, Leninskye Gory, Moskow, 119899, Russia (Received and revised 28 April 1992, accepted 4 May J992)
Abstract. The dynamics of Freederiks transition at bend deformation is used to study the visco- elastic properties of dilute solutions for three fractions of the side-chain mesogenic polyacrylate in the nematic solvent, pentylcyanobiphenyl (SCB). Values of the bend elastic constant K~ for
polymer solutions are higher than for pure SCB, especially for solutions of fractions with a
relatively high degree of polymerization. The strong effect of polymer molecules on twist viscosity
is also observed, but this effect has only a slight dependence on the degree of polymerization.
Analysis of obtained experimental data based on the Brochard theory gives the values of the
anisotropy of chain dimensions R~/Rj (where R~ and Rj are the dimensions perpendicular and
parallel to the nematic axis, respectively). Values of the rotational relaxation time of the polymer
chains are also obtained.
Introduction.
The study of liquid~crystalline (LC) polymers was the subject of intense scientific interest last decade. Particular attention was attracted to theoretical description of the behaviour of
polymer molecules in the nematic medium. At first de Gennes developed a phenomenological model giving the temperature dependence of dimensions of polymer linear chains in the
nematic environment [I]. Later Warner et al. [2], ten Bosch et al. [3], Rusakov and Schliomis [4] presented more detailed theories on this subject. The main result of these theories was the
dependence of macromolecular shape on both the intrinsic chain flexibility and the value of order parameter S of the nematic environment. Main~chain polymer molecules become
extended along the nematic director and the anisotropy of the shape increases with the order parameter. The situation is more complicated for comb~like polymer molecules for which the Renz and Wamer theory [5] predicts either prolate or oblate shape in a nematic environment
depending on the volume fraction of mesogenic side chains in the comb and the nematic order
parameter. Measurements of the gyration radii parallel (Rjj and normal (R~ ) to the director
by the small angle neutron scattering gave a strong anisotropy, R~ » R
ii, in the smectic phase
but a smaller one in the nematic phase [6-8].
Another experimental way to observe the chains behaviour in the anisotropic medium is to
study their dilute solutions in low molar mass liquid crystals. Individual polymer molecules contribute independently to the viscosity in such solutions and their shape and dimensions can be related to viscous properties of the solution. The theory of Brochard for dilute solutions of
anisotropic dumbbells in a nematic environnlent [9a] predicts a strong dependence of Miesowitch coefficients l~j, 1~~, 1~~, and twist viscosity yj on the anisotropy Rj/R~ and the rotational relaxation time T~ of the chain in the solution.
In a previous paper [10] we have developed the method for estimation of Rjj/R~ and T~ for main-chain mesogenic molecules dissolved in a low molar mass nematic solvent. This method was based on the measurements of the twist viscosity coefficient of polymer solutions
by the observation of Freederiks transition at bend deformation ii Ii and the comparison of obtained data with Brochard's theory [9a].
It was shown, for example, that the ratio Rj /R~ for main-chain mesogenic macromolecules
dissolved in the pentylcyanobiphenyl (SCB), changed from 1.85 to 1.75 with increasing
temperature. We have obtained also the temperature dependence of the rotational relaxation time of chains which obeyed the Arrhenius law : T~ oz exp(6 771/T).
In this paper we present a study of the visco-elastic properties of solutions of three fractions of the side-chain mesogenic polyacrylate with cyanobiphenyl mesogenic groups in the nematic solvent SCB. Estimates of the anisotropy and the rotational relaxation time of polymer chains in the nematic medium are provided. These data are compared to those obtained for main-
chain polymer solutions.
Experimental.
Three fractions of polyacrylate (') with cyanobiphenyl mesogenic side groups (PA-6)
-j-cH~CH ]-
,
N
= 25, 65 and 130
N
~ ~
~-(CH~)~-O / ~ / ~ CN
were dissolved in SCB at T
= 130 °C for I hour. We used SCB (T~i
=
33.5 °C) commercially produced in the USSR without further purification. Some molecular characteristics and
mesomorphic properties of three polymer fractions are given in table I. The homogeneity of
polymer solutions was checked by microscopic observations. Good quality of conoscopic pattems and homeotropic orientation of samples confirmed the homogeneity of solutions.
Determination of clearing temperatures T~i of the solutions (± 0.25 K) was carried out by using a polarizing microscope «Boetius» (VEB Analitik) with a hot stage. Careful
determination of T~i for studied solutions is necessary to compare the measured physical properties at the same reduced temperature, T~
=
T T~i. However, the determination of the clearing temperature for nematic solutions is a rather delicate procedure because of the existence of the nematic isotropic biphasic range. This problem was theoretically described
II) The synthesis of these samples is described in reference [12].
Table I. The value ofmolar mass Mw, polydispersity (Mw/M~), the degree ofpolymerization NW, concentration C and clearing temperature T~~(p for solutions of three polymer fractions
in SCB. N~~ and N are reentrant nematic and ordinary nematic phases and S~ and I are smecticA and isotropic phases respectively.
p/ jj io- 3 jj~/jj C, wt fb T~i(p) °C Transition temperatures *
25 8.53 1.39 3.44 36.0 N~~ 72 S~ 106 N 119
2 65 22. I 1.15 2.78 33.5 NRe 79 SA 123 N 1281
3 130 46.3 1.19 2.67 33.5 NRe 82 SA 129 N 1331
(*) Transition temperatures for bulk polymer samples are given in C.
by Brochard [9b] who showed that the pseudo~transition temperature, T~i(p) for a polymer
nematic solution is located betpeen the upper and lower temperature boundaries of the
biphasic range. According to lever law for phase diagrams this pseudo-transition point corresponds to equal contents of isotropic and nematic phases in the polymer solution. We
have determined the pseudo-transition visually as a point when the areas of dark and
birefringent regions were equal. The temperature T~~(p) determined in such a way was very close (0.5-1 K) to the lower temperature boundary of the biphasic range, whereas the upper
one was higher by about 15-20 K. Similar results were obtained by Mattoussi et al. [13] for dilute main-chain mesogenic polymer solutions in a nematic solvent.
These data are consistent with a very low value of the Flory-Huggins parameter for the
mesogenic polymer~nematic diluent system (see Eq. (13) in [9b]).
The theory of Brochard describes viscous properties of dilute nematic solutions [9a].
Therefore it is necessary to determine the range of concentrations corresponding to the dilute
regime. We have determined that the solutions with concentration C
~ 3.44 weight fb
correspond to the dilute regime as it follows from figure I which gives the concentration
dependence of the ratio yj/Xa (where yj is the twist viscosity coefficient and x~ is the
anisotropy of diamagnetic susceptibility). This dependence was obtained for the fraction 3 IN
= 130), which has the largest value of molar mass. As far as this dependence has a linear character we can conclude that for C
~ 3.5 weight fb and for fiiw
~ 44 100 at T
~ 21 °C the
dilute regime of studied solutions of polyacrylate fractions takes place. Thus the theory of Brochard can be applied to analyze the experimental data for solutions of polymer fractions listed in table I.
The twist viscosity coefficient and bend elastic constant K~ for solutions were measured by
the Freederiks transition experiment for bend deformation (homeotropic orientation of the
director and horizontal magnetic field). Homeotropic orientation was obtained by the
treatement of glass plates in I fb of cetylpiridiniumchloride in alkohol. The values of cell thickness were 80-100 ~Lm. All other details of measurements were described in our previous paper 110]. Here we would like to remind only some general points conceming the calculation of the ratio R~/Rj and the rotational relaxation time.
Brochard's theory predicts the increase of the twist viscosity and Miesowitch coefficients for
polymer solutions with respect to the values for the pure nematic solvent. Corresponding
increments of viscosity coefficients (for example, the Miesowitch coefficient 31~
j and the twist
viscosity coefficient 3yj) depend on polymer concentration C, degree of polymerization
YJ ~~-7jpoise/cm~.g~~)
/ ~
2
I
c, wt 9b
o ~ i
Fig. 1. Dependence of the value of yj/x~ on polymer concentration C of the nematic solution of PA-6 with N
=
130 at T
= 21 °C.
N, rotational relaxation time T~, and geometrical parameters of the chain, R~ and Rjj :
~
CkT R?
~~ N ~~R( 11)
~~ CkT
lR( -R?)~
N ~~ R?R( 12)
where k is the Boltzmann constant and T is the temperature. Dividing equation (2) by
equation ii) and solving obtained quadratic equation one has for the anisotropy of the chain the following expression :
iR~/Rjj>2 = ± 13yi/3ni>'/2 13>
where signs « + » or « » correspond to oblate or prolate shape of polymer molecules along
the nematic director.
In order to determine the values of 3 yj and 31~
j we used the theory of Pieranski et al. [I I]
for the dynamics of Freederiks transition at bend deformation. The dynamics of bend deformation allows to determine two ratios, K~/xa and yf/Xa, where K~ is the bend elastic constant and yi* is the effective twist viscosity. The value of yf(h) depends on the reduced
magnetic field h
= H/H~ (where H~ is the threshold field, above which the nematic layer
becomes distorted). Backflow effect, accompanied by the hydrodynamic motion of molecules
resulting from the director rotation in the magnetic field takes place at bend deformation.
This effect may be very pronounced and causes sufficient decrease of the measured twist
viscosity coefficient y((h) as compared to the value of yj for pure twist deformation.
The value of y((h) diminishes from
yj*io>
= viii -A/6> 14>
to
vii«>
= viii -A 15>
where the limiting values y((0) and y((m ) correspond to the relaxation of bend distortion in zero field (h
= 0) and deformation in infinite field (h
=
m) respectively, and the parameter A is a combination of yi, Leslie's coefficient a~ and the largest Miesowitch
coefficient ~
i
A=«]/Yi .Yti 16)
The absolute value of a~ is very close to yj as yj = a~ a~ and a~ « a~ [. Hence, the
value of A can be considered as the ratio of the rotational viscosity to the Miesowitch shear viscosity : A
= y j/~j. The higher is this ratio, the more pronounced is the backflow.
The parameter A was determined independently by fitting the experimental values of the response time of the nematic cell, obtained as a function of applied magnetic field, to the theoretical dependences given by Pieranski et al. [I Ii. This procedure is described in detail in [10]. The values of A were used to calculate the twist viscosity coefficient yj, given by equation (4). Values of yf(0) were measured at relaxation of the bend distortion in zero
field: yi*(0)=2XatoH/ (where Xa, to, and H~ are the anisotropy of diamagnetic
susceptibility, relaxation time, and threshold field, respectively). The procedure of determi-
nation to and H~ with high accuracy is described in detail in [11]. The values of
~j were calculated from the experimental data for A and yj and the literature data for the
ratio a~la~ for SCB, given by Scarp et al. [14]. As dilute solutions were studied, the
assumption was made that a~la~ for polymer solutions and SCB coincided. Furthermore, as it
has been mentioned above, the coefficient ~j can be calculated in assumption that
yj = a~ as yj = a~ a~ and a~la~ ~ 0.06 at T T~i ~ 3 K (T~~ is the clearing temperature). In both cases calculated values of ~
i were quite similar. Our calculations of the
R~/Rj ratio and the rotational relaxation time were restricted by the upper temperature limit
T T~~ ~ 3 K.
The values of x~ for SCB were calculated from the empirical dependence xa
= 0.17
11 0.9995 T/T~~) 0.141crn~ g~ ', given by Buka and de Jeu [15]. We have considered that x~ for dilute solutions and pure SCB coincided due to the similarity of the chemical structure of side mesogenic groups and solvent molecules.
Results and discussion.
The observation of the Freederiks transition provides both viscous and elastic properties of nematic liquid crystals. For convenience, at first we shall describe the elastic properties of nematic solutions at bend deformation.
Figure 2 shows the temperature dependences of the elastic constant K~ for the pure SCB and for solutions of polymer fractions in SCB. Our data for the pure SCB are in a very good
agreement with those obtained by Scarp et al. [14]. The values of K~ for dilute solutions of different fractions of PA-6 in SCB are higher than K~ for the pure solvent. The effect of solute
polymer on the elastic constant K~ is very pronounced for fractions with the degree of polymerization N
= 65 and N
= 130. The values of K~ for these solutions are approximately
twice higher than the values of K~ for the pure solvent. For the solution of the fraction with N
=
25 only nuoderate increase of the elastic constant K~ was observed.
It is interesting to compare these data with the results obtained by Mattoussi et al. for the solutions of the comb-like polydimethylsiloxane in the low molar mass nematic phenylben-
zoate II 6a]. No effect of polymer molecules on the splay elastic constant Kj was observed for
such solutions. We did not also observe the appreciable effect of main-chain polymer
molecules on the twist elastic constant K~ for concentrated nematic solutions [17]. One can conclude that the influence of polymer molecules on elastic properties of nematic solutions is
/l3 ./0~~fJ/)
a
Pa a
. Q
. Q
. ~
~ .
~ Q
~ . u
lo ~ .
6 ~ "
~ o ~
m6
m~ 6
7- 7~z It ) m
fl
~% -5 a
Fig. 2. Temperature dependences of the elastic constant K~ for SCB IA) and solutions of PA-6 fractions with N
= 25 (o), N
=
65 (Q) and N
=
130 (.) in SCB. The data obtained by Scarp et al. [15]
are depicted as (m).
not universal and depends on both the type of deformation and the molecular structure of the
polymer and the nematic solvent.
Figure 3 shows the temperature dependence of the twist viscosity coefficient yj for the pure SCB and the solutions of different fractions. The values of yj for SCB are somewhat higher
~~ j (Pl.£)
8
R ,z
R
~
~
~j
6
. "
~
. ~
m ~
T- v
la -I o
ig.
PA-6 ractions ith
[151 are as (m).
than those obtained by Scarp et al. [14], but this discrepancy is not significant. The values of yi for dilute solutions are approximately twice higher than the value of yj for SCB, but it is evident that the temperature dependences for all three solutions are situated very closely despite of the different values of the degree of polymerization N.
Equation (2) predicts that the effect of N on the value of 3yj is determined by the type of dependence of the rotational relaxation time on the degree of polymerization :
3yjjNoz T~(N)ccN" (7)
yic
The value of y) in the left side of (7) allows to exclude the temperature dependence of
T~(T~ cc y)(T T~ (N ) (~). The geometrical factor in equation (2), namely, (R( Rji)~/Rj(R(, does not depend on N for both Gaussian coils and globular molecules.
Therefore this factor is absent in equation (7). Figure 4 demonstrates a linear dependence of
In(3yiN/y)C) vs. lnN at three different temperatures for the solutions. The slope
a of this line was determined with a rather high accuracy despite of small number of fractions used in our study ; a = I.ll ± 0.08.
According to Brochard's theory, rotational relaxation time is the combination of two
relaxation times associated with motions of a chain parallel Tjj and perpendicular
T~ to the director :
TR " T[( + Tl (8)
Let us assume that the dependences of
Tjj and T~ on the chain dimensions are described by
the identical values of the dynamic critical exponent z [18] :
Tjj cc R( and T~ cc R[ (9)
8yj
In -N
CY)
3
2
In N
3 ( ~
Fig. 4. -The value of In (8y~N/Cy)) versus In IN) for dwferent T- Tm. lo) 21°C, IA)
26 °C and ID) 32 °C.
j2) ~~ ~z y)~z exp (WIT ),
as it is shown below.
Thus we obtain for the rotational relaxation time the following expression :
RiR[
~~ ~
T~cc ccN ccN (10)
Ri+R[
The exponent v characterizes the dependence of chain dimensions on N : Rjj cc R~ cc N ",
v = 1/2 for ideal statistical coils and v
= 1/3 for globules. The value of is equal to 3 in Zimm's
non-draining limit and experimental investigation of dynamic properties of polymer coils in
isotropic solutions gives usually z ~ 3 [18]. Therefore the result for comb-like chains of PA-6,
a =
I-I I is consistent with a rather compact conformation of polymer molecules in the solution, because for globules a
=
I.
We have also obtained different values of a for two main-chain mesogenic polymer with
different chemical structure [19, 20]. These values of a corresponded to non-draining
la =1.47 ±0.07) and free-draining la =1.98 ± 0.13) regimes of dynamic behaviour of
chains. However, it is difficult to estimate the conformation of macromolecules in nematic
solutions by using viscosity measurements. According to recent theory of Wang [21],
hydrodynamic radius of non-draining chains in the nematic solution is not a function of the
degree of polymerization alone, but also depends on Miesowitch viscosity coefficients of a nematic solvent and the anisotropy of chains. This situation is different from ordinary isotropic polymer solutions, where hydrodynamic properties of macromolecules are con-
sidered to be independent on the solvent viscosity.
Figures gives the dependences of the parameterA on the reduced temperature IT Tm) for solutions of different polymer fractions together with the pure solvent SCB.
The data obtained for the parameter A for all solutions and pure SCB can be approximated by
the unique curve :
A
= 1.2512(1- T/T~~)°.'~~
We can conclude that this parameter is quite similar for both SCB and PA-6 solutions. Hence, the backflow effects for polymer solutions and pure solvent are the same, since the value of A controls these effects, as was noted above.
o,
6
D a
f/ O~
°Q 6~
~ ~Q
k7
7 Twj (/~)
« IQ -< Q
Fig. 5. Temperature dependences of the parameter A for pure solvent SCB IA) and for solutions of PA-6 fractions with N
= 25 (o), N
= 65 (D) and N
= 130 (.),
