Comb-like macromolecule conformation in smectic
phase. Interpretation of neutron-scattering data
A.B. Kunchenko, D.A. Svetogorsky
To cite this version:
A.B. Kunchenko, D.A. Svetogorsky. Comb-like macromolecule conformation in smectic phase.
Interpretation of neutron-scattering data. Journal de Physique, 1986, 47 (12), pp.2015-2019.
<10.1051/jphys:0198600470120201500>. <jpa-00210396>
HAL Id: jpa-00210396
https://hal.archives-ouvertes.fr/jpa-00210396
Submitted on 1 Jan 1986
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of scientific research documents, whether they are published 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.
DTCEMBRE 1986
N° 12
Tome 47
LE JOURNAL DE
J.
Physique
47
(1986)
PHYSIQUE
DÉCEMBRE 1986,
2015-2019
2015
Classification
Physics Abstracts
61.30 - 61.40K
COMB-LIKE MACROMOLECULE CONFORMATION IN SMECTIC PHASE.
INTERPRETATION OF NEUTRON-SCATTERING DATA
A.B.
KUNCHENKO* and
*Laboratory
D.A.
of Neutron
**Laboratory
SVETOGORSKY
Physics
of Theoretical
Physics
Joint Institute for Nuclear Research Dubna, Head Post Office,
P.O. Box 79, 10 10 00 Moscow, U.S.S.R.
(Regu
te 20
juin 1986, r6visg Ze
ler
octobre, accepté
Résumé : Des considérations théoriques simples permettent de définir la conformation
de la chaîne principale d’une macromolécule
peigne sur la base des spectres de diffusion de neutrons
aux petits
angles. La
chaîne macromoléculaire en phase smectique
est représentée par des pelotes quasi-bidimensionnelles placées au hasard dans les
différentes couches smectiques.
La taille
de
ces
sous-chaînes ne dépend pas de la
masse
moléculaire globale du polymère. Les
sous-chaînes bidimensionnelles sont reliées
entre
elles par des passages à travers les
couches.
Elles
peuvent être considérées
comme des défauts de la phase smectique. Le
modèle proposé ici permet de calculer le
nombre
de ces défauts à partir du rayon de
giration de la macromolécule smectique tel
qu’il est mesuré par la technique de diffusion de neutrons aux petits angles.
en
Ze 7 octobre 1986)
Abstract :
Simple theoretical considerations
allow us
to define the conformation
of
the macromolecule main chain from neutron experiment
The macromolecular
data.
chain in the smectic phase is divided into
quasi-two-dimensional coils randomly placed
in
different smectic
layers. The size of
these coils is
independent of the polymer
molecular
weight. The two-dimensional subcoils
are connected
with each other by a
number of crossings of the layers. They can
be
considered as defects of the smectic
phase. The model proposed here allows us to
from the
calculate
the number of defects
radius
smectic
of
of
the
gyration
measured by small
macromolecule which was
angle neutron scattering.
’
There has been growing interest in the
study of the liquid-crystalline (LC) state
of polymers in different mesophases [1-3].
The method of selected deuteration provides
direct
information on the conformation of
the macromolecule in the bulk from neutron
scattering data.
mesophases performed by small angle neutron
scattering (SANS) are presented in [4,5].
In
[6] the interpretation of the neutron
scattering data for the LC polymer in the
nematic phase is given.
This
First
dius of
measurements of the main chain ragyration in the nematic and smectic
of
paper deals with the interpretation
data of neutron
available
on smectic polymers from [5].
presently
scattering
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198600470120201500
2016
1.
Experimental data 5 .
In the paper
[5]
the chain of the
type :
has
been investigated by SANS and neutron
diffractions
(ND). The molecular weight is
3 x 10‘5
Dalton. The macromolecule of such
a
polymer contains 680 monomers and has a
contour length 1700 A.
such defects.
The
measured values
of the projections
the radius of gyration for the macromolecule in the smectic phase are :
(1) The chain accomplishes random walks
in
the
smectic
layer plane so that the
backbone of the macromolecule is located in
the
aliphatic layer. Let us describe the
flexibility of such a two-dimensional chain
by the Kuhn segment b,.
of
where
radius
R.
and
Ry
are
of
gyration
pendicular (x) and
Let
us
jointed
construct
the model
of a freely
chain with the following proper-
ties :
the
projections of the
the directions perparallel (y) to the
on
smectic layer plane.
(2) The chain accomplishes random walks
between the
intermediate
layers with the
step equal to the inter/layer thickness D.
Since
crossing through the smectic
is quite difficult, it must be taken
into
account by introducing different probabilities for the
steps of the freely
jointed chain in the plane and between the
(3)
The
total radius
of gyration of the main
cromolecule
the
smectic phase can be
expressed by projections :
layer
layers.
The
measured value
of the radius of gyration in the isotropic phase is
The
simplest way to do it is to use the
lattice model.
In
this case
the space distribution function
for one segment of the freely jointed
chain is :
The
comparison between (2) and (3) shows
that
the rigidity of the macromolecule is
greater in the smectic than in the isotro-
pic phase.
The
thickness of
the smectic layer D is
measured by the ND method
2. The Model of
an
anisotropic freely
jointed chain.
The
large anisotropy of the projections
of the radius of gyration of the LC polymer
chain in the smectic phase
macromolecular
is the result of the difficulties in crossing through the mesogenic layer. It is
natural since the smectic phase can be conas
a
sidered
microphase separation of
mesogenic and aliphatic parts [7].
Let
us refer
to the part of the chain
layer as the
intersecting the smectic
crossing
segment. It is reasonable to
assume
that
the
crossing segment will
straighten and so will be practically persmectic
to
the
layer. The
pendicular
crossing segment forms a defect in the
smectic
layer on the-molecular level. The
this
defect is
of
structure
detailed
unknown,
though the SANS method, as shown
below, allows us to evaluate the number of
where
is the
is
the Dirac delta function and p
normalized probability of the inter-
6
layer crossing.
If
1/3, then the step probability is
p
equal for all three directions.
=
As is well-known, the mean square distanof a freely jointed
ends
the
between
chain is
ce
N is the number of chain segments, r
where
is
the radius vector of one Kuhn segment
and
(r)2
is
given by :
2017
Taking (5) and (7) into-account
for the anisotropic chain :
we
obtain
random walks will not affect the R,
owing to the small thickness of the
intermediate
layer, but
they must be
accounted for
in the
expression for the
contour length (12).
These
value
the mean square projections
of the
distance
between the
ends of the chain we
obtain :
For
Let us denote
the contour length of the
chain outside the plane by A L,. It is reasonable to suppose that :
where A is the
segment of the
mediate layer.
contour length per Kuhn
freely jointed in the inter-
mean
With
(16) taken
(12) becomes :
It
well-known
is
that
and average distance between the
those of the real chain.
ends
as
(5-10 A).
segment
where L is the contour
of the chain.
the
ized
from :
And
by
where A is an unknown quantity. Let us
it
is
of
the order of the
suppose that
thickness
of
the
intermediate
layer
A and
The magnitude of
the Kuhn
the number of
such segments
are defined as :
In
account equation
real chain
any
(without effects of excluded volume) can be
approximated by an equivalent freely jointed chain which has the same contour length
length
into
in the chain
For convenience we introduce in
(14),
(15)
and
(17)
the
equations
following nota-
tion :
then these equations become :
case when the chain is charactertwo
segment bl and D, we find N
using (5) and (7)
we
obtain :
and N1
are the
average numbers of the
chain segments oriented normally and parallel
to the smectic layer, respectively.
For the isotropic distribution :
N,
rhe radius of gyration depends on the distance between the ends of the chain as :
The
quantities R, and
perimentally,
Therefore,
radius of
for
gyration
the
we
projections
of
the
from
(19)
therefore
D are measured ex-
N,
can
be defined
as :
have :
this is the number of crossing segments
(defects) for one macromolecular
chain. The quantity
Ni :
In
equations (12) , (14) and (15) the
quantities Rx, Ry and D are determined experimentally, the contour length L is a
known quantity, and the chain parameters N,
b, and p are unknown quantities.
It
must be
taken into
account that the
real chain performs random walks not strictly in the plane, but within the whole
intermediate layer of a finite thickness.
is
a
Now
characteristic of the smectic phase.
let
us
estimate the accuracy of the
quantity k. Expression (24) is obtained under
the assumption
that the crossing
segment is stretched as far as possible,
2018
i.e.
it
Another
has
transconformation.
in (24) reflects the indefinite
thickness of
and mesogenic
intermediate
layers. Nevertheless, all this does not influence the quantity N//.
inaccuracy
Using equations (20)
and (21)
define
we
Correspondingly for the projection of the
of gyration and the chain length of
radius
one subcoil we obtain :
.
-
Li is the average length of the subchain. (In general,
and
largely
since crossing
segments appear occasionally for the real subcoil). Note that
the
quantities in (32) and (33) are independent of the uncertainty in A, while bl,
N and p
seen from
as is
(25),
(26) and
(28), depend on A. Here are these quantities for two values of A :
where
h1y
coil
vary
Ll
where :
The quantities bl and N1 are defined with
accuracy of the second order of the parameter
At last, let us express p in
terms of new variables :
an
A/bl.
3.
Calculation of
model chain.
Using experimental
we
the parameters
data from [5]
for the
and
(23)
obtain :
This
is the
number of crossing segments
for one macromolecular chain of the polymer
with a given molecular weight. From (24) we
obtain for k :t
i.e.
crossing segments
amount to approxima6 % of the total chain length.
tely
is seen
N and p
rameter A.
As
bi,
from (34)
and (35), values of
depend rather weakly on the pa-
Let
us
take bl - 60 A . The comparison
between bl
and
Kuhn segment for the
the
in the isotropic phase (39 A) indicacoil
the chain
tes
a considerable
increase of
rigidity in the two-dimensional subcoil. It
is
caused primarily by the decreasing numin the quasi-two-diber
of gauche-somers
mensional
chain and by effects of excluded
volume appearing in this case [8].
In
the three-dimensional
case, according
to
the Flory theorem, the chain behaves as
in ideal one and effects of excluded volume
can be neglected.
It follows from all this that it is desito measure the Kuhn segment directly
rable
by the Kratky technique [9]. Measuring only
Ry is not sufficient for a precise definition of b-L because of the uncertainty in A
off excluded volume
influence
the
and
effects.
crossing segments divide the chain
+ 1 quasi-two-dimensional subcoils.
typical conformation of the macromolecu-
N,
into
A
N,
lar
chain of
the
shown in figure 1.
The
of
mean
such
a
smectic
LC
polymer is
square distance between the ends
subcoil
its
internal
down :
Chy)z
structure
is
and
independent of
we
can
write
the
experimentally measured
projection of the radius of gyration for
the whole coil. Using (31) and from (1) we
obtain :
where
Ry
is
Fig. 1.- Typical conformation of the macrobackbone.
molecules
Quasi-two-dimensional
3 placed in the intermediate layer
connected with crossing segments 4.
These
segments create defects in the mesogenic layer 2. (Experimental data are taken
subcoil
1,
from
are
[5]).
2019
4. Temperature effects [10].
projection of the radius
in the
macromolecule
Studies of the temperature dependence of
the
projections of the macromolecule main
chain radius of gyration can give information on the nature of
defects of smectic
comb-like LC polymers.
Supose that the smectic phase is in the
equilibrium state, i.e. there is a dynamibalance in,the processes of appearance
disappearance of smectic defects at a
given temperature. In this case the probaof
defect
bility
appearance p can be
written down as follows :
cal
and
of gyration of the
direction x (Fig. 1)
determine the number
and using (23) one can
of crossing segments (defects)
N,,.
The crossing segments divide the macromolecular
chain into quasi-two-dimensional
parts with the conformation of a statistical
coil.
The
average size of these
subcoils can be defined using (31) and measuring the projection of the radius of
gyration in the y -direction.
influence of
Absence of data on the
excluded volume effects and random walks of
the main chain in the x. -direction in the
range of the intermediate sublayer prevent
a precise definition of the Kuhn segment bl
in
the plane.
Therefore, it is desirable
that the Kuhn
segment (or the persistence
length) should be directly measured in the
the
smectic
Kratky
layer
plane
by
technique.
where R is the molar gas constant, T is the
temperature and e- 6FIRT is the statistical
of
of
the
weight
appearance
crossing
segment.
Estimating with (36) the energy of a
smectic defect E (© F N E) at T = 330 K for
p = 0.01 obtained in (34) we have :
hope that the use of small-angle neuscattering and neutron diffraction
along with other methods (X-ray diffraction, NMR etc.) will soon give a complete
idea of the comb-like LC polymer structure.
We
tron
Acknowledgments
to V.P.
Shibaev, L.B.
R.V. Tal’roze and S.G. Kostromin
for numerous
from the Moscow University
thank our colleagues
also
discussions.We
V.K.
Ju.
M.
Ostanevich,
Fedyanin, J.
for discussions
and V.B.Prieszhev
Plestil
and critical comments.
We
grateful
are
Stroganov,
The
temperature
known E) is :
dependence
of
p (with
References
and using (14)
dependence :
we
obtain
the
temperature
[1]
Liquid
by
edited
New-York,
Cristalline Order in
Blumstein
London) 1978.
A.
[2] Shibaev V.P., Plate N.A.,
Sci. 60/61 (1984) 173.
The
polymer considered is
in the smectic
phase in the temperature range from 45°C to
110°C.
For this temperature difference, we
obtain, using (39) :
Thus the
increase
equilibrium theory predicts a 10 %
in the smectic temperature
of R.
range.
Note that the defect energy E is composed
of
the segregation energy of mesogens and
aliphatic parts of the macromolecule and
the energy of the main-chain bending.
5. Conclusions.
to the assumptions of the prepaper random walks of a polymer chain
two
can
be
into
divided
types - random
in
walks
smectic
the
layer and those
between layers In the latter case the step
of random walks equals the thickness of the
smectic
layer. Therefore, measuring the
According
sent
Adv.
Polym.
[3] Polymer Liquid Crystals, edited by
Ciferri A., Krigbaum W.R., Meyer R.B. (Academic press, New-York, London) 1982.
[4]
Rapid
---- , -m in ,
Polymers,
(Academic press,
Chem.
Kirste R.G., Ohm H.G., Makromol.
Commun. 6 (1985) 179.
[5] Keller P., Carvalho B., Cotton J.P.,
Lambert M., Moussa F. and Pépy G., J. Physique Lett. 46 (1985) L-1065.
[6] Kunchenko A.B., Svetogorsky D.A.,
mitted to Liquid Cristals.
[7]
de
Crystals
Sub-
P.G., The Physics of liquid
(Oxford Univ. Press, London and
Gennes
New-York) 1974.
P.G., Scaling Concepts in
(Cornell Univ. Press,
Ithaca and London) 1979.
[8]
de
Polymer
[9]
Gennes
Physics
Kratsky O.,
Pure
Appl.
Chem.
12
(1966)
483.
[10] The probability p of interlayer transition with a temperature dependence similar to (38) was also used by W. Renz and M.
Warner in Phys. Rev. Lett. 56 (1986) 1268.