Analysis/Reactions/Morphology

265 Pages·1985·5.215 MB·English

by  R. W. Richards (auth.)

Advances in Polymer Science
Fortschritte der Hochpolymeren-Forschung
Analysis/Reactions/
Morphology
With Contributions by
P.-J.M adec, E. Markchal, J. E. Mark,
T Otsu, R. W Richards, J. F?Q ueslel,
T Sato, B.Tieke
With 98 Figures and 31 Tables
Springer-Verlag
Berlin HeidelbergN ew York Tokyo
ISBN-3-540-15482-5 Springer-Verlag Berlin Heidelberg New York Tokyo
ISBN-0-387-15482-5 Springer-Verlag New York Heidelberg Berlin Tokyo
Library of Congress Catalog Card Number 61-642
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Editors
Prof. Henri Benoit, CNRS, Centre de Recherches sur les Macromolecules, 6,
rue Boussingault, 67083 Strasbourg Cedex, France
Prof. Hans-Joachim Cantow, Institut fur Makromolekulare Chemie der Uni-
versitlt, Stefan-Meier-Str. 31, 7800 Freiburg i. Br., FRG
Prof. Gino Dall’Asta, Via Pusiano 30, 20137 Milano, Italy
Prof. Karel DuSek, Institute of Macromolecular Chemistry, Czechoslovak
Academy of Sciences, 16206 Prague 616, CSSR
Prof. John D. Ferry, Department of Chemistry, The University of Wisconsin,
Madison, Wisconsin 53706, U.S.A.
Prof. Hiroshi Fujita, Department of Macromolecular Science, Osaka Univer-
sity, Toyonaka, Osaka, Japan
Prof. Manfred Gordon, Department of Pure Mathematics and Mathematical
Statistics, University of Cambridge CB2 ISB, England
Prof. Gisela Henrici-Olive, Chemical Department, University of California,
San Diego, La Jolla, CA 92037, U.S.A.
Prof. Dr. habil. Gtinter Heublein, Sektion Chemie, Friedrich-Schiller-Uni-
versitat, HumboldtstraBe 10, 69 Jena, DDR
Prof. Dr. Hartwig Hiicker, Universitat Bayreuth, Makromolekulare Chemie I,
Universitltsstr. 30, 8580 Bayreuth, FRG
Prof. Hans-Henning Kausch, Laboratoire de Polymeres, Ecole Polytechnique
Fed&ale de Lausanne, 32, ch. de Bellerive, 1007 Lausanne, Switzerland
Prof. Joseph P. Kennedy, Institute of Polymer Science, The University of
Akron, Akron, Ohio 44325, U.S.A.
Prof. Anthony Ledwith, Department of Inorganic, Physical and Industrial
Chemistry, University of Liverpool, Liverpool L69 3BX, England
Prof. Seize Okamura, No. 24, MinaAmigoshi-Machi Okazaki, Sakyo-Ku.
Kyoto 606, Japan
Prof. Salvador Olive, Chemical Department, University of California, San
Diego, La Jolla, CA 92037, U.S.A.
Prof. Charles G. Overberger, Department of Chemistry. The University of
Michigan, Ann Arbor, Michigan 48 104, U.S.A.
Prof. Helmut Ringsdorf, Institut fiir Organische Chemie, Johannes-Gutenberg-
Universitlt, J.-J.-Becher Weg 18-20,650O Mainz, FRG
Prof. Takeo Saegusa, Department of Synthetic Chemistry, Faculty of
Engineering, Kyoto University, Kyoto, Japan
Prof. Gtiter Victor Schulz, Institut fiir Physikalische Chemie der Universitat,
6500 Maim?, FRG
Prof. William P. Slichter, Chemical Physics Research Department, Bell Tele-
phone Laboratories, Murray Hill, New Jersey 07971, U.S.A.
Prof. John K. Stille, Department of Chemistry. Colorado State University, Fort
Collins, Colorado 80523, U.S.A.
Table of Contents
Small Angle Neutron Scattering from Block Copolymers
R. W. Richards . . . . . . . . . . . . . . . . . . . .
Formation of Living Propagating Polymer Radicals in Micro-
spheres dna Their Use in the Synthesis of Block Copolymers
T. Sato and T. Otsu . . . . . . . . . . . . . . . . . . . 41
Polymerization of Butadiene dna Butadiyne (Diacetylene)
Derivatives in Layer Structures
B. Tieke . . . . . . . . . . . . . . . . . . . . . . . 79
Kinetics dna Mechanisms of Polyesterifications.
H. Reactions of Diacids with Diepoxides
P.-J. Madec and E. Mar6chal . . . . . . . . . . . . . . 153
Swelling muirbiliuqE Studies of Structures Network Elastomeric
J. P. Queslel and J. E. Mark . . . . . . . . . . . . . . 229
Index Author Volumes 1-71 . . . . . . . . . . . . . . . 249
Subject Index . . . . . . . . . . . . . . . . . . . . . 259
Editorial
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Editors Publisher
Small Angle Neutron Scattering from Block Copolymers
R. W. Richards
Department of Pure and Applied Chemistry, University of Strathclyde, Glasgow,
G1 1XL/U.K.
The theory and essential principles of small angle neutron scattering are presented together with their
evolution to expressions useable in the interpretation of experimental data. The two components to the
scattering law, single particle scattering and interference function scattering are identified and some
classical expressions for the scattering of single particles are reviewed. Instrumental aspects are given
as a general overview of the features of small angle dif_fractometers. The major part of the review is
concerned with available experimental results on block copolymers in the solid state. The results are
compared with theoreticparle dictions and consequently theories of microdomain formation are briefly
considered. Apart from domain dimensions, and separations, results of the determination of block dimen-
sions are reported as well as attempts at modelling the complete scattering envelope. The few experiments
on block copolymers in solution and the application of contrast variation are reported and the review
concludes with a report on continuing work on structural changes consequent on uniaxial extension
of block copolymers.
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Theory of Neutron Scatterings . . . . . . . . . . . . . . . . . . . . . 2
3 Small Angle Neutron Scattering . . . . . . . . . . . . . . . . . . . . 5
4 Cross Sections, Scattering Lengths and Scattering Length Density . . . . . . 6
5 Scattering Functions . . . . . . . . . . . . . . . . . . . . . . . . . 8
6 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . 10
7 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 11
1.7 Solid State of Pure Block Copolymers . . . . . . . . . . . . . . . 21
7.2 Theories of Domain Formation . . . . . . . . . . . . . . . . . . 21
7.3 Pure Block Copolymers in the Solid State . . . . . . . . . . . . . . 14
7.4 Copolymer in Solution . . . . . . . . . . . . . . . . . . . . . . 29
7.5 Deformation of Block Copolymers in the Solid State . . . . . . . . . 34
8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2 R.W. sdrahciR
1 Introduction
There are few techniques which find application over a broad field of scientific
endeavourA.m ongst them we can include X-ray scattering, nuclemaarg netic resonance
and latterly neutron scattering. An inspection of the catalogu~ of experiments carried
out in any one year at a major European centre for neutron beam studies ij reveals
that neutron scattering has been used to investigate lattice dynamics and structure
in a variety of inorganic materials, excitations in Fermi fluids, quantised motion of
discrete groups in molecules, adsorption phenomena, Langmuir-Blodgett films,
colloidal dispersions and the structure and dynamics of biological and synthetic
macromolecules. The variety of research capable by neutron scattering is a testament
to the intrinsic properties of the neutron. Neutrons are unchargeds ub-atomic particles
with a mass of 1 a.u. and a spin of 1/2, due to their electrical neutrality and large mass
they are able to penetrate matter to a significant extent before being absorbed. Inter-
action with matter is via nuclear-neutron interaction and/or the magnetic moment
of the neutron. Neutron wavelength used are generally in the range 0.2 to 2.0 nm.
and in this region neutron energy is circa 0.1 kJmo1-1. The wavelengths are such
that the range of scattering vectors (see below) available by neutron scattering enables
the investigation of length scales upt o circa 200 rim. to be explored, whilst the neutron
energy approximates to that of many dynamic molecular processes and thus observa-
tion of the transfer of energy to and from the neutron allows such processes to be
studied.
Although neutron scattering has only been applied to polymers since the early
1970's, the uniqueness of the technique has provoked much published work and many
reviews at periodic intervals 2-s~. Much of the published work on synthetic polymers
has been concerned with small angle neutron scattering (SANS), i.e. structural
investigations of polymer melts, concentrated and dilute solutions, amorphous and
semi-crystalline polymers in the solid state. These results have contributed greatly
to discussions on the nature of semi-crystalline polymers ,~9 polymer blends and the
development of new theories of polymer solutions and networks .~0~ Some 051 papers
have been published in the decade 1973-1983 which deal with SANS from polymers.
Attention here is focused on the application of SANS to the morphological and
conformational examination of block copolymers. Little work has been reported
on these systems, however, as will be shown here the fundamental equations are such
that much information, in principle, is obtainable. The majority of the published
work is concerned with investigations in the bulk state of microphase separated
block copolymers and consequently the pertinant points of domain formation theory
are reviewed. Basic theory of SANS and scattering laws are given, since these are
essential in illustrating the utilisation of the technique. Since detailed description of
apparatus and data analysis are available in the literature, only a brief resum6 is given.
Experimental results are discussed for the solid state, for copolymers in solution,
mixed with homopolymers, and in extension.
2 Theory of Neutron Scattering
Rigorous derivation of the equations used in small angle neutron scattering is not
presented here. The interested reader can find such derivations in the textsb y Marshall
llamS Copolymers Block from Neutron Scattering Angle 3
and Lovesey, Turchin )21 and Kostorz )31 as well as in some reviews. What is presented
here is a precis of the derivation of the final equations which will bring out some of
the factors to be considered, furthermore, only elastic scattering is considered, i.e.
no transfer of energy to or from the incident neutrons. The intensity of neutrons
(number of scattering events) scattered per second by any process will be given by:
)1(
I = IoNo
Where o I is the incident neutron flux in neutrons per second per square centimetre,
N is the number of nuclei in a volume V and o the total scattering cross section per
nucleus. A scattering experiment is usually designed to provide a detailed analysis
of the scattering pattern as a function of incident beam characteristics (flux, wave
vector, polarisation, energy) the scattering being observed at some angle, 20, to
the incident wave vector and collected over a solid angle AlL Incident (ko) and
scattered (k) wave vectors are connected via the scattering vector, Q, by the relation:
Q = ko--k (2)
Figure 1 shows the generalised scattering experiment and the scattering diagram.
Specimen _k 0
........ 0
Fig. .1 diagram Schematic of diagram and scattering a the associated neutron experiment scattering
From the scattering diagram:
Q = (k z + k~ -- 2kk o cos (20)) 2/1 (3)
For elastic scattering, k = o k whence:
Q = Q = (4nfL) sin (0) (4)
since o = k 2n/Z and ~ is the incident neutron wavelength.
From this experimental arrangement then,
I = IoN ~fA-~-~ (5)
.~d
where dcr/df~ is the differential scattering cross section and is the parameter 'observed'
in an elastic neutron scattering experiment and which must he related to features
of the scattering material.
4 R.W. Richards
Fundamental neutron scattering theory shows that dcr/df~ is given by:
do/d~) = 1/N(Mn2nh2) 2 If V(r) exp (iQ • r d3r) 12
Where V(r) is the Fermi pseudo potential describing neutron-nucleus interaction
during scattering, M, the neutron mass and r the vector separation of neutron and
nucleus. Considering one nucleus then the scattering amplitude from that nucleus is:
-b = Mn/2nh f 2 V(r) d3r (6)
Where the integral is over the nuclear volume and thus exp (iQ • r) tends to I since r
is very small. The parameter b is the scattering length defined as the negative amplitude
of the scattered wave. The scattering length is a property of the nucleus and varies
from isotope to isotope, additionally for any one isotope with nuclear spin it may have
one of two values dependent on the interaction between the nuclear and neutron
spins. Consequently, the total differential scattering cross section for an assembly
of many nuclei is the sum of the individual differential scattering cross sections,
dcy/d~2 = t/N ~ ~bt exp (iQ. 012 (7)
r
Temporarily we introduce another position vector r', then:
dc~/dgq = 1/N ~ brb ,~ exp (iQ-(r - r'))
r,r ~
= ~ b, 2 + ~ b,b/exp (iQ. (r - r')) I/N
r r, r t
Z ~b z = N(b,Z>
r
and
b,b,, exp (iQ. (r - r')) = N (b,) z ~ exp (iQ. (r - r'))
r~ r t
= -'N(b,) 2 + N(b,) 2 ~ exp (iQ- (r - r'))
Therefore:
do/df~ = (b 2) - (b) 2 + (b): ~ lexp (iQ-r)l 2 (8)
Two contributions to Eq. (8) can be identified, the first of these is ((b 2) -- (b) 2)
and represents the mean square deviation of individual scattering lengths from the
average value. As such it is called the incoherent scattering cross section and con-
stitutes a uniform, isotropic background scattering since it retains no information
on the phase of the scattered neutrons. Incoherent scattering cross sections are tabu-
lated as values of~i. ¢ where:
ni'O c 4*t((b 2) -- (b) 2) (9)
=