Behavior of Macromolecules

169 Pages·1982·3.405 MB·English

by  Akira Takahashi, Masami Kawaguchi (auth.)

46
Advances in
Polymer Science
Fortschritte der Hochpolymeren-Forschung
Editors: H.-J. Cantow, Freiburg i. Br. • G. Dall'Asta, Colleferro • K. Du~ek,
Prague • J. D. Ferry, Madison • H. Fujita, Osaka • M. Gordon, Colchester
J. P. Kennedy, Akron • W. Kern, Mainz • S. Okamura, Kyoto
C. G. Overberger, Ann Arbor • T. Saegusa, Kyoto • G. V. Schulz, Mainz
W.P. Slichter, Murray Hill • J.K. Stille, Fort Collins
Behavior of Macromolecules
With Contributions by
R. C. Arridge J. P. Barham M. Kawaguchi
J. Kolah'k A. Takahashi
With 06 Figures
Springer-Verlag
Berlin Heidelberg New York 1982
Editors
Prof. Hans-Joachim Cantow, Institut for Makromolekulare Chemie der Universit/it,
Stefan-Meier-Str. 31, 7800 Freiburg .i Br., BRD
Prof. Gino Dall'Asta, SNIA VISCOSA- Centro Chimico, Studi Colleferro (Roma),
Italia
Prof. Karel Dugek, Institute of Macromolecular Chemistry, Academy Czechoslovak of
Sciences, 261 60 Prague 616, RSS~(
Prof. John D. Ferry, Department of Chemistry, The University of Madison, Wisconsin,
Wisconsin 53706, U.S.A.
Prof. Hiroshi Fujita, Department of Macromolecular Science, Osaka University,
Toyonaka, Osaka, Japan
Prof. Manfred Gordon, Department of Chemistry, University of Essex,
Wivenhoe Park, 3 Colchester 04 C SQ, England
Prof. Joseph P. Kennedy, Institute of Polymer Science, The University of Akron,
Akron, Ohio 44325, U.S.A.
Prof. Werner Kern, Institut for Organische Chemie der Universit/it, 6500 Mainz, BRD
Prof. Seizo Okamura, No. Minami-Goshomachi, 24, Okazaki, Sakyo-Ku, Kyoto 606,
Japan
Prof. Charles G. Overberger, Department of Chemistry, The University of Michigan,
Ann Arbor, Michigan 48104, U.S.A.
Prof. Takeo Saegusa, Department of Chemistry, Synthetic Faculty of Engineering,
Kyoto University, Kyoto, Japan
Prof. Giinter Victor Institut Schulz, rOf Chemie Physikalische der ,ti~tisrevinU
Mainz, 6500 BRD
Dr. William P. Slichter, Chemical Physics Research Department, Telephone Bell
Laboratories, Murray Hill, New Jersey 07971, U.S.A.
Prof. John K. Stille, Department of Chemistry, Colorado State University, Fort Collins,
Colorado 508 23, U.S.A.
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Table of Contents
The Structure of Macromolecules Adsorbed on Interfaces
A. Takahashi and M. Kawaguchi .......................
Polymer Elasticity - Discrete and Continuum Models
R. C. Arridge and P. J. Barham ........................ 67
Secondary Relaxations in Glassy Polymers - Hydrophilic Polymethacrylates
J. Kolah'k ................................... 119
Author Index Volumes 1-46 ........................... 163
The Structure of Macromolecules
Adsorbed on Interfaces
Akira Takahashi and Masami Kawaguchi
Department of Industrial Chemistry, Faculty otEngineering, Mie University, Tsu, 514, Mie Japan
This article reviews recent advances in polymer adsorption both in theory and experiment. The
adsorption of macromolecules on interfaces plays an essential role in the diversity of practical pro-
blems in industry, technology and biology such as adhesion, flocculation and stabilization of colloid
particles, chromatography, reinforcement, and artifical organs in medicine.
This review appeals to researchers in the above mentioned fields and helps not only experimenta-
lists but also theoreticians who are interested in polymer adsorption.
A. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
B. Theories of Polymer Adsorption ........................ 4
X.B Isolated Polymer sn~a~'-U ........................ 5
B.2 Number of Configurations of a Tail and a Loop ............. 6
B.3 Interacting Non-Ionic Polymer Chains ................. 6
B.3.1 The Theory ofH oeve ...................... 6
B.3.1.1 Adsorption Isotherms ................. 6
B.3.1.2 Segment Distribution Function for Loops ....... 8
B.3. t.3 Excluded Volume Effect ................ 10
B.3.2 The Theory of Silberberg .................... 11
B.3.3 The Theory of Scheutjens and Fleer .............. 16
B.3.4 Root-Mean-Square Thicknesses of Loops and Tails ...... 25
B.3.4.1 Root-Mean-Square Thickness of Loops ........ 25
B.3.4.2 Root-Mean-Square Thickness oTfa ils ......... 26
B.3.5 Diffusion Equation Approach ................. 26
B.3.6 The Scaling Theory ....................... 28
B.4 Theorieso f the Adsorption ofP olyelectrolytes ............. 30
B.4.1 The Theory of Frisch and Stillinger ............... 30
B.4.2 The Theory of Hesselink .................... 30
B.5 Summary ................................ 34
C. Experimental Techniques ........................... 35
C.1 Adsorption Isotherms ......................... 35
C.2 Thickness of the Adsorbed Layer .................... 35
C.] 1 Hydrodynamic,,M~hc,~3 .................... 35
e .~ | Ellipsometry .......................... 35
Advances Science in Polymers 64
© Springer-Verlag Heidelberg Berlin 2891
2 A. Takahashi and .M Kawaguchi
C.2.3 The ATR Method ....................... 36
C.3 Fraction of Adsorbed Segments and Fraction ofO ccupied Surface Sites
36
C.4 Heat of Adsorption ........................... 37
D. Experimental Results ............................. 37
D.1 Adsorption of Flexible Non-Ionic Polymers .............. 37
D.I.1 Ellipsometric Studies ...................... 37
D.I.I.1 Adsorption at the Theta Point ............. 37
D.l.l.2 Adsorption from Gcod Solvents ............ 42
D.1.2 Hydrodynamic Studies ..................... 44
D.123 Other Approaches ....................... 46
D.1.4 Attachment of Train Segments to Active Sites ......... 47
D.1.5 Heats of Adsorption ...................... 52
D.2 Adsorption of Branched Polymers ................... 52
D.3 Adsorption of Block Copolymers .................... 53
D.4 Adsorption of Polyelectrolytes ..................... 54
D.5 Adsorption of Block Polyelectrolytes .................. 59
D.6 Adsorption of Polyampholytes ..................... 60
D.7 Adsorption of Rod-Like Macromolecules ............... 60
E. Conclusions .................................. 61
F. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
The Structure of Adsorbed Macromolecules on Interfaces
A. Introduction
The adsorption of macromolecules on interfaces plays an essential role in the diversity of
practical problems in industry, technology and biology, such as adhesion, flocculation
and stabilization of colloid particles, chromatography, reinforcement, and artificial
organs in medicine. Its features are quite different from those of the adsorption of small
molecules. For example, the number of conformations displayed by a flexible polymer at
an interface increases tremendously with chain length. Figure t depicts various chain
conformations of adsorbed flexible and rod-like polymers. These conformations first
determine the dimensions or thickness of the adsorbed polymer normal to the surface
and second the configurational entropy and enthalpy of the adsorbed polymers. The free
energy should be negative for the adsorption to occur. It is the fundamental property
needed to calculate the extent of adsorption. Thus, the determination of conformations
of adsorbed macromolecules is the central issue for polymer adsorption studies.
In 1953, Frisch, Simha, and Eirich )6-1 first investigated the change in conformation
that occurs when a Gaussian coil is brought in contact with a reflecting wall, calculated
thermodynamic properties of the adsorbed layer, and deduced an adsorption isotherm
(FSE isotherm). The important conclusion was that the thickness of the adsorbed layer at
the theta point is proportional to the square root of the molecular weight of polymer.
However, in the early 1960's, their approach was criticized by Silberberg }7 and by DiMar-
zio s), who showed that Frisch et al. had overestimated the number of distinguishable
conformations of the adsorbed polymer chain. DiMarzio and McCrackin )9 showed that,
for the correct evaluation of the number of conformations, an adsorbing barrier must be
assumed just one step behind the wall.
In the mid-1960's extensive theoretical investigations of polymer adsorption began.
The earlier studies were chiefly concerned with the conformation of isolated polymers,
Ioop
1( b f~nr c
d e f g
Fig. .1 Various conformation models for adsorbed on macromolecules an interface, a) lying chain
totally on the interface; b) d) conformation; loop-train loop-train-tail conformation; adsorbed e) at
one chain end; e) random coil adsorbed at point; a single f) adsorbed rod-like macromolecules at
one end; g) rod-like adsorbed macromolecules located totally on an interface
4 A. ihsahakaT dna .M ihcugawaK
the distributions of loops, trains, and tails, and the average thickness of adsorbed chain,
statistical mechanical approaches s' ,)41-01 lattice model approaches '7 ,)61,51 and computer
simulations by the Monte Carlo methods '9 )12-71 being used.
Although these studies were of great theoretical value, the results had little practical
value since isolated adsorbed chains are inaccessible to experimental studies. The only
exception was electron microscopic visualization of the conformation of a single DNA
.)22niahc
Subsequently, there emerged a number of extensions which aimed at incorporating
lateral interactions of adsorbed polymers into the theory. The main interest was to
predict how the adsorbance (mass per unit area) (A), the adsorbed amount (total number
of segments adsorbed per site) (F), the fraction of segments in trains (p), and the
thickness of the adsorbed layer depend on such physical variables as polymer molecular
weight and thermodynamic interaction parameters between polymer-solvent and
between polymer-adsorbing surface. Attemps have also been made to formulate the
adsorption theory of polyelectrolytes )32 and to apply the scaling theory to polymer ad-
sorption .)42
Concerning the experimental side of polymer adsorption studies the quantity A was
only measurable at the early stage of the study, but in 1955 the thickness of the adsorbed
layer became accessible to measurement by a hydrodynamic method and in 1961 the
quantity p was first determinedb y infrared spectroscopy. Ellipsometry came up in 1963,
which enabled both the adsorbance and the thickness of the adsorbed layer to be mea-
sured simultaneously.
No quantitative comparison between theory and experiment on polymer adsorption
was attempted until the end of the 1970's. There were two reasons for this delayF.i rst, no
acceptable theory had been established. Second, some of the parameters used in most of
the published theories could not be directly correlated to experimentally measurable
quantities.
Polymer adsorption has been reviewed by many authors .)73-82 An earlier volume of
this journal presented an article which dealt with polymer adsorption studies made
before .)924691 This paper gives a review of subsequent advances in this field of study. In
Chap. B, the principal theories are described, confining ourselves to those which are
amenable to experimental tests. Chapter C gives a brief survey of typical measuring
techniques. In Chap. D, important experimental data on the thickness of the adsorbed
polymer layer and the fraction of adsorbed segments are summarized and discussed,
along with their comparison with relevant theories.
B. Theories of Polymer Adsorption
B.1 Chains Polymer Isolated
It is well known that a free flexible polymer chain in bulk solution behaves as a random
coil. When such a polymer chain is adsorbed on a surface, there occurs a change in its
conformation. Some portions of the polymer chain get in direct contact with the surface
The Structure of Macromolecules Adsorbed on Interfaces 5
as trains, and the remaining portions extend into the bulk solution as loops or tails (see
Fig. 1).
Loops and tails of an isolated adsorbed polymer chain assume a number of different
configurations and they substantially determine the configurational entropy of the
adsorbed polymer, while the interaction energy between trains and the surface deter-
mines the enthalpy of adsorption.
Many authors 7-2t) have theoretically investigated the conformation of an isolated
adsorbed polymer as a function of adsorption energy, using statistical mechanical
approaches. Some important conclusions are as follows:
1) At low adsorption energy, long loops or tails are favored and give rise to a conforma-
tion extended in the direction normal to the adsorbing surface, whereas at high
adsorption energy, small loops or tails and long trains predominate, leading to a
flattened conformation.
2) As intuitively expected, the number of train segments increases rapidly with increas-
ing adsorption energy.
3) The distribution of loop segments is a simple exponential function of the distance
from the surface while that of tail segments is the difference of two exponential
functions and has a maximum at an intermediate distance.
B.2 Number of Configurations of a Tail and a Loop
The number of configurations WA (i, z) for a tail consisting of i segments that starts at the
interface (z = 0) and ends at a distance z from the surface is given by )°4-s3
WA (i, Z) = (2/z) 2f1 i 2 zi 2/3- e -z2/2i (B-l)
The total number of configurations WA (i) for this tail is obtained by integrating Eq.
(B-l) over all allowable values of z, giving
WA (i) = (2 i i)-1/2 2 Z (B-2)
A loop consisting of i segments can be formed by linking a tail of (i - 1) segments that
ends at z = 1 with the i-th segment on the interface. This i-th segment has only one
possible orientation so that the number of configurations W2A (i) for a loop of i segments
is equal to that of a tail of (i - 1) segments that ends at z = 1. Thus, we have
WaA(i) = WA(i - 1, Z ~- 1) (B-3)
Substituting Eq. (B-l) into Eq. (B-3), we get
A2W (i) = (2 )"23 -1/2 i i 2 2/3- (B-4)
A comparison of Eqs. (B-2) and (B-4) shows that for the same i the tail formation is more
favored than loop formation.
6 A. Takahashi and M. Kawaguchi
B.3 Interacting Non-Ionic Polymer Chains
Most of the early theories of polymer adsorption were not concerned with the interaction
between adsorbed polymers so that they have little relevance for a comparison with
experimental results. In actuality, the adsorbed mass per unit area is very large even
when adsorption of polymers occurs from a very dilute solution. In this section, some
typical theories allowing for the interaction between adsorbed polymers are reviewed.
B.3.1 ehT Theory of Hoeve
B.3.1.1 Adsorption Isotherms
Before describing this theory, we outline the theory of Hoeve et al. )14 formulated under
the assumptions that the polymer chain is so long that end effects, i.e. tail formation, may
be neglected and that the surface coverage is so low that the interaction of adsorbed
polymer chains is negligible.
The following partition function qa was derived for an isolated polymer chain consist-
ing of trains and loops:
qa = Z(m'02 H (°im)/mJ o" H [(ci-3/2)nTni!] (B-5)
j i
where m is the number of trains, i.e. Em i, and equals the number of loops, i.e. Yni; a is
the internal partition function of a segment adsorbed on the surface relative to that in the
bulk solution and c a flexibility parameter of the chain (for a flexible chain c = i and for
a very stiff chain c = 0). The partition function for a loop of size i is obtained from
Eq. (B-l). The total number of polymer segments, n, is expressed in terms ofm i and ni as
n =Ejmi + Eini (B-6)
j i
By applying the Lagrangian multiplier method to Eq. (B-5), we obtain
ni = -m3cai e ~t ~ e (B-7)
i m = mdeJae -~ (B-8)
In q, = - 2 n (B-9)
where 2 and ~ are multipliers and 2kT may be regarded as the free energy of adsorption
per segment. From Eq. (B-9) the following useful relationships can be derived.
1) The fraction of adsorbed segments, p:
p = Zjmi/n = (1 + S_~)/(1 + S-la + S-3~) (B-IO)
2) The average loop size, (i):
(i) = Yini/Eni = S_1/2/5_3/2 (B-11)