Physics of Polymer Networks

255 Pages·1992·4.794 MB·English

by  S. Wartewig, G. Helmis (auth.)

Progress in Colloid & Polymer Science • Vol. 90
PROGRESS IN COLLOID & POLSYCMIEERN CE
Editors: H.-G. Kilian (Ulm) and G. Lagaly (Kiel)
Volume 09 )2991(
Physics of
Polymer Networks
Guest Editors:
.S Wartewig and G. Helmis (Merseburg)
0
Steinkopff Verlag • Darmstadt
Springer-Verlag • New York
ISBN X-4190-5897-3 (FRG)
ISBN (USA) 0-387-91411-0
ISSN 0340-255 X
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Preface
The 29th Europhysics Conference on This progress volume presents the major part of
Macromolecular Physics "Physics of Polymer Net- the lectures and posters from the conference. We
works" was organized by the Department of Physics hope that the objective of the conference, which
of the Technical University Merseburg, Germany was to reflect the present level of the researchi n the
under the auspices of the Macromolecular Division field of polymer networks and to provoke discus-
of the European Physicsl Society and took place at sions, is being expressed. Furthermore, we expect
Alexisbad/Harz (Saxony-Anhalt) 9--14 September that physicists, chemists and materials engineers
.1991 The scientific programme which was devoted employed in the network research can obtain
to the topics: theory of networks (equilibrium and valuable stimuli for their future work.
dynamical properties), formation of networks, sol-
gel transition, experimental investigations on struc-
ture and properties of polymer networks attracted
more then 001 scientifists from 41 European coun-
tries and the USA. Fortunately, one fifth of all par- .S Wartewig
ticipants came from the East European countries. G. Helmis
Contents VII
stnetnoC
Preface ............................................................................................. V
Vilgis TA: Theory of phantom networks -- topology, structure, elasticity: New and open problems ......... 1
Duering ER, Kremer K, Grest GS: Structural properties of randomly crosslinked polymer networks ........ 31
Heinrich G: The dynamics of tire tread compounds and their relationship to wet skid behavior ............ 61
Kraus ,V Kilian H-G, v. Soden W: Relaxation in permanent networks .................................... 27
Lairez D, Adam M, Raspaud E, Emery JR, Durand D: Do local motions influence rheological properties near
the gelation threshold? ............................................................................. 37
Sommer J-U: On the dynamics of moderately and lightly crosslinked polymer networks ................... 43
Heinrich G, Beckert W: A new approach to polymer networks including finite chain extensibility, topological
constraints, and constraints of overall orientation ..................................................... 47
Schulz M: Formation of networks -- a lattice model for kinetic growth processes ......................... 52
BabayevskyP G: Gelation and 1,1-transition in three-dimensional condensation and chain polymerization ... 57
Doublier JL, Cot6 I, Llamas G, Charlet G: Effect of thermal history on amylose gelation ................... 16
Gamier C, Axelos MAV, Thibault :FJ Rheological, potentiometric and 23Na NMR studies on pectin-calcium
systems ........................................................................................... 66
Strehmel ,B Anwand D, Timpe H-J: The formation of semiinterpenetrating polymer networks by photoinduced
polymerization .................................................................................... 07
Wetzel H, H/iusler K-G, Fedtke M: Observation of the curing process of epoxy resins by inverse gas
chromatography ................................................................................... 78
Strehmel ,B Younes M, Strehmel ,V Wartewig S: Fluorescence probe studies during the curing of epoxy systems 83
Mel'nichenko Yu, Klepko :V Conditions of formation and equilibrium swelling of polymer networks formed by
protein macromolecules ............................................................................ 88
Brereton MG: Cross-link fluctuations: NMR properties and rubber elasticity .............................. 90
Baumann K, Gronski W: Segmental orientation in filled networks ....................................... 97
Weber H-W, Kimmich R, K6pf M, Ramik ,T Oeser R: Field-cycling NMR relaxation spectroscopy of molten linear
and cross-linked polymers. Observation of 1 a ~ T °,2s v law for semi-global chain fluctuations ............ 401
Chapellier ,B Deloche ,B Oeser R: Segmental orientation of "long" and "short" chains in strained bimodal PDMS
networks: A 2H-NMR study ........................................................................ 111
Zielinski ,F Buzier M, Lartigue C, Bastide ,J Bou6 :F Small chains in a deformed network. A probe of
heterogeneous deformation? ........................................................................ 511
Oeser R: Aggregation of free chains within a deformed network: A SANS study .......................... 131
Kliippel M: Trapped entanglements in polymer networks and their influence on the stress-strain behavior up
to large extensions ................................................................................. 731
Apekis L, Pissis ,P Christodoulides C, Spathis G, Niaounakis M, Kontou E, Schlosser E, Sch6nhals A, Georing
H: Physical and chemical network effects in polyurethane elastomers .................................. 441
Rogovina L, Vasiliev ,V Slonimsky G: Influence of the thermodynamical quality of the solvent on the properties
of polydimethylsiloxane networks in swollen and dry states ........................................... 151
Halperin A, Zhulina :BE Triblock copolymers, mesogels and deformation behavior in poor solvents ........ 651
Eicke H-F, Hofmeier U, Quellet C, Z61zer U: Microemulsion mediated polymer networks .................. 561
Solovjev ME, Raukhvarger AB, Ivashkovskaya TK, Irzhak VI: Theory of the mechanical and swelling properties
of elastomers with chemical and physical networks ................................................... 471
Borisov ,VO Birshtein TM, Zhulina :BE The effect of free branches on the collapse of polyelectrolyte net-
works ............................................................................................ 771
Walasek J, Grela S: Local order and statistics of a polymer chain in an external field ...................... 281
Tamulis A, Bazhan L: Charge photogeneration in carbazole-containing compounds and valency bands of
oligomers ......................................................................................... 681
Rozenberg BA, Irzhak VI: The peculiarities and nature of large-scale motion of highly crosslinked polymers. 491
Scherzer ,T Strehmel ,V T~inzer ,W Wartewig S: FTIR spectroscopy studies on epoxy networks ............. 202
VIII Contents
StrehmeI ,V Zimmermann E, Hausler K-G, Fedtke M: Influence of imidazole on the structure of epoxy amine
networks ......................................................................................... 206
Kulik SG, Babayevsky PG, Borovko VV: Epoxy polymer networks: Relaxation processes and crack resistance 209
Pekcan O: Fluorescence study of interpenetrating network morphology of polymer films .................. 214
Smirnov ,PL Volkova NN: Kinetic regularities of polymer network thermal degradation .................... 222
Schulze U, Janke A, Pompe G, Meyer E, Rd~tzsch M: Interpenetrating polymer networks based on AVE
copolymer and PMMA ............................................................................. 227
Rizos AK, Fytas G, Wang CH, Meyer GC: Fast segmental dynamics in poly(methyl methacrylate)-polyurethane
interpenetrating networks .......................................................................... 232
Sandakov GI, Smirnov ,PL Sosikov AI, Summanen KT, Volkova NN: Thermally and mechanically activated
degradation of polyesterurethane networks. Analysis of molecular weight distribution functions .......... 235
Janik H, Foks J: The solidification of bulk and solution cast segmented polyurethanes ..................... 142
Author Index ....................................................................................... 247
Subject Index ....................................................................................... 248
Progress in Colloid & Polymer Science Progr Colloid Polyrn icS 90:1--12 (1992)
Theory of phantom networks --
topology, structure, elasticity: New and open problems
.T A. Vilgis
Max-Planck-Institut fiir Polymerforschung, Mainz, GRF
:tcartsbA The effects of structural elements on the elastic behavior of networks
is discussed. Heterogeneities of fractal nature embedded in networks will ef-
fect the elastic behavior and the neutron scattering as long as the fractal
regions are not saturated. This saturation depends on the topology (connec-
tivity) via the spectral dimension of the fractal. This has the effect that, if
fractals are embedded in the network, their internal crosslinks do not count
to the modulus if the fractals are saturated. The phase behavior of crosslink-
ed blends and semi-interpenetrating networks is also discussed. roF exam-
ple, crosslink a critical density of thenetwork is found for which free chains
solved in the network (semi IPN) are expelled from the network.
yeK :sdrow ;skrowteN_ fractals; heterogeneities; elasticity; IPN; semi IPN
Introduction pinski connectivity [8]. It has been suggested that
such fractal "left overs" from a vulcanization or
It was recently realised that the theory of rubber gelation process creates heterogeneities within the
elasticity and gels has to go in new directions, rubber sample which might affect the macroscopic
where novel ingredients play an important role. behavior of rubbers. Clearly, this will only be the
After the great success of phantom-type theories case if no entanglements are present between two
[1--3], i.e., non-interacting chains, the discussion in crosslinks. Trapped entanglements will introduce a
the past decade has been dominated by the role of new relevant length scale, i.e., the distance between
entanglements and their effects of elasticity from them, and the topological distance between
different points of view ,2[ 4--6]. The long dispute crosslinks will no longer matter.
in the literature can now probably be solved by A simple mean field theory of heterogeneous rub-
computer simulation where networks with and bers has been considered by the present author ]9[
without entanglements can be generated very simp- and independently by Heinrich and Schimmel [10].
ly [7]. It was found that such inhomogeneities do not af-
We do not go into these details here, but we pick fect the deformation behaviour, but strongly in-
up possible new directions in the theory of net- fluence the neutron scattering [9]. Moreover, in-
works. The basic effects of such new directions can homogeneities reduce the effective modulus [10].
be studied first along the lines of phantom-type We will not discuss this in detail here, but leave it
models. Phantom-type models consider networks for a separate paper [11].
composed of phantom chains, i.e., chains which do So far, we have spoken about the real topological
not have excluded volume interactions. Therefore, structure. Now, we want to introduce a "ther-
the problem of entanglements is irrelevant. The on- modynamic topology". By this term we mean that
ly fact which matters is the topology of crosslinking. thermodynamic interactions, as present in blends,
It has been reported recently that the topology of strongly influence the phase behavior and elasticity
crosslinkage deeply influences the behaviour of of crosslinked blends. It has been suggested [12]
networks. Model systems have been considered, that crosslinkage of partially miscible polymers
such as fractal networks, e.g., a network of the Sier- prevent complete phase separation. Crosslinked
2 Progress in Colloid & Polymer Science, Vol. 90 (1992)
blends cannot phase separate macroscopically, but
form a microdomain structure since they undergo a
microphase separation. The statistical mechanics of
such materials is completely unknown and only
first attempts have been made to solve this question
[13].
The paper is organised as follows. First, the
classical theories will be reviewed on their structure
and topology relationship. We then turn to fractal
networks and fractal containing networks. Finally,
we discuss the case of crosslinked blends and semi
IPNs.
Classical models of regularly crosslinked polymers
The classical models can be divided into two
.giF .1 The basic assumptions in the James and Guth
limiting cases. The first is the Kuhn model which is model. The surface crosslinks are fixed, whereas internal
essentially a single-chain approximation where it crosslinks are free to move
turns out that the free energy is a sum over all con-
tributions from each individual chain. Without go-
ing into details, we quote the result for the free
For arbitrary functionalities f this result has been
energy of deformation
generalized by Graessley [14] for an exact calcula-
tion for networks of tree-like structure.
1 3
]/F = -- N ~. ;t~, (2.1) The macroscopic free energy is given by
2 1=i
where N is the number of subchains between two 1 3
flF = -- N (1 -- 2If) ~. ,~, (2.3)
crosslinks and 2i is the deformation ratio in the i-th
2 1=i
cartesian direction. # is the inverse temperature.
The above model is quoted as an affine model since
the crosslink distance deforms in the same way as
the macroscopic dimensions. It is important to
realise that Eq. (2.1) does not depend on any struc-
tural parameter such as functionality of the
crosslinks, etc.
To find a dependence on structural parameters a
more sophisticated theory has to be employed. The
/ (
first step in this direction has been made by James
and Guth ]2[ for four functional crosslinks. Thier
basic assumption was that several crosslinks of the
rubber are fixed on the walls of the sample, forming
the surface, whereas the inner crosslinks are free to
move.
The result of their calculation is given by
1 3
]/F = N 2~, (2.2)
-- Z
4 1=i
which is one-half of the free energy of the Kuhn
Fig. .2 Tree-like structure of a network. The internal
model given by Eq. (2.1). This reduction of the free crosslinks are free to move. the surface crosslinks are kept
energy is due to additional motion of the crosslinks. fixed. Here, f = 3
Vilgis, Theory of phantom networks topology, structure, elasticity: New and open problems 3
--
which has become the basic formula for phantom Networks of non classical connectivity
networks. A nice independent proof of Eq. (2.3) has
been given recently by Higgs and Ball [15], who The physics of fractals has been explored deeply
have used an electrical analogy. It has to be noted during the last decase. Fractals are objects with
that Eq. (2.3) is only exact for tree-like structures, non-classical connectivity, i.e., they represent
corresponding to mean field solutions where no spaces with a non-integer dimension (fractal
fluctuations of the structure, i.e., loops are present. dimension). Typical examples are the infinite per-
This can be seen as an elementary example (see colation cluster [18], an example for a random frac-
[15]). On a cubic lattice (f = 6), one finds flF = 1/3N tal or the Sierpinski gasket as an example for a
~, ~t; :/=( 1 -- 2/f), whereas on a tetrahedral lattice regular fractal. The fractals are normally treated as
one finds flF = 1/2N ~, 2~, i (= 1 -- 2/f). Equation lattice fractals, i.e., that the bonds between the junc-
(2.3) has to be considered as a mean field solution tion points are rigid. It is now tempting to replace
which is exact for tree-like structures. We will come these rigid bonds by flexible Gaussian chains. This
back to this point later in the case of rod networks. will lead to polymeric fractals. This idea is due to
Nevertheless, in an exact solution on a Bethe lat- Cates [19]. The properties of such polymeric fractals
tice a dependence on a structural and topological are very different from those ofr igid lattice fractals,
parameter (functionality f) has been found. Note especially regarding the question of elasticity. In lat-
that a general answer to a structure-modulus rela- tice fractals each path through the fractal is rigid
tion is unknown. and the elasticity is enthalpic, whereas in polymeric
Flory [16] has generalized Eq. (2.3) to fractals one has entropic elasticity since each path
through the fractal is Brownian. Examples for
1 3 polymeric networks are shown in Fig. .3
= ¢ ~, 2~ , )4.2(
flF -- 2 1=i The Sierpinski network is a typical example of a
network with non-classical connectivity. It has
where ~ is the cycle rank, i.e., the number of in- functionality 4 but there exist holes on all scales,
dependent loops in the network which determines i.e., larger fluctuations in structure. The other exam-
the elastically active network strands and the ple -- the hierarchical fractal network -- is based on
elastically active crosslinks in the following graph the idea of modeling the backbone of the percola-
theoretical manner: tion cluster [20], and it has been demonstrated that
it has the property of multifractality of the voltage
--- N + 1--M = N--M, (2.5) distribution if a voltage is applied at both ends of
the network.
where M is the number of crosslinks. For perfect We hve to first define the size and the topological
networks, one has behavior of such (non-entangled) fractal networks
before we discuss typical network properties of
fM = 2N, (2.6) them. The basic quantities we need for later discus-
sions are the relations between size and topology,
and Eq. (2.4) reduces to Eq. (2.3) immediately. i.e., connectivity of the network and the swelling or
Hence, Eq. (2.3) is exact for perfect phantom net- collapse behavior of such networks in their own
works. The reduction of the modulus by (2/f)k B TN melts or in fractal solvent. We first need a relation
is due to fluctuations of the crosslink points. This between the connectivity (spectral dimension) and
can be made explicit in several ways [15--17]. the ideal Gaussian fractal dimension of the
The Kuhn model and the James and Guth model polymeric fractal. It can be shown that the Gaussian
are considered as two limiting cases, since in the fractal dimension is given by
first model one has purely affine deformation,
whereas in the latter the deformatin is now affine
2d S
since crosslinks are fluctuating in a range given by , (3.1)
the distance between two crosslinks. Attempts have - - 2 - -- s d
been made to interpolate between the two cases
(see ]2[ for a review), but such concepts become where s d is the spectral dimension of the lattice
unreliable if entangled networks are considered fractal which is, of course, the same as that of the
,4[ .15 polymeric fractal since the topology is preserved.
4 Progress in Colloid & Polymer Science, Vol. 90 (1992)
Fig. .3 a) Sierpinski network. The connectivity is given by
that of the Sierpinski gasket, but in reality the structure is
highly folded, b) A hierachical fractal network which has
been used as a model of the 2-d percolation cluster. The next
generation can be achieved if each chain becomes replaced by
the sequence of a chain, two chains forming a loop and
another chain
b
(3.1) suggests that the Gaussian dimension of the The first term is the usual elastic free enrgy (- 2 R
network is given by since the fractal is Brownian) and the second term
is the screened excluded volume. Note that if fO =
R~r- m, (3.2)
,0 we obtain the ordinary Flory free energy of swell-
where m is the total mass in the fractal. ing in point like (low molecular weight solvent) and
If this fractal is put in solvent, we expect it to swell if 6 = df we recover the classical expression for a
and a new fractal dimension is obtained. This me~t of fractals, i.e., for ~R - fm the Daoud-Family
phenomenon is well known in linear chains, which expression for swelling of lattice animals rd( = 4) is
are a special case of a polymeric fractal with s = d 1 recovered [22].
(see Eq. (3.1)). Here, we are interested in more Minimization of the free energy predicts a fractal
general situations, i.e., we can put the fractal into dimension
ordinary solvent or in more complex solvent such as
linear chains or another fractal with Gaussian d+2
Df = , )4.3(
dimension fO [21]. Excluded volume becomes
1
screened on the scale of the size of the different 2 -- -- (~f- 2)
a,
fractals and we obtain a generalized Flory free
energy [21]
where d is Euclidian space dimension. The reader
2 R v 2 X
may be convinced that Eq. (3.4) contains all well
F = kBT-- + (3.3)
~R N ~dq d R known cases [21]. Most remarkable is the result