Detection of the gel point of crosslinking high molecular weight precursor polymers can be quite difficult. Gel point determination can be made by extrapolating viscosity measurements during the crosslinking reaction as the gel point is approached. Dynamic mechanical methods of monitoring crosslinking reactions prove to be more informative because one can rheologically monitor the reaction from the liquid to the solid state. Though dynamic methods are effective in measuring changing structure during crosslinking, they are limited to probing the terminal zone where the change in structure is apparent. Due to entanglements in high molecular weight polymers, this terminal zone (low frequency regime) shifts to lower frequencies as the molecular weight increases. This shift makes it more difficult to observe the gelation process. In this study we used the dynamic mechanical technique of cyclic frequency sweeps (CFS) to monitor the random crosslinking of six high molecular weight, nearly monodisperse polybutadienes. We will show how physical entanglements interfere with gel point detection by the CFS method.
[F'31.02] Theory for Neutron Scattering from Polymers in Tubes: Lozenges, Dangling Ends and Retraction
D.J. Read, T.C.B. McLeish (University of Leeds, U.K.)
We present a consistent explanation for the 'lozenge' shapes in contour
plots of the two-dimensional neutron scattering intensity from stretched
polymer networks. By explicitly averaging over quenched variables in a
tube model, we show that lozenge patterns arise as a result of chain
material that is not directly deformed by the stretch. We also present a
complete theory for the calculation of neutron scattering functions in
the following experimental situation: a melt of partially deuterated
block copolymers is stretched and sufficient time allowed for the
polymers to retract along their tubes but for no further relaxation
processes to occur before quenching below the glass transition
temperature. The theory is necessary for the modelling of neutron
scattering experiments which test the retraction theory for strongly
stretched melts. We expect to be able to comment on the success of the
theory for one such experiment.
[F'31.03] A New Approach to Polymer-Network Stabilized Liquid Crystals for Improved Display Properties
U.P. Schröder (University of Stuttgart), D.Y. Yoon, K.P. Chan, R. Twieg, R.D. Miller (IBM Almaden Research Center), G.A. Held, A.S. Lien (IBM Watson Research Center)
The performance of liquid crystals in display cells can be greatly improved by stabilizing them with a small amount of in-situ polymerized networks. The polymer phase-separates during polymerization and crosslinking, and forms complicated structures of little-known morphology. It is generally believed that anisotropic features of the crosslinked polymer structure provide appropriate anchoring forces, and therefore improve the switching characteristics of liquid crystals. In previous approaches, the network forming material generally consists of difunctional monomers which form densely crosslinked system. We report a new method of designing polymer networks to stabilize liquid crystals. In this approach, the mesogenic character and the ability to form crosslinks are separated into two different monomers, so that the crosslinking density and anisotropic anchoring forces are controlled accurately. Our experiments show that with a proper combination of crosslinking density and mesogenic forces, the driving voltage or switching time of liquid crystals can be lowered significantly compared to the prior art.
[F'31.04] Simple Flory-type theory of a polymer with topological constraints
Alexander Grosberg (Physics Department, MIT), Yitzhak Rabin (Bar-Ilan University)
A mean field theory of the effect of knots on the statistical mechanics of ring polymers is presented. We introduce a topological invariant which is related to the primitive path in the ``polymer in the lattice of obstacles'' model and use it to estimate the entropic contribution to the free energy of a non--phantom ring polymer. The same entropy is employed to examine the probability distribution of the degree of knotting for equilibrium phantom ring. The most probable degree of knotting upon random closure of the chain grows dramatically with chain compression.
[F'31.05] Non-Gaussian Behaviour of Elastomers
Y. Mao, M. Warner, E.M. Terentjev (Cavendish Laboratory)
Ideal nematic elastomers are novel solids where some certain (so called 'soft') deformations can be achieved without cost of energy, as first shown by Golubovic and Lubensky on general symmetry grounds. In practice, such solids are not perfectly soft due to a number of limiting factors. Here we consider one of them, the finite chain extensibility, by examining a detailed molecular model. For any rubber, isotropic or otherwise, non-Gaussian effects such as these can only be fully treated in a tensorial manner, which is not the case in the classical treatments of rubber. In fact for isotropic rubber, non-Gaussian effects in the literature are in slight error. We first present the full tensorial treatment of this non-Gaussian effect, and then discuss the resulting implications on the soft deformations in nematic elastomers.
[F'31.06] Verification of the Ginzburg Criterion for Polymer Gelation
Charles P. Lusignan, Dennis R. Perchak (Eastman Kodak Company), Michael Rubinstein (University of North Carolina), Ralph H. Colby (The Pennsylvania State University)
We present results of a computer simulation of crosslinking that verifies de Gennes' calculation of the Ginzburg criterion for polymer gelation. The crossover between critical percolation close to the gel point and mean field farther away occurs at a relative extent of reaction that scales as the negative one-third power of the chain length between branch points N. We vary N by crosslinking different lengths of linear percursor chains. The Ginzburg point is evaluated from plots of weight-average cluster mass against z-average cluster mass during the course of gelation. The analysis is also shown to be consistent with experimental data on randomly branched polyesters.
[F'31.07] Viscoelasticity of Entangled Solutions of Stiff Polymers
David Morse (Univ. of Minnesota)
A reptation model is presented for the linear and nonlinear viscoelastic behavior of a concentrated solution of semi-flexible polymers. The model describes a `tightly-entangled' regime in which both the persistence length and the contour length of the polymers exceeds the effective entanglement length of the solution, where the relevant entanglement length is found to be a length of order the distance between collisions of the polymer with the surrounding `tube'. It is shown that for sufficiently stiff polymers such a regime may appear at concentrations much lower than those for which a nematic phase is expected. Predctions for linear and nonlinear viscoelasticity are obtained by assuming simple reptation dynamics, but using a stress tensor derived from a description of the tube as a semi-flexible (rather than freely jointed or rigid) chain. Differences between the predictions for the isotropic phase and those of the Doi-Edwards model of flexible polymers include: violation of the stress-optic law, significantly reduced shear thinning, a different predicted concentration dependence of the plateau modulus, and, for polymers with contour lengths of order the persistence or less, the appearance of distinct stress contributions (with different decay times) arising from deformations of the equilibrium distributions of, respectively, chain curvature and overall chain orientation.
[F'31.08] Chemically Driven Spinodal Decomposition
S. Sukumaran, G. Beaucage, B. Viers, J. E. Mark (University of Cincinnati), M. Saraf (University of Cairo)
Thermally driven spinodal decomposition in polymer/polymer systems is often observed through the growth of a peak in the small-angle light scattering pattern. Phase growth is related to an increase in intensity with time following Cahn-Hillard theory. Latter stage deviations from this thermodynamic prediction are described by Oswald ripening mechanisms. A parallel to thermally driven phase separation is seen in some systems where miscibility is governed not by a thermal driving force but by a chemical reaction which leads to immiscibility of a reaction product and a polymer phase. In this study hydroxyl terminated, low molecular weight polydimethyl siloxane is reacted with multi-functional silicon based crosslinking agents to form a two phase rubber with silica-like inclusions. By varying the molecular weight of the PDMS precursor, the catalyst type and other reaction conditions the phase separation process can be drastically altered. A modified Cahn-Hillard approach is described where extent of reaction substitutes for the thermal driving force in conventional spinodal decomposition.
[F'31.09] Linear Viscoelasticity of Concentrated DNA Solutions Studied with Dynamic Light Scattering from Tracer Particles.
Thomas Gisler, David A. Weitz (Department of Physics, University of Pennsylvania, Philadelphia, PA 19104)
We use quasielastic light scattering (QELS) and diffusing wave spectroscopy (DWS) to probe the diffusional motion of tracer particles in concentrated solutions of long-chain DNA. We analyze the mean-square displacement~\langle\Delta r\,^2\,(t)\rangle using a generalized Stokes-Einstein relation, from which we obtain a frequency dependent storage modulus~G'(ømega) and the corresponding loss modulus~G''(ømega) of the polymer network. At low concentrations of DNA \langle\Delta r\,^2\,(t)\rangle measured by QELS shows a hindered diffusion due to increased viscosity; at higher DNA concentrations the tracer particles become trapped within the polymer network. Here DWS resolves tracer motion at the sub-nm length scale; at short times (10\,ns--100\,ns) the tracer motion is diffusional, whereas at larger times the restoring forces exerted by the chain entanglements lead to an arrest of the particles' motion. We investigate the role of chain entanglements using tracer particles of different sizes. Finally, we compare the measured G'(ømega) and~G''(ømega) over a frequency range~10^-3Hz\leqømega/2\pi\leq 10^6Hz at different DNA concentrations to mechanical measurements using a controlled-strain rheometer.
[F'31.10] Viewing Entanglements as a Blended Phase in Polycarbonate.
J.P. Ibar (EKNET Research, New Canaan CT 06840 USA.)
We present the resulls of an extensive investigation of the deformation
behavior of an amorphous polymer, polycarbonate, and explain the
results in terms of the interactive coupling between conformers
belonging to interpenetrating coil-macromolecules. Our investigation
of the deformational properties includes viscous behavior (both capillary
and Dynamic shear viscosity), stress-strain tensile tests at various rates
and temperatures, flexural dynamic data below Tg, for both quenched and
aged PC, and PVT results from 1.42 Tg (K) down to room temperature.
All the results are consistent with a picture of the amorphous state
suggested by the EKNET model, in which coiled up macromolecules pack
and interpenetrate when interacting with one another, to create an interactive
phase which, in many respects, behave like a blended phase. The mechanisms
of toughening and embrittlement through physical aging are described in terms
of the continuity or segregation of the coil interfacial interactive phase,
which
defines "permanent" entanglements. Dynamic entanglements can be created
while deforming the melt below Tl,l and are responsible for shear-thinning.
However, the dynamic entanglements are not permanent since they are
only the reflection of the cooperative nature of the deformation process in
the rubbery state, which is strain rate dependent.
[F'31.11] Manipulation of Dynamic Entanglements during Processing. A new understanding of Shear-Thinning
Joan. Ortat, A.L. Apitchi, J.P. Ibar (EKNET Research, New Canaan CT 06840 USA.)
Dynamic entanglements in a melt are produced by the rate sensitive interactive coupling of
conformers reponding to a deformation. The extent of such coupling determines
the elasticity of the melt, which is a function of the rheological parameters,
temperature, pressure, strain rate, cooling rate and frequency/amplitude of
a vibration, when the melt is vibrated during processing.
We present a new model of non-linear viscoelastic melt behavior which explains how
and why shear-thinning occurs, and how it is influenced by pressure and cooling rate,
and vibration parameters. We present a new formulation of shear-thinning and
non-Newtonian viscous flow which directly correlates the extent of interactive
coupling and elasticity of the melt (dynamic entanglements) with viscosity.
We provide justification for the new model with experimental evidence on
polycarbonate and polystyrene.
[F'31.12] Phenomenological Model for Cross-linked Polymer Blends.
M.S.O. Massunaga, M. Paniconi, Y. Oono (Department of Physics and Beckman Institute - University of Illinois at Urbana-Champaign)
A simple phenomenological model for randomly cross-linked polymer blends is introduced by extending a successful cell-dynamical-system model of diblock copolymer melts. The essential feature of the inability of the network to move and form globally ordered spatial patterns is captured. The model does not exhibit any global ordering even under coercive conditions. We discuss the main distinction between quenched cross-linked polymer blends and quenched diblock copolymer melts under segregation conditions. Our model suggests experimental methods to discriminate cross-linked polymer blends and diblock copolymers even without fluid dynamic effects.