We discuss possible motions for one polymer molecule P (of mass M) performing wormlike displacements inside a strongly cross‐linked polymeric gel G. The topological requirement that P cannot intersect any of the chains of G is taken into account by a rigorous procedure: The only motions allowed for the chain are associated with the displacement of certain “defects” along the chain. The main conclusions derived from this model are the following:(a) There are two characteristic times for the chain motion: One of them (Td) is the equilibration time for the defect concentration, and is proportional to M2. The other time (Tr) is the time required for complete renewal of the chain conformation, and is proportional to M3.(b) The over‐all mobility and diffusion coefficients of the chain P are proportional to M−2.(c) At times t < Tr the mean square displacement of one monomer of P increases only like 〈(rt − r0)2〉 = const t1/4.These results may also turn out to be useful for the (more difficult) problem of entangle...

Reptation of a Polymer Chain in the Presence of Fixed Obstacles

We present an extensive molecular‐dynamics simulation for a bead spring model of a melt of linear polymers. The number of monomers N covers the range from N=5 to N=400. Since the entanglement length Ne is found to be approximately 35, our chains cover the crossover from the nonentangled to the entangled regime. The Rouse model provides an excellent description for short chains N<Ne, while the dynamics of the long chains can be described by the reptation model. By mapping the model chains onto chemical species we give estimates of the times and distances of onset of the slowing down in motion due to reptation. Comparison to neutron spin‐echo data confirm our mapping procedure, resolving a discrepancy between various experiments. By considering the primitive chain we are able to directly visualize the confinement to a tube. Analyzing the Rouse mode relaxation allows us to exclude the generalized Rouse models, while the original reptation prediction gives a good description of the data.

Dynamics of entangled linear polymer melts: A molecular‐dynamics simulation

Current status and future perspectives in atom transfer radical polymerization (ATRP) are presented. Special emphasis is placed on mechanistic understanding of ATRP, recent synthetic and process development, and new controlled polymer architectures enabled by ATRP. New hybrid materials based on organic/inorganic systems and natural/synthetic polymers are presented. Some current and forthcoming applications are described.

Atom Transfer Radical Polymerization (ATRP): Current Status and Future Perspectives

http://wwwcourses.sens.buffalo.edu/ce435/Pedersen97.pdf

Analysis of small-angle scattering data from colloids and polymer solutions: modeling and least-squares fitting

Recent attempts have been made to assess the relative merits of the free volume and entropy theories of viscous flow in glass‐forming liquids by accurate measurement of viscosity over wide temperature ranges, and subsequent comparison with the equations derived from these theories. In the author's view, this effort is misguided. The theories are crude and qualitative, and such tests are too stringent. It is better to make qualitative or semiquantitative comparison of a wide variety of physical phenomena; judged by this criterion, the entropy theory appears more successful. It is conjectured that further progress can be made by accepting the crude, naive character of any model we are likely to find tractable for the foreseeable future, and recognizing both the values and limitations of such models. A picture of the flow process in viscous liquids is proposed, in an attempt to answer certain questions about the molecular steps in flow either answered unsuccessfully or ignored by present theories, in the hop...

/pdf/viscous-liquids-and-the-glass-transition-a-potential-energy-47wz1nu6jb.pdf

Viscous Liquids and the Glass Transition: A Potential Energy Barrier Picture

Viscometric, static and light scattering data on several phenyl-ether-phenylketone copolymers (PEK, PEEK, PKEEK, PKEKEK) in solution in sulfuric acid are analyzed to elucidate the role of electrostatic interactions on the chain conformation and intermolecular interactions. It is concluded that although interactions do play an important part in intermolecular interactions, intramolecular excluded volume interactions are negligible, and the persistence length is not much affected by intramolecular electrostatic interactions. A larger than expected persistence length may be due to certain resonance-stabilized chain conformations

Studies on dilute solutions of phenyl ether ketone copolymers

Rheological and rheo-optical studies on solutions of the rod-like poly(1,4-phenylene-2,6-benzobisthiazole) are described for both isotropic and nematic solutions. The data include both steady-state and transient behaviour. For isotropic solutions it is found that a single-integral constitutive equation (a form of the B.K.Z. equation) represents the data available. For nematic solutions unexplained behaviour is observed for small κ, perhaps related to unstable flow in simple shear predicted for such solutions by some mechanistic theories for the parameters in the Leslie–Erickson constitutive equation. For larger κ the flow behaviour may be represented by a modified form of the single-integral equation.

Rheological and rheo-optical studies of a constitutive equation for nematogenic solutions of rod-like polymers

Light Scattering Studies on Dilute Solutions of Semiflexible Polyelectrolytes

A rheometer utilizing an eddy-current torque transducer and an air-bearing suspension is described. The rheometer is coupled with a computer-based data acquisition system and permits studies of shear deformation for several strain or stress histories. A sinusoidal stress history is used to determine the shear storage and loss compliances J′(ω) and J″(ω), respectively. Step stress histories are used to determine the shear creep compliance J(t) and the recoverable complaince R(t) or more complicated linear and nonlinear rheological responses related to these. Deformation at constant strain rate is used to determine the stress growth function or the steady-state viscosity. The rheometer may be used over the temperature range – 10–180°C, with torque from 1 to 106 dyn cm, and is adaptabel to use with a variety of sample geometrical shapes (e.g., cone and plate, parallel plate, etc.). Examples of measurements on on viscoelastic fluids and on gels below their yield strain are given.

A rotational rheometer for rheological studies with prescribed strain or stress history

The use of classical, or time-averaged, light scattering methods to characterize the size and size distribution of macromolecules in dilute solutions or particles in dilute dispersions is discussed. The necessary scattering relations are presented systematically, starting with three cases at infinite dilution: the scattering extrapolated to zero angle, the scattering at small angle, and the scattering for arbitrary angle, including the inversion of the scattering data to estimate the size distribution. The relationships needed to effect an extrapolation to infinite dilution from data on dilute solutions are also discussed. These are followed by remarks on light scattering methods, and the concluding sections give examples for several applications. The Rayleigh-Gans-Debye (RGD) approximation is usually appropriate in the scattering from dilute polymer solutions and is also adequate for the scattering from dilute dispersions of small particles. The approximation is assumed when appropriate, but more complete theories are introduced where necessary, as in the use of the Mie-Lorentz theory for large spherical particles.


Keywords:

light scattering;
Rayleigh-Gans-Debye;
Mie scattering;
static scattering;
Mie scatteing;
non-ergodic scattering;
diffuse scattering

Guy C. Berry

Papers

Studies on dilute solutions of phenyl ether ketone copolymers

Rheological and rheo-optical studies of a constitutive equation for nematogenic solutions of rod-like polymers

Light Scattering Studies on Dilute Solutions of Semiflexible Polyelectrolytes

A rotational rheometer for rheological studies with prescribed strain or stress history

Light Scattering, Classical: Size and Size Distribution Characterization