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...

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

Light scattering, intrinsic viscosity, gel-permeation chromatography, and fluorescence depolarization measurements are reported on dilute solutions of a heterocyclic polymer (BBL) prepared by polymerization of 1, 4, 5, 8-naphthalene tetracarboxylic acid with 1, 2, 4, 5-tetraaminobenzene. The light-scattering data on fractions of the polymer giving the anisotropy δ and the mean-square radius of gyration s2 are discussed in terms of equations for the scattering from polydisperse anisotropic polymer. It is concluded from the dependence of δ and 〈s2〉 on the molecular weight that the polymer has a nearly rodlike conformation. The intrinsic viscosity data are analyzed in terms of relations for rods and wormlike chains. The fluorescence emission anisotropy is found to be so sensitive to molecular-weight distribution that analysis in terms of molecular parameters is prohibited. Association that can occur under certain circumstances is discussed.

Properties of an optically anisotropic heterocyclic ladder polymer (BBL) in dilute solution

http://www.chem.cmu.edu/groups/Berry/906.pdf

Viscoelastic and dielectric studies on comb- and brush-shaped poly(n-butyl acrylate)

Studies on the properties of the double-chain ladder polymer of cis-syndiotactic poly(phenylsilsesquioxane) (PPSQ) in dilute and concentrated solutions are reported. Data on the intrinsic viscosity [η], the second virial coefficient A2, and the mean-square radius of gyration 〈s2〉 as functions of molecular weight M, temperature, and solvent lead to the conclusion that the conformation of PPSQ can be modeled with a wormlike chain model with a persistence length ρ of 74 A. These data cannot be used to assess the extent of intramolecular inflexibility, e.g., resistance to rotational isomerization, of PPSQ. For concentrated solutions (0.05 ⩽ c ⩽ 0.20 g/ml) the limiting viscosity ⩾0 at zero shear rate is proportional to cM for cM < ⩾2Mc and to (cM)3,4 for cM ⩾ ρ2Mc, where Mc = 9120. The product Xc (〈s20/M) × ρ2Mc/ma is equal to 356 × 10−17 for PPSQ, close to the value 400 × 10−17 typical of single-chain polymers. The reduced flow curve ηK/ϵ0 versus ηCK for the viscosity ϵK as a function of shear rate K is not far different from that for single-chain polymers—here, the time constant ηC is equal to η0R0 with R0 the limits of the recovery function RK, at small K(R0 is often denoted Je0). The values of ηc are intermediate to ηc for a flexible single-chain polymer and the relaxation time ηR for rotatory diffusion of a rigid coil. Plots of RK versus K superpose with plots of the transient recovery R0(ϑ) with ϑ = K−1 over the limited range ηCK < 1 where ϑ is the recovery time (R0(ϑ) goes to R0 for large ϑ), similar to behavior found with solutions of single-chain polymers.

Properties of the ladder polymer cis‐syndiotactic poly(phenylsilsesquioxane) in solution

Moderately concentrated solutions of polystyrene: 4. Elastic and quasi-elastic light scattering at the Flory theta temperature

Data on the viscosity of poly(vinyl acetate) (PVOAc) and its concentrated solutions in diethyl phthalate (DEP) and cetyl alcohol (CeOH) are examined over the molecular weight range 8 × 103 ca. 0.25, increasing with decreasing φ for smaller φ. Both β and T0 depend on φ, and T0 also depends on M at low M.

Guy C. Berry

Papers

Properties of an optically anisotropic heterocyclic ladder polymer (BBL) in dilute solution

Viscoelastic and dielectric studies on comb- and brush-shaped poly(n-butyl acrylate)

Properties of the ladder polymer cis‐syndiotactic poly(phenylsilsesquioxane) in solution

Moderately concentrated solutions of polystyrene: 4. Elastic and quasi-elastic light scattering at the Flory theta temperature

Viscosity of poly(vinyl acetate) and its concentrated solutions