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

Integrated intensity and photon correlation experiments are combined to study the effects of intermolecular association in dilute solutions of the rodlike poly(l,4-phenylene-2-6-benzobisthiazole) in dilute solution. The autocorrelation function g(2)(τ), the dependence of the second factorial moment n(2)(Δτ) on the sampling interval duration Δτ, and the integrated polarized and depolarized intensities are analyzed in terms of a quasi—two component mixture comprising unassociated chains and intermolecular aggregates. The latter persist in dilute solutions, even though the polymer exists as a macroion in the strong proton sulfonic acid used as a solvent. The unassociated chains which are 20–25 nm long are found to be predominant in weight fraction, but the aggregates, about 3 nm in diameter and 210 nm in length are large enough to dominate the scattering at small scattering angle.

Studies on Dilute Solutions of Rodlike Macroions III. Integrated Intensity and Photon Correlation Light Scattering Investigation of Association

: Rheological and rheo-optical properties of mesogenic solutions of rodlike polymers are discussed. Some of the salient features of the observed behavior with isotropic solutions described, including a single-integral constitutive equation that is found to be useful, and a review of certain aspects of theoretical treatments of the viscosity of nematic fluids. The light scattering experiments are discussed, including studies on a monodomain formed with a PBT solution. Aspects of the rheological behavior of nematic solutions of PBT are considered, first for recently small strain and then for deformation with large strain rates. Reprints, Thiazoles.

Rheological, Rheo-Optical and Light Scattering Studies on Nematic Solutions of Poly(1,4-Phenylene-2,6-Benzobisthiazole)

Three preparations of a phenyl-substituted polyphenylene were fractionated and studied in solution by light scattering, osmometry, viscometry, fluorescence depolarization, and exclusion chromatography. Three of the five main-chain phenylene groups in the repeat unit are linked para, but the other two may be either meta or para, with the latter linkage predominating. The data are consistent with a chain structure characterized by rigid segments about 70–75A long, on the average, joined with 120° bond angles, about which virtually free rotation is allowed. For chains of up to about 250 backbone phenylene units, the hydrodynamic behavior in tetrahydrofuran, and other solvents, is that of a freely draining coil with intrinsic viscosity proportional to molecular weight. The effect of intramolecular excluded volume on chain conformation is negligible, although intermolecular interactions are reflected by a positive second virial coefficient (in tetrahydrofuran). Study of polymers of higher molecular weight is hampered by formation of what appear to be metastable aggregates resembling randomly branched chains.

Properties of a phenyl‐substituted polyphenylene in dilute solution

3 – Polymer Solutions

Viscoelastic properties are followed during the formation of gels by moderately concentrated solutions of atactic polystyrene (aPS) in a mixed solvent of carbon disulfide and tri-m-tolyl phosphate (TCP). This mixture is a thermodynamically “good” solvent for aPS and with solution glass transition temperatures far below the temperatures used in the study. Gel formation is driven by the CS2 component, at temperatures and polymer concentrations similar to those observed in solutions of aPS in pure CS2. The TCP adjusts the viscoelastic response to a convenient range. The results show appreciable hysteresis in the melting and formation temperatures of gels, with the gel formation being a slow process, permitting dynamic mechanical or creep and creep recovery studies as a function of ageing during gel formation, as well as on the solutions prior to permit gel formation. These data reveal systematic behavior analyzed using the linear viscoelastic constitutive relation to obtain the viscosity and a measure of the...

Guy C. Berry

Papers

Studies on Dilute Solutions of Rodlike Macroions III. Integrated Intensity and Photon Correlation Light Scattering Investigation of Association

Rheological, Rheo-Optical and Light Scattering Studies on Nematic Solutions of Poly(1,4-Phenylene-2,6-Benzobisthiazole)

Properties of a phenyl‐substituted polyphenylene in dilute solution

3 – Polymer Solutions

Moderately concentrated solutions and gels of atactic polystyrene in solvent mixtures of carbon disulfide and tricresyl phosphate