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

Certain aspects of the physical chemistry of solutions rodlike polymers are reviewed. The range of concentrations includes infinite dilution ([ŋ]c<<l), dilute solutions ([ŋ,]c<l), moderately concentrated solutions (l<[ŋ]c<[ŋ]cNI), and concentrated solutions (c<cN,), where [ŋ] is the intrinsic viscosity and cNI. is the concentration required for a stable nematic phase. Studies of chain conformation are emphasized at infinite dilution, and rheological behavior is emphasized for more concentrated isotropic and nematic solutions. Both theoretical and experimental considerations are included.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S1946427400542699

Properties of Solutions of Rodlike Chains from Dilute Solutions to the Nematic State

Static and dynamic light scattering data are reported on dilute and moderately concentrated solutions of a high molecular weight polystyrene (Mw = 3.61 × 106) in bis(2-ethylhexyl) phthalate under Flory Theta conditions. The data cover a concentration range with 0.03 × [η]c × 3.5, with several concentrations large enough that the product cMw exceeds the value necessary for entanglement behavior. The results show that a certain intermolecular scattering function H(q, c) often approximated by unity should not be neglected in the evaluation of the correlation length in the static scattering from moderately concentrated solutions of flexible chain polymers. An approximate form for H(q, c) for moderately concentrated solutions is consistent with a soft spherically symmetric repulsive potential among the chains. The dynamic scattering show two distinct groups of relaxation rates at all concentrations, but the interpretation of the two modes changes as the concentration increases from low concentrations ([η]c 2.4 the slow mode is viscoelastic in origin, and the faster mode is diffusive. The behavior is compared with theoretical predictions in both regimes.

Moderately concentrated solutions of polystyrene, part 5. Static and dynamic light scattering in bis(2‐ethylhexyl) phthalate

The kinetics of the polycondensation of 3,3′-diaminobenzidine with 1,4,5,8-naphthalenetetracarboxylic acid (NTC) have been investigated. Polymerizations were carried out in solution in either polyphosphoric acid (PPA) or in PPA mixed with some sulfuric acid. The reaction is heterogeneous in PPA owing to partial solubility of NTC, whereas it is homogeneous in the mixed solvent. The rate of disappearance of NTC and of dicarboxylic endgroups on oligomers was followed as a function of time at several reaction temperatures. The results show that NTC is more reactive than oligomers, so that the principle of equal reactivity is not valid for the initial steps in the polycondensation reaction.

Kinetics of formation of polybisbenzimidazobenzophenanthroline‐dione (BBB polymer)

The anisotropic third-order nonlinear optical susceptibility χ(3) of monodomain samples of nematic solutions of poly[1,4-phenylene-2,6-benzobisthiazole], PBT, a rodlike polymer, have been studied by third harmonic generation. The principal component of χ(3)(−3ω;ω,ω,ω) is not along the nematic director, as opposed to the linear dielectric, which has the maximum refractive index along the director.

https://apps.dtic.mil/sti/pdfs/ADA270217.pdf

Anisotropic Third-Order Susceptibility of a Nematic Solution of a Rodlike Polymer (PBT)

Rheological and rheo-optical studies on isotropic and nematic solutions of poly (1,4-phenylene-2, 6-benzobisthiazole), PBT, are reviewed. The linear visco-elastic behavior is compared with theoretical models for the isotropic solutions. A BKZ-type constitutive equation coupled with an experimentally determined distribution of relaxation times is found to represent the nonlinear viscoelastic data reported for the isotropic data; comparisons with theoretical models are made. With the nematic solutions, nonlinear viscoelastic behavior is found even for very slow shearing deformations. This behavior may be related to orientation effects at the bounding surfaces. For more rapid shearing deformations, the bulk of the fluid is strongly oriented, similar to the orientation obtained in the isotropic fluid at high rates of shearing deformation. Comparisons are made among a number of rheological properties for isotropic and nematic solutions for the latter flows.

Guy C. Berry

Papers

Properties of Solutions of Rodlike Chains from Dilute Solutions to the Nematic State

Moderately concentrated solutions of polystyrene, part 5. Static and dynamic light scattering in bis(2‐ethylhexyl) phthalate

Kinetics of formation of polybisbenzimidazobenzophenanthroline‐dione (BBB polymer)

Anisotropic Third-Order Susceptibility of a Nematic Solution of a Rodlike Polymer (PBT)

Rheological and Rheo-Optical Studies with Nematogenic Solutions of a Rodlike Polymer: A Review of Data on Poly (Phenylene Benzobisthiazole)