http://wwwcourses.sens.buffalo.edu/ce435/Riess03.pdf

Micellization of block copolymers

Critical phenomena and renormalization-group theory

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

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

Crew-cut micelle-like aggregates of various morphologies prepared from polystyrene-b-poly(acrylic acid), PS-b-PAA, diblock copolymers under near-equilibrium conditions, were studied by transmission electron microscopy (TEM). The insoluble block (PS) contents in the copolymers ranged from 80 to 98 wt %. In spherical micelles, the micelle cores, formed by aggregation of the PS blocks, were generally monodisperse. A comparison between star and crew-cut micelles showed that the latter are distinguished by a low density of corona chains on the core surface and a low degree of stretching of the PS blocks in the cores. As the PAA content in block copolymer decreased, the morphology of the aggregates changed progressively from spheres to cylinders, to bilayers (both vesicles and lamellae), and eventually to compound micelles consisting of an assembly of inverted micelles surrounded by a hydrophilic surface. The compound micelles are believed to be a new morphology for block copolymers. The addition of homopolysty...

Multiple Morphologies and Characteristics of “Crew-Cut” Micelle-like Aggregates of Polystyrene-b-poly(acrylic acid) Diblock Copolymers in Aqueous Solutions

The entanglement concept in polymer rheology

The osmotic second virial coefficient of flexible polymer solutions is calculated on the basis of the pearl‐necklace model with continuous medium approximation. Proper account is taken not only of the intermolecular interaction but also of the intramolecular interaction of segments or the so‐called ``excluded volume effect.'' Evaluation is carried out to the triple contact approximation. The results show that the intramolecular interaction has a marked influence on the molecular weight dependence of the coefficient.Then, theories of the intrinsic viscosity and frictional coefficient are developed on the same model as above, following the Kirkwood and Riseman scheme. The results show that, if α is the linear expansion factor of the polymer coil, the intrinsic viscosity is asymptotically proportional to α2 for the free‐draining case and α2.43 for the impermeable case. This implies that even in the limit for impermeable molecule, the hydrodynamic radius of the polymer coil is not proportional to its statisti...

Theory of Dilute Polymer Solution. II. Osmotic Pressure and Frictional Properties

A series of approximations for the statistical mechanics of order‐disorder, proposed by Bethe, Takagi, Yang‐Li‐Hill, Kikuchi, and others, are investigated in detail in two ways. (1) A new interpretation of the method for constructing the combinatory factor is presented in order to give a better understanding of the nature of approximations. (2) The partition functions with approximate combinatory factors are expanded to compare with the rigorous expansion and the discrepancies between them are investigated in detail. One of the conclusions is that in order to obtain a higher approximation, it is necessary to use the basic figure ``closed'' with respect to the cluster of the preceding approximation. In appendices, an improved treatment of the body‐centered cubic lattice (Ising model) is given, and Bethe's fundamental assumptions are derived from our scheme.

A Theory of Cooperative Phenomena. III. Detailed Discussions of the Cluster Variation Method

A new closed expression for the excluded volume effect of linear polymer molecules is developed with the aid of an equivalent ellipsoid model, in which the polymer chain with fixed ends is replaced by a uniform distribution of unconnected segments within an ellipsoid whose dimensions are chosen to give the correct principal radii of gyration of the chain. The linear expansion factor α for a chain of N segments is given by (α3−α)/N12={(1+13α−2)−32}−1(4/3)5/2(3/2π)32(β/a3) where a is the effective bond length and β is the binary cluster integral of a segment pair. In contrast to Flory's familiar equation, the ratio (α5—α3)/N½ is an increasing function of α instead of a constant. The new equation is in excellent agreement with the Monte Carlo calculations of Wall and Erpenbeck for a diamond lattice chain and also with existing viscosity data for various polymer solutions, provided that the expansion factor is evaluated from the equation [η]/[η]θ=α2.43 in accord with the theories of Kurata‐Yamakawa and Ptitsyn‐Eisner. It is also shown that the present equation for α is in rather good agreement with the numerical solution of Fixman's differential equation.

Excluded Volume Effect of Linear Polymer Molecules

Material time constant characterizing the nonlinear viscoelasticity of entangled polymeric systems

The sedimentation constant of a series of multiple‐ring macromolecules has been calculated by the method of Kirkwood. The multiple‐ring form consists of m subrings of equal size linearly connected by universal joints. In the limit of large intersegmental hydrodynamic interaction, the ratio of the sedimentation constant of a multiple‐ring molecule to that of a linear chain of the same molecular weight is 1.18 for m=1, 1.32 for m=2, 1.40 for m=3, ··· and 2.00 for extremely large m. These values are found to be practically independent of the excluded volume effect.The intrinsic viscosity of a single‐ring macromolecule has also been calculated by the method of Zimm. The eigenvalue problem encountered in the Zimm theory can be solved exactly over the whole range of the hydrodynamic interaction parameter, h=0 to ∞. The ratio of intrinsic viscosities of ring and linear molecules is 0.500 for h=0 (free‐draining case) and 0.645 for h= ∞ (non free‐draining case). The latter value is slightly modified if the hydrody...

Michio Kurata

Papers

Theory of Dilute Polymer Solution. II. Osmotic Pressure and Frictional Properties

A Theory of Cooperative Phenomena. III. Detailed Discussions of the Cluster Variation Method

Excluded Volume Effect of Linear Polymer Molecules

Material time constant characterizing the nonlinear viscoelasticity of entangled polymeric systems

Hydrodynamic Properties of Flexible‐Ring Macromolecules