Properties of polystyrene-poly(methylmethacrylate) random and diblock copolymers in dilute and semidilute solutions

Solution properties for random and diblock copolymers of polystyrene (PS) and poly(methyl methacrylate) (PMMA) have been measured by dynamic and total intensity light scattering in solvents of differing quality. The results are compared with the corresponding properties for PS and PMMA homopolymers of similar molecular weight, in order to determine if interactions between unlike monomers are significant. The hydrodynamic radius (R_h) and diffusion second virial coefficient (k_d) for the random copolymer are found to be larger than the corresponding values for the homopolymers in a solvent which is near-theta for the two homopolymers, whereas no such effect is observed for the block copolymer. This suggests that most intrachain interactions occur a relatively short distance along the chain backbone. In a mutual good solvent R_h and k_d of the random copolymer are comparable to the average of the values for the homopolymers, indicating that in a good solvent monomer/solvent interactions dominate over monomer/monomer interactions. For an isolated diblock copolymer in a mutual good solvent, there is no evidence that interactions between unlike monomers lead to additional expansion of the entire molecule, as measured by R_h, nor expansion of the individual blocks as probed by light scattering with one block optically masked. However, at low but finite concentration there is evidence (the coefficients of the binary interaction terms in the viscosity and the mutual diffusion coefficient, and the second and third virial coefficients) that a weak ordering effect may exist in block copolymer solutions, far from the conditions where microphase separation occurs. Finally, measurements of ternary polymer-polymer-solvent solutions show no dependence on monomer composition or monomer distribution for the tracer diffusion of probe PS-PMMA copolymers in a PMMA/toluene matrix. This indicate that the frictional interaction is largely unaffected by interactions between unlike monomers. However, there is evidence that the thermodynamic interaction is more unfavorable between a random copolymer and the homopolymer matrix than between a diblock and the matrix. © 1994 John Wiley & Sons, Inc.     

Bundles, Handcuffs, and Local Freedom

We answer a question of J. Anderson's by producing infinitely many commensurability classes of fibered hyperbolic 3-manifolds whose fundamental groups contain subgroups that are locally free and not free. These manifolds are obtained by performing 0–surgery on a collection of knots with the same properties.     

Formation, isolation and characterization of an AB-biaryl atropisomer of oritavancin

Oritavancin is a semi-synthetic glycopeptide antibiotic which is structurally related to vancomycin. When oritavancin bisphosphate is dried in vacuo with heat, a new compound forms. This new compound is stable only in the solid state and reverts to oritavancin in solution. Highly enriched samples of this compound were obtained by preparative HPLC and the structure of this compound was elucidated by using one and two-dimensional (¹H and ¹³C) NMR spectroscopy in conjunction with computer-assisted molecular modeling. It has been determined that oritavancin adopts a conformation similar to that of vancomycin in solution, while the new compound is the unnatural R-AB-biaryl atropisomer of oritavancin. This is the first observation and isolation of an AB-biaryl atropisomer in an intact member of the vancomycin family of glycopeptide antibiotics.     

How History and Philosophy in the US Science Education Standards Could Have Promoted Multidisciplinary Teaching

Based on the forthcoming book, Time for Science Education ( Matthews, in press ), this article notes that the US National Science Education Standards advocate liberal, contextual, or cultural goals for science education, including the expectation that students will understand a certain amount of the historical and cultural significance of science. After mentioning something of the rich role played by the pendulum in the foundation of modern science, in solving the longitude problem, in establishing a universal length standard, and in allowing the creation of an accurate timekeeper, as well as the pendulum clock's function in philosophy and theology, the article draws attention to the scant treatment given the pendulum in the Standards. Opportunities are thus lost for realizing the Standards' laudable goals for US science education. Finally, it is claimed that realizing these cultural goals for science education requires more routine incorporation of the history and philosophy of science into preservice and inservice courses for science teachers.     

Constrained Lot-Sizes under Conditions of Inventory Growth

When average aggregate inventory levels are constrained to equal a constant level over time, optimal lot sizes can be identified which strike a balance between holding costs and set-up costs among items which form the aggregate. However, when it is desirable to change aggregate inventory levels over time, assumptions implicit in the traditional formulation are violated. The procedure proposed generates lot sizes which are consistent not only with the current average aggregate inventory level but also with its projected growth over the planning horizon. Comparison is made to lot sizes generated by the misapplication of traditional lot sizing methods to the inventory growth situation.