High-Pressure Micellar Solutions of Polystyrene-block-polybutadiene and Polystyrene-block-polyisoprene in Propane Exhibit Cloud-Pressure Reduction and Distinct Micellization End Points

Micellar solutions of polystyrene-block-polybutadiene and polystyrene-block-polyisoprene in propane are found to exhibit significantly lower cloud pressures than the corresponding hypothetical nonmicellar solutions. Such a cloud-pressure reduction indicates the extent to which micelle formation enhances the apparent diblock solubility in near-critical and hence compressible propane. Concentration-dependent pressure-temperature points beyond which no micelles can be formed, referred to as the micellization end points, are found to depend on the block type, size, and ratio. The cloud-pressure reduction and the micellization end point measured for styrene-diene diblocks in propane should be characteristic of all amphiphilic diblock copolymer solutions that form micelles in compressible solvents.

Association and Structure of Thermosensitive Comblike Block Copolymers in Aqueous Solutions

The structures and association properties of thermosensitive block copolymers of poly(methoxyoligo( ethylene glycol) norbornenyl esters) in D2O were investigated by small angle neutron scattering (SANS). Each block is a comblike polymer with a polynorbornene (PNB) backbone and oligo ethylene glycol (OEG) side chains (one side chain per NB repeat unit). The chemical formula of the block copolymer is (OEG3NB) 79- (OEG6.6NB) 67, where subscripts represent the degree of polymerization (DP) of OEG and NB in each block. The polymer concentration was fixed at 2.0 wt % and the structural changes were investigated over a temperature range between 25 and 68°C. It was found that at room temperature polymers associate to form micelles with a spherical core formed by the block (OEG3NB) 79 and corona formed by the block (OEG6.6NB) 67 and that the shape of the polymer in the corona could be described by the form factor of rigid cylinders. At elevated temperatures, the aggregation number increased and the micelles became more compact. At temperatures around the cloud point temperature (CPT) T ) 60 °C a correlation peak started to appear and became pronounced at 68 °C due to the formation of a partially ordered structure with a correlation length ∼349 Å.

Written Solutions of Mathematical Word Problems

In this action research study of my classroom of ten ninth grade algebra students, I investigated how my students expressed written solutions of mathematical word problems. I discovered that my students writing and performance improved as they experienced different strategies to attack problem solving. These experiences helped improve the confidence of my students in their problem solving skills and in their mathematical writing. I also discovered that my teaching style changed, as my students took on more responsibility for their learning. As a result of this research, I plan to implement problem solving activities in all my classrooms next year. I also plan to have my students develop their written communication skills by presenting their solutions to their problem solving activities in writing.

Deterministic Solutions for a Step-growth Polymerization

Chain topology, including branch node, chain link and cross-link dynamics that contribute to the number of elastically active strands and junctions, are calculated using purely deterministic derivations. Solutions are not coupled to population density distributions. An eigenzeit transformation assists in the conversion of expressions derived by chemical reaction principles from time to conversion space, yielding transport phenomena type expressions where the rate of change in the molar concentrations of branch nodes with respect to conversion is expressed as functions of the fraction of reactive sites on precursors and reactants. Analogies are hypothesized to exist in cross-linking space that effectively distribute branch nodes with i reacted moieties between cross-links having j bonds extending to the gel. To obtain solutions, reacted sites on nodes or links with finite chain extensions are examined in terms of stoichiometry associated with covalent bonding. Solutions replicate published results based on Miller and Macosko’s recursive procedure and results obtained from truncated weighted sums of population density distributions as suggested by Flory.