Unusual contributions of molecular architecture to rheology and flow birefringence in hyperbranched polystyrene melts

With the increase in sophisticated synthesis methods, it appears that polymer architecture may be a tunable property. Therefore, the role of architecture in rheological and processing properties has received renewed attention, mainly because of dendrimer synthesis and metallocene‐catalyst technology. Linear polymers and hyperbranched polymers represent two ends of branching complexity. Some previous studies have suggested that hyperbranched polymers may behave like unentangled polymers, whereas others have proposed that they exhibit the properties of soft colloids. In an effort to compare the responses of linear and hyperbranched polymers, we synthesized starlike hyperbranched polystyrenes (HBPSs) of various branch lengths and numbers of branches. The HBPSs used in this study were unentangled or weakly entangled, allowing us to study the effect of branch density more readily. Two linear polystyrene (L‐PS) melts and two HBPSs were studied. Using a custom‐built rheooptical apparatus, we characterized the rheology and flow birefringence of these materials. To our knowledge, these are the first flow birefringence measurements on highly branched polymer melts. Our results suggest that the flow behavior of HBPS is significantly different from that of L‐PS: (1) HBPS shows nonterminal behavior in the low‐frequency rheological response; (2) when the stress‐optical rule (SOR) holds, the stress‐optical coefficient of HBPS is much lower than those of analogous linear polymers; and (3) when the branch density is high and the branch length is sufficiently low, the SOR fails for these homopolymer melts. A significant increase in the birefringence for a given amount of stress in the low‐frequency region suggests that there may be a soft core in these materials due to the strong preferential radial orientation of chain segments near the center of a molecule versus those near the periphery. The predominantly elastic response of the soft structures may be responsible for the enhanced form birefringence. Our preliminary results indicate that these materials may exhibit both polymeric and soft‐colloid natures. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2562–2571, 2001     

One- and two-dimensional coordination networks of the tetracyanoethylene anion-radicals with potassium counter-ions

Potassium-mirror reduction of tetracyanoethylene (TCNE) acceptor in tetrahydrofuran affords K(THF)₂ TCNE salt (1) showing double TCNE/K chains assembled via unusual μ₃-TCNE-bridging of potassium cations. These parallel ladder-type chains are further tethered by pairs of THF bridges between potassium centers and by intermolecular π-bonding in (TCNE)₂^2? dimers, and this results in formation of quasi-2-D coordination networks. In the presence of crown-ether ligand, the same potassium-mirror reduction lead to formation of [K(18-crown-6)(THF)₂]TCNE salt (2) in which monomeric tetracyanoethylene anion-radicals are positioned between bulky [K⁺(18-crown-6)(THF)₂] counter-ions. In comparison, crystallization of tetracyanoethylene anion-radicals with K⁺(18-crown-6) counter-ions in dichloromethane affords K(18-crown-6)TCNE salt (3) consisting of 1-D chains with 1,2-(N,N’)-TCNE bindings of potassium cations (nested in the crown-ether cavities). Temperature-dependent magnetic susceptibility study revealed essentially isolated tetracyanoethylene anion-radicals (S = 1/2) in this 1-D coordination polymer.     

Influence of liquid layers on energy absorption during particle impact

The influence of the thickness of a covering liquid layer and its viscosity as well as the impact velocity on energy loss during the normal impact on a flat steel wall of spherical granules with a liquid layer was studied. Free-fall experiments were performed to obtain the restitution coefficient of elastic–plastic Al2O3 granules by impact on the liquid layer, using aqueous solutions of hydroxypropyl methylcellulose with different concentrations for variation of viscosity (1–300 mPa s). In the presence of a...     

Increasing engineering students' awareness to environment through innovative teaching of mathematical modelling

This article presents the results of two studies on using aninnovative pedagogical strategy in teaching mathematical modellingand applications to engineering students. Both studies are dealingwith introducing non-traditional contexts for engineering studentsin teaching/learning of mathematical modelling and applications:environment and ecology. The aims of using these contexts were:to introduce students to some of the techniques, methodologiesand principles of mathematical modelling for ecological andenvironmental systems; to involve the students in solving real-lifeproblems adjusted to their region emphasizing the aspects ofboth survival (short term) and sustainability (long term); toencourage students to pay attention to environmental issues.On one hand, the contexts are not directly related to engineering.On the other hand, the chances are that many graduates of engineeringwill deal with mathematical modelling of environmental systemsin one way or another in their future work because nearly everyengineering activity has an impact on the environment. The firststudy is a parallel study conducted in New Zealand and Germanysimultaneously with first-year students studying engineeringmathematics. The second study is a case study of the experimentalcourse Mathematical Modelling of Survival and Sustainabilitytaught to a mixture of year 2–5 engineering students inGermany by a visiting lecturer from New Zealand. The modelsused with the students from both studies had several specialfeatures. Analysis of students’ responses to questionnaires,their comments and attitudes towards the innovative approachin teaching are presented in the article.     

On connected dominating sets of restricted diameter

A connected dominating set (CDS) is commonly used to model a virtual backbone of a wireless network. To bound the distance that information must travel through the network, we explicitly restrict the diameter of a CDS to be no more than s leading to the concept of a dominating s-club. We prove that for any fixed positive integer s it is NP-complete to determine if a graph has a dominating s  -club, even when the graph has diameter s+1$s+1$. As a special case it is NP-complete to determine if a graph of diameter two has a dominating clique. We then propose a compact integer programming formulation for the related minimization problem, enhance the approach with variable fixing rules and valid inequalities, and present computational results.     

Algorithms for detecting optimal hereditary structures in graphs, with application to clique relaxations

Given a simple undirected graph, the problem of finding a maximum subset of vertices satisfying a nontrivial, interesting property Π that is hereditary on induced subgraphs, is known to be NP-hard. Many well-known graph properties meet the above conditions, making the problem widely applicable. This paper proposes a general purpose exact algorithmic framework to solve this problem and investigates key algorithm design and implementation issues that are helpful in tailoring the general framework for specific graph properties. The performance of the algorithms so derived for the maximum s-plex and the maximum s-defective clique problems, which arise in network-based data mining applications, is assessed through a computational study.