Topological phase transition in a RNA model in the de Gennes regime

We study a simplified model of the RNA molecule proposed by G. Vernizzi, H. Orland and A. Zee in the regime of strong concentration of positive ions in solution. The model considers a flexible chain of equal bases that can pairwise interact with any other one along the chain, while preserving the property of saturation of the interactions. In the regime considered, we observe the emergence of a critical temperature T_c separating two phases that can be characterized by the topology of the predominant configurations: in the large temperature regime, the dominant configurations of the molecule have very large genera (of the order of the size of the molecule), corresponding to a complex topology, whereas in the opposite regime of low temperatures, the dominant configurations are simple and have the topology of a sphere. We determine that this topological phase transition is of first order and provide an analytic expression for T_c. The regime studied for this model exhibits analogies with that for the dense polymer systems studied by de GennesComment: 15 pages, 4 figure

Thermodynamics of a model for RNA folding

We analyze the thermodynamic properties of a simplified model for folded RNA molecules recently studied by G. Vernizzi, H. Orland, A. Zee (in {\it Phys. Rev. Lett.} {\bf 94} (2005) 168103). The model consists of a chain of one-flavor base molecules with a flexible backbone and all possible pairing interactions equally allowed. The spatial pseudoknot structure of the model can be efficiently studied by introducing a $N \times N$ hermitian random matrix model at each chain site, and associating Feynman diagrams of these models to spatial configurations of the molecules. We obtain an exact expression for the topological expansion of the partition function of the system. We calculate exact and asymptotic expressions for the free energy, specific heat, entanglement and chemical potential and study their behavior as a function of temperature. Our results are consistent with the interpretation of $1/N$ as being a measure of the concentration of $\rm{Mg}^{++}$ in solution.Comment: 11 pages, 4 figure

Structure, properties and interfacial interactions in poly(lactic acid)/polyurethane blends prepared by reactive processing

Polyurethane elastomers are promising candidates for the impact modification of PLA producing blends for example for biomedicine. Poly(lactic acid) (PLA)/polyurethane elastomer (PU) blends were prepared by reactive processing and physical blending as comparison. The blends were characterized by a number of techniques including microscopy (scanning electron microscopy, SEM, and atomic force microscopy, AFM), rotational viscometry, thermal (dynamic mechanical analysis), DMA, and mechanical (tensile) measurements. The analysis and comparison of the structure and properties of physical and reactor blends proved the successful coupling of the phases. Coupling resulted in more advantageous structure and superior mechanical properties compared to those of physical blends as confirmed by morphology, macroscopic properties and the quantitative estimation of interfacial interactions. Structural studies and the composition dependence of properties indicated the formation of a submicron, phase-in-phase structure which positively influenced properties at large PU contents. The results strongly support that reactive processing is a convenient, cost-effective and environmentally friendly technique to obtain blends with superior properties