A model for phase transitions in Tetrathiafulvalene-Tetracyanoquinodimethane (TTF-TCNQ)

The observed phase transitions in Tetrathiafulvalene-Tetracyanoquinodimethane (TTF-TCNQ) are discussed using a simple model for the interchain coupling of charge density waves. Estimates based on Coulomb energies show that for 38 K < T < 49 K the components $\text{q}{}_{\mathrm{x}}\text{=}\text{π}\text{a}\text{+ q′}{}_{\mathrm{x}}$ and q_z of the wave vector associated with the charge density wave satisfy $\text{q}{}_{\mathrm{z}}\text{c}\text{q′}{}_{\mathrm{x}}\text{a?0.1}$, with $\text{q′}{}_{\mathrm{x}}\text{a～(T}{}_2\text{? T)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and T₂ = 49 K. A possible mechanism for the first order transition at 38 K is proposed. The results are compared with neutron and X-ray scattering and with isotope shifts of the transition temperatures.     

Networks of rigid molecules

Networks of rigid molecules do not fit into the paradigm of classical theories of rubber elasticity. Some experimental properties of rigid polyamide networks are summarised, and the basis for a theoretical understanding of such systems is discussed and elaborated in terms of the properties such as the existence of several conformational states and twist of such network elements.     

Why is the DNA denaturation transition first order?

We study a model for the denaturation transition of DNA in which the molecules are considered as being composed of a sequence of alternating bound segments and denaturated loops. We take into account the excluded-volume interactions between denaturated loops and the rest of the chain by exploiting recent results on scaling properties of polymer networks of arbitrary topology. The phase transition is found to be first order in d = 2 dimensions and above, in agreement with experiments and at variance with previous theoretical results, in which only excluded-volume interactions within denaturated loops were taken into account. Our results agree with recent numerical simulations.     

Probing intermolecular couplings in liquid water with two-dimensional infrared photon echo spectroscopy

Two-dimensional infrared photon echo and pump probe studies of the OH stretch vibration provide a sensitive probe of the correlations and couplings in the hydrogen bond network of liquid water. The nonlinear response is simulated using numerical integration of the Schrodinger equation with a Hamiltonian constructed to explicitly treat intermolecular coupling and nonadiabatic effects in the highly disordered singly and doubly excited vibrational exciton manifolds. The simulated two-dimensional spectra are in close agreement with our recent experimental results. The high sensitivity of the OH stretch vibration to the bath dynamics is found to arise from intramolecular mixing between states in the two-dimensional anharmonic OH stretch potential. Surprisingly small intermolecular couplings reproduce the experimentally observed intermolecular energy transfer times.     

Stochastic Liouville equation simulation of multidimensional vibrational line shapes of trialanine

The line shapes detected in coherent femtosecond vibrational spectroscopies contain direct signatures of peptide conformational fluctuations through their effect on vibrational frequencies and intermode couplings. These effects are simulated in trialanine using a Green's function solution of a stochastic Liouville equation constructed for four collective bath coordinates (two Ramachandran angles affecting the mode couplings and two diagonal energies). We find that fluctuations of the Ramachandran angles which hardly affect the linear absorption can be effectively probed by two-dimensional spectra. The signal generated at k(1)+k(2)-k(3) is particularly sensitive to such fluctuations.     

Rigid aromatic fractal polyamides

The preparation of rigid aromatic, highly branched polyamides is described. Owing to the method of preparation and the chosen ratio of difunctional to trifunctional monomers, these entities are highly porous and not dendrimeric in nature. They better conform with the fractal model and are therefore called fractal polyamides (FPs). The effects of variations in the polymerization procedure, in total monomer concentration, in the ratio of amine to carboxyl groups and in the duration of the polycondensation reaction are investigated. Some characterization was performed and the results are presented and briefly discussed.     

Water Solubilization in Nonionic Microemulsions Stabilized by Grafted Siliconic Emulsifiers

Microemulsions containing octanol, decanol, or dodecanol as the oil phase and oligomeric, grafted nonionic amphiphiles based on ethoxylated polymethylsiloxanes (Silwets) have been studied. It was demonstrated that significant amounts of water can be solubilized only when the hydrophobic siliconic backbone is very short (trimers). The water solubilization was evaluated using SAXS, DSC, and conductivity measurements. It was found that up to 40 wt% of water can be solubilized in dodecanol and Silwet L-7607 (MW 1000 and 75 wt% ethylene oxide (EO)). Surprisingly, no free water was detected in the aggregate core. All the solubilized water was confined in the vicinity of the interphasal region and froze at -10 degrees C and below. Up to three molecules of water can be associated with each EO headgroup. Based on SAXS measurements, the structural units of the microemulsions were interpreted to be lamellar-like, a form previously found for the related monomeric microemulsions. Copyright 2001 Academic Press.     

Moments of partitions and derivatives of higher order

Journal of Algebraic Combinatorics - We define moments of partitions of integers, and show that they appear in higher-order derivatives of certain combinations of functions.     

3D differential game guidance

Three-dimensional guidance in the neighborhood of collision course, based on a terminal differential game, renders ellipsoidal control sets. As a result, a saddle-point contains singularities. This paper (a) generalizes previous results on linear dynamics with terminal cost and ellipsoidal control sets and (b) applies the results to the above guidance problem to include general missile and target transfer functions. We further demonstrate the construction of the isocost surfaces (tubes).