Simple thermodynamics of jet engines

We use the first and second laws of thermodynamics to analyze the behavior of an ideal jet engine. Simple analytical expressions for the thermal efficiency, the overall efficiency, and the reduced thrust are derived. We show that the thermal efficiency depends only on the compression ratio r and on the velocity of the aircraft. The other two performance measures depend also on the ratio of the temperature at the turbine to the inlet temperature in the engine, T-3/T-i. An analysis of these expressions shows that it is not possible to choose an optimal set of values of r and T-3/T-i that maximize both the overall efficiency and thrust. We study how irreversibilities in the compressor and the turbine decrease the overall efficiency of jet engines and show that this effect is more pronounced for smaller T-3/T-i.

Synthesis, structure, and optical properties of an alternating calix[4]arene-based meta-linked phenylene ethynylene copolymer

Novel alternating copolymers comprising biscalix[4]arene-p-phenylene ethynylene and m-phenylene ethynylene units (CALIX-m-PPE) were synthesized using the Sonogashira-Hagihara cross-coupling polymerization. Good isolated yields (60-80%) were achieved for the polymers that show M-n ranging from 1.4 x 10(4) to 5.1 x 10(4) gmol(-1) (gel permeation chromatography analysis), depending on specific polymerization conditions. The structural analysis of CALIX-m-PPE was performed by H-1, C-13, C-13-H-1 heteronuclear single quantum correlation (HSQC), C-13-H-1 heteronuclear multiple bond correlation (HMBC), correlation spectroscopy (COSY), and nuclear overhauser effect spectroscopy (NOESY) in addition to Fourier transform-Infrared spectroscopy and microanalysis allowing its full characterization. Depending on the reaction setup, variable amounts (16-45%) of diyne units were found in polymers although their photophysical properties are essentially the same. It is demonstrated that CALIX-m-PPE does not form ground-or excited-state interchain interactions owing to the highly crowded environment of the main-chain imparted by both calix[4]arene side units which behave as insulators inhibiting main-chain pi-pi staking. It was also found that the luminescent properties of CALIX-m-PPE are markedly different from those of an all-p-linked phenylene ethynylene copolymer (CALIX-p-PPE) previously reported. The unexpected appearance of a low-energy emission band at 426 nm, in addition to the locally excited-state emission (365 nm), together with a quite low fluorescence quantum yield (Phi = 0.02) and a double-exponential decay dynamics led to the formulation of an intramolecular exciplex as the new emissive species.

Percolation of colloids with distinct interaction sites

We generalize the Flory-Stockmayer theory of percolation to a model of associating (patchy) colloids, which consists of hard spherical particles, having on their surfaces f short-ranged-attractive sites of m different types. These sites can form bonds between particles and thus promote self-assembly. It is shown that the percolation threshold is given in terms of the eigenvalues of a m x m matrix, which describes the recursive relations for the number of bonded particles on the ith level of a cluster with no loops; percolation occurs when the largest of these eigenvalues equals unity. Expressions for the probability that a particle is not bonded to the giant cluster, for the average cluster size and the average size of a cluster to which a randomly chosen particle belongs, are also derived. Explicit results for these quantities are computed for the case f = 3 and m = 2. We show how these structural properties are related to the thermodynamics of the associating system by regarding bond formation as a (equilibrium) chemical reaction. This solution of the percolation problem, combined with Wertheim's thermodynamic first-order perturbation theory, allows the investigation of the interplay between phase behavior and cluster formation for general models of patchy colloids.

Chiroptical and emissive properties of a calix[4]arene-containing chiral poly (P-phenylene ethynylene) with enantioselective recognition ability

Supramolecular chirality was achieved in solutions and thin films of a calixarene-containing chiral aryleneethynylene copolymer. The observed chiroptical activity, which is primarily allied with the formation of aggregates of high molecular weight polymer chains, is the result of a combination of intrachain and interchain effects. The former arises by the adoption of an induced helix-sense by the polymer main-chain while the latter comes from the exciton coupling of aromatic backbone transitions. The co-existence of bulky bis-calixKlarene units and chiral side-chains on the polymer skeleton prevents efficient pi-stacking of neighbouring chains, keeping the chiral assembly highly emissive. In contrast, for a model polymer lacking calixarene moieties, the chiroptical activity is dominated by strong interchain exciton couplings as a result of more favourable packing of polymer chains, leading to a marked decrease of photoluminescence in the aggregate state. The enantiomeric recognition abilities of both polymers towards (R)- and (S)-alpha-methylbenzylamine were examined. It was found that a significant enantiodiscrimination is exhibited by the calixarene-based polymer in the aggregate state.

Generalization of Wertheim's theory for the assembly of various types of rings

We generalize Wertheim's first order perturbation theory to account for the effect in the thermodynamics of the self-assembly of rings characterized by two energy scales. The theory is applied to a lattice model of patchy particles and tested against Monte Carlo simulations on a fcc lattice. These particles have 2 patches of type A and 10 patches of type B, which may form bonds AA or AB that decrease the energy by epsilon(AA) and by epsilon(AB) = r epsilon(AA), respectively. The angle theta between the 2 A-patches on each particle is fixed at 601, 90 degrees or 120 degrees. For values of r below 1/2 and above a threshold r(th)(theta) the models exhibit a phase diagram with two critical points. Both theory and simulation predict that rth increases when theta decreases. We show that the mechanism that prevents phase separation for models with decreasing values of theta is related to the formation of loops containing AB bonds. Moreover, we show that by including the free energy of B-rings ( loops containing one AB bond), the theory describes the trends observed in the simulation results, but that for the lowest values of theta, the theoretical description deteriorates due to the increasing number of loops containing more than one AB bond.

Self-interacting scalar field cosmologies: unified exact solutions and symmetries

We investigate a mechanism that generates exact solutions of scalar field cosmologies in a unified way. The procedure investigated here permits to recover almost all known solutions, and allows one to derive new solutions as well. In particular, we derive and discuss one novel solution defined in terms of the Lambert function. The solutions are organised in a classification which depends on the choice of a generating function which we have denoted by x(phi) that reflects the underlying thermodynamics of the model. We also analyse and discuss the existence of form-invariance dualities between solutions. A general way of defining the latter in an appropriate fashion for scalar fields is put forward.

Self-assembly in chains, rings, and branches: a single component system with two critical points

Agências financiadoras: FCT - PEstOE/FIS/UI0618/2011; PTDC/FIS/098254/2008 ERC-PATCHYCOLLOIDS e MIUR-PRIN

Three-dimensial patchy lattice model: Ring formation and phase separation

We investigate the structural and thermodynamic properties of a model of particles with 2 patches of type A and 10 patches of type B. Particles are placed on the sites of a face centered cubic lattice with the patches oriented along the nearest neighbor directions. The competition between the self- assembly of chains, rings, and networks on the phase diagram is investigated by carrying out a systematic investigation of this class of models, using an extension ofWertheim's theory for associating fluids and Monte Carlo numerical simulations. We varied the ratio r epsilon(AB)/epsilon(AA) of the interaction between patches A and B, epsilon(AB), and between A patches, epsilon(AA) (epsilon(BB) is set to theta) as well as the relative position of the A patches, i.e., the angle. between the (lattice) directions of the A patches. We found that both r and theta (60 degrees, 90 degrees, or 120 degrees) have a profound effect on the phase diagram. In the empty fluid regime (r < 1/2) the phase diagram is reentrant with a closed miscibility loop. The region around the lower critical point exhibits unusual structural and thermodynamic behavior determined by the presence of relatively short rings. The agreement between the results of theory and simulation is excellent for theta = 120 degrees but deteriorates as. decreases, revealing the need for new theoretical approaches to describe the structure and thermodynamics of systems dominated by small rings. (C) 2014 AIP Publishing LLC.