Equilibrium self-assembly of colloids with distinct interaction sites: Thermodynamics, percolation, and cluster distribution functions

We calculate the equilibrium thermodynamic properties, percolation threshold, and cluster distribution functions for a model of associating colloids, which consists of hard spherical particles having on their surfaces three short-ranged attractive sites (sticky spots) of two different types, A and B. The thermodynamic properties are calculated using Wertheim's perturbation theory of associating fluids. This also allows us to find the onset of self-assembly, which can be quantified by the maxima of the specific heat at constant volume. The percolation threshold is derived, under the no-loop assumption, for the correlated bond model: In all cases it is two percolated phases that become identical at a critical point, when one exists. Finally, the cluster size distributions are calculated by mapping the model onto an effective model, characterized by a-state-dependent-functionality (f) over bar and unique bonding probability (p) over bar. The mapping is based on the asymptotic limit of the cluster distributions functions of the generic model and the effective parameters are defined through the requirement that the equilibrium cluster distributions of the true and effective models have the same number-averaged and weight-averaged sizes at all densities and temperatures. We also study the model numerically in the case where BB interactions are missing. In this limit, AB bonds either provide branching between A-chains (Y-junctions) if epsilon(AB)/epsilon(AA) is small, or drive the formation of a hyperbranched polymer if epsilon(AB)/epsilon(AA) is large. We find that the theoretical predictions describe quite accurately the numerical data, especially in the region where Y-junctions are present. There is fairly good agreement between theoretical and numerical results both for the thermodynamic (number of bonds and phase coexistence) and the connectivity properties of the model (cluster size distributions and percolation locus).

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.

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.

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.

The condensation and ordering of models of empty liquids

We consider a simple model consisting of particles with four bonding sites ("patches"), two of type A and two of type B, on the square lattice, and investigate its global phase behavior by simulations and theory. We set the interaction between B patches to zero and calculate the phase diagram as the ratio between the AB and the AA interactions, epsilon(AB)*, varies. In line with previous work, on three-dimensional off-lattice models, we show that the liquid-vapor phase diagram exhibits a re-entrant or "pinched" shape for the same range of epsilon(AB)*, suggesting that the ratio of the energy scales - and the corresponding empty fluid regime - is independent of the dimensionality of the system and of the lattice structure. In addition, the model exhibits an order-disorder transition that is ferromagnetic in the re-entrant regime. The use of low-dimensional lattice models allows the simulation of sufficiently large systems to establish the nature of the liquid-vapor critical points and to describe the structure of the liquid phase in the empty fluid regime, where the size of the "voids" increases as the temperature decreases. We have found that the liquid-vapor critical point is in the 2D Ising universality class, with a scaling region that decreases rapidly as the temperature decreases. The results of simulations and theoretical analysis suggest that the line of order-disorder transitions intersects the condensation line at a multi-critical point at zero temperature and density, for patchy particle models with a re-entrant, empty fluid, regime. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3657406]

Patching up dipoles: can dipolar particles be viewed as patchy colloids?

We investigate whether the liquid-vapour phase transition of strongly dipolar fluids can be understood using a model of patchy colloids. These consist of hard spherical particles with three short-ranged attractive sites (patches) on their surfaces. Two of the patches are of type A and one is of type B. Patches A on a particle may bond either to a patch A or to a patch B on another particle. Formation of an AA (AB) bond lowers the energy by epsilon AA (epsilon AB). In the limit [image omitted], this patchy model exhibits condensation driven by AB-bonds (Y-junctions). Y-junctions are also present in low-density, strongly dipolar fluids, and have been conjectured to play a key role in determining their critical behaviour. We map the dipolar Yukawa hard-sphere (DYHS) fluid onto this 2A + 1B patchy model by requiring that the latter reproduce the correct DYHS critical point as a function of the isotropic interaction strength epsilon Y. This is achieved for sensible values of epsilon AB and the bond volumes. Results for the internal energy and the particle coordination number are in qualitative agreement with simulations of DYHSs. Finally, by taking the limit [image omitted], we arrive at a new estimate for the critical point of the dipolar hard-sphere fluid, which agrees with extrapolations from simulation.

Re-entrant phase behaviour of network fluids: A patchy particle model with temperature-dependent valence

We study a model consisting of particles with dissimilar bonding sites ("patches"), which exhibits self-assembly into chains connected by Y-junctions, and investigate its phase behaviour by both simulations and theory. We show that, as the energy cost epsilon(j) of forming Y-junctions increases, the extent of the liquid-vapour coexistence region at lower temperatures and densities is reduced. The phase diagram thus acquires a characteristic "pinched" shape in which the liquid branch density decreases as the temperature is lowered. To our knowledge, this is the first model in which the predicted topological phase transition between a fluid composed of short chains and a fluid rich in Y-junctions is actually observed. Above a certain threshold for epsilon(j), condensation ceases to exist because the entropy gain of forming Y-junctions can no longer offset their energy cost. We also show that the properties of these phase diagrams can be understood in terms of a temperature-dependent effective valence of the patchy particles. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3605703]

Reentrant Phase Diagram of Network Fluids

We introduce a microscopic model for particles with dissimilar patches which displays an unconventional "pinched'' phase diagram, similar to the one predicted by Tlusty and Safran in the context of dipolar fluids [Science 290, 1328 (2000)]. The model-based on two types of patch interactions, which account, respectively, for chaining and branching of the self-assembled networks-is studied both numerically via Monte Carlo simulations and theoretically via first-order perturbation theory. The dense phase is rich in junctions, while the less-dense phase is rich in chain ends. The model provides a reference system for a deep understanding of the competition between condensation and self-assembly into equilibrium-polymer chains.

Syntheses, Molecular Structures, Electrochemical Behavior, Theoretical Study, and Antitumor Activities of Organotin(IV) Complexes Containing 1-(4-Chlorophenyl)-1-cyclopentanecarboxylato Ligands

The organotin(IV) compounds [Me2Sn(L)(2)] (1), [Et(2)sn(L)(2)] (2), [(Bu2Sn)-Bu-n(L)(2)] (3), [(n)Oct(2)Sn(L)(2)] (4), [Ph2Sn(L)(2)] (5), and [PhOSnL](6) (6) have been synthesized from the reactions of 1-(4-chlorophenyl)-1-cyclopentanecarboxylic acid (HL) with the corresponding diorganotin(IV) oxide or dichloride. They were characterized by IR and multinuclear NMR spectroscopies, elemental analysis, cyclic voltammetry, and, for 2, 3, 4 and 6, single crystal X-ray diffraction analysis. While 1-5 are mononuclear diorganotin (IV) compounds, the X-ray diffraction of 6 discloses a hexameric drumlike structure with a prismatic Sn6O6 core. All these complexes undergo irreversible reductions and were screened for their in vitro antitumor activities toward HL-60, BGC-823, Bel-7402, and KB human cancer cell lines. Within the mononuclear compounds, the most active ones (3, 5) are easiest to reduce (least cathodic reduction potentials), while the least active ones (1, 4) are the most difficult to reduce. Structural rearrangements (i.e., Sn-O bond cleavages and trans-to-cis isomerization) induced by reduction, which eventually can favor the bioactivity, are disclosed by theoretical/electrochemical studies.

Synthesis of optimization of [11C] Pittsburgh compound B by the captive solvent method

Mestrado em Medicina Nuclear.

Demixing instability in coil-rod blends undergoing polycondensation reactions

The authors extend their earlier work on the stability of a reacting binary polymer blend with respect to demixing [D. J. Read, Macromolecules 31, 899 (1998); P. I. C. Teixeira , Macromolecules 33, 387 (2000)] to the case where one of the polymers is rod-like and may order nematically. As before, the authors combine the random phase approximation for the free energy with a Markov chain model for the chemistry to obtain the spinodal as a function of the relevant degrees of reaction. These are then calculated by assuming a simple second-order chemical kinetics. Results are presented, for linear systems, which illustrate the effects of varying the proportion of coils and rods, their relative sizes, and the strength of the nematic interaction between the rods. (c) 2007 American Institute of Physics.

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

Cobalt complexes with pyrazole ligands as catalyst precursors for the peroxidative oxidation of cyclohexane: Z-ray absorption spectroscopy studies and biological applications

[CoCl(-Cl)(Hpz(Ph))(3)](2) (1) and [CoCl2(Hpz(Ph))(4)] (2) were obtained by reaction of CoCl2 with HC(pz(Ph))(3) and Hpz(Ph), respectively (Hpz(Ph)=3-phenylpyrazole). The compounds were isolated as air-stable solids and fully characterized by IR and far-IR spectroscopy, MS(ESI+/-), elemental analysis, cyclic voltammetry (CV), controlled potential electrolysis, and single-crystal X-ray diffraction. Electrochemical studies showed that 1 and 2 undergo single-electron irreversible (CoCoIII)-Co-II oxidations and (CoCoI)-Co-II reductions at potentials measured by CV, which also allowed, in the case of dinuclear complex 1, the detection of electronic communication between the Co centers through the chloride bridging ligands. The electrochemical behavior of models of 1 and 2 were also investigated by density functional theory (DFT) methods, which indicated that the vertical oxidation of 1 and 2 (that before structural relaxation) affects mostly the chloride and pyrazolyl ligands, whereas adiabatic oxidation (that after the geometry relaxation) and reduction are mostly metal centered. Compounds 1 and 2 and, for comparative purposes, other related scorpionate and pyrazole cobalt complexes, exhibit catalytic activity for the peroxidative oxidation of cyclohexane to cyclohexanol and cyclohexanone under mild conditions (room temperature, aqueous H2O2). Insitu X-ray absorption spectroscopy studies indicated that the species derived from complexes 1 and 2 during the oxidation of cyclohexane (i.e., Ox-1 and Ox-2, respectively) are analogous and contain a Co-III site. Complex 2 showed low invitro cytotoxicity toward the HCT116 colorectal carcinoma and MCF7 breast adenocarcinoma cell lines.

Electrochemical porperties of (H5-C5Me5)-rhodium and – iridium complexes Bis(pyrazolyl)alkane ligands

The electrochemical properties of rhodium(III) 1-3 and iridium(III) 4-6 complexes containing bis(pyrazolyl)alkane ligands [MCp*Cl(R2C(3,5-R'2pz)2)]X (M = Rh (1) or Ir (4), R = R' = H, X = Cl; M = Rh (2) or Ir (5), R=H,R'=Me,X=Cl;M=Rh(3) or Ir (6), R=Me,R'=H,X=OTf;pz=pyrazolyl;Cp*=η5-C5Me5) were investigated by cyclic voltammetry and controlled potential electrolysis. They exhibit two sequential irreversible reductions assigned to the MIII → MII and MII → MI reductions, which are dependent on the methylation of the bis(pyrazolyl)alkane ligands.

Synthesis and characterization of COPPER(II) 4´-phenyl-terpyridine compounds and catalytic application for aerobic oxidation of benzylic alcohols

The reactions between 4'-phenyl-terpyridine (L) and nitrate, acetate or chloride Cu(II) salts led to the formation of [Cu(NO3)(2)L] (1), [Cu(OCOCH3)(2)L]center dot CH2Cl2 (2 center dot CH2Cl2)and [CuCl2L]center dot[Cu(Cl)(mu-Cl)L](2) (3), respectively. Upon dissolving 1 in mixtures of DMSO-MeOH or EtOH-DMF the compounds [Cu(H2O){OS(CH3)(2)}L]-(NO3)(2) (4) and [Cu(HO)(CH3CH2OH)L](NO3) (5) were obtained, in this order. Reaction of 3 with AgSO3CF3 led to [CuCl(OSO2CF3)L] (6). The compounds were characterized by ESI-MS, IR, elemental analysis, electrochemical techniques and, for 2-6, also by single crystal X-ray diffraction. They undergo, by cyclic voltammetry, two single-electron irreversible reductions assigned to Cu(II) -> Cu(I)and Cu(I) -> Cu(0) and, for those of the same structural type, the reduction potential appears to correlate with the summation of the values of the Lever electrochemical EL ligand parameter, which is reported for the first time for copper complexes. Complexes 1-6 in combination with TEMPO (2,2,6,6-tetramethylpiperidinyl-1-oxyl radical) can exhibit a high catalytic activity, under mild conditions and in alkaline aqueous solution, for the aerobic oxidation of benzylic alcohols. Molar yields up to 94% (based on the alcohol) with TON values up to 320 were achieved after 22 h.