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).

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

Quantitative description of the self-assembly of patchy particles into chains and rings

We numerically study a simple fluid composed of particles having a hard-core repulsion complemented by two patchy attractive sites on the particle poles. An appropriate choice of the patch angular width allows for the formation of ring structures which, at low temperatures and low densities, compete with the growth of linear aggregates. The simplicity of the model makes it possible to compare simulation results and theoretical predictions based on the Wertheim perturbation theory, specialized to the case in which ring formation is allowed. Such a comparison offers a unique framework for establishing the quality of the analytic predictions. We find that the Wertheim theory describes remarkably well the simulation results.

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.

Temperature-induced structural transitions in self-assembling magnetic nanocolloids

With the help of a unique combination of density functional theory and computer simulations, we discover two possible scenarios, depending on concentration, for the hierarchical self-assembly of magnetic nanoparticles on cooling. We show that typically considered low temperature clusters, i.e. defect-free chains and rings, merge into more complex branched structures through only three types of defects: four-way X junctions, three-way Y junctions and two-way Z junctions. Our accurate calculations reveal the predominance of weakly magnetically responsive rings cross-linked by X defects at the lowest temperatures. We thus provide a strategy to fine-tune magnetic and thermodynamic responses of magnetic nanocolloids to be used in medical and microfluidics applications.

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.

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.

Branching points in the low-temperature dipolar hard sphere fluid

In this contribution, we investigate the low-temperature, low-density behaviour of dipolar hard-sphere (DHS) particles, i.e., hard spheres with dipoles embedded in their centre. We aim at describing the DHS fluid in terms of a network of chains and rings (the fundamental clusters) held together by branching points (defects) of different nature. We first introduce a systematic way of classifying inter-cluster connections according to their topology, and then employ this classification to analyse the geometric and thermodynamic properties of each class of defects, as extracted from state-of-the-art equilibrium Monte Carlo simulations. By computing the average density and energetic cost of each defect class, we find that the relevant contribution to inter-cluster interactions is indeed provided by (rare) three-way junctions and by four-way junctions arising from parallel or anti-parallel locally linear aggregates. All other (numerous) defects are either intra-cluster or associated to low cluster-cluster interaction energies, suggesting that these defects do not play a significant part in the thermodynamic description of the self-assembly processes of dipolar hard spheres. (C) 2013 AIP Publishing LLC.

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.

Experimental study of the mechanical properties and durability of self-compacting mortars with nano materials (SiO2 and TiO2)

Resumo: Cement, as well as the remaining constituents of self-compacting mortars, must be carefully selected, in order to obtain an adequate composition with a granular mix as compact as possible and a good performance in the fresh state (self-compacting effect) and the hardened state (mechanical and durability-related behavior). Therefore in this work the possibility of incorporating nano particles in self-compacting mortars was studied. Nano materials are very reactive due mostly to their high specific surface and show a great potential to improve the properties of these mortars, both in mechanical and durability terms. In this work two nano materials were used, nano silica (nano SiO2) in colloidal state and nano titanium (nano TiO2) in amorphous state, in two types of self-compacting mortars (ratio binder:sand of 1:1 and 1:2). The self-compacting mortar mixes have the same water/cement ratio and 30% of replacement of cement with fly ashes. The influence of nano materials nano-SiO2 and nano-TiO2 on the fresh and hardened state properties of these self-compacting mortars was studied. The results show that the use of nano materials in repair and rehabilitation mortars has significant potential but still needs to be optimized. (C) 2015 Elsevier Ltd. All rights reserved.

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.

Conversor estático de potência tolerante a falhas

O trabalho apresentado nesta dissertação refere-se à concepção, projecto e realização experimental de um conversor estático de potência tolerante a falhas. Foram analisados trabalhos de investigação sobre modos de falha de conversores electrónicos de potência, topologias de conversores tolerantes a falhas, métodos de detecção de falhas, entre outros. Com vista à concepção de uma solução, foram nomeados e analisados os principais modos de falhas para três soluções propostas de conversores com topologias tolerantes a falhas onde existem elementos redundantes em modo de espera. Foram analisados os vários aspectos de natureza técnica dos circuitos de potência e guiamento de sinais onde se salientam a necessidade de tempos mortos entre os sinais de disparo de IGBT do mesmo ramo, o isolamento galvânico entre os vários andares de disparo, a necessidade de minimizar as auto-induções entre o condensador DC e os braços do conversor de potência. Com vista a melhorar a fiabilidade e segurança de funcionamento do conversor estático de potência tolerante a falhas, foi concebido um circuito electrónico permitindo a aceleração da actuação normal de contactores e outro circuito responsável pelo encaminhamento e inibição dos sinais de disparo. Para a aplicação do conversor estático de potência tolerante a falhas desenvolvido num accionamento com um motor de corrente contínua, foi implementado um algoritmo de controlo numa placa de processamento digital de sinais (DSP), sendo a supervisão e actuação do sistema realizados em tempo-real, para a detecção de falhas e actuação de contactores e controlo de corrente e velocidade do motor utilizando uma estratégia de comando PWM. Foram realizados ensaios que, mediante uma detecção adequada de falhas, realiza a comutação entre blocos de conversores de potência. São apresentados e discutidos resultados experimentais, obtidos usando o protótipo laboratorial.

Concessão Douro Litoral A32/IC2: passagens inferiores pré-fabricadas no sistema arco "Techspan" e muros ala de suporte de terras no sistema "Terra Armada": ponte sobre o rio Antuã: aplicação da tecnologia "Freyssinet"

O presente relatório visa apresentar o trabalho desenvolvido pelo estagiário na empresa Freyssinet – Terra Armada, S.A. (FTA). O relatório traduz o acompanhamento do estagiário na construção e aplicação da tecnologia Terra Armada em duas passagens inferiores, bem como o acompanhamento dos trabalhos efectuados pela empresa FTA no que diz respeito à aplicação da tecnologia Freyssinet na ponte sobre o rio Antuã, estando ambas as obras abordadas inseridas no Lote 8 – “A32/IC2 Oliveira de Azeméis/IP1 (S. Lourenço) trecho 2 e 3 – a cargo da empresa Alves Ribeiro S.A.. Com a construção dos trechos 2 e 3 da A32 surgiu a necessidade de se restabelecerem algumas ligações, o que fez com que após estudadas as soluções passíveis de serem utilizadas, se tivesse optado pela construção de túneis a céu aberto na execução dos restabelecimentos. Descreve-se neste documento a metodologia utilizada e as tecnologias patenteadas pela empresa Terra Armada, sendo estas compostas pelos Arcos “Techspan” e muros de ala executados com recurso à tecnologia “Terra Armada”. Em relação à ponte sobre o rio Antuã inserida no trecho 2 da empreitada de construção da A32, foi construída com recurso a cimbre auto-lançável e betonada in situ, havendo a necessidade de aplicação de tecnologias patenteadas pela Freyssinet no que diz respeito às actividades de pré-esforço, aparelhos de apoio nas ligações entre o tabuleiro e os pilares e juntas de dilatação na ligação do tabuleiro aos encontros. Apresentam-se os procedimentos de montagem e aplicação das tecnologias anteriormente referidas. No presente relatório estão descritos e explicados detalhadamente os trabalhos executados pela FTA, nomeadamente a aplicação da tecnologia “Terra Armada” no que diz respeito à construção das passagens inferiores, e a aplicação da tecnologia “Freyssinet” aplicada aquando da construção da ponte sobre o rio Antuã.