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).

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.

Comportamento dinâmico da rede eléctrica da ilha de São Vicente em Cabo Verde: estabilidade de tensão

Neste trabalho é efectuado, não só o diagnóstico em regime permanente, mas também o estudo, simulação e análise do comportamento dinâmico da rede eléctrica da ilha de São Vicente em Cabo Verde. Os estudos de estabilidade transitória desempenham um importante papel, tanto no planeamento como na operação dos sistemas de potência. Tais estudos são realizados, em grande parte, através de simulação digital no domínio do tempo, utilizando integração numérica para resolver as equações não-lineares que modelam a dinâmica do sistema e dependem da existência de registos reais de perturbação (ex: osciloperturbografia). O objectivo do trabalho será também verificar a aplicabilidade dos requisitos técnicos que as unidades geradoras devem ter, no que concerne ao controlo de tensão, estabelecidos na futura regulamentação europeia desenvolvida pela ENTSO-E (European Network Transmission System Operator for Electricity). De entre os requisitos analisou-se a capacidade das máquinas existentes suportarem cavas de tensão decorrentes de curto-circuitos trifásicos simétricos, Fault Ride Through, no ponto de ligação à rede. Identificaram-se para o efeito os factores que influenciam a estabilidade desta rede, em regime perturbado nomeadamente: (i) duração do defeito, (ii) caracterização da carga, com e sem a presença do sistema de controlo de tensão (AVR) em unidades de geração síncronas. Na ausência de registos reais sobre o comportamento do sistema, conclui-se que este é sensível à elasticidade das cargas em particular do tipo potência constante, existindo risco de perda de estabilidade, neste caso, para defeitos superiores a 5ms sem AVR. A existência de AVR nesta rede afigura-se como indispensável para garantir estabilidade de tensão sendo contudo necessário proceder a uma correcta parametrização.

Distribuição de vídeo sobre uma rede IEEE 802.11n

A recente norma IEEE 802.11n oferece um elevado débito em redes locais sem fios sendo por isso esperado uma adopção massiva desta tecnologia substituindo progressivamente as redes 802.11b/g. Devido à sua elevada capacidade esta recente geração de redes sem fios 802.11n permite um crescimento acentuado de serviços audiovisuais. Neste contexto esta dissertação procura estudar a rede 802.11n, caracterizando o desempenho e a qualidade associada a um serviço de transmissão de vídeo, recorrendo para o efeito a uma arquitectura de simulação da rede 802.11n. Desta forma é caracterizado o impacto das novas funcionalidades da camada MAC introduzidas na norma 801.11n, como é o caso da agregação A-MSDU e A-MPDU, bem como o impacto das novas funcionalidades da camada física como é o caso do MIMO; em ambos os casos uma optimização da parametrização é realizada. Também se verifica que as principais técnicas de codificação de vídeo H.264/AVC para optimizar o processo de distribuição de vídeo, permitem optimizar o desempenho global do sistema de transmissão. Aliando a optimização e parametrização da camada MAC, da camada física, e do processo de codificação, é possível propor um conjunto de configurações que permitem obter o melhor desempenho na qualidade de serviço da transmissão de conteúdos de vídeo numa rede 802.11n. A arquitectura de simulação construída nesta dissertação é especificamente adaptada para suportar as técnicas de agregação da camada MAC, bem como para suportar o encapsulamento em protocolos de rede que permitem a transmissão dos pacotes de vídeo RTP, codificados em H.264/AVC.

Contact angle of a hemispherical bubble: An analytical approach

We have calculated the equilibrium shape of the axially symmetric Plateau border along which a spherical bubble contacts a flat wall, by analytically integrating Laplace's equation in the presence of gravity, in the limit of small Plateau border sizes. This method has the advantage that it provides closed-form expressions for the positions and orientations of the Plateau border surfaces. Results are in very good overall agreement with those obtained from a numerical solution procedure, and are consistent with experimental data. In particular we find that the effect of gravity on Plateau border shape is relatively small for typical bubble sizes, leading to a widening of the Plateau border for sessile bubbles and to a narrowing for pendant bubbles. The contact angle of the bubble is found to depend even more weakly on gravity. (C) 2009 Elsevier Inc. All rights reserved.

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.

Real-time rheology of actively growing bacteria

The population growth of a Staphylococcus aureus culture, an active colloidal system of spherical cells, was followed by rheological measurements, under steady-state and oscillatory shear flows. We observed a rich viscoelastic behavior as a consequence of the bacteria activity, namely, of their multiplication and density-dependent aggregation properties. In the early stages of growth (lag and exponential phases), the viscosity increases by about a factor of 20, presenting several drops and full recoveries. This allows us to evoke the existence of a percolation phenomenon. Remarkably, as the bacteria reach their late phase of development, in which the population stabilizes, the viscosity returns close to its initial value. Most probably, this is caused by a change in the bacteria physiological activity and in particular, by the decrease of their adhesion properties. The viscous and elastic moduli exhibit power-law behaviors compatible with the "soft glassy materials" model, whose exponents are dependent on the bacteria growth stage. DOI: 10.1103/PhysRevE.87.030701.

Study of the one dimensional and transient bioheat transfer equation: Multi-layer solution development and applications

: In this work we derive an analytical solution given by Bessel series to the transient and one-dimensional (1D) bioheat transfer equation in a multi-layer region with spatially dependent heat sources. Each region represents an independent biological tissue characterized by temperature-invariant physiological parameters and a linearly temperature dependent metabolic heat generation. Moreover, 1D Cartesian, cylindrical or spherical coordinates are used to define the geometry and temperature boundary conditions of first, second and third kinds are assumed at the inner and outer surfaces. We present two examples of clinical applications for the developed solution. In the first one, we investigate two different heat source terms to simulate the heating in a tumor and its surrounding tissue, induced during a magnetic fluid hyperthermia technique used for cancer treatment. To obtain an accurate analytical solution, we determine the error associated with the truncated Bessel series that defines the transient solution. In the second application, we explore the potential of this model to study the effect of different environmental conditions in a multi-layered human head model (brain, bone and scalp). The convective heat transfer effect of a large blood vessel located inside the brain is also investigated. The results are further compared with a numerical solution obtained by the Finite Element Method and computed with COMSOL Multi-physics v4.1 (c). (c) 2013 Elsevier Ltd. All rights reserved.

Colloidal interactions in two-dimensional nematics

The interaction between two disks immersed in a 2D nernatic is investigated i) analytically using the tenser order parameter formalism for the nematic configuration around isolated disks and ii) numerically using finite-element methods with adaptive meshing to minimize the corresponding Landau-de Gennes free energy. For strong homeotropic anchoring, each disk generates a pair of defects with one-half topological charge responsible for the 2D quadrupolar interaction between the disks at large distances. At short distance, the position of the defects may change, leading to unexpected complex interactions with the quadrupolar repulsive interactions becoming attractive. This short-range attraction in all directions is still anisotropic. As the distance between the disks decreases, their preferred relative orientation with respect to the far-field nernatic director changes from oblique to perpendicular.

Particle agglomeration study in rf silane plasmas: In situ study by polarization-sensitive laser light scattering

To determine self-consistently the time evolution of particle size and their number density in situ multi-angle polarization-sensitive laser light scattering was used. Cross-polarization intensities (incident and scattered light intensities with opposite polarization) measured at 135 degrees and ex situ transmission electronic microscopy analysis demonstrate the existence of nonspherical agglomerates during the early phase of agglomeration. Later in the particle time development both techniques reveal spherical particles again. The presence of strong cross-polarization intensities is accompanied by low-frequency instabilities detected on the scattered light intensities and plasma emission. It is found that the particle radius and particle number density during the agglomeration phase can be well described by the Brownian free molecule coagulation model. Application of this neutral particle coagulation model is justified by calculation of the particle charge whereby it is shown that particles of a few tens of nanometer can be considered as neutral under our experimental conditions. The measured particle dispersion can be well described by a Brownian free molecule coagulation model including a log-normal particle size distribution. (C) 1996 American Institute of Physics.

How patchy can one get and still condense? The role of dissimilar patches in the interactions of colloidal particles

We investigate the influence of strong directional, or bonding, interactions on the phase diagram of complex fluids, and in particular on the liquid-vapour critical point. To this end we revisit a simple model and theory for associating fluids which consist of spherical particles having a hard-core repulsion, complemented by three short-ranged attractive sites on the surface (sticky spots). Two of the spots are of type A and one is of type B; the interactions between each pair of spots have strengths [image omitted], [image omitted] and [image omitted]. The theory is applied over the whole range of bonding strengths and results are interpreted in terms of the equilibrium cluster structures of the coexisting phases. In systems where unlike sites do not interact (i.e. where [image omitted]), the critical point exists all the way to [image omitted]. By contrast, when [image omitted], there is no critical point below a certain finite value of [image omitted]. These somewhat surprising results are rationalised in terms of the different network structures of the two systems: two long AA chains are linked by one BB bond (X-junction) in the former case, and by one AB bond (Y-junction) in the latter. The vapour-liquid transition may then be viewed as the condensation of these junctions and we find that X-junctions condense for any attractive [image omitted] (i.e. for any fraction of BB bonds), whereas condensation of the Y-junctions requires that [image omitted] be above a finite threshold (i.e. there must be a finite fraction of AB bonds).

Criticality of colloids with distinct interaction patches: The limits of linear chains, hyperbranched polymers, and dimers

We use a simple model of associating fluids which consists of spherical particles having a hard-core repulsion, complemented by three short-ranged attractive sites on the surface (sticky spots). Two of the spots are of type A and one is of type B; the bonding interactions between each pair of spots have strengths epsilon(AA), epsilon(BB), and epsilon(AB). The theory is applied over the whole range of bonding strengths and the results are interpreted in terms of the equilibrium cluster structures of the phases. In addition to our numerical results, we derive asymptotic expansions for the free energy in the limits for which there is no liquid-vapor critical point: linear chains (epsilon(AA)not equal 0, epsilon(AB)=epsilon(BB)=0), hyperbranched polymers (epsilon(AB)not equal 0, epsilon(AA)=epsilon(BB)=0), and dimers (epsilon(BB)not equal 0, epsilon(AA)=epsilon(AB)=0). These expansions also allow us to calculate the structure of the critical fluid by perturbing around the above limits, yielding three different types of condensation: of linear chains (AA clusters connected by a few AB or BB bonds); of hyperbranched polymers (AB clusters connected by AA bonds); or of dimers (BB clusters connected by AA bonds). Interestingly, there is no critical point when epsilon(AA) vanishes despite the fact that AA bonds alone cannot drive condensation.

Detecção de sectores cruzados e optimização de cobertura em redes LTE

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia de Electrónica e Telecomunicações

Surface morphology and phase transformations of femtosecond laser-processed saphire

The morphological and structural modifications induced in sapphire by surface treatment with femtosecond laser radiation were studied. Single-crystal sapphire wafers cut parallel to the (0 1 2) planes were treated with 560 fs, 1030 nm wavelength laser radiation using wide ranges of pulse energy and repetition rate. Self-ordered periodic structures with an average spatial periodicity of similar to 300 nm were observed for fluences slightly higher than the ablation threshold. For higher fluences the interaction was more disruptive and extensive fracture, exfoliation, and ejection of ablation debris occurred. Four types of particles were found in the ablation debris: (a) spherical nanoparticles about 50 nm in diameter; (b) composite particles between 150 and 400 nm in size; (c) rounded resolidified particles about 100-500 nm in size; and (d) angular particles presenting a lamellar structure and deformation twins. The study of those particles by selected area electron diffraction showed that the spherical nanoparticles and the composite particles are amorphous, while the resolidified droplets and the angular particles, present a crystalline a-alumina structure, the same of the original material. Taking into consideration the existing ablation theories, it is proposed that the spherical nanoparticles are directly emitted from the surface in the ablation plume, while resolidified droplets are emitted as a result of the ablation process, in the liquid phase, in the low intensity regime, and by exfoliation, in the high intensity regime. Nanoparticle clusters are formed by nanoparticle coalescence in the cooling ablation plume. (C) 2013 Elsevier B.V. All rights reserved.

Liquid crystal beads constrained on thin cellulosic fibers: Electric field induced microrotors and N-I transition

We directly visualize the response of nematic liquid crystal drops of toroidal topology threaded in cellulosic fibers, suspended in air, to an AC electric field and at different temperatures over the N-I transition. This new liquid crystal system can exhibit non-trivial point defects, which can be energetically unstable against expanding into ring defects depending on the fiber constraining geometries. The director anchoring tangentially near the fiber surface and homeotropically at the air interface makes a hybrid shell distribution that in turn causes a ring disclination line around the main axis of the fiber at the center of the droplet. Upon application of an electric field, E, the disclination ring first expands and moves along the fiber main axis, followed by the appearance of a stable "spherical particle" object orbiting around the fiber at the center of the liquid crystal drop. The rotation speed of this particle was found to vary linearly with the applied voltage. This constrained liquid crystal geometry seems to meet the essential requirements in which soliton-like deformations can develop and exhibit stable orbiting in three dimensions upon application of an external electric field. On changing the temperature the system remains stable and allows the study of the defect evolution near the nematic-isotropic transition, showing qualitatively different behaviour on cooling and heating processes. The necklaces of such liquid crystal drops constitute excellent systems for the study of topological defects and their evolution and open new perspectives for application in microelectronics and photonics.