The interaction of nanoparticles with biological systems, especially interactions with cell membranes, has been a subject of active research due to its numerous applications in many areas of soft-matter and biological systems. Within only a few relevant physical parameters profound structural properties have been discovered in the context of simple coarse-grained theoretical models. In this Thesis we study the structure of a tubular membrane adhering to two rigid cylindrical particles on a basis of a free-energy model that uses Helfrich energy for the description of the membrane. A numerical procedure is developed to solve the shape equations that determine the state of lowest energy. Several phase transitions exist in the system, arising from the competition between the bending energy of the membrane and the adhesion energy between the membrane and the particles. A continuous adhesion transition between the free and bound states, as well as several discontinuous shape transitions are identified, depending on the physical parameters of the system. The results are then generalized into a single phase diagram separating free, symmetric- and asymmetric-wrapping states in the phase space of the size of the particles and the adhesion energy. We show that for a relatively small size of the membrane tube the interaction between the cylinders becomes attractive in the strong curvature regime, leading to aggregation of the particles in the highly curved area of the tube that is characteristically different from the aggregation in a related three-dimensional system. For a relatively large membrane tube size the cylinders prefer to have a non-zero separation, even in the completely engulfed state. This indicates that, i) the spontaneous curvature of the membrane may play a role in the sign of the interaction of two colloidal particles adhered to a membrane and ii) cylindrical particles can aggregate on membrane tubes and vesicles if the curvature of the membrane around the aggregation region is sufficiently large.

The interaction of nanoparticles with biological systems, especially interactions with cell membranes, has been a subject of active research due to its numerous applications in many areas of soft-matter and biological systems. Within only a few relevant physical parameters profound structural properties have been discovered in the context of simple coarse-grained theoretical models. In this Thesis we study the structure of a tubular membrane adhering to two rigid cylindrical particles on a basis of a free-energy model that uses Helfrich energy for the description of the membrane. A numerical procedure is developed to solve the shape equations that determine the state of lowest energy. Several phase transitions exist in the system, arising from the competition between the bending energy of the membrane and the adhesion energy between the membrane and the particles. A continuous adhesion transition between the free and bound states, as well as several discontinuous shape transitions are identified, depending on the physical parameters of the system. The results are then generalized into a single phase diagram separating free, symmetric- and asymmetric-wrapping states in the phase space of the size of the particles and the adhesion energy. We show that for a relatively small size of the membrane tube the interaction between the cylinders becomes attractive in the strong curvature regime, leading to aggregation of the particles in the highly curved area of the tube that is characteristically different from the aggregation in a related three-dimensional system. For a relatively large membrane tube size the cylinders prefer to have a non-zero separation, even in the completely engulfed state. This indicates that, i) the spontaneous curvature of the membrane may play a role in the sign of the interaction of two colloidal particles adhered to a membrane and ii) cylindrical particles can aggregate on membrane tubes and vesicles if the curvature of the membrane around the aggregation region is sufficiently large.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-04-06T20:35:55Z No. of bitstreams: 1 ILIANA DE OLIVEIRA GUIMARÃES - TESE PPG-CEMat 2014..pdf: 50160837 bytes, checksum: 767ec5c57ef7319ccbd6b2d10571ff53 (MD5) / Made available in DSpace on 2018-04-06T20:35:55Z (GMT). No. of bitstreams: 1 ILIANA DE OLIVEIRA GUIMARÃES - TESE PPG-CEMat 2014..pdf: 50160837 bytes, checksum: 767ec5c57ef7319ccbd6b2d10571ff53 (MD5) Previous issue date: 2014-08-29 / Capes / O processo Bayer, utilizado para a obtenção de alumina, usa bauxita como matériaprima. Este processo abrange quatro estágios: digestão, clarificação, precipitação e calcinação. O resíduo gerado na etapa de calcinação é um produto com pequeno tamanho de partícula, conhecido como ESP dust. Esta pesquisa teve como objetivo desenvolver membranas cerâmicas tubulares utilizando em sua composição o ESP dust, um pó de alumina do precipitador eletrostático, e uma argila bentonítica. Inicialmente, foi realizada a caracterização dos precursores. Foram analisadas duas amostras do resíduo, uma do resíduo bruto e outra do resíduo calcinado a 1200°C. Essas amostras apresentaram um alto teor de alumina nas suas composições químicas. As fases gibbsita e α-alumina foram identificadas no resíduo bruto e, após sua calcinação, a gibbsita foi totalmente transformada em α-alumina. Observou-se que não houve alterações significativas no tamanho e morfologia das partículas após a calcinação, mas durante este processo, as partículas tornaram-se porosas, provavelmente devido às mudanças de fase cristalina da alumina e a saída de água dos cristais. Dentre vinte formulações diferentes testadas para produzir membranas cerâmicas, quatro composições apresentaram os melhores resultados com relação ao processamento por extrusão: duas composições com o resíduo bruto e duas com o resíduo calcinado. Neste trabalho, as membranas tubulares compostas pelo resíduo de alumina e pela argila bentonítica foram produzidas por extrusão e foram sinterizadas a 900, 1000 e 1100°C. Foi observado que as membranas produzidas apresentaram superfícies com poros distribuídos. A porosidade aparente variou entre 47,70% (composição com 60% de resíduo calcinado e 40% de argila bentonítica sinterizada a 1000°C) e 58,40% (composição com 70% de resíduo bruto e 30% de argila bentonítica sinterizada a 1000°C). Foram realizados ensaios de fluxo tangencial com água deionizada em pressões de 1,0; 1,5 e 2,0 Bar. O maior fluxo permeado (909,24L/h.m2) foi observado para as membranas feitas da composição contendo 70% de resíduo bruto e 30% de argila bentonítica sinterizadas a 1100°C, aplicando pressão de 1 Bar. / The Bayer process uses bauxite as raw material to obtain alumina. This process includes four stages: digestion, clarification, precipitation and calcination. The waste generated during the calcination step is a product with small particle size, known as ESP dust. This research aimed to develop tubular ceramic membranes using in its composition the ESP dust, an alumina powder from electrostatic precipitator, and a bentonite clay. Initially, the characterization of the precursors was performed. Two samples were studied, one from crude residue and other from calcined residue at 1200°C. These samples showed a high content of alumina in chemical compositions. The gibbsite and α-alumina phases were identified in crude residue and after calcination gibbsite was completely transformed into α-alumina. Were observed no significant changes in particles size and morphology after calcination, but during this process, the particles become porous, probable due changes in crystalline phase of alumina and the water outlet of crystals. Among twenty different formulations tested to produce ceramic membranes, four compositions showed better results with regard to the extrusion processing: two compositions with crude residue and two with calcined residue. In this paper, tubular membranes produced from alumina residue and bentonite clay were sintered at 900, 1000 and 1100°C. It was observed that the produced membranes had surfaces with distributed pores. The apparent porosity was between 47.70% (composition with 60% of calcined residue and 40% of bentonite clay sintered at 1000°C) and 58.40% (composition with 70% of crude residue and 30% of bentonite clay sintered at 1000°C). Tangential flow tests were performed with deionized water at pressures of 1.0; 1.5 and 2.0 Bar. Higher permeate flow rate (909,24L/h.m2) was observed for membranes made of a composition containing crude residue (70%) and bentonite clay (30%) sintered at 1100°C, applying pressure of 1 bar.