Generalization of Linearized Gouy-Chapman-Stern Model of Electric Double Layer for Nanostructured and Porous Electrodes: Deterministic and Stochastic Morphology

We generalize linearized Gouy-Chapman-Stern theory of electric double layer for nanostructured and morphologically disordered electrodes. Equation for capacitance is obtained using linear Gouy-Chapman (GC) or Debye-$\rm{\ddot{u}}$ckel equation for potential near complex electrode/electrolyte interface. The effect of surface morphology of an electrode on electric double layer (EDL) is obtained using "multiple scattering formalism" in surface curvature. The result for capacitance is expressed in terms of the ratio of Gouy screening length and the local principal radii of curvature of surface. We also include a contribution of compact layer, which is significant in overall prediction of capacitance. Our general results are analyzed in details for two special morphologies of electrodes, i.e. "nanoporous membrane" and "forest of nanopillars". Variations of local shapes and global size variations due to residual randomness in morphology are accounted as curvature fluctuations over a reference shape element. Particularly, the theory shows that the presence of geometrical fluctuations in porous systems causes enhanced dependence of capacitance on mean pore sizes and suppresses the magnitude of capacitance. Theory emphasizes a strong influence of overall morphology and its disorder on capacitance. Finally, our predictions are in reasonable agreement with recent experimental measurements on supercapacitive mesoporous systems

Vesicles in solutions of hard rods

The surface free energy of ideal hard rods near curved hard surfaces is determined to second order in curvature for surfaces of general shape. In accordance with previous results for spherical and cylindrical surfaces it is found that this quantity is non-analytical when one of the principal curvatures changes signs. This prohibits writing it in the common Helfrich form. It is shown that the non-analytical terms are the same for any aspect ratio of the rods. These results are used to find the equilibrium shape of vesicles immersed in solutions of rod-like (colloidal) particles. The presence of the particles induces a change in the equilibrium shape and to a shift of the prolate-oblate transition in the vesicle phase diagram, which are calculated within the framework of the spontaneous curvature model. As a consequence of the special form of the energy contribution due to the rods these changes cannot be accounted for by a simple rescaling of the elastic constants of the vesicle as for solutions of spherical colloids or polymers.Comment: 11 pages, 7 figures, submitted to Phys. Rev.

Bioprospecção de bactérias com potencial antagônico a fusarium spp. associado à morte de brachiaria brizantha

Há uma crescente busca nos últimos tempos por sistemas agropecuários que sejam produtivos, econômicos e sustentáveis. A síndrome da morte do capim Marandu (Brachiaria brizantha cv. Marandu) é um problema que vem crescendo nos últimos anos, um dos principais sinais de baixa sustentabilidade da pecuária brasileira. A morte das plantas forrageiras ocorre na época chuvosa, geralmente em solos mal drenados, devido a falta de adaptação da planta à baixa oxigenação das raízes, deixando-a suscetível ao ataque de fitopatógenos oportunistas. Diante da problemática, objetivou-se isolar e selecionar bactérias com potencial antagônico a Fusarium spp., um dos agentes fitopatogênicos que participam desse processo. Foram avaliados 10 sistemas, no período de chuva e seca: 1-F: floresta; 2-L: lavoura; 3-P: pecuária; 4-iPL: integração pecuária-lavoura; 5-iLP: integração lavoura-pecuária; 6-iLF: integração lavoura-floresta; 7-iPF: integração pecuária-floresta; 8-iLPF: lavoura e floresta por 2 anos e após pecuária e floresta por 2 anos; 9iLPF: pecuária e floresta por 2 anos e lavoura e floresta por 2 anos; 10-iLPF: integração lavoura-pecuária-floresta; além da mata nativa e área de pousio, distribuídos em blocos casualizados com 4 repetições. Os isolados bacterianos foram obtidos de amostras de solo diluídas, aplicadas em meio de cultura TSA 10% (Triptona soja ágar) e incubadas a 28ºC. Após a purificação os isolados foram armazenados em solução de glicerol 20% a -80°C. Foram testadas 20 bactérias em cada sistema. O método para avaliação de antagonismo foi o de cultura pareada em placa de Petri, por confronto direto, e em meio sólido BDA (Batata dextrose ágar). Na avaliação, foi considerado como positivo as bactérias que formaram halo de inibição ou quando o crescimento do corpo fúngico não encostou na bactéria. Dois isolados foram testados, Fusarium spp. isolado de planta de soja acometida (1) e Fusarium spp. isolado de solo onde ocorreu a morte da forrageira (2). Primeiramente, todos os isolados bacterianos foram testados contra o patógeno 1 e então, somente as bactérias antagônicas foram testadas contra o patógeno 2. Para o patógeno 1, na época da chuva, 7,5% dos isolados testados apresentaram antagonismo enquanto na seca esse valor foi maior (15%). Para o patógeno 2, nem todos os isolados positivos para o patógeno 1 foram eficientes no controle, demonstrando a ocorrência de interações entre isolados bacterianos e Fusarium spp. Quando considerados os sistemas, na chuva, para o patógeno 1, a mata apresentou maior número de isolados positivos (20%). Na seca, mata, 1-F e 8-iLPF para o patógeno 1, foram os que apresentaram maior número de positivos (25%). Dentre as épocas avaliadas, a seca teve mais bactérias antagonistas, e o tratamento 8-iLPF apresentou melhores resultados. O que demonstra possibilidade de encontrar um controlador biológico à Fusarium spp. neste sistema. Os sistemas mais biodiversos parecem favorecer o equilíbrio entre os microrganismos (antagonismo), o que pode reduzir ação do Fusarium spp. no capim Marandu. Isso deve ser evidenciado em análises posteriores com testes in vivo, a fim de comprovar e desenvolver novas biotecnologias. Palavras-chave: controle biológico, forragem, microbiologia

Geometric Mechanics of Curved Crease Origami

Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical frustration. We quantify this shape in terms of the radius of the circle, the dihedral angle of the fold and the mechanical properties of the sheet of paper and the fold itself. When the sheet is isometrically deformed everywhere except along the fold itself, stiff folds result in creases with constant curvature and oscillatory torsion. However, relatively softer folds inherit the broken symmetry of the buckled shape with oscillatory curvature and torsion. Our asymptotic analysis of the isometrically deformed state is corroborated by numerical simulations which allow us to generalize our analysis to study multiply folded structures

How to determine local elastic properties of lipid bilayer membranes from atomic-force-microscope measurements: A theoretical analysis

Measurements with an atomic force microscope (AFM) offer a direct way to probe elastic properties of lipid bilayer membranes locally: provided the underlying stress-strain relation is known, material parameters such as surface tension or bending rigidity may be deduced. In a recent experiment a pore-spanning membrane was poked with an AFM tip, yielding a linear behavior of the force-indentation curves. A theoretical model for this case is presented here which describes these curves in the framework of Helfrich theory. The linear behavior of the measurements is reproduced if one neglects the influence of adhesion between tip and membrane. Including it via an adhesion balance changes the situation significantly: force-distance curves cease to be linear, hysteresis and nonzero detachment forces can show up. The characteristics of this rich scenario are discussed in detail in this article.Comment: 14 pages, 9 figures, REVTeX4 style. New version corresponds to the one accepted by PRE. The result section is restructured: a comparison to experimental findings is included; the discussion on the influence of adhesion between AFM tip and membrane is extende

Planar sheets meet negative curvature liquid interfaces

If an inextensible thin sheet is adhered to a substrate with a negative Gaussian curvature it will experience stress due to geometric frustration. We analyze the consequences of such geometric frustration using analytic arguments and numerical simulations. Both concentric wrinkles and eye-like folds are shown to be compatible with negative curvatures. Which pattern will be realized depends on the curvature of the substrate. We discuss both types of folding patterns and determine the phase diagram governing their appearance.Comment: 5 pages, 4 figure

The Serret-Andoyer Riemannian metric and Euler-Poinsot rigid body motion

The Euler-Poinsot rigid body motion is a standard mechanical system and is the model for left-invariant Riemannian metrics on SO(3). In this article, using the Serret-Andoyer variables we parameterize the solutions and compute the Jacobi fields in relation with the conjugate locus evaluation. Moreover the metric can be restricted to a 2D surface and the conjugate points of this metric are evaluated using recent work [4] on surfaces of revolution