Computer simulation of liquid crystals

In this article we review the current status in the modelling of both thermotropic and lyotropic Liquid crystal. We discuss various coarse-graining schemes as well as simulation techniques such as Monte Carlo (MC) and Molecular dynamics (MD) simulations.In the area of MC simulations we discuss in detail the algorithm for simulating hard objects such as spherocylinders of various aspect ratios where excluded volume interaction enters in the simulation through overlap test. We use this technique to study the phase diagram, of a special class of thermotropic liquid crystals namely banana liquid crystals. Next we discuss a coarse-grain model of surfactant molecules and study the self-assembly of the surfactant oligomers using MD simulations. Finally we discuss an atomistically informed coarse-grained description of the lipid molecules used to study the gel to liquid crystalline phase transition in the lipid bilayer system.

Advances in the Mathematical Modelling of Hepatitis C Virus Dynamics

Mathematical models have provided key insights into the pathogenesis of hepatitis C virus (HCV) in vivo, suggested predominant mechanism(s) of drug action, explained confounding patterns of viral load changes in HCV infected patients undergoing therapy, and presented a framework for therapy optimization. In this article, I present an overview of the major advances in the mathematical modeling of HCV dynamics.

On the solution of bivariate population balance equations for aggregation: X-discretization of space for expansion and contraction of computational domain

A new structured discretization of 2D space, named X-discretization, is proposed to solve bivariate population balance equations using the framework of minimal internal consistency of discretization of Chakraborty and Kumar [2007, A new framework for solution of multidimensional population balance equations. Chem. Eng. Sci. 62, 4112-4125] for breakup and aggregation of particles. The 2D space of particle constituents (internal attributes) is discretized into bins by using arbitrarily spaced constant composition radial lines and constant mass lines of slope -1. The quadrilaterals are triangulated by using straight lines pointing towards the mean composition line. The monotonicity of the new discretization makes is quite easy to implement, like a rectangular grid but with significantly reduced numerical dispersion. We use the new discretization of space to automate the expansion and contraction of the computational domain for the aggregation process, corresponding to the formation of larger particles and the disappearance of smaller particles by adding and removing the constant mass lines at the boundaries. The results show that the predictions of particle size distribution on fixed X-grid are in better agreement with the analytical solution than those obtained with the earlier techniques. The simulations carried out with expansion and/or contraction of the computational domain as population evolves show that the proposed strategy of evolving the computational domain with the aggregation process brings down the computational effort quite substantially; larger the extent of evolution, greater is the reduction in computational effort. (C) 2011 Elsevier Ltd. All rights reserved.

An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems

A finite element method for solving multidimensional population balance systems is proposed where the balance of fluid velocity, temperature and solute partial density is considered as a two-dimensional system and the balance of particle size distribution as a three-dimensional one. The method is based on a dimensional splitting into physical space and internal property variables. In addition, the operator splitting allows to decouple the equations for temperature, solute partial density and particle size distribution. Further, a nodal point based parallel finite element algorithm for multi-dimensional population balance systems is presented. The method is applied to study a crystallization process assuming, for simplicity, a size independent growth rate and neglecting agglomeration and breakage of particles. Simulations for different wall temperatures are performed to show the effect of cooling on the crystal growth. Although the method is described in detail only for the case of d=2 space and s=1 internal property variables it has the potential to be extendable to d+s variables, d=2, 3 and s >= 1. (C) 2011 Elsevier Ltd. All rights reserved.

Mathematical Model of Viral Kinetics In Vitro Estimates the Number of E2-CD81 Complexes Necessary for Hepatitis C Virus Entry

Interaction between the hepatitis C virus (HCV) envelope protein E2 and the host receptor CD81 is essential for HCV entry into target cells. The number of E2-CD81 complexes necessary for HCV entry has remained difficult to estimate experimentally. Using the recently developed cell culture systems that allow persistent HCV infection in vitro, the dependence of HCV entry and kinetics on CD81 expression has been measured. We reasoned that analysis of the latter experiments using a mathematical model of viral kinetics may yield estimates of the number of E2-CD81 complexes necessary for HCV entry. Here, we constructed a mathematical model of HCV viral kinetics in vitro, in which we accounted explicitly for the dependence of HCV entry on CD81 expression. Model predictions of viral kinetics are in quantitative agreement with experimental observations. Specifically, our model predicts triphasic viral kinetics in vitro, where the first phase is characterized by cell proliferation, the second by the infection of susceptible cells and the third by the growth of cells refractory to infection. By fitting model predictions to the above data, we were able to estimate the threshold number of E2-CD81 complexes necessary for HCV entry into human hepatoma-derived cells. We found that depending on the E2-CD81 binding affinity, between 1 and 13 E2-CD81 complexes are necessary for HCV entry. With this estimate, our model captured data from independent experiments that employed different HCV clones and cells with distinct CD81 expression levels, indicating that the estimate is robust. Our study thus quantifies the molecular requirements of HCV entry and suggests guidelines for intervention strategies that target the E2-CD81 interaction. Further, our model presents a framework for quantitative analyses of cell culture studies now extensively employed to investigate HCV infection.

Kinetics of carbon monoxide oxidation with Sn(0.95)M(0.05)O(2-delta) (M = Cu, Fe, Mn, Co) catalysts

Base metal substituted Sn(0.95)M(0.05)O(2-delta) (M = Cu, Fe, Mn, Co) catalysts were synthesized by the solution combustion method and characterized by XRD, XPS, TEM and BET surface area analysis. The catalytic activities of these materials were investigated by performing CO oxidation. The rates and the apparent activation energies of the reaction for CO oxidation were determined for each catalyst. All the substituted catalysts showed high rates and lower activation energies for the oxidation of CO as compared to unsubstituted SnO(2). The rate was found to be much higher over copper substituted SnO(2) as compared to other studied catalysts. 100% CO conversion was obtained below 225 degrees C over this catalyst. A bifunctional reaction mechanism was developed that accounts for CO adsorption on base metal and support ions and O(2) dissociation on the oxide ion vacancy. The kinetic parameters were determined by fitting the model to the experimental data. The high rates of the CO oxidation reactions at low temperatures were rationalized by the high dissociative chemisorption of adsorbed O(2) over these catalysts.

Ultrasonic degradation of butadiene, styrene and their copolymers

Ultrasonic degradation of commercially important polymers, styrene-butadiene (SBR) rubber, acrylonitrile-butadiene (NBR) rubber, styrene-acrylonitrile (SAN), polybutadiene rubber and polystyrene were investigated. The molecular weight distributions were measured using gel permeation chromatography (GPC). A model based on continuous distribution kinetics approach was used to study the time evolution of molecular weight distribution for these polymers during degradation. The effect of solvent properties and ultrasound intensity on the degradation of SBR rubber was investigated using different pure solvents and mixed solvents of varying volatility and different ultrasonic intensities. (C) 2011 Elsevier B.V. All rights reserved.

Investigation of biodegradable and biocompatible castor oil poly(mannitol-citric-sebacate) polyester as a drug carrier

Castor oil-based poly(mannitol-citric sebacate) was synthesized by simple, catalyst-free melt condensation process using monomers having potential to be metabolized in vivo. The polymer was characterized using various techniques and the tensile and hydration properties of the polymers were also determined. The biocompatibility of the polymer was tested using human foreskin fibroblasts cells. The in vitro degradation studies show that the time for complete degradation of the polymer was more than 21 days. The usage of castor oil polyester as a drug carrier was analysed by doping the polymer with 5-fluorouracil model drug and the release rate was studied by varying the percentage loading of drugs and the pH of the PBS solution medium. The cumulative drug-release profiles exhibited a biphasic release with an initial burst release and cumulative 100% release within 42 h. To understand the role of the polymer as a drug carrier in the release behaviour, drug-release studies were conducted with another drug, isoniazid. The release behaviour of isoniazid drug from the same polymer matrix followed an nth order kinetic model and 100% cumulative release was achieved after 12 days. The variation in the release behaviour for two model drugs from the same polymer matrix suggests a strong interaction between the polymer and the drug molecule.

Structure and Photocatalytic Activity of Ti 1- x M x O 2±δ (M = W, V, Ce, Zr, Fe, and Cu) Synthesized by Solution Combustion Method

The W, V, Ce, Zr, Fe, and Cu metal ion substituted nanocrystalline anatase TiO2 was prepared by solution combustion method and characterized by XRD, Raman, BET, EPR, XPS, IR TGA, UV absorption, and photoluminescence measurements. The structural studies indicate that the solid solution formation was limited to a narrow range of concentrations of the dopant ions. The photocatalytic degradation of 4-nitrophenol under UV and solar exposure was investigated with Ti1-xMxO2±δ. The degradation rates of 4-nitrophenol with these catalysts were lesser than the degradation rates of 4-nitrophenol with undoped TiO2 both with UV exposure and solar radiation. However, the photocatalytic activities of most metal ion doped TiO2 are higher than the activity of the commercial TiO2, Degussa P25. The decrease in photocatalytic activity is correlated with decrease in photoluminescence due to electron states of metal ions within the band gap of TiO2.

Photocatalytic degradation of dimethoate using LbL fabricated TiO2/polymer hybrid films

Degradation of dimethoate under UV irradiation using TiO2/polymer films prepared by the layer-by-layer (LbL) method was investigated. The thin films were fabricated on glass slides and the surface morphology and roughness of the thin films were characterized using X-ray diffraction (XRD), scanning electron microscopy (SEM) and atomic force microscopy (AFM). The effect of lamp intensity, catalyst loading in the layers, number of bilayers, pH and initial dimethoate concentration on the degradation of dimethoate was systematically studied. The degradation was monitored using high performance liquid chromatography (HPLC) analysis and total organic carbon (TOC) measurements as a function of irradiation time, to see the change in concentration of dimethoate and mineralization, respectively. Complete degradation of dimethoate was achieved under TiO2 optimum loading of 4 g/L at an UV irradiation time of 180 min. Increase in the lamp intensity, catalyst loading and number of bilayers increased the rate of degradation. At a pH of 4.62, complete degradation of dimethoate was observed. The degradation efficiency decreased with increase in initial dimethoate concentration. The degradation byproducts were analyzed and confirmed by gas chromatography-mass spectra (GC-MS). Toxicity of the irradiated samples was measured using the luminescence of bacteria Vibrio fischeri after 30 min of incubation and the results showed more toxicity than the parent compound. Catalyst reusability studies revealed that the fabricated thin films could be repeatedly used for up to ten times without affecting the photocatalytic activity of the films. The findings of the present study are very useful for the treatment of wastewaters contaminated with pesticides. (C) 2011 Elsevier B.V. All rights reserved.

Effect of convection and viscoelasticity on spinodal decomposition in fluids

Current analytical work on the effect of convection and viscoelasticity on the early and late stages of spinodal decomposition is briefly described. In the early stages, the effect of viscoelastic stresses was analysed using a simple Maxwell model for the stress, which was incorporated in the Langevin equation for the momentum field. The viscoelastic stresses are found to enhance the rate of decomposition. In the late stages, the pattern formed depends on the relative composition of the two species. Droplet spinodal decomposition occurs when the concentration of one of the species is small. Convective transport does not have a significant effect on the growth of a single droplet, but it does result in an attractive interaction between non - Brownian droplets which could lead to coalescence. The effect of convective transport for the growth of random interfaces in a near symmetric quench was analysed using an 'area distribution function', which gives the distribution of surface area of the interface in curvature space. It was found that the curvature of the interface decreases proportional to t in the late stages of spinodal decomposition, and the surface area also decreases proportional to t.

Biosorption of heavy metal ions from aqueous and cyanide solutions using fungal biomass

A waste fungal biomass containing killed cells of Aspergillus niger was efficiently used in the removal of toxic metal ions such as nickel, calcium, iron and chromium from aqueous solutions. The role of different parameters such as initial metal ion concentration, solution pH and biomass concentration on biosorption capacity was established. The maximum metal uptake was found to be dependent on solution pH and increased with biomass loading upto 10g/L. The adsorption densities for various metal ions could be arranged as Ca>Cr (III)>Ni>Fe>Cr (VI). The effect of the presence of various metal ions in binary, ternary and quaternary combinations on biosorption was also assessed. Ni uptake was significantly affected, while that of Cr (VI) the least, in the presence of other metal ions. Uptake of base metals from an industrial cyanide effluent was studied using different species of fungi such as Aspergillus niger, Aspergillus terreus and Penicillium funiculosum and yeast such as Saccharomyces cerevisiae which were isolated from a gold mine. Traces of gold present in the cyanide effluent could be efficiently recovered. Among the four base metal contaminants present in the cyanide effluent, zinc was found to be most efficiently biosorbed, followed by iron, copper and lead. The role of both living and dead biomass on biosorption was distinguished and probable mechanisms illustrated.

Selective biodissolution of calcium and iron from bauxite in the presence of Bacillus polymyxa

A bacterium Bacillus polymyxa was found to be capable of selective removal of calcium and iron from bauxite. The bioleached residue was found to be enriched in its alumina content with insignificant amounts of iron and calcium as impurities. The developed bio- process was found to be capable of producing a bauxite product which meets the specifica- tions as a raw material for the manufacture of alumina based ceramics and refractories. The role of bacterial cells and metabolic products in the selective dissolution of calcium (present as calcite) and iron (present as hematite and goethite) from bauxite was assessed and possi- ble mechanisms illustrated. The effect of different parameters such as sucrose concentra- tion, pH, pulp density and time on selective biodissolution was studied. It was observed that periodic decantation and replenishment of the leach medium was beneficial in improving the dissolution kinetics. Calcium removal involves chelation with bacterial exopolysaccha- tides and acidolysis by organic acid generation. Hematite could be solubilized through a reductive dissolution mechanism.

Evolutionary Algorithm for the Determination of Optimal Mode of Bioreactor Operation

Stirred tank bioreactors, employed in the production of a variety of biologically active chemicals, are often operated in batch, fed-batch, and continuous modes of operation. The optimal design of bioreactor is dependent on the kinetics of the biological process, as well as the performance criteria (yield, productivity, etc.) under consideration. In this paper, a general framework is proposed for addressing the two key issues related to the optimal design of a bioreactor, namely, (i) choice of the best operating mode and (ii) the corresponding flow rate trajectories. The optimal bioreactor design problem is formulated with initial conditions and inlet and outlet flow rate trajectories as decision variables to maximize more than one performance criteria (yield, productivity, etc.) as objective functions. A computational methodology based on genetic algorithm approach is developed to solve this challenging multiobjective optimization problem with multiple decision variables. The applicability of the algorithm is illustrated by solving two challenging problems from the bioreactor optimization literature.