An introduction to flow and transport in fractal models of porous media: Part I

This special issue gathers together a number of recent papers on fractal geometry and its applications to the modeling of flow and transport in porous media. The aim is to provide a systematic approach for analyzing the statics and dynamics of fluids in fractal porous media by means of theory, modeling and experimentation. The topics covered include lacunarity analyses of multifractal and natural grayscale patterns, random packing's of self-similar pore/particle size distributions, Darcian and non-Darcian hydraulic flows, diffusion within fractals, models for the permeability and thermal conductivity of fractal porous media and hydrophobicity and surface erosion properties of fractal structures.

Capacidad y comportamiento de la adsorción de fenol en caolines naturales y modificados

En la actualidad las industrias químicas, farmacéuticas y clínicas, originan contaminantes en aguas superficiales, aguas subterráneas y suelos de nuestro país, como es el caso del fenol, contaminante orgánico común y altamente dañino para los organismos, incluso a bajas concentraciones. Existen en el mercado diferentes metodologías para minimizar la contaminación pero muchos de estos procesos tienen un alto coste, generación de contaminantes, etc. La adsorción de contaminantes por medio de arcillas es un método ampliamente utilizado, encontrándose eficaz y económico. Pero la dificultad de adsorber un contaminante orgánico como el fenol motiva la creación de un material llamado organoarcillas. Las organoarcillas son arcillas modificadas con un surfactante, a su vez, los surfactantes son moléculas orgánicas que confieren a la superficie de la arcilla carga catiónica en lugar de aniónica, haciendo más fácil la adsorción de fenol. Para esta tesis se ha elegido el caolín como material adsorbente, fácilmente disponible y relativamente de bajo coste. Se ha trabajado con: arenas de caolín, material directo de la extracción, y caolín lavado, originado del proceso de lavado de las arenas de caolín. Ambos grupos se diferencian fundamentalmente por su contenido en cuarzo, ampliamente mayor en las arenas de caolín. Con el objetivo de desarrollar un material a partir del caolín y arenas de éste con capacidad de retención de contaminates, en concreto, fenol, se procedió a modificar los materiales de partida mediante tratamientos térmicos, mecánicos y/o químicos, dando lugar a compuestos con mayor superficie química reactiva. Para ello se sometió el caolín y las arenas caoliníferas a temperaturas de 750ºC durante 3h, a moliendas hasta alcanzar su amorfización, y/o a activaciones con HCl 6M o con NaOH 5M durante 3h a 90ºC. En total se obtuvieron 18 muestras, en las que se estudiaron las características físico-químicas, mineralógicas y morfológicas de cada una de ellas con el fin de caracterizarlas después de haber sufrido los tratamientos y/o activaciones químicas. Los cambios producidos fueron estudiados mediante pH, capacidad de intercambio catiónico (CEC), capacidad de adsorción de agua (WCU y CWC), distribución de tamaño de partícula (PSD), área de superficie específica (SBET), difracción de rayos X (XRD), espectroscopía infrarroja por transformada de Fourier (FTIR), métodos térmicos (TG, DTG y DTA), y microscopía electrónica de transmisión y barrido (SEM y TEM). Además se analizó los cambios producidos por los tratamientos en función de las pérdidas de Al y Si que acontece en las 18 muestras. Los resultados para los materiales derivados de la arenas caoliníferas fueron similares a los obtenidos para los caolines lavados, la diferencia radica en la cantidad de contenido de caolinita en los diferente grupos de muestras. Apoyándonos en las técnicas de caracterización se puede observar que los tratamientos térmico y molienda produce materiales amorfos, este cambio en la estructura inicial sumado a las activaciones ácida y alcalina dan lugar a pérdidas de Si y Al, ocasionando que sus propiedades físico-químicas, mineralógicas y morfológicas se vean alteradas. Un fuerte aumento es observado en las áreas superficiales y en la CEC en determinadas muestras, además entre los cambios producidos se encuentra la producción de diferentes zeolitas en porcentajes distintos con el tratamiento alcalino. Para la obtención de las organoarcillas, las 18 muestras se sometieron a la surfactación con hexadeciltrimetil amonio (HDTMA) 20 mM durante 24h a 60ºC, esta concentración de tensioactivo fue más alta que la CEC de cada muestra. Los camext bios anteriormente producidos por los tratamientos y activaciones, afectan de forma diferente en la adsorción de HDTMA, variando por tanto la adsorción del surfactante en la superficie de las muestras. Se determinó el tensioactivo en superficie por FTIR, además se realizó un análisis de componentes principales (PCA) para examinar la dependencia entre las relaciones Si/Al de las muestras en la capacidad de adsorción de tensioactivo, y para el estudio de la adsorción de HDTMA en las muestras se realizaron además del análisis termogravimétrico, aproximaciones con los modelos de Freundllich y Langmuir. Se persigue conocer las diferentes formas y maneras que tiene el tensioactivo de fijarse en la superficie de las muestras. En las organoarcillas resultantes se cuantificó el fenol adsorbido cuando éstas fueron puestas en contacto con diferentes concentraciones de fenol: 50, 500, 1000, 2000, y 2500 mg/l durante 24h. El contaminante sorbido se calculó por medio de cromatografía de gases, y se realizaron aproximaciones con los modelos de Freundllich y Langmuir. El comportamiento de adsorción de fenol en arcillas orgánicas es regido por las características de las muestras. De forma general se puede decir que las muestras de caolines lavados tienen más capacidad de adsorción de fenol que las muestras de arenas de caolín y que la activación alcalina ha proporcionado una mejora en la adsorción de fenol en los dos grupos. En consecuencia se han obtenido materiales adsorbentes heterogéneos y por tanto, con propiedades diferentes. Se ha evaluado el comportamiento global de las arenas de caolín por un lado y del caolín lavado por otro. Las arenas de caolín presentan altos niveles de cuarzo y su uso para ciertos tipos de industrias no son recomendados en ocasiones por el alto costo que el proceso de limpieza y purificación implicaría. Por ello es importante reseñar en este proyecto las aplicaciones que ofrecen algunas muestras de este grupo. Los ensayos acontecidos en esta tesis han dado lugar a las siguientes publicaciones: • Pérdida de Al y Si en caolines modificados térmica- o mecánicamente y activados por tratamientos químicos. A. G. San Cristóbal, C Vizcayno, R. Castelló. Macla 9, 113-114. (2008). • Acid activation of mechanically and thermally modfied kaolins. A. G. San Cristóbal, R. Castelló, M. A. Martín Luengo, C Vizcayno. Mater. Res. Bull. 44 (2009) 2103-2111. • Zeolites prepared from calcined and mechanically modified kaolins. A comparative study. A. G San Cristóbal, R. Castelló, M. A. Martín Luengo, C Vizcayno. Applied Clay Science 49 (2010) 239-246. • Study comparative of the sorption of HDTMA on natural and modified kaolin. A. G San Cristóbal, R. Castelló, J. M. Castillejo, C Vizcayno. Aceptada en Clays and Clay minerals. • Capacity of modified kaolin sand and washed kaolin to adsorb phenol. A. G San Cristóbal, R. Castelló, C Vizcayno. Envío a revista sujeto a la publicación del artículo anterior. ABSTRACT Today’s chemical, pharmaceutical and clinical industries generate pollutants that affect the soils and surface and ground waters of our country. Among these, phenol is a common organic pollutant that is extremely harmful to living organisms, even at low concentrations. Several protocols exist to minimize the effects of pollutants, but most are costly procedures or even generate other pollutants. The adsorption of hazardous materials onto clays is perhaps the most used, efficient and cost-saving method available. However, organic compounds such as phenol are difficult to adsorb and this has led to the development of materials known as organoclays, which are much better at remediating organic compounds. Organoclays are clays that have been modified using a surfactant. In turn, surfactants are organic molecules that confer a cationic rather than anionic charge to the clay surface, improving it’s capacity to adsorb phenol. For this doctorate project, kaolin was selected as an adsorbent material for the removal of phenol given its easy sourcing and relatively low cost. The materials investigated were kaolin sand, a directly extracted material, and washed kaolin, which is the byproduct of the kaolin sand washing process. The main difference between the materials is their quartz content, which is much higher in the kaolin sands. To generate a product from kaolin or kaolin sand capable of retaining organic pollutants such as phenol, both materials were subjected to several heat, chemical and/or mechanical treatments to give rise to compounds with a greater reactive surface area. To this end the two starting materials underwent heating at 750ºC for 3 h, grinding to the point of amorphization and/or activation with HCl 6M or NaOH 5M for 3 h at 90ºC. These treatments gave rise to 18 processed samples, which were characterized in terms of their morphological, mineralogical, and physical-chemical properties. The behaviour of these new materials was examined in terms of their pH, cation exchange capacity (CEC), water adsorption capacity (WCU and WCC), particle size distribution (PSD), specific surface area (SBET), and their X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), thermal (DTG, DTA) and scanning and transmission electron microscopy (SEM and TEM) properties. The changes conferred by the different treatments were also examined in terms of Al and Si losses. Results for the materials derived from kaolin sands and washed kaolin were similar, with differences attributable to the kaolinite contents of the samples. The treatments heat and grinding produced amorphous materials, which when subjected to acid or alkali activation gave rise to Si and Al losses. This in turn led to a change in physico- chemical, mineralogical and morphological properties. Some samples showed a highly increased surface area and CEC. Further, among the changes produced, alkali treatment led to the generation of zeolites in different proportions depending on the sample. To produce the organoclays, the 18 samples were surfacted with hexadecyltrimethylammonium (HDTMA) 20 mM for 24 h at 60ºC. This surfactant concentration is higher than the CEC of each sample. The amount of HDTMA adsorbed onto the surface of each sample determined by FTIR varied according to treatment. A principle components analysis (PCA) was performed to examine correlations between sample Si/Al ratios and surfactant adsorption capacity. In addition, to explore HDTMA adsorption by the samples, DTG and DTA data were fitted to Freundllich and Langmuir models. The mechanisms of surfactant attachment to the sample surface were also addressed. The amount of phenol adsorbed by the resultant organoclays was determined when exposed to different phenol concentrations: 50, 500, 1000, 2000, and 2500 mg/l for 24 h. The quantity of adsorbed pollutant was estimated by gas chromatography and the data fitted to the models of Freundllich and Langmuir. Results indicate that the phenol adsorption capacity of the surfacted samples is dependent on the sample’s characteristics. In general, the washed kaolin samples showed a greater phenol adsorption capacity than the kaolon sands and alkali activation improved this capacity in the two types of sample. In conclusion, the treatments used gave rise to adsorbent materials with varying properties. Kaolin sands showed high quartz levels and their use in some industries is not recommended due to the costs involved in their washing and purification. The applications suggested by the data obtained for some of the kaolin sand samples indicate the added value of this industrial by-product. The results of this research project have led to the following publications: • Pérdida de Al y Si en caolines modificados térmica- o mecánicamente y activados por tratamientos químicos. A. G. San Cristóbal, C Vizcayno, R. Castelló. Macla 9, 113-114. (2008). • Acid activation of mechanically and thermally modfied kaolins. A. G. San Cristóbal, R. Castelló, M. A. Martín Luengo, C Vizcayno. Mater. Res. Bull. 44 (2009) 2103-2111. • Zeolites prepared from calcined and mechanically modified kaolins. A comparative study. A. G. San Cristóbal, R. Castelló, M. A. Martín Luengo, C Vizcayno. Applied Clay Science 49 (2010) 239-246. • Study comparative of the sorption of HDTMA on natural and modified kaolin. A. G. San Cristóbal, R. Castelló, J. M. Castillejo, C Vizcayno Accepted in Clays and Clay minerals. • Capacity of modified kaolin sand and washed kaolin to adsorb phenol. A. G San Cristóbal, R. Castelló, C Vizcayno. Shipment postponed, subject to the publication of the previous article.

Computer simulation of random parckings for self-similar particle size distributions in soil and granular materials: porosity and pore size distribution

A 2D computer simulation method of random packings is applied to sets of particles generated by a self-similar uniparametric model for particle size distributions (PSDs) in granular media. The parameter p which controls the model is the proportion of mass of particles corresponding to the left half of the normalized size interval [0,1]. First the influence on the total porosity of the parameter p is analyzed and interpreted. It is shown that such parameter, and the fractal exponent of the associated power scaling, are efficient packing parameters, but this last one is not in the way predicted in a former published work addressing an analogous research in artificial granular materials. The total porosity reaches the minimum value for p = 0.6. Limited information on the pore size distribution is obtained from the packing simulations and by means of morphological analysis methods. Results show that the range of pore sizes increases for decreasing values of p showing also different shape in the volume pore size distribution. Further research including simulations with a greater number of particles and image resolution are required to obtain finer results on the hierarchical structure of pore space.

Monte Carlo simulations of densely-packed athermal polymers in the bulk and under confinement

We review the main results from extensive Monte Carlo (MC) simulations on athermal polymer packings in the bulk and under confinement. By employing the simplest possible model of excluded volume, macromolecules are represented as freely-jointed chains of hard spheres of uniform size. Simulations are carried out in a wide concentration range: from very dilute up to very high volume fractions, reaching the maximally random jammed (MRJ) state. We study how factors like chain length, volume fraction and flexibility of bond lengths affect the structure, shape and size of polymers, their packing efficiency and their phase behaviour (disorder–order transition). In addition, we observe how these properties are affected by confinement realized by flat, impenetrable walls in one dimension. Finally, by mapping the parent polymer chains to primitive paths through direct geometrical algorithms, we analyse the characteristics of the entanglement network as a function of packing density.

Crystal structure of the HLA-Cw3 allotype-specific killer cell inhibitory receptor KIR2DL2

Killer cell inhibitory receptors (KIR) protect class I HLAs expressing target cells from natural killer (NK) cell-mediated lysis. To understand the molecular basis of this receptor-ligand recognition, we have crystallized the extracellular ligand-binding domains of KIR2DL2, a member of the Ig superfamily receptors that recognize HLA-Cw1, 3, 7, and 8 allotypes. The structure was determined in two different crystal forms, an orthorhombic P212121 and a trigonal P3221 space group, to resolutions of 3.0 and 2.9 Å, respectively. The overall fold of this structure, like KIR2DL1, exhibits K-type Ig topology with cis-proline residues in both domains that define β-strand switching, which sets KIR apart from the C2-type hematopoietic growth hormone receptor fold. The hinge angle of KIR2DL2 is approximately 80°, 14° larger than that observed in KIR2DL1 despite the existence of conserved hydrophobic residues near the hinge region. There is also a 5° difference in the observed hinge angles in two crystal forms of 2DL2, suggesting that the interdomain hinge angle is not fixed. The putative ligand-binding site is formed by residues from several variable loops with charge distribution apparently complementary to that of HLA-C. The packing of the receptors in the orthorhombic crystal form offers an intriguing model for receptor aggregation on the cell surface.

Supramolecular organization of immature and mature murine leukemia virus revealed by electron cryo-microscopy: Implications for retroviral assembly mechanisms

We have used electron cryo-microscopy and image analysis to examine the native structure of immature, protease-deficient (PR−) and mature, wild-type (WT) Moloney murine leukemia virus (MuLV). Maturational cleavage of the Gag polyprotein by the viral protease is associated with striking morphological changes. The PR− MuLV particles exhibit a rounded central core, which has a characteristic track-like shell on its surface, whereas the WT MuLV cores display a polygonal surface with loss of the track-like feature. The pleomorphic shape and inability to refine unique orientation angles suggest that neither the PR− nor the WT MuLV adheres to strict icosahedral symmetry. Nevertheless, the PR− MuLV particles do exhibit paracrystalline order with a spacing between Gag molecules of ≈45 Å and a length of ≈200 Å. Because of the pleomorphic shape and paracrystalline packing of the Gag–RNA complexes, we raise the possibility that assembly of MuLV is driven by protein–RNA, as well as protein–protein, interactions. The maturation process involves a dramatic reorganization of the packing arrangements within the ribonucleoprotein core with disordering and loosening of the individual protein components.

Crystal structure of chemically synthesized [N33A] stromal cell-derived factor 1α, a potent ligand for the HIV-1 “fusin” coreceptor

Stromal cell-derived factor-1α (SDF-1α ) is a member of the chemokine superfamily and functions as a growth factor and chemoattractant through activation of CXCR4/LESTR/Fusin, a G protein-coupled receptor. This receptor also functions as a coreceptor for T-tropic syncytium-inducing strains of HIV-1. SDF-1α antagonizes infectivity of these strains by competing with gp120 for binding to the receptor. The crystal structure of a variant SDF-1α ([N33A]SDF-1α ) prepared by total chemical synthesis has been refined to 2.2-Å resolution. Although SDF-1α adopts a typical chemokine β-β-β-α topology, the packing of the α-helix against the β-sheet is strikingly different. Comparison of SDF-1α with other chemokine structures confirms the hypothesis that SDF-1α may be either an ancestral protein from which all other chemokines evolved or the chemokine that is the least divergent from a primordial chemokine. The structure of SDF-1α reveals a positively charged surface ideal for binding to the negatively charged extracellular loops of the CXCR4 HIV-1 coreceptor. This ionic complementarity is likely to promote the interaction of the mobile N-terminal segment of SDF-1α with interhelical sites of the receptor, resulting in a biological response.

A structural view of evolutionary divergence

Two directed evolution experiments on p-nitrobenzyl esterase yielded one enzyme with a 100-fold increased activity in aqueous-organic solvents and another with a 17°C increase in thermostability. Structures of the wild type and its organophilic and thermophilic counterparts are presented at resolutions of 1.5 Å, 1.6 Å, and 2.0 Å, respectively. These structures identify groups of interacting mutations and demonstrate how directed evolution can traverse complex fitness landscapes. Early-generation mutations stabilize flexible loops not visible in the wild-type structure and set the stage for further beneficial mutations in later generations. The mutations exert their influence on the esterase structure over large distances, in a manner that would be difficult to predict. The loops with the largest structural changes generally are not the sites of mutations. Similarly, none of the seven amino acid substitutions in the organophile are in the active site, even though the enzyme experiences significant changes in the organization of this site. In addition to reduction of surface loop flexibility, thermostability in the evolved esterase results from altered core packing, helix stabilization, and the acquisition of surface salt bridges, in agreement with other comparative studies of mesophilic and thermophilic enzymes. Crystallographic analysis of the wild type and its evolved counterparts reveals networks of mutations that collectively reorganize the active site. Interestingly, the changes that led to diversity within the α/β hydrolase enzyme family and the reorganization seen in this study result from main-chain movements.

Measures of residue density in protein structures

A hierarchy of residue density assessments and packing properties in protein structures are contrasted, including a regular density, a variety of charge densities, a hydrophobic density, a polar density, and an aromatic density. These densities are investigated by alternative distance measures and also at the interface of multiunit structures. Amino acids are divided into nine structural categories according to three secondary structure states and three solvent accessibility levels. To take account of amino acid abundance differences across protein structures, we normalize the observed density by the expected density defining a density index. Solvent accessibility levels exert the predominant influence in determinations of the regular residue density. Explicitly, the regular density values vary approximately linearly with respect to solvent accessibility levels, the linearity parameters depending on the amino acid. The charge index reveals pronounced inequalities between lysine and arginine in their interactions with acidic residues. The aromatic density calculations in all structural categories parallel the regular density calculations, indicating that the aromatic residues are distributed as a random sample of all residues. Moreover, aromatic residues are found to be over-represented in the neighborhood of all amino acids. This result might be attributed to nucleation sites and protein stability being substantially associated with aromatic residues.

Parallel-up structure evidences the molecular directionality during biosynthesis of bacterial cellulose

The “parallel-up” packing in cellulose Iα and Iβ unit cells was experimentally demonstrated by a combination of direct-staining the reducing ends of cellulose chains and microdiffraction-tilting electron crystallographic analysis. Microdiffraction investigation of nascent bacterial cellulose microfibrils showed that the reducing end of the growing cellulose chains points away from the bacterium, and this provides direct evidence that polymerization by the cellulose synthase takes place at the nonreducing end of the growing cellulose chains. This mechanism is likely to be valid also for a number of processive glycosyltransferases such as chitin synthases, hyaluronan synthases, and proteins involved in the synthesis of nodulation factor backbones.

Chiral molecular self-assembly of phospholipid tubules: A circular dichroism study

We report on spectroscopic studies of the chiral structure in phospholipid tubules formed in mixtures of alcohol and water. Synthetic phospholipids containing diacetylenic moieties in the acyl chains self-assemble into hollow, cylindrical tubules in appropriate conditions. Circular dichroism provides a direct measure of chirality of the molecular structure. We find that the CD spectra of tubules formed in mixtures of alcohol and water depends strongly on the alcohol used and the lipid concentration. The relative spectral intensity of different circular dichroism bands correlates with the number of bilayers observed using microscopy. The results provide experimental evidence that tubule formation is based on chiral packing of the lipid molecules and that interbilayer interactions are important to the tubule structure.

Crystal structure of the Sec18p N-terminal domain

Yeast Sec18p and its mammalian orthologue N-ethylmaleimide-sensitive fusion protein (NSF) are hexameric ATPases with a central role in vesicle trafficking. Aided by soluble adapter factors (SNAPs), Sec18p/NSF induces ATP-dependent disassembly of a complex of integral membrane proteins from the vesicle and target membranes (SNAP receptors). During the ATP hydrolysis cycle, the Sec18p/NSF homohexamer undergoes a large-scale conformational change involving repositioning of the most N terminal of the three domains of each protomer, a domain that is required for SNAP-mediated interaction with SNAP receptors. Whether an internal conformational change in the N-terminal domains accompanies their reorientation with respect to the rest of the hexamer remains to be addressed. We have determined the structure of the N-terminal domain from Sec18p by x-ray crystallography. The Sec18p N-terminal domain consists of two β-sheet-rich subdomains connected by a short linker. A conserved basic cleft opposite the linker may constitute a SNAP-binding site. Despite structural variability in the linker region and in an adjacent loop, all three independent molecules in the crystal asymmetric unit have the identical subdomain interface, supporting the notion that this interface is a preferred packing arrangement. However, the linker flexibility allows for the possibility that other subdomain orientations may be sampled.

Electrostatic interaction between helical macromolecules in dense aggregates: An impetus for DNA poly- and meso-morphism

DNA exhibits a surprising multiplicity of structures when it is packed into dense aggregates. It undergoes various polymorphous transitions (e.g., from the B to A form) and mesomorphous transformations (from hexagonal to orthorhombic or monoclinic packing, changes in the mutual alignment of nearest neighbors, etc). In this report we show that such phenomena may have their origin in the specific helical symmetry of the charge distribution on DNA surface. Electrostatic interaction between neighboring DNA molecules exhibits strong dependence on the patterns of molecular surface groups and adsorbed counter-ions. As a result, it is affected by such structural parameters as the helical pitch, groove width, the number of base pairs per helical turn, etc. We derive expressions which relate the energy of electrostatic interaction with these parameters and with the packing variables characterizing the axial and azimuthal alignment between neighboring macromolecules. We show, in particular, that the structural changes upon the B-to-A transition reduce the electrostatic energy by ≈kcal/mol per base pair, at a random adsorption of counter ions. Ion binding into the narrow groove weakens or inverts this effect, stabilizing B-DNA, as it is presumably the case in Li+-DNA assemblies. The packing symmetry and molecular alignment in DNA aggregates are shown to be affected by the patterns of ion binding.

Hydrophobic sequence minimization of the α-lactalbumin molten globule

The molten globule, a widespread protein-folding intermediate, can attain a native-like backbone topology, even in the apparent absence of rigid side-chain packing. Nonetheless, mutagenesis studies suggest that molten globules are stabilized by some degree of side-chain packing among specific hydrophobic residues. Here we investigate the importance of hydrophobic side-chain diversity in determining the overall fold of the α-lactalbumin molten globule. We have replaced all of the hydrophobic amino acids in the sequence of the helical domain with a representative amino acid, leucine. Remarkably, the minimized molecule forms a molten globule that retains many structural features characteristic of a native α-lactalbumin fold. Thus, nonspecific hydrophobic interactions may be sufficient to determine the global fold of a protein.