Fractal Morphology and Breakage of DLCA and RLCA Aggregates

Latex aggregates, formed in 1 M McIlvaine buffer solution and 0.2 M NaCl solution, have been characterized in terms of aggregate size distribution and fractal morphology. This was achieved using three sizing techniques (image analysis, laser scattering, and electrical sensing) in which size distributions and fractal properties of the aggregates were measured. Estimates of fractal dimensions were made using the two-slope method based on dimensional analysis and the small-angle light scattering method. Aggregate suspensions were prepared using both water and a mixture of heavy water/ water as the solvent. The latter essentially eliminated sedimentation, which was observed after one day of aggregation when water alone was used as a solvent. Latex aggregates formed by diffusion-limited colloid aggregation (DLCA) and reaction-limited colloid aggregation (RLCA) had fractal dimensions close to 1.8 and 2.1, respectively. As observed through image analysis, DLCA aggregates possessed a loose tenuous structure, whereas RLCA aggregates were more compact. Disruption of both DLCA and RLCA aggregates has been investigated in laminar flow and turbulent capillary flow. The shear forces introduced by a laminar shear device with a shear rate up to 1711 s(-1) were unable to bring about aggregate breakup; shearing facilitates aggregate growth in the case of DLCA. However, latex aggregates were significantly disrupted after passage through a turbulent capillary tube at 95209 s(-1). Copyright 2000 Academic Press.     

Further insights into the universality of colloidal aggregation

Dynamic light scattering (DLS) performed at various scattering wave vectors provides detailed information about the aggregation kinetics and the cluster mass distribution (CMD) in colloidal dispersions. Detailed modeling of the aggregation kinetics with population balance equations requires a quantitative connection between the CMD and measurable quantities such as the angle dependent hydrodynamic radii obtained by DLS. For this purpose we evaluate and compare various models for the structure factor of fractal aggregates. Additionally, we introduce a simple scattering model that accounts for the contribution of internal cluster dynamics of fractal clusters to the first cumulant of the dynamic structure factor. We show that this contribution allows to quantitatively describe previously measured experimental data on the scattering wave vector dependence of the hydrodynamic radius in diffusion limited cluster-cluster aggregation (DLCA), which was shown to exhibit some kind of universality behavior (master curve). Using the same scattering model, we analyze a similar set of experimental data but in reaction limited cluster-cluster aggregation (RLCA). We find that in this case the crossover from RLCA to DLCA and gravitational settling both have a significant influence on the CMD and consequently on the scattering wave vector dependent DLS data. Only when accounting for both these effects they temporarily compensate each other and a satisfactory representation of the aggregation master curve is possible for the RLCA data at longer times. Indeed, we find that either crossover from RLCA to DLCA or gravitational settling, when present individually, causes the loss of a master curve for aggregation.     

Disruption of polystyrene latex aggregates in capillary flow

 Disruption of polystyrene latex aggregates, formed in 1 M citric acid/phosphate buffer solution at pH 3.8 through diffusion-limited colloid aggregation (DLCA) and in 0.2 M NaCl solution at pH 5.5 through reaction-limited colloid aggregation (RLCA), was studied with respect to aggregate size and fractal nature. This was achieved using small-angle laser scattering in conjunction with a specially designed sampling method, which brought about the elimination of the disruption of the aggregates caused by a commercial stirrer sample unit. Aggregations were carried out in a mixture of deuterium oxide and water instead of water alone as a solvent to minimise sedimentation resulting from the differences in density between the latex particles and the electrolytes. An initial “steady state” in terms of aggregate size and fractal dimension was found to occur after around 20 min and 2 days for DLCA and RLCA aggregates, respectively, at 25 °C. No aggregate disruption was detected for DLCA and RLCA aggregates after their passing through a capillary tube for shear rates up to 1584 and 2694 s⁻¹, respectively. At higher shear rates, significant decreases in the aggregate volume-mean diameter, D[4, 3], occurred after shearing. The degree of reduction in D[4, 3] was larger for DLCA aggregates in comparison to RLCA aggregates. The results would suggest that DLCA aggregates were more subject to disruption during shearing. A high degree of disruption was observed in turbulent flow for both aggregates. Received: 30 June 1999 Accepted in revised form: 11 November 1999     

Two-dimensional colloidal aggregation: concentration effects

Extensive numerical simulations of diffusion-limited (DLCA) and reaction-limited (RLCA) colloidal aggregation in two dimensions were performed to elucidate the concentration dependence of the cluster fractal dimension and of the different average cluster sizes. Both on-lattice and off-lattice simulations were used to check the independence of our results on the simulational algorithms and on the space structure. The range in concentration studied spanned 2.5 orders of magnitude. In the DLCA case and in the flocculation regime, it was found that the fractal dimension shows a linear-type increase with the concentration phi, following the law: d(f)=d(fo)+aphi(c). For the on-lattice simulations the fractal dimension in the zero concentration limit, d(fo), was 1.451+/-0.002, while for the off-lattice simulations the same quantity took the value 1.445+/-0.003. The prefactor a and exponent c were for the on-lattice simulations equal to 0.633+/-0.021 and 1.046+/-0.032, while for the off-lattice simulations they were 1.005+/-0.059 and 0.999+/-0.045, respectively. For the exponents z and z', defining the increase of the weight-average (S(w)(t)) and number-average (S(n)(t)) cluster sizes as a function of time, we obtained in the DLCA case the laws: z=z(o)+bphi(d) and z'=z'(o)+b'phi(d'). For the on-lattice simulations, z(o), b, and d were equal to 0.593+/-0.008, 0.696+/-0.068, and 0.485+/-0.048, respectively, while for the off-lattice simulations they were 0.595+/-0.005, 0.807+/-0.093, and 0.599+/-0.051. In the case of the exponent z', the quantities z'(o), b', and d' were, for the on-lattice simulations, equal to 0.615+/-0.004, 0.814+/-0.081, and 0.620+/-0.043, respectively, while for the off-lattice algorithm they took the values 0.598+/-0.002, 0.855+/-0.035, and 0.610+/-0.018. In RLCA we have found again that the fractal dimension, in the flocculation regime, shows a similar linear-type increase with the concentration d(f)=d(fo)+aphi(c), with d(fo)=1.560+/-0.004, a=0.342+/-0.039, and c=1.000+/-0.112. In this RLCA case it was not possible to find a straight line in the log-log plots of S(w)(t) and S(n)(t) in the aggregation regime considered, and no exponents z and z' were defined. We argue however that for sufficiently long periods of time the cluster averages should tend to those for DLCA and, therefore, their exponents should coincide with z and z' of the DLCA case. Finally, we present the bell-shaped master curves for the scaling of the cluster size distribution function and their evolution when the concentration increases, for both the DLCA and RLCA cases.     

Nondestructive technique for the characterization of the pore size distribution of soft porous constructs for tissue engineering

Polymer scaffolds tailored for tissue engineering applications possessing the desired pore structure require reproducible fabrication techniques. Nondestructive, quantitative methods for pore characterization are required to determine the pore size and its distribution. In this study, a promising alternative to traditional pore size characterization techniques is presented. We introduce a quantitative, nondestructive and inexpensive method to determine the pore size distribution of large soft porous solids based on the on the displacement of a liquid, that spreads without limits though a porous medium, by nitrogen. The capillary pressure is measured and related to the pore sizes as well as the pore size distribution of the narrowest bottlenecks of the largest interconnected pores in a porous medium. The measured pore diameters correspond to the narrowest bottleneck of the largest pores connecting the bottom with the top surface of a given porous solid. The applicability and reproducibility of the breakthrough technique is demonstrated on two polyurethane foams, manufactured using the thermally induced phase separation (TIPS) process, with almost identical overall porosity (60-70%) but very different pore morphology. By selecting different quenching temperatures to induce polymer phase separation, the pore structure could be regulated while maintaining the overall porosity. Depending on the quenching temperature, the foams exhibited either longitudinally oriented tubular macropores interconnected with micropores or independent macropores connected to adjacent pores via openings in the pore walls. The pore size and its distribution obtained by the breakthrough test were in excellent agreement to conventional characterization techniques, such as scanning electron microscopy combined with image analysis, BET technique, and mercury intrusion porosimetry. This technique is suitable for the characterization of the micro- and macropore structure of soft porous solids intended for tissue engineering applications. The method is sensitive for the smallest bottlenecks of the largest continuous pores throughout the scaffold that contributes to fluid flow.     

Cluster shape anisotropy in irreversibly aggregating particulate systems

The results for cluster shape anisotropy over a broad range (10)(-3)-10(-1)) of monomer volume fractions, fv values, are presented for both two- (2d) and three-dimensional (3d) simulations of diffusion-limited (DLCA), ballistic-limited (BLCA), and reaction-limited (RLCA) cluster-cluster aggregation classes. We find that all three aggregation classes have different dilute-limit shape anisotropies, with the diffusion-limited model having the largest value of anisotropy and the reaction-limited model having the smallest. The simulation result for the cluster shape anisotropy for each of the three aggregation classes is slightly less than the corresponding prediction of the hierarchial model. In addition, we find excellent agreement between the 2d DLCA simulation results and experimental measurements of shape anisotropy. At late times, shape anisotropy decreases from the dilute-limit value.     

A method for the determination of accessible surface area,pore volume,pore size and its volume distribution for homogeneous pores of different shapes

We develop a novel method to determine the accessible pore volume, the accessible pore size and its distribution for pores having homogeneous surfaces but taking an arbitrary shape. The accessible pore volume is essentially the volume space that is accessible to the centre of an adsorbate molecule, while the accessible pore size is defined by the largest sphere that can be accommodated in the accessible space. The size of this sphere depends on the point in the accessible volume that we select. The accessible pore size is therefore, a local variable and this means that even a geometrically simple pore can possess many sizes. Each local accessible pore size is associated with a local accessible pore volume and the relationship between this pore volume and pore size is called the accessible pore size distribution. In this paper, we illustrate this methodology with a number of model pores ranging from simple to complex geometry and present the analytical accessible pore size distribution.     

A new method to determine pore size and its volume distribution of porous solids having known atomistic configuration

A simple method, based on Monte Carlo integration, is presented to derive pore size and its volume distribution for porous solids having known configuration of solid atoms. Because pores do not have any particular shape, it is important that we define the pore size in an unambiguous manner and the volume associated with each pore size. The void volume that we adopt is the one that is accessible to the center of mass of the probe particle. We test this new method with porous solids having well defined pores such as graphitic slit pores and carbon nanotubes, and then apply it to obtain the pore volume distribution of complex solids such as disordered solids, rectangular pores, defected graphitic pores, metal organic framework and zeolite.     

Molecular simulation of pressure-driven fluid flow in nanoporous membranes

An extended nonequilibrium molecular dynamics technique has been developed to investigate the transport properties of pressure-driven fluid flow in thin nanoporous membranes. Our simulation technique allows the simulation of the pressure-driven permeation of liquids through membranes while keeping a constant driving pressure using fluctuating walls. The flow of argon in the liquid state was simulated on applying an external pressure difference of 2.4x10(6) Pa through the slitlike and cylindrical pores. The volume flux and velocity distribution in the membrane pores were examined as a function of pore size, along with the interaction with the pore walls, and these were compared with values estimated using the Hagen-Poiseuille flow. The calculated velocity strongly depends on the strength of the interaction between the fluid and the atoms in the wall when the pore size is approximately<20sigma. The calculated volume flux also shows a dependence on the interaction between the fluid and the atoms in the wall. The Hagen-Poiseuille law overestimates or underestimates the flux depending on the interaction. From the analysis of calculated results, a good linear correlation between the density of the fluid in the membrane pores and the deviation of the flux estimated from the Hagen-Poiseuille flow was found. This suggests that the flux deviation in nanopore from the Hagen-Poiseuille flow can be predicted based on the fluid density in the pores.     

不同电解质体系中土壤胶体凝聚动力学的动态光散射研究

利用动态光散射技术研究在不同浓度的KNO3和Mg(NO3)2中土壤胶体颗粒的凝聚过程动力学. 通过分析凝聚过程中光强和有效粒径随时间的变化得到: (1)根据凝聚过程中光强的稳定与否, 可以判断土壤胶体凝聚过程中碰撞的发生是由布朗运动支配还是由重力作用支配; (2)在不同的电解质体系下土壤胶体凝聚表现为快速凝聚特征或不同的慢速凝聚特征, 并且在慢速凝聚中存在一个对重力敏感的电解质浓度; (3)两种电解质作用下的土壤胶体凝聚特征相似, 但对Mg(NO3)2体系浓度变化的敏感性远远大于KNO3体系. 此外, 通过分析凝聚平均速率随电解质浓度的变化, 找到慢速凝聚与快速凝聚的电解质浓度转折点, 即临界絮凝浓度(CFC), 提供了一个实验测定CFC的可能方法.     

Characterization of pore structure in a nanoporous low-dielectric-constant thin film by neutron porosimetry and X-ray porosimetry

A small-angle neutron scattering (SANS) porosimetry technique is presented for characterization of pore structure in nanoporous thin films. The technique is applied to characterize a spin-on organosilicate low dielectric constant (low-k) material with a random pore structure. Porosimetry experiments are conducted using a "contrast match" solvent (a mixture of toluene-d8 and toluene-h8) having the same neutron scattering length density as that of the nanoporous film matrix. The film is exposed to contrast match toluene vapor in a carrier gas (air), and pores fill with liquid by capillary condensation. The partial pressure of the solvent vapor is increased stepwise from 0 (pure air) to P0 (saturated solvent vapor) and then decreased stepwise to 0 (pure air). As the solvent partial pressure increases, pores fill with liquid solvent progressively from smallest to largest. SANS measurements quantify the average size of the empty pores (those not filled with contrast match solvent). Analogous porosimetry experiments using specular X-ray reflectivity (SXR) quantify the volume fraction of solvent adsorbed at each step. Combining SXR and SANS data yields information about the pore size distribution and illustrates the size dependence of the filling process. For comparison, the pore size distribution is also calculated by application of the classical Kelvin equation to the SXR data.     

Formatation of pore structure in tape-cast alumina membranes – effects of binder content and firing temperature

Disc type ceramic aluminium oxide membrane has been prepared by tape casting technique. Thickness of this single layer membrane is in the range 200–300 μm. Porosity and pore size distribution have been determined by mercury porosimetry. Polymeric binder content of the green tape and the firing temperature are found to have strong influence on the average pore size, pore size distribution and overall porosity. Higher binder content promotes agglomeration of the ceramic particles, which on firing leads to wider pore size distribution and formation of closed pores. Pore coarsening is observed with increasing firing temperature.     

Ceramic membrane characterization via the bubble point technique

Porous membranes having nanometer and smaller pores challenge existing characterization methods. An easy, fast and inexpensive method to determine the maximum pore size and the pore size distribution is offered by the bubble point technique. Several methods based on similar principles have been presented in the literature. Here the original bubble point test and a liquid-liquid variation are considered. Two types of ceramic membranes with very different morphologies have been characterized with these methods in our labs. Results obtained for Anodisc^® flat disc membranes with straight, non-intersecting pores using binary and ternary probing liquid systems are in very good agreement with each other and the manufacturers characteristics. On the other hand, analysis of tubular γ-alumina membranes, i.e., Membralox^®, resulted in two phase flow within the pores, and hence information about the pore size distribution could not be extracted from these tests.     

Behavior of acetonitrile confined to mesoporous silica gels as studied by 129Xe NMR: a novel method for determining the pore sizes

129Xe NMR spectra of xenon dissolved in acetonitrile confined into three mesoporous silica gels with nominal pore diameters of 40, 60, and 100 A have been measured over the temperature range 170-245 K. The spectra consist of a number of lines, which contain detailed information on the system. The most interesting result is that the chemical shift of a particular signal observed below the melting point of confined acetonitrile is highly sensitive to the pore size, and hence its shape is sensitive to the pore size distribution function. This signal originates from the xenon atoms sited in very small cavities built up inside the pores during the freezing transition. It can be used to determine the size or even the size distribution function of the pores. In addition, the emergence of this signal reveals the phase transition temperature of acetonitrile inside the pores, which can also be used to determine the size of the pores. The difference in the chemical shifts of two other signals, which arise from xenon dissolved in bulk and confined acetonitrile, provides still another novel method for determining the size of the pores.     

Poly-L-lysine templated silicas: using polypeptide secondary structure to control oxide pore architectures

Utilizing polypeptide secondary structure as a means for controlling oxide pore architectures is explored. Poly-L-lysine is used as a model polypeptide as its folding behavior is well understood and compatible with the sol-gel chemistry of silica. Here, we show that silicas synthesized with poly-L-lysine in a alpha-helix conformation possess cylindrical pores that are approximately 1.5 nm in size, whereas silicas synthesized with poly-L-lysine in a beta-sheet conformation possess larger pores, the size of which are a function of the poly-L-lysine concentration, or in other words the size of the aggregate. In both cases, highly porous materials are obtained. In-situ circular dichroism measurements of the synthesis mixtures show that the poly-L-lysine secondary structure is not perturbed during synthesis. Infrared spectroscopy of the as-synthesized materials is consistent with the poly-L-lysine retaining its secondary structure. Grand canonical Monte Carlo simulations were also performed to validate the interpretation of the experimental adsorption results. The experimental isotherms are consistent with simulated isotherms of cylindrical pores 1.3-1.7 nm in size, in good agreement with expected values. Our results suggest a new avenue for synthesizing porous oxides with highly tuneable pore sizes and shapes under mild conditions.     

煤颗粒燃烧的孔隙特性研究

以实验为基础,系统研究了典型煤种燃烧时的颗粒孔隙过程。采用低温吸附法和电子显微图像计算机法测量了煤燃烧过程中的颗粒孔隙,获得了颗粒孔径分布和孔形分布等孔隙特性,建立了煤颗粒燃烧的微孔效应和亚微孔效应理论。     

Water in nanopores. I. Coexistence curves from Gibbs ensemble Monte Carlo simulations

Coexistence curves of water in cylindrical and slitlike nanopores of different size and water-substrate interaction strength were simulated in the Gibbs ensemble. The two-phase coexistence regions cover a wide range of pore filling level and temperature, including ambient temperature. Five different kinds of two-phase coexistence are observed. A single liquid-vapor coexistence is observed in hydrophobic and moderately hydrophilic pores. Surface transitions split from the main liquid-vapor coexistence region, when the water-substrate interaction becomes comparable or stronger than the water-water pair interaction. In this case prewetting, one and two layering transitions were observed. The critical temperature of the first layering transition decreases with strengthening water-substrate interaction towards the critical temperature expected for two-dimensional systems and is not sensitive to the variation of pore size and shape. Liquid-vapor phase transition in a pore with a wall which is already covered with two water layers is most typical for hydrophilic pores. The critical temperature of this transition is very sensitive to the pore size, in contrast to the liquid-vapor critical temperature in hydrophobic pores. The observed rich phase behavior of water in pores evidences that the knowledge of coexistence curves is of crucial importance for the analysis of experimental results and a prerequiste of meaningful simulations.     

煤焦在燃烧过程中孔隙结构变化的模拟

煤焦在燃烧过程中的物理特性，如比表面积和孔径分布会发生连续变化，直接测量煤焦在燃烧过程中的孔隙结构变化很困难，但可以通过合适的数学模型来观察，二维的圆柱孔模型已大量用来对煤焦气化与燃烧过程中表面积和孔隙结构的变化进行模拟，这个模型把孔隙分成两大部分－－大孔与小孔，因为小孔构成比表面的绝大部分，所以在反应过程中比表面积的变化可以由单一小孔模型来拟合，本文采用了用Ｔｓｅｎｇ和Ｅｄｇａｒ提出的孔模型对几     

Visualisation of the fibrillar and pore morphology of cellulosic fibres applying transmission electron microscopy

Applying transmission electron microscopy (TEM) on ultra-thin cross-sections of fibres, the main characteristics of the internal morphology of cotton and the main man-made cellulosic fibres (modal, viscose and lyocell) could be visualised. To obtain an appropriate contrast for TEM, isoprene was polymerised into the swollen fibres after a stepwise solvent exchange from water to acetone. The included polymer is stainable with osmium tetraoxide. Significant differences in distribution of pore sizes and pore arrangements in the cellulosic fibres were seen. Cotton showed very small pores in the bulk of the fibre, but drying cracks and flat pores between the sheets of the secondary wall appear as larger pores. Lyocell contains only nanopores in the bulk of the fibre with a slight gradient in pore density, and a very porous skin layer. In viscose and modal, a very wide pore size distribution from nanometer to micrometer size can be seen.     

Pores in bilayer membranes of amphiphilic molecules: coarse-grained molecular dynamics simulations compared with simple mesoscopic models

We investigate pores in fluid membranes by molecular dynamics simulations of an amphiphile-solvent mixture, using a molecular coarse-grained model. The amphiphilic membranes self-assemble into a lamellar stack of amphiphilic bilayers separated by solvent layers. We focus on the particular case of tensionless membranes, in which pores spontaneously appear because of thermal fluctuations. Their spatial distribution is similar to that of a random set of repulsive hard disks. The size and shape distribution of individual pores can be described satisfactorily by a simple mesoscopic model, which accounts only for a pore independent core energy and a line tension penalty at the pore edges. In particular, the pores are not circular: their shapes are fractal and have the same characteristics as those of two-dimensional ring polymers. Finally, we study the size-fluctuation dynamics of the pores, and compare the time evolution of their contour length to a random walk in a linear potential.