The scale behavior of fillers in elastomers by means of indentation tests

 Indentation tests were carried out on a carbon black filled rubber sample on different length scales. The experiments covered the range from aggregation of particles on the submicron scale up to structures which represent the bulk properties of the sample on the millimeter scale. The local stiffness was used to visualize the areas investigated; therefore, mechanical images were obtained for all length scales. So-called “mechanical units” were defined for every scale. The size distribution curves for the mechanical units were analyzed and they were found to be non-Gaussian-shaped for every scale. Moreover, the distribution curves of the mechanical units are similar to the distribution curves of particles and aggregates obtained by electron microscopy reported in the literature. Evaluation by means of fractal analysis led to fractal dimensions for the mechanical units. It could be shown in the present case that the fractal dimension D≈1.24 of the mechanical units in the range of submicrons up to several hundred microns is in good agreement with that of the filler aggregates proposed in the literature. Furthermore, D is constant over a wide range of about 6 decades in area scale starting from aggregates up to the size of agglomerates. This leads to the conclusion that the local arrangement of the filler ensembles seems to be self-similar from the smallest scale of aggregation of particles up to the largest formation observed by indentation testing on the millimeter scale. Received: 15 May 2001 Accepted: 18 August 2001     

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     

A Historical Introduction to Computer Models for Fractal Aggregates

It has been known for a century that small particles dispersed in liquids and gases can form aggregates with extraordinarily low densities, and a variety of studies in the 1960s and 1970s, based on conceptual models and computer models, suggested that anomalous scaling relationships were associated with the structures of these aggregates. However, the lack of a suitable theoretical framework and the limits of computer technology inhibited the development of a coherent understanding of the structures of these aggregates and the kinetics of their formation. In the 1980s, the popularization of fractal geometry and rapid advances in computer technology removed these barriers to progress. In this review, the early work on fractal aggregates is discussed and the basic particle-cluster and cluster-cluster aggregation models introduced in the 1980s are described. During the 1990s, interest has been focused on the subtle relationships between aggregation, gelation and spinodal decomposition and on the physical behavior of systems containing fractal aggregates. The following papers in this special issue of the Journal of Sol-Gel Science and Technology on Computer simulations of aggregation and sol-gel processes describe recent advances in these directions. They are previewed in this introductory contribution.     

Characterising latex particles and fractal aggregates using image analysis

The fractal nature of latex particles and their aggregates was characterised by image analysis in terms of fractal dimensions. The one- and two-dimensional fractal dimensions, D ₁ and D ₂, were estimated for polystyrene latex aggregates formed by flocculation in citric acid/phosphate buffer solutions. The dimensional analysis method was used, which is based on power law correlations between aggregate perimeter, projected area and maximum length. These aggregate characteristics were measured by image analysis. A two-slopes method using cumulative size distributions of aggregate length and solid volume has been developed to determine the three-dimensional fractal dimension (D ₃) for the latex aggregates. The fractal dimensions D ₁, D ₂ and D ₃ measured for single latex particles in distilled water agreed well with D ₁ = 1, D ₂ = 2 and D ₃ = 3 expected for Euclidean spherical objects. For the aggregates, the fractal dimension D ₂ of about 1.67 ± 0.04 (±standard deviation) was comparable to the fractal dimension D ₃ of approximately 1.72 ± 0.13 (±standard deviation), taking the standard deviations into account. The measured three-dimensional fractal dimension for latex aggregates is within the fractal dimension range 1.6–2.2 expected for aggregates formed through a cluster-cluster mechanism, and is close to the D ₃ value of about 1.8 indicated for cluster formation via diffusion-limited colloidal aggregation. Received: 28 September 1998 Accepted: 29 October 1998     

Image processing of the fractal aggregates composed of nanoparticles

The image-processing algorithms are described for chain branched aggregates composed of spherical particles. The processing procedure is based on setting off circles corresponding to the primary particles (spherules) in the images, followed by the construction of a digital model representing a set of diameters and coordinates of all spherules and their centers. The computational procedures are considered in which the digital model is used to calculate a series of parameters characterizing the aggregate’s structure and morphology, including fractal dimension for an individual aggregate and average dimension for a set of aggregates. The “clearance radius” of the aggregate is calculated as a half of geometric mean of the aggregate’s length L and width W. To determine L and W, the algorithm based on searching for the minimum-area (LW) rectangle circumscribing the aggregate’s contour is proposed.     

Destabilization of polystyrene latex particles induced by adsorption of polyvinylamine: mass, size and structure characteristics of the growing aggregates

The obviously visible aggregation of suspended colloidal particles resulting from the addition of polyvinylamine to the aqueous dispersion of polystyrene latex particles bearing surface sulfate groups set in with a delay of 24 h. The aggregation mechanisms and the fractal dimension of the aggregates were derived from the variations with time of the weight and number averaged masses of the aggregates as well as of the weight averaged harmonic mean diameter of the size distribution. Since the establishment of starved layers was determined to be relatively fast and to leave the liquid phase free of polymer, the delay for the obvious destabilization was attributed to the reconformation of adsorbed macromolecules that was expected to be extremely slow. This reconformation promoted the emergence of the diffusion-limited aggregation process that accompanies the permanent reaction-limited aggregation process. The fractal dimension of the latex particles/polyvinylamine aggregates was determined to be 2.12.     

Carbon blacks as dissipative colloid systems with universal properties

As a new approach the stationary size distribution of particles and aggregates of particles of carbon blacks is described with an extended version of the model of reversible aggregation. Computer simulations of aggregation in dissipative systems lead to ensembles the reduced size distributions of which are at not too short times identical with the universal stationary distribution of the aggregation model. A crucial general point seems to be that structural fluctuations activated by continuously running chemical reactions including viscous dissipation exhibits the same statistics as it is typical for thermally activated aggregation. This leads to the suggestion that the production of carbon blacks at very high temperatures or the reorganization during the so-called CAB-procedure should show a statistically analogous fluctuation-dissipation behaviour as thermally activated aggregation. The ensemble entropy is, in any case, rapidly maximized. In the reactor, for example, a sequence of generations with quasi-stationary ensemble structures is finally built up. Dissipation-fluctuation, including highly cooperative phenomena, guarantees a unique and optimized stationary, thermodynamically “essentially entropy controlled” colloid-structure. Universality is impressively verified by the finding that the particle and aggregate size distributions of different carbon blacks belong to the same “class” so that their reduced representations fall altogether on a master curve. Consequences of our interpretation are discussed. Received: 17 April 2001 Accepted: 1 August 2001     

Estimation of the dynamic size of fractal aggregates

A model is presented for an aggregation act occurring between two aggregates of any mass and fractal dimension. The kinetics of aggregation is also analyzed, as well as some previous works concerning the structure of fractal aggregates. As a result, a generalized curve is derived describing the normalized dynamic radius of clusters of spherical character as dependent on both the aggregate fractal dimension and the space dimension. It is shown how the curve may be utilized to determine the dynamic size of anisotropic aggregates. The obtained dependence can be used to estimate the dynamic size of fractal aggregates, to evaluate the prefactor in mass–radius relation and to model the aggregation kinetics.     

The effects of pretreatment of polycrystalline gold with OH<Superscript>•</Superscript> radicals on the electrochemical nucleation and growth of platinum

The nucleation and growth of platinum on polycrystalline gold was studied by chronoamperometry, cyclic voltammetry, and atomic force microscopy before and after treatment of the gold surface with hydroxyl (OH^•) radicals. Two different procedures of mechanical polishing of the gold surface (“coarse polish” and “fine polish”) were applied before the treatment with OH^• radicals. The nucleation and growth of Pt was much better reproducible on electrodes which underwent a “coarse polish”. The treatment of the Au surface with OH^• radicals decreased the number of active sites; however, the nucleation growth mode remained the same (3-D instantaneous). The spontaneous Pt deposition (no externally applied potential) on Au was unaffected by the treatment with OH^• radicals. In situ atomic force microscopy experiments showed that the Pt starts to grow only on some of the Au grains, most probably on those which have active sites on their surface. This leads to a roughening of the electrode surface upon Pt deposition. Treatment with OH^• radicals did only quantitatively diminish the amount of deposited Pt, but qualitatively the imaging of the Pt growth remained the same. Obviously, the OH^• radicals lead to a knockout (decreasing number) of active sites for Pt nucleation, while the nature of the remaining active sites stays unaffected.     

Characterization of fractal particles using acoustics, electroacoustics, light scattering, image analysis, and conductivity

Fractals are aggregates of primary particles organized with a certain symmetry defined essentially by one parameter-a fractal dimension. We have developed a model for the interpretation of acoustic data with respect to particle structure in aggregated fractal particles. We apply this model to the characterization of various properties of a fumed silica, being but one example of a fractal structure. Importantly, our model assumes that there is no liquid flow within the aggregates (no advection). For fractal dimensions of less than 2.5, we find that the size and density of aggregates, computed from the measured acoustic attenuation spectra, are quite independent of the assumed fractal dimension. This aggregate size agrees well with light-scattering measurements. We applied this model to the interpretation of electroacoustic data as well. A combination of electroacoustic and conductivity measurements yields sufficient data for comparing the fractal model of the particle organization with a simple model of the separate primary particles. Conductivity measurements provide information on particle surface conductivity reflected in terms of the Dukhin number (Du). Supporting information for the zeta potential and Du can also be provided by electroacoustic measurements assuming thin double-layer theory. In comparing values of Du from these two measurements, we find that the model of separate solid particles provides much more consistent results than a fractal model with zero advection. To explain this, we first need to explain an apparent contradiction in the acoustic and electroacoustic data for porous particles. Although not important for interpreting acoustic data, advection within the aggregate does turn out to be essential for interpreting electrokinetic and electroacoustic phenomena in dispersions of porous particles.     

Growth of Fractal Aggregates in the Intermediate Regime of Particle Accommodation

The growth dynamics of fractal aggregates was studied within the framework of continuum model in the self-consistent mean field approximation. The regime that is intermediate between the diffusion-limited aggregation and reaction-limited aggregation was considered. The dependence of aggregate fractal dimension on the attachment probability of particles during their collisions with an aggregate was obtained. In the limiting cases, the values of fractal dimension coincide with those determined earlier. The domain of the values of attachment probability was revealed where several regions characterized by their own values of fractal dimension were specified in the structure of growing cluster. Physical nature of the emergence of various regions in the aggregate structure was discussed.     

Effect of size, proteic composition, and heat treatment on the colloidal stability of proteolyzed bovine casein micelles

The casein micelles of reconstituted nonfat milk that have been fractionated by controlled pore glass chromatography showed a relationship between their size and their proteic composition: The fractions containing the smaller particles were richer in κ-casein than the fractions containing the bigger ones, in accordance with the casein micelle model of submicelles. The initial aggregation rate of micelles of different sizes, partially proteolyzed with chymosin (para-casein micelles), was measured in conditions of enzyme excess in which aggregation is the rate-limiting step of enzymatic coagulation, showing higher rates for the smaller micelles with the production of less compact para-casein micelle networks. This behavior could be explained in terms of electrostatic and steric colloidal stabilization due to their lower negative net charge and size and to a higher surface density of hydrophobic “patches” of proteolyzed κ-casein related to a higher probability of effective collisions between particles. Differences in the β-casein content did not seem to affect the initial aggregation rate of the micelles. On the contrary, the modifications of the micelle surface by heating affected the colloidal stability of the hydrolyzed micelles in different ways. The denaturation of the whey proteins and the formation of covalent complexes with κ-casein modify the micelle surface, increasing specially the steric stabilization, and produces a diminution in the number of hydrophobic sites that could be able to give interparticle hydrophobic interactions.     

Separation of the stereoisomers of a homologeous series of bis-amides on chiral stationary phases

Summary A homologeous series of stereoisomericbis-amides derived from racemic N-(3,5-dinitrobenzoyl)leuchine and various α,ω-diamines has been chromatographed on chiral stationary phases (CSP) derived from N-(2-naphthyl)alanine. Plots of α, the separation factor for enantiomers, versus N, the number of methylene groups in the α,ω-diamines, are convex in shape and show a maximum in α when N=B. This maximum is attributed to optimal “bridging” between adjacent binding sites on the CSP. “Bridging” is simultaneous interaction of the two ends of thebis-derivative with sites on the CSP. Separation factors for thebis-analytes are approximately the square of those of correspondingmono-amides. Presented at the 11^th International Symposium on Column Liquid Chromatography, Amsterdam, June 28–July 3, 1987.     

Nonequilibrium structure of primary particles in colloidal bidispersion

The nonequilibrium aggregation structure of primary particles in colloidal bidispersions is investigated at high volume fractions by Brownian dynamics simulations. It is found that introducing limited different sized particles in the monodispersion can obviously affect the short-range structures of primary particles. In a bidispersion, fractal dimension of aggregates, only consisting of primary particles, increases with increasing the size difference in the long-range scale. The structure factor S(q) of aggregates, obtained from the particle correlation function g(r), suggests that fractal structure disappears when the primary particles become not “primary” in volume fraction.     

Deposition of spherical particles onto cylindrical solid surfaces. I. Numerical simulations

The permeability of fractal porous aggregates with realistic three-dimensional structure is investigated theoretically using model aggregates composed of identical spherical primary particles. Synthetic aggregates are generated by several techniques, including a lattice-based method, simulation of aggregation by differential settling and turbulent shear, and the specification of simple cubic structures, resulting in aggregates characterized by the number of primary particles, solid fraction, characteristic radius, and fractal dimension. Stokesian dynamics is used to determine the total hydrodynamic force on and the distribution of velocity within an aggregate exposed to a uniform flow. The aggregate permeability is calculated by comparing these values with the total force and velocity distribution calculated from the Brinkman equation applied locally and to the entire aggregate using permeability expressions from the literature. The relationship between the aggregate permeability and solid fraction is found to be best predicted by permeability expressions based on cylindrical rather than spherical geometrical elements, the latter tending to underestimate the aggregate permeability significantly. The permeability expressions of Jackson and James or Davies provide good estimates of the force on and flow through porous aggregates of known structure. These relationships are used to identify a number of general characteristics of fractal aggregates.     

Evidence of Shear Rate Dependence on Restructuring and Breakup of Latex Aggregates

Small-angle static light scattering has been used to probe the evolution of aggregate size and structure in the shear-induced aggregation of latex particles. The size of aggregates obtained from the particle-sizing instrument (Coulter LS230) was compared with the size of those obtained with another approach utilizing the Guinier equation on the scattering data. Comparison of the two methods for studying the effects of mixing on the evolution of the aggregate size with time revealed similar trends. The aggregate structures were quantified in terms of their fractal dimensions on the grounds of the validity of Rayleigh-Gans-Debye scattering theory for the fractal aggregates. Analysis of the scattering patterns of aggregates verified that restructuring of the aggregates occurred as the aggregates were exposed to certain shear environments, resulting in a scale-dependent structure that could not be quantified by a fractal dimension. The effect of restructuring on aggregate size was particularly noticeable when the aggregates were exposed to average shear rates of 40 to 80 s(-1), whereas no significant restructuring occurred at lower shear rates. At 100 s(-1), the fragmentation of aggregates appeared to be more significant than aggregate compac-tion. Copyright 2001 Academic Press.     

Island formation in chemisorption 1. Chemisorption model

A model of dissociative chemisorption on a surface with a square lattice was studied using the Monte Carlo method. The model is based on two chemisorption pathways: “direct”—nucleation of adsorption islands, and “indirect”—their growth. The development of the surface distribution picture of chemisorbed particles was found to depend significantly on the contribution of these two pathways (S_indir/S_dir).     

Aggregation behavior of latex particles in shear flow confined between two parallel plates

In this study, the aggregation and breakup behaviors of latex particles in shear flow confined between two parallel plates were investigated using an in situ observation apparatus with a laser scanning confocal microscope. To investigate the effects of shear rate and the gap width between two parallel plates on the size and structure of the aggregates in the steady state, the distributions of the projected cross-sectional area and perimeter-based fractal dimension of the aggregates were measured. As a result, the average size of the aggregates decreases as shear rate increases and the gap width decreases due to the hydrodynamic effect acting on the aggregates. The size distributions of the aggregates become narrow as the gap width decreases. In addition, the fractal dimension, that is, the structure of the aggregates, was almost independent of shear rate and the gap width and approximately 1.2, which suggests that the aggregates are relatively compact.     

Effect of freezing on amyloid peptide aggregation and self-diffusion in an aqueous solution

Pulsed-field gradient ¹H NMR is employed to investigate the self-diffusion of amyloid Aβ-peptide in an aqueous buffer solution (pH 7.44) with a protein concentration of 50 μmol at 20°C. The self-diffusion coefficient of the peptide in a freshly prepared solution corresponds to its monomeric form. The storage of the solution at 24°C causes part of the peptide molecules to form amyloid aggregates as soon as over 48 h. However, the ¹H NMR echo signal typical of aggregated molecules is not observed because of their dense packing in the aggregates and a large mass of the latter. A freezing-fusion of the solution after the aggregation does not cause changes in the self-diffusion coefficients of the peptide. After a peptide solution free of amyloid aggregates is subjected to a freezing-fusion cycle, part of the peptide molecules also remains in the monomeric form in the solution, while another part forms amyloid aggregates, with a portion of the aggregated peptide molecules retaining a high rotational mobility with virtually absolute absence of a translational mobility. The results obtained are interpreted in terms of the formation of “porous aggregates” of amyloid fibrils, with “pores” having sizes comparable with those of peptide molecules, though, being larger than water molecules. Peptide molecules, which do not form fibrils, are captured in the pores. Temperature regime is shown to be of importance for the aggregation of amyloid peptides. In particular, freezing, which is traditionally considered to be a method for the prevention from or temporary interruption of aggregation, may itself lead to the formation of amorphous amyloid aggregates, which remain preserved in solutions after their unfreezing.     

Drying dissipative structures of the aqueous suspensions of palygorskite and tungstic acid particles

Macroscopic and microscopic dissipative structural patterns during dryness of the aqueous suspensions of palygorskite (PGK, needle-like shaped) and tungstic acid (TA, plate-like) have been studied on a cover glass. The coexistence of the broad ring of the hill accumulated with the particles and the round hills is observed around the outside edges of the dried film and in the center, respectively. These patterns differ from those of the suspensions of spherical particles. Furthermore, the spoke-like patterns, which have been observed for the suspensions of the spherical particles so often, are not observed at all for PGK and TA suspensions. These characteristic macroscopic patterns of PGK and TA are quite similar to those of the fractionated and monodispersed bentonites (plate-like) reported previously Yamaguchi et al. (Colloid Polymer Sci 283:1123, 2005). Wrinkled and/or branch-like fractal patterns are observed in the microscopic scale, which are quite similar to those of bentonites. “Shape information” of the colloidal particles is clarified to be “transferred” to the drying patterns via the convectional and sedimentary patterns during the course of dryness.