A simple model for the structure of fractal aggregates

Structural properties of small aggregates containing up to 100 particles have been studied through detailed Monte Carlo cluster-cluster aggregation simulations in both diffusion-limited and reaction-limited conditions. First, the radius of gyration, the radius of the smallest sphere encompassing the cluster, and the particle-particle correlation function, g(r), have been computed based on the positions of all the particles in the cluster, and their fractal scaling has been analyzed. Then, an empirical model has been developed to simulate the g(r) function for aggregates of any size and used to determine the corresponding structural properties and scattering structure factors. Finally, in order to illustrate the application of the structural properties thus computed, two experiments on diffusion-limited aggregation have been performed, and the average scattering structure factors have been measured as a function of time using a small-angle light-scattering device. The obtained average scattering structure factors have been simulated using the Smoluchowski population balance equations, using the single aggregate structural properties and scattering structure factor predicted by the developed empirical g(r) model.     

A model to describe the settling behavior of fractal aggregates

A model to predict fractal dimension from sedimentating fractal aggregates has been successfully developed. This model was developed using the settling rate and size data of fractal aggregates. In order to test the validity of the model, a purpose-built settling rig, equipped with lens with magnification of 1200x, which can capture images of particles/flocs down to 2 microm in diameter was used. The performance and technique of the settling rig were validated by comparing the measured settling rates of 30- and 50.7-microm standard particles with their theoretical settling rates calculated using Stokes' law. The measured settling rates were within 10% agreement with the calculated Stokes' velocities. The settling rates and sizes of the particles/flocs were analyzed using image analysis software called WiT 5.3. The maximum temperature gradient across the settling column was 0.1 degrees C, which effectively eliminated convective currents due to temperature differences in the settling column. A total of 1000 calcium phosphate flocs were analyzed. Calcium phosphate flocs with fractal dimensions varying from 2.3 to 2.8 were generated via orthokinetic aggregation. Measurements of fractal dimensions, using light scattering, were done simultaneously with the settling experiments and they were found to be constant. The fractal dimensions calculated using the model agreed with those obtained by light scattering to within 12%.     

Viscosity of liquid suspensions with fractal aggregates: Magnetic nanoparticles in petroleum colloidal structures

New physical model is presented resulting in a simple formula for the dependence of viscosity η of colloidal liquid solution on the shear rate G applicable to a wide variety of systems including complex natural liquids like petroleum. The principal point of the model is the fractal nature of colloid particle aggregates present in the liquid. Such aggregates are experimentally detected now in non-Newtonian liquids. The model is based on calculation of energy loss on colloidal particle aggregate of fractal structure localized in the flow of liquid with shear rate. We have performed the viscosity measurement experiments which confirmed successfully the developed physical model. Also, we demonstrate experimentally that petroleum colloidal particles and magnetic iron oxide nanoparticles can form composite fractal-like aggregates in natural petroleum materials. Our model can explain both the non-Newtonian properties of petroleum and sensitivity of petroleum viscosity to external magnetic fields.     

Reverse Monte Carlo modeling of the structure of colloidal aggregates

In this work we present results for the structure of aerogels coming from the diffusion-limited cluster aggregation simulation method. Pair distribution functions and structure factors, resulting from simulation, were considered as experimental input for reverse Monte Carlo modeling. The modeling yielded structural models with pair distribution functions and structure factors nearly identical to the results of the simulations. Particle configurations from both the simulations and reverse Monte Carlo modeling have been analyzed in terms of the distribution of the number of neighbors. It is suggested that the reverse Monte Carlo method, when applied to the structure factor, may be a suitable technique for the interpretation of experimental scattering data on colloidal aerogels.     

Conversion of colloidal aggregates into polymer networks on aging

After long-term aging, surfactant-mediated colloidal aggregates of sulfonated polyaniline (S-PANI) and poly(vinylidene fluoride) (PVF₂) converted into three-dimensional polymer networks, whereas colloidal crystals prepared from pure PVF₂ remained unaltered. A model, where the surfactant tails anchored from the colloidal particles interdigitate with time resulting in coalescence of the particles to form the network morphology, has been proposed. X-ray photoelectron spectroscopy (XPS) revealed higher relative abundances of carbon atoms on the surface of the polymer networks than those of the colloidal aggregates, which adequately supports the proposed model.     

Growth of colloidal aggregates through polymer bridging

The stability of colloidal dispersions can be altered through the addition of adsorbing macromolecules. Adsorption of macromolecules on the particle surfaces results in a stepwise aggregation process. We consider the early destabilization steps for nanometric ceria particles dispersed in water. These steps have been characterized through light scattering; they are: i) finite multiplets involving one macromolecule and a small number of particles; ii) bridging between mul tiplets; iii) formation of three-dimensional network of bridges. Each stage can be obtained as an equilibrium state, provided there is an adequate balance of electrostatic repulsions and polymer-induced attractions. Altering this balance may push the system from one state into another, or it may change the structure within one state. For instance, multiplets may be pushed to bind more particles or spill them out, depending on the equilibrium length of bridge; gels may reject solvent and turn into flocs if the equilibrium length of bridges becomes shorter than the average distance between particles.     

Prediction of three-dimensional fractal dimensions using the two-dimensional properties of fractal aggregates

Fractal dimension analysis using an optical imaging analysis technique is a powerful tool in obtaining morphological information of particulate aggregates formed in coagulation processes. However, as image analysis uses two-dimensional projected images of the aggregates, it is only applicable to one and two-dimensional fractal analyses. In this study, three-dimensional fractal dimensions are estimated from image analysis by characterizing relationships between three-dimensional fractal dimensions (D(3)) and one (D(1)) and two-dimensional fractal dimensions (D(2) and D(pf)). The characterization of these fractal dimensions were achieved by creating populations of aggregates based on the pre-defined radius of gyration while varying the number of primary particles in an aggregate and three-dimensional fractal dimensions. Approximately 2000 simulated aggregates were grouped into 33 populations based on the radius of gyration of each aggregate class. Each population included from 15 to 115 aggregates and the number of primary particles in an aggregate varied from 10 to 1000. Characterization of the fractal dimensions demonstrated that the one-dimensional fractal dimensions could not be used to estimate two- and three-dimensional fractal dimensions. However, two-dimensional fractal dimensions obtained statistically, well-characterized relationships with aggregates of a three-dimensional fractal characterization. Three-dimensional fractal dimensions obtained in this study were compared with previously published experimental values where both two-dimensional fractal and three-dimensional fractal data were given. In the case of inorganic aggregates, when experimentally obtained three-dimensional fractal dimensions were 1.75, 1.86, 1.83+/-0.07, 2.24+/-0.22, and 1.72+/-0.13, computed three-dimensional fractal dimensions using two-dimensional fractal dimensions were 1.75, 1.76, 1.77+/-0.04, 2.11+/-0.09, and 1.76+/-0.03, respectively. However, when primary particles were biological colloids, experimentally obtained three-dimensional fractal dimensions were 1.99+/-0.08 and 2.14+/-0.04, and computed values were both 1.79+/-0.08. Analysis of the three-dimensional fractal dimensions with the imaging analysis technique was comparable to the conventional methods of both light scattering and electrical sensing when primary particles are inorganic colloids.     

Preparation of composite films with silver nanoparticles and their fractal aggregates in a polymeric matrix

Conditions were examined for preparation of film materials with polyacrylamide matrix, promising for optical applications and containing both single silver particles and their fractal aggregates.     

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.     

Role of anisotropy in electrodynamically induced colloidal aggregates

We investigate the assembly of spherical and anisotropic colloidal particles with the shape of peanuts when subjected to an external alternating electric field. By varying the strength and frequency of the applied field, we observe that both types of particles form clusters at low frequencies due to attractive electrohydrodynamic interactions or disperse into a liquidlike phase at high frequencies due to repulsive dipolar interactions. We characterize the observed structures via pair correlation functions and radius of gyration, and observe a clear difference in the ordering process between the isotropic and anisotropic colloids. Further on, we interpret the cluster formation kinetics in terms of dynamic scaling theory, and observe a faster aggregation of the anisotropic colloids with respect to the isotropic ones.     

Structure and dynamic properties of colloidal asphaltene aggregates

The abundant literature involving asphaltene often contrasts dynamic measurements of asphaltene solutions, highlighting the presence of small particle sizes between 1 and 3 nm, with static scattering measurements, revealing larger aggregates with a radius of gyration around 7 nm. This work demonstrates the complementary use of the two techniques: a homemade dynamic light scattering setup adapted to dark and fluorescent solutions, and small-angle X-ray and neutron scattering. Asphaltene solutions in toluene are prepared by a centrifugation separation to investigate asphaltene polydispersity. These experiments demonstrate that asphaltene solutions are made of Brownian colloidal aggregates. The hydrodynamic radii of asphaltene aggregates are between 5 and 10 nm, while their radii of gyration are roughly comparable, between 3.7 and 7.7 nm. A small fraction of asphaltenes with hydrodynamic and gyration radii around 40 nm is found in the pellet of the centrifugation tube. The fractal character of the largest clusters is observed from small angle scattering nearly on a decade length scale. Previous results on aggregation mechanisms are confirmed ( Eyssautier, J., et al. J. Phys. Chem. B 2011 , 115 , 6827 ): nanoaggregates of 3 nm radius, and with hydrodynamic properties also frequently illustrated in the literature, aggregate to form fractal clusters with a dispersity of aggregation number.     

Directed assembly and rupture mechanics of colloidal aggregates

The macroscopic rheological behavior of colloidal gels arises from the micromechanical properties of the gel backbone, which are governed by nanoscale particle interactions. These colloidal interactions have been commonly understood in terms of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Recent work has shown, however, that nonidealities, such as surface roughness and charge nonuniformity, may cause the particle interactions to significantly deviate from DLVO predictions at near-contact separations. Here we present novel techniques for directing the assembly of colloidal aggregates that mimic the gel backbone, based on optical micromanipulation of multiple particles using laser tweezers. This also provides an in situ method for measuring near-contact interactions via single-bond rupture forces. We find that PMMA particles aggregated in the presence of nonorganic salts exhibit interparticle bond strengths more than 10 times greater than those predicted by DLVO theory. However, good agreement is found with DLVO predictions when the anionic surfactant sodium dodecyl sulfate (SDS) is used as the flocculant.     

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.     

Viscosity of nanofluids: particle shape and fractal aggregates

Colloidal dispersions of nanoparticles in thermal base fluids are known to alter their spherical shapes thereby affecting their surface properties. This aspect has been investigated with respect to the effective viscosity of nanofluids presuming the particles to acquire the shape of prolate spheroid. Also, the contributions of the interfacial layer formed around these particles and their possible agglomeration has been taken in to account. The analysis has been carried out by modifying the Krieger and Dougherty model. The relative viscosity of these nanofluids has been computed as a function of volume fraction, particle size and the eccentricity of the particle. The model also incorporates the concept of fractal dimensions. The results thus obtained compare significantly well with the available experimental data and reaffirms an improvement over earlier models.     

Modified fractal model and rheological properties of colloidal networks

The scaling relationship between the storage modulus (G(')) and the volume fraction of solids (Phi) in fat crystal networks has been explained by the fractal model developed by our group. However, many experimental results and simulation studies suggest that the stress distribution within a colloidal network is dramatically heterogeneous, which means that a small part of the network carries most of the stress, while the other part of the network does not contribute much to the elastic properties of the system. This concept was introduced into a modified fractal model. The volume fraction of solids term (Phi) in the original fractal model was replaced by Phi(e), the effective volume fraction of solids, in the modified fractal model, which represents the volume fraction of stress-carrying solids. A proposed expression for Phi(e) is given and a modified expression for the scaling relationship between G(') and Phi is obtained. The modified fractal model fits the experiment data well and successfully explains the sometimes observed nonlinear log-log behavior between the storage modulus of colloidal networks and their volume fraction of solids.     

Effects of the structure of anionic polyelectrolytes on surface potentials of their aggregates in water

The surface potential, ψ in mV, was determined for the following polyelectrolytes and co-polyelectrolytes in aqueous solution: sodium poly(styrene sulfonate); sodium poly(vinyl sulfonate); poly(vinyl alcohol-co-55% sodium vinyl sulfate); poly(methylmethacrylate-co-40% sodium styrene sulfonate); poly (methylmethacrylate-co-60% sodium styrene sulfonate); poly(styrene-co-56% styrene sulfonate); and poly(styrene-co-80% styrene sulfonate). For comparison, the surface potentials of aqueous sodium dodecyl sulfate and sodium dodecylbenzene sulfonate micelles were also determined. The dyes neutral red and safranine-T were used as indicators. ThepKa of the former was calculated from the Henderson-Hasselbach equation, using UV-VIS spectroscopy to determine the concentration of protonated ground state as a function of pH. The surface potential of the aggregates was culculated from the equation: $$pKa_{\text{i}} = pKa_0 - {{F\Psi } \mathord{\left/ {\vphantom {{F\Psi } {2.3RT}}} \right. \kern-\nulldelimiterspace} {2.3RT}}$$ wherepKa _i andpKa _o refer to the indicatorpKa in the presence of charged and nonionic interfaces, respectively, and the other terms have their usual meaning. The protonation kinetics of the triplet state of safranine-T (measured from the decay of its transient absorption at 830 nm) was used to determine hydronium ion concentrations at aggregate interfaces, and the corresponding surface potentials were calculated from: $$a_{{\text{Hi}}} = a_{{\text{Haq}}} \times \exp \left( {{{ - F\Psi } \mathord{\left/ {\vphantom {{ - F\Psi } {RT}}} \right. \kern-\nulldelimiterspace} {RT}}} \right)$$ wherea _Hi anda _Haq refer to the hydronium ion activity at the aggregate interface, and in bulk water, respectively. Surface potentials determined by both techniques were in excellent agreement. Values of ψ were found to depend on the structure of the polyelectrolyte, sodium poly(styrene sulfonate) versus sodium poly(vinyl sulfonate) and, for the same type of co-polyelectrolyte, on the percentage of charged monomer.     

Dependence of the composition of the products of thermal fragmentation of thiacyanine dyes on the length of their polymethine chain

The pathways of thermal fragmentation of thiacyanine dyes with different lengths of the external polymethine chain were investigated. The results of thermolysis of the thiacyanines are compared with the results of quantum-chemical calculations of their molecules.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 188–192, February, 1982.     

Diastereoselective fragmentation of chiral alpha-aminophosphonic acids/metal ion aggregates

Diastereomeric clusters of general formula [MAB(2)](+) and [MA(2)B](+) (M = Li(I), Na(I), Ag(I), Ni(II)-H, or Cu(II)-H; A = (R)-(-)- and (S)-(+)-(1-aminopropyl)phosphonic acid; B = (1R)-(-)- and (1S)-(+)-(1-aminohexyl)phosphonic acid) have been readily generated in the electrospray ionization (ESI) source of a triple-quadrupole mass spectrometer and their collision-induced dissociation (CID) investigated. CID of diastereomeric complexes, e.g. [MA(S)(B(S))(2)](+) and [MA(R)(B(S))(2)](+), leads to fragmentation patterns characterized by R(homo) = [MA(S)B(S)](+)/[M(B(S))(2)](+) and R(hetero) = [MA(R)B(S)](+)/[M(B(S))(2)](+) abundance ratios, which depend upon the relative stability of the diastereomeric [MA(S)B(S)](+) and [MA(R)B(S)](+) complexes in the gas phase. The chiral resolution factor R(chiral) = R(homo)/R(hetero) is found to depend not only on the nature of the M ion but also on that of the fragmenting species, whether [MAB(2)](+) or [MA(2)B](+). The origin of this behavior is discussed.