Diffusion-controlled Aggregation Research Articles

Prediction of the aggregation rate of nanoparticles in porous media in the diffusion-controlled regime.

The fate and aggregation of nanoparticles (NPs) in the subsurface are important due to potentially harmful impacts on the environment and human health. This study aims to investigate the effects of flow velocity, particle size, and particle concentration on the aggregation rate of NPs in a diffusion-limited regime and build an equation to predict the aggregation rate when NPs move in the pore space between randomly packed spheres (including mono-disperse, bi-disperse, and tri-disperse spheres). The flow of 0.2M potassium chloride (KCl) through the random sphere packings was simulated by the lattice Boltzmann method (LBM). The movement and aggregation of cerium oxide (CeO2) particles were then examined by using a Lagrangian particle tracking method based on a force balance approach. This method relied on Newton's second law of motion and took the interaction forces among particles into account. The aggregation rate of NPs was found to depend linearly on time, and the slope of the line was a power function of the particle concentration, the Reynolds (Re) and Schmidt (Sc) numbers. The exponent for the Sc number was triple that of the Re number, which was evidence that the random movement of NPs has a much stronger effect on the rate of diffusion-controlled aggregation than the convection.

Effects of Syndiotacticity on the Dynamic and Static Phase Separation Properties of Poly(N-isopropylacrylamide) in Aqueous Solution.

The dynamic and static phase separation behavior in aqueous poly(N-isopropylacrylamide) (PNIPAM) solutions is highly sensitive to the tacticity of PNIPAM. We investigated the phase separation dynamics of aqueous solutions of PNIPAM with different tacticities (atactic and syndiotactic-rich types) and found that the phase separation dynamics of syndiotactic-rich PNIPAM was much different from that of atactic-type PNIPAM. First, phase separation in syndiotactic-rich PNIPAM was faster. Second, there was a critical point (Ccp) in the concentration dependence of the phase separation rate: the phase separation accelerated dramatically when the solution concentration was higher than 2.0 wt % (= Ccp). Third, syndiotactic-rich PNIPAM required a higher thermal energy for phase separation compared to atactic PNIPAM. Such behavior can be explained on the basis of the high hydrophobicity of syndiotactic-rich PNIPAM in a dehydrated state and a diffusion-controlled aggregation model. The present study shows that precise control of the stereoregularity will open new channels toward the design and development of stimuli-responsive-polymer-based smart materials.

Generation modes of Eu2+ nonequilibrium dimers and influence of a magnetic field on their reconstruction in NaCl: Eu crystals

Three generation modes have been experimentally revealed for impurity-vacancy Eu2+ dimers with the atomic structure determined by the spin-selective transitions to equilibrium configurations in a constant magnetic field of 5–15 T in NaCl: Eu crystals. It has been shown that, under conditions of linearly increasing mechanical stresses, the plastic strain of the NaCl: Eu crystals accelerates the aggregation of impurities and generates magnetically sensitive dimers several tens of times more rapidly than in the case of diffusion-controlled aggregation. Under conditions of linearly increasing strains, magnetically sensitive dimers arise as a result of the destruction of impurity precipitates by moving dislocations. The identification of dimers and the determination of their average spin in the process of spin-dependent reorganization of the atomic structure of the dimers have been performed using optical spectroscopy and SQUID magnetometry.

Modeling the Crossover between Chemically and Diffusion-Controlled Irreversible Aggregation in a Small-Functionality Gel-Forming System

The analysis of realistic numerical simulations of a gel-forming irreversible aggregation process provides information on the role of cluster diffusion in controlling the late stages of the aggregation kinetics. Interestingly, the crossover from chemically controlled to diffusion-controlled aggregation takes place well beyond percolation, after most of the particles have aggregated in the spanning network and only small clusters remain in the sol. The simulation data are scrutinized to gain insight into the origin of this crossover. We show that a single additional time scale (related to the average diffusion time) is sufficient to provide an accurate description of the evolution of the extent of reaction at all times.

Effect of annealing on the microwave magnetoresistance of thin Ge0.96Mn0.04 films

It is established that annealing of ion-implanted thin Ge0.96Mn0.04 films with a thickness of 120 nm induces an increase in the microwave resistivity and a change in the mechanism of dephasing of charge carriers. The effect of annealing on the microwave transport properties of the thin films is due to the diffusion-controlled aggregation of dispersed Mn2+ impurity ions to form Ge3Mn5 clusters.

Influence of Salts and Natural Organic Matter on the Stability of Bacteriophage MS2

The stability of functionalized nanoparticles generally results from both steric and electrostatic interactions. Viruses like bacteriophage MS2 have adopted similar strategies for stability against aggregation, including a net negative charge under natural water conditions and using polypeptides that form loops extending from the surface of the protein capsid for stabilization. In natural systems, dissolved organic matter can adsorb to and effectively functionalize nanoparticle surfaces, affecting the fate and transport of these nanoparticles. We used time-resolved dynamic light scattering to measure the aggregation kinetics of a model virus, bacteriophage MS2, across a range of solution chemistries to determine what factors might destabilize viruses in aquatic systems. In monovalent electrolytes (LiCl, NaCl, and KCl), aggregation of MS2 could not be induced within a reasonable kinetic time frame, and MS2 was stable even at salt concentrations greater than 1.0 M. Aggregation of MS2 could be induced in divalent electrolytes when we employed Ca(2+). This trend was also observed in solutions containing 10 mg/L Suwannee River organic matter (SROM) reference material. Even at Ca(2+) concentrations as high 200 mM, diffusion-controlled aggregation was never achieved, demonstrating an additional barrier to aggregation. These results were confirmed by small-angle X-ray scattering experiments, which indicate a transition from repulsive to attractive interactions between MS2 virus particles as monovalent salts are replaced by divalent salts.

Particle development in apple juice determined by light scattering and electron microscopy.

Light scattering was used to detect the kinetic development of particles in apple juices produced with and without oxidation and in procyanidin extracts prepared from these two juices. Particle size developed exponentially in both oxidized and unoxidized juices, suggesting an enzymatic origin for the particle forming reactions. The procyanidin extract from oxidized juices produced particles which grew linearly, suggesting diffusion-controlled aggregation or coalescence of particles. Procyanidins from unoxidized juice showed no particle development over at least 60 days of storage. Electron microscopy showed particles similar to those seen previously and some newly described morphologies. The mechanism of haze particle development is discussed in the light of the light scattering and electron microscopic results.

Modeling of pattern development during fibronectin nanofibril formation

Formation of fibrillar fibronectin networks is a major process during embryogenesis and tissue formation, but the molecular details of fibril assembly remain poorly understood. Based on current ideas of fibronectin fibrillogenesis, a stochastic model was developed to enlighten the mechanism of the formation of paired fibronectin nanofibrils by adherent endothelial cells, which has been observed recently. The development of fibronectin clusters and fibrils was investigated by means of Monte Carlo simulations, including diffusion-controlled aggregation and myosin-driven transport of fibronectin-integrin complexes in the vicinity of a focal adhesion. Different evolving growth patterns were summarized in a morphological diagram as a function of the fibronectin substrate and fibronectin-fibronectin interaction energies. The formation of paired nanofibrils was found to occur in a certain region of interaction parameters. Beyond this region branched fibronectin clusters as well as tear-off of fibronectin fibrils were observed.

The magnetic properties of Eu nanoclusters formed in NaCl crystals during plastic deformation and aggregation

Plastic deformation of aged crystals and diffusion-controlled aggregation of Eu2+ ions in freshly quenched NaCl: Eu crystals causes the formation of complexes bound by exchange interaction. The solution of large-sized precipitates by quenching followed by impurity aggregation results in the nucleation of magnetically sensitive clusters comprising few atoms. A constant magnetic field with induction 5 T increases the probability of the transition of magnetically sensitive clusters from the high-to low-spin metastable state and induces changes in their atomic structure.

Diffusion-controlled annihilation and aggregation of F-centers in thermochemically reduced MgO crystals

The dynamics of F-center (an oxygen vacancy which has trapped two electrons) aggregation in thermochemically reduced MgO single crystals with an exceptionally high F-center concentration (6×10 18 cm −3) is discussed. A theory of the Mg nanocavity formation process is developed based on diffusion-controlled aggregation of elastically interacting F centers and their annihilation at traps. We show that in contrast to the generally accepted viewpoint, the F centers in the bulk are not annealed out at the external sample surface but at internal defects, such as dislocations, subgrain boundaries and impurities. The mutual attraction of the F centers is a key factor controlling the aggregation process.

The kinetics of defect aggregation and metal colloid formation in ionic solids under irradiation

Results of a microscopic theory describing diffusion-controlled aggregation of radiation Frenkel defects — F and H centers — are discussed. We suggest interpretation of experimental data on metal colloid formation in the two ionic solids with different crystalline structures — LiF and CaF2 — observed under electron irradiation with subsequent heating. Theory successfully reproduces the main experimental observations including Ostwald ripening of small colloids into large colloids in the narrow temperature interval and suggests that radiation-enhanced F center diffusion occurs in CaF2 with as low activation energy as 0.4 eV. In contrast, the activation energy for a single F center diffusion in LiF is found to be as high as 1.5 eV. The key role of mutual defect elastic attraction in their aggregation is demonstrated.

Kinetics of nanocavity formation based onF-center aggregation in thermochemically reduced MgO single crystals

The dynamics of interacting F centers resulting in F aggregates and nanocavities is modeled in thermochemically reduced MgO single crystals. We have recently shown that thermal annealing of thermochemically reduced MgO with an exceptionally high F-center concentration $(6\ifmmode\times\else\texttimes\fi{}{10}^{18}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3})$ induces a brown coloration in the crystals, which was attributed to scattering from nanosize cavities with their walls plated with magnesium metal [Phys. Rev. B 62, 9299 (2000)]. In the present paper, a theory of the nanocavity formation process is developed based on diffusion-controlled aggregation of elastically interacting F centers and their annihilation at traps. We show that in contrast to the generally accepted viewpoint, the F centers in the bulk are not annealed out at the external sample surface but at internal defects, such as dislocations, subgrain boundaries, and impurities. The mutual attraction of the F centers is a key factor controlling the aggregation process.

Dynamics of spheroid self‐assembly in liquid‐overlay culture of DU 145 human prostate cancer cells

The in vitro self-assembly of multicellular spheroids generates highly organized structures in which the three-dimensional structure and differentiated function frequently mimic that of in vivo tissues. This has led to their use in such diverse applications as tissue regeneration and drug therapy. Using Smoluchowski-like rate equations, herein we present a model of the self-aggregation of DU 145 human prostate carcinoma cells in liquid-overlay culture to elucidate some of the physical parameters affecting homotypic aggregation in attachment-dependent cells. Experimental results indicate that self-aggregation in our system is divided into three distinct phases: a transient reorganization of initial cell clusters, an active aggregation characterized by constant rate coefficients, and a ripening phase of established spheroid growth. In contrast to the diffusion-controlled aggregation previously observed for attachment-independent cells, the model suggests that active aggregation in our system is reaction-controlled. The rate equations accurately predict the aggregation kinetics of spheroids containing up to 30 cells and are dominated by spheroid adhesive potential with lesser con- tributions from the radius of influence. The adhesion probability increases with spheroid size so that spheroid–spheroid adhesions are a minimum of 2.5 times more likely than those of cell–cell, possibly due to the upregulation of extracellular matrix proteins and cell-adhesion molecules. The radius of influence is at least 1.5 to 3 times greater than expected for spherical geometry as a result of ellipsoidal shape and possible chemotactic or Fröhlich interactions. Brownian-type behavior was noted for spheroids larger than 30 μm in diameter, but smaller aggregates were more motile by as much as a factor of 10 for single cells. The model may improve spheroid fidelity for existing applications of spheroids and form the basis of a simple assay for quantitatively evaluating cellular metastatic potential as well as therapies that seek to alter this potential. © 2001 John Wiley & Sons, Inc. Biotechnol Bioeng 72: 579–591, 2001.

Dynamics of spheroid self-assembly in liquid-overlay culture of DU 145 human prostate cancer cells

The in vitro self-assembly of multicellular spheroids generates highly organized structures in which the three-dimensional structure and differentiated function frequently mimic that of in vivo tissues. This has led to their use in such diverse applications as tissue regeneration and drug therapy. Using Smoluchowski-like rate equations, herein we present a model of the self-aggregation of DU 145 human prostate carcinoma cells in liquid-overlay culture to elucidate some of the physical parameters affecting homotypic aggregation in attachment-dependent cells. Experimental results indicate that self-aggregation in our system is divided into three distinct phases: a transient reorganization of initial cell clusters, an active aggregation characterized by constant rate coefficients, and a ripening phase of established spheroid growth. In contrast to the diffusion-controlled aggregation previously observed for attachment-independent cells, the model suggests that active aggregation in our system is reaction-controlled. The rate equations accurately predict the aggregation kinetics of spheroids containing up to 30 cells and are dominated by spheroid adhesive potential with lesser contributions from the radius of influence. The adhesion probability increases with spheroid size so that spheroid-spheroid adhesions are a minimum of 2.5 times more likely than those of cell-cell, possibly due to the upregulation of extracellular matrix proteins and cell-adhesion molecules. The radius of influence is at least 1.5 to 3 times greater than expected for spherical geometry as a result of ellipsoidal shape and possible chemotactic or Fröhlich interactions. Brownian-type behavior was noted for spheroids larger than 30 microm in diameter, but smaller aggregates were more motile by as much as a factor of 10 for single cells. The model may improve spheroid fidelity for existing applications of spheroids and form the basis of a simple assay for quantitatively evaluating cellular metastatic potential as well as therapies that seek to alter this potential.

Characterization of a Polydisperse Depletion-Flocculated Emulsion: III. Oscillatory Rheological Measurements

The addition of nonadsorbing polymer to an alkane-in-water emulsion causes the droplets to flocculate into a space-spanning, stress-bearing network. We report rheological measurements of an emulsion of 1-bromohexadecane-in-water flocculated by hydroxy-ethylcellulose. Small-deformation oscillatory measurements allowed characterization of the structure during formation and an indication of the strength of the resulting network. Emulsions without polymer, and polymer solutions alone, showed essentially viscous behavior, with dominant viscous modulus over the whole frequency range (0.01–10 Hz). However, the emulsion containing polymer demonstrated a significant elastic modulus, dependent on the oil and polymer concentrations, attributable to interdroplet depletion interactions. Power-law relationships were observed between the elastic modulus, elastic strain limit, and oil volume fraction, but the indices were lower than those predicted by fractal models, giving unrealistic fractal dimensionalities. The modulus increased exponentially with polymer concentration, but the elastic strain limit was independent of added polymer. The rate of formation of the network was not consistent with diffusion-controlled aggregation.

Luminescence studies of CdS spherical particles via hydrothermal synthesis

The spherical particles of CdS consisting of nanoparticles (∼100nm) were synthesized by a hydrothermal process. The particle formation and growth depend on the rate of sulfide-ion generation and diffusion-controlled aggregation of nanoparticles. As demonstrated in the profiles of powder X-ray diffraction, the crystalline phases are governed by the reaction temperature. Photoluminescence studies on CdS particles show two emission bands at the room temperature. The red emission at 680nm is due to sulfur vacancies, and a new infrared red (IR) emission at 760nm is attributed to self-activated centers. A red shift of IR band with the decrease of temperature was explained with a configurational coordinate model. The different saturation limits for the red and IR bands are discussed in terms of the formation of donor–acceptor pairs and exciton in CdS particles.

Discrete-lattice theory for Frenkel-defect aggregation in irradiated ionic solids

Institut fu ¨r Physikalische und Theoretische Chemie, Technische Universitat Braunschweig, D-38106 Braunschweig, Germany~Received 11 September 1997; revised manuscript received 6 April 1998!A microscopic theory of diffusion-controlled aggregation of radiation Frenkel defects—called in ionic solidsH and F centers—is presented. This is based on a discrete-lattice formalism for the single defect densities~concentrations! and the coupled joint densities of similar and dissimilar defects treated in terms of a modifiedKirkwood superposition approximation. The kinetics of defect aggregation is studied in detail; the cooperativecharacter of this process for both types of complementary defects is shown. The theory is applied to thedescription of the kinetics of metal colloid formation during heating of electron-irradiated CaF

The microscopic theory of diffusion-controlled defect aggregation

The kinetics of diffusion-controlled aggregation of primary Frenkel defects (F and H centers) in irradiated CaF2 crystals is theoretically studied. Microscopic theory is based on the discrete-lattice formalism for the single defect densities (concentrations) and the coupled joint densities of similar and dissimilar defects treated in terms of the Kirkwood superposition approximation. Conditions and dynamics of the efficient F center aggregation during crystal heating after irradiation are analyzed.

Theory of diffusion-controlled colloid formation in irradiated solids

The kinetics of diffusion-controlled aggregation of Frenkel defects (interstitial atoms and vacancies) under irradiation of solids is studied on a microscopic level. The theory is based on the discrete-lattice formalism for the single defect densities (concentrations) and coupled joint densities of similar and dissimilar defects treated in terms of the Kirkwood superposition approximation. The physical model takes into account random defect creation, diffusion, attraction and bimolecular, A + B → 0 recombination. Conditions of the efficient aggregation of vacancies and interstitials are studied. The cooperative character of the aggregation process is shown.

Kraft Lignin−Poly(DADMAC) Precipitate Formation

The precipitation of kraft lignin with poly(diallyldimethylammonium chloride), poly(DADMAC), was characterized as a function of pH. At a mass mixing ratio of poly(DADMAC) to lignin of 0.53 at pH 12.6, approximately 80% of the added lignin was removed, whereas the precipitate contained less than 35% of the added poly(DADMAC). Lignin precipitated with as much as 75% of the charges not associated with poly(DADMAC). Lower pH solutions required less poly(DADMAC) for lignin precipitation. Colloidal complex formation was measured as a function of time by dynamic light scattering, and the results could be fitted by a diffusion-controlled aggregation model.