Relation between aggregation kinetics and the structure of kaolinite aggregates

Dynamic and static light scattering were applied to the determination of the stability ratio and fractal dimension of kaolinite (KGa-2) at different kaolinite or/and electrolyte concentrations at pH 9.5. Dynamic light scattering was used to measure the kinetics of early stage aggregation to determine the stability ratio, W, as well as the cluster sizes which determine the fractal regime. Static light scattering was used to measure the fractal dimension, D(f). Results show that the two classes of "universality" (Lin et al. Nature 1989, 339, 360) characterizing the diffusion- and reaction-limited regimes of cluster-cluster aggregation do apply to colloidal kaolinite as limit cases when W approximately 1 or W > 100, respectively. In the intermediate regime where 5 < W < 100, the growth of the aggregate radius showed a power-law behavior similar to diffusion-limited cluster aggregation. For the intermediate aggregation regime, a scaling relation between fractal dimension and stability ratio, reflecting a continuous increase in particle packing density in the aggregate as the sticking probability of particles was reduced, was demonstrated.     

Experimental investigation of colloidal gel structures

We investigate experimentally the structural properties of colloidal gels, formed under both diffusion-limited and reaction-limited aggregation conditions, using light scattering measurements and compare the results with the literature Monte Carlo (MC) simulations. The scattering structure factors have been measured for the two classes of gels in the range of the particle volume fractions between 0.02 and 0.07. From these, the corresponding fractal dimension values have been estimated. These have been found to be in good agreement with those estimated from the structure factors computed from MC simulated gels. On the basis of our previous research (Lattuada et al. Langmuir 2003, 19, 6312), this confirms that the scattering structure factor of a gel provides erroneously a small fractal dimension value, which decreases as the particle volume fraction increases. Furthermore, it is observed that the average size of the fractal clusters is larger in real gels than in simulated gels.     

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.     

Solvent-induced lysozyme gels: rheology, fractal analysis, and sol-gel kinetics

In this work, the gelation kinetics and fractal character of lysozyme gel matrices developed in tetramethylurea (TMU)-water media were investigated. Gelation times were determined from the temporal crossover point between the storage, G', and loss, G', moduli, as a function of the binary solvent composition and of protein concentration. The inverse dependence of the upper limit of the linear viscoelastic region (gamma0) on protein concentration indicate that the lysozyme gels belong to the "strong link" kind, a gel category where interparticle links are stronger than intraparticle ones. Lysozyme gel fractal dimensions (Df) were determined from the analysis of rheological data according to a scaling theory by Shih et al. [Phys. Rev. A 42 (1990) 4772-4779] and were found to be compatible with a diffusion-limited cluster-aggregation kinetics (DLCA) for lysozyme gels formed at the TMU mass fraction in the binary organic-aqueous solvent, wTMU=0.9, and with a reaction-limited cluster aggregation kinetics (RLCA) for wTMU in the 0.6< or =wTMU< or =0.8 range.     

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.     

Facile Assembly of 3D Binary Colloidal Crystals from Soft Microgel Spheres

It still remains a big challenge to fabricate binary colloidal crystals (binary CCs) from hard colloidal spheres, although a lot of efforts have been made. Here, for the first time, binary CCs are assembled from soft hydrogel spheres, PNIPAM microgels, instead of hard spheres. Different from hard spheres, microgel binary CCs can be facilely fabricated by simply heating binary microgel dispersions to 37 °C and then allowing them to cool back to room temperature. The formation of highly ordered structure is indicated by the appearance of an iridescent color and a sharp Bragg diffraction peak. Compared with hard sphere binary CCs, the assembly of PNIPAM microgel binary CCs is much simpler, faster and with a higher “atom” economy. The easy formation of PNIPAM microgel binary CC is attributed to the thermosensitivity and soft nature of the PNIPAM microgel spheres. In addition, PNIPAM microgel binary CCs can respond to temperature change, and their stop band can be tuned by changing the concentration of the dispersion.

     

Detailed model of the aggregation event between two fractal clusters

A model has been developed for describing the aggregation process of two fractal clusters under quiescent conditions. The model uses the approach originally proposed by Smoluchowski for the diffusion-limited aggregation of two spherical particles but accounts for the possibility of interpenetration between the fractal clusters. It is assumed that when a cluster diffuses toward a reference cluster their center-to-center distance can be smaller than the sum of their radii, and their aggregation process is modeled using a diffusion-reaction equation. The reactivity of the clusters is assumed to depend on the reactivity and number of their particles involved in the aggregation event. The model can be applied to evaluate the aggregation rate constant as a function of the prevailing operating conditions by simply changing the value of the particle stability ratio, without any a priori specification of a diffusion-limited cluster aggregation, reaction-limited cluster aggregation, or transition regime. Furthermore, the model allows one to estimate the structure properties of the formed cluster after the aggregation, based on the computed distance between the aggregating clusters in the final cluster.     

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.     

聚(N-异丙基丙烯酰胺)水凝胶微球体积相变的研究

窄分散的聚（Ｎ 异丙基丙烯酰胺）水凝胶微球用乳液聚合方法制备，并用动态和静态光散射对其体积相变进行了研究．与水中聚（Ｎ 异丙基丙烯酰胺）线性单链比较，水中凝胶微球的体积相变温度较高，对温度的响应比较平缓．相变是连续的，有别于大块凝胶非连续的体积变化．在体积相变过程中，凝胶微球始终是密度均一的热力学稳定球体．从相变过程网络密度的变化可以确定，绝大部分的水在收缩过程被排了出来，但在紧缩的凝胶微球中仍含有约７０％的水．     

Fractal-type particle gel formed from gelatin + starch solution

Using confocal microscopy and small-deformation rheology, we demonstrate the formation of stable thermoreversible gelatin-based gels with colloidal fractal-type microstructure. The opaque particle gels were made by cooling of transparent mixed aqueous solutions of gelatin (1-3 wt %) and starch (7 wt %) from 40 to 24 degrees C. The mechanism involves starch-induced gelatin self-association into phase-separated gelatin-rich microgel particles, followed by diffusion-limited cluster aggregation into a particle gel network.     

Colloidal Fouling of Ultrafiltration Membranes: Impact of Aggregate Structure and Size

A close coupling between the structure and size of hematite flocs formed in suspension and the permeability of the cake that accumulates on ultrafiltration membranes is observed. Specific resistances of cakes formed from flocs generated under diffusion-limited aggregation conditions are at least an order of magnitude lower than those of cakes formed from flocs generated under reaction-limited aggregation conditions. Similar effects are observed whether the aggregation regime is controlled by salt concentration, pH, or added organic anions. This dramatic difference in cake resistance is considered to arise from the size and fractal properties of the hematite assemblages. The ease of fluid flow through these assemblages will be influenced both by the fractal dimension of the aggregates and by their size relative to primary particle size (since, for fractal aggregates, porosity increases as the size of the aggregate increases). The size and strength of aggregates are also important determinants of the relative effects of permeation drag, shear-induced diffusion, and inertial lift and result, in the studies reported here, in relatively similar rates of particle deposition for both rapidly and slowly formed aggregates. The results presented here suggest that control of cake permeability (and mass) via control of aggregate size and structure is an area with scope for further development though the nature and extent of compaction effects in modifying the fractal properties of aggregates generated in suspension requires attention. Copyright 1999 Academic Press.     

Self-assembly of Hollow PNIPAM Microgels to Form Discontinuously Hollow Fibers

A new kind of hollow hydrogel microfiber with discontinuous hollow structure was prepared by an ice-segregation-induced self-assembly process. Monodisperse thermo-responsive hollow poly（N-isopropylacrylamide）（PNIPAM） microgels were first synthesized by seed precipitation polymerization using colloidal Si O2 nanoparticles as seeds, followed by removing the silica cores of the formed Si O2/PNIPAM core/shell composite microgels with hydrofluoric acid. Then, the discontinuously hollow hydrogel microfibers were produced by unidirectional freezing of 1 wt% hollow PNIPAM microgel aqueous dispersion in liquid nitrogen bath, followed by freeze-drying to remove the formed ice crystals. Many orderly arrayed dents were observed on the surfaces of the hydrogel microfibers by field-emission scanning electron microscopy, indicating that they are constructed by closely packed monodisperse hollow PNIPAM microgels. The effect of freezing method and the hollow microgel concentration in the aqueous dispersion on the morphological structure of the hollow hydrogel microfibers was investigated.     

Computer simulation of selective aggregation in binary colloids

The morphology of clusters formed by selective aggregation of binary colloids is studied in a two-dimensional Monte Carlo simulation for a large range of number fractions (200:1, 100:1, 10:1, 2:1). We find remarkable similarity in morphology to those observed in experiments, from the formation of closed "micelles" to large branched clusters. Quantitative studies of the fractal dimension, kinetics, and cluster size distribution are also carried out and compared with diffusion-limited cluster aggregation and reaction-limited cluster aggregation models.     

Phase-field modeling of two-dimensional solute precipitation∕dissolution: solid fingers and diffusion-limited precipitation

Two-dimensional dendritic growth due to solute precipitation was simulated using a phase-field model reported earlier [Z. Xu and P. Meakin, J. Chem. Phys. 129, 014705 (2008)]. It was shown that diffusion-limited precipitation due to the chemical reaction at the solid-liquid interface has similarities with diffusion-limited aggregation (DLA). The diffusion-limited precipitation is attained by setting the chemical reaction rate much larger compared to the solute diffusion to eliminate the effect of the interface growth kinetics. The phase-field simulation results were in reasonable agreement with the analytical solutions. The fractal solid fingers can be formed in the diffusion-limited precipitation and have a fractal dimension measured d(f)=1.68, close to 1.64, the fractal dimensionality of large square lattice DLA clusters.     

Influence of natural organic matter and ionic composition on the kinetics and structure of hematite colloid aggregation: implications to iron depletion in estuaries

The stability and aggregation behavior of iron oxide colloids in natural waters play an important role in controlling the fate, transport, and bioavailability of trace metals. Time-resolved dynamic light scattering experiments were carried out in a study of the aggregation kinetics and aggregate structure of natural organic matter (NOM) coated hematite colloids and bare hematite colloids. The aggregation behavior was examined over a range of solution chemistries, by adjusting the concentration of the supporting electrolyte-NaCl, CaCl2, or simulated seawater. With the solution pH adjusted so that NOM-coated and bare hematite colloids were at the same zeta potential, we observed a significant difference in colloid stability which results from the stability imparted to the colloids by the adsorbed NOM macromolecules. This enhanced stability of NOM-coated hematite colloids was not observed with CaCl2. Aggregate form expressed as fractal dimension was determined for both NOM-coated and bare hematite aggregates in both NaCl and CaCl2. The fractal dimensions of aggregates formed in the diffusion-limited regime indicate slightly more loosely packed aggregates for bare hematite than theory predicts. For NOM-coated hematite, a small decrease in fractal dimension was observed when the solution composition changed from NaCl to CaCl2. For systems in the reaction-limited regime, the measured fractal dimensions agreed with those in the literature. Colloid aggregation was also studied in synthetic seawater, a mixed cation system to simulate estuarine mixing. Those results describe the important phenomena of iron oxide aggregation and sedimentation in estuaries. When compared to field data from the Mullica Estuary, U.S.A., it is shown that collision efficiency is a good predictor of the iron removal in this natural system.     

Monitoring coalescence behavior of soft colloidal particles in water by small-angle light scattering

The fractal dimension (D _f) of the clusters formed during the aggregation of colloidal systems reflects correctly the coalescence extent among the particles (Gauer et al., Macromolecules 42:9103, 2009). In this work, we propose to use the fast small-angle light scattering (SALS) technique to determine the D _f value during the aggregation. It is found that in the diffusion-limited aggregation regime, the D _f value can be correctly determined from both the power law regime of the average structure factor of the clusters and the scaling of the zero angle intensity versus the average radius of gyration. The obtained D _f value is equal to that estimated from the technique proposed in the above work, based on dynamic light scattering (DLS). In the reaction-limited aggregation (RLCA) regime, due to contamination of small clusters and primary particles, the power law regime of the average structure factor cannot be properly defined for the D _f estimation. However, the scaling of the zero angle intensity versus the average radius of gyration is still well defined, thus allowing one to estimate the D _f value, i.e., the coalescence extent. Therefore, when the DLS-based technique cannot be applied in the RLCA regime, one can apply the SALS technique to monitor the coalescence extent. Applicability and reliability of the technique have been assessed by applying it to an acrylate copolymer colloid.     

Light-scattering study of the aggregation of syndiotactic poly(methyl methacrylate) in solution.

Syndiotactic poly(methyl methacrylate (s-PMMA) may undergo aggregation in n-butyl chloride (n-BuCl) at temperatures below the theta temperature. The aggregation behavior of the s-PMMA with weight-average molecular weight M(w) =6.06 x 10(5) g mol(-1) was studied by a combination of static and dynamic laser-light-scattering experiments. A solution of concentration 1.12 x 10(-4) g mL(-1) was quenched from 50 degrees C (above the theta temperature in n-BuCl, 35 degrees C to 12 degrees C, and the aggregation process was measured over 60 h. The time dependence of M(w) the root-mean-square z-average radius of gyration < R(g) >, and the average hydrodynamic radius were used to monitor the growth of the aggregates, with the result M(w) approximately < R(g) > d(f) (where d(f) = 1.98 +/- 0.02), which implies the formation of a fractal aggregate. The observed fractal dimension, d(f), is close to that expected for a reaction-limited cluster aggregation for which d(f) = 2.1. In addition, atomic force microscopy was used to image the aggregates.     

Aggregate restructuring by polymer solvency effects

This study investigates the aggregation in cyclohexane of silica particles initially stabilized by grafted polystyrene and destabilized by temperature reduction. It complements an earlier study by Zhu and Napper (P.W. Zhu, D.H. Napper, Phys. Rev. E 50 (1994) 1360) in which the aggregation of polystyrene latex particles with tethered poly(N-isopropyl acrylamide) (PNIPAM) in water was investigated. Their dynamic light scattering results showed that both the rate of aggregation and the aggregate fractal dimension increased with a sufficient decrease in the PNIPAM adlayer solvency, achieved by means of either salt (NaNO3) addition or temperature rise. This result stands in contrast to those obtained when an electrostatically stabilized colloid is destabilized, i.e., that the more rapidly aggregates are formed, the lower the resulting fractal dimension. The authors explained their results in terms of the effects of both salt effects and increased temperature on the extent of the hydrophobic interactions between the adlayer-covered surfaces in the water. The present study examines a sterically-stabilized colloid in a nonaqueous solvent, where neither salt effects nor hydrophobic effects play a role. Temperature is decreased to bring the system from better-than-theta-conditions to worse-than-theta-conditions. Power-law aggregation kinetics are observed at 15.7 degrees C by dynamic light scattering. The particles first undergo reduced rate aggregation, producing low-fractal-dimension aggregates, which after some time, restructure into more compact aged clusters. The fractal dimension of these aged clusters increases with increasing initial aggregation rate, consistent with results seen by Zhu and Napper, but without the presence of hydrophobic effects. The ability of the polymer-grafted particles to rearrange suggests aggregation into a secondary minimum, with the ability to slide over one another to achieve a more energetically favorable, denser configuration. The reversible nature of the aggregation is verified by additional experiments gradually bringing the system from worse-than-theta-conditions back to better-than-theta-conditions, with an attendant decrease in aggregate fractal dimension, and ultimately full redispersion.     

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.