Scaling of the kinetics of slow aggregation and gel formation for a fluorinated polymer colloid

The aggregation and gelation kinetics in moderately concentrated (0.004 相似文献   

Orthokinetic Aggregation in Two Dimensions of Monodisperse and Bidisperse Colloidal Systems

Orthokinetic aggregation of colloids trapped at the air–liquid interface was studied by direct imaging in a couette cell. This method allowed us to follow the temporal evolution of both the cluster-mass distribution and the cluster structure at a shear rate where Brownian aggregation is suppressed. The interactions between the monodisperse latex particles floating at the air–liquid interface were controlled either by varying the electrolyte concentration or by creating a bidisperse system through the addition of small particles. The results show that the clusters in all of the systems are characterized by a high fractal dimension, indicating that the clusters are rearranged and densified by the shear. Kinetic analysis suggests that aggregation of monodisperse systems mainly proceeds through homogeneous aggregation, i.e., large clusters sticking to other large clusters. The bidisperse system, finally, with a size ratio around 10, favored a more heterogeneous aggregation among small and large clusters throughout the aggregation process; a slightly lower fractal dimension was observed compared to the strongly aggregated monodisperse system.     

Formation and structure of pachyman aggregates in dimethyl sulfoxide containing water

The aggregation of pachyman, β-(1 → 3)-D -glucan (M_w = 1.68 × 10⁵) from the Poria cocos mycelia, was investigated using static and dynamic laser light scattering (LLS) in dimethyl sulfoxide (DMSO) containing about 15% water, which leads to large aggregates. Both the time dependence of hydrodynamic radius and the angle dependence of the scattering intensity were used to calculate the fractal dimension (d_f) of the aggregates. The aggregation rate and average size of aggregates increase dramatically with increasing the polymer concentration from 1.7 × 10⁻⁴ g/mL to 8.6 × 10⁻⁴ g/mL, and with the decrease of the solvent quality, that is, water content from 13 to 15%. In the cases, the fractal dimensions change from 1.94 to 2.43 and from 1.92 to 2.54, respectively, suggesting that transforms of aggregation processes: a slow process called reaction-limited cluster aggregation (RLCA) to a fast process called diffusion-limited cluster aggregation (DLCA) in different polymer concentrations and water content. The fractal dimensions above 2 of the fast aggregation is larger than the 1.75 predicted for the ideal DLCA model, suggesting that the aggregation involves a restructuring process through the interchain hydrogen bonding interaction. There are no aggregates of pachyman in DMSO without water, but aggregates formed in the DMSO containing 15% water at 25°C as a compact structure. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3201–3207, 1999     

Self‐assembled supramolecular microgels: Fractal structure and aggregation mechanism

Multifunctional molecules were designed to produce microgels with specific structures. Both static light scattering and dynamic light scattering were employed to determine the fractal dimension of the microgels. The protein, avidin, was strongly bound to four biotin moieties. Biotin was attached covalently to specifically engineered peptide nucleic acid (PNA) oligomers. Three designed DNA oligomers self‐assembled to produce a trifunctional three‐way junction (TWJ) with single‐stranded ends that were complementary to the PNA sequence. The sizes of the supramolecular aggregates were characterized by dynamic light scattering. The fractal dimension was obtained from the angular dependence of the scattered intensity when the microgels were large enough. When the microgels were formed via cooling from a temperature above the melting point of the PNA–DNA helices, reversible structures with a fractal dimension of approximately 1.86 were formed, which is consistent with a cluster–cluster aggregation mechanism. When the microgels were formed by the slow addition of biotinylated PNA bound to the TWJ to a solution of avidin at room temperature, the observed fractal dimension approached 2.6, which is consistent with a point–cluster aggregation mechanism. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3037–3046, 2003     

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.     

Fractality and activity of acid catalysts in the liquid-phase synthesis of ethyl <Emphasis Type="Italic">tert-</Emphasis>butyl ether

A study was carried out on the synthesis of ethyl tert-butyl ether from ethanol and 2-methylpropene on silica gel samples modified by the addition of ZrO₂ and Al₂O₃. A decrease in the turnover frequency (TOF) of the reaction is observed with increasing acidity of surface of the modified silica gels. A relationship was found between the TOF of the reaction and the fractal dimension of the catalyst. The TOF of the reaction decreases with increasing fractal dimension of the catalyst.     

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.     

Aggregation Behavior of Alkoxide-Derived Silica in Sol-Gel Process in Presence of Poly(ethylene oxide)

Growth behavior of silica in an acid catalyzed sol-gel process from silicon alkoxide in the presence of poly(ethylene oxide), PEO, was investigated by in situ small angle X-ray scattering, SAXS, and ²⁹Si NMR measurements. The results of SAXS, that aggregation and gel formation behaviors of silica were affected by the presence of PEO, suggested a strong attractive interaction between silica oligomers and PEO. A possible reaction scheme of silica in the presence of PEO is as follows; (1) PEO and small silica oligomers coexist in the solution without specific interaction just after hydrolysis of the silicon alkoxide. (2) With the progress of condensation, a ramified aggregated complex between PEO and silica oligomers is formed, which is characterized by larger apparent value of radius of gyration and smaller fractal dimension than in the PEO-free system. (3) After gelation, the fractal dimension of scatterers remains to be smaller than that in the PEO-free system, because PEO associated with the silica network inhibits aggregation within the gel networks. Furthermore, PEO inhibits the condensation in the aging and in the drying process, leading to less strongly crosslinked dry gel. A temporal maximum in the time evolution of R_g was observed for the samples separated into two phases with their characteristic domain size being larger than several micrometers. This is considered to be a phenomenon related to increase and divergence of correlation length near and at the critical point.     

A fractal model for the molecular organization in the alkylbenzenesulphonate/electrolyte/water system

Under conditions where individual molecules are no longer soluble, the association of amphiphiles occurs as a sequence of growth and aggregation processes: the formation of dimers, bilayers and multilayer assemblies culminates with the production of myelin cylinders and chains or spherulitic arrays of focal-conic units. We have examined this process using the alkylbenzenesulphonate/electrolyte/water system as a model. The phase diagram was obtained using optical microscopy. The kinetics of the aggregation process were followed by lightscattering measurements and the structures of the one- and two-phase regions were examined by optical microscopy and freeze-fracture electron microscopy. The fractal nature of the aggregation process was investigated using an indirect Fourier transform study of the lightscattering data. The fractal character of the whole self-assembly process was confirmed and an experimental value of 2.17 was determined for the fractal dimension (in close agreement with the expected theoretical value of 2.16).     

A bidimensional simulation of particle-cluster aggregation with variable active sites particles

 In this work a simple program has been developed which simulates the process of particle– cluster aggregation limited by diffusion. All the simulation have been carried out using 2d square lattices with square “particles” having a variable number of active inter-action sites (from 3 to 8) for each particle in order to analyze the effect of such limitation on the fractal dimension of the aggregates. The fractal dimension of such aggregates was calculated by the so-called “box counting” method. It has been shown that there is no change in the value of the fractal dimension (1.70) as the active site number is increased. Instead it appears that there is an average number of active sites of about 2.3 for all the structures no matter how many active interaction sites the particles have. This appears as an interesting result in connection with the aggregation of particles such as renneted casein micelles, which could present differences in the surface density of active sites. Received: 11 February 1997 Accepted: 8 January 1998     

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.     

Control over colloidal aggregation in monolayers of latex particles at the oil-water interface

The controlled generation of 2D aggregate networks is studied experimentally using micrometer-sized polystyrene latex particles attached to the oil-water interface. Starting from an initially crystalline monolayer, appropriate combinations of carefully added electrolyte and surfactant enable control over both the fractal dimension and the kinetics of aggregation. Remarkably, the colloidal crystals formed upon first spreading remain stable, even for days, when substantial amounts of electrolyte are added to the aqueous phase. Pressure-area isotherms reveal a slow time evolution of the electrostatic dipole-dipole interaction. When the electrostatic interaction has been sufficiently weakened, aggregation proceeds in well-defined, reproducible manner. The aggregation process is analyzed using quantitative video microscopy. The evolution of the cluster size distribution and its moments is characterized, and static and dynamic scaling exponents are derived to identify the nature of the aggregation process. In the range of concentrations studied here, the kinetics all agree with a "fast", diffusion-limited cluster type of aggregation. However, the fractal dimension strongly depends on the composition of the aqueous subphase. Rather dense structures are found when only electrolyte is used, whereas more open structures are obtained when even small amounts of surfactant are added. It is suggested that this structural dependency is related to the effect of surfactant on the contact angle and its consequences for the anisotropic nature of the capillary interactions.     

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.     

Fractal analysis of a discotic texture

The dendritic-type texture displayed by low molar mass discotic charge transfer systems possessing a columnar hexagonal ordered phase has been subjected to a fractal analysis. The diffusion limited aggregation approach was used to simulate the growth of the texture. The results are that the texture displays a fractal geometry and that the prominent features of the discotic texture are correctly reflected by the simulated clusters, including the fractal dimension. The conclusion is that the texture is conditioned by the lattice structure of the discotic phase and the kinetic processes, the sticking rules in the terms of diffusion limited aggregation model, responsible for the growth of the texture.     

Thermoreversible gels of polymers in recycled motor oil

A study of the dynamic viscoelastic properties of gels of Ethylene Vinyl Acetate (EVA) and Styrene‐Butadiene‐Styrene (SBS) copolymers in recycled motor oil is presented. Both systems form gels with enhanced elastic moduli, with respect to SBS/aromatic oil gels which have been used to develop synthetic binders. Although the procedure described by Winter is conveniently applied to obtain gel‐sol transition of EVA/oil gels, it is not suitable for SBS/oil gels which do not give rise to a homogeneous liquid when they melt. For EVA/oil gels the relaxation exponent at the gel point is Δ=0.5, which according to Muthukumar's model corresponds to a fractal dimension d_f=2. The variation of the elastic modulus with polymer concentration follows the scaling law G_e‐cⁿ, with n=2.8 for EVA/oil and n=1.3 for SBS/oil. In the case of EVA/oil gels the validity of theoretical models relating fractal dimension to n exponent is discussed.     

Investigations on the semi-batch precipitation of silica

The semi-batch precipitation process of silica from sodium silicate and sulphuric acid has been structured into a primary particle production stage, an aggregation process until the gel point is reached and finally a gel fragmentation and compaction process. The progress of aggregation was analyzed by photon correlation spectroscopy. The reaction limited aggregation kernel was found to be proportional to B'(t)(q(p - q))A/2, where A assumes the value of one. The quantity B'(t) varies between 3.4 x 10(-20) and 2.6 x 10(-20) 1/min and is only a weak function of time. The stability ratio W for the aggregation process decreases with increasing aggregate size. During the period after the gel point the gel fragmentates. The gel clusters have an initial fractal dimension of approximately 1.8 which rapidly increases to 2.4 and stays roughly constant until the end of the process. The specific surface area decreases from 480 to 300 m2/g. The primary particles have a uniform size of 22.7 nm.     

Fractal Characterization of Silica Sol Prepared by the Sol-Gel Method: From the Sol Formation to the Flocculation Process

The fractal characterization of silica particles prepared by the sol-gel method was obtained; from the beginning of the sol-gel synthesis to the aggregation process of these particles by adding metal ions in solution, the fractal dimension was determined. At the beginning of the sol-gel process, unstable structures were formed due, essentially, to the auto-catalytic nature of the sol-gel condensation reactions; these particles are fractal structures with a fractal exponent corresponding to a reaction limited aggregation regime. As the time proceeds, the reactants are consumed approaching the system to equilibrium, stabilizing the size of the silica particles. The silica sol can be flocculated by adding metal ions in solution. The fractal exponent for the aggregation process was determined, obtaining a value corresponding to a diffusion limited aggregation regime.     

扩散模型和凝聚模型耦合作用下胶体凝聚动力学的Monte Carlo模拟研究

以扩散模型(Ds(γ)=D0×sγ)和凝聚模型(Pij(σ)=P0×(i×j)σ)为基础,对胶体体系随时间的演变、团簇大小分布及其标度关系、团簇的重均大小S(t)的变化规律以及模型对最终分形维数的影响四个角度进行了比较研究,发现扩散指数γ0和凝聚概率指数σ0对胶体的凝聚动力学过程有相似的影响.本文在较宽的γ和σ取值范围内,对胶体的凝聚动力学进行了模拟研究,对慢速凝聚向快速凝聚的转化机理作了定量分析,并进一步分析了在团簇-团簇凝聚(CCA)模型下,得到类似扩散置限凝聚(DLA)模型的凝聚体的物理意义,结果表明:(1)γ0代表了体系中团簇或单粒做"定向运动"而非无规则的布朗运动的情况.这种"定向运动"的推动力可能来自于大团簇产生的强"长程范德华力"、"电场力"等,或来自于体系边界处的外力场的作用.(2)当σ0时,体系成为先快后慢的慢速凝聚,这可能对应大团簇为一排斥中心,即胶体颗粒存在"排斥力场"的现象.(3)证实了团簇的重均大小在凝聚过程的早期按指数规律增长,而后期按幂函数规律增长的实验现象.模拟研究还表明,胶体体系的凝聚动力学过程,在σ0时是一个存在正反馈机制的非线性动力学过程,而在σ0时则体现出负反馈的特征.