Characterization of Enzymatically Induced Aggregation of Casein Micelles in Natural Concentration by in Situ Static Light Scattering and Ultra Low Shear Viscosimetry

The aggregation of casein micelles in undiluted skim milk after the addition of chymosin was studied by static light scattering and ultra low shear viscometry. The static light scattering measurements were made with two different sample thicknesses, 72 and 16 μm. The scattering data were analyzed by indirect Fourier transformation and by the polydispersity inversion technique which led to pair distance distribution functions and size distribution function, respectively. The minimum scattering angle was 1 degrees, which allows for the determination of particle sizes up to a maximum diameter of 12 μm. The fractal dimension determined from double logarithmic plots of intensity versus scattering vector resulted in values between 1.9 and 2.0. The influence of multiple scattering was determined by comparison of the measurements with the different sample thicknesses. The measurements show no significant influence of multiple scattering when the transmission is above 0.85. Due to the very complex and porous structure of the casein aggregates the Rayleigh-Debye-Gans scattering theory has been used in the data analysis. Measurements with a new instrument using ultra low shear showed good agreement with theory. Copyright 1999 Academic Press.     

Measurement of Fractal Aggregates of Polydisperse Particles Using Small-Angle Light Scattering

The effect of primary particle polydispersity on the structure of fractal aggregates has been investigated through the salt-induced, diffusion-limited aggregation of mixtures of hematite. The fractal dimension was determined experimentally using three independent methods: q dependence of static light scattering, kinetic scaling, and correlation of aggregate mass and linear size both determined from Guinier scattering. The fractal dimensions D(f) obtained were 1.75+/-0.03, 1.76+/-0.03, and 1.70+/-0.05, respectively. The use of a previously derived fractal mean particle size was validated in allowing data collapse to master curves for the aggregation kinetics data. The fractal mean particle size is shown to have general utility by taking a number weighting to describe polydisperse aggregation kinetics and a mass weighting to describe small q scattering behavior. Copyright 2000 Academic Press.     

Micro- to nanoscale structure of biocompatible PLA-PEO-PLA hydrogels

We observe large-scale structures in hydrogels of poly(l-lactide)-poly(ethylene oxide)-poly(l-lactide) (PLLA-PEO-PLLA) ranging in size from a few hundred nanometers to several micrometers. These structures are apparent through both ultra-small angle scattering (USAS) techniques and confocal microscopy. The hydrogels showed power law scattering in the USAS regime, which is indicative of scattering from fractal structures. The fractal dimension of the scattering from hydrogels revealed that the gels have large size aggregates with a mass fractal structure over the nanometer-to-micrometer length scales. The aggregates also seem to become more "dense" with an increase in the molecular weight of crystalline PLLA domains. Visualization through confocal microscopy confirms that the gels have a microstructure of interspersed micrometer-sized polymer inhomogeneities with water channels running between them. The presence of micrometer-sized water channels in the hydrogels has very important implications for biomedical applications.     

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.     

Structural Interpretations of Static Light Scattering Patterns of Fractal Aggregates

A method based on static light scattering by fractal aggregates is introduced to extract structural information. In this study, we determine the scattered intensity by a fractal aggregate calculating the Structure and the Form factors noted, respectively, S(q) and F(q). We use the approximation of the mean field Mie scattering by fractal aggregates (R. Botet, P. Rannou, and M. Cabane, appl. opt. 36, 8791, 1997). This approximation is validated by a comparison of the scattering and extinction cross sections values calculated using, on the one hand, Mie theory with a mean optical index n) and, on the other hand, the mean field approximation. Scattering and extinction cross sections values differ by about 5%. We show that the mean environment of primary scatterers characterized by the optical index n(s) must be taken into account to interpret accurately the scattering pattern from fractal aggregates. Numerical simulations were done to evaluate the influence of the fractal dimension values (D(f)>2) and of the radius of gyration or the number of primary particles within the aggregates (N=50 to 250) on the scatterers' mean optical contrast (n(s)/n). This last parameter plays a major role in determining the Form factor F(q) which corresponds to the primary particles' scattering. In associating the mean optical index (n) to structural characteristics, this work provides a theoretical framework to be used to provide additional structural information from the scattering pattern of a fractal aggregate (cf. Part II). Copyright 2000 Academic Press.     

On techniques for the measurement of the mass fractal dimension of aggregates

A review is presented of a number of techniques available for the characterisation of the structure of aggregates formed from suspensions of sub-micron particles. Amongst the experimental techniques that have been commonly used are scattering (light, X-ray or neutron), settling and imaging and these are the focus of this work. The theoretical basis for the application of fractal geometry to characterisation of flocs and aggregates is followed by a discussion of the strengths and limitations of the above techniques. Of the scattering techniques available, light scattering provides the greatest potential for use as a tool for structure characterisation even though interpretation of the scattered intensity pattern is complicated by the strong interaction of light and matter. Restructuring further complicates the analysis. Although settling has long been used to characterise particle behaviour, the absence of an accurate permeability model limits the technique as a means of determining the porosity of fractal aggregates. However, it can be argued that the determination of fractal dimension is relatively unaffected. The strength of image analysis lies in its ability to provide a great deal of information about particle morphology and the weaknesses lie in the difficulties with image processing and sample size as this is a particle counting technique. There are very few papers which compare the fractal dimension measured by more than one technique. Light scattering potentially provides a useful tool for checking settling results. However, further work is required to develop proper models for aggregate permeability and flow-through effects.     

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%.     

Critical behavior of trifunctional randomly branched polycyanurates

The behavior near the gelation threshold of trifunctional randomly branched polycyanurates is studied by static and dynamic light scattering. By static measurements the critical exponents γ, σ and η were obtained, which describe the divergence of the weight average (M_w) and the cutoff (M*) molecular weights and the radius of gyration (R_g) respectively. All these independently measured exponents together with τ, characterizing the power law behavior of the molecular weight distribution and measured by size exclusion chromatography coupled with light scattering, confirm the predictions of the three-dimensional percolation theory. With the help of size exclusion chromatography coupled with a light scattering and a viscosity detector, a fractal dimension D = 2.24 is obtained. On the other side, from the corresponding exponent for the whole unfractionated samples a fractal dimension D = 2.21 results, using a theory of Daoud. This suggests that the fractal dimension of the polycyanurates in dilute solution lies between the theoretical predictions D = 2.5 for the unswollen and D = 2.0 for the completely swollen state. Furthermore, it is shown by dynamic light scattering that the power law behavior over some decades in time of the time autocorrelation function and the divergence of the mean relaxation time are characteristics of the gelpoint. The development with increasing reaction time of the time correlation function of the gelling system from the pregel through the gelpoint into the gel state is analyzed quantitatively by a hybrid of a stretched exponential and a power law function.     

Structure of Hydrous Ferric Oxide Aggregates

The small angle light scattering behavior of hydrous ferric oxide flocs is examined here and found to provide useful insights into the nature of the aggregates formed despite the large size of these aggregates at later times. The flocs appear to exhibit fractal properties over a significant size range though the aggregates appear to be easily disrupted through mixing effects resulting in breakup and/or restructuring to denser assemblages. Background electrolyte concentrations also have some impact on floc structure but mixing effects and apparent destabilization by ferric ions limit the effect of added electrolytes on the stability and structure of ferric oxyhydroxides. Similar estimates of fractal dimensions of these hydrous ferric oxide flocs are obtained both by static light scattering analysis and by a cluster mass scaling approach. The choice of density distribution cutoff function has some impact on derived size and structure parameters and further refinement in this area is needed. Copyright 2000 Academic Press.     

Salt-induced fast aggregation of nano-emulsions: structural and kinetic scaling

Salt-induced fast aggregation of oil-in-water nano-emulsions stabilized by the anionic surfactant sodium dodecyl sulfate was analyzed by employing dynamic and static light scattering techniques. Nano-emulsions with different ratios of dodecane/hexadecane were studied. The time evolution of the average size of all nano-emulsions collapsed in the same curve despite differences in the composition of the oil phase. A power law growing and a value of the homogeneity parameter similar to that typically found in model solid particle systems in diffusive aggregation regime were found. A value of 2.4 was estimated for the effective fractal dimension both from the scaling of scattered intensity with scattering wave vector modulus and from the kinetic scaling. This result indicates that the aggregates are more compact structures compared with model solid systems. It can be explained as a result of the effect of polydispersity in the primary droplet size and the coalescence events that occur inside the aggregates.     

Formation of Small Silica Aggregates by Turbulent Aggregation

Aggregation of silica powder in water has been experimentally studied by turbidimetry. Aggregation was carried out in a stirred tank under physicochemical conditions corresponding to attractive interparticle forces. The effects of different primary particle sizes and stirring rates on aggregation dynamics have been studied. The scattering cross sections of silica aggregates were calculated in the framework of the anomalous diffraction approximation of light scattering theory. Aggregation has been studied by using Kusters's and Brakalov's approaches. By comparison between experimental and theoretical turbidity changes with time it has been shown that aggregates are small and slightly porous. The aggregation process is characterized by a weak fractal dimension D(wf) and an aggregate limit size L.D(wf) is found in the range 2.4-2.5. D(wf) (respectively L) is a weakly increasing (respectively decreasing) function of the stirring rate or of the shear rate. Copyright 2001 Academic Press.     

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     

Scattering Behavior of Restructured Aggregates: A Simulation Study

Simulations of diffusion-limited cluster-cluster aggregation (DLCA) with no restructuring, full restructuring, and partial restructuring have been performed. The scattering patterns produced from these aggregates have been simulated using the Rayleigh-Gans-Debye approximation. Pure DLCA aggregates produced a scattering pattern with the slope of the fractal region being about -1.8. In contrast, the slope of the fractal region of the scattering pattern for fully restructured aggregates was about -2.1, indicating an increase in fractal dimension. Partial restructuring at large length scales produced an upward turn in the scattering pattern at low qr(o), while at high qr(o) the fractal section of the pure DLCA aggregate was retained. This last result was expected and is consistent with the results and postulations of several other workers. This simulation shows that the type of scattering pattern often obtained from orthokinetic or sheared aggregation can be produced by restructuring of aggregates at large length scales. Copyright 2001 Academic Press.     

Fractal Morphology and Breakage of DLCA and RLCA Aggregates

Latex aggregates, formed in 1 M McIlvaine buffer solution and 0.2 M NaCl solution, have been characterized in terms of aggregate size distribution and fractal morphology. This was achieved using three sizing techniques (image analysis, laser scattering, and electrical sensing) in which size distributions and fractal properties of the aggregates were measured. Estimates of fractal dimensions were made using the two-slope method based on dimensional analysis and the small-angle light scattering method. Aggregate suspensions were prepared using both water and a mixture of heavy water/ water as the solvent. The latter essentially eliminated sedimentation, which was observed after one day of aggregation when water alone was used as a solvent. Latex aggregates formed by diffusion-limited colloid aggregation (DLCA) and reaction-limited colloid aggregation (RLCA) had fractal dimensions close to 1.8 and 2.1, respectively. As observed through image analysis, DLCA aggregates possessed a loose tenuous structure, whereas RLCA aggregates were more compact. Disruption of both DLCA and RLCA aggregates has been investigated in laminar flow and turbulent capillary flow. The shear forces introduced by a laminar shear device with a shear rate up to 1711 s(-1) were unable to bring about aggregate breakup; shearing facilitates aggregate growth in the case of DLCA. However, latex aggregates were significantly disrupted after passage through a turbulent capillary tube at 95209 s(-1). Copyright 2000 Academic Press.     

Dependence of aggregate strength, structure, and light scattering properties on primary particle size under turbulent conditions in stirred tank

The steady-state size and structure of aggregates produced under turbulent conditions in stirred tank, for primary particle diameter, d(p), equal to 420 nm and 120 nm, were studied experimentally for various values of the volume average shear rate, G, and solid volume fraction, phi, and compared with data for d(p) = 810 nm. To exclusively investigate the effect of dp, polystyrene latexes with same type and similar density of surface charge groups (sulfate) were used. The mass fractal dimension, d(f), obtained by image analysis, was found to be invariant of d(p) and G, with a value equal to 2.64 +/- 0.18. Small-angle static light scattering was used to characterize the cluster mass distributions by means of the root-mean-square radius of gyration, R(g), and the zero-angle intensity of scattered light, I(0), whose steady-state values proved to be fully reversible with respect to G. The absolute values of R(g) obtained for similar phi and G proved to be independent of d(p), and for all studied conditions, R(g) was proportional to G-1/2. At very low phi, a critical aggregate size for breakage was obtained and used to evaluate the aggregate cohesive force, as a characteristic for the aggregate strength. The aggregate cohesive force was found to be independent of aggregate size, with similar values for the investigated dp. Due to large d(p) and high d(f), the effect of multiple light scattering within the aggregates was found to be present, and by relating the scaling of R(g) with I(0) to d(f), the corresponding correction factors were evaluated. By combination of the independently measured aggregate size and structure, it is possible to experimentally determine the relation between the maximum stable aggregate mass and the hydrodynamic stresses independent of the multiple light scattering present for large d(p) and compact aggregates.     

Experimental and modeling study of breakage and restructuring of open and dense colloidal aggregates

In this work we present experimental and simulation analysis of the breakage and restructuring of colloidal aggregates in dilute conditions under shear. In order to cover a broad range of hydrodynamic and interparticle forces, aggregates composed of primary particles with two sizes, d(p) = 90 and 810 nm, were generated. Moreover, to understand the dependence of breakage and restructuring on the cluster structure, aggregates grown under stagnant and turbulent conditions, having substantially different initial internal structures with fractal dimension d(f) equal to 1.7 and 2.7, respectively, were used. The aggregates were broken by exposing them to a well-defined elongational flow produced in a nozzle positioned between two syringes. To investigate the evolution of aggregate size and morphology, respectively, the mean radius of gyration, , and d(f) were monitored during the breakup process using light scattering and confocal laser scanning microscopy. It was found that the evolution of aggregates' fractal dimension during breakage is solely controlled by their initial structure and is independent of the primary particles size. Similarly, the scaling of the steady-state vs the applied hydrodynamic stress is independent of primary particle size, however, depends on the history of aggregate structure. To quantitatively explain these observations, the breakage process was modeled using stokesian dynamics simulations incorporating DLVO and contact interactions among particles. The required flow-field for these simulations was obtained from computational fluid dynamics. The complex flow pattern was simplified by considering a characteristic stream line passing through the zone with the highest hydrodynamic stress inside the nozzle, this being the most critical flow condition experienced by the clusters. As the flow-field along this streamline was found to be neither pure simple shear nor pure extensional flow, the real flow was approximated as an elongational flow followed by a simple shear flow, with a stepwise transition between them. Using this approach, very good agreement between the measured and simulated aggregate size values and structure evolution was obtained. The results of this study show that the process of cluster breakup is very complex and strongly depends on the initial aggregate structure and flow-field conditions.     

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.     

Scattering structure factor of colloidal gels characterized by static light scattering, small-angle light scattering, and small-angle neutron scattering measurements

The scattering structure factor of a colloidal gel in a q range of 5 orders of magnitude has been determined by combining static light scattering, small-angle light scattering, and neutron scattering measurements. It exhibits simultaneously two types of structure information: a mass fractal scaling within the clusters that constitute the gel and a surface fractal scaling for length scales larger than that of the clusters. Such scattering behavior can be well interpreted by the pair-correlation function proposed in the literature to model an ideal structure constituted of mass fractal objects inside surface fractal objects.     

Fractal structure of asphaltene aggregates

A photographic technique coupled with image analysis was used to measure the size and fractal dimension of asphaltene aggregates formed in toluene-heptane solvent mixtures. First, asphaltene aggregates were examined in a Couette device and the fractal-like aggregate structures were quantified using boundary fractal dimension. The evolution of the floc structure with time was monitored. The relative rates of shear-induced aggregation and fragmentation/restructuring determine the steady-state floc structure. The average floc structure became more compact or more organized as the floc size distribution attained steady state. Moreover, the higher the shear rate is, the more compact the floc structure is at steady state. Second, the fractal dimensions of asphaltene aggregates were also determined in a free-settling test. The experimentally determined terminal settling velocities and characteristic lengths of the aggregates were utilized to estimate the 2D and 3D fractal dimensions. The size-density fractal dimension (D(3)) of the asphaltene aggregates was estimated to be in the range from 1.06 to 1.41. This relatively low fractal dimension suggests that the asphaltene aggregates are highly porous and very tenuous. The aggregates have a structure with extremely low space-filling capacity.