Modelling of polymer aggregates in solution

The self-consistent mean field model of Scheutjens and Fleer is used to model spherical aggregates of homopolymers and monomer—polymer particles in solution. For homopolymer aggregates we found that the chain ends are preferentially located at the exterior side of the polymer/solvent interface. The distribution of the end segments may be an important parameter in latex film formation. For monomer—polymer particles a “core-shell” structure is found with an extended core containing a monomer—polymer mixture and a thin shell a few nanometres thick strongly enriched with monomer. The monomer-enriched shell seems to function as a solvating envelope for the dangling chain ends. These results are compared with other simulations based on a single chain in a spherical-cavity model.     

Asphaltenic aggregates are polydisperse oblate cylinders

Small-angle neutron scattering (SANS) has proven to be very useful for deducing the sizes and morphologies of asphaltenic aggregates in solution. A wide variety of intra-particle structure factors have previously been applied to SANS scattering spectra, but the studies often provided limited information concerning the quality of the fits and the Q range over which the models were applied. Selection of an appropriate form factor that closely approximates the structure of asphaltenic aggregates is important for determining the properties of asphaltenic aggregates, such as the radius of gyration (R(G)), molar mass, and apparent fractal dimension. This study evaluates various mono- and polydisperse intra-particle structure factor models as applied to four asphaltene scattering spectra. Agreement of the model fit parameters (I(0) and R(G)) with those obtained from Guinier analyses suggests that such a form factor model is physically reasonable. Reduced chi2 values for each non-linear least squares fit indicates how well a given model fits to the entire Q range studied for the scattering intensity distribution. In the polydispersity analyses, an analytical function is introduced to model the scattering behavior of oblate cylinders with a Schultz distribution of radii. Results indicate that the polydisperse radius oblate cylinder model best approximates the shape of asphaltenic aggregates.     

Statistics of aggregates

Aggregation phenomena of elementary particles into clusters has received considerable attention during the past few decades. We adopt here a stochastic approach for the modeling of these phenomena. More precisely, we formulate the problem in the following dynamical setup: given a population of n discernible atoms partitioned into p discernible (model 1) or indiscernible (model 2) groups, how does a new atom eventually connect to any of these p groups forming up a new partition of n+1 atoms into a certain amount of clusters? Nucleation is said to occur when the inserted atom does not connect (it nucleates), whereas aggregation takes place if it does (clusters coalesce). Depending on this local “logic” of pattern formation, the asymptotic structure of groups can be quite different, in the thermodynamic limit N→∞. These studies are the main purpose of this work. Understanding these aggregation phenomena requires first to derive the fragment size distributions (that is, the number P of fragments, or clusters, and the number n_m of size-m fragments with m fragments with constitutive atoms), as a function of the control parameter which is chosen here to be the average number of atoms 〈N〉. As 〈N〉 approaches infinity, we derive the study of these variables in the thermodynamic limit n → ∞. It is shown, making extensive use of combinatorics, that two regimes are to be distinguished: the one of weakly connected aggregates where nucleation dominates aggregation and the one of strongly connected aggregates where aggregation dominates nucleation. In the first (“diluted”) regime, the number of clusters P(n) always diverges as n → ∞, the asymptotic equivalent of which being under control in most cases. Large deviation results are shown to be available. Concerning N _m(n), distinct behaviours are observed in models 1 and 2. In the second (“condensed”) regime, the number of groups P(n) and size-m groups N _m(n) may converge in the thermodynamic limit, with a special role played by the geometric and Poisson distributions. The asymptotic variables become observable macroscopically. This work is therefore aimed toward a better understanding of the fundamentals involved in clusters' formation processes.     

Monte carlo simulations of self-assembled surfactant aggregates

Monte Carlo simulations provide some insight into the self-assembly of amphiphiles in aqueous environment. A rather simple solvent-free model, with only two adjustable parameters in the effective pair potential, allows one to describe the formation of micelles, stable curved membranes, and metastable vesicles. Characteristic features of the self-assembled aggregates, such as the distribution of the micelle size and the value of the curvature elastic constant for membranes, can be obtained from simulated data. The capability of the simple approach was demonstrated for a surfactant model with three spherical segments. The extension of the simulation to molecules with more segments and branched amphiphiles is straightforward.     

Modelling the precipitation of copper oxalate aggregates

The precipitation of copper oxalate has been studied in a batch reactor. Like many other systems, the morphology of these particles suggests that they were formed by an aggregation mechanism. A mathematical model has been developed to predict particle-size distributions grown in a batch reactor, which accounts for growth by two competing mechanisms, i.e., atomistic growth and particle aggregation. The results of this model are in good agreement with experimental observations for the precipitation of copper oxalate aggregates and other spherical aggregation systems cited in the literature.     

Fractal aggregates in protein crystal nucleation

Monte Carlo simulations of homogeneous nucleation for a protein model with an exceedingly short-ranged attractive potential yielded a nonconventional crystal nucleation mechanism, which proceeds by the formation of fractal, low-dimensional aggregates followed by a concurrent collapse and increase of the crystallinity of these aggregates to become compact ordered nuclei. This result corroborates a recently proposed two-step mechanism for protein crystal nucleation from solution.     

Kinetics of growth of chain aggregates in magnetic suspensions

Theoretical study of the kinetics of the growth of chain aggregates in suspensions of magnetizing non-Brownian particles is performed. An analytical model for calculating the time-dependent distribution function over the number of particles in the chains is developed and computer experiments on the kinetics of the aggregation of these particles are carried out. Results of calculations using an analytical model are in good agreement with the data of computer experiments when the volume concentration of particles is in the range of 1–2%, which corresponds to many modern magnetorheological suspensions. This allows us to recommend the developed mathematical model as a basis for describing kinetic phenomena in magnetorheological suspensions with low or moderate particle concentrations.     

Computer simulation studies of aggregates of associating polymers: Influence of low-molecular-weight additives solubilizing the aggregates

The structure of aggregates in solutions of chain molecules with associating groups at one of the ends is studied by Monte Carlo computer simulations using the bond fluctuation model. The main attention is paid to the influence of additives of low-molecular-weight solvent solubilizing the aggregates. It is shown that upon the addition of solvent the aggregates adopt a three-layer structure with the ‘lake’ of the solvent molecules in the central region surrounded by the layer of associating end-groups of polymer chains, which in turn is surrounded by the outer corona formed by the chain tails. The equilibrium form of the aggregates becomes close to that of a droplet of low-molecular-weight liquids. The regimes are found when the addition of the low-molecular-weight solvent stabilizes the multiplets and even induces the aggregate formation.     

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 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.     

Restructuring and break-up of two-dimensional aggregates in shear flow

We consider single two-dimensional aggregates, containing glass particles, placed at a water/air interface. We have investigated the critical shear rate for break-up of aggregates with different sizes in a simple shear flow. All aggregates break-up nearly at the same shear rate (1.8 +/- 0.2 s(-)(1)) independent of their size. The evolution of the aggregate structure before break-up was also investigated. With increasing shear rate, the aggregates adopt a more circular shape, and the particles order in a more dense, hexagonal structure. A simple theoretical model was developed to explain the experimentally observed break-up. In the model, the aggregate is considered as a solid circular disk that will break near its diameter. The capillary and drag force on the two parts of the aggregate were calculated, and from this force balance, the critical shear rate was found. The model shows a weak size dependence of the critical shear rate for the considered aggregates. This is consistent with the experimental observations.     

Electronic excitations of C(60) aggregates

Excitation properties of the isolated C(60) and (C(60))(N) model clusters (N = 2, 3, 4, 6 and 13) are studied using an a priori parameterized and self-consistent Hamiltonian, the Complete Neglect of Differential Overlap considering the l azimuthal quantum number method. This method properly describes electron excitations of the isolated C(60) after the configuration interaction of singles (CIS) procedure, when those are compared with experimental data in n-hexane solution and in a molecular beam. Geometry models of (C(60))(N) clusters to model the effect of aggregation were obtained from the fullerene fcc crystal. Some peaks in the low energy edge of the absorption spectrum appear corresponding to clustering effects, as well as small increases of bandwidths in the strong bands at the UV region. An analysis of the theoretical absorption spectrum for dimer models has been carried out, taking into account the influence of the distance between fullerene centers. The density of states of CIS for fullerene clusters in the range from 2.0 to 6.5 eV shows the possibility of electron transitions as functions of the size of the clusters.     

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.     

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.     

A simple model for polysoaps' thread-like aggregates

The equilibrium polymerization, a model for one-dimensional reversible aggregates is used under conditions of theta and bad solvent to describe thread-like aggregates of polysoaps. In two dimensions, the aggregate size distribution decreases always more slowly than an exponential distribution and the dependence of the mean aggregate size L on the density φ and end-cap energy E of the polysoap cylindrical micelle is of the form L[φexp(E/KT)]^δ with δ<1/2. On the other hand, in three dimensions in the bad solvent regime, the dependence of L on φ becomes exponential explaining the high φ dependence of the viscosity in experimental results.     

Chirality control in optically active polysilane aggregates

A novel strategy for controlling the higher order chirality of aggregates prepared from enantiopure polysilanes is experimentally probed and discussed. Structurally similar poly[n-alkyl(aryl)]silanes were synthesized in which one side chain comprised the chiral (S)-2-methylbutyl group and the other an achiral m- or p-alkyl-substituted phenyl ring. In solution the polymers adopt helical conformations with the same induced preferential screw sense chirality, as evidenced by circular dichroism (CD) spectroscopy. Aggregates, however, formed by addition of a nonsolvent to a polymer solution, show oppositely signed CD spectra. Consistent results were obtained for another series of poly[p-n-alkyl(aryl)]silanes where alkyl is butyl, propyl, and ethyl. The sense of the aggregate higher order chirality is dependent on the chemical composition and environment and is coarse-tunable by adjusting the length of the achiral side chain and fine-tunable by adjusting the good/poor solvent ratio. The origin of these effects is discussed with reference to a simple model.     

Highly magnetizable superparamagnetic colloidal aggregates with narrowed size distribution from ferrofluid emulsion

An empirical model for the concentrations of monomeric and micellized surfactants in solution is presented as a consistent approach for the quantitative analysis of data obtained with different experimental techniques from surfactant solutions. The concentration model provides an objective definition of the critical micelle concentration (cmc) and yields precise and well defined values of derived physical parameters. The use of a general concentration model eliminates subjective graphical procedures, reduces methodological differences, and thus allows one to compare directly the results of different techniques or to perform global fits. The application and validity of the model are demonstrated with electrical conductivity, surface tension, NMR chemical shift, and self-diffusion coefficient data for the surfactants SDS, CTAB, DTAB, and LAS. In all cases, the derived models yield excellent fits of the data. It is also shown that there is no need to assume the existence of different premicellar species in order to explain the chemical shifts and self-diffusion coefficients of SDS as claimed recently by some authors.     

Self-assembly of beta-sheet forming peptides into chiral fibrillar aggregates

The authors introduce a novel mid-resolution off-lattice coarse-grained model to investigate the self-assembly of beta-sheet forming peptides. The model retains most of the peptide backbone degrees of freedom as well as one interaction center describing the side chains. The peptide consists of a core of alternating hydrophobic and hydrophilic residues, capped by two oppositely charged residues. Nonbonded interactions are described by Lennard-Jones and Coulombic terms. The influence of different levels of "hydrophobic" and "steric" forces between the side chains of the peptides on the thermodynamics and kinetics of aggregation was investigated using Langevin dynamics. The model is simple enough to allow the simulation of systems consisting of hundreds of peptides, while remaining realistic enough to successfully lead to the formation of chiral, ordered beta tapes, ribbons, as well as higher order fibrillar aggregates.