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.     

Fractal aggregates of conjugated polymer in solution state

Semirigid conjugated polymers have received much scientific and technological interest due to their unique electrical and photonic semiconducting properties. Spectroscopic studies have indicated that these polymers underwent interchain aggregation in the solution state even at large dilution; however, the origin of this event and the structure of the resultant aggregates remained the crucial issues to be resolved. In the present study, we revealed that the interchain aggregation of a conjugated polymer, poly(2,3-diphenyl-5-hexyl-1,4-phenylenevinylene) (DP6-PPV), in solutions with chloroform and toluene generated network aggregates with the hydrodynamic radii of several micrometers. Small angle neutron scattering (SANS) demonstrated that the internal structure of these aggregates could be characterized by the mass fractal dimensions of 2.2-2.7. The networks were looser in chloroform but became highly compact in the poorer toluene solvent due to severe segmental association. Increasing the temperature alleviated the segmental association in toluene while largely retaining the mass fractal dimension of the aggregates. However, the interchain aggregation was never completely dissipated by the heating, suggesting the existence of two types of segmental association with distinct stability. The highly stable segmental association that could neither be solvated by chloroform nor be disrupted thermally in toluene was attributed to the pi-pi complex already present in the DP6-PPV powder used for the solution preparation. The chains tied firmly by this complex formed network aggregates in the solution and hence reduced the entropy of mixing of the polymer. In the poorer toluene solvent, further segmental association took place within the preexisting aggregates, making the networks more compact. This type of segmental association could be disrupted by moderate heating, and its occurrence was ascribed to the poor affinity of the aliphatic side chains of DP6-PPV for toluene.     

Fractal approach of nucleation in liquid and gas phases

Summary The authors present a generalised fractal treatment of the nucleation from the liquid solution or gas-phase reactant.     

The kinetics of homogeneous and two-step nucleation during protein crystal growth from solution

Many experimental reports for the kinetics of crystal nucleation and growth, from an isothermal solution, point to a sigmoidal-like behavior for the process. Here we consider three different nucleation models from the literature and show that all lead to sigmoidal or sigmoidal-like behavior for the kinetics of nucleation. A two-step nucleation process is known to occur within certain supersaturated protein solutions, and it is demonstrated in this report how the sigmoidal law yields kinetic information for the two-step and homogeneous nucleation modes. We propose here that two-step solute-rich associates form in the solution around seed nuclei that are already present at or near the point in time when the solution is prepared. Using this hypothesis, we are able to model the time-dependent volume of the two-step phase per unit volume of solution and show that this compares well with reported experimental data. A kinetic model is given for the proposed process, which leads to a sigmoidal rate law. Additionally, a relation between the initial and final nuclei densities and the induction time is derived. As a result of this study, the conclusion is that two-step activity increases with increasing initial supersaturation or increasing salt concentration.     

Rate of homogeneous crystal nucleation in molten NaCl

We report a numerical simulation of the rate of crystal nucleation of sodium chloride from its melt at moderate supercooling. In this regime nucleation is too slow to be studied with "brute force" molecular-dynamics simulations. The melting temperature of ("Tosi Fumi") NaCl is approximately 1060 K. We studied crystal nucleation at T = 800 and 825 K. We observe that the critical nucleus formed during the nucleation process has the crystal structure of bulk NaCl. Interestingly, the critical nucleus is clearly faceted, the nuclei have a cubical shape. We have computed the crystal-nucleation rate using two completely different approaches, one based on an estimate of the rate of diffusive crossing of the nucleation barrier, the other based on the forward flux sampling and transition interface sampling methods. We find that the two methods yield the same result within an order of magnitude. However, when we compare the extrapolated simulation data with the only available experimental results for NaCl nucleation, we observe a discrepancy of nearly five orders of magnitude. We discuss the possible causes for this discrepancy.     

Molecular mechanism of crystal nucleation from solution

Nucleation from solution is fundamental to many natural and industrial processes. The understanding of molecular mechanism of nucleation from solution is conducive to predict crystal structure, control polymorph and design desired crystal materials. In this review, the nucleation theories, including classical nucleation theory(CNT), nonclassical nucleation theory, as well as other new proposed theories, were reprised, and the molecular mechanism of these theories was compared. Then, the molecular process of nucleation, including the current study techniques, the effect of molecular self-assembly in solutions, desolvation process, as well as the properties of solvent and crystal structure on nucleation from solution were summarized. Furthermore, the relationship of molecular conformation in solution and in crystal, and the effect of solute molecular flexibility on nucleation were discussed.Finally, the current challenges and future scopes of crystal nucleation from solution were discussed.     

Secondary nucleation in the formation of methane crystal hydrate

The kinetic data on crystallization and a morphological analysis of a layer of CH₄ · 6H₂O hydrate crystals formed on the surface of water as a result of methane absorption showed that secondary nucleation occurred during hydrate crystallization. The mutual arrangement of crystals in the layer revealed photographically in situ was evidence that part of nuclei produced on the surface of previously formed crystals went away from the surface into solution and grew there independently of “mother” crystals, although the probability of such transfer into an immobile solution remained low. In view of this, a model of crystal growth generating secondary crystals was developed.     

Homogeneous crystal nucleation triggered by spinodal decomposition in polymer solutions

We report dynamic Monte Carlo simulations of polymer crystal nucleation initiated by prior spinodal decomposition in polymer solutions. We observed that the kinetic phase diagrams of homogeneous crystal nucleation appear horizontal in the concentration region below their crossovers with the theoretical liquid-liquid spinodal. When the solution was quenched into the temperature beneath this horizontal boundary, the time evolution of structure factors demonstrated the spinodal decomposition at the early stage of crystal nucleation. In comparison with the case without a prior liquid-liquid demixing, we found that the prior spinodal decomposition can regulate the nanoscale small polymer crystallites toward a larger population, more uniform sizes, and a better spatial homogeneity, whereas chain folding in the crystallites seems little affected.     

Thermodynamics of heterogeneous crystal nucleation in contact and immersion modes

One of the most intriguing problems of heterogeneous crystal nucleation in droplets is its strong enhancement in the contact mode (when the foreign particle is presumably in some kind of contact with the droplet surface) compared to the immersion mode (particle immersed in the droplet). Heterogeneous centers can have different nucleation thresholds when they act in contact or immersion modes. The underlying physical reasons for this enhancement have remained largely unclear. In this paper we present a model for the thermodynamic enhancement of heterogeneous crystal nucleation in the contact mode compared to the immersion one. To determine if and how the surface of a liquid droplet can thermodynamically stimulate its heterogeneous crystallization, we examine crystal nucleation in the immersion and contact modes by deriving and comparing with each other the reversible works of formation of crystal nuclei in these cases. The line tension of a three-phase contact gives rise to additional terms in the formation free energy of a crystal cluster and affects its Wulff (equilibrium) shape. As an illustration, the proposed model is applied to the heterogeneous nucleation of hexagonal ice crystals on generic macroscopic foreign particles in water droplets at T = 253 K. Our results show that the droplet surface does thermodynamically favor the contact mode over the immersion one. Surprisingly, the numerical evaluations suggest that the line tension contribution (from the contact of three water phases (vapor-liquid-crystal)) to this enhancement may be of the same order of magnitude as or even larger than the surface tension contribution.     

Hyper-Rayleigh scattering as a means of monitoring crystal nucleation in solution

Hyper-Rayleigh scattering is revealed as a very sensitive monitor of cluster formation in solution, and as a means of studying the mechanism of crystal nucleation in molecular species. Two compounds are selected with particularly high second harmonic generation (SHG) powers in the crystalline state and experimental conditions are defined allowing the measurement of the beta value for one of these as 18+/-1x10(-30) esu. It is found to agree with current theoretical prediction of 20x10(-30) esu. In the more powerful of these, two photon induced fluorescence is found to be partly responsible for the SHG. The solubilities of both compounds in methanol are measured and it is observed that these differ by a factor of ten. When the solution concentration is increased beyond 45% of the saturation value, the quadratic coefficient exhibits non-linear behaviour with respect to concentration. Additionally, the widths of the distributions of the HRS signals increase initially with concentration as expected, but, beyond 45% saturation concentrations, these narrow again. These phenomena are interpreted as indicators of cluster formation in these solutions well below saturation concentrations. A future experimental design is proposed in which the coherent component will yield information on the organisation of the molecules in such clusters.     

A ternary nucleation model for the nucleation pathway of protein folding

Recently [Y. S. Djikaev and E. Ruckenstein, J. Phys. Chem. B 111, 886 (2007)], the authors proposed a kinetic model for the nucleation mechanism of protein folding where a protein was modeled as a heteropolymer consisting of hydrophobic and hydrophilic beads and the composition of the growing cluster of protein residues was assumed to be constant and equal to the overall protein composition. Here, they further develop the model by considering a protein as a three-component heteropolymer and by allowing the composition of the growing cluster of protein residues to vary independently of the overall one. All the bonds in the heteropolymer (now consisting of hydrophobic, hydrophilic, and neutral beads) have the same constant length, and all the bond angles are equal and fixed. As a crucial idea of the model, an overall potential around the cluster wherein a residue performs a chaotic motion is considered to be a combination of the average dihedral and average pairwise potentials assigned to the bead. The overall potential as a function of the distance from the cluster center has a double well shape which allows one to determine its emission and absorption rates by using a first passage time analysis. Knowing these rates as functions of three independent variables of a ternary cluster, one can develop a self-consistent kinetic theory for the nucleation mechanism of folding of a protein using a ternary nucleation formalism and evaluate the size and composition of the nucleus and the protein folding time. As an illustration, the model is applied to the folding of bovine pancreatic ribonuclease consisting of 124 amino acids whereof 40 are hydrophobic, 81 hydrophilic, and 3 neutral. With a reasonable choice of diffusion coefficients of the residues in the native state and potential parameters, the model predicts folding times in the range of 1-100 s.     

Hierarchical organization in aggregates of protein molecules

The aggregation of proteins into small clusters is studied by atomic force and electron microscopy. Scaling laws and fractal behaviour in the growth of the aggregates and in the correlation between aggregates is seen. A phase diagram of the aggregation process where the protonic concentration of the solution and the density of protein are varied shows the existence of specific growth processes resulting in different branch-like structures. The resulting structures are strongly influenced by the shape of each protein molecule. Lysozyme and ribonuclease are found to form spherical structures with a narrow size distribution.     

Doubled heterogeneous crystal nucleation in sediments of hard sphere binary-mass mixtures

Crystallization during the sedimentation process of a binary colloidal hard spheres mixture is explored by Brownian dynamics computer simulations. The two species are different in buoyant mass but have the same interaction diameter. Starting from a completely mixed system in a finite container, gravity is suddenly turned on, and the crystallization process in the sample is monitored. If the Peclet numbers of the two species are both not too large, crystalline layers are formed at the bottom of the cell. The composition of lighter particles in the sedimented crystal is non-monotonic in the altitude: it is first increasing, then decreasing, and then increasing again. If one Peclet number is large and the other is small, we observe the occurrence of a doubled heterogeneous crystal nucleation process. First, crystalline layers are formed at the bottom container wall which are separated from an amorphous sediment. At the amorphous-fluid interface, a secondary crystal nucleation of layers is identified. This doubled heterogeneous nucleation can be verified in real-space experiments on colloidal mixtures.     

Sonochemical synthesis and liquid crystal assembly of PS-b-PEO-titania aggregates

A facile ultrasonication process was developed for the controlled creation of PS-b-PEO-titania hybrid micelles and vesicles, which are assembled into three-dimensional hierarchical architectures via a liquid-crystal templating route.     

Uncovering molecular processes in crystal nucleation and growth by using molecular simulation

Exploring nucleation processes by molecular simulation provides a mechanistic understanding at the atomic level and also enables kinetic and thermodynamic quantities to be estimated. However, whilst the potential for modeling crystal nucleation and growth processes is immense, there are specific technical challenges to modeling. In general, rare events, such as nucleation cannot be simulated using a direct "brute force" molecular dynamics approach. The limited time and length scales that are accessible by conventional molecular dynamics simulations have inspired a number of advances to tackle problems that were considered outside the scope of molecular simulation. While general insights and features could be explored from efficient generic models, new methods paved the way to realistic crystal nucleation scenarios. The association of single ions in solvent environments, the mechanisms of motif formation, ripening reactions, and the self-organization of nanocrystals can now be investigated at the molecular level. The analysis of interactions with growth-controlling additives gives a new understanding of functionalized nanocrystals and the precipitation of composite materials.     

Molecular simulation of the homogeneous crystal nucleation of carbon dioxide

We report on a molecular simulation study of the homogeneous nucleation of CO2 in the supercooled liquid at low pressure (P = 5 MPa) and for degrees of supercooling ranging from 32% to 60%. In all cases, regardless of the degree of supercooling, the structure of the crystal nuclei is that of the Pa3 phase, the thermodynamically stable phase. For the more moderate degree of supercooling of 32%, the nucleation is an activated process and requires a method to sample states of high free energy. In this work, we apply a series of bias potentials, which promote the ordering of the centers of mass of the molecules and allow us to gradually grow crystal nuclei. The reliability of the results so obtained is assessed by studying the evolution of the nuclei in the absence of any bias potential, and by determining their probability of growth. We estimate that the size of the critical nucleus, for which the probability of growth is 0.5, is approximately 240 molecules. Throughout the nucleation process, the crystal nuclei clearly exhibit a Pa3 structure, in apparent contradiction with Ostwald's rule of stages. The other polymorphs have a much larger free energy. This makes their formation highly unlikely and accounts for the fact that the nucleation of CO2 proceeds directly in the stable Pa3 structure.