Large amplitude oscillatory shear study of a colloidal gel near the critical state.

A system undergoing sol-gel transition passes through a unique point, known as the critical gel state, where it forms the weakest space spanning percolated network. We investigate the nonlinear viscoelastic behavior of a colloidal dispersion at the critical gel state using large amplitude oscillatory shear rheology. The colloidal gel at the critical point is subjected to oscillatory shear flow with increasing strain amplitude at different frequencies. We observe that the first harmonic of the elastic and viscous moduli exhibits a monotonic decrease as the material undergoes a linear to nonlinear transition. We analyze the stress waveform across this transition and obtain the nonlinear moduli and viscosity as a function of frequency and strain amplitude. The analysis of the nonlinear moduli and viscosities suggests intracycle strain stiffening and intracycle shear thinning in the colloidal dispersion. Based on the insights obtained from the nonlinear analysis, we propose a potential scenario of the microstructural changes occurring in the nonlinear region. We also develop an integral model using the time-strain separable Kaye-Bernstein-Kearsley-Zapas constitutive equation with a power-law relaxation modulus and damping function obtained from experiments. The proposed model with a slight adjustment of the damping function inferred using a spectral method, compares well with experimental data at all frequencies.

Mathematical foundations of an ultra coarse-grained slip link model.

The master equation underlying ecoSLM, an ultra-coarse-grained slip link model, is presented. In the absence of constraint release, the equilibrium and dynamic properties of the discrete master equation for large chains are found to be virtually identical to the continuous Fokker-Planck equation for Brownian particles diffusing in a potential. A single-chain microscopic model with repulsion between adjacent slip links is described. It is approximately consistent with the quadratic fluctuation potential used in ecoSLM. Mapping ecoSLM with fine-grained slip link models or experiments requires specification of an effective friction as a function of molecular weight. Methods to accomplish this are discussed. Collectively, the mathematical framework described provides an interface for fine-grained slip link models to potentially use ecoSLM for extreme coarse-graining.

The electroneutrality constraint in nonlocal models.

We develop a nonlocal Nernst-Planck model for reaction and diffusion in multicomponent ionic systems. We apply the model to the one-dimensional liquid junction problem, in which two electrolytic solutions of different ionic concentrations are brought into contact via a permeable membrane. Transport of ions through the membrane induces an electric field which is modeled using two separate nonlocal conditions: charge conservation and Gauss' law. We investigate how well they satisfy the criterion of strict electroneutrality which stipulates that the net charge at each point in the domain is zero, by considering four different initial scenarios. Charge conservation and Gauss' law yield similar results for most practical scenarios in which the initial condition satisfies strict electroneutrality. However, Gauss' law has two important advantages over charge conservation: (i) it is numerically more stable and can be applied even when the concentration of all the charged species drops to zero and (ii) computationally, it is significantly cheaper. Further, this study provides insights on the prescription of electroneutrality conditions necessary to handle the physics of evolving charges in nonlocal peridynamic models that are aimed at modeling nonlocal reaction-diffusion or corrosion-type processes.

Nonmonotonic DNA-length-dependent mobility in pluronic gels.

Two-dimensional electrophoresis was used to analyze the mobility of DNA fragments in micellar gels of pluronic F127 (EO_{100}PO_{70}EO_{100}) and pluronic P123 (EO_{20}PO_{70}EO_{20}). The 20-3500 base pair DNA fragments were separated by size first in agarose gels, and then in pluronic gels at room temperature. In agarose gels, the DNA mobility decreases monotonically with increasing DNA length. In pluronic gels, however, the mobility varies nonmonotonically according to fragment lengths that are strongly correlated with the diameter of the spherical micelles. Brownian dynamics (BD) simulations with short-ranged intra-DNA hydrodynamic interactions were performed to numerically calculate the length-dependent mobility in pluronic lattices. The rising and falling trends, as well as the oscillations of mobility, were captured by the coarse-grained BD simulations. Molecular dynamics simulations in pluronic F127, with explicitly modeled micelle coronas, justified that the hydrodynamic interactions mediated by the complex fluid of hydrated poly(ethylene oxide) are a possible reason for the initial rise of mobility with DNA length.

What Happens When Threading is Suppressed in Blends of Ring and Linear Polymers?

Self-diffusivity of a large tracer ring polymer, D r , immersed in a matrix of linear polymers with N l monomers each shows unusual length dependence. D r initially increases, and then decreases with increasing N l . To understand the relationship between the nonmonotonic variation in D r and threading by matrix chains, we perform equilibrium Monte Carlo simulations of ring-linear blends in which the uncrossability of ring and linear polymer contours is switched on (non-crossing), or artificially turned off (crossing). The D r ≈ 6 . 2 × 10 - 7 N l 2 / 3 obtained from the crossing simulations, provides an upper bound for the D r obtained for the regular, non-crossing simulations. The center-of-mass mean-squared displacement ( g 3 ( t ) ) curves for the crossing simulations are consistent with the Rouse model; we find g 3 ( t ) = 6 D r t . Analysis of the polymer structure indicates that the smaller matrix chains are able to infiltrate the space occupied by the ring probe more effectively, which is dynamically manifested as a larger frictional drag per ring monomer.

Extraction of self-diffusivity in systems with nondiffusive short-time behavior.

We consider a toy model that captures the short-time nondiffusive behavior seen in many physical systems, to study the extraction of self-diffusivity from particle trajectories. We propose and evaluate a simple method to automatically detect the transition to diffusive behavior. We simulate the toy model to generate data sets of varying quality and test different methods of extracting the self-diffusion coefficient and characterizing its uncertainty. We find that weighted least-squares with statistical bootstrap is the most accurate and efficient means for analyzing the trajectory data. The analysis suggests an iterative recipe for designing simulations to conform to a specified level of accuracy.

Conformational free energy of melts of ring-linear polymer blends.

The conformational free energy of ring polymers in a blend of ring and linear polymers is investigated using the bond-fluctuation model. Previously established scaling relationships for the free energy of a ring polymer are shown to be valid only in the mean-field sense, and alternative functional forms are investigated. It is shown that it may be difficult to accurately express the total free energy of a ring polymer by a simple scaling argument, or in closed form.

On the relationship between two popular lattice models for polymer melts.

A mapping between two well known lattice bond-fluctuation models for polymers [I. Carmesin and K. Kremer, Macromolecules 21, 2819 (1988); J. S. Shaffer, J. Chem. Phys. 101, 4205 (1994)] is investigated by performing primitive path analysis to identify the average number of monomers per entanglement. Simulations conducted using both models, and previously published data are compared in an attempt to establish relationships between molecular weight, lengthscale, and timescale. Using these relationships, an examination of the self-diffusion coefficient yields excellent agreement not only between the two models, but also with experimental data on polystyrene, polybutadiene, and polydimethylsiloxane. However, it is shown that even with the limited set of criteria examined in this paper, a true mapping between these two models is elusive. Nevertheless, a practical guide to convert between models is provided.

Conformational properties of blends of cyclic and linear polymer melts.

An adapted version of the annealing algorithm to identify primitive paths of a melt of ring polymers is presented. This algorithm ensures that the primitive path length becomes zero for nonconcatenated rings, and that no entanglements are observed. The bond-fluctuation model was used to simulate ring-linear blends with N=150 and 300 monomers. The primitive path length and the average number of entanglements of the linear component were found to be independent of the blend composition. In contrast, the primitive path length and the average number of entanglements on a ring molecule increased approximately linearly with the fraction of linear chains, and for large N , they approached values comparable with linear chains. Threading of ring molecules by linear chains, and ring-ring interactions were observed only in the presence of linear chains. It is conjectured that for large N , these latter interactions facilitate the formation of a percolating entangled network, thereby resulting in a disproportionate retardation of the dynamical processes.

Self-organization of Te nanorods into V-shaped assemblies: a Brownian dynamics study and experimental insights.

Computer modeling of nanoscale processes provides critical quantitative insights into nanoscale self-organization, which is hard to achieve by other means. Starting from a suspension of Te nanorods, it was recently found that short nanorods (50 nm) self-organized into checkmark-like V-shaped assemblies over a period of a few days, whereas long nanorods (2200 nm) did not. This experimental fact was difficult to explain, and so here we use Brownian dynamics simulations of a dilute suspension of hard spherocylinders to better understand the process of self-organization. With the assumption that close encounters between nanorod tips result in their merger into V-particles, it was found that the ratio of the initial rate of nanorod formation for the short and long rods was 3760. By systematically varying the length and the concentration, we found that the concentration of the nanorods, rather their length, was primarily instrumental in setting the initial rate of checkmark formation. Using a simple kinetic model in conjunction with experimental data, we find that approximately 30,000 close encounters are required on average for a single successful merger. This study gives an important reference point for understanding the mechanism of the formation of complex nanostructured system by oriented attachment; it also can be extended to and provides conceptual leads for other self-organized systems.

On the origin of a permanent dipole moment in nanocrystals with a cubic crystal lattice: effects of truncation, stabilizers, and medium for CdS tetrahedral homologues.

A large anomalous dipole moment has previously been reported for nanocrystals with a cubic crystal lattice. By considering truncations of a regular tetrahedral CdS nanocrystal, the hypothesis that shape asymmetry is responsible for the observed dipole moment was tested and verified. The location and degree of the truncations were systematically varied, and corresponding dipole moments were calculated by using a PM3 semiempirical quantum mechanical algorithm. The calculated dipole moment of 50-100 D is in good agreement with a variety of experimental data. This approach also affords simple evaluation of the potential effect of the media for aqueous dispersions of nanocrystals. The substitution of the truncated corner(s) by molecules of H2O typically results in a substantial increase of the dipole moment, and often, in the reversal of its direction. The molecular modeling approach presented here is suitable for detailed theoretical studies of the dipole moments of II-VI and other nanoparticles and interparticle interactions in fluids. The data obtained from these calculations can be the starting point for modeling of agglomeration and self-organization behavior of large nanoparticle ensembles.

Spontaneous transformation of CdTe nanoparticles into angled Te nanocrystals: from particles and rods to checkmarks, X-marks, and other unusual shapes.

CdTe nanoparticles spontaneously transform into the branched Te nanocrystals with the unique, highly anisotropic shape of checkmarks after partial removal of the stabilizers of L-cysteine. The Te checkmarks are made in a relatively high yield and uniformity; the length of the arms is ca. 150 nm, whereas the angle between the arms is 74 degrees . Subsequent growth of the particle yields mothlike nanocrystals retaining geometrical anisotropy. Unlike the previous synthesis methods of branched nanocrystals, they are formed via a merger of individual rod-shaped crystallites. High-energy crystal faces on their apexes act as the sticky points causing the particles to join in the ends. This is the first demonstration of spontaneous transformation of binary semiconductor particles into highly anisotropic nanocolloids in an angled conformation. The end reactivity of starting Te rods can be used both for bottom-up fabrication of nanoscale electronics and relatively safe and nontoxic method of synthesis of Te-based optical and other materials.

Spontaneous CdTe --> alloy --> CdS transition of stabilizer-depleted CdTe nanoparticles induced by EDTA.

CdTe nanoparticles stabilized by l-cysteine are chemically transformed into CdS nanoparticles of the same diameter via an intermediate CdTeS alloy without any auxiliary source of sulfur. The reaction is induced by ethylenediaminetetraacetic acid dipotassium salt dehydrate (EDTA), which was demonstrated experimentally to act as a catalyst by partially removing thiol stabilizers from the nanoparticle surface. It is hypothesized that addition of EDTA facilitates Te(2-) release, and oxidation of Te(2-) drives the nanoparticle transition process. Unlike many reports on reactions catalyzed by nanocolloids, this is likely to be the first observation of a catalytic reaction in which nanoparticles function as a substrate rather than a catalyst. It opens new pathways for the synthesis of novel nanoscale II-VI and other semiconductors and represents an interesting case of chemical processes in nanocolloids with reactivity increased by depletion of the surface layer of thiol stabilizers. This includes but is not limited to accurate control over the particle composition and crystallization rate. The slow rate of the CdTe --> alloy --> CdS transition is important for minimizing defects in the crystal lattice and results in a substantial increase of the quantum yield of photoluminescence over the course of the transition.

Diffusion in three-dimensionally ordered scaffolds with inverted colloidal crystal geometry.

Inverted colloidal crystal geometry has been recently utilized in the design of highly organized 3D cell scaffolds. The regularity of the resulting scaffolds enables computational modeling of scaffold properties. In this work we probe the resistance offered by these scaffolds to nutrient transport, by using Brownian dynamics and Monte Carlo simulations to model the effective nutrient diffusivity. Brownian dynamics simulations indicate that the effective diffusivity for small nutrients in the scaffold, D(eff)=0.3D(0), where D(0) is the free solution diffusivity. Further, results of Monte Carlo simulations for dilute solutions of larger particles show that the D(eff) decreases linearly with the size of the particles.

Chain retraction potential in a fixed entanglement network.

When a chain, tethered at one end, is immersed in a fixed entanglement network, the mobile tip of the chain encounters an entropic potential barrier that penalizes deep fluctuations needed to bring the tip close to the tethering point. Using the tube model, Doi and Kuzuu [J. Polym. Sci., Polym. Lett. Ed. 18, 775 (1980)] estimated that this potential, which is crucial to describe the rheology of branched polymers in fixed networks and melts, has a quadratic form with a prefactor nu = 1.5. Later calculations based on regular lattices indicated that the potential is nonquadratic, and its steepness depends on the lattice coordination number. In this Letter, we analyze the primitive paths obtained using the bond-fluctuation model for chains with up to 12.5 entanglements. Our simulations confirm a quadratic form for the potential with a prefactor close to the Doi-Kuzuu value, nu approximately 1.5.

Cell distribution profiles in three-dimensional scaffolds with inverted-colloidal-crystal geometry: modeling and experimental investigations.

Limited ingrowth of stromal cells is observed when a three-dimensionally ordered scaffold possessing inverted-colloidal-crystal geometry is used to culture adherent cells. In this work, a computational model explaining, as well as predicting, experimental cell distributions is developed. It incorporates a modified Contois cell-growth model that includes the effects of nutrient saturation, competitive product inhibition, and cell-contact inhibition to describe the scaffold-cell system. Our results agree with the hypothesis that the rapid growth of cells on the surface of the scaffold depletes the nutrient supply to the core, resulting in the preferential growth on the exterior of the scaffold. When the cells are cultured in a scaffold subjected to a uniform velocity field, they penetrate to a greater extent into the scaffold core. Alternative seeding and culture strategies are suggested and evaluated.