Intrinsic Viscosity and the Polarizability of Particles Having a Wide Range of Shapes

Influence of network defects on the conformational structure of nanogel particles: From "closed compact" to "open fractal" nanogel particles

We propose an approach to generate a wide range of randomly branched polymeric structures to gain general insights into how polymer topology encodes a configurational structure in solution. Nanogel particles can take forms ranging from relatively symmetric sponge-like compact structures to relatively anisotropic open fractal structures observed in some nanogel clusters and in some self-associating polymers in solutions, such as aggrecan solutions under physiologically relevant conditions. We hypothesize that this broad "spectrum" of branched polymer structures derives from the degree of regularity of bonding in the network defining these structures. Accordingly, we systematically introduce bonding defects in an initially perfect network having a lattice structure in three and two topological dimensions corresponding to "sponge" and "sheet" structures, respectively. The introduction of bonding defects causes these "closed" and relatively compact nanogel particles to transform near a well-defined bond percolation threshold into "open" fractal objects with the inherent anisotropy of randomly branched polymers. Moreover, with increasing network decimation, the network structure of these polymers acquires other configurational properties similar to those of randomly branched polymers. In particular, the mass scaling of the radius of gyration and its eigenvalues, as well as hydrodynamic radius, intrinsic viscosity, and form factor for scattering, all undergo abrupt changes that accompany these topological transitions. Our findings support the idea that randomly branched polymers can be considered to be equivalent to perforated sheets from a "universality class" standpoint. We utilize our model to gain insight into scattering measurements made on aggrecan solutions.

Structure and conformational properties of ideal nanogel particles in athermal solutions

We investigate the conformational properties of "ideal" nanogel particles having a lattice network topology by molecular dynamics simulations to quantify the influence of polymer topology on the solution properties of this type of branched molecular architecture. In particular, we calculate the mass scaling of the radius of gyration (Rg), the hydrodynamic radius, as well as the intrinsic viscosity with the variation of the degree of branching, the length of the chains between the branched points, and the average mesh size within these nanogel particles under good solvent conditions. We find competing trends between the molecular characteristics, where an increase in mesh size or degree of branching results in the emergence of particle-like characteristics, while an increase in the chain length enhances linear polymer-like characteristics. This crossover between these limiting behaviors is also apparent in our calculation of the form factor, P(q), for these structures. Specifically, a primary scattering peak emerges, characterizing the overall nanogel particle size. Moreover, a distinct power-law regime emerges in P(q) at length scales larger than the chain size but smaller than Rg of the nanogel particle, and the Rg mass scaling exponent progressively approaches zero as the mesh size increases, the same scaling as for an infinite network of Gaussian chains. The "fuzzy sphere" model does not capture this feature, and we propose an extension to this popular model. These structural features become more pronounced for values of molecular parameters that enhance the localization of the branching segments within the nanogel particle.

Analysis of Different Computational Techniques for Calculating the Polarizability Tensors of Stem Cells with Realistic Three-Dimensional Morphologies

Recently, the National Institute of Standards and Technology has developed a database of three-dimensional (3D) stem cell morphologies grown in ten different scaffolds to study the effect of the cells' environments on their morphologies. The goal of this work is to study the polarizability tensors of these stem cell morphologies, using three independent computational techniques, to quantify the effect of the environment on the electric properties of these cells. We show excellent agreement between the three techniques, validating the accuracy of our calculations. These computational methods allowed us to investigate different meshing resolutions for each stem cell morphology. After validating our results, we use a fast and accurate Pad' approximation formulation to calculate the polarizability tensors of stem cells for any contrast value between their dielectric permittivity and the dielectric permittivity of their environment. We also performed statistical analysis of our computational results to identify which environment generates cells with similar electric properties. The computational analysis and the results reported herein can be used for shedding light on the response of stem cells to electric fields in applications such as dielectrophoresis and electroporation and for calculating the electric properties of similar biological structures with complex 3D shapes.

Evaluating models for polycaprolactone crystallization via simultaneous rheology and Raman spectroscopy

The crystallization of a polymer melt is characterized by dramatic structural and mechanical changes that significantly impact the processing conditions used to generate industrially-relevant products. Relationships between crystallinity and rheology are necessary to simulate and monitor the effect of processing conditions on the properties of the final product. However, separate measurements of crystallinity and rheology are difficult to correlate due to differences in sample history, geometry, and temperature. Recently, we have developed a rheo-Raman microscope for simultaneous rheology, Raman spectroscopy, and polarized reflection-mode optical measurements of soft materials, which allows for quantitative crystallinity measurements through features in the Raman spectrum. In this work, we apply this technique to monitor the isothermal crystallization of polycaprolactone to probe the relationship between structure, crystallinity, and rheology. Both crystallinity and the shear modulus vary over comparable timescales, but the birefringence increases much earlier in the crystallization process. We directly plot rheological parameters as a function of crystallinity to probe a range of suspension-based and empirical models relating the complex modulus to crystallinity, and we find that the previously developed models cannot describe the crystallinity-modulus relationship over the crystallization process. By developing a suspension-based model we can fit the complex modulus over the crystallization range. The crystallization process is characterized by a critical percolation fraction and a single scaling exponent.

Intrinsic conductivity of carbon nanotubes and graphene sheets having a realistic geometry

The addition of carbon nanotubes (CNTs) and graphene sheets (GSs) into polymeric materials can greatly enhance the conductivity and alter the electromagnetic response of the resulting nanocomposite material. The extent of these property modifications strongly depends on the structural parameters describing the CNTs and GSs, such as their shape and size, as well as their degree of particle dispersion within the polymeric matrix. To model these property modifications in the dilute particle regime, we determine the leading transport virial coefficients describing the conductivity of CNT and GS composites using a combination of molecular dynamics, path-integral, and finite-element calculations. This approach allows for the treatment of the general situation in which the ratio between the conductivity of the nanoparticles and the polymer matrix is arbitrary so that insulating, semi-conductive, and conductive particles can be treated within a unified framework. We first generate ensembles of CNTs and GSs in the form of self-avoiding worm-like cylinders and perfectly flat and random sheet polymeric structures by using molecular dynamics simulation to model the geometrical shapes of these complex-shaped carbonaceous nanoparticles. We then use path-integral and finite element methods to calculate the electric and magnetic polarizability tensors (αE, αM) of the CNT and GS nanoparticles. These properties determine the conductivity virial coefficient σ in the conductive and insulating particle limits, which are required to estimate σ in the general case in which the conductivity contrast Δ between the nanoparticle and the polymer matrix is arbitrary. Finally, we propose approximate relationships for αE and αM that should be useful in materials design and characterization applications.

Fifth to eleventh virial coefficients of hard spheres

Virial coefficients B(n) of three-dimensional hard spheres are reported for n=5 to 11, with precision exceeding that presently available in the literature. Calculations are performed using the recursive method due to Wheatley, and a binning approach is proposed to allow more flexibility in where computational effort is directed in the calculations. We highlight the difficulty as a general measure that quantifies performance of an algorithm that computes a stochastic average and show how it can be used as the basis for optimizing such calculations.

Driving self-assembly and emergent dynamics in colloidal suspensions by time-dependent magnetic fields

In this review we discuss recent research on driving self-assembly of magnetic particle suspensions subjected to alternating magnetic fields. The variety of structures and effects that can be induced in such systems is remarkably broad due to the large number of variables involved. The alternating field can be uniaxial, biaxial or triaxial, the particles can be spherical or anisometric, and the suspension can be dispersed throughout a volume or confined to a soft interface. In the simplest case the field drives the static or quasistatic assembly of unusual particle structures, such as sheets, networks and open-cell foams. More complex, emergent collective behaviors evolve in systems that can follow the time-dependent field vector. In these cases energy is continuously injected into the system and striking flow patterns and structures can arise. In fluid volumes these include the formation of advection and vortex lattices. At air-liquid and liquid-liquid interfaces striking dynamic particle assemblies emerge due to the particle-mediated coupling of the applied field to surface excitations. These out-of-equilibrium interface assemblies exhibit a number of remarkable phenomena, including self-propulsion and surface mixing. In addition to discussing various methods of driven self-assembly in magnetic suspensions, some of the remarkable properties of these novel materials are described.

Intrinsic viscosity of a suspension of cubes

We report on the viscosity of a dilute suspension of cube-shaped particles. Irrespective of the particle size, size distribution, and surface chemistry, we find empirically that cubes manifest an intrinsic viscosity [η]=3.1±0.2, which is substantially higher than the well-known value for spheres, [η]=2.5. The orientation-dependent intrinsic viscosity of cubic particles is determined theoretically using a finite-element solution of the Stokes equations. For isotropically oriented cubes, these calculations show [η]=3.1, in excellent agreement with our experimental observations.

Properties of knotted ring polymers. II. Transport properties

We have calculated the hydrodynamic radius R(h) and intrinsic viscosity [eta] of both lattice self-avoiding rings and lattice theta-state rings that are confined to specific knot states by our path-integration technique. We observe that naive scaling arguments based on the equilibrium polymer size fail for both the hydrodynamic radius and the intrinsic viscosity, at least over accessible chain lengths. (However, we do conjecture that scaling laws will nevertheless prevail at sufficiently large N.) This failure is attributed to a "double" cross-over. One cross-over effect is the transition from delocalized to localized knotting: in short chains, the knot is distributed throughout the chain, while in long chains it becomes localized in only a portion of the chain. This transition occurs slowly with increasing N. The other cross-over, superimposed upon the first, is the so-called "draining" effect, in which transport properties maintain dependence on local structure out to very large N. The hydrodynamic mobility of knotted rings of the same length and backbone structure is correlated with the average crossing number X of the knots. The same correlation between mobility and knot complexity X has been observed for the gel-electrophoretic mobility of cyclic DNA molecules.

Influence of variable hydrodynamic interaction strength on the transport properties of coiled polymers

We have computed the hydrodynamic radius Rh and intrinsic viscosity [eta] of a large number of random coil polymer models by path integration. We examine the effects of chain length, solvent quality, monomer size and shape, and chain stiffness on the approach of these transport properties to the limit of large molecular mass. For many of the models, we have also calculated the ensemble-averaged solvent velocity field in the vicinity of the coil as it moves with constant drift velocity under the action of an external force. Naive scaling arguments predict alpha=nu and beta=3(nu-1) , where alpha , beta , and nu are the exponents controlling the chain length behavior of Rh , [eta] , and Rg , respectively. We present evidence for a "draining crossover" that quantifies the slow convergence of the transport properties to their asymptotic scaling behavior. Indeed, the convergence is so slow that effective alpha and beta exponents rarely agree with the naive predictions at typical molecular masses. For the same chain models, Rg converges rapidly to its asymptotic behavior, indicating that the effect is not due to a crossover from theta to swollen behavior, as often stated. Solvent quality, monomer size, and chain stiffness all influence the draining crossover. Our results call into question the common practice of extracting metrical data, e.g., characteristic ratios, directly from polymer solution transport properties.

A comparison of viscosity-concentration relationships for emulsions

Differential effective medium theory (D-EMT) has been used by a number of investigators to derive expressions for the shear viscosity of a colloidal suspension or an emulsion as a function of the volume fraction of the dispersed phase. Pal and Rhodes [R. Pal, E. Rhodes, J. Rheol. 33 (7) (1989) 1021-1045] used D-EMT to derive a viscosity-concentration expression for non-Newtonian emulsions, in which variations among different oil-water emulsions were accommodated by fitting the value of an empirical solvation factor by matching the volume fraction at which the ratio of each emulsion was experimentally observed to have a viscosity 100 times greater than that of the pure solvent. When the particles in suspension have occluded volume due to solvation or flocculation, we show that the application of D-EMT to the problem becomes more ambiguous than these investigators have indicated. In addition, the resulting equations either do not account for the limiting behavior near the critical concentration, that is, the concentration at which the viscosity diverges, or they incorporate this critical behavior in an ad hoc way. We suggest an alternative viscosity-concentration equation for emulsions, based on work by Bicerano and coworkers [J. Bicerano, J.F. Douglas, D.A. Brune, J. Macromol. Sci., Rev. Macromol. Chem. Phys. C 39 (4) (1999) 561-642]. This alternative equation has the advantages that (1) its parameters are more closely related to physical properties of the suspension and (2) it recovers the correct limiting behavior both in the dilute limit and near the critical concentration for rigid particles. In addition, the equation can account for the deformability of flexible particles in the semidilute regime. The proposed equation is compared to the equation proposed by Pal and Rhodes.

Improved path integration method for estimating the intrinsic viscosity of arbitrarily shaped particles

In previous work, we have established that the intrinsic viscosity [eta] of an object is nearly proportional to the average electrical polarizability tensor alphae = tr(alphae)/3 of a conducting object having the same shape, or equivalently, to the intrinsic conductivity [sigma]=alphae/V , which characterizes the conductivity of a dilute mixture of randomly oriented conducting objects (V being the volume of the object). This hydrodynamic-electrostatic analogy is useful because alphae can be determined accurately and efficiently by numerical path integration for objects of arbitrary shape. Here, we show that the uncertainty in [eta] can be reduced to a relatively small value (< 1.5% relative uncertainty) by utilizing additional information from the full tensor alphae, rather than just its average. Specifically, we determine the exact constant of proportionality between [eta] and [sigma] for triaxial ellipsoids as a function of the ratios of the eigenvalues of alphae and apply this relation to particles of general shape. In addition to an improved estimation of [eta] , the ratios of the components of alphae provide useful measures of particle anisotropy. We also present an improved method for applying the technique to flexible particles, which requires performing a conformational ensemble average. Conformational averages of alphae generate systematic errors that can be avoided by performing the conformational average at an earlier stage in the computation.

Dielectric study of the antiplasticization of trehalose by glycerol

Recent measurements have suggested that the antiplasticizing effect of glycerol on trehalose can significantly increase the preservation times of proteins stored in this type of preservative formulation. In order to better understand the physical origin of this phenomenon, we examine the nature of antiplasticization in trehalose-glycerol mixtures by dielectric spectroscopy. These measurements cover a broad frequency range between 40 Hz to 18 GHz (covering the secondary relaxation range of the fragile glass-former trehalose and the primary relaxation range of the strong glass-former glycerol) and a temperature (T) range bracketing room temperature (220 K to 350 K). The Havriliak-Negami function precisely fits our relaxation data and allows us to determine the temperature and composition dependence of the relaxation time tau describing a relative fast dielectric relaxation process appropriate to the characterization of antiplasticization. We observe that increasing the glycerol concentration at fixed T increases tau (i.e., the extent of antiplasticization) until a temperature dependent critical "plasticization concentration" xwp is reached. At a fixed concentration, we find a temperature at which antiplasticization first occurs upon cooling and we designate this as the "antiplasticization temperature," Tant. The ratio of the tau values for the mixture and pure trehalose is found to provide a useful measure of the extent of antiplasticization, and we explore other potential measures of antiplasticization relating to the dielectric strength.

Finite-element simulation of the depolarization factor of arbitrarily shaped inclusions

An understanding of the polarization characteristics is a prevailing issue in electrostatics and scattering theory and is also vital to the rational design of future dielectric nanostructures. In this work, a finite-element methodology has been applied to simulate two-phase heterostructures containing a polarizable dielectric inclusion. The inclusions investigated can be considered as arbitrarily shaped cross sections of infinite three-dimensional objects, where the properties and characteristics are invariant along the perpendicular cross-sectional plane. Given the paucity of experimental and numerical data, we set out to systematically investigate the trends that shape and permittivity contrast between the inclusion and the host matrix have on the depolarization factor (DF). The effect of the first-versus second-order concentration virial coefficient on the value of the DF is considered for a variety of inclusion shapes and a large set of material properties. Our findings suggest that the DF for such inclusions is highly tunable depending on the choice of these parameters. These results can provide a useful insight for the design of artificial two-phase heterostructures with specific polarization properties.