Katerina Foteinopoulou

Topological analysis of polymeric melts: chain-length effects and fast-converging estimators for entanglement length.

Primitive path analyses of entanglements are performed over a wide range of chain lengths for both bead spring and atomistic polyethylene polymer melts. Estimators for the entanglement length N_{e} which operate on results for a single chain length N are shown to produce systematic O(1/N) errors. The mathematical roots of these errors are identified as (a) treating chain ends as entanglements and (b) neglecting non-Gaussian corrections to chain and primitive path dimensions. The prefactors for the O(1/N) errors may be large; in general their magnitude depends both on the polymer model and the method used to obtain primitive paths. We propose, derive, and test new estimators which eliminate these systematic errors using information obtainable from the variation in entanglement characteristics with chain length. The new estimators produce accurate results for N_{e} from marginally entangled systems. Formulas based on direct enumeration of entanglements appear to converge faster and are simpler to apply.

Structure, Dimensions, and Entanglement Statistics of Long Linear Polyethylene Chains

This work elucidates the effect of both temperature and molecular length on the conformational and structural properties as well as on the entanglement statistics of long amorphous, polydisperse, and molten linear polyethylene (PE). A large number of PE samples are modeled in atomistic detail, with average molecular lengths ranging from C24 up to C1,000 over a wide range of temperatures in the interval of 300 <or= T <or= 600 K under constant pressure (P ) 1 atm). By employing enhanced chain-connectivity-altering moves, full-scale equilibration is achieved within modest computational time even for the longest molecules at ambient conditions.At a second stage, direct geometrical analysis is applied on all equilibrated polymer configurations providing the corresponding primitive paths and intermolecular entanglements. Simulation findings on the characteristic ratio, density, and atomic packing are in excellent agreement with available experimental data. The same holds for the calculated plateau modulus; simulation predicts 1.8 ( 0.1 MPa. Regarding the primitive path statistics, the average contour length and the number of entanglements are found to exhibit a simple exponential type dependency on temperature. For the polydisperse samples studied here, a superposition of Poissonians(often represented by a negative binomial) describes best the distribution of entanglements of the primitive paths.

The structure of random packings of freely jointed chains of tangent hard spheres.

We analyze the structure of dense random packings of freely jointed chains of tangent hard spheres as a function of concentration (packing density) with particular emphasis placed on the behavior in the vicinity of their maximally random jammed (MRJ) state. Representative configurations over the whole density range are generated through extensive off-lattice Monte Carlo simulations on systems of average chain lengths ranging from N=12 to 1000 hard spheres. Several measures of order are used to quantitatively describe either local structure (sphere arrangements and bonded geometry) or global behavior (chain conformations and statistics). In addition, the employed measures are used to elucidate the effect of connectivity on structure, by comparing monatomic and chain assemblies of hard spheres at the MRJ state.

The characteristic crystallographic element norm: A descriptor of local structure in atomistic and particulate systems

We introduce the characteristic crystallographic element (CCE) norm as a powerful descriptor of local structure in atomistic and particulate systems. The CCE-norm is sensitive both to radial and orientational deviations from perfect local order. Unlike other measures of local order, the CCE-norm decreases monotonically with increasing order, is zero for a perfectly ordered environment, and is strictly discriminating among different, competing crystal structures in imperfectly ordered systems. The CCE-norm descriptor can be used as a sensitive, quantitative measure to detect and track changes in local order in atomistic and general particulate systems. In a specific example we show the ability of the CCE-norm to monitor the onset and evolution of order in an initially amorphous, densely packed assembly of hard-sphere chains generated through extensive Monte Carlo simulations [Phys. Rev. Lett. 100, 050602 (2008)].

Numerical simulation of multiple bubbles growing in a Newtonian liquid filament undergoing stretching

Our recent finite element-based study of the deformation of a single bubble in a Newtonian or viscoelastic filament undergoing stretching is extended here to the case of multiple bubbles simultaneously growing in the stretched medium. The filament, having initially the shape of a cylinder with uniform radius, is confined between two disks and is continuously stretched by pulling the upper disk along the filament axis with a constant velocity; the lower disk is assumed stationary. All bubbles are taken to lie along the axis of symmetry of the filament and undergo deformation and/or growth with the medium being stretched. The governing equations are solved by a finite element/Galerkin method coupled with an implicit Euler method for the time integration, using an adaptive time step. The problem of the multiple bubble-liquid interfaces is addressed by a robust mesh-generation scheme that solves a set of elliptic differential equations for the locations of the nodal points. The resulting numerical scheme is a...

Numerical simulation of bubble dynamics in a Phan-Thien–Tanner liquid: Non-linear shape and size oscillatory response under periodic pressure

We study non-linear bubble oscillations driven by an acoustic pressure with the bubble being immersed in a viscoelastic, Phan-Thien-Tanner liquid. Solution is provided numerically through a method which is based on a finite element discretization of the Navier-Stokes flow equations. The proposed computational approach does not rely on the solution of the simplified Rayleigh-Plesset equation, is not limited in studying only spherically symmetric bubbles and provides coupled solutions for the velocity, stress fields and bubble interface. We present solutions for non-spherical bubbles, with asphericity being addressed by means of Legendre polynomials or associated Legendre functions. A parametric investigation of the bubble dynamical oscillatory response as a function of the fluid rheological properties shows that the amplitude of bubble oscillations drastically increases as liquid elasticity (quantified by the Deborah number) increases or as liquid viscosity decreases (quantified by the Reynolds number). Extensive numerical calculations demonstrate that increasing elasticity and/or viscosity of the surrounding liquid tend to stabilize the shape anisotropy of an initially non-spherical bubble. Results are shown for pressure amplitudes 0.2-2MPa and Deborah, Reynolds numbers in the intervals of 1-8 and 0.094-1.256, respectively.

Spontaneous Crystallization in Athermal Polymer Packings

We review recent results from extensive simulations of the crystallization of athermal polymer packings. It is shown that above a certain packing density, and for sufficiently long simulations, all random assemblies of freely-jointed chains of tangent hard spheres of uniform size show a spontaneous transition into a crystalline phase. These polymer crystals adopt predominantly random hexagonal close packed morphologies. An analysis of the local environment around monomers based on the shape and size of the Voronoi polyhedra clearly shows that Voronoi cells become more spherical and more symmetric as the system transits to the ordered state. The change in the local environment leads to an increase in the monomer translational contribution to the entropy of the system, which acts as the driving force for the phase transition. A comparison of the crystallization of hard-sphere polymers and monomers highlights similarities and differences resulting from the constraints imposed by chain connectivity.

Modeling of crystal nucleation and growth in athermal polymers: self-assembly of layered nano-morphologies

We describe the salient characteristics and analyze the entropic origins of the spontaneous crystal nucleation and growth as observed in extensive Monte Carlo simulations of dense packings of athermal polymers of freely-jointed chains of tangent hard spheres of uniform size (N. Karayiannis, K. Foteinopoulou and M. Laso, Phys. Rev. Lett., 2009 (103), 045703). Self-assembly of well-defined nano-patterns, in the form of randomly alternating layers of hexagonal close packing (hcp) or face centered cubic (fcc) character with a single stacking direction, is realized spontaneously at volume fractions (packing densities) of 0.58 and above independently of the average chain length and the shape of the applied molecular weight distribution. Finally, the entropic origins of the crystallization are revealed: throughout the ordering transition, while the free volume around each monomer site remains unaltered in size, its shape becomes more spherical and more symmetric. In turn, spheres along the chains are able to explore more efficiently their accessible volume in the ordered (crystalline) state increasing the translational entropy of the system.

Jamming and crystallization in athermal polymer packings

Dense packings of chains of hard spheres possess characteristic features that do not have a counterpart in corresponding packings of monomeric spheres especially near the maximally random jammed (MRJ) state. From the modelling perspective the additional requirement that spheres keep their connectivity while maximizing the occupied volume fraction imposes severe constraints on generation algorithms of dense chain configurations. The extremely sluggish dynamics imposed by the uncrossability of chains precludes the use of deterministic or stochastic dynamics to generate all but dilute polymer packings. As a viable alternative, especially tailored chain-connectivity-altering Monte Carlo (MC) algorithms have been developed that bypass this kinetic hindrance and have actually been able to produce packings of hard-sphere chains in a volume fraction range spanning from infinite dilution up to the MRJ state. Such very dense athermal polymer packings share a number of structural features with packings of monomeric hard spheres, but also display unique characteristics due to the constraints imposed by connectivity. We give an overview of the most relevant results of our recent modeling work on packings of freely-jointed chains of tangent hard spheres about the MRJ state, local structure, chain dimensions and their scaling with density, topological constraints in the form of entanglements and knots, contact network at jamming, and entropically driven crystallization.

Modeling the effect of cell-associated polymeric fluid layers on force spectroscopy measurements. Part II: experimental results and comparison with model predictions.

In this paper, experimentally obtained force curves on Staphylococcus aureus are compared with a previously developed model that incorporates hydrodynamic effects of extracellular polysaccharides together with the elastic response of the bacterium and cantilever. Force-displacement curves were predicted without any adjustable parameters. It is demonstrated that experimental results can be accurately described by our model, especially if viscoelastic effects of the extracellular polysaccharide layer are taken into account. Polysaccharide layer viscoelasticity was treated by means of a multimode Phan-Thien/Tanner (PTT) constitutive equation. Typical maximum relaxation times range from 0.2 to 2 s, whereas the corresponding zero-shear-rate viscosities are 6-9 Pa.s, based on published, steady-state rheological measurements on Staphylococcus aureus polysaccharide extracted from its native environment. The bacterial elastic constant is found to be in the range 0.02-0.4 N/m, corresponding to bacterial wall Youngs moduli in the range of a few hundred MPa. Repeatability of measurements performed on different bacteria is found to be only fair, due to large individuum variability, whereas repetitions of measurements on the same bacterium showed high reproducibility. Improved force-indentation curve predictions are expected if transient rheological characterization of extracellular polysaccharides is available. More desirable however is the direct, in vivo rheological characterization of the extracellular polysaccharide. A model-based analysis of experimental force-indentation curves shows that appreciable further experimental improvements are still necessary to achieve this goal.