Lipid aggregate formation at an oscillating bubble surface: A simulation study

We perform a molecular dynamics simulation study of the behavior of a lipid coating layer on an oscillating bubble surface. Micrometer sized bubbles, stabilized with a lipid monolayer coating, are used in acoustic imaging as a contrast agent. The coating layer is expected to be strongly influenced by the oscillation of the bubble in the high frequency sound field, with a period of a microsecond. The typical time scale of molecular motion, however, is of the order of femtoseconds. One of the challenges is to bridge this nine decade gap in time scales. To this end we have developed a model that is highly coarse grained, but still features the essential mechanisms determining lipid dynamics, with time scales of picoseconds. This approach allows us to severely restrict the computing times, although we make use of very modest computing equipment. We show in our simulation that the amphiphilic monolayer folds upon contraction of the bubble, and forms micellar aggregates at the air-water interface. Some micellar structures survive consecutive re-expansion and indeed remain persistent over several cycles. These structures may add to the anisotropic behavior of the bubbles under oscillating conditions. We also investigated temperature and frequency dependenc

Dynamics of chains grafted on solid wall during polymer melt extrusion

The objective of the present work is the mathematical modeling of the dynamics of polymer molecules grafted on a solid boundary during polymer melt extrusion. This topic is closely related to the long-standing problem of polymer flow instabilities encountered in industry when extruding melts. In order to describe the behavior of the tethered chains, we introduce the bond vector probability distribution function (BVPDF) which appears to be a simple, yet effective mathematical 'tool'. The bond vector, i.e. the tangent vector to a polymer chain depending on the position along the chain and on time, describes the local geometry via its direction and the local stretching of the chain via its length. The BVPDF contains all information about the geometry of the ensemble of chains. Via averaging over the BVPDF we can calculate all interesting macrsocopic quantities, e.g. the thickness of and stress in the layer of tethered molecules. The time dependence of the BVPDF yields the time evolution of the system. We derive the equation of motion for the BVPDF taking into account all important mechanisms, such as reptation and (convective) constraint release. Besides that, we show that all macroscopic quantities of practical interest can be expressed via second order moments of this distribution function. \u

A rigorous model for constraint release in the bulk and the near-wall region

In the present work an attempt is made to build a rigorous theoretical model for the constraint release mechanism found to play an important role in the dynamics of polymer melts. Our goal is a formalism free of adjustable parameters and ''ad-hoc'' assumptions which are inherent to existing theories for constraint release. Our model is capable to describe both thermal and convective constraint release. These processes have the same effect on chains and accordingly can be unified in a single framework. Since polymer chains in the bulk and in the near-wall layer may experience different types of constraint release, the latter case is studied separately. This topic is closely related to the long-standing problem of polymer melt flow instabilities encountered during extrusion. Nowadays it is believed that constraint release plays a crucial role in the dynamics of tethered chains preventing them from being squeezed against the wall. The resulting non-monotonous slip-law is the most probable reason of the so-called spurt instability. \u

A universal constitutive model for the interfacial layer between a polymer melt and a solid wall

In a preceeding report we derived the evolution equation for the bond vector probability distribution function (BVPDF) of tethered molecules. It describes the behavior of polymer molecules attached to a solid wall interacting with an adjacent flowing melt of bulk polymer molecules and includes all the major relaxation mechanisms such as constraint release, retraction and convection. The derived equation is quite universal and valid for all flow regimes. In the present paper the developed formalism is further analyzed. We begin our analysis with the simple case of slow flows. Then, as expected, a remarkable reduction of the theory is possible. Later on the more general case is considered. \u

Flow-induced correlation effects within a linear chain in a polymer melt

A framework for a consistent description of the flow-induced correlation effects within a linear polymer chain in a melt is proposed. The formalism shows how correlations between chain segments in the flow can be incorporated into a hierarchy of distribution functions for tangent vectors. The present model allows one to take into account all the major relaxation mechanisms. Special cases of the derived set of equations are shown to yield existing models and shed some light on the connection between them. Consequences of several assumptions widely used in the literature are analyzed within the developed framework

How to Mix Molecules with Mathematics

In this paper we develop two methods to calculate thermodynamic properties of mixtures. Starting point are the basic assumptions that also form the basis for the COSMO-RS model. In this approach, the individual molecules are represented by their geometrical shape with an electrical charge density on their surfaces. Next, the surface is split up into surface segments each with its own charge. In COSMO-RS a strong reduction is introduced by treating the segments as if they are completely independent. In the present study we take into account that the coupling between two patches is essentially dependent on the charge distribution on neighboring segments and on the local geometrical structure of the surface. Two approaches are followed. The first one points out how the model equations, which comprise the optimization of the entropy and conservation of internal energy, can efficiently be solved in general, thus also if the dependency between segments and the local geometry is included in the expression for the coupling energy between segments. In the second method the configuration with maximal entropy and prescribed energy is sought via simulation. Successive molecular configurations of the mixture are simulated and updated via a genetic algorithm to optimize the entropy. The second method is more time consuming but very general