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

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

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

A Rouse-like model for highly ordered main-chain liquid crystalline polymers containing hairpins

Main-chain liquid crystalline polymers (LCPs) are used to produce strong fibers due to their ability to form highly-ordered orientational states. For sufficiently long chains it is known that loss of entropy in such highly-ordered states is partly recovered by the formation of so-called hairpins or kinks. The presence of hairpins not only modifies the microstructure of LCPs, but it has also been conjectured that hairpins influence their macroscopic mechanical behavior. In this paper the influence of hairpins on the rheological properties of concentrated solutions of LCPs is studied

A rod-spring model for main-chain liquid crystalline polymers containing hairpins

Main-chain liquid crystalline polymers (LCPs) are used to produce strong ¿bers due to their ability to form highly-ordered orientational states. For su¿ciently long chains it is known that loss of entropy in such highly-ordered states is partly recovered by the formation of so-called hairpins or kinks. The presence of hairpins not only modi¿es the microstructure of LCPs, but it has also been conjectured that hairpins in¿uence their macroscopic mechanical behavior. In this paper the in¿uence of hairpins on the rheological properties of concentrated solutions of LCPs is studied

Bond vector probability distribution function of bulk molecules

In our previous work we studied dynamics of the interfacial layer between flowing polymer melt and a solid wall. We showed that the ensemble-averaged behavior of the polymer molecules grafted on the wall could be successfully described in terms of the so-called bond vector probability distribution function (BVPDF). As was shown, the BVPDF satisfies a certain nonlinear integro-differential equation with all the major relaxation mechanisms taken into account. The goal of the present work is to extend the developed formalism to the bulk flow region. For that the corresponding equation of motion for the BVDPF is derived which allows for reptation and the isotropic boundary conditions inherent to the bulk chains. \u

Weakly nonlinear thermoacoustics for stacks with slowly varying pore cross-sections

A general theory of thermoacoustics is derived for arbitrary stack pores. Previous theoretical treatments of porous media are extended by considering arbitrarily shaped pores with the only restriction that the pore cross-sections vary slowly in the longitudinal direction. No boundary-layer approximation is necessary. Furthermore, the model allows temperature variations in the pore wall. By means of a systematic approach based on dimensional analysis and small parameter asymptotics, we derive a set of ordinary differential equations for the mean temperature and the acoustic pressure and velocity, where the equation for the mean temperature follows as a consistency condition of the assumed asymptotic expansion. The problem of determining the transverse variation is reduced to finding a Green's function for a modified Helmholtz equation and solving two additional integral equations. Similarly the derivation of streaming is reduced to finding a single Green's function for the Poisson equation on the desired geometr

Development curves of communication and social interaction in individuals with cerebral palsy

Aim: To determine development curves of communication and social interaction from childhood into adulthood for individuals with cerebral palsy (CP). Method: This Pediatric Rehabilitation Research in the Netherlands (PERRIN)-DECADE study longitudinally assessed 421 individuals with CP, aged from 1 to 20 years at baseline, after 13 years (n=121 at follow-up). Communication and social interactions were assessed using the Vineland Adaptive Behavior Scales. We estimated the average maximum performance limit (level) and age at which 90% of the limit was reached (age90) using nonlinear mixed-effects modeling. Results: One-hundred individuals without intellectual disability were aged 21 to 34 years at follow-up (39 females, 61 males) (mean age [SD] 28y 5mo [3y 11mo]). Limits of individuals without intellectual disability, regardless of Gross Motor Function Classification System (GMFCS) level, approached the maximum score and were significantly higher than those of individuals with intellectual disability. Ages90 ranged between 3 and 4 years for receptive communication, 6 and 7 years for expressive communication and interrelationships, 12 and 16 years for written communication, 13 and 16 years for play and leisure, and 14 and 16 years for coping. Twenty-one individuals with intellectual disability were between 21 and 27 years at follow-up (8 females, 13 males) (mean age [SD] 24y 7mo [1y 8mo]). Individuals with intellectual disability in GMFCS level V showed the least favourable development, but variation between individuals with intellectual disability was large. Interpretation: Individuals with CP and without intellectual disability show developmental curves of communication and social interactions similar to typically developing individuals, regardless of their level of motor function. Those with intellectual disability reach lower performance levels and vary largely in individual development. What this paper adds: Communication and social interactions in individuals with cerebral palsy without intellectual disability develop similarly to typically developing individuals. Communication and social interactions of individuals with intellectual disability develop less favourably and show large variation