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

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

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

Estimation of intraband and interband relative coupling constants from temperature dependences of the order parameter for two-gap superconductors

We present temperature dependences of the large and the small superconducting gaps measured directly by SnS-Andreev spectroscopy in various Fe-based superconductors and MgB$_2$. The experimental $\Delta_{L,S}(T)$ are well-fitted with a two-gap model based on Moskalenko and Suhl system of equations (supplemented with a BCS-integral renormalization). From the the fitting procedure, we estimate the key attribute of superconducting state \textemdash relative electron-boson coupling constants and eigen BCS-ratios for both condensates. Our results evidence for a driving role of a strong intraband coupling in the bands with the large gap, whereas interband coupling is rather weak for all the superconductors under study.Comment: 7 pages, 5 figures, accepted to J. Supercond. Novel Mag

Experimental study of intrinsic multiple Andreev reflections effect in GdO(F)FeAs superconductor array junctions

We report the first observation of the intrinsic multiple Andreev reflections effect (IMARE) in S-n-S-...-S-arrays (S = superconductor, n = normal metal) formed by "break-junction" technique in GdO(F)FeAs superconductor (Tc = 48 - 53 K). We show that superconducting gap peculiarities at dI/dV-spectra sharpen dramatically in the arrays as compared with that in the single-contact spectra; this enables to improve significantly accuracy of the bulk superconducting parameters determination. Using IMARE, we determined the large and the small gap values \Delta_L = 11 +- 1.1 meV and \Delta_S = 2.6 +- 0.4 meV. The BCS-ratio 2\Delta_L/kTc^{local} = 5.0 - 5.9 > 3.52 (Tc^{local} is the contact area critical temperature) evidences for a strong electron-boson coupling. The results obtained agree well with our previous data by Andreev spectroscopy for single SnS-contacts.Comment: 6 pages, 6 figure