Model Macromolecules Research Articles

Polymer migration phenomena based on the general bead-spring model for flexible polymers

This paper is concerned with the migration of general bead spring model macromolecules in inhomogeneous flows. The corresponding diffusion equation is derived. In order to obtain the translational diffusion tensor 𝒟 and the polymer migration velocity vm, respectively, some special models are considered. For Zimm coils, 𝒟 is isotropic with a constant diffusivity D. This implies that these molecules do not migrate across streamlines in unidirectional flows. For Zimm coils, the forms of D and vm, respectively, are obtained and explicit results are provided in the limit of no hydrodynamic interaction (Rouse coils). For more general models, the tensorial character of 𝒟 comes into play. For the simplest model (dumbbell with nonaveraged Oseen tensor), the predictions for channel flow seem unacceptable, which this author associates with an inadequacy of the dumbbell model.

Nonuniform concentration profiles of dilute macromolecular solutions in rotational viscometric flows

Some dilute solution kinetic theory results for dumbbell model macromolecules in nonuniform flows are obtained. Concentrating on rotational flows, it turns out that the flow induced cross-stream migration of the dissolved macromolecules is (a) due to the curvilinearity of the streamlines and (b) directed strictly towards the axis of rotation. For the special case of a Gaussian spring, explicit results are obtained and compared to a continuum approach using the constitutive equation for a dilute Hookean dumbbell solution. As long as wall effects are neglected, identical results are obtained. This fact enables us to immediately obtain explicit results for Rouse model macromolecules as well.

Macromolecules in nonhomogeneous flow fields: A general study for dumbbell model macromolecules

The hydrodynamics of bead-spring model macromolecules in nonhomogeneous flows has recently been worked out. By taking a non-infinite distance between the beads (relative to the bead size) into account a hydrodynamic driving force was found. In this paper we explore the kinetic theory consequence of that force and show that non-uniform (polymer) concentration profiles are to be expected in nonhomogeneous flows. The diffusion equation for a dilute polymer solution is derived from the continuity equation for the distribution function. Arguments, leading to a well-ordered pertubation expansion of the continuity equation are advanced and the zeroth order function of this hierarchy is studied for models with linear springs. Details for the channel flow system are worked out with special emphasis on the relation between the polymer concentration and the parameters of the system. Explicit results are presented for models with linear springs. It is shown that if the Oseen tensor is not preaveraged, inadmissible results emerge.

Macromolecules in nonhomogeneous velocity gradient fields. II

Bead-spring model macromolecules in nonhomogeneous flows migrate relative to the local solvent velocity at the center of mass. We show that this is the result of the net viscous forces acting on all the beads. The analogy between these results and continuum mechanical results on suspensions of neutrally buoyant rigid particles is discussed. Detailed comparisons of this model with the available experimental data in the concentric cone geometry is made. Models with linear springs are found to over-predict the migration somewhat, but all qualitative features of the phenomenon are well represented. This provides a new means of testing macromolecular models.

Grafting and branching of polymers

Abstract

Theory of chromatography of macromolecules with rigid structures on hydroxyapatite columns. II. Dynamic part

AbstractIn the second or dynamic part of a theory for the chromatography of rigid macromolecules on hydroxyapatite columns the adsorption and the desorption of macromolecules were studied as a function of their position on the column and of time, the phosphate concentration also being a function of position and time. Theoretical chromatograms for model macromolecules were calculated.