Intrinsic viscosity bead-spring model

Internal Viscosity and Cerf-Peterlin Theory. The concept of the internal viscosity was first employed by Kuhn and Kuhn 120) in an attempt to describe the shear-rate dependent viscosity with a dumbbell model or a bead-spring model with N = 1. They assumed that a force proportional to the relative velocity of the beads is exerted on the bead from the connector (spring) in addition to the spring force which is proportional to the relative position of the beads. This force intrinsic to the polymer molecule is compared with the frictional force from the viscous medium and is associated with the term internal viscosity . 

Summary. The non-Newtonian intrinsic viscosity of xanthan can be explained either by a bead-spring model or by a rigid rod model with appropriate parameters. A Kuhn-equivalent chain with about 200 repeating units per link and about 50 links per molecule is in my view more consistent with all the data than is a rigid rod model. 

To estimate the intrinsic viscosity in the bead-spring model, we need to find how much the stress tensor in the flowing fluid changes when a unit amount of the polymer is added. At low concentrations, the increase in the stress tensor (a, /3 = x, y, z) due to the presence of bead-spring chains is given as... 

Is such a deformable chain model inconsistent with the non-Newtonian intrinsic viscosity Finding an answer to this question is the goal of this paper. To this end, the viscosity of xanthan solutions was measured over a broad range of shear stress, including especially the low-shear Newtonian limit which has not been measured by Whitcomb and Macosko. The intrinsic viscosity at various shear stresses was then determined and the resultant experimental curve was compared to theoretical expectations for a flexible chain (bead-and-spring) model. 

Only recently has the theory of chain dynamics been extended by Peterlin (J [) and by Fixman (12) to encompass the known non-Newtonian intrinsic viscosity ofTlexible polymers. This theory, which is an extension of the Rouse-Zimm bead-and-spring model but which includes excluded volume effects, is much more complex than that for undeformable ellipsoids, and approximations are needed to make the problem tractable. Nevertheless, this theory agrees remarkably well (J2) with observations on polystyrene, which is surely a flexible chain. In particular, the theory predicts quite well the characteristic shear stress at which the intrinsic viscosity of polystyrene begins to drop from its low-shear Newtonian plateau. 

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