No abstract

Macromolecular theory for the rheology of polymer liquids usually proceeds from a scale much larger than chemical bonding. For instance, a bead in a general rigid bead-rod theory can represent a length of polymer. This is why we sculpt the shape of the macromolecule with a rigid bead-rod model. From the macromolecular hydrodynamics that follows, we then discover that the rheology of polymer liquids depends on the macromolecular moments of inertia. In this paper, we use this discovery to arrive a way of proceeding directly from the chemical bonding diagram to dimensionless complex viscosity curves. From the equilibrium conformation of the macromolecule, its atomic masses and positions, we first arrive at the macromolecular principal moments of inertia. From these we then get the shapes of the complex viscosity curves from first principles thusly. We call this the macromolecular moment method. The zero-shear viscosity and relaxation time must still be fit to measurement. Using space-filling equilibrium structures, we explore the roles of (i) end group type, (ii) degree of polymerization, and (iii) pendant group type. We compare our results with complex viscosity measurements of molten atactic polystyrene.

Recent work arrived at expressions for the complex viscosity of a suspension of star-branched macromolecules [Coombs, Phys Fluids, 33, 093111 (2021)] using general rigid bead-rod theory without hydrodynamic interaction. In this work, we advance the theory by accounting for intramolecular interactions modelled with the interferences of Stokes flow solvent velocity profiles between adjacent beads. We derive the analytical expression for the complex viscosity of a suspension of 4-arm star-branched macromolecules as a function of the number of beads in each arm and of the hydrodynamic interaction parameter . We test our comprehensive theory against complex viscosity measurements of a cis-polybutadiene silicon-centered 4-arm star suspension. We find the incorporation of hydrodynamic interaction improves the fit to complex viscosity measurements.

By virtue of their lack of motility, viruses rely entirely on their own temperature (Brownian motion) to position themselves properly for cell attachment. Spiked viruses use one or more spikes (called peplomers) to attach. The coronavirus uses adjacent peplomer pairs. These peplomers, identically charged, repel one another over the surface of their convex capsids to form beautiful polyhedra. We identify the edges of these polyhedra with the most important peplomer hydrodynamic interactions. These convex capsids may be spherical or not, and their peplomer population declines with infection time. These peplomers are short, equidimensional, and bulbous, with triangular bulbs. In this short paper, we explore the interactions between nearby peplomer bulbs. By interactions, we mean the hydrodynamic interferences between the velocity profiles caused by the drag of the suspending fluid when the virus rotates. We find that these peplomer hydrodynamic interactions raise rotational diffusivity of the virus, and thus affect its ability to infect.

A new method of classification of tasters and non-tasters is suggested here by following the technique of separation of Gaussian components from a mixed distribution as developed by Preston [Biometrika 40: 460–464, 1953]. The improvement achieved by the present method over the existing methods is shown to be quite appreciable for populations where non-tasters are rare as compared to the tasters.