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A key assumption of polymer physics is that the random chains polymers extendin flow. Recent experimental evidence has shown that polymer chains compress inCouette flow in a manner counter to expectation. Here, scaling argumentsdeveloped previously are used to determine the relationship between theviscosity and chain radius of gyration. Scaling arguments determine theviscosity-radius of gyration relationship to be such that the viscosity isproportional to the radius to the power of 9. The viscosity is shown to be apower law function of the radius, and to decrease with decreasing radius underconditions where the chains are ideal random walks in concentrated solution.Furthermore, this relationship is consistent with both the widely observedviscosity-temperature and viscosity-shear rate behavior observed in polymerrheology. The assumption of extension is not consistent with these observationsas it would require that the chains increase in size with increasingtemperature. Shear thinning is thus a result of a decreasing radius withincreasing shear rate as the radius is proportional to the the shear rateraised to the power law exponent divided by 9. The thermal expansioncoefficient determines the variation in the power law exponents that aremeasured for different polymer systems. Typical values on n enable the measuredreduction in coils size behavior to be fitted. Furthermore, the absurd notionthat polymer chains extend to reduce the viscosity implies that an increasingchain size results in a reduced viscosity is addressed. This assumption wouldrequire that the viscosity increases with reducing coil radius which is simplyunphysical.

The viscosity-radius relationship for concentrated polymer solutions