Eur. Phys. J. E 6, 49-55 (2001)

Probing viscosity of a polymer melt at the nanometre scale with an oscillating nanotip

F. Dubourg¹, J.P. Aimé¹, S. Marsaudon¹, R. Boisgard¹ and P. Leclère<sup>2

1</sup>  CPMOH, Universitè Bordeaux 1, 351 Cours de la Libération, F-33405 Talence, France
²  Service de Chimie des Matériaux Nouveaux, Centre de Recherche en Science des Matériaux Polymères (CRESMAP), Université de Mons-Hainaut, Place du Parc 20, B-7000 Mons, Belgium

jpaime@cribx1.u-bordeaux.fr

(Received 13 April 2001 and Received in final form 1 August 2001)

Abstract
The Navier-Stokes equation is used to analyze the additional phase delay when an oscillating nanotip touches intermittently an entangled polymer melt. Even when the tip oscillates at frequencies of several hundred kilohertz, it is shown that the inertial contributions are negligible as long as the indentation depth is no more than a few ten nanometers. Consequently, a stationary solution can be used leading to the simple Stokes formula. Two simple geometries of the tip are investigated. A smooth tip apex with a spherical shape and an elongated tip apex that aims at mimicking a single asperity. The tip shape has a drastic influence on the measured viscosity at the local scale. A simple calculation indicates that the viscous force acting against the tip motion may exhibit several different behaviors as a function of the indentation depth. Using the variational principle of least action, we derive the corresponding phase variation of the oscillator as a function of the indentation depth. It is shown that there exist situations for which an absolute value of the local viscosity could be measured.

PACS
07.79.Lh - Atomic force microscopes.
47.80.+v - Instrumentation for fluid dynamics.
83.85.Cg - Rheological measurements - rheometry.


© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2001