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POLYMER-MEDIATED FORCES: OPTICAL TENSIOMETRY AND OPTICAL FORCE
MICROSCOPY
R. Rajagopalan
Department of Chemical Engineering, University of Florida,
Gainesville, Florida 32611-6005, USA
email: Raj@ChE.UFL.edu
ABSTRACT
Introduction
Intensive research over the last two decades has established that polymer adsorption on surfaces is far
more subtle than previously recognized (Scheutjens 1985; Fleer 1993). Whether interaction between polymer-laden
surfaces is attractive or repulsive depends on the amount of polymer between the two surfaces
and on the precise conformational details of the adsorbed chains, a fact that is all the more important in the
case of physisorbed layers, especially under “starved” (undersaturated) conditions. The latter situation is of
particular interest in a number of practical contexts, as physisorbed polymer layers under less-than-saturation
conditions are often the rule in colloid stabilization or in polymer interfaces of biomedical and biological
interest. The structure of adsorbed polymer chains (especially the role of tails) has been debated since the
early work of Scheutjens and Fleer and has been clarified to some extent only recently by Semenov and
coworkers (e.g., Semenov 1996), who revisited this problem in the last few years using an extension of the
ground state dominance approximation within a mean-field framework, and by Fleer and coworkers
(1999a,b), who developed an analytical approximation for the numerical mean-field theory and related it to
the approach of Semenov and coworkers. Simultaneously, a parallel effort to study interaction forces
between polymer layers using simulations has also been initiated (Jimenez 1998, 2000). Although these
simulations are based on self-avoiding random walk chains and therefore cannot be compared directly (or,
used to “test”) mean-field theories, such simulations do provide a way to assess how mean-field approximations
perform relative to realistic chains. Despite the approximations or simplifications involved, the
Scheutjens-Fleer (SF) lattice mean-field theory provides an important framework for studying polymer/
interface systems that are not amenable to scaling theories and to the Edwards-equation-based analytical
mean-filed formulations. In particular, the SF theory allows one to examine low-molecular-weight polymers
and chains of complicated molecular architecture.
The extensive work available in the literature based on mean-filed theories and simulations have also set
the stage for systematic experimental measurements of polymer-mediated forces down to the level of single
chains. The extension to single chains implies that one should be able to measure forces of the order of tens
of femtoNewtons – a level of sensitivity not readily accessible through atomic force microscopy (AFM).
However, the required level of sensitivity and resolution (in force) can be achieved if one uses optical
tweezers to hold and manipulated polymer chains and as force transducers. In this talk, we describe an
optical force microscope (analogous to an AFM), in which a probe particle held by a diffraction-limited optical
trap is used in place of the cantilever of an atomic force microscope. Examples of static and dynamic
measurements and related possibilities will be described.
Optical Force Microscopy
As well-known, members of the family of scanning probe microscopes differ from each other with respect
to the type of probe used and the type of substrate/probe interaction that is used as the basis of the measurement.
The sensitivity of the force measurement and the resolution of the distances depend on the
characteristics of the probe and the probe/substrate interactions, among others. The stiffness of a typical
AFM cantilever is typically of the order of 1000 pN/nm, but cantilevers with stiffnesses in the neighborhood of
1 pN/nm can be fabricated. Nevertheless, when dealing with soft interfaces such as a polymer layer, it is