Scaling Exponent and Kuhn Length of Pinned Polymers by Single Molecule Force Spectroscopy

The end-to-end distance and the contour length of single polymers in dynamic adsorbate layers were measured with a mechanical approach. Individual polysaccharide chains were covalently pinned to the surface with one segment and picked up randomly with an atomic force microscope tip. The polymer section between pinpoint and the pickup point was stretched by retracting the tip from the surface. The pinpoint was derived by measuring the normal force while laterally scanning the surface at constant height. For carboxy-methyl-amylose, a Kuhn length of 0.44 nm and a scaling exponent of 0.74 were found.

Figure 1

Schematics of the experimental strategy. Polymers were covalently pinned onto a surface at very low density, restricting only their overall diffusion, not their segment mobility. Individual polymers were randomly picked up with an AFM-cantilever tip and stretched.

Figure 2

Force extension curve (a) for a long CMA polymer, with the two-state FJC fit (dashed black line). Between 200 and 300 pN, the pyranose rings change their conformation, which was used as an internal force sensor in the polymer. In (b), the geometry of the cantilever is sketched. Normal forces acting on the cantilever tip result in an out-of-plane bend of the cantilever along the east-west direction. This bend is measured with the reflected laser beam and after calibration converted into a force. Tangential forces acting on the tip result in a torque and cause an additional bend of the cantilever. However, only the east-west components of the lateral forces are picked up this way. The north-south components are not detected. This effect can be seen in (c) and (d), where this bend is measured when pulled at an angle with respect to the surface. Whereas in the north-south direction (c) the transition force decreases with the angle, the force additionally differs markedly, when pulled east or west (d).

Figure 3

Master-force map of a CMA molecule generated by interpolation between many force curves such as the ones in Fig. 2. It gives the normal force component when the tip is scanned above the surface at a constant height of $1/3$ of its total length. The asymmetry of the force map reflects the cantilever asymmetry as described before.

Figure 4

In (a), the protocol for the cantilever motion is sketched. The cantilever is retraced and scanned parallel to the surface while the force is recorded. (b) The resulting force curve. Obviously, only a segment of the entire force map was visited. In comparison with the master curve, the pinpoint was localized southwest of the origin (see Fig. 3).

Figure 5

End-to-end distance of CMA-polymer sections plotted against their contour length. The red dashed line is the fit with a scaling factor of $0.74\pm 0.04$ and a segment length of $b=0.44\pm 0.14\mathrm{nm}$. The blue and black dotted lines are plots with $\nu =0.588$ and $\nu =1$ with $b=0.44\mathrm{nm}$, respectively.