Polyelectrolyte-Compression Forces between Spherical DNA Brushes

Optical tweezers are employed to measure the forces of interaction within a single pair of DNA-grafted colloids, dependent on the molecular weight of the DNA chains, and the concentration and valence of the surrounding ionic medium. The resulting forces are short range and set in as the surface-to-surface distance between the colloidal cores reaches the value of the brush height. The measured force-distance relation is analyzed by means of a theoretical treatment that quantitatively describes the effects of compression of the chains on the surface of the opposite-lying colloid. Quantitative agreement with the experiment is obtained for all parameter combinations.

Figure 1

$F(D)$ curves between DNA-grafted colloids in buffered solution (10 mM ${\mathrm{C}}_4{\mathrm{H}}_{11}{\mathrm{NO}}_3$, $p\mathrm{H}$ 8.5) for grafting density $\sigma =8.2\times {10}^{-5}{\mathrm{nm}}^{-2}$ and various bp-number $N$, indicated in the legend. Symbols: experiments; lines: theory according to Eq. (2), with the values for $L_0$ and $Z_{\mathrm{eff}}$ given in Table . The inset illustrates the dependence of the interaction length ${\lambda }_F$ on $N$ for three different values of the force.

Figure 2

$F(D)$ dependence for various ionic strengths $I$ and types of salt. (a) NaCl; (b) ${\mathrm{CaCl}}_2$; (c) ${\mathrm{LaCl}}_3$. Here, $N=1000\mathrm{bp}$ and $\sigma =8.2\times {10}^{-5}{\mathrm{nm}}^{-2}$. Symbols: experiment; lines: theory according to Eq. (2), $L_0$ and $Z_{\mathrm{eff}}$ are given in Table .

Figure 3

Double-logarithmic plot of the interaction length for a force $F=2\mathrm{pN}$ versus the ionic strength of the added salt. Here, the molecular weight of the grafted DNA is $N=1000$. Different types of symbols correspond to different salt valencies. The dashed line of slope $-1/3$ indicates theoretical scaling law predictions for comparison.

Figure 4

Effective force-distance curves for DNA-grafted colloids at different grafting densities $\sigma$, fixed molecular weight $N=1000\mathrm{bp}$ and no added salt. Symbols: experiment; lines: theory. For the lowest $\sigma$, the solid line also includes an entropic contribution to force, derived from Eq. (1), which is illustrated by the dashed line.