Scale-Dependent Stiffness and Internal Tension of a Model Brush Polymer

Bottle-brush polymers exhibit closely grafted side chains that interact by steric repulsion, thereby causing stiffening of the main polymer chain. We use single-molecule elasticity measurements of model brush polymers to quantify this effect. We find that stiffening is only significant on long length scales, with the main chain retaining flexibility on short scales. From the elasticity data, we extract an estimate of the internal tension generated by side-chain repulsion; this estimate is consistent with the predictions of blob-based scaling theories.

Figure 1

(a) Sketch of brush polymer geometry: a main chain (Kuhn length $b_m$) is attached every $m$ monomers to side chains of extent $R_s$; the resulting complex has an effective diameter $D$. (b) Schematic of experimental geometry: a brush polymer containing an ssDNA main chain and PEG side chains is attached to a glass surface and magnetic bead, and its length $L$ is measured as a function of force $f$.

Figure 2

Force-extension data for densely and sparsely branched chains, along with an unbranched control. Each curve represents binned and averaged data for six (unbranched), seven (sparsely branched), and ten (densely branched) separate force extension curves. Extension is normalized to the extension at 50 pN. Error bars are the SEM.

Figure 3

Representative $f$ vs $L$ data for a densely branched polymer (circles) with fits to Eq. (1) (yellow line; best-fit parameters $l_p=3.5\mathrm{nm}$, $L_0=6000\mathrm{nm}$; ${\overline{\chi }}^2=11.6$) and Eq. (2) (blue line; best-fit parameters $l_p=2.2$, $f_{\mathrm{int}}=1.2\mathrm{pN}$, $L_0=6150\mathrm{nm}$; ${\overline{\chi }}^2=2.5$). Inset: Standardized residuals, $\mathrm{\Delta }f/{\sigma }_f$, vs $L$ for each fit. $\mathrm{\Delta }f=f-f^{*}$ is the difference between data $f$ and fit $f^{*}$, and ${\sigma }_f=0.05f$ is the estimated 5% error in force.