Amplification of Tension in Branched Macromolecules

We propose a method for the design of branched macromolecules that are capable of building up high tension ($\sim \mathrm{nN}$) in their covalent bonds without applying an external force. The tension is self-generated due to repulsion between branches and depends on the molecular architecture leading to amplification and focusing of tension in specific bonds. The simplest architecture is a pom-pom composed of a linear spacer and two $z$-arm stars at its ends resulting in $z$-fold tension amplification. Adsorption of those macromolecules on a substrate results in further increase in tension as compared to molecules in solution.

Figure 1

Architecture of a pom-pom macromolecule including a dense (solid) branching core of radius $R_c$, a region ($R_c<r<d$) of unperturbed star arms, and the corona of $2z$ arms whose conformation is perturbed by linking (pushing) together two $z$-arm stars.

Figure 2

Strategy for synthesizing pom-pom macromolecules which includes three major steps: (i) synthesizing a linear linker endcapped with branching functionalities, (ii) introducing $z$ branches with reactive end groups, and (iii) growing $z$ arms from these groups.

Figure 3

Log-log plot of tension $f_{\mathrm{sp}}$ in a spacer with $m$ Kuhn segments for pom-pom in different solvents. Upper curve—$\theta$-solvent, middle curves—poor solvent; lower curve—melt condition.

Figure 4

Diagram of states of a pom-pom in a poor and theta ($\theta$) solvents. The four regimes depicted in the diagram are $\theta$ solvent for arms with strongly ($\theta \mathrm{S}$) and weakly ($\theta \mathrm{W}$) stretched spacer as well as poor solvent for arms with strongly (PS) and weakly (PW) stretched spacer. The boundary between strongly and weakly stretched spacer (thick line in the diagram) is given by the fully extended chain ($d\simeq bN$). The logarithmic axes are $\ln (m)$ and $-\ln |\tau |$.