Granular polymer solution

We have measured the spectrum of fluctuations in the size of a granular polymer in a granular solvent. The system consists of a linear chain of plastic spheres immersed in a planar fluid of self-propelled balls. The time average of the end-to-end length r of the chain scales with the number of links N according to $〈r^2〉\sim N^{2\nu },$ with $\nu =0.75\mathrm{}\pm \mathrm{0.01.}$ This provides an experimental test of the theoretical value $\nu =\frac{3}{4}$ of the critical exponent for a self-avoiding random walk in two dimensions. The measured probability distribution $P\left(r\right)\mathrm{}$ is compared with the universal function of the scaling theory.