Crosslink-induced shrinkage of grafted Gaussian chains

The statistical mechanics of polymers grafted on surfaces has been the subject of intense research activity because of many potential applications. In this paper, we analytically investigate the conformational changes caused by a single crosslink on two ideal (Gaussian) chains grafted onto a rigid planar surface. Both the crosslink and the surface reduce the number of allowed configurations. In the absence of the hard substrate, the sole effect of the crosslink is a reduction in the effective Kuhn length of a tethered chain. The crosslink-induced shrinkage (collapse) of the grafted chains (mushrooms) turns out to be a reduction in the variance of the distribution of the height of the chain rather than a reduction of the height itself.

Figure 1

A schematic diagram of two ideal chains (mushrooms) with a single crosslink grafted on a rigid planar substrate.