Giant fluctuations of crosslink positions in gels

We study a tetrafunctional network of freely jointed rigid rods in two dimensions and show that, at equilibrium, it will be in a highly swollen state. Surprisingly, such a network is a critical object with large crosslink density fluctuations on all length scales and anomalously low shear modulus. These conclusions are very different from the classical picture and raise questions of how large are crosslink fluctuations in real gels and rubbers.