Stretching instability of a two-dimensional freely rotating chain

We study the mechanical property of a two-dimensional free rotating chain (FRC). We find that at low force and with a scaled bond length, the relation between extension and applied force of a FRC obeys the same linear law as that of a free jointed chain (FJC), agreeing with the conclusion that free of applied force the end-to-end distances of two models have the same power law. But beginning from a moderate force, the two models become very different even with a scaled bond length. Especially, when the bond angle is small, the relative extension of a FRC is always smaller than that of a FJC; but with a large bond angle the relative extension of a FRC becomes larger than that of a FJC. Moreover, the extension of FJC is a smooth function of applied force, but the extension of a long FRC can subject to a first order transition when the bond angle is large.