  We present results for the nonequilibrium dynamics of collapse for a model
flexible homopolymer on simple cubic lattices with fixed and fluctuating bonds
between the monomers. Results from our Monte Carlo simulations show that,
phenomenologically, the sequence of events observed during the collapse are
independent of the bond criterion. While the growth of the clusters (of
monomers) at different temperatures exhibits a nonuniversal power-law behavior
when the bonds are fixed, the introduction of fluctuations in the bonds by
considering the existence of diagonal bonds produces a temperature independent
growth, which can be described by a universal nonequilibrium finite-size
scaling function with a non-universal metric factor. We also examine the
related aging phenomenon, probed by a suitable two-time density-density
autocorrelation function showing a simple power-law scaling with respect to the
growing cluster size. Unlike the cluster-growth exponent $\alpha_c $, the
nonequilibrium autocorrelation exponent $\lambda_C$ governing the aging during
the collapse, however, is independent of the bond type and strictly follows the
bounds proposed by two of us in Phys. Rev. E 93, 032506 (2016) at all
temperatures.
