Performing
dynamic off-lattice multicanonical Monte Carlo simulations, we study
the statics, dynamics, and scission–recombination kinetics
of a self-assembled in situ-polymerized polydisperse
living polymer brush (LPB), designed by surface-initiated living polymerization.
The living brush is initially grown from a two-dimensional substrate
by end-monomer polymerization–depolymerization reactions through
seeding of initiator arrays on the grafting plane which come in contact
with a solution of nonbonded monomers under good solvent conditions.
The polydispersity is shown to significantly deviate from the Flory–Schulz
type for low temperatures because of pronounced diffusion limitation
effects on the rate of the equilibration reaction. The self-avoiding
chains take up fairly compact structures of typical size R
g(N) ∼ N
ν in rigorously two-dimensional (d =
2) melt, with ν being the inverse fractal dimension (ν
= 1/d). The Kratky description of the intramolecular
structure factor F(q), in keeping
with the concept of generalized Porod scattering from compact particles
with fractal contour, discloses a robust nonmonotonic fashion with q
d
F(q) ∼
(qR
g)−3/4 in the intermediate-q regime. It is found that the kinetics of LPB growth, given
by the variation of the mean chain length, follows a power law ⟨N(t)⟩ ∝ t
1/3 with elapsed time after the onset of polymerization,
whereby the instantaneous molecular weight distribution (MWD) of the
chains c(N) retains its functional
form. The variation of ⟨N(t)⟩ during quenches of the LPB to different temperatures T can be described by a single master curve in units of
dimensionless time t/τ∞,
where τ∞ is the typical (final temperature T
∞-dependent) relaxation time which is
found to scale as τ∞ ∝ ⟨N(t = ∞)⟩5 with
the ultimate average length of the chains. The equilibrium monomer
density profile ϕ(z) of the LPB varies as ϕ(z) ∝ ϕ–α with the concentration
of segments ϕ in the system and the probability distribution c(N) of chain lengths N in the brush layer scales as c(N) ∝ N
–τ. The computed
exponents α ≈ 0.64 and τ ≈ 1.70 are in good
agreement with those predicted within the context of the Diffusion-Limited
Aggregation theory, α = 2/3 and τ = 7/4.