Microstructural Capture of Living Ultrathin Polymer Brush Evolution via Kinetic Simulation Studies

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^dF(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.