Conclusions

We used molecular dynamics simulations to examine the chain conformations, entanglement densities, and diffusion coefficients of polymer chains under athermal cylindrical confinement. The simulation systems covered a range of chain lengths,

N 25–500, spanning the unentangled and entangled regimes. By using a variety

of pore sizes,r 2.5–20σ, confinement spanned both weak and strong regimes as

well as systems undergoing confinement induced chain segregation. Additionally, a random walk (RW) model was applied over the same range of chain length and pore sizes to isolate the effects of excluded volume and geometric confinement on chain conformations.

To examine the confined chain conformations, the shape anisotropy of the

averageRgvectors was calculated for each system in MD simulations and confined

random walk models. We observed that in the MD simulations Rg,z > Rg,bulk 1D

and Rg,xy < Rg,bulk 1D, while in the random-walk model Rg,z Rg,bulk 1D and

Rg,xy < Rg,bulk 1D. Despite the differences in confined Rg behavior in the MD

simulations and RW model, the hκ2_{i behavior was similar for a given degree of}

confinement, with each system showing a dip in hκ2i _at δ _{1. Thus, the shape}

anisotropy parameter is a robust measure of confined chain conformation, dependent

only on the degree of confinement,δ. Calculating the shape anisotropy parameter

in additional pore geometries (e.g., square or rectangular cross sections) will enable κ2

The entanglement density as a function of radial position was used to develop a simple two-layer model (Equation 2.2) that captures the number of entanglements per chain as a function of the pore radius and the chain length. Examining entanglement behavior in additional geometries will determine whether it is possible to generalize our two-layer model.

The diffusive behavior was examined by normalizing the axial diffusion

coefficient to the bulk diffusion coefficient, and it was shown thatDnorm changes

nonmonotonically as a function of the pore radius. This is in contrast to our early experimental and simulation work. By extending to more confined systems and chain lengths, this paper demonstrates the competing effects of chain disentanglement increasing diffusivity and chain segregation decreasing diffusivity. Because chains are slowed due to the increased free energy barrier for segregated chains to diffuse

past each other, the dramatic decrease in Dnorm for small reff may be particular

to cylindrical confinement. In thin film (1D) confinement, this effect of chain segregation might be less pronounced.

2.5

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