Polymer Diffusion in Confinement

the debate as to howDscales in confinement is still ongoing. The majority of the research into confined polymer dynamics, both in simulations and experiments, is devoted to measuring segmental dynamics and understanding changes in the

glass transition temperature, most often in thin films.19,21–25,27,28,52,59–61,79–85In some

instances, measurements of segmental or Rouse motions are used to determine

diffusion coefficients using scaling laws developed for bulk polymer melts.86–94In

cylindrical pores, for example, nuclear magnetic resonance (NMR) diffusometry and relaxometry measurements of polymer dynamics over time scales between the Rouse relaxation and reptation times demonstrate slower relaxation of PEO in

methacrylate pores with increasing confinement, implying slower PEO diffusion.86,87

Inelastic neutron scattering measurements of the Rouse relaxations of polymers, including PDMS and PEO, confined to AAO or silica pores also report evidence of

slowed88–90,93or unchanged91,92polymer dynamics.

The applicability of bulk polymer scaling laws (in which slowed Rouse relaxations indicate slowed diffusion) to confined polymer diffusion is uncertain, however, a few experimental studies measure polymer dynamics over larger time and length scales, providing a better indication of polymer diffusivity in thin film and cylindrical confinement. Fluorescence recovery after patterned photobleaching (FRAPP) is a useful experimental method for measuring the in-plane diffusion of polymer chains confined to a thin film. FRAPP measurements of silica supported

while measurements of silica supported poly(isobutyl methacrylate) (PiBMA) by

Geng et al. show no dependence ofD on film thickness.21,26Dynamic secondary

ion mass spectroscopy (SIMS) measurements of silica supported PS demonstrate

slowed diffusion of PS in thin film confinement in the out-of-plane dimension.23,24,95

In cylindrical confinement, Shin et al. measure capillary rise of PS into AAO pores and observe decreased polymer viscosity, which they interpret to mean increased

polymer diffusivity, although this is complicated by the interfacial components.44

Proton pulsed-gradient stimulated-echo NMR measurements of PB in anodic aluminum oxide (AAO) pores, measuring micrometer scale diffusion, demonstrate that confined polymer diffusivity decreases in confinement, but only as a function

of pore size, not polymer molecular weight.94 Measurements of polymer diffusion

over hundreds of nanometers, performed by Tung et al. using elastic recoil detection (ERD), show an increase in the polymer diffusion coefficient with increasing

confinement.18

While experiments measuring segmental dynamics in cylindrical confinement

suggest slowed86,87,95–97or unchanged91,92,94 polymer diffusion using scaling rules,

faster diffusion has been shown when measuring polymer dynamics over longer

time and length scales.18,44The disagreement between confined polymer diffusivity

calculated from polymer segmental relaxations and from chain scale motion suggest bulk polymer scaling laws may not apply in confined systems.

dynamics is the interaction between the polymer and the confining wall. In general, systems with attractive polymer-wall interactions demonstrate slower segmental

dynamics and slower polymer diffusion.88–90,93,98 PEO has a stronger attractive

interactions with AAO and silica than PS, and this may be an additional factor

as to why PEO diffusion in AAO pores is said to remain unchanged91,92while PS

diffusion has been shown to increase.44,99Developing experimental systems with

reduced polymer-wall interactions is critical to isolating the effects of confining geometry on polymer diffusivity.

In simulations, it is trivial to ensure that there are no attractive interactions between the polymer and the confining wall. Simulations of thin film confinement, with no polymer-wall interaction, have shown polymer diffusivity to increase within the plane of the film and decrease in the out-of-plane direction with increasing

confinement.36,80,100,101 Similar behavior is observed in simulations of entangled

polymers under cylindrical confinement; polymer diffusivity increases along the

pore axis.18 The contrast between the computational and experimental results

further implies that slowed diffusion in confinement could be due to attractive polymer-wall interactions and highlights the need for further experiments with neutral polymer-wall interactions.

1.6

Outline of Thesis Chapters

This thesis examines the effect of confinement on polymer diffusion and chain conformation under cylindrical and planar confinement, with athermal polymer- wall interactions, using computational and experimental techniques. These simple confining geometries, and lack of polymer-wall attraction, allow us to develop theories describing confined polymer behavior that can later be applied to more complex confining systems.

Chapter 2 uses molecular dynamics (MD) simulations to examine polymer conformation and diffusion under cylindrical confinement. Polymer chain lengths

of 25–500 beads are confined to cylindrical pores with radii ofr 2.5–20σ. Our

measurements of chain conformation show an increase inRg along the pore axis

and a decrease in the radial direction, in agreement with previous simulations. We also observe a decrease in the entanglement density as the polymer chains become more confined. Polymer diffusivity along the pore axis is shown to behave nonmonotonically with decreasing pore size, increasing initially due to chain disentanglement before decreasing due to entropically induced phase segregation.

In Chapter 3, we expand upon the simulations in Chapter 2 by using MD simulations to examine polymers under planar confinement. These simulations use polymers with chain lengths of 25–400 beads confined between parallel plates with

trends as in cylindrical confinement, though the magnitude of the changes is less. Unlike in cylindrical confinement, polymer diffusivity increases continuously in planar confinement, despite polymer chains tending toward segregation in the strongest confinement.

In Chapter 4 we focus on experimental measurements of polymer diffusion using elastic recoil detection (ERD). The diffusion of polystyrene into cylindrical AAO pores is examined as a function of temperature and compared to the cylin- drically confined polymer simulations in Chapter 2. In contrast to the cylindrical confinement simulations, the ERD measurements indicate slower diffusion into the AAO pores, relative to bulk polymer diffusion, with increased slowing occurring at higher temperatures. This behavior is similar to polymer diffusion into polymer

nanocomposites.99 We use the D(_T)_{measurements to calculate the entropic free}

energy barrier for a polymer chain to diffuse in cylindrical confinement.

In Chapter 5 we use SANS and dynamical theory analysis (DTA) to measure polymer conformation in thin film confinement. Polymer chains are confined to approximately 350 nm deep and 40 nm wide channels in a silica-alumina template. We find that the DTA model is able to accurately represent the scattering patterns from the empty 1D periodic confining template, however, the polymer scattering volume is determined to be too small and the intensity too weak to isolate the

confined polymer scattering pattern and measure Rg. We conclude that single

component templates with a uniform scattering length density are necessary for future measurements of confined polymer conformation.

Chapter 6 summarizes the conclusions of this thesis and discusses future research directions. Appendices A and B provide supporting information for Chapters 2 and 3, respectively. Appendix C describes the phenyl-capping procedure performed on the confining templates. Appendix D demonstrates successful filling and rinsing of excess polymer from the AAO membranes. Appendix E contains additional diffusion profiles for dPS into bulk PS and 40-nm AAO pores. Appendix F describes the channel template fabrication developed by IBM for the confining templates used in Chapter 5. Finally, Appendix G presents the results of a contrast matching experiment for determining the scattering length density of the AAO membranes.