PS674

Surfaces

The surface region of a polymer has different structure, energy, and dynamics from those regions of the polymer that are far removed from the nearest surface. The special environment at the surface depends on whether the surface is presented to a vacuum or to another material. If the latter, the effect also depends on the nature of the interaction with the second material.

The inherent difference between the surface region and the bulk can be seen by considering a free-standing film composed of an amorphous polymeric hydrocarbon, with both surfaces exposed to a vacuum. If the film is thick enough, a chain in the middle of the film does not feel any influence from the surfaces. But a segment at the surface experiences an anisotropic environment.

This segment can interact attractively (via the attractive part of a Lennard-Jones potential energy function) with nearby segments in the direction away from the surface.
But there is no attractive interaction in the other direction, because that direction leads into the vacuum.

As a consequence, segments at the surface have a higher average energy than segments in the interior of the polymer. The surface energy is positive. Surface energies for many polymers are in the range 20-50 erg/cm².

A typical density profile along the direction normal (taken to be the z direction) to the surface of the film has three distinct regions, as illustrated for amorphous polyethylene in Doruker, P.; Mattice, W. L. "Simulation of Polyethylene Thin Films on a High Coordination Lattice" Macromolecules, 1998, 31, 1418-1426.

The density is, of course, zero in the vacuum.
The density reaches a maximum in the middle of the film. For all but the thinnest films, this maximum density is identical with the density of the bulk polymer.
The change from the zero density of the vacuum to the density of the bulk is not a step function, but instead takes place over a distance that is on the order of 1 nm for polymeric hydrocarbons. In this surface region, the local structural and dynamic properties are expected to be different from those of the bulk. The density profile, rho(z), can be described by a hyperbolic tangent function, with xi defining the width of the surface region.
rho(z) = (rho₀ / 2) [1 - tanh (z/xi)]

The surface region can be defined by properties other than the density. The extent of this special region may depend on the property by which it is defined. For example,

Bonds experience no preferred orientation in the isotropic environment in the middle of a film of an amorphous polymer, but the environment near the surface is anisotropic, producing a preferred orientation measured by an order parameter S.
S = (1/2) [3 (cos² theta_z)_average - 1]
Here theta_z denotes the angle between a bond and the z axis. An isotropic system has S = 0. For amorphous polymeric hydrocarbons, backbone bonds of segments in the surface region have negative values of S, but the bonds far removed from the nearest surface have S = 0. The width of the surface region, as defined by S for bond orientation, is similar to the width defined by the density profile. In both cases, the surface region is defined by a local portion (atoms or bonds) of a chain.
The surface region can also be defined using entire chains. For example, one might look at the distribution of the centers of mass of the chains, along the normal to the surface. When defined in this way, the surface region is of greater extent than when it is defined by the density of chain atoms. Further, when defined with the entire chain, the width of the surface region will depend on the molecular weight of the chain.

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July 12, 1999

Wayne L. Mattice: wlm@polymer.uakron.edu