Configurational statistics of confined polymer chains
- Univ. of Illinois, Urbana-Champaign, IL (United States)
The work on confined chain statistics is reviewed. The work on the general statistics is discussed first, and then some of the theories for the applications of statistics are considered. Two methods for determining the general statistics of a confined chain are discussed. The first is the method of images. The second method involves the use of differential equations. In a specific case the statistics of the unconfined chain are chosen to be defined by the Gaussian real chain distribution. The confinement is provided by two parallel walls. The distribution for the four possible types of chains, bridges (tie chains), loops, cilia (dangling chain ends), and floating (unattached) chains, are derived. These statistics are then applied to two polymer systems in which the confinement is due to internal surfaces, semicrystalline polymers and block copolymers. Both systems are modelled by chains between two walls for a number of morphologies. Mechanical properties are calculated for both systems and for block copolymers swelling is also considered. The main result of this work is that there are two effects which determine the behavior of the chains in these systems. The first is the effect of the confinement which operates on all the chains, since the mode of attachment is not important. The confinement reduces the number of configurations available to the chains. This effect is larger the closer the walls are, relative to the length and stiffness of the chains. The second effect operates only on bridges, since it requires that the ends of the chain be attached to different walls. This is the inherent elastic nature of the bridge, which means that the number of configurations is reduced when it is stretched beyond its equilibrium length. All the behavior calculated here can be explained by these two effects.
- Research Organization:
- Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Metallurgy and Mining Engineering
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- EY-76-C-02-1198
- OSTI ID:
- 6627506
- Report Number(s):
- COO-1198-1220
- Resource Relation:
- Other Information: Thesis
- Country of Publication:
- United States
- Language:
- English
Similar Records
Block copolymer deformation
Amorphous contribution to the modulus of a semi-crystalline polymer