Solid or Liquid?

Is there any Chain Order in Amorphous State? Short Range Interactions In axial direction of a chain Kuhn segment length The persistence length In the radial direction Long Range Interactions Conformation of Single Chains Surface Inhomogeneities

Results of Short Range Interactions The basic conclusion is that intramolecular orientation is little affected by the presence of other chains in the bulk amorphous state. The extent of order indicated by several techniques (Birefringence, Raman Spectroscopy and Scattering Methods and so on), is limited to at most a few tens of angstroms, approximately that which was found in ordinary low-molecular weight liquids.

Birefringence For stretching at 45° to the polarization directions, the fraction of light transmitted is given by where d represents the thickness, λ 0 represents the wavelength of light in vacuum.

Birefringence, Examples

Anisotrop materials and polarization

where fi is an orientation function of such units given by where  i is the angle that the symmetry axis of the unit makes with respect to the stretching direction, n is the average refractive index, and b1 and b2 are the polarizabilities along and perpendicular to the axes of such units. Perfect Orientation Zero Orientation θ= 0 ̊ θ = 54 ̊

Stress induced birefringence When squeezed or bent the plastic becomes anisotropic and therefore birefringent and bands of color can be seen. The protractor shows colored bands without being deformed because anisotropies arise when the plastic solidifies when manufactured. The colored patterns reveal internal stresses. Place saran wrap between crossed polarizers and stretch along a direction 45° to the polarization axes to show that it becomes birefringent and allows a component of the light to pass.

The stress–optical coefficient (SOC) is a measure of the change in birefringence on stretching a sample under a stress σ For an Elastic Rubber:

Models of Polymer Chains in the Bulk Amorphous State H. Mark and P. J. Flory Random coil model; chains mutually penetrable and of the same dimension as in θ- solvents: P. J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, P. J. Flory, Faraday Discuss. Chem. Soc., 68, 14 (1979).

V. P. Privalko and Y. S. Lipatov Conformation having folded structures with Rg equaling the unperturbed dimension: V. P. Privalko and Yu. S. Lipatov, Makromol. Chem., 175, 641 (1974)

G. S.Y.Yeh Folded-chain fringed-micellar grain model. Contains two elements: grain (ordered) domain of quasi-parallel chains, and intergrain region of randomly packed chains: G. S. Y. Yeh, J. Macromol. Sci. Phys., 6, 451 (1972).

W. Pechhold Meander model, with defective bundle structure, with meander-like folds: W. Pechhold, M. E.T. Hauber, and E. Liska, Kolloid Z. Z. Polym., 251, 818 (1973). (i) W. R. Pechhold and H. P. Grossmann, Faraday Discuss. Chem.Soc., 68, 58 (1979)

Why Multiplicity in Models

A major advantage of the random coil model, interestingly, is its simplicity. By not assuming any particular order, the random coil has become amenable to extensive mathematical development. Thus, detailed theories have been developed including rubber elasticity and viscosity behavior, which predict polymer behavior quite well. By difference, little or no analytical development of the other models has taken place, so few properties can be quantitatively predicted. Until such developments have taken place, their absence alone is a strong driving force for the use of the random coil model. Clearly, the issue of the conformation of polymer chains in the bulk amorphous state is not yet settled; indeed it remains an area of current research. The vast bulk of research to date strongly suggests that the random coil must be at least close to the truth for many polymers of interest. Points such as the extent of local order await further developments.

MACROMOLECULAR DYNAMICS Polymer motion can take two forms: (a) the chain can change its overall conformation, as in relaxation after strain, or (b) it can move relative to its neighbors. Both motions can be considered in terms of self- diffusion (Brownian motion). For high enough temperatures, an Arrhenius temperature dependence is found. Polymer chains find it almost impossible to move “sideways” by simple translation, for such motion is exceedingly slow for long, entangled chains.

The Rouse–Bueche Theory The first molecular theories concerned with polymer chain motion were developed by Rouse (a) and Bueche (b), and modified by Peticolas (c). a. P. E. Rouse, J. Chem. Phys., 21, 1272 (1953). b. F. Bueche, J. Chem. Phys., 22, 1570 (1954). c.W. L. Peticolas, Rubber Chem. Tech., 36, 1422 (1963). This theory begins with the notion that a polymer chain may be considered as a succession of equal submolecules. These submolecules are replaced by a series of beads of mass M connected by springs with the proper Hooke’s force constant.

The Rouse–Bueche Theory (cont.) The restoring force, f, where  x is the displacement and r is the end-to-end distance of the chain or Gaussian segment.

The Rouse–Bueche Theory (cont.) The segments move through a viscous medium (other polymer chains and segments) in which they are immersed. The viscous force on the ith bead is given by where  is the friction factor. Zimm (d) advanced the theory by introducing the concepts of Brownian motion and hydrodynamic shielding into the system. Finally led to relaxation time definition: where  0 is the bulk-melt viscosity, p is a running index, and c is the polymer concentration. d. B. H. Zimm, J. Chem. Phys., 24, 269 (1956).

Polymer Dynamic

The Rouse–Bueche Theory (cont.)  The Rouse–Bueche theory is useful especially below 1% concentration.  However, only poor agreement is obtained on studies of the bulk melt. The theory describes the relaxation of deformed polymer chains, leading to advances in creep and stress relaxation. While it does not speak about the center-of-mass diffusional motions of the polymer chains, the theory is important because it serves as a precursor to the de Gennes reptation theory, described next.