Polymeric Alloys: Model Materials for the Understanding of the Statistical Thermodynamics of Mixtures

Abstract

Polymeric materials find industrial applications that are comparable to those of metals and ceramics.¹ In addition to the great variability via the synthesis of various monomers and the choice of the degree of polymerization (N), alloying of polymers finds increasing attention for combining favorable materials properties.^1,2 But polymeric (binary) alloys (A,B) of flexible polymers with chain lengths N_A, N_B are also most interesting for testing theoretical concepts: changing N_A, N_B one controls the entropy of mixing, keeping intermolecular forces invariant. Variation of these control parameters thus allows stringent tests of the theories on miscibility, unmixing etc. Furthermore, the large size of the random-walklike polymer coils (gyration radius $\textup{R}_\textup{{gyr}} \approx \textup{a} \sqrt{\textup{N}/6}$ when a is the size of an effective statistical segment³) yields several simplifying features: (i) R_gyr enters as a prefactor in the correlation length ξ of concentration fluctuations, the width w of interfaces between coexisting phases near the critical point, the wavelength λ_max of maximum growth during spinodal decomposition in unstable mixtures,^4,5 etc. This larger length scale of cooperative phenomena allows the application of experimental techniques that would work for metallic alloys only in the immediate vicinity of the critical point.^4–7 (ii) Large polymer coils are objects that also move only very slowly, and thus early stages of processes such as spinodal decomposition,^4–6 dynamics of the formation of enrichment layers at surfaces^7–9, etc. become easily accessible over a wide temperature range. (iii) Large polymer coils are rather loose, floppy objects (the monomer density ρ = N/V inside the volume taken by a coil, V ∝ R_gyr ∝ a³N^3/2 scales as ρ ∝ a^-3N^-1/2 ). In order to have a melt density of order a^-3, N^1/2 coils interpenetrate each other: in other words, every coil interacts with³ N^1/2 “neighbors”.