ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
We present a molecular theory of the phenomena of single-chain collapse and phase separation into a polymer-rich and a polymer-poor phase, which occur in polymer solutions below the aitch-theta temperature. The theory extends the Fourier self-consistent approach of Allegra and Ganazzoli from the study of single-chain properties to that of an ensemble of interacting chains. We derive an expression for the free energy of a "Gaussian cluster'' made up of ν chains of length N (ν=1,2,3,...; N(very-much-greater-than)1). In the limit ν→∞ this yields a mean-field expression for the solution free energy per chain as a function of the reduced temperature τ=(T−aitch-theta)/T, the polymer volume fraction cursive-phi and the mean-square radius of gyration of the chains. From this we calculate the chain dimensions in solution and several thermodynamic properties, such as the osmotic pressure and the polymer–solvent phase diagram. We find that the contraction ratio of the chain radius of gyration is a single-valued function of (τB+K1Fcursive-phi)(square root of)N, where B and K1 specify the strength of the two- and three-body interactions and F is a polymer-dependent positive constant. We provide numerical evidence for a possible universality of the binodal line for different polymer-solvent systems; the spinodals do not share this characteristic of universality. © 1996 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.470750
