Lattice theory of polymer solutions with endgroup effects

Incipient microphase separation in short chain perfluoropolyether-block-poly(ethylene oxide) copolymers

Incipient microphase separation is observed by wide angle X-ray scattering (WAXS) in short chain multiblock copolymers consisting of perfluoropolyether (PFPE) and poly(ethylene oxide) (PEO) segments. Two PFPE-PEO block copolymers were studied; one with dihydroxyl end groups and one with dimethyl carbonate end groups. Despite having a low degree of polymerization (N ∼ 10), these materials exhibited significant scattering intensity, due to disordered concentration fluctuations between their PFPE-rich and PEO-rich domains. The disordered scattering intensity was fit to a model based on a multicomponent random phase approximation to determine the value of the interaction parameter, χ, and the radius of gyration, R_g. Over the temperature range 30-90 °C, the values of χ were determined to be very large (∼2-2.5), indicating a high degree of immiscibility between the PFPE and PEO blocks. In PFPE-PEO, due to the large electron density contrast between the fluorinated and non-fluorinated block and the high value of χ, disordered scattering was detected at intermediate scattering angles, (q ∼ 2 nm^-1) for relatively small polymer chains. Our ability to detect concentration fluctuations was enabled by both a relatively large value of χ and significant scattering contrast.

Significance of the free volume for metastability, spinodals, and the glassy state: an exact calculation in polymers

A lattice model of semiflexible linear chains (with equilibrium polydispersity) containing free volume is solved exactly on a Husimi cactus. A metastable liquid (ML) is discovered to exist only at low temperatures and is distinct (and may be disjoint) from the supercooled liquid (SCL) that exists only at high temperatures. The free volume plays a significant role in that the spinodals of the ML and SCL merge and then disappear as the free volume is reduced. The Kauzmann temperature T(K) occurs in the ML without any singularity. At T(MC)>T(K), the ML specific heat has a peak. For infinitely long polymers, the peak height diverges and the free volume vanishes at T(MC), resulting in a continuous liquid-liquid transition. Contrary to the conventional wisdom, both T(K) and T(MC) occur in the ML and not in the SCL.

Importance of interactions for free-volume and end-group effects in polymers: an equilibrium lattice investigation

We consider a lattice model of a polymer system in which we distinguish between the end (E) and the middle (M) groups. The free volume is represented as a "hole" or "void" (0), which constitutes a separate species in addition to the two "species" M and E. There are three different exchange interaction energies, and correspondingly three Boltzmann weights w(ij), i not equal j=0,E,M between different species. We define the free volume associated with the species j=M or E, as the average number of voids next to j. Using a recently developed equilibrium lattice theory, we calculate the free volume v(E) and v(M) associated with an end group and a middle group, respectively, and investigate the effects of interactions among them. Our calculations show that v(E) and v(M) are intricate functions of w(ij), the pressure and the molecular weight, and that their difference can change sign under certain conditions. These conditions are elucidated. We demonstrate that when the end group is chemically dissimilar from the middle group, the middle group may have more free volume than the end group. We find that the conditions that favor a middle group having more free volume over an end group are w(E0)<1, w(M0)<1, and w(ME)>1. The effect of pressure and molecular weight can be of either type and appears to be dependent on the interactions.