# Macroscopic Volume and Free Volume of Polymer Blends and Pressure-densified Polymers

[Doktorsavhandling]

The macroscopic volume *V* as a function of pressure *P* and temperature *T* is obtained from *PVT* measurements. *PVT* data is sensitive to the state of polymers and changes therein. Moreover, *PVT* data gives access to the free-volume fraction. In polymers, free volume is the void space that is available for segmental motions and that plays a key role in a range of mechanical and physical properties. Thus, both a qualitative and quantitative understanding of free volume is essential for understanding and predicting polymer properties. The free volume in the equilibrium melt as well as in the glassy state can be studied *indirectly* as a free-volume fraction (*h *= 1 - y ) determined from PVT data and the Simha-Somcynsky equation-of-state (EOS) theory. A *direct* measure of free volume is the mean free-volume cavity size that is uniquely determined from positron annihilation lifetime spectroscopy (PALS).

The aim of this doctoral thesis was to investigate the relation between the macroscopic *PVT* properties and the free-volume quantities from EOS analysis and from PALS in polymers and polymer blends. The effects of blend composition and the thermomechanical history on the free-volume quantities were studied. Possible relations between mechanical properties and free volume were explored, and their theoretical and practical implications were discussed.

An EOS analysis of the *PVT* properties of melt-miscible blends of poly(methyl methacrylate) (PMMA) and poly(ethylene oxide) (PEO) revealed a mainly negative volume of mixing and a free-volume dilation in the equilibrium melt. The temperature and pressure coefficients of the free-volume fraction correlated with the blends' thermal expansivities and compressibilities, respectively. A combined study of one of the blends' time-dependent specific volume and free volume showed that the structural relaxations share the same time scale and that they can be attributed to upper-critical-solution (UCST) phase separation prior to crystallization below the glass transition temperature. Relatively small macroscopic volume changes in isotropic pressure-densified amorphous polymer glasses resulted in large changes in their free-volume fraction (*PVT*-EOS analysis) as well as in their free-volume hole size (PALS). A unique relation between the latter and the former could be established for every polymer. On the other hand, a *universal* relation between the bulk modulus and the free-volume hole size could be established for all the pressure-densified glasses. A similar universal relation was established in the equilibrium melt and is not restricted to polymers. Both relations allow the prediction of *PVT* data from a set of a density and a PALS measurement at two different temperatures either in the glassy state or in the melt. Predictions of PALS data from PVT data alone are also possible. Moreover, the correlation constant that can relate free-volume fractions from *PVT*-EOS analysis to those from PALS is not general but unique for every polymer. A much improved correlation between the two free-volume fractions was obtained by *omitting* the *ortho*-positronium intensity. From a Raman quasielastic scattering study on densified PMMA glasses it could be concluded that the damping of the Boson peak vibrations cannot be explained on the basis of PALS free-volume quantities.

**Nyckelord: **PVT, pressure dilatometry, bulk modulus, thermal expansivity, compressibility, positron annihilation, positronium, polymers, pressure-densified polymers, polymer blends, copolymers, Tait equation of state, free-volume theories, free volume, cavity size, freezing fractions, free-volume distributions, Lorentz-Lorenz equation, refractive index, dynamic-mechanical analysis, loss tangent, phase separation, entropy of melting, Avrami equation

Denna post skapades 2006-08-28. Senast ändrad 2013-09-25.

CPL Pubid: 824