Segmental relaxation in semicrystalline polymers: a mean-field model for the distribution of relaxation times in confined regimes.

The effect of confinement in the segmental relaxation of polymers is considered. On the basis of a thermodynamic model we discuss the emerging relevance of the fast degrees of freedom in stimulating the much slower segmental relaxation, as an effect of the constraints at the walls of the amorphous regions. In the case that confinement is due to the presence of crystalline domains, a quasi-Poissonian distribution of local constraining conditions is derived as a result of thermodynamic equilibrium. This implies that the average free-energy barrier DeltaF for conformational rearrangement is of the same order of the dispersion of the barrier heights, delta(DeltaF) , around DeltaF. As an example, we apply the results to the analysis of the alpha-relaxation as observed by dielectric broad-band spectroscopy in semicrystalline poly(ethylene terephthalate) cold-crystallized from either an isotropic or an oriented glass. It is found that in the latter case the regions of cooperative rearrangement are significantly larger than in the former.

The role of the amorphous phase in the re-crystallization process of cold-crystallized poly(ethylene terephthalate).

The process of re-crystallization in poly(ethylene terephthalate) is studied by means of X-ray diffraction (SAXS and WAXS) and dynamical mechanical thermal analysis. Samples cold-crystallized for 9h at the temperatures T(c) = 100°C and T (c) = 160°C, i.e. in the middle of the alpha relaxation region and close to its upper bound, respectively, are analyzed. During heating from room temperature, a structural rearrangement of the stacks is always found at T (r) approximately T (c) + 20°C. This process is characterized by a decrease of the linear crystallinity, irrespective of T(c); on the other hand, the WAXS crystallinity never increases with T below T(c+30)°C. The lamellar thickness in the low-T(c) sample decreases significantly after the structural transition, whereas in the high-T(c) sample the lamellar thickness remains almost unchanged. In both, high- and low-T(c), the interlamellar thickness increases above T(r). Moreover, the high-T(c) sample shows a lower rate of decrease of the mechanical performance with increasing T as the threshold T(r) is crossed. This result is interpreted in terms of the formation of rigid amorphous domains where the chains are partially oriented. The presence of these domains would determine i) the stabilization of the crystalline lamellae from the thermodynamic point of view and ii) the increase of the elastic modulus of the amorphous interlamellar regions. This idea is discussed by resorting to a phase diagram. An estimation of the chemical-potential increase of the interlamellar amorphous regions, due to the enhancement of the structural constraints hindering segmental mobility, is offered. Finally, previous calculations developed within the framework of the Gaussian chain model (F.J. Baltá Calleja et al., Phys. Rev. B 75, 224201 (2007)) are used here to estimate the degree of chain orientation induced by the structural transition of the stacks.

A mean field analysis of the O-H stretching Raman spectra in methanol/carbon tetrachloride mixtures.

The O-H stretching region of the Raman spectra obtained from methanol/carbon tetrachloride mixtures of different compositions is analyzed. The various components of the spectra associated with methanol molecules with different H-binding states (i.e., non-H-bonded, chain-end, and doubly bonded) are quantitatively related with the alcohol cluster distribution derived by means of a simple lattice model. This comparison allows for the estimate of the mean overall hydrogen bonding energy by means of a best fitting procedure on the Raman data obtained at low-to-moderate alcohol contents; the solvation energy contribution of carbon tetrachloride is then also included. The result (approximately 3 kcal/mol) is found to be in agreement with the estimates from calorimetric and dielectric measurements.

Calculation of the local optical density of states in absorbing and gain media.

The local optical density of states plays a key role in a wide range of phenomena. Near to structures displaying optical absorption or gain, the definition of the photonic local density of states needs to be revised. In this case two operative different definitions can be adopted to characterize photonic structures. The first (ρ(A)(r, ω)) describes the light intensity at a point r when the material system is illuminated isotropically and corresponds to what can be measured by a near-field microscope. The second (ρ(B)(r, ω)) gives a measure of vacuum fluctuations and coincides with ρ(A)(r, ω) in systems with real susceptibility. Scattering calculations in the presence of dielectric and metallic nanostructures show that these two definitions can give rather different results, the difference being proportional to the thermal emission power of the photonic structure. We present a detailed derivation of this result and numerical calculations for nanostructures displaying optical gain. In the presence of amplifying media, ρ(B)(r, ω) displays regions with negative photon densities, thus failing in describing a power signal. In contrast, ρ(A)(r, ω), positive definite, properly describes the near-field optical properties of these structures.

Phenomenological model for the confined dynamics in semicrystalline polymers: the multiple alpha relaxation in cold-crystallized poly(ethylene terephthalate).

The segmental relaxation in poly(ethylene terephthalate), crystallized from either an isotropic or a cold-drawn glass, is investigated by means of dielectric spectroscopy. It is shown that there exist two distinct alpha relaxation modes: a slow one, characterized by a rather wide frequency interval, and a faster, much narrower one. A simple phenomenological model is developed in order to analyze the polarization autocorrelation functions phi(t)'s associated with these relaxation modes. The model is based on the idea that the growth of crystalline domains causes a progressive confinement of the amorphous regions where, eventually, the observed alpha processes take place. The mechanism of confinement is accounted for by applying to the case of constrained density fluctuations, well known concepts introduced by Adam and Gibbs [J. Chem. Phys. 43, 139 (1965)] concerning the relaxation dynamics in liquids close to the glass transition. Randomness on confining conditions is then introduced, leading to the derivation of analytical expressions which are used afterwards to fit the asymptotic behavior of the phi's for long-time tails. It is found that the slow, broad alpha process takes place in regions where the confining effect of crystals is strong, whereas the amorphous domains relaxing via the fast mode are those where the confinement effect of crystals is weak. The analysis of the phi's by means of this model allows us to relate the fitting exponents to the dispersion in the free energy associated with structural rearrangement.

A mean field analysis of the static dielectric behavior of linear lower alcohols.

The static dielectric responses of methanol, ethanol, and 1-propanol up to 1-hexanol are discussed in terms of a stiff-chain lattice model for the alcohol clusters. An analytical expression for the Kirkwood correlation factor gK is derived in terms of the canonical partition function associated to the configurational statistics of any of the dimers building up a chain. This allows for the estimate of the dipole moment mu0 of an alcohol molecule in the liquid phase from the temperature dependence of the dielectric constant. All alcohol species appear to be characterized by a dipole moment larger than in the vapor phase. The Kirkwood correlation factor is found to be an increasing function of the alkyl tail length.

Single-particle dynamics of water molecules confined in a lecithin-based gel.

We present experimental measurements, obtained by a quasielastic neutron scattering experiment, of the self-diffusion coefficient of water confined in the dense structure of lecithin-based gels. The inelastic neutron scattering (INS) technique was also used to monitor the dynamic state of water molecules involved in the gel structure. It is shown that, at least in highly concentrated systems, the diffusional properties of water can be related with the growth process of worm-like aggregates. However, an interpretation of our data consistent with a number of experimental results in the literature and with INS indications requires the adoption of a model in which the gel structure is better described in terms of percolating aggregates rather than the usually described polymer-like entangled (not interconnected) network. In such a way, we are pointing out the existence of an interpretative controversy calling for further investigation to be disentangled. The source of the inconsistencies is found in the commonly accepted basic assumption of the existence of a simple scaling law, relating the average micellar length to the concentration.