Jacques Rault

Origin of the Vogel-Fulcher-Tammann law in glass-forming materials : the α-β bifurcation

Abstract All glass-forming materials, simple liquids and polymers, show the α–β bifurcation; above a cross-over temperature T ∗ , the glass α transition and the β secondary transition merge together. Below this bifurcation temperature the relaxation times τ and τβ of the cooperative (α) and non-cooperative (β) movements verify, respectively, the Vogel–Fulcher–Tammann (VFT) and Arrhenius laws. This temperature is of the order of 1.3Tg and in crystallizable materials T ∗ is found equal to the melting temperature; the frequency of the α and β motions at that temperature is of the order of 107–109 s−1 depending on the nature of the material. One shows that in this domain, Tg T ∗ and T0 increase linearly with pressure, then n at constant temperature is also a decreasing function of pressure; 1/n can be considered as the number of individual units (of β type) participating to the α motion, therefore the relaxation time τ verifies the power law: τ=τ0(τβ/τ0)1/n between T0 and T ∗ , τ0 being the phonon frequency and τβ the frequency of the β movements; this equation is not very different from the Ngai relation concerning the relaxation time of complex systems. Combining both relations n∼ and τ∼(τβ)1/n, one finds that the relaxation time is given by the relation: log τ/τ 0 ≈A/T(T−T 0 ) , with A=Eβ(T*−T0)/2.3R; Eβ being the activation energy of the β motions. This law, called modified VFT law, fits the experimental results better than the other phenomenological or theoretical models. This law, without adjustable parameter, is compared to the VFT law obtained if one assumes that the cooperativity parameter n varies as −1/T. The relationships between the fragility index, capacity jump and the ng value at Tg are discussed.

Remarks on the α and β transitions in swollen polyamides

Abstract The glass transition (α) and secondary transition (β) are compared in various aliphatic polyamides swollen by water, alcohol and acid. For all these polymer-solvent systems, the evolution of the temperature Tα with the equilibrium sorption ratio presents two regimes. In the low-concentration regime, the dependence of Tα on the number n of absorbed solvent molecules per accessible amide group follows a master curve independent of the nature of the system. No master curve is, however, observed for the β transition. In the second regime, above a critical ratio n∗ dependent on the nature of both the solvent and the polymer, Tα levels off, and the maximum concentration of absorbed solvent is proportional to n∗. These effects are explained in terms of solvent clustering around the amide groups.

Structural–dynamical relationship in silica PEG hybrid gels

Hybrid organic–inorganic materials have been prepared from mixtures of tetraethoxysilane and poly(ethylene glycol) (PEG) of low molecular mass. These materials are diphasic systems in which silica aggregates, controlling the mechanical properties, are wrapped around by the polymer phase. Strong correlations between the synthesis scheme, the structure and the properties of these materials are evidenced. Solid-state29Si NMR points out the change of the silica morphology with the nature of the catalyst (acidic, [HCl] or nucleophilic, [NH4F]). In addition, these changes induce strong variations of the thermal properties of the PEG phase. The structural and dynamical inhomogeneities of the PEG are analyzed using 13C NMR and EPR spectroscopies. Near the SiO2 surfaces, hydrogen bonding hinders the motion of the PEG chains, while the bulk of the polymeric phase possesses the same properties as the polymer melt. Thermal analyses (DSC) disclose the difference between materials prepared with the various catalysts which are related to the degree of interpenetration between the two phases.

Yielding in amorphous and semi-crystalline polymers: the compensation law

Abstract The linear variations of the yield stress of amorphous and semi-crystalline polymers with temperature and hydrostatic pressure (Coulomb–Mohr criteria) is explained in the framework of the cooperative process, when thermally activated, taking into account: (a) the compensation law, the compensation temperature T * being the glass temperature T g in amorphous polymers and the secondary transition temperature T α c in semi-crystalline polymers; (b) the variation of these mobility temperatures, T g and T α c , with hydrostatic pressure.

Crystallization of polymers

Abstract Kinetic theories of crystallization of polymers do not apply to high supercooling. The thickness of the crystalline lamellae becomes independent of the crystallization temperature and is a characteristic parameter of the polymer. We relate this limiting thickness to the flexibility of the polymer chain in the pure liquid or in solution before crystallization. The folded chain in the crystalline state is analogous to the coiled chain before crystallization. Flexibility and limiting thickness depend in a similar way on the solvent, defect concentration in the polymer chains, pressure, pH, and salt concentration in case of crystallization of polyelectrolytes. Folded chains appear also in oligomer crystals when the oligomers have a coiled shape in the liquid state. The limiting fold period of crystalline polymers and oligomers is found to be an order of magnitude greater than the persistence length of the Gaussian chain in the liquid state.

Mobility and relaxation of amorphous chains in drawn polypropylene: 2H-NMR study

Abstract Mobility and orientation of amorphous chains in cold drawn films of isotactic polypropylene (PP) are studied by 2 H-NMR as a function of the annealing temperature. It is shown that the deformation is not affine. The relaxation of amorphous chains in materials annealed with free and clamped ends appears respectively at T *≈ T g +50°C and at T α c ≈80°C. Above these transition temperatures, corresponding to the onset of the chain mobility in the amorphous and crystalline states, the orientation of amorphous chains decreases linearly with the temperature. These reports show that the 2 H-NMR technique provides important information on the plastic deformation of semi-crystalline polymers.

Mobility range in hybrid materials

The dynamical properties of hybrid materials obtained from mixtures of silicon alkoxides and polyethers are studied. Different techniques are used to analyze the mobility of the different parts of the material: thermal analysis (DSC, DTMA) and NMR to probe the collective motion modes and EPR to probe the local scale. The motions are dependent on the organic ratio in the blend and the covalent grafting between the two phases. Some structural models of these blends are proposed.

Remarks on the Kohlrausch exponent and the Vogel-Fulcher-Tamann law in glass-forming materials

Abstract In complex systems like polymer glass-forming materials the relaxation is well described by the Kohlrausch equation ϕ(t)∼ exp −(t/τ) n . The exponent n is interpreted as the inverse of the number of simple motions (of β type) which must occur simultaneously to give a cooperative motion (of α type), then a coupling relation between the relaxation time τ and the Kauhlrausch exponent n is similar to the Ngai relation. It is shown that the scaling law n = T and n ∼−1/ T leads to the VFT law and to a modified VFT law without adjustable parameter, valid between the Kauzmann temperature and the bifurcation temperature T ∗ where the α and β relaxations merge together.

SAXS studies of blends of high- and low-density polyethylene

Abstract It is shown that in blends of PE having different melting temperatures the morphology depends drastically on the cooling rate. In these heterogeneous PE, the correlation relationship L = r between the long period L of the solid state and the dimension of the coils r in the liquid state is observed only in rapidly quenched materials. In slowcooled materials the SAXS spectra are interpreted in terms of segregation of two types of PE, on a scale of the order of the dimension of the coils, the arrangement of the crystalline lamellae being paracrystalline and statistical.

Influence of the crosslinks density on the crystallization of water in PAA gels

Abstract It is shown that confinement of water in crosslinked PAA gels cannot be compared to that of water in solid porous materials. In crosslinked gels the ice melting temperature and the amount of non-crystallizable water is explained by the classical variations of the glass temperature and the ice dissolution temperature with the concentration of water.