Some remarks on the relation between free-volume fractions and ortho-positronium lifetimes in amorphous polymers

Unique information about the properties of free-volume sites in polymers is gained from Positron Annihilation Lifetime (PAL) measurements. After calibration with data from other techniques the method may be used to determine free-volume fractions. From pressure–volume–temperature (PVT) and PAL (ortho-Ps lifetime τ₃) data, measured on identical amorphous poly(methyl methacrylate) (PMMA) samples with controlled thermal histories, we find a linear relationship between free-volume fractions, derived from PVT measurements, the Simha–Somcynsky equation-of-state theory and the mean subnanometer free-volume size both below and above the glass transition temperature.     

Can a newly developed AMOC technique be applied to determine the para-positronium lifetime?

It is investigated whether a new method to analyze the short lifetime component by using the positron age-momentum correlation technique (AMOC) can be applied to determine the lifetime of para-positronium in some insulation materials. The results indicate that the method is not applicable to the case.     

Positronium lifetime in polymers

A model describing the relationship between the orthopositronium lifetime and the volume of a void, located in a synthetic zeolite, is analyzed. Our idea, which allows us to take into account the effects of temperature, comprises the introduction of a non-Hermitian term in the Hamiltonian, which accounts for the annihilation of the orthopositronium. The predictions of the present model are also confronted against an already known experimental result.     

Structural relaxation in amorphous polymers

A theoretical calculation based on the general solution of a multi-ordering-parameter model is found to be in good agreement with the measured volume relaxation of poly(vinyl acetate). This suggests that a limiting equilibrium state is eventually reached, which may resolve the disagreement between the behavior of the model and experiments discussed in the literature. In addition, the asymmetric character of the isothermal response and memory effect is satisfactorily calculated from the same basic equation. The distribution function and the temperature-structure dependence of relaxation times are discussed.     

Depolarization thermocurrents in amorphous polymers

The depolarization thermocurrent (DTC) method gives the dependence of the dielectric relaxation time on temperature. It has been used for investigations of relaxations obeying an Arrhenius-like law in crystalline polymers. The analysis of this method shows it is possible to study mechanisms described by the Williams-Landel-Ferry (WLF) equation. The critical temperature appearing in the free-volume theory of Cohen and Turnbull and also in the statistical thermodynamic theory of Adam and Gibbs can then be measured with good accuracy. The thermal coefficient of expansion of the free-volume and the WLF coefficient for any reference temperature can also be obtained. Since analysis of the experimental DTC spectrum is particularly simple, this method seems to be a very useful tool for examination of relaxation transitions in amorphous polymers. As an example, results obtained for poly(methyl methacrylate) are presented; they are consistent with published data.     

Orientation of amorphous polymers

Orientation of amorphous polymers stretched at a temperature above their glass-transition temperature, is involved in thermoforming processing. The molecular processes controlling the orientation and chain relaxation of polymers have been investigated by infrared dichroism in a large series of materials: polystyrene, polymethylmethacrylate of various tacticity and its copolymers with styrene and acrylonitrile. Polystyrene with hydrogenated and deuterated blocks leads to information on the behavior of each block (central part, chain ends) and allows a quantitative comparison with the Doi-Edwards model for chain relaxation. In order to analyse the effect of polydispersity, blends of hydrogenated and deuerated polystyrene chains with various molecular weights have been studied. Short chains with molecular weights smaller than the molecular weight between entanglements, enhance the relaxation of long chains. Furthermore an anisotropic orientational coupling effect exists between a chain segment and its oriented surrounding. By comparing the orientation of polymers with different chemical structures, it results that they behave differently under temperature conditions where T - T_g = const, but they undergo identical relaxations when the experiments are performed at temperatures chosen in such a way that the monomer friction coefficients are identical. In copolymers of styrene and methylmethacrylate, the two monomer units have different orientations due to local conformational constraints. This effect also accounts for the difference observed between an alternated and a random copolymer.     

Density fluctuations in amorphous and semicrystalline polymers

Summary The small-angle scattering of amorphous and semicrystalline polymers contains an intensity component due to density fluctuations within the crystalline and amorphous domains.For amorphous polymers, the density fluctuations aboveT _g correspond to the theoretical value for a fluid system in thermodynamic equilibrium. BelowT _g , a temperature dependence proportional to T is observed over a range of about 50°. At lower temperatures, a linear relationship with a smaller slope has been found which extrapolates to a non-zero value at 0 °K. This value corresponds to the frozen-in disorder, the slope at low temperatures is related to thermal vibrations and can be evaluated in terms of photon-phonon scattering.Semicrystalline polymers show a temperature dependence of the density fluctuation similar to that of the amorphous polymers. At constant temperature the density fluctuations vary linearly with crystallinity.Natural rubber shows an increase of the density fluctuations with increasing cross-linking densities from which information on the density changes in the vicinity of a cross-link and on the statistics of the distribution of cross-linking can be obtained.

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Zusammenfassung Die Kleinwinkelstreuung amorpher und teilkristalliner Polymere besitzt eine Intensitätskomponente, die von Dichtefluktuationen innerhalb der kristallinen und amorphen Bezirke herrührt. Für amorphe Polymere entspricht die Dichtefluktuation oberhalb vonT _g dem theoretischen Wert für ein fluides System im thermodynamischen Gleichgewicht. UnterhalbT _g wird eine Temperaturabhängigkeit proportional zuT über einen Bereich von etwa 50° beobachtet. Bei tieferen Temperaturen wird eine lineare Beziehung mit einer geringeren Steigung gefunden, welche zu einem endlichen Wert bei 0 °K extrapoliert werden kann. Dieser Wert bezieht sich auf die eingefrorene Fehlordnung, die Steigung bei tiefen Temperaturen ist auf thermische Schwingungen zurückzuführen und kann als Photon-Phonon-Streuung ausgewertet werden.Teilkristalline Polymere zeigen eine Temperaturabhängigkeit der Dichtefluktuation, die der von amorphen Polymeren ähnlich ist. Bei konstanter Temperatur ändert sich die Dichtefluktuation linear mit der Kristallinität.Naturkautschuk zeigt eine mit der Vernetzungsdichte ansteigende Dichtefluktuation, aus der man Information über die Dichteänderung in der Umgebung eines Netzpunktes und die Statistik der Netzpunktverteilung erhalten kann.

     

PVT of amorphous and crystalline polymers and their nanocomposites

The Pressure-Volume-Temperature (PVT) of polystyrene (PS), polyamide-6 (PA-6) and their clay-containing polymeric nanocomposites (CPNC) were determined at T = 300-600 K and P = 0.1-190 MPa, thus in the molten, glassy and semicrystalline phase. The melt and glass behavior was interpreted following the Simha-Somcynsky (S-S) cell-hole free volume theory while that of the semicrystalline phase using S-S and the Midha-Nanda-Simha-Jain (MNSJ) cell theory describing crystalline quantum interactions. The theoretical analysis yielded two sets of the interaction parameters, one from the S-S and the other from the MNSJ model. The derivative properties: the compressibility, κ, and thermal expansion coefficient, α, were computed as functions of T, P and clay content, w. These functions, crossing several transition regions, were significantly different for the amorphous PS than for the semicrystalline PA-6. The isobaric PS plots of κ and α vs. T detected secondary transitions at T_β/T_g ≈ 0.9 ± 0.1 and at T_c/T_g = 1.2 ± 0.1. Addition of clay severely affected the vitreous phase (physical aging). In PA-6 systems the behavior was distinctly different than in PS, viz. κ = κ(T) followed a similar function across the melting zone, while α = α(T) dependencies were dramatically different for the solid and molten phase. The theoretical functions in reduced variables provided good basis for explanation of the observed dependencies.     

Positron lifetime spectroscopy in ordered nanoporous polymers

Positron annihilation lifetime spectroscopy (PALS) is a common technique used to characterize the porosity of polymers. Here, we expand its use to the study of ordered nanoporous polymer monoliths. Polystyrene (PS) monoliths with aligned cylindrical pores ranging in diameters from 15 to 35 nm were examined. Such large pores push the boundaries of the PALS technique. To achieve robust measurement, our system used larger detectors than those typically used for monolithic polymer samples. This was done to improve data rates while sacrificing timing resolution. Pore sizes determined using PALS were consistent with measurements made using small angle x‐ray scattering. In addition, PALS was able to detect the collapse of the pores when the monolithic sample was heated above the T_g of PS. Because PALS measurements are not sensitive to the nature of the order within the structure nor are they, sensitive to the open or closed nature of the pores this technique could be expanded to a variety of other sample types. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 1157–1161     

Solvent diffusion in amorphous glassy polymers

In this article, a mathematical model is proposed for predicting solvent self‐diffusion coefficients in amorphous glassy polymers based on free volume theory. The basis of this new model involves consideration of the plasticization effects induced by small molecular solvents to correctly estimate the hole‐free volume variation above and below the glass‐transition temperature. Solvent mutual‐diffusion coefficients are calculated using free volume parameters determined as in the original theory. Only one parameter, which can be predicted by thermodynamic theory, is introduced to express the plasticization effect. Thus, this model permits the prediction of diffusion coefficients without adjustable parameters. Comparison of the values calculated by this new model with the present experimental data, including benzene, toluene, ethyl benzene, methyl acetate, and methyl ethyl ketone (MEK) in polystyrene (PS) and poly(methyl methacrylate) (PMMA), has been performed, and the results show good agreement between the predicted and measured values. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 846–856, 2000     

Miscibility of crystalline and amorphous polymers: Poly-ethylene/polyisobutylene blends

Blends were prepared from a linear low density polyethylene and a polyisobutylene in the entire composition range. Flory-Huggins interaction parameters were determined from DMTA and DSC measurements. The usual technique had to be modified in the case of DSC data, since the T_g of PE cannot be determined by this technique. The two methods yielded identical results and indicated good interaction of the components, which was supported also by a SEM study and the mechanical properties of the blends.     

Photoresponsive liquid crystalline and amorphous polymers

Isomerization processes of azobenzene dyes dissolved in a glassy polymeric matrix or attached in glassy amorphous or liquid crystalline polymers to the backbone as side groups are induced by light. The isomerization process, in turn, causes the dye to reorient provided that polarized light is used: the long axis of the dye is oriented perpendicular to the polarization direction in the stationary case. Such a reorientation gives rise to strong modifications of the optical properties. This contribution is concerned with the analysis of the correlation between the nature of the azobenzene dyes, the isomerization, reorientation and modulations discussed above and with possible applications in the optical holographic storage. Considered are, in particular, dye/matrix combinations giving rise to nonlinear holographic responses, two photon holography, transient holographic modes applicable for holographic displays and the optical switching of other than optical properties.     

Brillouin scattering and hypersonic relaxation in amorphous polymers

Mechanical relaxation at hypersonic frequencies is measured using Brillouin spectroscopy for polyisobutylene, atactic polypropylene, polydimethyl siloxane, and polyvinyl acetate. The temperatures of maximum loss determined in the gigahertz range are compared to the published transitions maps for the above polymers. It is found that the hypersonic relaxation data fall on an extrapolation of the secondary main chain glass–rubber relaxation line above the region where the primary and secondary lines merge.     

Meander model of amorphous polymers

Assuming bundles (of shortrange ordered macromolecules, folding back and forth statistically), their equilibrium superstructure and diameter are described on the basis of cluster-entropy-hypothesis (CEH). As primary blocks in the bulk polymer and in thin films coupled meander cubes are most probable, which are linked via their cube diagonals serving as axis of statistical rotation and aggregate to coarse grains. Magnetic birefringence, SANS and elctronmicroscopy are used as further methods to determine the cube side length. Applying the same concept to myosin-, collagen-, and elastin-aggregates, these can be interpreted as equilibrium meander fibrils, additionally stabilized by specific interactions and by the length of the molecules.     

Ultimate toughness of amorphous polymers

The deformation and toughness of amorphous glassy polymers is discussed in terms of both the molecular network structure and the microscopic structure at length scales of 50–300 nm. Two model systems were used: polystyrene-poly(2,6-dimethyl-1,4-phenylene ether) blends (PS-PPE; where PS possesses a low entanglement density and PPE a relatively high entanglement density) and epoxides based on diglycidyl ether of bisphenol A (DGEBA) with crosslink densities comparable with up to values much higher than the thermoplastic model system. The microscopic structure was controlled by the addition of different amounts of non-adhering core-shell-rubber particles. Toughness is mainly determined by the maximum macroscopic draw ratio since the yield stress of most polymers approximately is identical (50–80 MPa). It is shown that the theoretical maximum draw ratio, derived from the maximum (entanglement or crosslink) network deformation, is obtained macroscopically when the characteristic length scale of the microstructure of the material is below a certain dimension; i.e. the critical matrix ligament thickness between added non-adhering rubbery particles (‘holes’). The value of the critical matrix ligament thickness (ID_c) uniquely depends on the molecular structure: at an increasing network density, ID_c increases independent of the nature of the network structure (entanglements or crosslinks). A simple model is presented based on an energy criterion to account for the phenomenon of a critical ligament thickness and to describe its strain-rate and temperature dependency.     

Calculation of rotational barriers in amorphous polymers

The Monte Carlo method was used for generation of amorphous polyethylene configurations on a diamond lattice. Chain building was performed on the tetrahedral lattice of edges 36, 62 and 43 Å with periodic boundary conditions imposed.32 chains were generated, each with a length of 100 CH₂-groups (resulting density = 0.81 g·cm⁻³). Small spherical volumes with a radius of 10 Å were chosen at random from the total volume for the calculation of rotational barriers. The rotating bond was chosen to be close to the center of this sphere. We employed the method of molecular mechanics in order to calculate the rotational barriers. The calculation was made for 578 rotating bonds and the obtained distribution of rotational barriers is approximated by the corresponding Γ-distribution.     

Modelling of solid polymers in chemical detail - gases in amorphous polymers

The diffusion of gases in dense polymers, above and below the glass-transition temperature, is described with a new Transition State Theory model that is based on the concept that the dynamics of small molecules dissolved in dense polymers is separated from the structural relaxation of the dense polymers. The model is used to study the dynamics of rare gases dissolved in atomistic micro-structures of four polymers at 300 K: poly(dimethylsiloxane), poly(isobutylene), atactic poly(vinylchloride) and the polycarbonate of 4,4′-isopropylidenediphenol (bisphenol-A). Short-time-scale MD runs (5 ps) are used to characterize the elastic thermal motion of the host matrix; this information on mobility is then used for a stochastic simulation of solute dynamics up to ca. 1ms. All dissolved molecules show similar behavior by displaying three time regimes: a short-time, high-mobility domain, an intermediate time domain of anomalous diffusion, and a diffusive regime at long times. From the long-time data diffusion coefficients are estimated; comparison with experimental data results in good agreement.