Photon correlation spectroscopy of polymers in the glassy state

Photon correlation spectroscopy has proven to be a very useful technique for studying slowly relaxing density and optical anisotropy fluctuations in bulk polymers near the glass transition. When some of the fluctuations achieve relaxation times much longer than the typical averaging time for the intensity autocorrelation function (10⁴ s), the result must be treated in the partially heterodyned limit. Also, when the sample is near the glass transition but not at equilibrium the correlation function is not stationary in time because the system is relaxing as a whole toward the equilibrium state. The above effects are discussed theoretically and demonstrated experimentally in polystyrene as a function of temperature and pressure. Light scattering with coherent excitation also fluctuates in space as well as in time (as shown in the accompanying paper). The consequences of this effect are discussed. When most of the intensity is associated with fluctuations whose relaxation times are very long in polystyrene, there is still a broad relaxation function evident. This is characteristic of a secondary relaxation process.     

The thermoelastic effect in glassy polymers

The thermoelastic effect has been measured in compression on four glassy polymers; namely, polystyrene, poly(methyl methacrylate), polycarbonate, and epoxy resin. Quantitative results have been obtained for the first time on three of these polymers. It has been shown that by paying attention to specimen geometry and instrumentation results can be obtained to a high degree of accuracy (better than ±1.5% on a given set of measurements). The polymers are shown to obey the classical Thompson equation for thermoelasticity in solids over the temperature range studied (ca. 220–350°K). By inference such materials can be expected to behave classically in general. The results have been used, as first suggested by Trainor and Haward, to obtain values for the linear thermal expansion coefficient and the values so obtained are shown to be in excellent agreement, in general, with literature values obtained by more conventional methods. Results are given for a range of stress from 5 MN m^?2 to between 25 and 50 MN m^?2 according to ambient temperature. The method affords a measurement of parameters, in particular, linear thermal expansion coefficient. Values of specific heat for the four plastics have been measured by differential scanning calorimetry and the results compared with published data.     

Theory of the local mode relaxation in the glassy state of polymers

The local modes refer to vibrational motions of the main chain in the glassy state which are thermally excited with a relatively large amplitude and are consequently strongly damped into relaxational motions by the intermolecular viscous force. This paper describes a theory of strengths of the dynamic mechanical and dielectric local mode relaxations, in the latter of which the correlation of dipole arrangement along the main chain is considered. The results are compared with the observed strength and its dependence on temperature and pressure, in particular for the dielectric β relaxation of poly(vinyl chloride). Satisfactory agreement is obtained between theory and experiment.     

Diffusion in glassy polymers

Two versions of the free‐volume theory of diffusion are compared by considering differences in the predictions for the activation energy for the diffusion process. A number of data‐theory comparisons for free‐volume theory are discussed and evaluated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 785–788, 2003     

Dynamic heterogeneities in glassy polymers

The photoinduced isomerization of molecules incorporated in a glassy polymer matrix exhibits a wide spectrum of quantum yields. The source of the spectrum is matrix heterogeneities. The kinetics of the photoisomerization of 1-naphthyl-p-azomethoxybenzene in poly(ethyl methacrylate) and poly(n-butyl methacrylate) films is first used to study the rearrangement of the environments of photochromic molecules. The nonequilibrium distribution of cis molecules over the spectrum is obtained via conversion of trans molecules with the highest quantum yield into the cis form with the use of 405-nm light. The kinetics of attainment of the photostationary ratio for concentrations of cis and trans isomers under the action of light with a wavelength of 546 nm is studied through variation in the pause between the conversion of molecules into the cis form and the beginning of the studied process. It is shown that reversible changes in the structure of polymer matrices occur at a high rate at temperatures much lower than the glasstransition temperature.     

On some mechanical effects in glassy polymers attributed to chain entanglements

The important role of the entanglements in the deformation of high-molecular-weight glassy polymers is demonstrated by two phenomena: the build-up of material resistance in polymethylmethacrylate after chain interpenetration and the intrinsic crazing of polycarbonate which is observed when the entanglement network reaches its limits of extension.Dedicated to Prof. Dr. F. H. Müller.     

Hydrogen bonding effects in the glassy state of random copolyamides

The thermal behavior of random copolyamides which are used as model polymers with hydrogen bonds has been investigated by differential scanning calorimetry (DSC), x-ray diffraction, and infrared spectroscopy. The quenched copolyamides have only halo patterns in their x-ray diffraction photographs. A random copolymer of nylons 6, 66, and 610 (in a composition ratio of 3: 4: 3) was found to have 20% of unbonded amide groups immediately after quenching. When the sample was kept at the glass transition temperature (20°C), no change in x-ray diffraction was observed after the treatment. The free amide band in the infrared spectrum at 3450 cm^-1, however, was decreased in intensity by keeping the sample at the glass transition temperature. The transition peak height observed in a DSC curve also increased in the same experiment. Large glass transition peaks were found in DSC curves after annealing of the random copolyamides in the vicinity of the glass transition temperature. It is probable that the free amide groups in the amorphous chains were rearranged and formed new hydrogen bonds during the heat treatment at the glass transition temperature. Packing and restriction of the amorphous chains due to the increase in hydrogen bonding seemed to increase the height of the transition peak in a DSC curve. It is inferred from the above results that in the case of the random copolyamide, structures corresponding to a given enthalpy of the glassy state can be related to the number of hydrogen bonds.     

The influence of surface phenomena on molecular mobility in glassy polymers

Literature data on molecular mobility in glassy polymers have been analyzed. It has been shown that, in the temperature range corresponding to the glassy state of a polymer, a large-scale (segmental) molecular motion is possible, with this motion being responsible for the physical (thermal) aging of the polymer. Heating of an aged polymer restores its initial state, and the aging process begins again (effect of “rejuvenation”). At the same time, aging processes may be initiated by a mechanical action on a glassy polymer. It is sufficient to subject an aged polymer to a mechanical action to transfer it to a state characteristic of a polymer heated above the glass-transition temperature. It should be noted that deformation of a glassy polymer is nonuniform over its volume and occurs in local zones (shear bands and/or crazes). It is of importance that these zones contain an oriented fibrillized polymer with fibril diameters of a few to tens of nanometers, thereby giving rise to the formation of a developed interfacial surface in the polymer. The analysis of the published data leads to a conclusion that the aging of a mechanically “rejuvenated” polymer is, as a matter of fact, the coalescence of nanosized structural elements (fibrils), which fill the shear bands and/or crazes and have a glasstransition temperature decreased by tens of degrees.     

Structure as a function of relaxation in glassy polymers

Previously, amorphous glasses were simulated by carrying out energy minimization on initial conformations generated by growing polymer chains in a periodic cube. It was not known what degree of relaxation these simulated glasses possessed. The degree relaxation is determined by the thermal history of the bulk polymer and in turn determines numerous important properties. Constant stress molecular dynamics (CSMD) followed by energy minimization was used to simulate different thermal histories of an isotactic poly(propylene) glass. This simulation approach produced glasses in which the degree of energetic relaxation was a function of the thermal history. Based on the simulated cohesive energy density, the simulation using minimization alone produced a glass that was energetically annealed. However, the local geometry and x-ray structure factor indicate that it has a different structure than those obtained using CSMD followed by energy minimization and may not be structurally relaxed.     

Photoviscoelastic behavior of amorphous polymers during transition from the glassy to rubbery state

Tensile stress‐relaxation experiments with simultaneous measurements of Young's relaxation modulus, E, and the strain‐optical coefficient, C_?, were performed on two amorphous polymers—polystyrene (PS) and polycarbonate (PC)—over a wide range of temperatures and times. Master curves of these material functions were obtained via the time‐temperature superposition principle. The value of C_? of PS is positive in the glassy state at low temperature and time; then it relaxes and becomes negative and passes through a minimum in the transition zone from the glassy to rubbery state at an intermediate temperature and time and then monotonically increases with time, approaching zero at a large time. The stress‐optical coefficient of PS is calculated from the value of C_?. It is positive at low temperature and time, decreases, passes through zero, becomes negative with increasing temperature and time in the transition zone from the glassy to rubbery state, and finally reaches a constant large negative value in the rubbery state. In contrast, the value of C_? of PC is always positive being a constant in the glassy state and continuously relaxes to zero at high temperature and time. The value of C_σ of PC is also positive being a constant in the glassy state and increases to a constant value in the rubbery state. The obtained information on the photoelastic behavior of PS and PC is useful for calculating the residual birefringence and stresses in plastic products. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2252–2262, 2001     

Fundamental relationship between the nonequilibrium glassy state and yield stress of amorphous polymers

This paper reports the theoretical prediction and experimental verification of the connection between the yield stress of amorphous polymers and the physical aging phenomenon. The analysis reveals the existence of a fundamental relationship between the nonequilibrium glassy state and the thermally activated process controlling viscoelastic and plastic deformation. The results show that the volume relaxation and deformation kinetics share the same relaxation times, and that the activation energy for deformation below T_g is much smaller than previously mentioned in the literature. This indicates that the phenomenon of physical aging plays a very important role in the deformation and processing of polymers at low temperatures. The effect of quenching and annealing on the yield stress is described in terms of the mean energy of hole formation, the departure of volume from its equilibrium state, the distribution of hole energies, and lattice volume. The same set of molecular parameters obtained from the molecular kinetic theory of the glass transition and volume relaxation predicts the yield stress as a function of cooling rate, annealing time, temperature, and strain rate.     

The entanglement network and craze micromechanics in glassy polymers

Crazes have been grown from crack tips in thin films of the following five polymers: polytertbutylstyrene (PTBS), polystyrene (PS), poly(styrene-acrylonitrile) (PSAN), poly(phenylene oxide) (PPO), and poly(styrene-methyl methacrylate) (PSMMA). These polymers represent a wide range of l_e values, where l_e is the chain contour length between entanglements. Quantitative transmission electron microscopy has been used to analyze the extension ratio λ_craze and displacement profiles for these crazes. From these measurements the craze surface stresses have been computed by using the method of distributed dislocations. This analysis also permits an accurate measure of the level of the applied stress σ_∞. These measurements show that the stress necessary for crazing increases as l_e decreases and that the higher surface stresses present at crack tips generate crazes that have higher λs than isolated crazes in the same polymers. Surface drawing is shown to be the dominant mechanism for craze thickening in all five polymers.     

Strain-induced fibrillation of glassy polymers

Literature data on structural rearrangements taking place in amorphous glassy polymers upon their plastic deformation are analyzed. This deformation is shown to be primarily accompanied by polymer self-dispersion into fibrillar aggregates composed of oriented macromolecules with a diameter of 1—10 nm. The above structural rearrangements proceed independently of the deformation mode of polymers (cold drawing, crazing, or shear banding of polymers under the conditions of uniaxial drawing or uniaxial compression). Principal characteristics of the formed fibrils and the conditions providing their development are considered. Information on the properties of the fibrillated glassy polymers is presented, and the pathways of their possible practical application are highlighted.     

Diffusion in glassy polymers. III

The diffusion studies of several solvents in epoxy polymer reported by Kewi and Zupko in Part I of this series are explained with the solution obtained from the generalized diffusion equation which includes the internal stress contribution. The rate of permeation of a penetrant through a polymer film and the time lag needed to reach steady state are also given for the generalized diffusion equation.     

Diffusion in glassy polymers. I

Synopsis The diffusion of six solvents in three crosslinked, glassy epoxy polymers is studied. Case II swelling and Fickian sorption are observed as two simple limiting cases. The mechanism of diffusion changes from one limit to another as the nature of the solvent or the crosslink density of the polymer is altered. With mixed solvents, properly chosen, a superposition of Fickian diffusion and case II swelling is observed.     

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