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     

Residual stresses and birefringence in injection molding of amorphous polymers: Simulation and comparison with experiment

A physical modeling and a two‐dimensional numerical simulation of the injection‐molding of a disk cavity by using a hybrid finite element method (FEM) and finite difference method (FDM) are presented. Three stages of the injection‐molding cycle––filling, packing, and cooling––are included. The total residual stresses are taken to be a sum of the flow stresses calculated using a compressible nonlinear viscoelastic constitutive equation and the thermal stresses calculated using a linear viscoelastic constitutive equation. The total residual birefringence is taken to be the sum of the flow birefringence related to the flow stresses through the stress–optical rule, and the thermal birefringence related to the thermal stresses through the photoviscoelastic constitutive equation. The Tait equation is used to describe the P‐V‐T relationship. The simulation shows that without packing the birefringence in the surface layer of moldings, with its maximum near the surface, is caused by the frozen‐in flow birefringence (flow stresses) and in the core region by the frozen‐in thermal birefringence (thermal stresses). With packing, a second birefringence maximum appears between the center and the position of the first maximum due to flow in the packing stage. The predicted birefringence profiles and extinction angle profiles are found to be in fair agreement with corresponding measurements in literature for disk moldings. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 622–639, 2006     

Dynamic birefringence of oligostyrene: A symptom of “polymeric” mode

The dynamic birefringence and the dynamic viscoelasticity of an oligostyrene, A1000, whose molecular weight (M_w = 1050) was comparable to the Kuhn segment size, M_K, were examined near and above the glass‐transition temperature in order to characterize polymeric features of very short chains with M ∼ M_K. The complex shear modulus, G*(ω), was similar to that for supercooled liquids: No polymeric modes such as the Rouse mode were detected at low frequencies of viscoelastic spectrum. On the other hand, the strain‐optical coefficient was found to be negative in the terminal flow zone and positive in the glassy zone. Because the negative birefringence of polystyrene is originated by polymeric modes associated with chain orientation, the present results indicate that polymeric modes exist and become dominant for birefringence in the terminal flow. The data were analyzed using a modified stress‐optical rule: The modulus and the strain‐optical ratio were separated into polymeric (rubbery) and glassy components. The total modulus, G*(ω), was mostly due to the glassy component, G_G*(ω), resulting in the positive birefringence. G_G*(ω) for A1000 agreed with that for high M polystyrenes when compared at a comparable reduced frequency scale. The polymeric component, G_R*(ω), giving rise to the negative birefringence was lower than G_G*(ω) over the whole frequency range but its contribution to the birefringence exceeded that of the glassy component at low frequencies because of the larger optical anisotropy and longer characteristic relaxation time of the former. The limiting modulus of G_R* at high frequencies was about 3 times lower than that for high M polystyrenes, indicating that the main‐chain orientation of the oligostyrene on instantaneous deformation was reduced compared with that of high M polystyrenes. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 954–964, 2000     

Effect of pressure and temperature history on volume relaxation of amorphous polystyrene

Control of volume changes with time has a critical industrial relevance for the production of objects made of thermoplastic materials (obtained, e.g., by injection molding), but this phenomenon is completely disregarded by commercial codes for simulation of processes. In this work, attention is focused on the relevance of thermomechanical history on volume relaxation at room conditions of an amorphous polystyrene. A set of data of volume relaxation of samples obtained in an extremely wide range of thermomechanical treatments was collected. Data were analyzed with the aim of applying a simplified model on the basis of the well‐known KAHR model, which describes the postprocessing volume relaxation of amorphous polymers by adopting a minimum number of material parameters. Despite the fact that only two relaxation times are considered, the model satisfactorily describes volume evolution (either contraction or expansion) at room conditions after a given thermomechanical treatment if an appropriate partition of free volume into two fractions is provided. Furthermore, in its present form that neglects the effect of pressure on volume relaxation, the model satisfactorily describes the effect of a given thermal treatment (at room pressure), starting from the melt, on both specific volume and its relaxation rate after treatment. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1526–1537, 2003     

Spectrophotometric determination of thermal transition of polymeric systems using photochromic probes

Mercury-dithizone complex both free and bonded to a polymeric system has been synthesized and used to measure the thermal transition of polystyrene, poly(vinyl acetate), and some other polymers. The thermal relaxation rate of the activated complex in dark has been found to be dependent on the free volume of a polymer matrix. The rate goes through a maximum above T_g of a polymer. A very sensitive method, based on thermal recovery of activated photochromic probe chromophore has been devised to measure the thermal transition of both single and multicomponent polymer matrices. © 1995 John Wiley & Sons, Inc.     

PVT properties of linear and dendritic polymers

The aim of this article is to examine the limits of applicability of the Simha‐Somcynsky (S‐S) equation of state (EOS) by comparing the pressure‐volume‐temperature (PVT) data and the derivatives (compressibility, κ, and thermal expansion coefficient, α) of anionic linear polystyrene (PS) with poly(benzyl ether) dendrimers (PBED). Fitting the PVT of PBED data to the S‐S EOS was similarly satisfactory as that of PS and the computed Lennard‐Jones (L‐J) interaction parameters showed similar errors of ca. 1%. Next, the experimental derivatives, α and κ of PS and PBED were compared with these functions computed from the S‐S EOS—good agreement was obtained for α at ambient pressure, P, indicating validity of the S‐S theory at least up to the first derivative. While the predicted κ = κ(P) dependence for PS and a linear PBED homologue was correct, for dendrimers the compressibility was higher at low pressure and it was lower at high P than theory predicts. Also the extracted values of the L‐J repulsion volume, v*, between a segment pair was smaller than expected. The specific architecture of dendrimer molecules is responsible for this behavior, since their 3D configuration is significantly different from the S‐S model with uniform segmental density and oxygen bonds in the main and side chains add flexibility. © 2009 NRC Canada. J Polym Sci Part B: Polym Phys 48: 322–332, 2010     

Residual stress and optical properties of fully rod-like poly(p-phenylene pyromellitimide) in thin films: Effects of soft-bake and thermal imidization history

A soluble poly(amic acid) precursor solution of fully rod-like poly(p-phenylene pyromellitimide) (PMDA-PDA) was spin cast on silicon substrates, followed by soft bake at 80–185°C and subsequent thermal imidization at various conditions over 185–400°C in nitrogen atmosphere to be converted to the polyimide in films. Residual stress generated at the interface was measured in situ during imidization. In addition, the imidized films were characterized in the aspect of polymer chain orientation and ordering by prism coupling and X-ray diffraction. The soft-baked precursor film revealed a residual stress of 16–28 MPa at room temperature, depending on the soft bake condition: higher temperature and longer time in the soft bake gave higher residual stress. The stress variation in the soft-baked precursor film was not significantly reflected in the final stress in the resultant polyimide film. However, the residual stress in the polyimide film varied sensitively with variations in imidization process parameters, such as imidization temperature, imidization steps, heating rate, and film thickness. The polyimide film exhibited a wide range of residual stress, −7 MPa to 8 MPa at room temperature, depending on the imidization condition. Both rapid imidization and low-temperature imidization generated high stress in the tension mode in the polyimide film, whereas slow imidization as well as high temperature imidization gave high stress in the compression mode. Thus, a moderate imidization condition, a single- or two-step imidization at 300°C for 2 h with a heating rate of < 10 K/min was proposed to give a relatively low stress in the polyimide film of < 10 μm thickness. However, once a precursor film was thermally imidized at a chosen process condition, the residual stress–temperature profile was insensitive to variations in the cooling process. All the films imidized were optically anisotropic, regardless of the imidization history, indicating that rod-like PMDA-PDA polyimide chains were preferentially aligned in the film plane. However, its degree of in-plane chain orientation varied on the imidization history. It is directly correlated to the residual stress in the film, which is an in-plane characteristic. For films with residual stress in the tension mode, higher stress films exhibited lower out-of-plane birefringence, that is, lower in-plane chain orienta-tion. In contrast, in the compression mode, higher stress films showed higher in-plane chain orientation. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1261–1273, 1998     

Prediction of solvent diffusion coefficient in amorphous polymers based on an equation‐of‐state

This study develops a modified free‐volume model to predict solvent diffusion coefficients in amorphous polymers by combining the Vrentas–Duda model with the Simha–Somcynsky (S‐S) equation‐of‐state (EOS), and all the original parameters can be used in the modified model. The free volume of the polymer is estimated from the S‐S EOS together with the Williams‐Landel‐Ferry fractional free volume, and the complex process of determining polymer free‐volume parameters in the Vrentas–Duda model and measuring polymer viscoelasticity can be avoided. Moreover, the modified model includes the influence of not only temperature but also pressure on solvent diffusivity. Three common polymers and four solvents are employed to demonstrate the predictions of the modified model. The calculation results are generally consistent with the experimental values. It is reasonable to expect that the modified free‐volume model will become a useful tool in polymer process development. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1000–1009, 2006     

Physical aging of epoxy polymers and their composites

Exposure to extended periods of sub‐T_g temperatures causes physical changes in the molecular structure of epoxy resins and epoxy‐based materials to occur. These physical aging mechanisms include the reduction in free volume and changes to the molecular configuration. As a result, mechanical, thermodynamical, and physical properties are affected in ways that can compromise the reliability of epoxy‐based engineering components and structures. In this review, the physical changes in the molecular structure of epoxies are described, and the influence of these changes on the bulk‐level response is detailed. Specifically, the influence of physical aging on the quasistatic mechanical properties, viscoelasticity, fracture toughness, thermal expansion coefficient, volume relaxation, enthalpy relaxation, endothermic peak temperature, fictive temperature, and moisture/solvent absorption capability is reviewed. Also discussed are relationships between relaxation functions, crosslink density, composite reinforcement, and epoxy/copolymer blending and the physical aging response of epoxies. Finally, the concepts of thermal and mechanical rejuvenation are discussed. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Copolymers of methyl methacrylate with N‐trifluorophenyl maleimides: High glass transition temperature and low birefringence polymers

Copolymers of methyl methacrylate (MMA) with 2,3,4‐ and 2,4,6‐trifluorophenyl maleimides (TFPMIs) were synthesized by a free radical initiator, azobisisobutyronitrile, in 1,4‐dioxane and also in bulk. The refractive indexes of the copolymers were in the range of 1.49–1.52 at 532 nm. The T_gs were 133–195 °C depending on copolymer compositions. In addition, the copolymers were thermally stable, T_d > 350 °C. The orientational and photoelastic birefringence of the copolymers were also investigated. As both of the orientational and photoelastic birefringences of PMMA are negative, whereas those of poly(TFPMI)s are positive, we could obtain nearly zero orientational and photoelastic birefringence polymers when the ratios of 2,3,4‐TFPMI/MMA were 15/85 and 5/95 mol %, respectively. For 2,4,6‐TFPMI, zero orientational and photoelastic birefringences could be obtained when the ratios of 2,4,6‐TFPMI/MMA were 12/88 and 3/97 mol %, respectively. The T_gs of those copolymers with zero birefringences were in the range of 135–140 °C. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Simulation of plastic deformation in glassy polymers: Atomistic and mesoscale approaches

The mechanism of deformation in glasses is very different from that of crystals, even though their general behavior is very similar. In this study, we investigated the deformation of polycarbonate on the atomistic scale with molecular dynamics and on the continuum scale with a new simulation approach. The results indicated that high atomic/segmental mobility and low local density enabled the formation (nucleation) of highly deformed regions that grew to form plastic defects called plastic shear transformations. A continuum-scale simulation was performed with the concept of plastic shear transformations as the basic region of deformation. The continuum simulations were able to predict the primary and secondary creep behavior. The slope of the secondary creep depended on the interactions between the plastic shear transformations. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 994-1004, 2005     

Physical aging in polycarbonate nanocomposites containing grafted nanosilica particles: A comparison between enthalpy and yield stress evolution

Understanding and controlling physical aging below the glass transition temperature (T_g) is very important for the long‐term performance of plastic parts. In this article, the effect of grafted silica nanoparticles on the physical aging of polycarbonate (PC) below the T_g is studied by using the evolution of the enthalpy relaxation and the yield stress. The nanocomposites were found to reach a thermodynamic equilibrium faster than unfilled PC, implying that physical aging is accelerated in presence of grafted nanosilica particles. The Tool‐Narayanaswamy‐Moynihan model shows that the aging is accelerated by the grafted silica nanoparticles, but the molecular mechanism responsible for physical aging remains unaltered. Furthermore, dynamic mechanical analysis shows that the kinetics of physical aging can be related to a free volume distribution or a local attraction‐energy distribution as a result of the change in mobility of the polymer chain. Finally, a qualitative equivalence is observed in the physical aging followed by both the enthalpy relaxation and yield stress. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2069–2081     

Physical aging in amorphous poly(ethylene furanoate): Enthalpic recovery,density, and oxygen transport considerations

The current work utilizes three separate techniques to study the physical aging process in amorphous poly(ethylene furanoate) (PEF), which is a recently introduced engineering thermoplastic with enhanced properties compared to petroleum‐sourced poly(ethylene terephthalate). Differential scanning calorimetry aging experiments were conducted at multiple aging temperatures and times, and the resultant enthalpic recovery values compared to the theoretical maximum enthalpy loss evaluated from calculations involving extrapolation of the equilibrium liquid line. Density measurements reveal densification of the matrix for the aged versus unaged samples, and provide an estimate for the reduction in free volume for the aged samples. Complementary oxygen permeation and pressure‐decay sorption experiments provide independent verification of the free volume reduction mechanism for physical aging in glassy polymers. The current work provides the first detailed aging study for PEF. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 389–399     

Effect of annealing temperature on interrelation between the microstructural evolution and plastic deformation in polymers

The mechanical loading induced flow of glassy polymers is triggered by the nucleation of shear transformation units, and strongly depends on the initial microstructural state of the material. Therefore, investigation of the possible relationship between the microstructural state variables and plastic deformation is required for a better understanding of the macroscopic response of this class of materials during large deformation. In this study, free volume content is considered as a state variable and thermal treatment is selected as a process through which the accelerated and forced evolution of the free volume can be imposed. For two well‐known glassy polymers, poly(methyl methacrylate) and polycarbonate, the free volume content alteration upon annealing is monitored via positron annihilation spectroscopy, and the changes of the micro‐ and macromechanical properties are also obtained by utilizing nanoindentation technique and employing the homogeneous amorphous flow theory. The correlation between the microstructural state variable, that is, free volume, and the micromechanical state variable, that is, shear activation volume, is then investigated. The results reveal opposite direction of alterations of free volume and shear activation volume with annealing temperature. Accordingly, the possibility of the existence of an interrelation between these two state variables is critically discussed. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1286–1297     

Characterization of the motion of spin probes and spin labels in amorphous polymers with two-dimensional field-step ELDOR

The motion of nitroxide spin probes and spin labels in amorphous polymers is studied below the glass transition temperature with a two-dimensional pulsed electron double-resonance experiment. Polystyrene and a liquid crystalline side group polymer are studied using both spin probes and spin labels covalently bound to specific sites along the polymer chain. Two methyl acrylic polymers differing only in their side group structure and polyvinylacetate are compared and large differences in the molecular dynamics deduced from both the nuclear and the electron spin relaxation rates are observed as the glass transition is approached. The results demonstrate the complexity of small amplitude motion in simple polymers below the glass transition temperature and show that it is very sensitive to the packing in the polymer. © 1996 John Wiley & Sons, Inc.     

Study of relaxation processes in polyethylene and polystyrene by positron annihilation

Relaxation processes in polyethylene (PE) and polystyrene (PS) were studied by positron annihilation technique. For PE, above the glass transition temperature, T_g, the size of free volumes and its concentration were increased by the micro-Brownian motion of molecules. For PS, local motions of molecules in backbone chains were found to start above 260 K. However, these local motions were suppressed by an interphenyl correlation. For both PE and PS, below 250–260 K, the formation probability of positronium atoms increased with decreasing temperature. This fact was assigned to the freezing in of the local motions of molecules. For PS, an onset of the local motions of molecules was observed above 100 K. These motions were expected to be associated with liberation of phenyl groups. © 1996 John Wiley & Sons, Inc.     

Recent progress in microporous polymers from thermally rearranged polymers and polymers of intrinsic microporosity for membrane gas separation: Pushing performance limits and revisiting trade-off lines

Polymers are promising materials for gas separation membranes. However, the trade-off relationship between gas permeability and selectivity remains an obstacle for achieving polymer membranes that exhibit high gas permeation with desirable separation efficiency. Improving polymer microporosity is of interest in gas separation membranes to enhance gas transport behavior. Polymer modifications by (a) incorporating intrinsically microporous units and/or (b) increasing chain rigidity can enhance microporosity in conventional polymer membrane materials such as polyimides. These strategies are adopted for new classes of microporous polymers, thermally rearranged (TR) polymers, and polymers with intrinsic microporosity (PIMs), to maximize gas transport properties. Their outstanding gas separation performances have redefined the traditional trade-off lines. This review aims to explore the advances in microporous polymers for gas separation applications. The approaches on TR polymers and PIMs to enhance their microporosity are listed, and their developments are evaluated in the context of revisiting performance limits for industrially relevant gas separation applications.