A new formula for the entropy of mixing in polymer systems and free volume

The famous equations of Flory-Huggins for the entropy of mixing with one highmolecular component are of great importance for polymer physics. But Gujrati stated in 1980 [12] that these equations cannot be exact. This is why we derived a new formula for the dependence of the entropy from the fraction of vacant sites in a quasi-lattice. It differs significantly from that of Huggins and still more from that of Flory in the case of low free volume. The equations of Flory-Huggins are correct with reference to low polymer content only.If our formula for entropy is used instead of that of Huggins an important result of the theory of Gibbs-DiMarzio is called in question. The increase of thermal expansion at the glass transition cannot be explained by an increase of vacant sites. A growth of the number of unoccupied sites according to the thermodynamic equilibrium condition would bring about a far too great thermal expansion coefficient. From estimations of the energy of interaction between polymer molecules, which can be found in literature, it follows that the increase of entropy is far too small to enable the formation of vacant sites above the glass transition. It is unambiguously shown that the free volume, commonly regarded to be the decisive quantity with respect to glass transition, cannot consist of holes as considered in the quasi-lattice model and in many theoretical treatments.     

Viscoelasticity and birefringence of polyisoprene

The complex Young's modulus, E^*(ω), and the complex strain-optical coefficient, O^*(ω), which is the ratio of the birefringence to the strain, were measured for polyisoprene (PIP) over a frequency range of 1 ～ 130 Hz and a temperature range of 22 ～ ?100°C. The imaginary part of O^*, O″, was positive at low frequencies and negative at high frequencies. The real part, O′, was always positive and showed a maximum. The complicated behavior of O^* could be understood by the assumption that E^* = E_R^* + E_G^* and O^* = C_RE_R^* + C_GE_G^*, where E_R^* and E_G^* were complex quantities and C_R and C_G were constants. The C_R value, equal to the ordinary stress-optical coefficient measured in the rubbery plateau zone, was 2.0 × 10^?9 Pa^?1. The C_G value, defined as the ratio O″/E″ in the glassy zone, was ?1.1 × 10^?11 Pa^?1. The E_G^*, which was the major component of E^* in the glassy zone, showed almost the same frequency dependence as that of polystyrene and polycarbonate. The E_R^*, which was dominant in the rubbery zone, was described well by the bead-spring theory. The temperature dependence of the E_G^* was stronger than that of the E_R^*. This difference caused the breakdown of the thermorheological simplicity for E^* and O^* around the glass-to-rubber transition zone. © 1995 John Wiley & Sons, Inc.     

Viscoelasticity and birefringence of polyisobutylene

The complex Young's modulus, E*(ω), and the complex strain-optical coefficient, O*(ω), were measured for polyisobutylene (PIB) over a wide temperature range near and above its glass transition temperature. The master curves could be constructed well for each function with the method of reduced variables. The shift factor, a_T, for E*(ω) is the same as that for O*(ω). The ratio of the imaginary parts of O*(ω) and E*(ω), O″(ω)/E″(ω), takes an extremum, which has never been observed for other polymers. The relation between O*(ω) and E*(ω) cannot be described by a modified stress-optical rule (MSOR) which has been found valid for various polymers. The basic concept of the MSOR. i.e., the chain orientation and the orientation of flat monomer units in the stretch direction, is not sufficient to describe the behavior of PIB and another origin of stress, presumably due to the fluctuation of local stress, should be included. This term does not contribute to the birefringence. The main maximum of tan δ is ascribed to the relaxation of the chain orientation in contrast with many other polymers, such as polyisoprene and polycarbonate, for which the maximum of tan δ is ascribed to the rotational relaxation of monomer units. © 1995 John Wiley & Sons, Inc.     

A structural interpretation of the two components governing the kinetic fragility from the example of interpenetrated polymer networks

Kinetic fragility and cooperativity length, two major characteristics of the relaxation dynamics at the glass transition, are, respectively, investigated by dynamic mechanical analysis and modulated temperature differential scanning calorimetry in a series of interpenetrated polymer networks based on acrylate and epoxy systems. The relaxation dynamics are impacted by two variables: the rigidity of the network, and the structural heterogeneity resulting from blending. However, the fragility and the cooperativity do not vary similarly. The glass transition progressively broadens as the mass fractions of acrylate and epoxy become equivalent, leading to a strong decrease in cooperativity. On the other hand, under the same conditions, the fragility transitions between the lower value of pure acrylate and the higher value of pure epoxy. This divergence helps concluding that the variations in the temperature dependence of the relaxation time are not purely related to the more or less cooperative nature of the glass transition. By splitting the fragility index in a volume contribution and an energetic contribution, it is shown that the contribution of cooperativity to the variations of the relaxation time with temperature is increased under two structural conditions: low backbone rigidity and high intermolecular interactions. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1393–1403     

Positron annihilation: a unique method for studying polymers

Positron annihilation is a unique technique for studying the local free volume of polymers. Employing the positron annihilation lifetime spectroscopy (PALS) the size and size distribution of subnanometer size holes which constitute the excess free volume may be studied. In combination with macroscopic volume data the fractional free volume and the number density of holes may be estimated. After presenting the principles of the method, some examples typically for the investigation of the free volume in polymers will be given. Moreover, the study of interdiffusion in demixed polymer blends and further applications are shortly reviewed     

Application of free‐volume theory to self diffusion of solvents in polymers below the glass transition temperature: A review

Theories based on free‐volume concepts have been developed to characterize the self and mutual‐diffusion coefficients of low molecular weight penetrants in rubbery and glassy polymer‐solvent systems. These theories are applicable over wide ranges of temperature and concentration. The capability of free‐volume theory to describe solvent diffusion in glassy polymers is reviewed in this article. Two alternative free‐volume based approaches used to evaluate solvent self‐diffusion coefficients in glassy polymer‐solvent systems are compared in terms of their differences and applicability. The models can correlate/predict temperature and concentration dependencies of the solvent diffusion coefficient. With the appropriate accompanying thermodynamic factors they can be used to model concentration profiles in mutual diffusion processes that are Fickian such as drying of coatings. The free‐volume methodology has been found to be consistent with molecular dynamics simulations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Nonlinear Viscoelasticity Raised at Low Temperatures by Intermolecular Cooperation of Bulk Amorphous Polymers

We performed dynamic Monte Carlo simulations of stress relaxation in parallel-aligned and uniaxially stretched bulk amorphous polymers at low temperatures.We observed an extra-slowing down in the early stage of stress relaxation,which causes nonlinear viscoelasticity as deviated from Debye relaxation and Arrhenius-fluid behaviors observed previously at high temperatures.Meanwhile,fluctuation analysis of stress relaxation revealed a substantial increase in the stretch fractions of polymers at the transient periods of high-temperature Debye relaxation.Structural analysis of free volume further revealed the scenario that,at low temperatures,the modulus of polymer entropy elasticity decreases with temperature and eventually loses its competition to the imposed modulus (Deborah number becomes larger than one),and hence upon stress relaxation under constant strains,monomers are firstly accumulated nearby two stretching ends of polymers,resulting in tentative global jamming like physical cross-linking there,and thus retarding the coming transient state of stress relaxation.We concluded that intermolecular cooperation raises physical crosslinking for nonlinear viscoelasticity of polymer stress relaxation as well as the rubbery states unique to bulk amorphous polymers.The new microscopic mechanism of the fluid-rubbery transition of polymers may bring insights into the intermolecular cooperation mechanism of glass transition of small molecules,if the fluid-rubbery transition is regarded as an extrapolation of glass transition from low to high molecular weights.     

Interfacial Adhesion and Composite Viscoelasticity

Summary: The viscoelastic properties of 30 vol.‐% composites of calcite, surface‐treated with fatty acids of different chain length, and polyethylene were studied. The alkyl chains decrease the surface energy of the particles and the adhesion between the polymer and the filler. The moduli of the composites decrease with decreasing interfacial adhesion. When the shear forces applied overcome the adhesion forces, interfacial slippage takes place. Terminal OH groups in the alkyl chains enhance the particles' agglomeration, leading to a solid‐like response in the low frequency region. The presence of a plateau in the log moduli versus log frequency plot can be due to local structures and is not necessarily an evidence of a percolating filler network.

Steady shear viscosity (σ = 1 000 Pa) of 30 vol.‐% surface‐treated (different acids) CaCO₃‐HDPE composites plotted as a function of the number of carbon atoms in the alkyl chains of the coated monolayer. The dotted line is simply a guide to the eye.     

Free volumes in polystyrene probed by positron annihilation

Free volume characteristics in three samples of monodisperse polystyrene were investigated by positron annihilation technique over a temperature range from 300 to 380 K. The number-average molecular weight of the samples ranged from 5730 to 1,524,000. The observed lifetime spectra were resolved into three components, where the longest lifetime, τ₃ was associated with the pick-off annihilation of ortho-positronium (o-Ps) trapped by free volumes. The change of the temperature coefficient of τ₃ was observed at around 350 K, at which the value of τ₃ was a constant value of 2,3 ns for all specimens with different molecular weights. There was no discrete change of τ₃ in intensity, which is corresponding to the number of free volumes. The size of free volume at glass transition was evaluated to be 0.l nm³. © 1996 John Wiley & Sons, Inc.     

Effect of CO2 exposure on free volumes in polystyrene studied by positron annihilation spectroscopy

Free‐volume properties, size and distribution, in amorphous polystyrene exposed to CO₂ gases have been measured as a function of pressure to 800 psi (5.5 MPa), of time, and of temperature using positron annihilation lifetime spectroscopy. The free volume increases significantly and its distribution broadens as a function of pressure. The free volume relaxes as a function of time with a characteristic time of 15 h, and 5.7 h for 400, and 800 psi, respectively, after depressurizing under vacuum. A portion of free volume created by CO₂ exposure remains permanently in the polymer after CO₂ exposure. The glass transition temperature decreases significantly as a function of CO₂ pressure from the free‐volume data and is compared with the differential scanning calorimeter results. The observed free‐volume variations as a function of pressure, time, and temperature are discussed in terms of hole expansion, creation, free‐volume relaxation, plasticization, and hole filling in amorphous polymers. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 388–405, 2008     

Fragility of short-chain poly(lactic acid)s derivatives by combining dielectric spectroscopy and fast scanning calorimetry

Low-molecular-mass bio-polyesters, such as lactic acid oligomers, constitute a growing category of plasticizers for poly (lactic acid), since they show good compatibility and are respectful of the environment. This study focuses on the glass transition of a series of oligomers with different molecular weights, with the aim of investigating how their associated dynamics occur. Dielectric and calorimetric results are combined to study the molecular mobility in a large temperature range. In comparison with poly (lactic acid), the oligomers exhibit a lower fragility index and smaller cooperative rearranging regions. Among oligomers, the fragility is clearly dependent on the molecular weight, whereas the variations of the cooperativity are subtler.     

Molecular mobility in polymers studied with thermally stimulated recovery

Thermally stimulated recovery, TSR, like as thermally stimulated depolarisation currents, is a suitable technique that allows for the study of conformational mobility in polymeric systems. Due to its relatively low equivalent frequency and transient nature, the viscoelastic data obtained from this technique are complementary to conventional dynamic mechanical analysis (DMA). In this work TSR-like experiments, including TSR, thermally stimulated creep and thermal sampling (TS) experiments were carried out in the same commercial DMA equipment, allowing for the direct comparison of the data. Some advises for running TSR experiments are presented, such as the need of performing blank experiments and temperature calibrations. The analysis of the data to obtain the thermokinetic parameters of TS experiments is revised. In particular, from the direct fitting of the data, it is reported a tendency for a linear relationship between the pairs of values of (E _a, log τ₀) that best adjust any TS single experiment. It is concluded that the usual equation for describing TS experiments possesses an intrinsic compensation between these two thermokinetic parameters. This revised version was published online in August 2006 with corrections to the Cover Date.     

A predictive approach based on the Simha–Somcynsky free‐volume theory for the effect of dissolved gas on viscosity and glass transition temperature of polymeric mixtures

The gas concentration and pressure effects on the shear viscosity of molten polymers were modeled by using a unified approach based on a free volume theory. A concentration and pressure dependent “shift factor,” which accounts for free volume changes associated with polymer‐gas mixing and with variation of absolute pressure as well as for dilution effects, has been herein used to scale the pure polymer viscosity, as evaluated at the same temperature and atmospheric pressure. The expression of the free volume of the polymer/gas mixture was obtained by using the Simha and Somcynsky equation of state for multicomponent fluids. Experimental shear viscosity data, obtained for poly(ε‐caprolactone) with nitrogen and carbon dioxide were successfully predicted by using this approach. Good agreement with predictions was also found in the case of viscosity data reported in the literature for polystyrene and poly(dimethylsiloxane) with carbon dioxide. Free volume arguments have also been used to predict the T_g depression for polystyrene/carbon dioxide and for poly(methyl methacrylate)/carbon dioxide mixtures, based on calculations performed, again, with the Simha and Somcynsky theory. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1863–1873, 2006     

Difference in Glass Transition Behavior Between Semi Crystalline and Amorphous poly(lactic acid) Thin Films

Summary: Semi crystalline and amorphous poly(lactic acid) (PLA) thin films exhibit different glass transition temperature and behaviour, as revealed by ellipsometry. For semi-crystalline poly(L-lactic acid) (PLLA) thin film (with crystalline content between 40 and 60%), the glass transition temperature (T_g) is found to decrease below a film thickness of 50 nm. This depression was interpreted in term of disentenglement effect which is likely to occur upon confining the amorphous PLA phase near a non interacting surface. New results performed on non completed films, i.e. isolated objects, also reveal the lower transition temperature, thus underlying the importance of the entanglement state of the polymer chains on their mobility. For amorphous PLA thin film, obtained from the L and D copolymer, two distinct glass transitions were observed, with the highest Tg attributed to the presence of some nano-phase domains, formed by a possible cooperation of the D and L blocks to form stereocomplexes sequences, within the film. Furthermore, if these T_g remained constant as film thicknesses decrease down to 50 nm, they were also found to slightly decrease for isolated objects, thus supporting the importance of the entanglement hypothesis on the glass transition.     

A Definition of Dynamically Accessible Volume for Thermal Systems

Summary: The glass transition and physical aging processes of a polymeric material have been simulated using the bond fluctuation model. Two potentials that represent intra‐ and inter‐molecular interactions have been employed. Simulations of different thermal histories that include cooling from equilibrium have been performed. The evolution of the system and the structure attained at low temperature are analyzed as a function of the assumed weight of inter‐ and intra‐molecular potentials in the total energy of the system. A new way of characterizing the free volume of the system and its evolution with the temperature or time is proposed. It is based on the concept of dynamically accessible volume but modified in the sense of considering the probability of an empty site to be accessed according to a Metropolis criterion. The results obtained show that the thermal redefinition of the dynamically accessible volume, TDAV, offers a better representation of the real mobility of the polymeric systems. The use of information on the structure of the system coming from the pair‐correlation function and the molecular mobility in the glassy state characterized by the time evolution of TDAV allows to reach the conclusion that a combination of inter‐ and intra‐molecular potentials produces the vitrification of the polymer system on cooling.

     

The effects of molecular orientation on the physical aging and mobility of polycarbonate—solid state NMR and dynamic mechanical analysis

Solid‐state NMR and dynamic mechanical (DMA) measurements were performed on a series of uniaxially hot‐drawn bisphenol‐A polycarbonate samples in order to determine the effects of stretching on the structure, mobility, and local orientation environment. Proton spin‐lattice relaxation times, ¹H T_1ρ, for the phenylene carbon protons were fitted to a biexponential decay function, and both the long and short relaxation times initially increased with stretching. Intensity data indicated an increase in the number of short relaxation time protons and a decrease in the number of long relaxation protons with orientation. Similarly, DMA spectra showed that the β‐relaxation strength also increased with drawing, which implied an increase in the number of localized segmental relaxations. It is theorized that the long and short ¹H T_1ρ relate to protons within tightly packed “cooperative domains,” and to those with greater localized free‐volume, respectively. Stretching is known to distort the free‐volume distribution, causing a decrease in the mean free‐volume but an increase in the number of larger, more elliptical holes. This is expected to cause a decrease in the α‐transition mobility (due to larger cooperative domains) and an increase in the β‐mobility (due to the increase in the number of β‐relaxing segments associated with the larger free‐volume holes). These predictions are consistent with results recently reported by Shelby and Wilkes on the physical aging and creep behavior of these samples (M. D. Shelby & G. L. Wilkes, Polymer 1998, 39, 6767; M. D. Shelby & G. L. Wilkes, J Polym Sci Part B: Polym Phys 1998, 36, 2111). © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 32–46, 2001     

Thermal reactions of solid-state amorphized borates and borate glasses

The properties and course of phase transition of amorphous borates obtained by solid-state thermal and mechanical treatment of hydrated borates and melt quenched glasses with the compositions of these borates were studied. Processes of structural relaxation and crystallization were considered.It was found that different methods of preparation of amorphous borates and the differences in their structural ordering resulting from these methods affect the rate and the mechanism of transformations occurring during their heating.Support for this work was provided by the Polish Committee of Scientific Research (KBN) — grant No. 3 P407 034 06.     

A calorimetric study of the glass transition kinetics in polyisoprene

The connection between the dielectric and calorimetric relaxation behaviours of synthetic polyisoprene Cariflex IR 305 is studied. A similar comparison of dielectric and dilatometric results was described in [1]. The heat capacity was measured during heating of samples prepared with different thermal history. Experimental results were compared with the heat capacity curves calculated for a model based on the multiparameter theory of Kovacs et al. [4]. The model considers the relaxation system as being composed of a set of subsystems characterized by different relaxation times. The distribution of relaxation times and their temperature dependence were taken from the diclectric measurement. The relaxation time of a subsystem from posed to depend, not only on the actual, temperature of the sample, but also on the deviation of this subsystem from equilibrium, or alternatively, on the deviation of the system as a whole. The comparison between the measured and modeled curves shows that both influences must be taken into account in order to explain the experimental results.Dedicated to Prof. Dr. W. Pechhold on the occasion of his 60th birthday.