Viscoelastic properties of linear polymers in the high-elastic state

The relation between molecular weight, chain rigidity and the length of the high-elasticity plateau is determined from frequency and temperature dependences of the storage modulus for polybutadienes and polystyrenes with M _w/M _n ? 1.1. Use is made of the concept of equivalence of high-elastic states characterized by equal lengths of high-elastic plateaus for linear polymers. The high-elastic states of the linear polymers studied are equivalent if the polymer chains have equal numbers of dynamic segments and if the reference temperature is T₀ = 1.22T_g, where T_g is the glass transition temperature. The viscoelastic properties of the polymers in the high-elastic state are determined unambiguously by T_g and the molecular weight of the dynamic segment. The quantitative relation between thermomechanical characteristics obtained by measuring deformation versus temperature under a constant time regime and dependence of storage modulus versus frequency under isothermal conditions is discussed.     

Isothermal crosslinking studies on polyquinoxalines by dynamic mechanical methods

Torsional braid analysis was used to investigate the crosslinking behavior of linear quinoxaline polymers with and without reactive side groups. The kinetic parameter followed was the glass transition temperature during isothermal exposure in an inert atmosphere. With high molecular weight polyamide-quinoxaline copolymers (PPAQ), an initial decrease in T_g was observed during heat exposure which was followed by a subsequent increase in T_g. This was attributed to simultaneous chain scission and crosslinking reactions. Since the effect of random chain scission on the initial change in T_g of the highest molecular weight polymer samples is much stronger than on low molecular weight analogues, a T_g minimum was observed only on the highest molecular weight polymers. Because of the complexity of the reactions occurring one must consider the activation energies obtained from the Arrhenius plots as “apparent” activation energies. No attempt was made to elucidate the mechanisms of these reactions. It has been shown that isothermal heat exposure of high-temperature aromatic polymers in an inert atmosphere leads to crosslinking. In general, however, linear polymers that have reactive side groups such as methyl or carboxyphenyl groups along the polymer chain crosslink more rapidly than the analogs without these groups.     

Glass Transition Temperature and Value of the Relaxation Time at Tg in Vitreous Polymers

Summary: Many works focused on glassy polymers determine values of glass transition temperature (T_g) and an overview of the literature shows that depending on the method used, values of T_g are found different for the same material. In this paper, a review of data collected on different materials are used and interpreted in term of molecular mobility characterized by relaxation time functions. By using three independent experimental procedures (dielectric, thermally depolarized current and calorimetric), we show that the value of the glass transition and the value of the relaxation time at T_g can be correctly determined. It is also shown that the assumption: τ _(Tg) = 100 s is constant, is not correct. The protocol proposed also allows the determination of the value of the fragility index “m” of the glass forming liquid with a great accuracy.     

Model phase diagrams of binary nematic mixtures. A comparative study between linear and crosslinked polymers

Model calculations of phase diagrams of side chain liquid crystal polymers (SCLCP) and low molecular weight liquid crystals (LMWLC) are presented. The polymer is assumed to have grafted side chain units characterized by a nematic‐isotropic transition temperature T_{NI 2}, and the LMWLC presents also a similar transition at a temperature T_{NI 1} . The model calculations can accommodate for the cases where the latter two temperatures are comparable or widely different. For the sake of illustration, the case T_{NI 1} = 60°C and T_{NI 2} = 80°C is adopted here. The main point of interest here is to perform a comparative study of the equilibrium phase diagrams of SCLCP made either of linear free chains or crosslinked chains forming a single network. To our knowledge this is the first comparative study of the phase behavior of binary nematic mixtures involving linear and crosslinked polymer matrices which permits to clearly identify the effects of crosslinks present in the polymer matrix. The crosslinks attribute elasticity to the polymer constituent which induces important distortions in the phase diagram. To highlight these distortions, examples of hypothetical binary nematic mixtures are chosen involving both linear and crosslinked polymers with side chain mesogen units. The quadrupole interaction parameter between the two nematogens is related to individual parameters via a geometric average ν²₁₂ = κν₁₁ν₂₂ with a coupling parameter κ. Different values of this parameter are considered and the impact of coupling strength on the phase diagram is discussed for crosslinked and linear polymers.     

Glass‐Transition Temperature as a Function of Conversion in Hyperbranched Polymers Obtained by Self‐Condensing Vinyl Polymerization

Chain‐end free volume theory is extended for studying the glass‐transition temperature (T_g) as a function of conversion in hyperbranched polymers. T_g is found to have a non‐linear inverse relationship to the molecular weight for polymers obtained by self‐condensing vinyl polymerization (SCVP). During the monomer conversion process, T_g decreases with the increase in molecular weight (P) in the low conversion range, then levels off in the high conversion range.     

Theoretical and Predictive Modelling of Physical Properties of Polymers

The application of Boltzmann statistics to a complete distribution of molecular conformation energies of simplified homo‐ and copolymer models gives meaningful information about temperatures at which phase transitions take place in the bulk. We have calculated in the conformation statistical distribution (CSD) approximation Helmholtz free energy variation versus temperature δF = δU–TδS, where U and S are, respectively, the internal molecular energy and the Gibbs statistical entropy of the considered polymeric model. The deepest minima correspond to glass‐transition temperature (T_g) and melting temperature (T_m) of modelled polymers, while the remaining peaks are related to some other transitions, the existence of which is also experimentally proven. The adopted method is able to give T_g and T_m as a function of the molecular weight of polymers. Some indications can also be achieved about the instability of polymers. The same procedure has been applied to copolymers and blends and has given acceptable results for T_g and T_m as functions of the material microstructure and composition. Other thermal and mechanical properties, such as moduli, mobilities, chemical resistance to oxidation, physical tendency to miscibility, have been directly or indirectly estimated.     

Extension of the chain‐end,free‐volume theory for predicting glass temperature as a function of conversion in hyperbranched polymers obtained through one‐pot approaches

Compared with linear polymers, more factors may affect the glass‐transition temperature (T_g) of a hyperbranched structure, for instance, the contents of end groups, the chemical properties of end groups, branching junctions, and the compactness of a hyperbranched structure. T_g's decrease with increasing content of end‐group free volumes, whereas they increase with increasing polarity of end groups, junction density, or compactness of a hyperbranched structure. However, end‐group free volumes are often a prevailing factor according to the literature. In this work, chain‐end, free‐volume theory was extended for predicting the relations of T_g to conversion (X) and molecular weight (M) in hyperbranched polymers obtained through one‐pot approaches of either polycondensation or self‐condensing vinyl polymerization. The theoretical relations of polymerization degrees to monomer conversions in developing processes of hyperbranched structures reported in the literature were applied in the extended model, and some interesting results were obtained. T_g's of hyperbranched polymers showed a nonlinear relation to reciprocal molecular weight, which differed from the linear relation observed in linear polymers. T_g values decreased with increasing molecular weight in the low‐molecular‐weight range; however, they increased with increasing molecular weight in the high‐molecular‐weight range. T_g values decreased with increasing log M and then turned to a constant value in the high‐molecular‐weight range. The plot of T_g versus 1/M or log M for hyperbranched polymers may exhibit intersecting straight‐line behaviors. The intersection or transition does not result from entanglements that account for such intersections in linear polymers but from a nonlinear feature in hyperbranched polymers according to chain‐end, free‐volume theory. However, the conclusions obtained in this work cannot be extended to dendrimers because after the third generation, the end‐group extents of a dendrimer decrease with molecular weight. Thus, it is very possible for a dendrimer that T_g increases with 1/M before the third generation; however, it decreases with 1/M after the third generation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1235–1242, 2004     

Liquid dewetting of ultrathin polystyrene films: Is there a molecular architecture effect?

We have used a liquid dewetting method to investigate the glass transition temperature T_g of high molecular weight linear, long branched 3-arm star, and short branched 8-arm star polystyrene (PS) in the form of ultrathin films. The results of these dewetting experiments are consistent with prior studies of dewetting of linear PS films and show that, independent of molecular architecture, the glass transition temperature T_g reductions with decreasing film thickness, while important below about 20 nm, are weaker than those observed for linear PS supported on a rigid substrate and as well as those observed in freely standing films. The lack of a strong molecular architecture effect on the T_g-reductions is consistent with the T_g reductions for the dewetting from a liquid substrate reflects changes in segmental dynamics upon confinement rather than chain effects. This contrasts with changes, including increases seen in dewetting from a rigid substrate, for different molecular architectures reported in the literature.     

The linear rheological responses of wedge‐type polymers

The linear rheological responses of a series of specially designed wedge‐type polymers synthesized by the polymerization of large molecular weight monomers have been measured. These wedge polymers contained large side groups which contained three flexible branch chains per polymer chain unit. The master curves for these polymers were obtained by time temperature superposition of dynamic data at different temperatures from the terminal flow regime to well below the glass transition temperature, T_g. While these polymers maintained a behavior similar to that of linear polymers, the influence of the large side group structure lead to low entanglement densities and extremely low rubbery plateau modulus values, being near to 13 kPa. The viscosity molecular weight dependence was also somewhat higher than that normally observed for linear polymers, tending toward a power law near to 4.2 rather than the typical 3.4 found in entangled linear chains. The glassy modulus of these branched polymers is also found to be extremely low, being less than 100 MPa at T_g ?60 °C. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 899–906     

Influence of local chain dynamics on diffusion of gases in polymers as determined by pulsed field gradient NMR

Diffusion of gases in polymers below the glass transition temperature, T_g, is strongly modulated by local chain dynamics. For this reason, an analysis of pulsed field gradient (PFG) nuclear magnetic resonance (NMR) diffusion measurements considering the viscoelastic behavior of polymers is proposed. Carbon‐13 PFG NMR measurements of [¹³C]O₂ diffusion in polymer films at 298 K are performed. Data obtained in polymers with T_g above (polycarbonate) and below (polyethylene) the temperature set for diffusion measurements are analyzed with a stretched exponential. The results show that the distribution of diffusion coefficients in amorphous phases below T_g is wider than that above it. Moreover, from a PFG NMR perspective, full randomization of the dynamic processes in polymers below T_g requires long diffusion times, which suggests fluctuations of local chain density on a macroscopic scale may occur. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 231–235, 2010     

A novel approach toward the prediction of the glass transition temperature: Application of the EVM model,a designer QSPR equation for the prediction of acrylate and methacrylate polymers

We describe an original QSPR model called the EVM model (Energy, Volume, Mass) to calculate the glass transition temperature (T_g) of aliphatic acrylate and methacrylate homopolymers using classical molecular mechanics and dynamics. The latter was used to calculate an energy density function related to the cylindrical volume of a 20 monomer unit polymer segment (TSSV, Total Space around a Standard deviation Volume). We then calculated the T_g as a function of this density function and the repeat unit molecular weight, although no interchain interactions were taken into account. For linear and branched aliphatic acrylate and methacrylate polymers, the standard deviation from linear regression was 12 K, and the r² was 0.96. The model allows calculation of the T_g with an average absolute error of error of 10% for linear and branched derivatives not included in the original linear regression analysis. The results obtained with the EVM model are compared with those obtained with Bicerano's model. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 2579–2590, 1997     

Relation between the network structure and dynamic mechanical properties of a typical amine-cured epoxy polymer

The dynamic mechanical properties of a series of epoxy polymers of known network structure have been investigated. It was shown that the distance between crosslinks could be predicted from either the shift in the glass transition temperature T_g or by use of the dynamic modulus above T_g. The front factor in the equation of state for rubber elasticity was near unity for stoichiometric equivalence of epoxy and amine and increased slowly with excess of either component.     

Synthesis,characterization, and thermal and dielectric properties of three different methacrylate polymers with zwitterionic pendant groups

The synthesis, characterization, thermal, and dielectric properties of three different zwitterionic methacrylates of the sulfobetaine type are presented. Diethylamine-ethyl-, 2-(diethylaminoethoxy)-ethyl-, and 2-(2-diethylaminoethoxy) ethoxy-ethyl-methacrylates were made to react with butanosultone to prepare monomers with variable flexibility. The flexibility of the lateral chain of the polymethacrylates decreased the glass transition temperature (T_g down to 300 K) of the polymers. A linear relationship between T_g and the number of carbon atoms was shown for these materials. X-ray diffraction and DSC experiments showed the formation of new ordered phases in these polymers, which inhibited their dipole conductivity. On heating, these phases were destroyed and values of conductivity of 10⁻⁷–10⁻³ S cm⁻¹ were obtained in the studied range of temperature. Variation of conductivity with temperature was established according to the Arrhenius equation. Dielectric properties exhibited a small deviation of the Debye type behavior, and β parameters of the Cole–Cole equations were calculated for the synthesized polymers. © 1997 John Wiley & Sons, Inc.     

Nuclear relaxation in atactic polystyrenes: T1 and T1ρ measurements

Measurements have been made on a series of linear atactic polystyrenes whose molecular weights range from 900 to 1.8 × 10⁶, where M _w/M _n ? 1.2. Spin lattice relaxation times have been measured in the laboratory frame (T₁) and in the rotating frame (T_1ρ) in the temperature range 90–500°K. Two major relaxation minima were observed in both sets of measurements. The high temperature process corresponds to the glass transition (α process), the position of the minimum depending on the chain length. The low temperature process appears to originate from the n-butyl endgroups in the polymer, its position being independent of chain length while its intensity is inversely proportional to molecular weight. No other minima were observed, in contrast to some other observations made by broadline and pulsed NMR techniques. Relaxation was exponential in all cases except in the region of the high temperature T_1ρ minimum and above. This nonexponential behavior is possibly connected with the transition at T > T_g observed by a number of other techniques and which is thought to correspond to a transition between two types of liquid state. A correlation frequency diagram has been drawn for all the processes observed in polystyrene by other techniques, (α, β, αβ, γ, and δ) which shows that the T₁ and T_1ρ minimum positions correlate well with the α process and that there is a possible contribution to the relaxation due to the γ process on the low temperature side of the α process. At these measurement frequencies the α and β processes are merged into an αβ process. There is no evidence for a contribution from the mechanical δ process. The effect of the endgroups is observed to very high molecular weights (4.98 × 10⁵), and it seems that a three-dimensional diffusion model would be more adequate than the one-dimensional model used to interpret similar behavior of paraffins and polyethylenes. Measurements of T₁ in the low-temperature region would constitute a method for a rough measurement of the molecular weight of these polymers.     

Thiol–ene polymerizations using imide‐based monomers

New diene and dithiol monomers, based on aromatic imides such as benzophenone‐3,3′,4,4′‐tetracarboxylic diimide were synthesized and used in thiol‐ene polymerizations which yield poly(imide‐co‐thioether)s. These linear polymers exhibit limited solubility in various organic solvents. The molecular weights of the polymers were found to decrease with increasing imide content. The glass transition temperature (T_g) of these polymers is dependent on imide content, with T_g values ranging from ?55 °C (with no imide) up to 13 °C (with 70% imide). These thermal property improvements are due to the H‐bonding and rigidity of the aromatic imide moieties. Thermal degradation, as studied by thermogravimetric analysis, was not significantly different to the nonimide containing thiol‐ene polymers made using trimethyloylpropane diallyl ether and 3,5‐dioxa‐1,8‐dithiooctane. It is expected that such monomers may lead to increased glass transition temperatures in other thiol‐ene polymer systems as these normally exhibit low glass transition temperatures. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4637–4642     

Calculation of the glass transition temperatures of polymers. Part I. Homopolymers and copolymers with alkyl side chains

Four equations, relating the glass transition temperatures T_g of homopolymers and copolymers to invariant additive temperature parameters (ATP) associated with their constituent groups, but weighted in different ways, have been applied to the calculation of the T_g of seven series of polymers having alkyl side chains. It is shown that the T_g of the 32 polymers considered may be calculated, within 7°K of the observed values, without the use of interaction coefficients from 15 independent variables, representing summations of the ATP's. The present calculations are confined to those structures which may be formed by a recombination of the structures corresponding to these independent variables. It is an essential feature of the approach that a distinction is made between groups with different nearest neighbors. Alternative methods of calculation are considered. The temperature parameter for a sequence of three or more methylene groups is estimated as 141°K, in conformity with the transition in polyethylene at 148°K. Nearest-neighbor interactions, stereoregularity, and crystallinity effects are discussed.     

Tensile yield-stress behavior of poly(vinyl chloride) and polycarbonate in the glass transition region

The yield-stress behavior of two glassy polymers is studied through the glass transition region over a wide range of strain rates. For temperatures below the glass transition temperature, the yield stress behavior could be described as a non-Newtonian flow in agreement with Eyring's theory, if one excepts a narrow range relating to the slowest strain rates. For temperatures above T_g, the yield-stress behavior is still nonlinear but fits the relations based on the concept of free volume.