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     

Similarity of the relaxation modulus of polydisperse polymers

A similarity rule due to Markovitz is used for the correlation of the relaxation modulus for different polymeric materials. This rule has long been employed implicitly in the empirical shifting rules for the reduction to common curves of viscoelastic data measured on the same polymer over a range of temperatures and concentrations. It is shown here for the rubbery regime of polydisperse polymers that when relaxation moduli are scaled with the steady-state compliance and the time with the mean relaxation time, data for a variety of amorphous polymeric materials tend to plot on a common curve. This suggests that the dimensionless rubber modulus is, to first order, a common function of dimensionless time for materials which include whole polymers and polymer solutions, the effects of temperature and concentration being automatically incorporated into the two scaling parameters. For materials with sufficient polydispersity the correlation appears to be valid over a wide range of the available experimental data. These amorphous materials appear to share only one feature, flexible molecules with broadly distributed molecular weights. For narrowly dispersed polymers the modulus in the terminal zone is also correlated according to the above rule, but the influence of other parameters appears as the transition to the glassy regime is approached. An additional application of the similarity rule allows the relaxation modulus computed from molecular dynamics simulations of idealized polymers to be compared with experimental moduli for real materials even though the characteristic times for these systems differ by more than ten orders of magnitude.     

Gas sorption and diffusion processes in polymer matrices at high pressures

A theoretical approach has been developed to describe the processes of gases diffusion and sorption in rubbery and glassy polymers. Various models (Flory-Huggins, dual-mode sorption, gas-polymer-matrix) used for interpreting the sorption-diffusion experiments are discussed within this approach framework. Experimental data on carbon dioxide sorption in glassy and rubbery polymers have been considered using the proposed approach. The comparison of the experimental and theoretical data has permitted to make the conclusion on the developed concepts adequacy. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1339–1348, 1997     

Influence of molecular weight and degree of segregation on local segmental dynamics of ordered block copolymers

Experiments in the context of block copolymer electrolyte materials have observed intriguing dependence of the ionic conductivities upon the polymer molecular weight and the degree of segregation between the blocks. Such results have been partly rationalized by invoking the spatial extent of dynamical inhomogeneities that manifest in ordered phases of block copolymers comprised of a rubbery and a glassy block. Motivated by such observations, we use molecular dynamics simulations to study the extent of spatial inhomogeneities in segmental dynamics of lamellar diblock copolymer systems where the blocks possess different mobilities. We probed the local average relaxation times and the dynamical heterogeneities as a function of distance from the interface. Our results suggest that the relaxation times of rubbery segments are strongly influenced by both the spatial proximity to the interface and the relative mobility of the glassy segments. Scaling of our results indicate that the interfacial width of the ordered phases serves as the length scale underlying the spatial inhomogeneities in segmental dynamics of the fast monomers. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 859–864     

A molecular dynamics simulation study of surface effects on gas permeation in free-standing polyimide membranes

A 141100-atom model of a glassy ODPA–ODA polyimide free-standing membrane, corresponding to a thickness of two average radii of gyration for the 40-mers chains, has been studied using molecular dynamics (MD) simulations. Due to the large-scale of the fully atomistic model, a parallelized particle-mesh technique using an iterative solution of the Poisson equation had to be implemented for the efficient evaluation of the electrostatic interactions. With flattened-chain configurations, the density was found to adjust itself naturally in the middle of the membrane to 95% of the ODPA–ODA experimental value. At the free-standing surfaces, the density profile became sigmoïdal, indicating surface roughness. For comparison, two isotropic bulk models, one at the “normal” density as obtained for ODPA–ODA under ambient conditions and the other one at 95% of the normal-density, were built. Small gas probes were inserted into all three models in order to investigate whether the interfacial structure of the glassy free-standing membrane can influence penetrant transport. Gas diffusion in the low-density part of the interface was found to be very fast. The limiting value for the gas diffusion coefficient D_membrane is only attained when the probes enter more dense regions in the membrane. Indeed, D_membrane compares well with D_bulk obtained for the 95%-density bulk system, i.e. about twice that in the normal-density bulk. Solubility is larger in the membrane than in both bulk models, thus suggesting an effect of chain flattening in addition to the density. Adsorption is particularly high at the free-standing interfaces.     

Thermomechanical enhancement of DPP-4T through purposeful π-conjugation disruption

The design of polymer-based organic semiconductors that offer mechanical deformability while maintaining efficient semiconducting characteristics remains a significant challenge. Recent synthetic efforts have incorporated small alkyl segments directly into otherwise π-conjugated polymer backbones to enhance processability, mechanical deformability, and other properties. The resulting polymers can be used as stand-alone materials or as matrix polymers in complementary semiconducting polymer blends offering reasonable charge-carrier transport properties, thermal healing, and deformability. Here, a family of diketopyrrolopyrrole-tetrathiophene variants is explored via large-scale atomistic molecular dynamics simulations to examine the effect of alkyl segments incorporated into the polymer backbone on the polymer structure, dynamics, and thermal properties. Longer alkyl segments lead to polymer chains that are more flexible, compact, and mobile, with lower glass transition temperatures for the condensed phase.     

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     

Anomalous transport of penetrants in glassy polymers

Solutions are presented for the Fickian and non-Fickian equations describing the case of penetrant transport in a glassy polymer. Due to associated macromolecular relaxation, a sharp penetrant front is observed which separates the glassy core from the rubbery (gel-like) layer at the surface. Concentration profiles are compared and general comments about Fickian versus non-Fickian transport in polymers are made.     

Crosslinked oligoethylene glycols: Correlation between their structure and some rheological properties

Six oligoethylene glycols were crosslinked with triphenylmethane triisocyanate, and polymers with systematically changing network chain lengths were obtained and investigated. The 10-sec. torsion moduli versus temperature, glass transition temperatures, and cohesive energy densities of the polymers were determined and studied. The 10-sec. torsion modulus versus temperature plots show that all six polymers have a glassy transition and rubbery region of rheological behavior. The front factor calculated from the equation for the torsion modulus in the rubbery region when measured values of the modulus were used was compared with the front factor computed from equations that take into consideration molecular structures of the rubbery networks. With the exception of the case of crosslinked diethylene glycol the agreement in all the other cases between the values obtained for the front factor in both ways was good. In the investigated range of temperatures the polymers have below the glass transition temperature another transition point. The solubility parameters of the polymers, calculated from swelling experiments, were with the exception of the first member in the series almost identical.     

A dendronized polymer is a single-molecule glass

The molecular architecture of dendronized polymers can be tuned to obtain nanoscale objects with desired properties. In this paper, we bring together experiments and computer simulations to study the thermodynamic and dynamic properties of a single dendronized polymer chain. We find that, upon changing certain architectural features, dynamic correlations characterizing backbone conformational fluctuations of a dendronized polymer exhibit dynamics akin to glass-forming bulk liquids. Thus, a dendronized polymer chain is a novel macromolecule that is a single-molecule glass. Over a range of conditions that lead to glassy dynamics, there does not appear to be any thermodynamic singularities. We discuss how a dendronized polymer is a molecular system that can directly test different models of glassy dynamics. We also show that defect densities characteristic of typical synthesis conditions do not alter the material properties of dendronized polymers.     

Dispersions of polymer ionomers: I

The principal subject discussed in the current paper is the effect of ionic functional groups in polymers on the formation of nontraditional polymer materials, polymer blends or polymer dispersions. Ionomers are polymers that have a small amount of ionic groups distributed along a nonionic hydrocarbon chain. Specific interactions between components in a polymer blend can induce miscibility of two or more otherwise immiscible polymers. Such interactions include hydrogen bonding, ion-dipole interactions, acid-base interactions or transition metal complexation. Ion-containing polymers provide a means of modifying properties of polymer dispersions by controlling molecular structure through the utilization of ionic interactions. Ionomers having a relatively small number of ionic groups distributed usually along nonionic organic backbone chains can agglomerate into the following structures: (1) multiplets, consisting of a small number of tightly packed ion pairs; and (2) ionic clusters, larger aggregates than multiplets. Ionomers exhibit unique solid-state properties as a result of strong associations among ionic groups attached to the polymer chains. An important potential application of ionomers is in the area of thermoplastic elastomers, where the associations constitute thermally reversible cross-links. The ionic (anionic, cationic or polar) groups are spaced more or less randomly along the polymer chain. Because in this type of ionomer an anionic group falls along the interior of the chain, it trails two hydrocarbon chain segments, and these must be accommodated sterically within any domain structure into which the ionic group enters. The primary effects of ionic functionalization of a polymer are to increase the glass transition temperature, the melt viscosity and the characteristic relaxation times. The polymer microstructure is also affected, and it is generally agreed that in most ionomers, microphase-separated, ion-rich aggregates form as a result of strong ion-dipole attractions. As a consequence of this new phase, additional relaxation processes are often observed in the viscoelastic behavior of ionomers. Light functionalization of polymers can increase the glass transition temperature and gives rise to two new features in viscoelastic behavior: (1) a rubbery plateau above T(g) and (2) a second loss process at elevated temperatures. The rubbery plateau was due to the formation of a physical network. The major effect of the ionic aggregate was to increase the longer time relaxation processes. This in turn increases the melt viscosity and is responsible for the network-like behavior of ionomers above the glass transition temperature. Ionomers rich in polar groups can fulfill the criteria for the self-assembly formation. The reported phenomenon of surface micelle formation has been found to be very general for these materials.     

Oxygen transport as a solid‐state structure probe for polymeric materials: A review

In the quest to elucidate the solid‐state structures of polymers, insight into the amorphous phase is particularly elusive. Although the permeability of small molecules is often measured as an important performance property, numerous researchers have found that a deeper analysis of the transport characteristics provides insight into polymer morphology, especially if used in combination with more usual characterization techniques. The transport of small gas molecules senses the permeable amorphous structure and probes the nature of the free volume. In recent years, our interest in the gas barrier of polyesters has resulted in an unusual opportunity to investigate the nature of the free volume in the polymer glassy state. This effort has been aided by access to aromatic polyesters with designed variations in their chemical structure. This review focuses on oxygen transport, supplemented with other methods of physical analysis, as a probe of the excess‐hole free volume. The review addresses the profound effects of orientation and crystallization on the free volume of the glassy state. The discussion also presents a simple odel for the gas permeability of the isotropic glass based on lattice concepts and tests more sophisticated models for the gas permeability of semicrystalline polymers. The final section addresses other opportunities for fruitful applications of oxygen transport as a solid‐state structure probe. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1047–1063, 2005     

Simulation of experimentally observed dilation phenomena during integral gas sorption in glassy polymers

A molecular modeling investigation of dilation effects induced by sorbed gas molecules in two glassy polymers is presented. As experimental reference, integral sorption of CO₂ and CH₄ was measured for polysulfone (PSU) and a polyimide (6FDA‐TrMPD, PI4) at 308 K and a pressure of 10 bar. Simultaneously, the gas induced swelling effect was measured with a dilatometer based on a capacitive distance sensor recorded. The experimental evidence of the (on the observed time scale and concentration levels) elastic nature of the gas induced dilation is supported by the dilation and contraction behavior observed in molecular dynamics (MD) simulations of respective detailed atomistic packing models. These models were constructed in accordance with gas concentration levels obtained from the experimental sorption results. Quantitative deviations between simulated and measured dilations are discussed as a consequence of an anelastic response of the polymer matrix which is too fast to be resolved in the experiments whose kinetics is dominated by diffusional processes. In the simulation, the initial insertion of penetrant molecules into equilibrated packing models “circumvents” the slow diffusional process of the experiment and allows a reasonable representation of the dilation process as well as a closer investigation. Our simulation approach reveals a different behavior for PSU and PI4 on the corresponding time scale. Most likely, the different chain mobility of the two polymers is responsible for the respective response to the inserted amount of gas molecules which is discussed in terms of the different chain mobilities of the two polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 59–71, 2008     

取代聚炔的合成及其分离性能

具有优异物理和化学性能的新聚合物开发推动了取代聚炔的设计与合成。聚炔中功能侧基的引入赋予其非线性光学、液晶、发光、螺旋手性和高气体渗透等性能。作为一种重要的分离膜材料,与传统的玻璃态聚合物膜材料不同,这种无定形、高刚性的聚合物的显著特点是具有非常高的气体渗透系数和蒸汽／气体分离系数。有关其气体分离、天然气净化和对映体拆...     

Confined crystallization in lamellae forming poly(3-(2′-ethyl)hexylthiophene) (P3EHT) block copolymers

Charge transport in poly(3-alkylthiophene)s (P3AT)s is closely linked to the nanoscale organization of crystallites. Block copolymer morphologies provide an ideal platform to study crystallization as the chain ends are tethered at a known interface in a well-defined geometry. The impact of soft versus hard confinement on P3EHT crystallization was studied using poly(3-(2′-ethyl)hexylthiophene) (P3EHT) containing diblocks with both rubbery poly(methyl acrylate) (PMA) and glassy polystyrene (PS) blocks. Here, P3EHT's lower melting point relative to the commonly studied poly(3-hexylthiophene) (P3HT) facilitated its confined crystallization and makes it an ideal model system. While transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS) revealed well-ordered lamellar morphologies both in the melt and post-crystallization for both sets of diblocks, the glassy blocks inhibit confined crystallization of P3EHT relative to rubbery matrix blocks. Analysis of aligned diblocks by both SAXS and wide angle X-ray scattering (WAXS) revealed that the P3EHT chain axis aligns perpendicular to domain interfaces, allowing preferential growth of the alkyl-chain and π–π stacking directions parallel to lamellae. Finally, it was shown that following diblock self-assembly in the melt, crystallite growth drives expansion of microdomains to match the P3EHT contour length. It was concluded that P3EHT chains adopted an extended conformation within confined crystallites due to the rigid nature of polythiophenes relative to flexible chain crystalline polymers. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 205–215     

Permeation of CO2 and N2 through glassy poly(dimethyl phenylene) oxide under steady- and presteady-state conditions

Glassy polymers are often used for gas separations because of their high selectivity. Although the dual-mode permeation model correctly fits their sorption and permeation isotherms, its physical interpretation is disputed, and it does not describe permeation far from steady state, a condition expected when separations involve intermittent renewable energy sources. To develop a more comprehensive permeation model, we combine experiment, molecular dynamics, and multiscale reaction–diffusion modeling to characterize the time-dependent permeation of N₂ and CO₂ through a glassy poly(dimethyl phenylene oxide) membrane, a model system. Simulations of experimental time-dependent permeation data for both gases in the presteady-state and steady-state regimes show that both single- and dual-mode reaction–diffusion models reproduce the experimental observations, and that sorbed gas concentrations lag the external pressure rise. The results point to environment-sensitive diffusion coefficients as a vital characteristic of transport in glassy polymers.     

Collapse of an <Emphasis Type="Italic">AB</Emphasis> copolymer single chain with alternating blocks of different stiffness

Using the Langevin dynamics, we studied the conformational properties of an AB copolymer single chain built of alternating stiff and flexible blocks having different steady-state affinities to a solvent. Two opposite conditions were simulated, viz., where a solvent is poor for stiff blocks and good for flexible blocks and vice versa. The behavior of the molecules built of equal-length blocks and long stiff blocks linked through short flexible junctions were considered. Upon transition of a chain to the compact state, nanostructures with different morphologies, such as bunches, networks, and others, can form.