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     

Free volume and oxygen transport in cold‐drawn polyesters

Poly(ethylene terephthalate) (PET), poly(ethylene terephthalate‐co‐4,4′‐bibenzoate) (PETBB55), and poly(ethylene 2,6‐naphthalate) (PEN) were cold‐drawn to achieve uniform extension without crystallization or stress whitening, and oxygen transport properties were studied at temperatures from 10 to 40 °C. Correlation of oxygen solubility and polymer specific volume made it possible to consider the oriented polyester as a one‐phase densified glass. Orientation was viewed as decreasing the amount of excess‐hole free volume and bringing the nonequilibrium polymer glass closer to the equilibrium condition. Between 10 and 40 °C, the amount of excess‐hole free volume in PET decreased as the polymer approached the glass transition temperature. In contrast, temperature changes in this range had little effect on the excess‐hole free volume in PETBB55 and PEN, which were well below their glass transition temperature. Gas diffusion was viewed as discrete jumps of the oxygen molecule between holes of excess‐free volume. The jump length was extracted from the activation energy for diffusion according to a channel‐formation model. The result agreed well with the hole spacing estimated from a simple lattice model using the hole density reported in the literature. Extending the lattice model to estimate the mean excess‐free volume hole radius from the fractional free volume resulted in good correlation with the hole radius obtained from positron annihilation lifetime spectroscopy. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 493–504, 2004     

Structural and free‐volume analysis for alkyl‐substituted palladium‐catalyzed poly(norbornene): A combined experimental and Monte Carlo investigation

Increasing the length of an alkyl side chain on a rigid polynorbornene (PNB) backbone is shown to decrease the glass‐transition temperature of the resultant polymer, decrease the density of the bulk polymer, decrease the number and average free‐volume element size present, and decrease the permeability of gases through the polymer. Methyl‐, butyl‐, and hexyl‐substituted PNBs were investigated. Experimental results were compared with predictions based on molecular modeling. By using models that provided good agreement between the experimental and simulated wide‐angle diffraction patterns, the distributions of free‐volume elements were predicted. These predictions clearly indicate that the number of large free‐volume elements decreases as the length of the side chain increases, suggesting that the flexible aliphatic side chains can be largely accommodated within the free volume between the rigid PNB backbones. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 215–233, 2006     

Effect of orientation on the free volume and oxygen transport of a polypropylene copolymer

The effect of uniaxial orientation on the free‐volume and oxygen‐transport properties of a propylene copolymer with 4.5 wt % ethylene was examined. The free‐volume hole size and hole density were measured with positron annihilation lifetime spectroscopy. Subsequently, the free‐volume characteristics were correlated with the oxygen‐transport properties. Orientation had only a small effect on the total amount of free volume: a small increase in the hole density was offset by a small decrease in the hole size. As a result, the oxygen solubility and amorphous‐phase density were unchanged by orientation. However, a pronounced decrease in the oxygen diffusivity when the draw ratio exceeded 6 indicated a change in the dynamic free volume. This was attributed to an increasing number of taut tie chains, which retarded oxygen diffusion. The reduced amorphous chain mobility was also manifest in the increased glass‐transition temperature, decreased bulk thermal expansivity, and decreased expansivity of free‐volume holes. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1230–1243, 2005     

Effect of molecular association on solubility,diffusion, and permeability in polymeric membranes

The filling‐type membrane is composed of grafted polymer and solvent‐resistant substrate; the calculation of solubility, diffusivity and swelling‐suppression effect by the substrate permits the prediction of solvent permeability. As noted in our previous article, the use of this approach, called membrane design, resulted in accurate prediction of the permeability of aromatic compounds. In this study, the influence of hydrogen bonding on solubility and diffusivity is investigated both theoretically and experimentally. The solubility of chloroform and dichloromethane in poly(acrylate)s increases, and their diffusivity decreases, compared with that estimated without considering the hydrogen‐bonding effect. Solubilities predicted by the lattice‐fluid hydrogen‐bonding (LFHB) model show good agreement with the results of vapor sorption. Comparison of diffusion coefficients measured by vapor permeation with those predicted from free volume theory reveals that the decrease of solvent diffusion coefficient is approximately proportional to the fraction of associated molecules. Fluxes of chloroform and dichloromethane were measured by vapor permeation experiments through filling‐type acrylate membranes, and predictions agree well with experiments. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 171–181, 2000     

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     

Solubility and diffusivity of methylmethacrylate and butylacrylate monomers in a MMA–BA copolymer

Mutual diffusion coefficients and sorption isotherms of methyl methacrylate (MMA) and butyl acrylate (BA) monomers in methyl methacrylate‐butyl acrylate copolymer (MMA‐BA) have been measured by gravimetric sorption. MMA is found to have higher solubility and diffusion rates in the copolymer than BA. Sorption data for MMA were interpreted using classical Flory‐Huggins thermodynamic theory with a constant interaction parameter (χ). A modified version of this theory has been applied to correlate the sorption data of BA, which exhibit a temperature and concentration‐dependent χ parameter. For MMA, the isotherm data reveal enhanced polymer‐solvent interactions with increasing temperature, while for BA the data indicate a drive toward phase separation with increasing temperature. Despite the difference in thermodynamic behavior, both monomers are found to exhibit Fickian diffusion and the diffusivity data are correlated reasonably well with the Vrentas‐Duda free volume theory. Some deviation between the free‐volume correlation and the experimental data is observed at the lowest temperature and BA concentration examined. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1996–2006, 2007     

Solution properties,unperturbed dimensions,and chain flexibility of poly(1‐adamantyl acrylate)

Poly(1‐adamantyl acrylate) (PAdA) exhibits much higher glass transition and degradation temperatures than other polyacrylates. However, the quantitative evaluation of the stiffness of this polymer chain has not been reported previously. In this study, the dilute solution properties and conformational characteristics of PAdA were evaluated using viscometry and scattering techniques. The unperturbed dimensions of this polymer were evaluated using the Burchard–Stockmayer–Fixman extrapolation and the touched‐bead wormlike chain model. The PAdA chain has a comparable persistence length, diameter per bead and characteristic ratio to poly(methyl methacrylate) and polystyrene. All these results indicate that PAdA is less flexible than common polyacrylates. In addition, the second virial coefficients (A₂) of PAdA in different solvents obtained by static light scattering were compared. Among the solvents investigated, tetrahydrofuran is a moderate solvent. Radius of gyration of a polymer sample in the various solvents ranged from 16.8 to 30.3 nm. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1526–1531     

Synthesis and characterization of graft polymethacrylates containing conducting diphenyldithiophene for organic thin‐film transistors

A class of [5,5′]‐diphenyl‐[5,5′]‐dithiophene (PTTP)‐modified methacrylates has been synthesized and free radically polymerized to form graft polymethacrylates with the conducting PTTP segments as pendant side chains. Both the terminal alkyl side chain and spacer between the PTTP segments and polymer backbone could be varied to study fundamental structure–property relationships for this class of materials. Specifically, a group of three different PTTP graft polymethacrylates has been successfully synthesized with the alkyl side chain varying from hexyl to dodecyl. For the dodecyl‐terminated poly(4‐(5′‐(4‐dodecylphenyl)‐[2,2′‐bithiophen]‐5‐yl)phenethyl methacrylate), p(DPTTPEM), a counterpart, poly(4‐(5′‐(4‐dodecylphenyl)‐[2,2′‐bithiophen]‐5‐yl)phenbutyl methacrylate), p(DPTTPBM), where the ethyl spacer was replaced by a butyl group, was synthesized. The experimental results indicated that both the alkyl side chain and spacer significantly affected the reactivity of the PTTP‐modified methacrylates during free radical polymerization as well as the physical properties of the resultant graft polymers including solubility, morphology, and electrochemical and electrical properties. Typical field‐effect mobilities on the order of 10^?5 cm² V^?1 s^?1 were observed for all the PTTP monomers in air, which was attributed to their crystalline phase as revealed by differential scanning calorimetry and X‐ray diffraction studies. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Structure and rheology of polymers with arbitrary flexibility: A numerical approach

A numerical approach, based on the configurational distribution function of a polymer chain in flow, has been used to calculate the zero-shear rheological properties. Starting from a bead-spring representation of the chain, the stiffness is introduced by repulsive springs between next-nearest neighbors. The connection to models based on the bending equation and their limitation is discussed. To obtain a correct model of a semiflexible chain, an inhomogeneous spring constant has to be used. Calculations have been carried out for the free draining case, and a simple relation between the intrinsic viscosity, the translational diffusion coefficient and the persistence length for arbitrary solvent conditions is proposed. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1995–2003, 1998     

Depth profiling of latex blends of fluorinated and fluorine‐free acrylates with laser‐induced secondary mass spectrometry

We explored phase separation and self‐assembly of perfluoroalkyl segments at the surface of polymer films obtained from latices of semifluorinated acrylate copolymers and the corresponding latex blends of nonfluorinated and semifluorinated polyacrylates. With laser‐induced secondary mass spectrometry the fluorine distribution was measured after annealing above the minimum film‐forming temperature of the polymers up to a depth of several micrometers. Depth profiles of a semifluorinated acrylate homopolymer and latex blends thereof with fluorine‐free alkylacrylates with 25, 50, and 75 mol % semifluorinated acrylate as well as a copolymer comprised of alkyl acrylate and semifluorinated acrylate (50/50 mol %) were investigated. In the case of latex blends containing both semifluorinated polyacrylates and fluorine‐free or low‐fluorine polymers, self‐assembly accounted for enrichment of the perfluoroalkyl segments at the surface. Coatings exhibiting low surface energy and having a substantially reduced total fluorine content were obtained. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 360–367, 2003     

Investigating the Dynamic Viscoelasticity of Single Polymer Chains using Atomic Force Microscopy

In single‐molecule force spectroscopy (SMFS), many studies have focused on the elasticity and conformation of polymer chains, but little attention has been devoted to the dynamic properties of single polymer chains. In this study, we measured the energy dissipation and elastic properties of single polystyrene (PS) chains in toluene, methanol, and N,N‐dimethylformamide using a homemade piezo‐control and data acquisition system externally coupled to a commercial atomic force microscope (AFM), which provided more accurate information regarding the dynamic properties of the PS chains. We quantitatively measured the chain length‐dependent changes in the stiffness and viscosity of a single chain using a phenomenological model consistent with the theory of viscoelasticity for polymer chains in dilute solution. The effective viscosity of a polymer chain can be determined using the Kirkwood model, which is independent of the intrinsic viscosity of the solvent and dependent on the interaction between the polymer and solvent. The results indicated that the viscosity of a single PS chain is dominated by the interaction between the polymer and solvent. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1736–1743     

Permeability,permselectivity, and penetrant‐induced plasticization in fluorinated polyimides studied by positron lifetime measurements

The ortho‐positronium (o‐Ps) lifetime τ₃ and its intensity I₃ in various fluorinated polyimides were determined by the positron annihilation technique and were studied with the spin–lattice relaxation time T₁ and the propylene permeability, solubility, diffusivity, and permselectivity for propylene/propane in them. τ₃, I₃, and the distribution of τ₃ changed when the bulky moieties in the polyimides were changed. The polyimides, having both large τ₃ and I₃ values, exhibited a short T₁ and a high permeability with a low permselectivity. The propylene permeability and diffusivity were exponentially correlated with the product of I₃ and the average free‐volume hole size estimated from τ₃. In highly plasticized states induced by the sorption of propylene, the permeability increased with the propylene pressure in excellent agreement with the change in the free‐volume hole properties probed by o‐Ps. The large and broad distribution of the free‐volume holes and increased local chain mobility for the 2,2‐bis(3,4‐decarboxyphenyl) hexafluoropropane dianhydride‐based polyimides are thought to be important physical properties for promoting penetrant‐induced plasticization. These results suggest that o‐Ps is a powerful probe of not only the free‐volume holes but also the corresponding permeation mechanism and penetrant‐induced plasticization phenomenon. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 308–318, 2003     

Spinodal decomposition with varying chain lengths and its application to designing polymer blends

The diffusion equations of spinodal decompositions with unique diffusivities for each species are derived for binary systems and ternary systems. These dynamic equations are linearized to show that the minimum size for growth is independent of diffusivity and is identical to the thermodynamic minimum on phase volume. Increases in chain length will destabilize mixtures and increase quench depth. Numerical simulations were conducted for two-dimensional systems. The considerable influences of chain lengths on morphology represent a competition between smaller diffusivities and larger quench depth when chain length is increased. These influences on several important morphologies in binary and ternary systems are described. The understanding of independent variable chain lengths represents one further step towards the systematical design of polymer blends. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 897–907, 1997     

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     

Intramolecular screening effects in nondilute polymer solutions: An equation‐of‐state approach

In a previous article, we presented a simple modification of the traditional Flory–Huggins theory that took intramolecular screening effects (or same chain contacts) into account. In this article, we present a natural extension of that work, in which free‐volume effects are also explained with an equation‐of‐state model. The predictions of the interaction parameter, χ, for several polymer–solvent systems are presented, over the entire concentration range, in θ solvents and good solvents. A geometric mean assumption is applied to the calculation of an exchange energy interaction term. The predictions of χ are successful to various degrees when internal pressures are used, whereas the use of solubility parameters in most cases produces fairly good agreement with experimental results. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2911–2922, 2003     

Chain confinement in polymer nanocomposites and its effect on polymer bulk properties

The issue of chain confinement in nanocomposites remains largely unanswered because experimental systems are plagued by additional complicating variables such as particle–polymer interactions and free volume increases brought upon by the addition of the particles. Using computer simulation of high length chain polymers, we show that simple excluded volume interactions between polymer and nanoparticles lead to a wealth of changes in the diffusion coefficient and entanglement density of the chains. This opens up the possibility of using nanoparticles for tuning polymer properties, such as toughness, melt viscosity, and transient rubberlike behavior. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 687–692, 2010     

Characteristics of a single‐layered organic electroluminescent device using a carrier‐transporting copolymer and a nonconjugated light‐emitting polymer

We have synthesized a novel carrier‐transporting copolymer and a nonconjugated light‐emitting polymer. The carrier‐transporting copolymer has a triphenylamine moiety as a hole‐transporting unit and a triazine moiety as an electron‐transporting unit, both of which are located in the polymer side chain. The nonconjugated light‐emitting polymer has a perylene moiety, which acts as an emitting unit in the polymer side chain. These polymers are very soluble in most organic solvents, such as monochlorobenzene, tetrahydrofuran, chloroform, and benzene. A single‐layered electroluminescent device consisting of ITO/copolymer and emitting‐material 4‐(dicyanomethylene)‐2‐methyl‐6‐(4‐dimethylaminostyryl)‐4H‐pyran (DCM) or light‐emitting polymer)/Al mixtures exhibits maximum external quantum efficiency when the concentration of the emitting material is 30 wt %. The device emits red or blue light according to the emitting material. When CsF is used as the electron‐injecting material, the drive voltage decreases drastically to 7 V, and the highest quantum efficiency is 0.5%. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2733–2743, 2003     

Effect of blend composition on diffusivity and solubility of small molecules in polystyrene/poly(vinyl methyl ether) blends

The capillary column inverse gas chromatography technique was used to determine diffusivity and solubility data for several solvents in polymer blends composed of polystyrene and poly(vinyl methyl ether) (PVME). Diffusivity behaved as expected, increasing as the concentration of PVME increased in the blend. Knowing only the free‐volume parameters for the pure polymers, the free‐volume theory was successfully applied to predict the dependence of the diffusion coefficients on the blend composition. Transport in blends above the glass transition temperature is controlled by free volume, and the effect of concentration fluctuations is minimal at the temperatures studied. Experimental data show an increase in the partition coefficient of some solvents in the blends with respect to the pure polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2071–2082, 2007     

Evaluation of the free‐volume theory of diffusion

General characteristics of the free‐volume theory of diffusion are discussed, and a recent data‐theory comparison involving free‐volume theory is critically evaluated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 501–507, 2003