Diffusion of small molecules in glassy polymers

Small molecules in glassy polymers are considered to occupy sites with a distribution of free energies of dissolution. Then their diffusivity depends on concentration and temperature in the same way as it has been derived for hydrogen atoms in metallic glasses. For hydrogen it was shown that the tracer diffusion coefficient is proportional to the activity coefficient of the solute atoms. The latter can be evaluated from measured data of sorption of the small molecules in the polymer. Knowing this quantity, the thermodynamic factor can be calculated and the concentration dependence of the mutual diffusion coefficient is obtained in excellent agreement with published experimental results. New experimental results are presented for the diffusion coefficient of CO₂ in Kapton and four polycarbonates (BPA-PC, BPZ-PC, TMBPA-PC, and TMC-PC) in the low CO₂ pressure range of a few mbar up to 1 bar. The results are in agreement with the model developed for hydrogen. The reference diffusion coefficient, which is a fitting parameter of the model that is independent of the distribution of free energies is smallest for the polycarbonate BPZ-PC having a high γ-relaxation temperature. This correlation between the diffusion coefficient and the dynamics of the polymer can be found for other substituted polycarbonates as well. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2397–2408, 1997     

Effective intraparticle diffusion coefficients of CoCl2 in mesoporous functionalized silica adsorbents

The scope of this work is to determine the effective intraparticle diffusion coefficient of CoCl₂ over mesoporous functionalized silica. Silica is selected as a carrier of the functionalized groups for its rigid structure which excludes troublesome swelling, often found in polymeric adsorbents. 2-(2-pyridyl)ethyl-functionalized silica is selected as a promising affinity adsorbent for the reversible adsorption of CoCl₂. The adsorption kinetics is investigated with the Zero Length Column (ZLC) method. Initially, experiments were performed at different flow rates to eliminate the effect of external mass transfer. The effect of pore size (60 Å and 90 Å), particle size (40?10^?6 m–1000?10^?6 m) and initial CoCl₂ concentration (1 mol/m³–2.0 mol/m³) on the mass transfer was investigated. A model was developed to determine the pore diffusion coefficient of CoCl₂ by fitting the experimental data to the model. The pore diffusion coefficients determined for two different pore sizes of silica are D _p (60 Å) =1.95?10^?10 [m²/s] and D _p (90 Å) =5.8?10^?10 [m²/s]. The particle size and the initial CoCl₂ concentration do not have an influence on the value of diffusion coefficient. However, particle size has an influence on the diffusion time constant. In comparison with polymer adsorbents, silica based adsorbents have higher values of diffusion coefficients, as well as a more uniform and stable pore structure.     

Molecular mobility of poly(methyl methacrylate) glass during uniaxial tensile creep deformation

An optical photobleaching method has been used to measure the segmental dynamics of a poly(methyl methacrylate) (PMMA) glass during uniaxial creep deformation at temperatures between T_g ? 9 K and T_g ? 20 K. Up to 1000‐fold increases in mobility are observed during deformation, supporting the view that enhanced segmental mobility allows flow in polymer glasses. Although the Eyring model describes this mobility enhancement well at low stress, it fails to capture the dramatic mobility enhancement after flow onset, where in addition the shape of the relaxation time distribution narrows significantly. Regions of lower mobility accelerate their dynamics more in response to an external stress than do regions of high mobility. Thus, local environments in the sample become more dynamically homogeneous during flow. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1713–1727, 2009     

Effect of supercritical carbon dioxide on the diffusion coefficient of phenol in poly(bisphenol A carbonate)

For some polymers, the rate of solid‐state polymerization (SSP) is higher with supercritical carbon dioxide (scCO₂) as the sweep gas than with atmospheric N₂. One explanation for this higher rate is that the diffusion coefficient of the condensate molecule is higher in the CO₂‐swollen polymer. To investigate this hypothesis, we measured the diffusion coefficient of phenol in poly(bisphenol A carbonate) (BPA‐PC) by carrying out SSP of this polymer under diffusion‐limited conditions. Under these conditions, the diffusion coefficient of the condensate molecule could be calculated from the profile of the molecular weight versus time. The phenol diffusivity was determined between 135 and 180 °C in the presence of N₂ at about 1 bar and in the presence of scCO₂ at about 138, 207, and 345 bar. The diffusion coefficient of phenol was up to 200% higher in scCO₂ than in N₂, depending on the temperature and CO₂ pressure. With both N₂ and scCO₂, the activation energy for phenol diffusion in BPA‐PC was larger than the activation energy for the reaction between hydroxyl and phenyl end groups that occurred during SSP of BPA‐PC. As a result, the overall SSP reaction shifted from diffusion control at low temperatures toward chemical‐reaction control at high temperatures. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1143–1156, 2003     

Diffusion coefficients of the monomer and oligomers in hydroxyethyl methacrylate

The diffusion coefficients are reported of rubbery ternary systems consisting of the polymer, its monomer analogue (i.e., the saturated equivalent of the monomer), and trace quantities of oligomers (dimer, trimer, tetramer and hexamer) for 2‐hydroxyethyl methacrylate (HEMA). These have been obtained with pulsed‐field‐gradient NMR spectroscopy with a polymer weight fraction (f_p) of 0 ≤ f_p ≤ 0.4. The oligomers are macromonomers synthesized with a cobalt catalytic chain‐transfer agent. The diffusion coefficients are about an order of magnitude smaller than those for monomers such as methyl methacrylate; this effect is ascribed to hydrogen bonding in HEMA. The diffusion coefficient D_i of an i‐meric oligomer has been fitted with moderate accuracy by an empirical universal scaling relation, D_i(f_p)/D₁(f_p) ≈ i, previously found to provide an adequate fit to corresponding data for styrene and for methyl and butyl methacrylates. The approximate empirical scaling relation seems to hold for a remarkably wide range of types of monomer/polymer systems. These results are of use in modeling rates and molecular weight distributions in free‐radical polymerization, particularly for termination (which is chain‐length‐dependent and is controlled by the diffusion coefficient of chains of the low degrees of polymerization studied here). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2491–2501, 2003     

Monolayer and multilayer compact film formations on different substrates by physical deposition

Dissipative particle dynamics simulations are applied to investigate the monolayer and multilayer film formations on different solid substrates by physical deposition. The influences of the polymer concentration, the polymer chain length, the solvent quality, and the interactions between the polymer solution and the solid substrate surface on the film formation dynamics and the mechanism are studied in detail. The results are analyzed in terms of the thickness and the shape of the deposited film, the kinetics of phase separation in the polymer solution, and the contact angle formed between the polymer aggregations and the substrate surface. Moreover, we suggest two strategies, designing a deposition process analogous to “chemical titration” and physically blocking interlayer diffusion by a simple crosslinked network barrier, to deposit the compact monolayer and multilayer films with better quality, respectively. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 353–365, 2009     

Probe diffusion in homogeneous diblock copolymers

Forced Rayleigh scattering was used to investigate the diffusion of a photoreactive dye molecule in two homogeneous poly(styrene-b-isoprene) (SI) diblock copolymers with overall molecular weights of approximately 2000. Although diffusion rates were intermediate to TTI transport in homopolymer polystyrene (PS) and polyisoprene (PI), system dynamics appear to be largely dictated in each case by the PI block. The size of the polymer jumping unit, on the other hand, is evaluated from a free-volume analysis of the data, and is found to be governed predominantly by the PS component of the copolymer. The mechanism for tracer diffusion in low-molecular-weight block copolymers appears analogous to transport in a high molecular weight SI diblock copolymer (M_n = 13,600) that has been solvated sufficiently in toluene to be microstructurally disordered. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1739–1746, 1998     

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     

Thermal curing behavior of MWCNT modified vinyl ester‐polyester resin suspensions prepared with 3‐roll milling technique

This study aims to investigate the curing behavior of a vinyl ester‐polyester resin suspensions containing 0.3 wt % of multiwalled carbon nanotubes with and without amine functional groups (MWCNTs and MWCNT‐NH₂). For this purpose, various analytical techniques, including Differential Scanning Calorimetry (DSC), Fourier infrared spectroscopy (FTIR), Raman Spectroscopy, and Thermo Gravimetric Analyzer (TGA) were conducted. The resin suspensions with carbon nanotubes (CNTs) were prepared via 3‐roll milling technique. DSC measurements showed that resin suspensions containing CNTs exhibited higher heat of cure (Q), besides lower activation energy (E_a) when compared with neat resin. For the sake of simplicity of interpretation, FTIR investigations were performed on neat vinyl ester resin suspensions containing the same amount of CNTs as resin. As a result, the individual fractional conversion rates of styrene and vinyl ester were interestingly found to be altered dependent on MWCNTs and MWCNT‐NH₂. The findings obtained from RS measurements of the cured samples are highly proportional to those obtained from FTIR measurements. TGA measurements revealed that CNT modified nanocomposites have higher activation energy of degradation (E_d) compared with the cured polymer. The findings obtained revealed that CNTs with and without amine functional groups alter overall thermal curing response of the surrounding matrix resin, which may probably impart distinctive characteristics to mechanical behavior of the corresponding nanocomposites achieved. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1511–1522, 2009     

Controlled/living heterogeneous radical polymerization in supercritical carbon dioxide

Supercritical carbon dioxide (scCO₂) is an inexpensive and environmentally friendly medium for radical polymerizations. ScCO₂ is suited for heterogeneous controlled/living radical polymerizations (CLRPs), since the monomer, initiator, and control reagents (nitroxide, etc.) are soluble, but the polymer formed is insoluble beyond a critical degree of polymerization (J_crit). The precipitated polymer can continue growing in (only) the particle phase giving living polymer of controlled well‐defined microstructure. The addition of a colloidal stabilizer gives a dispersion polymerization with well‐defined colloidal particles being formed. In recent years, nitroxide‐mediated polymerization (NMP), atom transfer radical polymerization (ATRP), and reversible addition fragmentation chain transfer (RAFT) polymerization have all been conducted as heterogeneous polymerizations in scCO₂. This Highlight reviews this recent body of work, and describes the unique characteristics of scCO₂ that allows composite particle formation of unique morphology to be achieved. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3711–3728, 2009     

Self‐diffusion of styrene, 2,2′‐azobisisobutyronitrile,and polystyrene in bulk polymerization by pulsed‐gradient spin‐echo nuclear magnetic resonance spectroscopy

The self‐diffusion of styrene, polystyrene, and 2,2′‐azobisisobutyronitrile has been determined in the bulk polymerization of styrene with pulsed‐gradient spin‐echo nuclear magnetic resonance at 25 °C. Data on small molecules are discussed with respect to recent diffusion models. They can fit self‐diffusion coefficient data of small molecules in dilute or semidilute polymer solutions; in concentrated solutions, however, there is a breakdown. A semiempirical model based on scaling laws is used to describe the self‐diffusion of styrene and 2,2′‐azobisisobutyronitrile over the whole range of concentrations studied. The dependence of the polystyrene self‐diffusion coefficient on the polymer concentration is described with a stretched exponential function, D = D₀ exp(?αc^ν), where α depends on the molecular weight of the polymer and ν depends on the kind of solvent. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1605–1614, 2003     

Synthesis and properties of through‐space conjugated polymers based on cyano‐substituted poly(p‐arylenevinylene)s

New through‐space cyano‐substituted poly(p‐arylenevinylene)s containing a [2.2]paracyclophane unit were synthesized by the Knoevenagel reaction. Polymers 5 and 7 have cyano groups at α‐positions and β‐positions from the dialkoxyphenylene unit, respectively. Their optical and electrochemical behaviors were investigated in detail in comparison with their model compounds. Polymers 5 and 7 exhibited through‐space conjugation via the cyclophane units. Polymer 5 showed greenish blue emission (λ_max = 477 nm) in diluted solution with fluorescence quantum efficiency (?_F) of only 0.007, whereas polymer 7 emitted in the bluish green region (λ_max = 510 nm) with ?_F of 0.32. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5979–5988, 2009     

Synthesis and characterization of a new ethynyl‐linked alternating anthracene/fluorene copolymer for organic thin film transistor

A new p‐type conjugated copolymer, poly(9,10‐diethynylanthracene‐alt‐9,9‐didodecylfluorene) (PDADF), which is composed of ethynyl‐linked alternating anthracene/fluorene, is synthesized via a palladium(II)‐catalyzed Sonogashira coupling reaction with 9,10‐diethynylanthracene and 2,7‐diiodo‐9,9‐didodecyl‐fluorene. The obtained polymer is confirmed by FTIR, ¹H‐NMR, ¹³C‐NMR and elemental analysis. The PDADF had very good solubility in organic solvents such as chloroform and had a weight average molecular weight of 29,300 with a polydispersity index of 1.29. The PL maximum of the polymer was found at 533 and 568 nm for a solution and 608 nm for film, respectively. The highest occupied molecular orbital (HOMO) energy of the polymer is ?5.62 eV as measured via cyclic voltammetry (CV). A solution‐processed thin film transistor device showed a carrier mobility value of 6.0 × 10^?4 cm²/Vs with a threshold voltage of ?17 V and a capacitance (C_i) of 10 nF/cm². The out‐of‐plane and in‐plane GIXD pattern of spin‐coated polymer on SiO₂ dielectric surfaces showed an amorphous halo near 2θ = 20°. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 1609–1616, 2009     

Morphology and interactions of polymer brush‐coated spheres in a polymer matrix

Using a real space implementation of the self‐consistent field theory, we calculated the morphology and interactions of spherical nanoparticles with radius R_p that are grafted by polymer chains of N monomers immersed in a chemically identical polymer melt of polymerization index P. The calculation shows that, for big particles (R_p ? N^1/2a, with a the segment size), the interactions and density profiles of the grafted layers are that of brushes at flat interface; While for small particles (R_p ? N^1/2a), the interactions and density profiles are characteristic of star polymers. In the case of intermediate grafted chain lengths, that is, R_p ～ N^1/2a, we found that the grafting density of the polymers and the radius of the spherical nanoparticles are both important in determining the structure and interactions of the grafted layers. Our findings suggest possible ways to tailor the structure and interactions of the nanoparticles to benefit the fabrication of polymeric nanocomposites. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2811–2820, 2006     

Low‐oxidation‐potential conducting polymers derived from 3,4‐ethylenedioxythiophene and dialkoxybenzenes

Monomers derived from 3,4‐ethylenedioxythiophene and phenylenes with branched or oligomeric ether dialkoxy substituents were prepared with the Negishi coupling technique. Electrooxidative polymerization led to the corresponding dialkoxy‐substituted 3,4‐ethylenedioxythiophene–phenylene polymers, with extremely low oxidation potentials (E_1/2,p = ?0.16 to ?0.50 V vs Ag/Ag⁺) due to the highly electron‐rich nature of these materials. The polymers were electrochromic, reversibly switching from red to blue upon oxidation, with bandgaps at about 2 eV. The electrochemical behavior of the oligomeric ether‐substituted polymer was investigated in the presence of different metal ions. Films of the polymer exhibited electrochemical recognition for several alkali and alkaline‐earth cations with selectivity in the order Li⁺ > Ba²⁺ > Na⁺ > Mg²⁺. Cyclic voltammetry showed a decrease in the oxidation potential and an improvement in the definition of the voltammetric response, as well as an increase in the overall electroactivity of the polymer films when the concentration of the cations in the medium was increased. These results are discussed in terms of the electrostatic interactions between the complexed cation and the redox center, as well as the diffusion of the ionic species into the polymer matrix. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2164–2178, 2001     

Kinetics of styrene emulsion polymerization above the critical micelle concentration: Effect of the initial monomer concentration on the molecular weight

The emulsion polymerization of styrene above the critical micelle concentration has been experimentally studied from a low final polymer content up to a high polymer content (～50%). A maximum in the molecular weight (M) evolution has been observed in all cases. The presence or absence of such a maximum depends on the relative values of the rate of free‐radical entry (ρ) and the rate of chain transfer to the monomer (K_trC_Mp, where K_tr is the chain transfer to monomer rate coefficient and C_Mp is the monomer concentration in particles). If ρ ? K_trC_Mp, M is constant and equal to K_p/K_tr (where K_p is the propagation rate coefficient), except at very low particles sizes typical of the early stages of the reaction, in which the chain length is limited by the particle size. On the other hand, if ρ ? K_trC_Mp, M is determined by both C_Mp and ρ. It is proposed that ρ is determined by the sum of the entry of the oligomeric radicals formed in the aqueous phase and those contained in particles that undergo limited coagulation. This coagulative entry can become very significant; therefore, reactor hydrodynamics can play a major role in the kinetic behavior observed. Disagreement between Clay and Gilbert's model and molecular weight distribution data can be ascribed, to a lesser or greater extent, to the degree of correctness of the quasi‐steady‐state and instantaneous‐termination approaches. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1963–1972, 2005     

Mobility of Spherical Probe Objects in Polymer Liquids

We use scaling theory to derive the time dependence of the mean-square displacement ?Δr(2)? of a spherical probe particle of size d experiencing thermal motion in polymer solutions and melts. Particles with size smaller than solution correlation length ξ undergo ordinary diffusion (?Δr(2) (t)? ~ t) with diffusion coefficient similar to that in pure solvent. The motion of particles of intermediate size (ξ < d < a), where a is the tube diameter for entangled polymer liquids, is sub-diffusive (?Δr(2) (t)? ~ t(1/2)) at short time scales since their motion is affected by sub-sections of polymer chains. At long time scales the motion of these particles is diffusive and their diffusion coefficient is determined by the effective viscosity of a polymer liquid with chains of size comparable to the particle diameter d. The motion of particles larger than the tube diameter a at time scales shorter than the relaxation time τ(e) of an entanglement strand is similar to the motion of particles of intermediate size. At longer time scales (t > τ(e)) large particles (d > a) are trapped by entanglement mesh and to move further they have to wait for the surrounding polymer chains to relax at the reptation time scale τ(rep). At longer times t > τ(rep), the motion of such large particles (d > a) is diffusive with diffusion coefficient determined by the bulk viscosity of the entangled polymer liquids. Our predictions are in agreement with the results of experiments and computer simulations.     

Mutual diffusion and thermodynamics in the blends of polystyrene and tetramethylbisphenol-A polycarbonate

A study was made of miscible polymer blends of deuterated polystyrene (d-PS) and tetramethylbisphenol-A polycarbonate (TMPC). The Flory interaction parameter χ was obtained from the relation between mutual and tracer diffusion coefficients, D? and D^*, which were measured by forward recoil spectrometry. The temperature dependence of diffusion at PS weight fractions ω of 0.25 and 0.5, and the composition dependence at temperatures 45°C above the glass transition temperature, T_g, were investigated. A stronger dependence of χ on both temperature (at ω = 0.5) and composition was observed in comparison with other miscible binary polymer blends involving PS. Analysis using the generalized lattice-fluid model of Sanchez and Balazs¹ showed that the incorporation of a significant specific interaction is needed to explain the temperature dependence of χ. The diffusion coefficients obtained in the one-phase region were extrapolated to the two-phase region, and these were compared with the effective diffusion coefficient extracted from phase separation dynamics measured by light scattering.² A significant discrepancy between the extrapolated and effective diffusion coefficients was observed. © 1995 John Wiley & Sons, Inc.     

Viscoelasticity and self-diffusion in melts of entangled asymmetric star polymers

The crossover from linear to branched polymer dynamics in highly entangled melts was investigated with a series of asymmetric three-arm stars of poly(ethylene-alt-propylene). Two arms of equal length formed a linear backbone, kept constant through the series, while branches of various length were appended as the third arm. The materials were made by carbanionic polymerization of isoprene and the judicious application of chlorosilane linking chemistry. Subsequent saturation of the polymeric double bonds with deuterium and hydrogen, followed by fractionation, led to a set of structurally matched, nearly monodisperse pairs of deuterium-labeled and fully hydrogenous samples. Dynamic moduli were measured over wide ranges of frequency and temperature. With increasing branch length, the resulting master curves evolve smoothly, but with surprising rapidity, from the relatively narrow terminal spectrum of linear polymers to the much broader spectrum of symmetric stars. The viscosity η_o increases rapidly with branch length, and the diffusion coefficient D, obtained by forward recoil spectrometry, decreases even more rapidly. The product η_oD, however, distinguishes the transition from linear to branched polymer dynamics most clearly: for a backbone with about 38 entanglements, the crossover is already approaching completion for a single mid-backbone branch with only about three entanglements. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1943–1954, 1997