Holographic grating relaxation studies of probe diffusion in amorphous polymers

Probe diffusion of camphorquinone, thymoquinone, and diacetyl in polymers was studied by the laser-induced holographic grating relaxation (HGR) technique in polymers. The effects of changing the probe size and various parameters of the polymer, such as the molecular weight, chain conformation, and the glass transition temperature, on the probe diffusion coefficient have been investigated. Furthermore, effects of cross-linking and plasticizing the chains of the polymer host on the probe diffusion coefficient were also studied. Temperature-dependent studies show that except for the very low molecular weight poly(methyl methacrylate), all probe diffusion coefficient data above the glass transition temperature fit well to the WLF equation. ©1995 John Wiley & Sons, Inc.     

Reactions of free radicals with polymers—II: Abstraction reactions of methyl and acetyl radicals with poly(vinyl acetophenone)

The kinetics of H abstraction by methyl and acetyl radicals from poly(vinyl acetophenone) (PVAP) films (4 × 10³ mm thick) have been investigated, both radicals being derived from the polymer by photolysis (λ ≥ 300 nm) under high vacuum conditions (pressure < 10^?4 Pa). Differential equations have been obtained to describe the simultaneous diffusion and reaction of each of the radicals, and the solutions (both steady and non-steady state conditions) have been used in conjunction with experimental data (including yields of methane and acetaldehyde) to obtain values of rate constants for abstraction. which it is argued is likely to occur predominantly at the α-carbon atoms in the polymer. Both steady and non-steady state calculations yield the same values of rate constants. Values of these constants have been compared with each other and that for methyl radical abstraction is compared with data obtained for abstraction from other styrene polymers. PVAP is less reactive than polystyrene towards methyl radicals. Factors accounting for these differences, including diffusant volume, polymer free volume and the energetics of formation of the transition state for abstraction in the various polymers, are considered. Theoretical rates of product formation, based on the solutions of the equations, are compared with the experimental yields of methane and acetaldehyde; a good correspondence is observed for approx. 3 hr reaction time. Subsequent discrepancies between the two sets of data are attributed to the radiation modified diffusion and optical characteristics of the polymer.     

A theory-based approach to thermal field-flow fractionation of polyacrylates

A theory-based approach is presented for the development of thermal field-flow fractionation (ThFFF) of polyacrylates. The use of ThFFF for polymer analysis has been limited by an incomplete understanding of the thermal diffusion which plays an important role in retention and separation. Hence, a tedious trial-and-error approach to method development has been the normal practice when analyzing new materials. In this work, thermal diffusion theories based on temperature dependent osmotic pressure gradient and polymer-solvent interaction parameters were used to estimate thermal diffusion coefficients (D(T)) and retention times (t(r)) for different polymer-solvent pairs. These calculations identified methyl ethyl ketone as a solvent that would cause significant retention of poly(n-butyl acrylate) (PBA) and poly(methyl acrylate) (PMA). Experiments confirmed retention of these two polymers that have not been previously analyzed by ThFFF. Theoretical and experimental D(T)s and t(r)s for PBA, PMA, and polystyrene in different solvents agreed to within 20% and demonstrate the feasibility of this theory-based approach.     

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     

Comparison of permeability coefficients of organic vapors through non-porous polymer membranes by two different experimental techniques

The permeability coefficients of saturated and non-saturated vapors of benzene, hexane and cyclohexane through flat polymer membranes (low density polyethylene BRALEN FB2-30 and polyether-block-amide PEBA 4033-PE) by two different experimental techniques at 298.15 K are reported. The permeation data have been obtained using the differential flow permeameter and sorption ones by glass sorption apparatus with McBain’s spiral balance. The so-called stationary (steady) diffusion theory has been applied for evaluating the permeability coefficients from sorption (equilibrium) data and obtained values have been compared with the permeability coefficients from permeation (steady-state) measurements. In the case of relative lower vapors sorption in polymers (hexane and cyclohexane) good agreement between permeability coefficients from sorption and permeation is obtained. Hence, this paper proves the possibility to estimate the permeability coefficients of organic vapors from sorption data without need of performing the permeation experiments.     

A nuclear magnetic resonance study of toluene-polyisobutylene solutions. 2. Vrentas-Duda theory

The self-diffusion coefficients of toluene in polyisobutylene have been analyzed using the Vrentas-Duda free volume diffusion model. The diffusion coefficients were determined at different temperatures and concentrations, using the pulsed field gradient nuclear magnetic resonance technique. The data were satisfactorily described by the model and the size of the polymer jumping unit was extracted. Comparisons were made with the Fujita free volume theory and the Fujita free volume parameters were extracted from the Vrentas-Duda free volume parameters. From the diffusion data that now available, it can be concluded that for most polymers the jumping unit is about 1.5 times the polymer monomer molecular weight. The activation energy of the toluene diffusion in polyisobutylene is compared with the activation energies of other penetrants in the same polymer. The diffusion data presented in this work show that the energy per mole required to overcome the attractive forces which constrain a diffusing species to its neighbors should be considered to be zero, in order to be able to extract the free volume parameters (from viscosity and diffusion data) with an acceptable uncertainty. ©1995 John Wiley & Sons, Inc.     

On the Origin of Heterogeneous Diffusion in Glassy Poly(alkyl methacrylates)

The diffusion of small molecules through amorphous polymers proceeds by the thermally activated jumps whose rate changes from one region to another due to polymer heterogeneity. Little is known at present about the origin of diffusion heterogeneity. The oxidation of triplet nitrene and quenching of phenanthrene phosphorescence have been used to study the movement of molecular oxygen on a nanometer length scale in glassy poly(ethyl methacrylate) and poly(n‐butyl methacrylate) far below the glass transition temperature. It has been found that, as temperature increases, the jump rates in all regions increase by the same factor. This finding points to the equality of the activation energies of oxygen jumps in different regions of the polymers. We conclude that the correlated elastic displacements of polymer chains inside regions about several nanometers in size provide molecules jumps. Due to the large size of these regions, the activation energy of jump does not depend on local polymer structure. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1097–1104     

Diffusion behavior in polymer–clay nanocomposites

This paper reviews our previous studies on the diffusion behavior in polymers clay nanocomposites. A geometric model for predicting the effective diffusivity through this type of systems as a function of clay sheets orientation, volume fraction, polymer clay interaction, and aspect ratio is proposed. Model predictions are compared to the effective diffusivity generated using random walk simulations as well as with predictions obtained from already existing theoretical models. Fair agreement is found between the model prediction and the results of numerical simulations. With respect to the already existing theoretical models, the present mathematical derivation seems more adequate to describe diffusion behavior in conventional nanocomposites systems (i.e. when fillers present very low values of volume to surface ratio). Experimental diffusion tests are discussed and interpreted with the aid of the proposed model. In addition to the aspect ratio and clay concentration, the polymer clay interactions as well as the sheets orientation are the factors controlling the barrier properties of polymer‐layered silicate nanocomposites. Good agreement was found in the case of samples containing exfoliated clay, whereas the model fails in the case of micro‐composites, in which the inorganic lamellae are agglomerated in clusters. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 265–274, 2006     

Simultaneous measurement of vapor diffusion and solubility coefficients in polymers by frequency response techniques

An experimental technique for the simultaneous measurement of solubility and diffusion coefficients in polymers by frequency response techniques has been developed. A sample of polymer suspended from an electrobalance is exposed to a permeating gas whose pressure is being varied sinusoidally at ultra-low frequencies. The phase angle and amplitude of the weight changes are measured as a function of the frequency of the pressure wave. It is shown that in the linear range the diffusivity coefficient for polyethylene–ethane calculated from the phase angle lag and the Henry's law solubility and the diffusivity obtained from the amplitude ratios are in excellent internal agreement and also agree with values obtained from transient measurements.     

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     

Measurement of sorption and diffusion in nonporous membranes by transient permeation experiments

The knowledge of sorption and diffusion of liquids or vapors and their mixtures in nonporous membranes facilitates systematic membrane selection and process design. A novel experimental technique for the measurement of sorption and diffusion in nonporous membranes is described. An experimental apparatus has been designed for carrying out the transient permeation experiments. A general time-lag analysis procedure has also been developed in order to obtain the sorption and diffusion parameters from the transient permeation data. The effects of concentration dependent diffusivities, polymer swelling and a thermodynamic correction factor have been included in the analysis. Transient permeation experiments have been carried out to determine the sorption and diffusion of acetone in polydimethylsiloxane (PDMS). The results obtained are in good agreement with data from the literature, indicating that the proposed technique is suitable for the measurement of sorption and diffusion in nonporous membranes.     

Self‐diffusion coefficient of ring polymers in semidilute solution

In a topologically constraining environment the size of a flexible nonconcatenated ring polymer (macrocycles) and its dynamics are known to differ from that of linear polymers. Hence, the diffusion coefficient of ring polymers can be expected to be different from linear chains. We present here scaling arguments for the concentration and molecular weight dependence of self‐diffusion coefficient of ring polymers in semidilute solutions, and show that contrary to expectations these scaling relations are identical to what is known for linear polymers. At higher concentrations excluded volume interactions arising from possibilities of segmental overlap can become effective for large ring polymers. In this regime the diffusion coefficient of large ring polymers shows a relatively weaker dependence on concentration and molecular weight. ©2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2370–2379, 2008     

Time-dependent Diffusion Coefficient and Conventional Diffusion Constant of Nanoparticles in Polymer Melts by Mode-coupling Theory (cited: 2)

Time-dependent diffusion coefficient and conventional diffusion constant are calculated and analyzed to study diffusion of nanoparticles in polymer melts. A generalized Langevin equa-tion is adopted to describe the diffusion dynamics. Mode-coupling theory is employed to calculate the memory kernel of friction. For simplicity, only microscopic terms arising from binary collision and coupling to the solvent density fluctuation are included in the formalism. The equilibrium structural information functions of the polymer nanocomposites required by mode-coupling theory are calculated on the basis of polymer reference interaction site modelwith Percus-Yevick closure. The effect of nanoparticle size and that of the polymer size are clarified explicitly. The structural functions, the friction kernel, as well as the diffusion coefficient show a rich variety with varying nanoparticle radius and polymer chain length. We find that for small nanoparticles or short chain polymers, the characteristic short time non-Markov diffusion dynamics becomes more prominent, and the diffusion coefficient takes longer time to approach asymptotically the conventional diffusion constant. This constant due to the microscopic contributions will decrease with the increase of nanoparticle size, while increase with polymer size. Furthermore, our result of diffusion constant from mode-coupling theory is compared with the value predicted from the Stokes-Einstein relation. It shows that the microscopic contributions to the diffusion constant are dominant for small nanoparticles or long chain polymers. Inversely, when nanonparticle is big, or polymer chain is short, the hydrodynamic contribution might play a significant role.     

DYNAMIC LIGHT SCATTERING STUDY ON TRANSLATION DIFFUSION OF 8-ARM STAR POLYSTYRENE IN GOOD AND THETA SOLVENTS

The technique of dynamic light scattering has been used to investigate the translation diffusion behavior of 8-arm star polystyrene (SPS)in a good solvent, tetrahydrofuran (THF) or benzene (BZ) and a theta solvent, cyclohexane (CH), by homodyne photon correlation spectroscopy .The intensityintensity autocorrelation function was analyzed by the method of cumulant. The translation diffusion coefficients have been obtained as a function of temperature and concentration. Under theta condition ,the non-concentration dependence of diffusion coefficient showed the unperturbed Gaussian state o the SPS molecular chain. The different hydrodynamic radii estimated from Stokes- Einstein equation reflected the stretch extent of the arm chain for regular star polymer. The data of diffusion activation energy of SPS in THF, BZ and CH were also obtained respectively.     

The Soret effect in dilute polymer solutions: influence of chain length, chain stiffness, and solvent quality

Thermal diffusion in dilute polymer solutions is studied by reverse nonequilibrium molecular dynamics. The polymers are represented by a generic bead-spring model. The influence of the solvent quality on the Soret coefficient is investigated. At constant temperature and monomer fraction, a better solvent quality causes a higher affinity for the polymer to the cold region. This may even go to thermal-diffusion-induced phase separation. The sign of the Soret coefficient changes in a symmetric nonideal binary Lennard-Jones solution when the solvent quality switches from good to poor. The known independence of the thermal diffusion coefficients of the molecular weight is reproduced for three groups of polymers with different chain stiffnesses. The thermal diffusion coefficients reach constant values at chain lengths of around two to three times the persistence length. Moreover, rigid polymers have higher Soret coefficients and thermal diffusion coefficients than more flexible polymers.     

Treatment of high molecular weight wormlike polymers as random coiled polymers

The possibility of treating a wormlike polymer as a random coiled polymer is examined. Taking from the literature intrinsic viscosity data concerning several wormlike polymers, we use two graphical methods which have been proposed for flexible polymers. These methods are only applicable in the region of molecular weights where the wormlike polymer presents a relatively great number of statistical segments. From the values of unperturbed dimensions obtained by the graphical methods, we obtain the statistical segment of wormlike polymers at Θ conditions.     

Responsive hydrogel layers—from synthesis to applications

Responsive polymer networks are interesting materials for a variety of different applications due to the fact that they can perform a large volume transition. However, the swelling transition is a diffusion limited process. Thus, the decrease of the feature size (e.g., in thin layers) is an appropriate way to create structures with reasonable response time. The possibility to pattern responsive polymer networks makes them useful for application in microsystem technology as well as in biomedicine. The transition behavior of these films showed similar trends to those of the corresponding linear polymers whereas confinement effects have been found for thin hydrogel layers. The ability to optimize the integration of these polymers is critical for the fabrication and development of platforms that harness the unique abilities of responsive polymer networks. Here, recent developments on chemically cross-linked hydrogel layers with respect to synthesis, characterization, and application are highlighted.     

Model for the photooxidation of parylenes

Parylenes belong to a family of polymers that have been investigated for use in electronic and medical applications. The photooxidation of these materials is of interest both to prevent degradation and to induce targeted chemical changes. This article describes a transport and reaction model for the photooxidation of parylenes. This model is based on existing polymer photooxidation mechanisms that have been adapted to this system. The model has been compared with existing parylene photooxidation data for this system and shows qualitative agreement with surface oxidation profiles and oxidation depth profiles. On the basis of the results of the model comparison, it has been determined that the key parameters that appear to affect the photooxidation of parylenes are the diffusion coefficient of oxygen in these films and the concentration of oxygen initially present in these films. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2666–2677, 2004     

Study on thermal stability of poled non-linear optical polymers

A logarithmic expression is proposed to describe relaxation of the polar order in side chain polymers,together with a new way of plotting temperature dependent relaxation data.This results in a straight line extending even below the glass transition temperature in the case of poled nonlinear optics (NLO) side chain polymers.A simple procedure to determine the rotational diffusion constant Dr is given and Dr values of several polymer systems have been evaluated and compared with each other.It appears that,starting from the conventional and well known poled polymer system currently applied,a further lowering of Dr by about 3 orders of magnitude is necessary in order to reach an acceptable orientational stability or lifetime of poled polymers for practical applications.Attempts have been made to introduce electron push-pull substituents into high thermostable molecular frameworks and results of preliminary measurements are reported.     

Polymer dynamics in hydrogenous systems by neutron reflectivity

Neutron reflectivity is a powerful tool for exploring polymer dynamics above the glass-transition temperature at short diffusion times in layered thin-film systems. Recent studies of membrane-mediated interdiffusion in deuterium-labeled systems have shown that ultrathin membranes can track the position of the interface in binary polymeric diffusion couples and also can discriminate between perdeuterated and hydrogenous polymers of the same molecular weight. This report shows that similar dynamic information can be obtained for binary hydrogenous polystyrene (hPS) diffusion couples separated by an ultrathin (6-nm) isopentylcellulose cinnamate (IPCC) membrane on Si wafers (air//hPS/IPCC/hPS//Si, where “//” represents an interface between obviously different phases and “/” represents a dynamic interface between polymeric species). In particular, the air//hPS/IPCC/hPS//Si system provides the same information as perdeuterium-labeled polystyrene (dPS) diffusion couples separated by the same IPCC membrane (air//dPS/IPCC/dPS//Si). This technique has potential applications for the study of confinement effects on thin-film dynamics and macromolecular transport across membranes. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3248–3257, 2004