Dynamic mechanical properties of three‐component composites (acrylic polymer/epoxy/SiO2) in the glass‐transition region

In previous studies, we reported the linear and nonlinear rheological properties of three‐component composites consisting of acrylic polymer (AP), epoxy resin (EP), and various SiO₂ contents (AP/EP/SiO₂) in the molten state. In this study, the dynamic mechanical properties of AP/EP/SiO₂ composites with different particle sizes (0.5 and 8 μm) were investigated in the glass‐transition region. The EP consisted of three kinds of EP components. The α relaxation due to the glass transition shifted to a higher temperature with an increase in the volume fraction (?) for the AP/EP/SiO₂ composites having a particle size of 0.5 μm, but the α relaxation scarcely shifted for the composite having a particle size of 8 μm as a general result. This result suggested that the SiO₂ nanoparticles that were 0.5 μm in size adsorbed a lot of the low‐glass‐transition‐temperature (T_g) component because of their large surface area. The AP/SiO₂ composites did not exhibit a shift in T_g; this indicated that the composite did not adsorb any component. The modulus in the glassy state (E′_g) exhibited a very weak &phis; dependence for the AP/EP/SiO₂ composites having particle sizes of 0.5 and 8 μm, although E′_g of the AP/SiO₂ composites increased with &phis;. The AP/EP/SiO₂ composites exhibited a peculiar dynamic mechanical behavior, although the AP/SiO₂ composites showed the behavior of general two‐component composites. Scanning electron microscopic observations indicated that some components in the EP were adsorbed on the surface of the SiO₂ particles. We concluded that the peculiar behavior of the AP/EP/SiO₂ composites was due to the selective adsorption of the EP component. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40409.     

Systematic Control of Structural Changes in GeO2 Glass Induced by Femtosecond Laser Direct Writing

We report the structural changes inside germania glass induced by femtosecond laser pulses. Inspection by polarization microscopy and secondary electron microscopy indicate that the periodic nanostructures consist of oxygen defects such as ODCs (oxygen deficient centers) and NBOHCs (nonbridging oxygen hole centers) for laser pulse energy less than 0.2 μJ. However, the glass network was dissociated and O₂ molecules were generated for laser pulse energy greater than 0.4 μJ. Two different structural changes, form‐birefringence and dissociation, were induced in GeO₂ glass, depending on the laser pulse energy. The form‐birefringence exhibited by the nanogratings in GeO₂ glass is larger than that in SiO₂ glass for pulse energy less than 0.2 μJ, as the density of nanovoids enclosed by ODCs in GeO₂ glass is higher than that in SiO₂ glass. Arrhenius plots of the phase retardation caused by the nanogratings in GeO₂ and SiO₂ indicate that the oxygen defects are relaxed at a temperature 100°C above the glass‐transition temperature.     

Effect of Nitrogen on Properties of Na2O–CaO–SrO–ZnO–SiO2 Glasses

Glasses in the Na₂O–CaO–SrO–ZnO–SiO₂ system have previously been investigated for suitability as a reagent in Al‐free glass polyalkenoate cements (GPCs). These materials have many properties that offer potential in orthopedics. However, their applicability has been limited, to date, because of their poor strength. This study was undertaken with the aim of increasing the mechanical properties of a series of these Zn‐based GPC glasses by doping with nitrogen to give overall compositions of: 10Na₂O–10CaO–20SrO–20ZnO–(40?3x)SiO₂–xSi₃N₄ (x is the no. of moles of Si₃N₄). The density, glass‐transition temperature, hardness, and elastic modulus of each glass were found to increase fairly linearly with nitrogen content. Indentation fracture resistance also increases with nitrogen content according to a power law relationship. These increases are consistent with the incorporation of N into the glass structure in threefold coordination with silicon resulting in extra cross‐linking of the glass network. This was confirmed using ²⁹Si MAS‐NMR which showed that an increasing number of Q² units and some Q³ units with extra bridging anions are formed as nitrogen content increases at the expense of Q¹ units. A small proportion of Zn ions are found to be in tetrahedral coordination in the base oxide glass and the proportion of these increases with the presence of nitrogen.     

A Complete Solid Solution with Rutile‐Type Structure in SiO2–GeO2 System at 12 GPa and 1600°C

High pressure and temperature synthesis of compositions made of (Si_1?x,Ge_x)O₂ where x is equal to 0, 0.1, 0.2, 0.5, 0.7, and 1 was performed at 7–12 GPa and 1200–1600°C using a Kawai‐type high‐pressure apparatus. At 12 GPa and 1600°C, all the run products were composed of a single phase with a rutile structure. The lattice constants increase linearly with the germanium content (x), which indicates that the rutile‐type phases in the SiO₂–GeO₂ system form a complete series of solid solutions at these pressure and temperature conditions. Our experimental results show that thermodynamic equilibrium state was achieved in this system at 12 GPa and 1600°C, but not at 1200°C. At lower pressures (7 and 9 GPa) and 1600°C, we observed the decomposition of (Si_0.5,Ge_0.5)O₂ into SiO₂‐rich coesite and GeO₂‐rich rutile phases. The silicon content in the rutile structure increases sharply with pressure in the vicinity of the coesite–stishovite phase transition pressure in SiO₂.     

Microstructural and Microwave Dielectric Properties of Bi12GeO20 and Bi2O3‐Deficient Bi12GeO20 Ceramics

Bi₁₂GeO₂₀ ceramics sintered at 800°C had dense microstructures, with an average grain size of 1.5 μm, a relative permittivity (ε_r) of 36.97, temperature coefficient of resonance frequency (τ_f) of ?32.803 ppm/°C, and quality factor (Q × f) of 3137 GHz. The Bi_12‐xGeO_20‐1.5x ceramics were well sintered at both 800°C and 825°C, with average grain sizes exceeding 100 μm for x ≤ 1.0. However, the grain size decreased for x > 1.0 because of the Bi₄Ge₃O₁₂ secondary phase that formed at the grain boundaries. Bi_12‐xGeO_20‐1.5x (x ≤ 1.0) ceramics showed increased Q × f values of >10 000 GHz, although the ε_r and τ_f values were similar to those of Bi₁₂GeO₂₀ ceramics. The increased Q × f value resulted from the increased grain size. In particular, the Bi_11.6GeO_19.4 ceramic sintered at 825°C for 3 h showed good microwave dielectric properties of ε_r = 37.81, τ_f = ?33.839 ppm/°C, and Q × f = 14 455 GHz.     

Preparation of antireflection coatings with novel cationic–nonionic PU‐SiO2 core–shell particle dispersions

A novel polyurethane (PU)‐SiO₂ core–shell particle dispersion was prepared by an acid‐catalyzed sol–gel process using cationic–nonionic PU particle as template. Results of average sizes, polydispersity index, and transmission electron microscope indicated that tetramethylorthosilicate were first diffused to the surface of PU particles, then occurring hydrolysis–condensation reaction to form core–shell particles. Antireflection coating formulation was prepared by as‐prepared core–shell particle dispersion and SiO₂ sol binder. After dip‐coating in the formulation, antireflection coating was formed on glass surface by calcination. Scanning electron microscopy images showed that pores had been formed inside coating after removing PU template particles, and the coating surface could be almost fully closed. In addition, ultraviolet–visible spectrophotometer analysis showed that the maximum transmittance of antireflection glasses can be as high as 98.6% at 548 nm. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018 , 135, 45762.     

Chemical nature of active sites for defect‐mediated nucleation on silicon dioxide

Germanium nanoparticle growth on SiO₂ proceeds via defect‐mediated nucleation and particle density can be enhanced by chemically treating the SiO₂ with SiH_x. The influence of SiH_x fragments on SiO₂ surface sites is studied using a fluorescent probe‐based technique to understand the chemical nature of the inherent defect trapping sites and the chemical nature of the additional trapping sites formed by SiH_x. Oxygen‐vacancy sites on SiO₂ are the inherent sites for defect‐mediated nucleation. SiH_x fragments, generated by cracking disilane on a hot tungsten filament, are shown to react with strained siloxane sites, leading to a conversion of these strained siloxane sites into a different low density defect site that is shown to display reactive characteristics similar to the oxygen‐vacancy defect sites. Previous work demonstrating an increased density of Ge nuclei on SiO₂ surfaces with increasing SiH_x exposure is interpreted in the context of the current experimental results. © 2015 American Institute of Chemical Engineers AIChE J, 62: 367–372, 2016     

High Na‐ion conducting Na1+x[SnxGe2−x(PO4)3] glass‐ceramic electrolytes: Structural and electrochemical impedance studies

Na‐ion conducting Na_1+x[Sn_xGe_2?x(PO₄)₃] (x = 0, 0.25, 0.5, and 0.75 mol%) glass samples with NASICON‐type phase were synthesized by the melt quenching method and glass‐ceramics were formed by heat treating the precursor glasses at their crystallization temperatures. XRD traces exhibit formation of most stable crystalline phase NaGe₂(PO₄)₃ (ICSD‐164019) with trigonal structure. Structural illustration of sodium germanium phosphate [NaGe₂(PO₄)₃] displays that each germanium is surrounded by 6 oxygen atom showing octahedral symmetry (GeO₆) and phosphorous with 4 oxygen atoms showing tetrahedral symmetry (PO₄). The highest bulk Na⁺ ion conductivities and lowest activation energy for conduction were achieved to be 8.39 × 10^?05 S/cm and 0.52 eV for the optimum substitution levels (x = 0.5 mol%, Na_1.5[Sn_0.5Ge_1.5(PO₄)₃]) of tetrahedral Ge⁴⁺ ions by Sn⁴⁺ on Na–Ge–P network. CV studies of the best conducting Na_1.5[Sn_0.5Ge_1.5(PO₄)₃] glass‐ceramic electrolyte possesses a wide electrochemical window of 6 V. The structural and EIS studies of these glass‐ceramic electrolyte samples were monitored in light of the substitution of Ge by its larger homologue Sn.     

Second harmonic generation in germanotellurite bulk glass‐ceramics

In this study, we have investigated the use of silver cation as nucleating agent in germanotellurite glass matrix of compositions (100?x) [70TeO₂–10GeO₂–10Nb₂O₅–10K₂O]–xAg₂O (x=0‐6 mol%), in order to promote bulk crystallization. Density measurements, differential scanning calorimetry, X‐ray diffraction, UV‐Vis, and Raman spectroscopies have been performed to study the crystallization process. We have observed bulk crystallization of a unique noncentrosymmetric phase, K[Nb_1/3Te_2/3]₂O_4.8, which has been investigated for its second‐order optical activity. Transparent to translucent glass‐ceramics have been successfully tailored under thermal treatment and second harmonic generation signals were recorded on the glass‐ceramic samples as a function of their synthesis procedure. It is suggested that the second‐order optical properties observed are strongly related to the organization of crystallites within phase‐separated domains.     

Low‐temperature sintering and thermal stability of Li2GeO3‐based microwave dielectric ceramics with low permittivity

A low‐permittivity dielectric ceramic Li₂GeO₃ was prepared by the solid‐state reaction route. Single‐phase Li₂GeO₃ crystallized in an orthorhombic structure. Dense ceramics with high relative density and homogeneous microstructure were obtained as sintered at 1000‐1100°C. The optimum microwave dielectric properties were achieved in the sample sintered at 1080°C with a high relative density ~ 96%, a relative permittivity ε_r ~ 6.36, a quality factor Q × f ~ 29 000 GHz (at 14.5 GHz), and a temperature coefficient of resonance frequency τ_f ~ ?72 ppm/^°C. The sintering temperature of Li₂GeO₃ was successfully lowered via the appropriate addition of B₂O₃. Only 2 wt.% B₂O₃ addition contributed to a 21.2% decrease in sintering temperature to 850°C without deteriorating the dielectric properties. The temperature dependence of the resonance frequency was successfully suppressed by the addition of TiO₂ to form Li₂TiO₃ with a positive τ_f value. These results demonstrate potential applications of Li₂GeO₃ in low‐temperature cofiring ceramics technology.     

Y3Al5O12–SiO2 Glasses: Structure and Polyamorphism

Aerodynamic levitation and CO₂ laser melting have been used to synthesize the yttrium aluminosilicate glasses zY₂O₃–yAl₂O₃–xSiO₂ with z/y = 3/5 corresponding to the YAG (Y₃Al₅O₁₂) composition and x between ~5 and ~45 mol%. The low‐ and high‐density (LDA inclusion and HDA matrix) polyamorphic phases in glasses with less than ~14 mol% SiO₂ were identified with backscattering electron imaging. Polarized and depolarized Raman spectra show the formation of various Qⁿ SiO₄ species whose relative populations change smoothly as the SiO₂ content is altered. The AlOs (s = 4–6) and YOz (z = 6–9) polyhedra formed in the YAG glass are preserved upon silica additions while the terminal oxygens of the Q²AlO₄ tetrahedra are gradually bridged to the Qⁿ‐SiO₄ species. The low‐frequency Boson Peak overlaps with the vibrational spectrum and its maximum is redshifted with increasing silica content. Micro‐Raman spectra measured for the LDA and HDA amorphous phases are found to be similar to the spectra of the bulk glass indicating common structural characteristics. The stability of the LDA phase against crystallization appears to be lower than that of the HDA phase. The crystallinity on certain inclusions consisted of YAG microcrystals and a new unidentified microcrystalline phase within Y₄Al_2(1?x)Si_2xO_(9+x) solid solution.     

Electrochemical Deposition of 58SiO2‐33CaO‐9P2O5 Nanobioactive Glass Particles on Ti‐6Al‐4V Alloy for Biomedical Applications

The nanobioactive glass (58SiO₂‐33CaO‐9P₂O₅) powders were synthesized by simple sol–gel method. The prepared samples reveal amorphous nature, agglomerated spherical morphology with particle size of 100–150 nm. The specific surface area of nanobioactive glass (NBG) particle is 147 m²/g. The NBG samples were coated on titanium (Ti‐6Al‐4V) alloy through electrochemical deposition method. The particle size of the NBG‐coated surface was in the order of 200–300 nm, and it was confirmed by atomic force microscopy (AFM) analysis. In vitro and AFM studies reveal the existence of higher bioactivity and uniform coating of NBG on implants at 80 V for 1 h.     

Structure and electrical properties of perovskite layer (1−x)Sr2Nb2O7‐x(Na0.5Bi0.5)TiO3 high‐temperature piezoceramics

The structure and electrical properties of perovskite layer structured (PLS) (1?x)Sr₂Nb₂O₇‐x(Na_0.5Bi_0.5)TiO₃ (SNO‐NBT) prepared by solid‐state reaction method are investigated. The addition of NBT is beneficial to speed up mass transfer and particle rearrangement during sintering, leading to better sinterability and higher bulk density up to 96.8%. The solid solution limit x in the SNO‐NBT system is below 0.03, over which Ti⁴⁺ is preferable to aggregate and results in the generation of secondary phase. After the modification by NBT, all SNO‐NBT ceramics have a Curie temperature T_c up to over 1300°C and piezoelectric constant d₃₃ about 1.0 pC/N. The breakthrough of piezoelectricity can mainly be attributed to rotation and distortion of oxygen octahedron as well as higher poling electric field resulting from the improved bulk density. This study not only demonstrates how to improve piezoelectricity by NBT addition, but also opens up a new direction to design PLS piezoceramics by introducing appropriate second phase.     

Comparative study of Al2O3, HfO2, and HfAlOx for improved self‐compliance bipolar resistive switching

The comparison of resistive switching (RS) storage in the same device architecture is explored for atomic layer deposition (ALD) Al₂O₃, HfO₂ and HfAlO_x‐based resistive random access memory (ReRAM) devices. Among them, the deeper high‐ and low‐ resistance states, more uniform V_SET‐V_RES, persistent R_OFF/R_ON (>10²) ratio and endurance up to 10⁵ cycles during both DC and AC measurements were observed for HfAlO_x‐based device. This improved behavior is attributed to the intermixing of amorphous Al₂O₃/HfO₂ oxide layers to form amorphous thermally stable HfAlO_x thin films by consecutive‐cycled ALD. In addition, the higher oxygen content at Ti/HfAlO_x thin films interface was found within the energy dispersive spectroscopy analysis (EDS). We believe this higher oxygen content at the interface could lead to its sufficient storage and supply, leading to the stable filament reduction‐oxidation operation. Further given insight to the RS mechanism, SET/RESET power necessities and scavenging effect shed a light to the enhancement of HfAlO_x‐based ReRAM device as well.     

Dielectric polarizability of SiO2 in niobiosilicate glasses

Understanding the mechanisms contributing to dielectric properties of glasses is critical for designing new compositions for microwave frequency applications. In this work, dielectric permittivity was measured using a cavity perturbation technique at 10 GHz for a series of niobiosilicate glasses with the compositions (100-2x)SiO₂- xNb₂O₅- xLi₂O where x = 32.5, 30, 25, and 15 mol%. Permittivity measurements and glass compositions were used to calculate the polarizability of each cation-anion unit in the glass network using the Clausius-Mossotti equation. The SiO₂ polarizability in niobiosilicates was calculated to be 6.16 ų, which is much higher than the SiO₂ polarizability in fused silica glass (5.25 ų), alkali modified silicates (5.37 ų), and aluminosilicates (5.89 ų). The increasing trend in SiO₂ polarizability is attributed to the disruption in the connectivity of the SiO₄ tetrahedral network as it accommodates different network formers. The high SiO₂ polarizability of 6.16 ų accurately predicts measured dielectric permittivity when Nb₂O₅ = 25, 30, and 32.5 mol%, but overpredicts measured permittivity when Nb₂O₅ ≤ 15 mol%, which is attributed to a decrease in SiO₂ polarizability as the percentage of corner sharing SiO₄ tetrahedra with NbO₆ octahedra goes down. This work demonstrates that SiO₂ polarizability depends on chemistry and connectivity of the glass, which has important implications in designing glass compositions for microwave frequency applications.     

Nano‐sio2‐reinforced ultraviolet‐curing materials for three‐dimensional printing

As an additive manufacturing technology, ultraviolet (UV)‐curing three‐dimensional printing, which requires the use of a photocurable resin, is increasingly being used to produce customized end‐user parts of many complex shapes. In this study, to improve the strength and ductility of printing materials, nano‐SiO₂‐reinforced photocurable resins were prepared by a planetary ball mill; then, the morphology, photochemistry, thermal property, and mechanical properties of the nanocomposites were investigated and characterized. Transmission electron microscopy analysis indicated that the modified nano‐SiO₂ was well dispersed in the photocurable resin. The glass‐transition temperature increased from 67.2°C for the unfilled resin to 71.7 and 80.1°C for nanocomposites with nano‐SiO₂ contents of 0.3 and 0.7 wt %, respectively. The tensile strength and impact strength were increased by 46.7 and 165.3% for nanocomposites with 0.3 wt % nano‐SiO₂. The flexural modulus of the nanocomposites increased from 1.7 to 8.0 GPa when 0.7 wt % nano‐SiO₂ was added to the photocurable resin; this appeared to originate from the relatively high level of dispersion and the intimate combination of the nano‐SiO₂ with the matrix. The investigation of the physical and chemical properties of such UV‐curing materials showed that the low filler concentration (<1 wt %) of nano‐SiO₂ did not affect the processability of the nanocomposites. © 2015 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 42307.     

Effects of Na+ substitution Cs+ on the microstructure and thermal expansion behavior of ceramic derived from geopolymer

As part of a series of studies, effects of Na⁺ substitution on the thermal evolution of cesium‐based geopolymers on heating were studied. A series of sodium‐substituted cesium‐based geopolymers, Cs_(1?x)Na_xGPs (where x=0, 0.1, 0.2, 0.3, and 0.4), were prepared and treated at 1300°C for 2 hours to obtain the corresponding ceramic products. The thermal evolution process was disclosed by virtue of a variety of technical, including TG‐DTA, thermal shrinkage, XRD analysis, SEM, and TEM investigation. The results indicated that unheated Cs_(1?x)Na_xGPs was not completely amorphous after the substitution of Na⁺ and the crystallinity of Cs_(1?x)Na_xGPs gradually increased with the rise of sodium content. Meanwhile, the average particle sizes of Cs_(1?x)Na_xGPs also increased evidently with increases in sodium substitution. The final product after heat treatment mainly consisted of pollucite (CsAlSi₂O₆) and amorphous glass phase. The particle size of pollucite grain gradually decreased as more Cs⁺ were replaced maybe owing to the role of Na⁺ in the nucleation process of pollucite. Two forms of Na⁺ present in the final products: A small portion was present in the pollucite grains due to Na⁺ partial occupied the crystallographic sites of Cs⁺; and the rest were present in the amorphous glass phase among the pollucite grains. The average coefficient of thermal expansion (CTE) of resulting Cs_(1?x)Na_xGPs ceramics increased from 4.80×10^‐6 K^?1 (x=0) to 7.26×10^?6 K^?1 (x=0.4) with increases in sodium substitution, which could be due to the amorphous glass phase had a relatively higher CTE than that of pollucite.     

In situ crystallization and elastic properties of transparent MgO–Al2O3–SiO2 glass‐ceramic

Glass‐ceramics (GC) generally possess enhanced mechanical properties compared to their parent glasses. The knowledge of how crystallization evolves and affects the mechanical properties with increasing temperature is essential to optimize the design of the crystallization cycle. In this study, we crystallized a glass of the MgO–Al₂O₃–SiO₂ system with nucleating agents TiO₂ and ZrO₂. The crystallization cycle comprised a 48 hour nucleation treatment at the glass‐transition temperature followed by a 10 hour growth step at a higher temperature. During this cycle, the evolution of crystalline phases was followed by high‐temperature X‐ray diffraction (HTXRD), which revealed the presence of karooite (MgO·2TiO₂), spinel (MgO·Al₂O₃), rutile (TiO₂), sillimanite (Al₂O₃·SiO₂), and sapphirine (4MgO·5Al₂O₃·2SiO₂). The same heat treatment was applied for in situ measurement of elastic properties: elastic modulus, E, shear modulus, G, and Poisson's ratio, ν. The evolution of these parameters during the heating path from room temperature to the final crystallization temperature and during the nucleation and the crystallization plateaus is discussed. E and G evolve significantly in the first two hours of the growth step. At the end of the crystallization process, the elastic and shear moduli of the GC were approximately 20% larger than those of the parent glass.     

High niobium oxide content in germanate glasses: Thermal,structural, and optical properties

Niobium alkali germanate glasses were synthesized by the melt‐quenching technique. The ternary system (90‐x)GeO₂–xNb₂O₅–10K₂O forms homogeneous glasses with x ranging from 0 to 20 mol%. Samples were investigated by DSC and XRD analysis, FTIR and Raman spectroscopy, and optical absorption. Structural and physical features are discussed in terms of Nb₂O₅ content. The niobium content increase in the glass network strongly modifies the thermal, structural and optical properties of alkali germanate glasses. DSC, Raman and FTIR analysis suggest niobium addition promotes NbO₆ groups insertion close to GeO₄ units of the glass network. XRD analysis also pointed out that samples containing high niobium oxide contents exhibit preferential niobium oxide‐rich phase after crystallization after heat treatment, which is similar to orthorhombic Nb₂O₅. Absorption spectra revealed high transmission range between 400 nm to 6.2 μm, added to a considerably decreased hydroxyl group content as the addition of niobium in the alkali germanate network. The niobium oxide‐rich phase crystallization process was studied and activation energy was determined, as well as nucleation and crystal growth temperatures and time for obtaining transparent glass‐ceramics.     

PMMA‐grafted‐silica/PVC nanocomposites: Mechanical performance and barrier properties

Poly(vinyl chloride) (PVC)/SiO₂ nanocomposites were prepared via melt mixture using a twin‐screw mixing method. To improve the dispersion degree of the nanoparticles and endow the compatibility between polymeric matrix and nanosilica, SiO₂ surface was grafted with polymethyl methacrylate (PMMA). The interfacial adhesion was enhanced with filling the resulting PMMA‐grafted‐SiO₂ hybrid nanoparticles characterized by scanning electron microscopy. Both storage modulus and glass transition temperature of prepared nanocomposites measured by dynamic mechanical thermal analysis were increased compared with untreated nanosilica‐treated PVC composite. A much more efficient transfer of stresses was permitted from the polymer matrix to the hybrid silica nanoparticles. The filling of the hybrid nanoparticles caused the improved mechanical properties (tensile strength, notched impact strength, and rigidity) when the filler content was not more than 3 wt %. Permeability rates of O₂ and H₂O through films of PMMA‐grafted‐SiO₂/PVC were also measured. Lower rates were observed when compared with that of neat PVC. This was attributed to the more tortuous path which must be covered by the gas molecules, since SiO₂ nanoparticles are considered impenetrable by gas molecules. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008