Free-volume Hole Distributions Research Articles

Correlating Free-Volume Hole Distribution to the Glass Transition Temperature of Epoxy Polymers.

A new algorithm is developed to quantify the free-volume hole distribution and its evolution in coarse-grained molecular dynamics simulations of polymeric networks. This is achieved by analyzing the geometry of the network rather than a voxelized image of the structure to accurately and efficiently find and quantify free-volume hole distributions within large scale simulations of polymer networks. The free-volume holes are quantified by fitting the largest ellipsoids and spheres in the free-volumes between polymer chains. The free-volume hole distributions calculated from this algorithm are shown to be in excellent agreement with those measured from positron annihilation lifetime spectroscopy (PALS) experiments at different temperature and pressures. Based on the results predicted using this algorithm, an evolution model is proposed for the thermal behavior of an individual free-volume hole. This model is calibrated such that the average radius of free-volumes holes mimics the one predicted from the simulations. The model is then employed to predict the glass-transition temperature of epoxy polymers with different degrees of cross-linking and lengths of prepolymers. Comparison between the predicted glass-transition temperatures and those measured from simulations or experiments implies that this model is capable of successfully predicting the glass-transition temperature of the material using only a PDF of the initial free-volume holes radii of each microstructure. This provides an effective approach for the optimized design of polymeric systems on the basis of the glass-transition temperature, degree of cross-linking, and average length of prepolymers.

In situ measurements of free volume during recovery process of a shape memory polymer

The physics and mechanics governing the shape memory effect in shape memory polymers is not fully understood at the nanoscale. A very recent publication highligths a possible link between the free volume of the polymer and its ability to recover the original shape in shape memory cycles. In this study, it is demonstrated that there is a reorganisation of the monomeric unit of polymer chains via molecular sized free volume that makes the shape recovery possible. For that purpose, the free volume properties are measured in situ during the shape recovery process of a crosslinked polycyclooctene shape memory polymer by employing positron annihilation lifetime spectroscopy. By this technique, the size and distribution of the dynamic subnanoscale free volume holes are obtained by measuring the lifetime of the positrons inside the polymer at different stages of the shape recovery.

Effect of supercritical carbon dioxide on nanoporous polyhexafluoropropylene

The effect of supercritical CO2 (sc-CO2) on the size distribution of free volume holes (nanopores) in a polyhexafluoropropylene (PHFP) polymer matrix has been studied. Residual (after CO2 release) swelling improves gas transport properties of the material. Relaxation of these properties over time has been compared with changes in permeability and nanoporosity. For PHFP samples with different histories, the data on nanoporosity have been obtained using positron annihilation lifetime spectroscopy (micropores) and the lowtemperature gas sorption technique (mesopores and part of micropores). Matching of the data is intended to reveal the role of pores of different sizes in permeability of membrane materials to different gases and determine the specifics of application of the positron annihilation technique to studying sc-CO2-modified objects.

Specifics of positron studies of microheterogeneous systems as applied to new polymeric sorbents

The size distribution of free volume holes in mesoporous, microheterogeneous polymer sorbents based on linear rubber-modified divinylbenzene copolymers has been studied. Analysis of the results of the study and published data has shown that positron annihilation lifetime spectroscopy (PALS) applied to microheterogeneous systems, in contrast to homogeneous systems, is not necessarily sensitive to mesopores that occur at the boundaries of heterogeneities and determine the sorption or membrane properties of the modified materials. To obtain the complete information, additional procedures such as low-temperature (BET) gas adsorption and thermally stimulated luminescence (TSL) need to be used. This circumstance is due to a considerably long distance between mesopores in heterogeneous systems and limited mobility of positronium during its localization in a pore. In addition to the BET data, which largely give information on mesopores, PALS appears useful for studying micropores. The TLS technique makes it possible to judge on heterogeneity of test materials. The minimal concentration of mesopores detectable by the positron technique in the systems of interest has been determined.

Synthesis and gas transport properties of novel poly(aryl ether ketone)s with branched structure

Poly(aryl ether ketone)s (PAEKs) based on 2-(3′-trifluoromethylphenyl) hydroquinone and 4,4′-difluorobenzophenone were synthesized and characterized in the presence or absence of 2,4′,6-trifluorobenzophenone (BB′2 monomer). The influence of the incorporation of a branched structure (BB′2 monomer) on the gas transport properties of PAEKs was investigated. The results showed that PAEKs with a branched structure possess a higher permeability and selectivity than PAEKs without a branched structure. Moreover, improvements in the permeability and selectivity were enhanced with increasing content of BB′2 monomer. This synergistic effect on permeability and selectivity was mainly due to the higher fractional free volume and the unique size and distribution of free volume holes arising from the incorporation of the branched structure. © 2013 Society of Chemical Industry

Effect of Water on the Size Distribution of Free-Volume Holes in Nafion Membrane

Positron lifetime spectroscopy was employed for investigation of the size distribution of free volume holes in Nafion N-1110 membrane. Size distribution of free volume holes was determined in the as-received and dried membrane and in the membrane immersed in water at various temperatures. It was found that absorbed water causes reduction of the mean size of free volume holes and increase of their dispersion and concentration. This indicates that free volumes are split by swollen ionic clusters absorbing water. The kinetics of water uptake and the amount of absorbed solvent was determined by in-situ measurement of the weight increase.

Retrostructural Model To Predict Biomass Formulations for Barrier Performance

Barrier performance and retrostructural modeling of the macromolecular components demonstrate new design principles for film formulations based on renewable wood hydrolysates. Hardwood hydrolysates, which contain a fair share of lignin coexisting with poly- and oligosaccharides, offer excellent oxygen-barrier performance. A Hansen solubility parameter (HSP) model has been developed to convert the complex hydrolysate structural compositions into relevant matrix oxygen-permeability data allowing a systematic prediction of how the biomass should be formulated to generate an efficient barrier. HSP modeling suggests that the molecular packing ability plays a key role in the barrier performance. The actual size and distribution of free volume holes in the matrices were quantified in the subnanometer scale with Positron annihilation lifetime spectroscopy (PALS) verifying the affinity-driven assembly of macromolecular segments in a densely packed morphology and regulating the diffusion of small permeants through the matrix. The model is general and can be adapted to determine the macromolecular affinities of any hydrolysate biomass based on chemical composition.

The Spin Probe Dynamics and the Free Volume in a Series of Amorphous Polymer Glass‐Formers

AbstractWe report the results of a combined study of the local structure and the reorientation dynamics in a series of five amorphous polymers of different fragility: cis‐trans‐1,4‐poly(butadiene) (c‐t‐1,4‐PBD), cis‐1,4‐poly(isoprene) (cis‐1,4‐PIP), poly(isobutylene) (PIB), poly(vinyl methylether)(PVME) and poly (propylene glycol) (PPG) by using two different probe methods. The reorientation dynamics of the molecular spin probe 2,2,6,6‐tetramethyl‐1‐piperidinyloxy (TEMPO) from electron spin resonance (ESR) is related to the annihilation behaviour of the atomic ortho‐positronium (o‐Ps) one as obtained by positron annihilation lifetime spectroscopy (PALS). It was found that a slow to fast transition in the spin probe rotation mobility at the operationally defined spectral temperature parameter, T50G, is connected with the mean o‐Ps lifetime, τ3 (T50G) = (2.04 ± 0.26) ns. Consequently, using the free‐volume concept of the o‐Ps annihilation in terms of a quantum‐mechanical model of o‐Ps lifetime this transition can be connected with the occurrence of the mean free volume hole, Vh (T50G) = (102 ± 17) Å3, nearly independent of the chemical composition and the basic structural relaxation parameters of the amorphous polymers investigated. Finally, the free volume hole distribution aspect of the slow to fast transition indicates the presence of a sufficient free volume fluctuation at T50G for both typical fragile PVME and strong PIB polymer and emphasizes the essential role of free volume in the spin probe dynamics.

A free-volume hole-filling model for the solubility of liquid molecules in glassy polymers 1: Model derivation

The use of hole-filling models is quite common for the sorption of gases into glassy polymers, but these have yet to be explicitly applied to the case of liquid immersion, where extensive use of Flory–Huggins theory dominates. This paper explores how the models based on the idea of sequential filling of a Gaussian distribution of pre-existing free-volume holes within the structure of the glassy polymer can be modified to allow the prediction of the equilibrium solubility of a liquid penetrant. For liquids, the driving force for sorption is more subtle than for gases, with more emphasis on molecular interactions rather than external pressure. For this reason, terms relating to the molecular interactions of a liquid molecule filling a hole were developed, including the effects of elastic constraint for small holes. Consideration of thermal fluctuations show that configurational entropy provides much of the driving force for sorption. Some comparisons with experimental data show a reasonable agreement, and one which is far better than the Flory–Huggins theory.

Dynamic study of free volume properties in polyethylene/styrene butadiene rubber blends by positron annihilation lifetime method

AbstractPositronium (Ps) formation in low and high‐density polyethylene (LDPE and HDPE) and styrene butadiene rubber (SBR), as well as in their blends (LDPE/SBR: 50/50 and HDPE/SBR: 50/50) has been investigated by positron annihilation lifetime (PAL) measurements as a function of low temperature (100–300 K). The glass transition temperature (Tg) for the initial polymers and their blends are determined by ortho‐positronium (o‐Ps) lifetime, τ3 versus temperature as well as by differential scanning calorimetry (DSC) measurements. The temperature dependence of nanoscale free volume size shows similar trend for all the investigated samples indicating an abrupt change at Tg, which is found to be higher for SBR sample characterized by its high chain mobility. In addition, The Tg values deduced from PAL measurements are compared with the corresponding data deduced from DSC. The variation of o‐Ps formation probability I3 versus temperature for polyethylene and their blends were interpreted in the frame work of spur reaction model of Ps formation. On the other hand, the lifetime coefficient below and above Tg is found to be one order of magnitude larger than the linear expansion coefficient. This constitutes evidence that Ps is only probing free volumes. The results obtained from change in free volume–hole distribution with temperature reflect both thermal expansion and increase in free volume–hole size with the rise in temperature. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

Positronium annihilation data and actual free-volume distribution in polymers

Determination of the size distribution of free-volume holes in solids, in particular, polymers, is an important physicochemical problem. The positron annihilation technique has been proposed for this purpose. The central point in this technique is the quantitative interpretation of data, especially, for substances with a high specific surface area. A developed free-volume system in open-pore membrane materials, such as poly(trimethylsilylpropyne) PTMSP and the spirocyclically bound benzodioxane polymer PIM-1, and polymeric sorbents (hypercrosslinked polystyrenes) makes it possible for the first time to compare the sorption characteristics and positron annihilation data on the character of size distribution of nanopores in these polymers. In combination with the results of mathematical simulation of the structure and radiothermoluminescence measurements, the array of data indicate the structural inhomogeneity of the test amorphous materials. It was shown that this inhomogeneity in relation to the positron annihilation technique is expressed in the insufficiency of the representation of the orthopositronium decay curve by one component that takes into account the Gaussian lifetime distribution (symmetrical pore size distribution) and in the necessity of use of several decay components. The feasibility of revealing a nonrandom character of pore size distribution gives the positron annihilation technique an advantage over other approaches (inverse gas chromatography, 129Xe NMR) to investigation of nanopores in polymers.

Temperature dependence of the free volume holes in polyhydroxybutyrate biopolymer: A positron lifetime study

AbstractThe size of the free volume holes and their distributuion in polyhydroxybutyrate (PHB) biopolymer have been studied using positron annihilation lifetime spectroscopy (PALS). The measurements were performed as a function of the temperature from 243 to 363 K. The temperature dependence of the free volume hole shows a glass transition temperature, Tg at 278 K. The free volume behaviour of PHB shows a small linear increase with temperature below Tg and a steeper increase above Tg. The thermal expansion coefficients of the free volume hole were determined to be 4.78 x 10–3 and 12.5 x 10–3 / K below and above Tg, respectively. The free volume hole distribution shows a narrow distribution below Tg. With increasing temperature, the maximum of the distributions of the free volume holes shifts to higher values. Meanwhile, widening of the distribution is smaller in lower temperature ranges and more pronounced at higher temperatures, especially above Tg. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Free volume study of 70 MeV carbon induced modification in polymers through positron annihilation

Free volume properties of polymers have strong correlation with macroscopic properties and can be modified by radiations and ions. Positron annihilation lifetime spectroscopy (PALS) provide direct information about the dimension, content and size distribution of free volume holes in polymers. CR-39 (DOP), a polycarbonate widely used as ion track detector and polyamide Nylon-6, a high performance plastic having a unique combination of superior mechanical, electrical, chemical and thermal properties were irradiated with 70MeV C5+ ion beam to different fluences ranging from 1011 to 3.7×1013ions/cm2. The results of characterization by PALS are reported here. o-Ps lifetime and the average free volume for both the polymers are found to decrease with fluence, indicating the facilitation of cross-linking. The results are interpreted in terms of change in the free volume. Maximum change of 9.7% in average free volume was observed in PN-6 irradiated to 3.7×1013ions/cm2.

Gas transport properties of 6FDA-TAPOB hyperbranched polyimide membrane

Physical and gas transport properties of the hyperbranched polyimide prepared from a triamine, 1,3,5-tris(4-aminophenoxy)benzene (TAPOB), and a dianhydride, 4,4′-(hexafluoroisopropylidene) diphthalic anhydride (6FDA), were investigated and compared with those of linear-type polyimides with similar chemical structures prepared from diamines, 1,4-bis(4-aminophenoxy)benzene (TPEQ) or 1,3-bis(4-aminophenoxy)benzene (TPER), and 6FDA. 6FDA-TAPOB hyperbranched polyimide exhibited a good thermal stability as well as linear-type analogues. Fractional free volume (FFV) value of 6FDA-TAPOB was higher than those of the linear-type analogues, indicating looser packing of molecular chains attributed to the characteristic hyperbranched structure. It was found that increased resistance to the segmental mobility decreases the gas diffusivity of 6FDA-TAPOB, in spite of the higher FFV value. However, 6FDA-TAPOB exhibited considerably high gas solubility, resulting in high gas permeability. It was suggested that low segmental mobility and unique size and distribution of free volume holes arising from the characteristic hyperbranched structure of 6FDA-TAPOB provide effective O 2/N 2 selectivity. It is concluded that the 6FDA-TAPOB hyperbranched polyimide has relatively high permeability and O 2/N 2 selectivity, and is expected to apply to a high-performance gas separation membrane.

Influence of Chemical Reactions of Positronium on Annihilation Characteristics in Polymeric Sorbents

Size distribution of free volume holes for several types of polymeric sorbents based on crosslinked polystyrene was studied using the positron annihilation and Brunauer–Emmett–Teller low-temperature nitrogen sorption techniques. It turned out that the ranges of free volume size detectable by the positron and sorption techniques partially overlap, wherein the positron annihilation technique covers the region of nanopores and the sorption method covers submicronic pores and a part of nanopores. Thus, both methods well complement one another. Information obtained by means of the positron technique can be confused if the positronium atoms produced by positrons injected in a material of interest take part in chemical reactions. Cases when such reactions can be suppressed by lowering the temperature are discussed.

Physical Aging of Poly(vinylpyrrolidone) under Different Humidity Conditions

The physical aging of poly(vinylpyrrolidone) (PVP K25) was studied under different storage conditions by positron lifetime spectroscopy and scanning electron microscopy. The transition from the glassy state (at RT and 55% RH) to the completely plasticized wet rubbery state (at RT and 75% RH) is not continuous in PVP K25. It was found that not only the actual water content of the material but also its storage history determines the size distribution of free volume holes in it. At 65% RH a slow anomalous structure formation was observed. By the means of ab initio calculations on simplified model molecules, it was determined that polymer chains and water molecules are able to form a hydrogen bound “network” under certain humidity conditions.

Positron annihilation studies on radiation-crosslinked poly(N-isopropylacrylamide) hydrogels

The temperature-sensitive poly(N-isopropylacrylamide) hydrogels, prepared by γ and electron-beam (EB) irradiation, were studied using positron annihilation lifetime spectroscopy (PALS). The effect of water content in the hydrogel on the ortho-positronium (o-Ps) lifetime and intensity was investigated. The observed positronium lifetime suggests microstructural differences between γ- and EB-synthesized hydrogels. The distribution in positronium lifetime indicates nonhomogeneity in the distribution of free-volume holes in EB-synthesized hydrogels. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3462–3466, 2000

Compositional and temperature dependence of free volume in segmented copolymer PET/PEO studied by positron annihilation lifetime measurement

Positron lifetime measurements were performed for segmented copolymer poly(ethylene oxide)–poly(ethylene terephthalate) (PEO/PET) as a function of the hard segment content (PET) and the temperature, which is used to study the free volume properties, structural transition and miscibility behaviour of segmented copolymer PEO/PET. From the variation of the ortho-positronium ( o-Ps) lifetimes with changes in the hard segment content, we find that the free volume decreases with increase of the hard segment, this fact means that the hard segment microdomains act as physical cross-links that suppress movement of the chains and that the interactions between the hard segment (PET) and soft segment (PEO) also plays an important role. On the other hand, the temperature dependence of positron lifetimes reveals the existence of two glass transition temperatures. This experimental results show that the hard segment PET is immiscibility with soft segment PEO in segmented copolymer PEO/PET (PEO molecular weight 4000, PET content 30 wt.%). The maximum entropy lifetime method (MELT) is used to detect the distributions of the free volume holes. Large differences in width of the free volume hole distributions as a function of temperature are observed.

Free Volume Microstructure and Its Relationship to the Chain Dynamics incis-1,4-Poly(butadiene) As Seen by Positron Annihilation Lifetime Spectroscopy

The annihilation characteristics of the orthopositronium (o-Ps) in the structurally simplest elastomer cis-1,4-poly(butadiene) has been measured in the temperature range from 15 to 313 K and interpreted in the framework of the free volume concept. The temperature dependence of the mean lifetime of the o-Ps, τ 3 , and its relative intensity, 13, reflect a fine interplay between the free volume and microscopic chain dynamics. In addition to a pronounced break on the τ 3 -T plot at the glass transition temperature, Tg, a further two bends exist. The first, in glassy state, is relatively slight. The other one, in an elastic state, can be correlated with the melting temperature T m of the crystalline phase. The order agreement between the temperature coefficients of free volume hole expansion α h and the mean square displacement of chain atoms α (u 2 ) from a recent neutron scattering study indicates a microscopic cause for the hole size growth with temperature. The decrease of I 3 with temperature T above 120 K correlates with the onset temperature of the so-called fast motion from neutron scattering measurements as well as with the so-called Vogel temperature T o for the primary segmental dynamics. The N-like shape course above Tg correlates with the cold crystallization from DSC measurements. In the melt region above 265 K, the slightly dependent τ 3 and I 3 quantities correspond to a formation of the bubble states of the o-Ps in the soft matrix. Finally, the temperature dependence of free volume hole distributions exhibits the essential changes from relative narrow distributions in the glassy state to wide distributions above Tg and ones that do not change much in the melt region of the polymer matrix.

Change of distribution of free volume holes during crystallization of poly(ethylene terephthalate) revealed by positron annihilation lifetime spectroscopy

Change of free volume holes during crystallization of amorphous poly(ethylene terephthalate) at 130 °C was investigated by positron annihilation lifetime technique together with the measurements of specific density and wide angle x-ray scattering (WAXS). The o-Ps intensity, I3, decreased by 24.6% with the crystallization. This value agreed with the degree of crystallinity determined by the specific density and WAXS, which indicates that o-Ps annihilation takes place in the amorphous part. The average o-Ps lifetime increased slightly by the crystallization. Detailed analysis of the o-Ps lifetime by a continuous distribution model showed that the small size component of the distribution disappeared due to the crystallization. The result is favorably compared with the recently proposed picture of crystallization which deals with the conformational change of ethylene group.