Hole Size Distribution Research Articles

Experimental evidence for high noble gas solubilities in silicate melts under mantle pressures

The solubilities of Ar and Xe in Fe-free synthetic haplogranitic and tholeiitic melts were experimentally determined in the pressure range of 1–11 GPa and at temperatures between 1500 and 2000°C. Experiments were performed in a piston cylinder apparatus (1–3 GPa) and in a multi-anvil apparatus (2–11 GPa). The noble gas concentrations in the quenched glasses were determined with electron microprobe. As a function of pressure, Ar solubility increases linearly up to about 4–5 GPa where it reaches about 4.0 and 0.8 wt% for the haplogranitic and tholeiitic melt, respectively. At higher pressure the amount of dissolved Ar remains constant, suggesting that some threshold concentration is reached. The Xe solubility in tholeiite melt exhibits a very similar pattern. It increases linearly up to about 6 GPa, where a threshold concentration of 0.8 wt% is reached. A further increase of pressure up to 11 GPa does not result in changes in Xe solubility. The leveling off in noble gas solubility at high pressures may imply that the interstitial sites in the melt structure, suitable for the accommodation of noble gas atoms, are fully occupied. Indeed, the experimental data can be successfully reproduced with the Langmuir isotherm, implying a solubility model in which the gas atoms occupy a certain population of interstitial sites. However, the data can be equally well described by a model assuming mixing of the noble gas atoms with the oxygen atoms of the silicate melt. From a thermodynamic point of view, the constant noble gas solubility at high pressures simply implies that the partial molar volumes of the respective noble gas in the fluid and in the melt are equal. Our results differ from those of Chamorro-Perez et al. [Earth Planet. Sci. Lett. 145 (1996) 97–107; Nature 393 (1998) 352–355] who reported an abrupt, order-of-magnitude drop of Ar solubility in silica and olivine melt at around 5 GPa, suggesting that melt densification results in an abrupt decrease of the hole size distribution. A geochemical consequence of our results is that noble gases remain incompatible elements at pressure conditions covering most of the upper mantle. Therefore partial melting remains an efficient process in extracting noble gases and other volatiles from the Earth’s mantle.

Spontaneous Dewetting and Ordered Patterns in Evaporating Thin Liquid Films on Homogeneous and Heterogeneous Substrates

The growth of instabilities and the initial stages of dewetting of volatile thin aqueous films on partially wettable solid substrates are investigated based on 2D nonlinear simulations. Dewetting by the formation of holes occurs by a spinodal mechanism due to the hydrophobic attraction on chemically homogeneous surfaces. The number density of holes and, consequently, the rate of dewetting can be enhanced by as much as an order of magnitude by evaporation on a homogeneous surface. At moderate to high rates of evaporation, all the holes do not form at the same time uniformly over the surface but form gradually in a rather ordered way around the earliest holes which act as “seeds”. On a chemically heterogeneous substrate, spatial gradients of the interaction potential and the rate of evaporation engender the surface instability. A chemical heterogeneity can induce faster rupture at a higher mean thickness and, thus, control the hole size distribution and the pattern of drying very significantly. A locally ordered, complex pattern often forms that consists of a central giant “nucleated” hole surrounded by a few concentric rings of smaller spinodally created satellite holes. An increase in the rate of evaporation encourages the formation of a larger number of ringlike structures containing the satellite holes but reduces the size difference between the spinodal satellite holes and the heterogeneously nucleated holes. The results obtained are in accord with recent experimental observations.

On the architecture of the gram-negative bacterial murein sacculus.

The peptidoglycan network of the murein sacculus must be porous so that nutrients, waste products, and secreted proteins can pass through. Using Escherichia coli and Pseudomonas aeruginosa as a baseline for gram-negative sacculi, the hole size distribution in the peptidoglycan network has been modeled by computer simulation to deduce the network's properties. By requiring that the distribution of glycan chain lengths predicted by the model be in accord with the distribution observed, we conclude that the holes are slits running essentially perpendicular to the local axis of the glycan chains (i. e., the slits run along the long axis of the cell). This result is in accord with previous permeability measurements of Beveridge and Jack and Demchik and Koch. We outline possible advantages that might accrue to the bacterium via this architecture and suggest ways in which such defect structures might be detected. Certainly, large molecules do penetrate the peptidoglycan layer of gram-negative bacteria, and the small slits that we suggest might be made larger by the bacterium.

Free Volume Distributions in Glassy Polymer Membranes: Comparison between Molecular Modeling and Experiments

We compare molecular modeling results of two glassy polymer membranes and one rubbery polymer membrane with gas transport parameters and free-volume-related quantities from positronium annihilation. A simple geometric model reveals hole size distributions of asymmetric shape. Among glassy polymers, the distribution parameters show a good correlation with average hole sizes determined by positron annihilation lifetime spectroscopy. Higher permeability is measured in the glassy polymer with the higher mean value of the hole size distribution. The permselectivity of the membranes for permanent gases can be interpreted in terms of the distribution broadness via free-volume-controlled diffusion selectivity. A comparison with the rubbery polymer shows that the permeation behavior is not determined only by the free volume concentration. The thermal fluctuations of the polymer matrix play an important role for gas transport properties.

Influence of generation number on the dewetting of hypergraft poly(2-ethyl-2-oxazoline) films

We investigate the influence of polymer branching (generation number G) on the dewetting of hypergraft poly(2-ethyl-2-oxazoline) (PEOX) polymer films from model non-polar synthetic polymer and inorganic substrates. The present study contrasts the cases of a zeroth generation G0 hypergraft, which is a comb polymer, and a G2 hypergraft, which resembles a nearly spherical 'microgel' particle. The early stage of dewetting is found to be similar in the G0 and G2 films and is largely independent of substrate (entangled polystyrene film or acid-cleaned silica wafer). However, the late stage of dewetting in the G2 films differs significantly from the GO films because of an inhibition of hole coalescence in the intermediate stage of film dewetting. The holes in the G2 hyperbranched films continue to grow in size until they impinge on each other to form a foam-like structure with a uniform 'cell' size. The boundaries of these cells break up and the vertices of the former cellular network retract to form a relatively uniform droplet configuration. In contrast, hole coalescence in the GO films occurs readily, leading to a polydisperse hole size distribution, and the fluid borders of the holes break up to form the non-uniform 'Voronoi' droplet configuration normally associated with film dewetting. Similar trends have been observed in the dewetting of linear polymer films where entangled polymers behave similarly to the branched (G2) polymers of the present study. This effect is attributed to the viscoelasticity of the G2 hyperbranched polymer fluid.

Mesoscopic patterning of cell adhesive substrates as novel biofunctional interfaces

In this report, cell adhesion to honeycomb-patterned films is described with respect to the dimensions of the honeycomb structure. The honeycomb-patterned films can be fabricated by casting a dilute solution of amphiphilic polymers on solid substrates. The honeycomb structure is not homogeneous in all dimensions. Analysis of distribution of the honeycomb hole sizes demonstrates a gradual decrease in honeycomb hole diameter along the radius of the cast area. The largest holes were located near geometric center of the cast area. The diameter of the largest honeycomb holes in the cast area could be controlled by varying the cast volume of the polymer solution. Cell cultures on the honeycomb films demonstrated that cell adhesion could be inhibited at the outer region of the cast area. The extent of the inhibition of cell adhesion was influenced by the chemical properties of the polymers constituting the honeycomb films.

Techniques for modelling the frequency of explosions on offshore platforms

This paper describes a scheme by which the explosion frequencies and resulting overpressures can be predicted for modules on an offshore platform. Given a leak of gas, the success and failure of the isolation, blow-down and deluge systems, which are designed to activate following a leak to mitigate the consequences, are considered. The frequency of each possible response to the leak is predicted using a conventional event tree and fault tree approach. Each scenario has a potential escape inventory, which together with the hole size distribution provides the escaping mass flowrate. Once the flowrate into the module is established, the wind conditions are used to determine the gas in air concentration build-up. The concentration profile with respect to time is linked to the ignition source probabilities, from which calculations can be made to assess the likelihood that an explosion will occur within a specific concentration range. The initial models assume that the gas concentration at any specific time is uniform within the locality of the leak. The work presented in this paper proposes an approach that determines the explosion probability dependent on the volume fraction of gas within the module and the likelihood of encountering an ignition source.

Free Volume and Tacticity in Polystyrenes

Measurements of the free volume hole size distributions obtained from positron annihilation lifetime spectroscopy (PALS) in relation to the chain tacticity in polystyrene and poly(p-methylstyrene), and in relation to the static free volume distribution in modeled amorphous cells of these polymers are reported. The free volume distribution was estimated using the Voronoi tessellation of space and direct calculations of unoccupied space in modeled amorphous cells of the polystyrenes. The results indicate that the syndiotactic polystyrene and the syndiotactic poly(p-methylstyrene) have broader hole distributions than the more atactic samples. The polystyrenes have a maximum in the free volume hole size distribution at volumes smaller than for the poly(p-methylstyrenes). The calculations indicate the presence of a large portion of holes too small to be detected with positron annihilation. The small holes are related to structural features of the polymer chain itself. The calculated distribution of large holes...

Do MELT or CONTIN Programs Accurately Reveal the o-Ps Lifetime Distribution in Polymers? Analysis of Simulated Lifetime Spectra

Simulated positron lifetime spectra consisting of three components, among them a Gaussian o-Ps lifetime distribution of different width σ 3 , were extensively analysed using the MELT and CONTIN routines. Conclusions were reached on the relevance of the shape and width of the analysed o-Ps lifetime distributions as a function of simulated standard deviation σ 3 (0 to 500 ps), the total number of counts (1 M, 10 M, 50 M), and the regularization (entropy weight). Furthermore, the ability of the techniques to distinguish broad distributions from (discrete) neighbour lifetimes, and to resolve close neighbour lifetimes was investigated. The behaviour of the characteristic lifetimes τ i and intensities I i of the three spectrum components was studied and compared with results coming from the discrete-term analysis. The results of the study lead to a critical view on the current use of the routines in estimating o-Ps lifetime distributions and from these the free-volume hole size distributions in polymers.

Effect of Cross-Linking on the Free-Volume Properties of Diethylene Glycol Bis(allyl carbonate) Polymer Networks: A Positron Annihilation Lifetime Study

The effect of cross-linking on the free-volume properties of poly(diethylene glycol bis(allyl carbonate)) networks was studied using a series of networks with progressively decreasing density of cross-links. The networks were prepared by bulk copolymerization of ethylene glycol bis(allyl carbonate) with an increasing amount of allyl ethoxyethyl carbonate. The mean free-volume hole radius (r) and the hole volume (v) as well as the hole radius and hole volume density distributions were estimated from positron lifetime measurements. It was found that with increasing concentration of monoallyl comonomer, the mean hole size increases from r = 0.250 nm (v = 0.066 nm3) for the pure diallyl component to 0.300 nm (0.114 nm3) for the 75% concentration of the monoallyl comonomer. Similarly, the hole size distributions shift to larger values. The local free-volume properties were correlated with the glass transition temperature and the specific volume. The comparison of the hole volume with the specific volume allowed us to estimate the number density of holes of ∼1 × 1027 m-3 and a free-volume hole fraction which increases with the concentration of the monoallyl from 0.066 to 0.113.

Do the CONTIN or the MELT programs accurately reveal the o-Ps lifetime distribution in polymers? Analysis of experimental lifetime spectra of amorphous polymers

High quality positron lifetime spectra (total count of 70 million) were taken for polycarbonate (PC) and polystyrene (PS Hoechst). The spectra were analysed employing the routines CONTIN and MELT which both assume continuous lifetime distributions, as well as the discrete-term analysis routine LIFSPECFIT. The lifetime distributions consist of three peaks, of these, the long-lived one, corresponding to the o-Ps lifetime distribution, splits for low regularization into two sub peaks. No way was found to decide whether these sub peaks, or the smoothed o-Ps lifetime distribution obtained for higher regularization, were due to two (discrete) close neighbour lifetimes, or came from a single, broad o-Ps lifetime distribution. Assuming discrete lifetimes, values of approximately 1700 ps and 2350 ps were estimated for PS (1750 and 2400 ps for PC). Assuming a single but broad o-Ps lifetime distribution, the mass centre τ 3 of that in PS was estimated to 1985 ps (2020 ps in PC). The same analysis was carried out with distributions from simulated lifetime spectra for comparison with experimental data. From this comparison the full width at half maximum (FWHM) of the o-Ps lifetime distribution was estimated to 800–950 ps for both PS and PC. The o-Ps lifetime results may be attributed to two different Ps states or, alternatively, to hole size distributions ranging approximately from r=0.24–0.32 nm ( v=0.06–0.14 nm 3). Furthermore, short comments on how to estimate a reliable width for the o-Ps lifetime distribution and on the handling and resolving power of CONTIN and MELT are given.

The local free volume in deformed polyethylene: a positron lifetime study

We report and discuss the change in free volume in high density polyethylene due to inelastic deformation under plain strain conditions as a function of the draw ratio λd, studied via positron lifetime spectroscopy. Two long-lived ortho-positronium pick-off lifetimes are observed and attributed to the (interstitial) free volume in crystallites (τ3 ∼ 1.4 ns) and to local free volumes in the amorphous phase (τ4 ∼ 2.7 ns). From this we estimate the crystalline packing density and the average size of the free volume holes, r = 0.343 nm and υ = 0.170 nm3. From the continuous positron lifetime intensity distribution derived via Laplace inversion of the lifetime spectra, we obtained free volume hole size distributions in the samples. The hole size distributions are bimodal with maxima corresponding to τ3 and τ4. We observe an increase in τ3 but a decrease in τ4 at small draw ratios. The increase in τ3 indicates increasing free volume in the crystalline region, which may be attributed to an increase in the paracrystalline disorder. The decrease in τ4 is attributed to the decrease in free volume hole sizes in the amorphous phase or to a change in the shape of the holes from ‚spheres’︁ to ‚ellipsoids’︁.

Measurement of free-volume hole size distribution in Nafion-117 using positron annihilation spectroscopy

We report a new result of free-volume hole size distribution in water and ethanol-swollen Nafion-117 polymer. With the increase in water content, free-volume hole size decreases, but overall the volume fraction increases. The hole size distribution in dry polymer is seen to be distinctly different from hydrated membranes. The narrow and symmetric distribution in hydrated membrane as compared to dry membrane is believed to be a consequence of crosslinking due to cluster formation. In alcohol-swollen membranes, on the other hand, not only are the free-volume size and fraction seen to be higher, the hole size distribution is seen to be broader compared to dry or hydrated membranes, indicating the effect of penetration of alcohol into the hydrophobic backbone region. We have also examined our results vis-a-vis reported gas diffusion studies in Nafion in the framework of existing free-volume model. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 983–989, 1998

Measurement of free‐volume hole size distribution in Nafion‐117 using positron annihilation spectroscopy

We report a new result of free-volume hole size distribution in water and ethanol-swollen Nafion-117 polymer. With the increase in water content, free-volume hole size decreases, but overall the volume fraction increases. The hole size distribution in dry polymer is seen to be distinctly different from hydrated membranes. The narrow and symmetric distribution in hydrated membrane as compared to dry membrane is believed to be a consequence of crosslinking due to cluster formation. In alcohol-swollen membranes, on the other hand, not only are the free-volume size and fraction seen to be higher, the hole size distribution is seen to be broader compared to dry or hydrated membranes, indicating the effect of penetration of alcohol into the hydrophobic backbone region. We have also examined our results vis-a-vis reported gas diffusion studies in Nafion in the framework of existing free-volume model. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 983–989, 1998

Compaction of granular mixtures: a free volume model

We describe compaction, induced by weak tapping of a powder, as a process where a grain can jump into a hole, only if the hole is large enough. The distribution of hole sizes is taken to be the Poisson type, with a certain characteristic free volume. For macrodisperse powders, this leads to a classical logarithmic law of compaction, already derived by Knight et al. Here we focus our attention on the case of mixtures, between two populations: large grains ( L) and small grains ( S) with very different sizes, so that the ( S) grains may fill the interstices of the ( L) grains. Geometrically, these mixtures can exist as “gravels” (where the intersices are not completely filled) or “puddings” (where the L grains are not tighlty packed). Dynamically, we expect a cross over curve between L-type compaction and S-type compaction, which is different from the geometrical boundary. This implies that, for certain material ratios ρ = L/ S, the plot of density versus number of tappings should show two distinct branches.

High sensitivity of positron annihilation lifetime to time and pressure effects in gas-exposed polymers

Positron annihilation lifetime (PAL) experiments are performed in polycarbonate (PC) exposed to CO2 and He gases as a function of time and pressure. In PC/CO2 systems, hole size and fraction reduced from PAL data increase as a function of CO2 pressure and exposure time. Significant hysteresis in positron lifetime data is observed during CO2 abasorption/desorption. In PC/He systems, no variation is observed. Hole size distribution in the CO2-exposed polymers is found to be significantly broader than in unexposed samples. The high sensitivity of PAL results to CO2 exposure of PC is thought to relate to the microstructural changes in the polymer matrix, such as penetrant plasticization, gas hydrostatic pressure effect, and molecular filling and creation of holes.

Positron lifetime studies of free volume hole size distribution in amorphous and in semi-crystalline polymers

Positron lifetime spectroscopy has been applied to estimate the free-volume hole size distribution in glassy polycarbonate (PC) and polystyrene (PS) as well as in plastically deformed and undeformed, semi-crystalline polyethylene (HDPE). The hole radius density distribution is determined from the ortho-positronium lifetime distribution which is obtained via a Laplace-inversion of the positron lifetime spectrum. The hole volume density distribution and the number density distribution of holes is estimated from the hole radius density distribution. In PC and in PS all of the distributions may be well approximated by a single Gaussian. The hole radius and the hole number density distributions have centres and at 0.29 nm and 0.1 nm3 in PC, and at 0.28 nm and 0.09 nm3 in PS. The FWHM of the corresponding distributions are 0.042 nm and 0.040 nm3 (PC), and 0.039 nm and 0.34 nm3 (PS), respectively. Both, the shape and the width of the distributions correlate well with the free volume theory of BUECHE. In PE the lifetime spectra consist of four components. The o-Ps lifetime distribution is bimodal and may be attributed to o-Ps annihilation in the crystalline and in the amorphous phase of the polymer. The corresponding hole size distributions show definite changes of their position and width following plastic deformation which we attribute to homogeneous crystal lattice dilatation and/or a local disorder in the crystals and to an increase in the eccentricity of holes in the amorphous phase.

Positron lifetime studies of free volume hole size distribution in glassy polycarbonate and polystyrene

Positron lifetime spectroscopy has been applied to estimate the free volume hole size distribution in polycarbonate (PC) and in polystyrene (PS) at room temperature. The hole radius density distributions are determined from the ortho-positronium lifetime distributions obtained via a Laplace inversion of the measured positron lifetime spectra. The hole volume density distributions and the number density distributions of holes are estimated from the hole radius density distributions. All of the distributions may be well approximated by single Gaussians. The hole radius and the hole number density distributions have centres 〈rf〉 and 〈vfn〉 at 0.29 nm and 0.1 nm3 in PC, and 0.28 nm and 0.09 nm3 in PS. The FWHM of the corresponding distributions are 0.042 nm and 0.040 nm3 (PC), and 0.039 nm and 0.34 nm3 (PS), respectively. Both, the shape and the width of the distributions correlate well with the free volume theory of Bueche. The possible influence of different effects, such as a nonspherical shape of holes and a scanning of several holes by positronium before annihilation, on the mean hole size and the hole size distribution as detected by the positron lifetime method is finally discussed.

Comments on the Paper “Can Positron Annihilation Lifetime Spectroscopy Measure the Free-Volume Hole Size Distribution in Amorphous Polymers?”

We discuss the theoretical basis for relating the mean ortho-positronium (o-Ps) lifetime to free-volume hole sizes using a finite spherical potential well model. The status of the localized o-Ps atom in amorphous polymers is evaluated by calculation of the o-Ps barrier transmission probability. The results indicate that the relative probability for an o-Ps atom to remain in a particular hole during its entire lifetime is on the order of 10 -2 . We conclude that there is no justification for a one-to-one correlation of o-Ps lifetime components with specific hole sizes.

The Effects of CO2-Conditioning of Polymers on Positron Annihilation and Gas Permeation Properties

Abstract The effects of CO2-conditioning, i.e. exposing a polymer film to high pressure CO2 and degassing it in vacuo, on positron annihilation and gas permeation properties of polyimides and polyethylene were investigated. Both lifetime and intensity of ortho-positronium (o-Ps) (τ3 and I3, respectively) increased for polyimides by the CO2-conditioning. The size distribution of free space holes, which was evaluated from annihilation rate distribution of o-Ps, became broader and shifted to larger size. Permeability, diffusion, and solubility coefficients of gases for polyimides increased by the CO2-conditioning. The increases in diffusion coefficient are attributed to increases in volume fraction of free space holes, VF. The increases in τ3 and in I3 were much larger than those expected from the increases in VF. This may be explained by a model based on an interplay between electron affinity and size of free space holes for Ps formation. In the CO2-conditioned films, permeability and diffusion coefficients, VF, and I3 gradually decreased with lapse of time but after five months they were still larger than those in the as-cast films, whereas τ3 remained almost constant. No effect of the CO2-conditioning was observed for polyethylene.