Some aspects of diffusion: fluctuations in reaction diffusion,and geometric influences in nonuniform media

Summary We deal with two diffusion problems: Space-integrated conserved entities characterizing very fast - diffusion - controlled reactions, such as time lags, etc. are universal. They are given by relationships which do not reflect the failure of the mean field hydrodynamic equations. We present another application which does not reflect this failure, for determining the surface flux via a diffusion controlled reaction producing a colored product. Another anomalous diffusion process we considered is transport through cellular materials whose cell sizes are highly nonuniform. We have analyzed the effects of extreme nonuniformity by considering fractal-like models of cellular solids. The diffusion current through these models can exhibit anomalous time-dependencies which are not predicted by the diffusion equation. In particular, it is shown that the initial diffusion current can be characterized by a power-law dependence on the time. Furthermore, the exponent of the power law is given in terms of the distribution of cell sizes in the fractal-like cellular solid.     

On some natural and model 2D bimodal random cellular structures

The topological and metric properties of a few natural 2D random cellular structures, namely an armadillo shell structure and young soap froths, which are formed from two classes of cells, large and small, have been characterized. The topological properties of a model generated from a Kagome tiling, which mimics such random binary structures, have also been exactly calculated. The distribution of the number of cell sides is bimodal for the structures investigated. In contrast to the classical Aboav-Weaire law for homogeneous 2D random cellular structures, nm(n), the mean total number of edges of neighbouring cells of cells with n sides does not vary linearly with n. Only the nm(i, n) (i=1,2) determined separately for every class of cells are linear in n for all investigated structures. Topological properties and correlations between metric and topological properties are finally compared with the predictions of various literature models. Received: 24 December 1997 / Revised: 7 April 1998 / Accepted: 20 April 1998     

Symmetry-breaking transitions and dissociation of two-dimensional Plateau borders

We have experimentally studied the dissociation/coalescence of internal Plateau borders (PBs) in simple monolayer bubble clusters, as a result of changing the liquid fraction. At large liquid content, the clusters consist of n bubbles of the same size, symmetrically placed around an internal n-sided PB (n-PB). On decreasing the liquid fraction we observed symmetry-breaking transitions in the 4- and 5-bubble clusters (but not in the 3-bubble cluster), followed by dissociation of the PBs. We used the Surface Evolver to determine the various equilibrium configurations of the corresponding two-dimensional wet clusters and their surface energies. The sequence of 4-bubble cluster configurations observed on varying the liquid fraction correlates qualitatively with that predicted on the basis of Surface Evolver calculations. The same is not true of the 5-bubble cluster.     

Bubbles under stress

We present an experimental and theoretical investigation of a system composed of two soap bubbles strained between two parallel solid surfaces. The two-bubble cluster can be found in several configurations. The existence and stability of each of these states is studied as a function of the distance between the two facing surfaces. The change of this distance can induce a transition from one configuration to another; we observe that most transitions are subcritical, showing that the system is often trapped in states where the minimum of free energy is only local. The hysteretic transitions are responsible for the dissipation of elastic energy. The existence of more than one stable states for given boundaries conditions combined with the absence of thermalization means that the history of the system has to be taken into account and that there is no unique stress-strain relation. In the present system, because of its simplicity, a complete quantitative analysis of these general processes is obtained. The presented results may contribute to a better understanding of the dynamics of more complex systems such as foams or granular materials where similar processes are at work.     

Flame‐retardant and mechanical properties of phenolic foams toughened with polyethylene glycol phosphates

Three kinds of polyethylene glycol phosphates (PEGPs) toughening agents were synthesized by esterification of phosphorus pentoxide (P₂O₅) with polyethylene glycol and characterized by Fourier transform infrared spectra and ³¹P nuclear magnetic resonance. A series of lightweight phenolic foams toughened with different loadings of PEGPs were prepared. Optical microscopy results show that the addition of PEGPs with small molecular weight PEG improves the structural homogeneity of phenolic foams obviously. The flame retardancy of toughened phenolic foams was evaluated by using UL 94, limiting oxygen index, and cone calorimeter. The results indicate that the incorporation of PEGPs not only increases the toughness of phenolic foams but also improves their flame retardancy. Moreover, the thermal stability of PEGPs and the toughened foams was investigated by thermogravimetric analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Preparation and performance of a novel polyimide foam

A new type of polyimide foam (PIF) was prepared and characterized based on a one‐pot process by the reaction of a first solution with different ratios of a second solution. The first solution was comprised of pyromellitic dianhydride (PMDA), N, N‐dimethyl formamide (DMF), methanol, water, surfactant, and catalysts, while the second solution contained polyaryl polymethylene isocyanate (PAPI). In the present study, the relationships among compositions, structures, and properties of PIFs were investigated. The results indicated that with the increase in the weight ratio of PAPI/(first solution), the foaming degrees of PIFs increased from 10.14 to 10.52 times and the apparent densities before postcure decreased from 15.96 to 14.51 kg/m³. The open cell contents, average sound absorption coefficients, and average cellular diameters of PIFs after postcure increased with increase in the weight ratio of PAPI/(first solution). The glass transition temperatures (T_g) of PIFs after postcure first increased from 287 to 299°C, then decreased to 292°C, and the 5% weight loss temperatures and 10% weight loss temperatures presented the same trend as well. The compressive and flatwise tensile properties scaled very well with the relative densities of the foams after postcure, with the highest compressive strength of 0.03 MPa and the highest flatwise tensile strength of 0.15 MPa. Copyright © 2011 John Wiley & Sons, Ltd.     

Foaming behavior,cellular structure and physical properties of polybenzoxazine foams

In this paper, polymer foams based on a benzoxazine resin have been successfully prepared using azodicarbonamide (ADC) as a chemical blowing agent and have been characterized regarding their foaming behavior, cellular structure, and physical properties. The effect of the ADC on the curing process of the resin was analyzed using differential scanning calorimetry and blowing agent decomposition was followed by thermogravitmetric analysis (TGA). The characterization of the cellular structure of the foamed samples was done using scanning electron microscopy. The mechanical properties of the foams were determined using compression tests and the thermal conductivity was assessed using the transient plane source method. The results indicated that the curing process and gas release took place in a similar time interval. The foams showed an isotropic cellular structure with relative densities in the range 0.35–0.60, and showed compressive strengths and compressive moduli in the range of 10–70 MPa and 400–1100 MPa, respectively. Thermal conductivities were in the range of 0.06–0.12 W m^?1K^?1. The findings in this paper demonstrate the possibility of producing polybenzoxazine foams using a simple process in which curing and foaming take place simultaneously. In addition, the mechanical characterization of these materials indicates that they are suitable for structural applications. Copyright © 2011 John Wiley & Sons, Ltd.     

A new technique for measuring retrograde vitrification in polymer–gas systems and for making ultramicrocellular foams from the retrograde phase

A stepwise temperature‐ and pressure‐scanning thermal analysis method was developed to measure glass‐transition temperature T_g in the two‐phase polymer–gas systems as a function of gas pressure p, and was used to confirm recent theoretical predictions that certain polymer–gas systems exhibit retrograde vitrification, that is, they undergo rubber‐to‐glass transition on heating. A complete T_g‐p profile delineating the glass–rubber phase envelope was established for the PMMA‐CO₂ system. The retrograde vitrification behavior observed, where at certain gas pressures the polymer exists in the rubbery state at low and high temperatures and in the glassy state at intermediate temperatures, was similar to that reported previously based on the creep‐compliance measurements. The existence of the rubbery state at low temperatures was used to generate foams by saturating the polymer with CO₂ at 34 atm and at temperatures in the range −0.2 to 24 °C followed by foaming at temperatures in the range 24 to 90 °C. Foams with very fine cell structure never reported before could be prepared by this technique. For example, PMMA foams with average cell size of 0.35 μm and cell density of 4.4 × 10¹³ cells/g were prepared by processing the low temperature rubbery phase. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 716–725, 2000     

Use of blowing catalysts for integral skin polyurethane applications in a controlled molecular architectural environment: Synthesis and impact on ultimate physical properties

Polyurethane elastomers of a controlled molecular architecture were synthesized using a two‐step polymerization technique. The building blocks of the elastomeric materials included urea–urethane prepolymers end‐capped with diisocyanate groups and had an exact number of urea groups at both ends. Two‐dimensional bifurcated hydrogen‐bonding networks incorporating the urea groups were, with differential scanning calorimetric and dynamic mechanical thermal analyzer techniques, responsible for the increase in the glass‐transition temperature (T_g) of the hard block and sharp interface morphology between the pure “hard” domains and pure “soft” domains. The higher extent of the phase separation between the two phases contributed to higher elastic moduli for the hard blocks and higher tensile strength for the elastomeric samples. Higher elongation values were attributed to the liberation of the elastomeric chain ends that otherwise would have been constrained in the interface region. The higher T_g values of the hard blocks corresponded to an increase in the hardness values and a decrease in the tear‐strength values. The increase in the amount of urea groups within the hard segments, as a result of the increased amount of water and blowing catalyst, resulted in elastomeric foams with higher open‐cell content. This resulted in lower resilience values as measured using the pendulum rebound test and was attributed to the ability of the open cells to absorb and dissipate energy. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2526–2536, 2002