Diffusion of particles moving with constant speed

The propagation of light in a scattering medium is described as the motion of a special kind of a Brownian particle on which the fluctuating forces act only perpendicular to its velocity. This enforces strictly and dynamically the constraint of constant speed of the photon in the medium. A Fokker-Planck equation is derived for the probability distribution in the phase space assuming the transverse fluctuating force to be a white noise. Analytic expressions for the moments of the displacement $$ along with an approximate expression for the marginal probability distribution function $P(x,t)$ are obtained. Exact numerical solutions for the phase space probability distribution for various geometries are presented. The results show that the velocity distribution randomizes in a time of about eight times the mean free time ($8t^*$) only after which the diffusion approximation becomes valid. This factor of eight is a well known experimental fact. A persistence exponent of $0.435 \pm 0.005$ is calculated for this process in two dimensions by studying the survival probability of the particle in a semi-infinite medium. The case of a stochastic amplifying medium is also discussed.Comment: 9 pages, 9 figures(Submitted to Phys. Rev. E

Diffusion coefficients of lithium chloride and potassium chloride in hydrogel membranes derived from acrylamide

Diffusion of non-associated electrolytes (potassium chloride and lithium chloride) in concentrated aqueous solutions (0.1-1.0 moldm-3) has been studied in hydrogels derived from acrylamide and methyl methacrylate to study the mechanism of electrolyte transport. The preparation of two gels with different monomer ratio compositions resulted in obtaining membranes of substantially different hydrophilic character with polymer fractions of 0.3 and 0.5. Cukier hydrodynamic model was applied to explain the dependence of the diffusion coefficients of KCl and LiCl on the electrolyte concentration in hydrogel obtained experimentally. It was shown that the increase of the diffusion coefficients is accompanied with a decrease of the mean distance of approach of the ions. This can be explained by the formation of ion-pairs, resulting in a further contribution to diffusion once there is a decrease in the hydrodynamic resistance of the medium to the diffusing particles. Parameters, which characterise such a behaviour quantitatively, are different for different electrolytes and depend on water content in the gel. © 2001 Published by Elsevier Science Ltd.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Transport of solutes through calix[4]pyrrole-containing cellulose acetate films

Films of cellulose acetate containing different concentrations of meso-octamethyl-porphyrinogen (calix[4]pyrrole) were prepared and characterized using UV-vis and FTIR spectroscopy, DSC and SEM. Incorporation of calix[4]pyrrole into cellulose acetate leads to a decrease in the degree of hydrophilicity of the polymeric matrix. However, a slight increase in the percentage of water uptake of the polymer is found with an increase of the initial amount of calix[4]pyrrole in the composite composition. This effect can be related to the plasticizing effect that the calix[4]pyrrole provokes in the cellulose acetate. A comparative study of transport parameters of oxygen and some non-associated electrolytes (sodium, copper(II) and nickel chlorides) was carried out. The diffusion coefficients of molecular oxygen through cellulose acetate films decrease with an increase of the concentration of calix[4]pyrrole in the composite films. The transport (diffusion and permeation) of the above mentioned electrolytes through a set of composite films shows a decrease of permeability and diffusion coefficients with an increase of calix[4]pyrrole concentration. Such behaviour is typical of systems where interactions between the polymer and diffusing species occur. However, from the analysis of the distribution coefficient, it was found that those interactions are only dependent on the calix[4]pyrrole content for 2:1 electrolytes.http://www.sciencedirect.com/science/article/B6TWW-4NFR5CN-3/1/c8e93beea778c4b90e5b2ead92581bb

Permeation of sodium dodecyl sulfate through polyaniline-modified cellulose acetate membranes

The preparation of polyaniline (PANi)-cellulose acetate (CA) blends by casting films from a suspension, is reported. Two membranes were prepared from different solvents, one with a homogeneous and the other a heterogeneous dispersion of PANi in CA matrices. The membranes were characterized by X-ray diffraction, SEM, DSC, and FTIR, and the results were compared with those obtained for pure CA and PANi films. The transport properties of water and sodium dodecyl sulfate (SDS) in membranes of the PANi-CA blends and of CA were analysed. The transport of SDS and water depends on both the bulk/polymer density and the PANi content. In the homogeneous blend, the interaction between SDS and the polymer plays an important role in the transport mechanism. An irreversible interaction is observed, which can be monitored by UV-vis spectroscopy. The spectra of homogeneous, highly transparent PANi-CA blends show a pronounced sensitivity to SDS concentration, with detection limits [SDS]>=0.1 mM for films with a PANi concentration of 0.05% w/v.http://www.sciencedirect.com/science/article/B6TXW-4GCX1K6-C/1/14a4cf07e9dd93654b4cba319350f27

Sorption/diffusion behaviour of anionic surfactants in polyacrylamide hydrogels: from experiment to modelling

The sorption and diffusion processes of anionic surfactants with different chain length through polyacrylamide hydrogels with low swelling degree have been studied by electrical conductivity measurements. The multicomponent equilibrium equation has been used to model the sorption isotherms of different anionic surfactant in the hydrogels. Such isotherms show that initial rapid sorption of unimer surfactant into the membranes occurs, suggesting that non-freezing water can be involved in these interactions. In aqueous solution, at concentrations near and above the critical micelle concentration an anti-co-operative region is found. The diffusion coefficients of the anionic surfactants inside the hydrogel matrix show that the mobility of diffusing surfactant entities is dependent on cross-linker concentration and chain length. The Cukier hydrodynamic model and the free volume theory as modified by Peppas and Reinhart were applied to explain the dependence of the diffusion coefficients of surfactant on surfactant concentration inside the hydrogel. The hydrodynamic model was applied with success to the more hydrophilic surfactant, sodium 1-octanesulfonate, showing that the diffusion coefficients, D, increase when the resistance to hydrodynamic medium decreases; when the surfactant chain length increases (sodium dodecyl sulfate and sodium 1-hexadecane sulphonate) the variation of D with the free volume can only be understood considering the sieving effect produced by the surfactant inside gel.http://www.sciencedirect.com/science/article/B6TWW-48TM93Y-4/1/cd15a2b758be12fc526c852e9f96195