Anomalous Diffusion Mechanism Research Articles

Numerical approach to the fractional Klein-Kramers equation

Subdiffusion in the presence of an external force field can be described in phase space by the fractional Klein-Kramers equation. In this paper, we explore the stochastic structure of this equation. Using a subordination method, we define a random process whose probability density function is a solution of the fractional Klein-Kramers equation. The structure of the introduced process agrees with the two-stage scenario underlying the anomalous diffusion mechanism, in which trapping events are superimposed on the Langevin dynamics. We develop an efficient computer algorithm for visualization of fractional Klein-Kramers dynamics and present some simulation results based on Monte Carlo techniques.

Once-daily tablet formulation and in vitro release evaluation of cefpodoxime using hydroxypropyl methylcellulose: A technical note.

Decreasing the dose frequency of cefpodoxime proxetil increases patient compliance; patients prefer to take the drug once daily. It also improves the rate of bacterial killing and hastens the cure from the indications, and therefore increases compliance. The hydrophilic matrix of HPMC controlled the cefpodoxime proxetil release effectively for 24 hours; hence, the formulation can be considered as a once-daily sustained-release tablet of cefpodoxime proxetil. The formulation showed acceptable pharmacotechnical properties and assay requirements. In vitro dissolution studies indicated a sustained-release pattern throughout 24 hours of the study that was comparable to the theoretical release profile. Drug release kinetics indicated that drug release was best explained by Higuchi's equation, as these plots showed the highest linearity (r 2=0.9734), but a close relationship was also noted with zero-order kinetics (r 2=0.9708). Korsmeyer's plots indicated ann value of 0.57, which was indicative of an anomalous diffusion mechanism or diffusion coupled with erosion; hence, the drug release was controlled by more than one process. Hixson-Crowell plots indicated a change in surface area and diameter of the tablets with the progressive dissolution of the matrix as a function of time.

The release dynamics of salicylic acid and tetracycline hydrochloride from the psyllium and polyacrylamide based hydrogels (II)

Psyllium, a medicinally active natural polysaccharide, has been modified with polyacrylamide to develop the hydrogels; those can act as the potential candidate for novel drug delivery systems. In the present studies, the release dynamics of model drugs (salicylic acid and tetracycline hydrochloride) from the drug-loaded hydrogels have been discussed, for the evaluation of the drug release mechanism and diffusion coefficients. It has been observed that diffusion exponent ‘ n’ have 0.68 and 0.74 values and gel characteristic constant ‘ k’ have 1.625 × 10 −2 and 1.272 × 10 −2 values, respectively, for the release of salicylic acid and tetracycline hydrochloride in distilled water from the drug loaded hydrogels. Therefore, drug release from the drug loaded hydrogels through Non-Fickian or Anomalous diffusion mechanism where the rate of drug diffusion and rate of polymer relaxation were comparable. The effect of pH on the release pattern of tetracycline has been studied by varying the pH of the release medium. However, in each release medium, the Initial diffusion coefficient was observed to be more than the late time diffusion coefficient.

Perspectives on modeling the release of hydrophobic organic contaminants drawn from model polymer release systems

This work critically evaluates current practices in modeling the release of hydrophobic organic contaminants (HOCs) from complex matrices. Using well-constrained model polymer release systems (MPRS), we evaluate several empirical kinetic release models and one class of semi-empirical diffusion model; generally these models either do not describe release well, and are thus not useful, or they describe release well but are overparameterized, thus decreasing confidence in the fitting parameters. Results indicate that the n-phasic release often attributed to soil and sediment matrices is a non-mechanistic operational definition, arising from bias in the choice of empirical fitting expression. Further analysis illustrates pitfalls in common approaches to characterizing desorption from complex environmental matrices with respect to parameter interpretation, particularly effective diffusion coefficients. We also consider MPRS release in the context of other models and find that, though release occurs from these materials via a mechanism of anomalous (non-Fickian) diffusion, Fickian diffusion models nonetheless describe release well. This finding reconciles previous reports about anomalous release from environmental matrices with the hitherto success of Fickian diffusion models of desorption.

The effect of composition of poly(acrylic acid)–gelatin hydrogel on gentamicin sulphate release: in vitro

Hydrogels based on poly(acrylic acid) and gelatin crosslinked with N,N′-methylene bisacrylamide (0.5 mol%) and glutaraldehyde (4%), respectively, forming an interpenetrating network were employed as matrices, for studying the loading and release of gentamicin sulphate. The release kinetics of gentamicin sulphate was evaluated in water (pH ∼5.8), phosphate buffer (pH 7.4) and citrate buffer (pH 4) at 37±0.1°C. The drug release in phosphate buffer was faster as compared to water or citrate buffer. Fitting the data of release studies in Peppas model indicated that the release of drug from full IPNs in phosphate buffer (pH 7.4), water (pH∼5.8) and citrate buffer (pH 4) were diffusion controlled. However, semi-IPNs showed both anomalous and Fickian diffusion mechanisms. With increasing gelatin percentage in the polymer, rate of drug release was faster and almost 85% of the loaded drug was released within 7 days in phosphate buffer (pH 7.4).

Mechanisms of primary relaxation near orientational-glass and structural-glass transitions

We discuss the universal features of the relaxation observed in glass formers near the structural-glass transformation temperature Tg. A macroscopic analysis of the relaxation dynamics is given using the correlation-length growth concept and the relevant diffusion exponent zg. Macroscopic relations, which expose temporal and spatial correlations, are proposed in terms of the characteristic temperatures, the exponent zg, and the fragility mg, related to the timescale. A stochastic approach to the problem at a mesoscopic level results in kinetic relations for zg, and the late-time and short-time asymptotic decay-law exponents; the Kohlrausch-Williams-Watts exponent βg and the von Schweidler exponent bg, respectively. A primary relaxation mechanism of anomalous diffusion, established for the amorphous polymers, leads to the kinetic equation zg=3(1/βg−1). Predictions for zg, based on the same mechanism, are given for the family of site-substituted orientational glasses. For the orientational glass in plastic crystals a distinct mechanism yields a new relation, zg=C(2−1/βg) with a constant C, deduced from dielectric loss data.

Analysis and modeling of potassium sorbate diffusion through edible whey protein films

The mechanism of potassium sorbate release from edible whey protein films was investigated. Anomalous or non-Fickian diffusion mechanism with diffusional exponents ( n) between 0.55 and 0.86 were found. A model describing the diffusion of potassium sorbate from whey protein films that swelled due to countercurrent diffusion of solvent was used to determine potassium sorbate and solvent diffusion coefficients. The diffusivities of potassium sorbate at 25°C ranged from 5.38 to 9.76×10 −11 m 2/s, while those of the solvent from 1.29 to 7.43×10 −10 m 2/s, depending on film composition.

On a possible mechanism of anomalous diffusion by Rossby waves

We study the advection of passive tracers by traveling plane Rossby waves of finite amplitude. In distinction with previous studies the nonlinearity of the wave field is taken into account in the first order of perturbation theory by considering the Lagrangian transport by resonant wave triads. Using the waves’ phases as new dynamical variables we reduce the problem to the study of a specific one-and-a-half degree of freedom Hamiltonian system with nonharmonic modulation. By using a symplectic integrator we study this system numerically and find an interesting series of bifurcations of its phase portrait as the nonlinearity increases. As is standard in the systems of this type we commonly see a chaotic sea with elliptic islands in the phase space, which means that in the physical space the resonant triads give rise to chaotic mixing and ballistic transport, respectively. The relevance of these results to the transport properties of β-plane turbulence is discussed.

Simulation of boron, phosphorus, and arsenic diffusion in silicon based on an integrated diffusion model, and the anomalous phosphorus diffusion mechanism

Boron (B), phosphorus (P), and arsenic (As) in-diffusion profiles were simulated based on an integrated diffusion model that takes into account the vacancy mechanism, the kick-out mechanism and the Frank–Turnbull mechanism. The simulations were done using just three parameters for B and P, and four parameters for As, each of which has a clear physical meaning and a physically reasonable value, with no additional ad hoc hypothesis. These parameters correspond to the diffusion of dopant species and of point defects that contribute to dopant diffusion. For the anomalous P diffusion profile, the vacancy mechanism governs the diffusion in the plateau region, while the kick-out mechanism governs it in the deeper region, where self-interstitials dominate in the kink region and P interstitials dominate in the tail region. This changeover from the vacancy contribution to the kick-out contribution is shown to be the mechanism for the appearance of the kink-and-tail profiles of P. Moreover, the comparison among B, P, and As diffusion is made to review the diffusion of these three dopants by means of a unified model.

Progesterone-loaded albumin microparticles

Bovine serum albumin (BSA) was used to prepare microspheres and microcapsules containing progesterone. The microparticles were obtained by means of a multiple emulsion method and by thermal or chemical crosslinking. The drug loading was higher for microspheres than microcapsules and varied for the different crosslinking methods: higher with thermal than chemical crosslinking and, among the chemical crosslinkers, loading was higher for formaldehyde than 2,3-butanedione and glutaraldehyde, respectively. Drug release was well differentiated for the different systems: the microspheres released 60% of their content according to an anomalous diffusion mechanism in the shorter periods, whereas microcapsules released 60% of their content according to different kinetic trends and for longer periods of time. The duration of each kinetic period and the relative drug fraction released, depends on the crosslinking method (thermal or chemical) and the nature of the crosslinking agent. Among the systems examined, the glutaraldehyde crosslinked microspheres show the higher release rate while the thermally crosslinked microcapsules had the lowest release rate which is characterized by the longest lasting zero order period.

Anomalous diffusion in aqueous solutions of gelatin.

Dynamic-light-scattering experiments on semidilute aqueous solutions of gelatin indicate three relaxation processes: an exponential for times less than \ensuremath{\sim}50 \ensuremath{\mu}sec followed by a power law at intermediate time and then a stretched exponential at long time. The characteristic time of the stretched exponential diverges as the system evolves to a gel. The latter two relaxations can be explained in terms of an anomalous diffusion mechanism where the mean-square displacement behaves as 〈${\mathit{R}}^{2}$〉\ensuremath{\sim}lnt at intermediate time and 〈${\mathit{R}}^{2}$〉\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{\beta}}}$ with \ensuremath{\beta}1 at late time. Length scales derivable from these diffusion mechanisms obey scaling, and it is proposed that \ensuremath{\beta} is related to the fracton density-of-states exponent and the fractal dimension of the gelatin molecules.

On the mechanism of anomalous surface diffusion of silver in an amorphous chalcogenide/silver structure

physica status solidi (a)Volume 115, Issue 2 p. K139-K141 Short Note On the mechanism of anomalous surface diffusion of silver in an amorphous chalcogenide/silver structure A. V. Kolobov, A. V. Kolobov A. F. Ioffe Physico-Technical Institute, Academy of Sciences of the USSR, Leningrad Search for more papers by this authorV. M. Lyubin, V. M. Lyubin A. F. Ioffe Physico-Technical Institute, Academy of Sciences of the USSR, Leningrad Search for more papers by this authorJ. Tröltzsch, J. Tröltzsch Technische Universität Karl-Marx-Stadt Search for more papers by this author A. V. Kolobov, A. V. Kolobov A. F. Ioffe Physico-Technical Institute, Academy of Sciences of the USSR, Leningrad Search for more papers by this authorV. M. Lyubin, V. M. Lyubin A. F. Ioffe Physico-Technical Institute, Academy of Sciences of the USSR, Leningrad Search for more papers by this authorJ. Tröltzsch, J. Tröltzsch Technische Universität Karl-Marx-Stadt Search for more papers by this author First published: 16 October 1989 https://doi.org/10.1002/pssa.2211150234Citations: 5 Politekhnicheskaya 26, SU-194021 Leningrad, USSR. PSF 964, DDR-9010 Karl-Marx-Stadt, GDR. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume115, Issue216 October 1989Pages K139-K141 RelatedInformation

The Condor Equatorial Electrojet Campaign: Radar results

A review of the experimental and theoretical background to the Condor equatorial electrojet campaign is followed by the presentation and discussion of VHF radar interferometer and HF radar backscatter data taken concurrently with two rocket in situ experiments reported in companion papers (Pfaff et al., this issue (a, b). Both experiments were conducted in strongly driven periods with the on‐line radar interferometer displaying signatures of what has been interpreted in earlier radar work (Kudeki et al., 1982) as kilometer scale gradient drift waves. Low‐frequency density fluctuations detected by in situ rocket sensors confirm the earlier interpretation. VHF radar/rocket data comparisons also indicate the existence of a turbulent layer in the upper portion of the daytime electrojet at about 108 km altitude driven purely by the two‐stream instability. Nonlinear mode coupling of linearly growing two‐stream waves to linearly damped 3‐m vertical modes could account for the radar echoes scattered from this layer, which showed no indication of large‐scale gradient drift waves. Nonlinear mode coupling may therefore compete with the wave‐induced anomalous diffusion mechanism proposed recently by Sudan (1983) for the saturation of directly excited two‐stream waves. Nighttime radar data show a bifurcated layer with the two parts having comparable echo strength but oppositely directed zonal drift velocities. The lower layer shows narrow backscatter spectra; the upper layer is characterized by kilometer scale waves and vertically propagating type 1 waves. The charateristics of the topside large‐scale waves show clear consistency with the predictions of nonlocal gradient drift instability theories. The observed sheared flow could be due to neutral winds or a reversal of the vertical polarization fields. Lack of concurrent in situ polarization field or density profile measurements, unfortunately, prevents us from determining the actual cause unambiguously.

Magnetic and Diffusional Properties of Compositionally modulated Amorphous CoTi/CoNb Alloys

Studies to determine the effects of alternating layers of positive-magnetostriction a-CoTi and negative-magnetostriction a-CoNb, to investigate the consequences for the film magnetic properties, and to elucidate the Nb-Ti interdiffusion mechanism, are described. Co 80 Ti 20 /Co 80 Nb 20 and Co 80 Ti 20 /Co 70 Si 15 B 15 films, compositionally modulated with wavelengths of 30 to 60 A, were prepared by sputtering. The CoTi/CoNb coercivity was found to be increased compared with CoNb, CoTi, and CoNbTi films. The compositionally modulated structure changes to a simple periodic structure through low-temperature heat treatment, but this transition is apparently reversible at higher temperatures through some anomalous diffusion mechanism.

Effect of the morphology of hydrophilic polymeric matrices on the diffusion and release of water soluble drugs

Drug release mechanisms from, and diffusion processes in, hydrophilic crosslinked polymeric systems were investigated in two macromolecular states: in the glassy and rubbery states during the early part of countercurrent water diffusion, and in the rubbery state after thermodynamic equilibrium between the network and the surrounding dissolution medium (water) was attained. Dilute, aqueous poly(vinyl alcohol) (PVA) solutions containing theophylline were crosslinked with glutaraldehyde. The crosslinking ratio, X, varied between 0.01 and 0.20 moles glutaraldehyde per mole of PVA repeating unit. Theophylline release from these rubbery matrices was followed as a function of time. It was determined that, within the range of crosslinking ratios studied, the crosslinked macromolecular structure affected the solute diffusion process. Theophylline release from crosslinked PVA slabs, which were originally dehydrated at 30°C, was also measured. The drug release process was significantly impeded in these systems, especially for samples with crosslinking ratio X ≥ 0.10. This behavior was explained in terms of relaxation of the macromolecular chains and possible existence of ordered chain structures. Glass-to-rubber transitions, a result of the countercurrent diffusion of water into the originally dried (glassy) polymer, shifted the fractional release of theophylline from a f( t 1/2) to a f( t n) time dependence, with n taking values between 0.50 and 0.76. This type of release behavior indicates anomalous diffusion mechanisms. These results may be helpful in the development of swelling controlled drug delivery systems.

Transverse-discharge excitation of the 1.315-μm atomic iodine laser I. Experiment

Prompt laser emission of 100 nsec fwhm from the 5 2P 1 2 → 5 2P 3 2 atomic iodine transition has been produced by a transverse electrical discharge. Electron impact dissociation of i-C 3F 7I in He buffer gas populates the excited state, and UV photodissociation and/or anomalous diffusion mechanisms are shown not to be responsible for the observed emission.

Ionization-enhanced diffusion: Ion implantation in semiconductors

A model for the diffusion of implanted interstitials during implantation is introduced and shown to be able to account for the tails observed in ion profiles. It is argued that mechanisms of ionization-enhanced diffusion can explain some of the anomalous diffusion mechanisms observed in semiconductors. Indications for the existence of such mechanisms in the field of ion implantation in semiconductors are discussed.

Ion-Implanted Phosphorous in Silicon: Profiles Using C-V Analysis

Depth distributions are presented for 200-, 300-, and 600-keV phosphorus ions either channeled along the 〈111〉 axis or implanted away from any major axis or plane in silicon. The profiles were obtained using the differential capacitance technique, and the technique is discussed along with a description of an automatic data-acquisition system which allows precise C-V data to be accumulated. The ``random''-direction implant profiles exhibit a definite exponential tail on the deep side of the implant. The characteristics of this tail appear to be material dependent but independent of the implantation energy. Thus, the tail probably results from an anomalous diffusion mechanism. The observed projected range for the random implants is 1.1 μm/MeV, with a range straggle nearly equal to that predicted by the range theory of Lindhard, Scharff, and Schiott (LSS). The channeled profiles exhibit a near flat characteristic to a depth of 2.2 μm/(MeV)1/2.