Sorbate Diffusion Research Articles

Potassium sorbate diffusion in multilayer polymer films: Effects of water activity and pH

The main aim of this study was to estimate the effect of acidity and water activity (aw) on the diffusion of potassium sorbate (PS) into model aqueous systems at 25 °C from an industrially produced multilayer active film (LPDE/polyamide/LPDE containing 2%PS). The releases of PS from films were set according to two factors face-centered central composite design of the response surface method (RSM). The ANOVA, 3D response surface, and 2D contour plots showed that pH and aw were effective factors in the diffusion coefficient (D) of PS from the films, and these two variables had an important interaction between them. Film samples within the liquid medium with low aw and pH values had the highest D. This might have occurred owing to the swelling of films within the solution with lower aw and high solubility of PS, and within the solution having lower pH, the faster diffusion of PS might have occurred. Practical applications In this study, the diffusion kinetic of potassium sorbate was observed under various conditions, such as pH and water activity. These conditions are the most important physico-chemical properties for food products. Moreover, the efficiency of the sorbate depends on the pH of the medium; with increasing pH, the efficiency is decreased, and above pH = 6.5, sorbic acid loses its antimicrobial property. Thus, the pH level is very important for the application of such films. Furthermore, these properties can affect both food product specialists and antimicrobial agent release. The pH and water activity were found to be very effective in diffusion kinetics of potassium sorbate. The results showed that antimicrobial diffusion from an active packaging film should be evaluated according to the food properties. We also observed adverse changes in the film structure, especially at lower water activity values. It was possible to relate the effect of aw on diffusion with the characteristics of film, the incorporated agents, and the used system. Depending on the diffusion medium, the film structure might change, and this could accelerate or limit the migration.

Calculation of pore diameters in zeolites

Pore diameters of zeolites are calculated using a new freely available software tool which identifies rings based on the crystallographic notation of atoms. In addition, an automated algorithm allows to extract information from molecular dynamics outputs so that dynamic pore diameters are calculated and compared to an experimental reference. This is useful in order to identify different rings along a given channel as well as for the calculation and analysis of ring deformations due to framework dynamics and sorbate diffusion.

Diffusion Analysis and Modeling of Potassium Sorbate in Gelatin Based Antimicrobial Film

The diffusion of potassium sorbate incorporated into gelatin based antimicrobial film was measured. Fick’s second law was applied to investigate the mechanism of potassium sorbate released from the films. The mathematical model was established. The result showed that the diffusion coefficient D increased with the increase of potassium sorbate concentration. The effects of temperature 5?C, 25?C and 35?C on diffusion were investigated. The mechanisms of potassium sorbate diffusion through gelatin films were mainly Fickian and determined by the power law model Mt/M∞ = k × tn. A decrease in temperature from 35?C to 5?C resulted in a reduction of diffusion coefficients from 5.20 × 10?12 to 1.36 × 10?12 m2/s. The diffusion coefficient of potassium sorbate is influenced by receiving solution pH values.

Relationship between long-range diffusion and diffusion in the ZIF-8 and polymer phases of a mixed-matrix membrane by high field NMR diffusometry

Pulsed field gradient (PFG) NMR is applied to resolve different modes of ethene self-diffusion inside a mixed-matrix membrane (MMM) consisting of ZIF-8 particles embedded in 6FDA–DAM polymer: (i) diffusion inside the ZIF-8 particles, (ii) diffusion inside the surrounding polymer matrix, and (iii) diffusion under conditions of an exchange between the particles and the polymer over length scales smaller than and comparable with the membrane thickness. This resolution is achieved using C-13 PFG NMR studies at a high magnetic field of 17.6T and large magnetic field gradients up to 30T/m. C-13 PFG NMR was also applied to measure ethene diffusion in the constituent components used in the MMM formation: a bed of ZIF-8 particles and a pure 6FDA–DAM polymer. It is shown that the comparison of all the measured diffusion data elucidates details of sorbate diffusion and diffusion mediated exchange dynamics between the ZIF-8 particles and the polymer in the MMM. An exchange model is applied to connect the long-range diffusivity measured for displacements larger than the size of ZIF-8 particles in the MMM with the diffusivities measured inside the ZIF-8 particles and the polymer.

Modeling of sorption kinetics: the pseudo-second order equation and the sorbate intraparticle diffusivity

The applicability of the pseudo-second order equation (PSOE) has been explained on the ground of the model assuming that the overall sorption rate is limited by the rate of sorbate diffusion in the pores of sorbent (intraparticle diffusion model). Mathematical expressions have been proposed in order to describe the dependence of the pseudo-second order constant on such parameters as the initial sorbate concentration, the progress of the sorption process and the solid/solution ratio. Further, it has been shown that equilibrium sorption capacities estimated by using PSOE may be much lower than the actual ones: it depends mainly on how the sorption system is close to equilibrium. The values of parameters applied in calculations were taken from the literature and correspond to the biosorption systems designed to remove the heavy metals from the aqueous solution.

Potassium sorbate controlled release from corn starch films

Active starch films with glycerol and potassium sorbate were obtained by casting. Native and acetylated corn starches, as well as the mixture of them in equal proportions were used and filmogenic suspensions with pH 4.5 were also prepared. Sorbate concentration decreased during film storage due to its oxidative degradation. Active films resulted more yellow and less transparent than films without sorbate. The minimum inhibitory concentration of sorbate resulted 0.3%, regardless of the starch type and the formulation pH. The use of antimicrobial package was more effective to prevent microbial growth on food surfaces than the use of conventional methods. Additive kinetic release was neither affected by the starch type nor by the formulation pH. Sorbate diffusion process was mathematically modeled satisfactorily. Active films were able to inhibit Candida spp., Penicillium spp., S. aureus and Salmonella spp. growth. Active films extended 21% the shelf life of refrigerated cheese, regardless of the formulation pH.

Liberação de benzoato de cálcio de filmes de alginato de sódio reticulados com íons cálcio

Biofilmes confeccionados à base de alginato de sódio foram reticulados com íons Ca++ provenientes de duas fontes, cloreto e benzoato de cálcio, e continham glicerol como plastificante. Inicialmente, devido ao alto poder gelificante do Ca++, um filme de baixo grau de reticulação foi confeccionado por casting (1º estágio). Esse filme sofreu uma reticulação complementar por imersão em uma solução contendo de 3 a 7% de CaCl2.2H2O, além de glicerol (2º estágio). A liberação de benzoato de cálcio foi avaliada em diferentes concentrações de agente ativo no filme e dois níveis de reticulação do alginato. O mecanismo envolvido no processo de difusão foi investigado usando o modelo da Lei de Potência. Os resultados indicaram que a difusão de benzoato de cálcio em filmes de alginato apresenta características de comportamentos Fickiano e não-Fickiano. Os coeficientes de difusão efetivos obtidos usando a solução em série derivada da 2ª Lei de Fick são próximos aos valores obtidos pela solução em tempos curtos, com valores de difusividade efetiva do benzoato variando de 3 a 5.10-7 cm²/s. Os valores de difusividade diminuíram com o aumento da intensidade de reticulação e aumentaram com a concentração de benzoato no filme.

Modeling of potassium sorbate diffusion through chitosan films

The mechanism of potassium sorbate (K-sorbate) release from chitosan films was studied as a function of immersion time in aqueous solution. Fick's law was applied to calculate the diffusion coefficient and the power law defining the type of diffusion mechanism. The novelty in this study is the compound diffusion mechanisms comparison through chitosan film (CF) and chitosan emulsion film. Initially, the lipid was selected to obtain the emulsion films. The evaluation was based on the water vapor permeability (WVP). The lower WVP (32.45% less than chitosan film) was found using 0.5 g/100 g of palmitic acid for 2.0 g/100 g of chitosan. Then, active chitosan films (ACF) were obtained incorporating K-sorbate on CF at 0.1 and 0.5 g/100 g of K-sorbate. Also, active palmitic acid-chitosan films (APEF) were obtained, incorporating 0.1 g/100 g of K-sorbate. The mechanisms of K-sorbate diffusion through ACF and APEF were mainly non-Fickian. However, the K-sorbate diffusion coefficient did not reduced in lipid presence.

Release of potassium sorbate from active films of sodium alginate crosslinked with calcium chloride

AbstractThe release of potassium sorbate from alginate films was evaluated considering different active agent concentrations in the film and three levels of alginate crosslinking. The mechanism involved in the diffusional process was investigated using the Power Law Model. The results indicated that potassium sorbate diffusion in alginate films has characteristics of Fickian and non‐Fickian behaviour. Effective diffusion coefficients obtained using the solution in series derived from Fick's Second Law are close to values obtained by the short‐time solution, indicating that the influence of swelling on effective diffusivity, although perceptible, is small, allowing the use of an average effective diffusivity. The values of effective diffusivity found indicate that alginate films have a potential use as systems for release of active substances. Copyright © 2009 John Wiley & Sons, Ltd.

Sorption kinetics of n-alkane vapours on isomorphously substituted MFI-type materials

Sorption kinetics of vapours of n-butane, n-pentane, n-hexane, and n-heptane on MFI-type materials isomorphously substituted with Al, V, Sb, Ti, As, W, and Mo was investigated. Uptake curves and sorption isotherms were determined. A clear decrease in the sorbate diffusion coefficient with the length of the hydrocarbon chain of a sorbate molecule was observed. Practically, no dependence of the diffusion coefficient on the chemical composition and size of the zeolite crystals were found.

Estimation of the kinetic characteristics of sorption of an organic ion on a heterogeneous crosslinked polymer sorbent within the framework of a bidisperse model

For the sorption of rubomycin, an antitumor athracycline-type antibiotic, on BDM-12 carboxyl-containing heterogeneous crosslinked polymer sorbent, it was shown that the measured time dependences of the extent of process are determined by two characteristic times: τ1 (in the range of short times) and τ2 (at long times). A phenomenological theory of the kinetics of sorption on the heterogeneous sorbent was developed on the basis of a biporous sorbent model. The dependences of the characteristic times τ1 and τ2 on the sorbent grain radius were obtained. It was concluded that the theory makes predictions in good agreement with experimental data and allows calculating the most important kinetic parameters of sorption of organic ions on polymer sorbents: the time of diffusion of the sorbate into microgranules, the diffusion coefficient of the sorbate in transport pores, the effective coefficient of the sorbate diffusion into the heterogeneous sorbent, etc.

A Mathematical Model for Potassium Sorbate Diffusion Through Whey Protein Films

A mathematical model was constructed and solved to quantitatively describe the dynamic behavior of the potassium sorbate diffusion through whey protein films. The model results were compared with the experimental data of the potassium sorbate diffusion through whey protein films, and excellent agreements between the experimental data and the model results are observed. The experimental data for potassium sorbate diffusion through whey protein films were used for mathematical model of potassium sorbate diffusion through whey protein films and the determination of both potassium sorbate and solvent diffusion coefficients. The diffusivities of potassium sorbate at 25°C ranged from 4.12 to 9.34 × 10−11 m2/s, while that of the solvent was between 1.38 and 8.74 × 10−10 m2/s, depending on the film composition.

Film Composition Effects on Diffusion of Potassium Sorbate Through Whey Protein Films

ABSTRACT: The effect of film composition on potassium sorbate diffusion in whey protein films was studied using mixture response surface methodology. The model developed for potassium sorbate diffusivity was statistically significant (P < 0.01) with no significant lack of fit. The diffusivities of potassium sorbate in the films at 25 °C varied between 5.4 and 9.8 × 10−11 m2/s. Amounts of protein, sorbitol, beeswax, and potassium sorbate in the films significantly affected potassium sorbate diffusion coefficients. Increasing the relative amounts of protein and beeswax in the films decreased potassium sorbate diffusivity, while increasing the relative amounts of sorbitol and initial potassium sorbate in the films increased the diffusion of potassium sorbate. Strong interactions were observed between protein and beeswax, and potassium sorbate and beeswax. Keywords: edible films, whey protein, potassium sorbate, diffusivity, mixture design

Comment on “Does lattice vibration drive diffusion in zeolites?” [J. Chem. Phys. 114, 3776 (2001)

Abstract

The frequency response of sorbate diffusion in one-dimensional channels

The theoretical diffusion of ideal sorbate molecules along one-dimensional channels containing random sequences of high-energy and low-energy barriers has been studied. This situation might occur in the case of sorbate diffusion in one-dimensional zeolite channels containing two cationic species of different diameters attached to the aluminosilicate framework. Using a master equation with appropriate microscopic transfer rates characterising the transfer of sorbate molecules between neighbouring cells, the frequency response of the number of absorbed molecules to a periodic modulation of the sorbate concentration at the entrances to the channels has been calculated. For channels consisting of about 100 equal-height energy barriers the frequency response function agrees well with the continuum result obtained from the Fickian diffusion equation. Predictions for the frequency response functions when fast and slow microscopic transfer rates operate in each channel have been made. The presence of two distinct transfer rates gives rise to well-resolved low- and high-frequency features. The relevance of these results to experiments on porous materials is discussed.

Does lattice vibration drive diffusion in zeolites?

A method of estimation of the effect of lattice vibration as a driving force for sorbate diffusion in zeolites is proposed. A realistic lattice model is employed to cut off unrealistic long vibrational modes and eliminate feedback due to lattice periodicity. A generalized Langevin equation for sorbate motion is then derived with the magnitude of the lattice vibration captured by two parameters, μ and ν, which can be readily computed for any system. The effect of lattice vibration is then estimated for a variety of sorbate–zeolite pairs. Lattice vibration is found to be a negligible driving force for some systems (e.g., methane and xenon in silicalite) and an important driving force for other systems. In the latter case, the lattice vibration can provide either linear stochastic Langevin-type force (e.g., for benzene in silicalite) or nonlinear deterministic force (e.g., for argon in sodalite).

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.

The adsorption of the vapors of various organic compounds. 4. Kinetics of the adsorption of vapors of organic compounds by sorbents with various types of micropore structures

1. A study has been made of the adsorption of vapors of organic compounds (benzene and 1,3,5-triethylbenzene) in the region of internal diffusion mass transport. 2. The method of statistical moments has been used to estimate the significance of sorbate diffusion in transport and adsorption pores in internal diffusion mass transport.