• Proceedings of the Membrane Society of Korea Conference
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• 1995.10a
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• pp.43-44
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• 1995

The diffusion behavior of liquid into polymer has been described by Fick's law, but the departure from Fickian diffusion is frequently found. In this study, 'noble' expressions for the rates of relaxation and sorption are introduced to eliminate these limitations. The ralaxation-sorption coupled mechanism model are based on the possibility of contacting liquid molecule and the active site which has the numerical concept of free volume. The concept has an analogy of reaction rate expressed by the possibility of collision with molecules and used in adsorption and reactive extraction etc. The new model simulated by Rungc-Kutta method for initial-value problem and Fickian diffusion is caompared with experimental data. The results show that the ralaxation-sorption coupled mechanism is able to account well for Fickian and non-Fickian sorption behavior including sigmoid and two-stage. In addition, this model has a chance of expansion to multi-component sorption with ease.

• Korean Chemical Engineering Research
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• v.43 no.2
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• pp.299-304
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• 2005

There have been many efforts to use anionic hydrogels as oral protein delivery carriers due to their pH-responsive swelling behavior. The dynamic swelling behavior of poly(methacrylic acid-co-methacryloxyethyl glucoside) [P(MAA-co-MEG)] hydrogels was investigated to determine the mechanism of water transport through these anionic hydrogels. The exponential relation $M_t/M_{\infty}=kt^n$ was used to calculate the exponent, n, describing the Fickian or non-Fickian behavior of swelling polymer networks. The mechanism of water transport through these gels was significantly affected by the pH of the swelling medium. The mechanism of water transport became more relaxation-controlled in the swelling medium of pH 7.0 that was higher than the $pK_a$ of the gels. Experimental results of time-dependent swelling behavior of the gels were analyzed with several mathematical models. Using ATR-FTIR spectroscopy, the effect of ionization of the carboxylic acid groups in the polymer networks on the water transport mechanism was investigated.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.11
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• pp.1297-1303
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• 2012

In this paper, the standard procedures for measuring the moisture sorption properties of thin polymeric materials such as polyethylene terephthalate (PET) by using the thermo-gravimetric method to characterize the moisture diffusion in the polymer are presented, and the sorption properties are quantified. The moisture diffusivity and solubility are characterized to investigate the effect of temperature and humidity on the moisture sorption properties according to the Arrhenius equation. The validation of the obtained sorption properties using thermogravimetry is discussed with the measured permeability based on Fickian diffusion. The nonlinear behavior of the concentration dependent moisture diffusion is investigated experimentally, and the nonlinearity is characterized numerically for the case of having an interface with an inorganic material such as a metal. The Fickian/Non-Fickian model based on the obtained moisture sorption properties is compared and discussed.

• Polymer(Korea)
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• v.25 no.5
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• pp.665-670
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• 2001

The solvent extraction of polyethylene glycol (PEG) by ethanol has been studied for the powder injection molded compacts of Sr-ferrite/PEG/carnauba wax/HDPE. The extraction rate of PEG is sensitively proportional to the solvent temperature whereas it is inversely proportional to the contents of PEG, the molecular weight of PEG. and the specimen thickness. The high extraction rate of PEG is achieved under the following conditions: solvent temperature of $70^{\circ}C$, PEG contents of 30%, and PEG molecular weight of 400 g/mol. In the early stage of solvent extraction, the non-linear relationship between the extraction rate and the square root of the extraction time indicates that the extraction of PEG does not follow the Fickian behavior. At extraction times longer than 180 min. however, the extraction of PEG follows the Fickian behavior. The extraction fate of PEG by ethanol is about$1.0{ imes}10^{-6}g/cm^2sec$ enough for common applications.

• Membrane Journal
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• v.10 no.3
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• pp.139-147
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• 2000

Non-Fickian (or anomalous) diffusion was observed in transient sorption of aromatic solvents(such as benzene, toluene, and chlorobenzene) in fluoropolymers (such as ETFE, ECTFE and PVDF). In this study, five other transient sorption models (Crank, Long ＆ Richman, Berens ＆ Hopfenberg, Neogi, Li) based on Fick's law were employed to fit the anomalous sorption data for aromatic solvents. The adjustable parameters were determined by least square analysis of the measured and predicted fractional uptake. For ETFE sorption data slightly deviating from Fickian behavior, all the models exhibited satisfactory results in fitting the anomalous sorption data. In particular, Neogj model predicted intrinsic diffusivity (0.4～0.8$\times$10$^{-5}$ $\textrm{cm}^2$/day) and equilibrium diffusivity (0.13～0.31$\times$10$^{-4}$ $\textrm{cm}^2$/day) as well as relaxation kinetics related to non-Fickain diffusion. For a typical sigmoidal sorption behavior in PVDF, only Crank's model could give the reasonable evaluation on transport properties. The ratio of intial diffusivity (D$_{i}$) to final equilibrium diffusivity (D$_{\infty}$) was ranged from 80 to 200. For the final stage of uptake In ECTFE with drastic acceleration, all the models exhibited significant deviations from the sorption data. New diffusion models based on thermodynamics and continuum mechanics should be employed to get valuable information on transport properties as well as relaxation kinetics coupled with non-Fickian diffusion.

• Polymer(Korea)
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• v.28 no.1
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• pp.24-34
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• 2004

Transient sorption experiments were conducted among several combinations of fluoropolymers and various organic solvents. Fully fluorinated polymer tended to exhibit ideal sorption behavior, while partially fluorinated polymers showed anomalous sorption behaviors with a drastic acceleration at the final stage of uptake. Minimization of least-squares of the measured and predicted fractional uptake, which indicated the increasing degree of deviation from Fickian diffusion, gave values of 3.0${\times}$10$\^$-4/, 1.75${\times}$10$\^$-3/, 8.68${\times}$10/sup-3/, 1.75${\times}$10$\^$-2/, respectively, for perfluoroalkoxy copolymer, poly(ethylene-co-tetrafluoroethylene), poly(vinylidene fluoride), poly(ethylene-co-chlorotrifluoroethylene). From stress-strain tests, it was confirmed that non-Fickian diffusion is closely related to the significant variation of mechanical properties (such as modulus and tensile strength) of swollen polymer. Anomalous sorption behavior stemmed from non-Fickian diffusion caused by nonlinear disruption of polar inter-segmental bonds due to solvent-induced plasticization. Thus, it is imperative to investigate the diffusion behavior of swelling solvents in partially fluorinated polymers, especially for the application to barrier materials or perm-selective membranes.

• Proceedings of the Membrane Society of Korea Conference
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• 1996.04a
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• pp.34-35
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• 1996

The diffusional behavior of many non-solvents in glassy or semicrystalline polymers cannot be adequately described by a concentration-dependent form of Fick's law, especially when mass transfer is coupled with structural changes. Many mathematical models have been devised to interprete non-Fickian diffusion dominated by relaxation kinetics. In formulation of non-Fickian diffusion mathematics, therefore, the most important factor to consider is how relaxation effects can influence the governing constitutive equation and boundary conditions. That is, relaxation parameters can be accommodated by variable boundary conditions or a modified continuity equation, or both, depending on specific systems and conditions (Frish, 1980). Accoring to Astarita and Nicolais (1983), the model equations can be broadly categorized as continuous or discontinuous. Continuous model equations encompass phenomena where the structural change takes place gradually over the whole volume of the polymer sample (Crank, 1953; Long and Richman, 1961; Berens and Hopfenberg, 1978). On the other hand, discontinuous model equations deal with the phenomena where the morphological change appears to be abrupt (Li, 1984). Four mathematical models with different relaxation parameters were applied to fit the anomalous sorption data observed in fluoropolymers (PVDF, ECTFE). The fitted result for PVDF-benzene sorption data is shown in Fig. 1.

• Polymer(Korea)
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• v.32 no.3
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• pp.219-229
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• 2008

A pH sensitive ternary copolymer gel was synthesized in the presence of ethylene glycol dimethacrylate (EGDMA) as a crosslinking agent through radical polymerization of vinyl acetate (VA), acrylic acid (AA) and methyl acrylate(MA) with a weight ratio of 1 : 1.3 : 1. A number of experiments were carried out to determine the swelling behavior of the gel under a variety of pH conditions of the swelling medium. As the pH of the swelling medium was changed from 1.0 to 8.0 at $37^{\circ}C$, the gel showed a shift in the pH-dependent swelling behavior from Fickian (n=0.3447) to non-Fickian (n=0.9125). The resulting swelling parameters were analyzed using graphical and statistical methods. The results showed that the swelling of the gel was controlled by the pH of the medium, i.e. $n=n_o{\exp}(S_{C}pH)$, where n is the diffusion exponent, $n_o(=28.9645{\times}10^{-2})$ is the pre-exponential factor and $S_C$(=0.1417) is pH sensitivity coefficient. The swelling behavior of the gel was also examined in aliphatic alcohols. The results showed that the rate of swelling increased with increasing number of carbon atoms in the alcoholic molecular chain.

• Applied Chemistry for Engineering
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• v.30 no.2
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• pp.233-240
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• 2019

Molecular recognition technology has attracted considerable attention for improving the selectivity of a specific molecule by imprinting it on a polymer matrix. In this study, adsorption and release characteristics of chitosan based drug delivery films imprinted with sulindac (SLD) were investigated in terms of the plasticizer, temperature and pH and the results were also interpreted by the related mathematical models. The adsorption characteristics of target molecules on SLD-imprinted polymer films were better explained by the Freundlich and Sips equation than that of the Langmuir equation. The binding site energy distribution function was also useful for understanding the adsorption relationship between target molecules and polymer films. The drug release of SLD-imprinted polymer films followed the Fickian diffusion mechanism, whereas the drug release using artificial skin followed the non-Fickian diffusion behavior.

• KOREAN JOURNAL OF PACKAGING SCIENCE & TECHNOLOGY
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• v.4 no.1
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• pp.11-16
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• 1997

Sorption studies involving the sorption of n-propanol by an Amorphous Nylon(Nylon 6I/6T) were carried out as a function of sorbate vapor activity at $23^{\circ}C$. Vapor activity levels from 0.035 to 0.91 were investigated to evaluate the concentration dependency of sorption mechanism. Sorption behavior of propanol by Nylon 6I/6T showed distinctive two mode sorption phenomena as a function of Vapor activity. At Vapor activity levels below a=0.11, equilibrium sorption was achieved within a short period of time(less than 20hrs), which can be interpreted as following a Fickian diffusion model. A Langmuir-Flory-Muggins Dual Mode Sorption model can also be applied at these concentration levels. However, for Vapor activities above a=0.11, the sorption process appeared to be non-Fickian and resulted in a lack of equilibrium being attained.