Penetrant diffusion

The quantities of prime interest here are the solubility and diffusion coefficient of the penetrant molecules and how these quantities are related to the structure of the host polymer. Comparisons with the extensive experimental data available for a wide range of polymers provides a stiff test not only of the accuracy of potential functions but perhaps more importantly of the method of preparation techniques and methods of sampling representative polymer structures. So far only limited quantitative success has been achieved, and that is under system conditions where the diffusion rate is 

Self-diffusion coefficients in fluids are most commonly obtained in molecular dynamics simulations using the Einstein relation 

Molecular dynamics studies of penetrant diffusion have so far been performed for polyethylene, polyisobutylene and polydimethylsiloxane. Calculated diffusion coefficients have not been in particularly good agreement with experiment. In the case of polyethylene, modeled using the united atom approximation, diffusion coefficients were much higher than expected and the activation energies too small although much better results have been obtained using PE IV. Reliable comparisons with experimental data are made difficult by uncertainties as to the true diffusion coefficients 

The sorption and diffusion of small gas molecules such as He, O2 and H2 in polyisobutylene has also been studied. An all-atom force field with carefully chosen parameters was used but it was still found that the diffusion coefficients were up to an order of magnitude too high. Loose coupling was used to control the pressure around zero but there are no details of the system density. 

Gas solubiUties can also be determined by molecular dynamics simulations, using the Widom test particle insertion method to calculate the excess chemical potential fiex. or free energy of the penetrant molecules. The solubility can be obtained using Henry s law. If E is the interaction energy of a virtual penetrant molecule with the polymer inserted at random within the sample (the molecule is invisible to the polymer) then 

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In this chapter, the subscript 1 denotes the penetrant and subscript 2, the polymer. The term penetrant refers to solvents which have sufficient thermodynamic affinity for and interaction with the polymer. It is because of this interaction that penetrant diffusion exhibits a significant concentration dependence. This orientation excludes consideration of the permeation of small gaseous molecules. 

In addition to temperature and concentration, diffusion in polymers can be influenced by the penetrant size, polymer molecular weight, and polymer morphology factors such as crystallinity and cross-linking density. These factors render the prediction of the penetrant diffusion coefficient a rather complex task. However, in simpler systems such as non-cross-linked amorphous polymers, theories have been developed to predict the mutual diffusion coefficient with various degrees of success [12-19], Among these, the most notable are the free volume theories [12,17], In the following subsection, these free volume based theories are introduced to illustrate the principles involved. 

When a penetrant diffuses into a polymer, the perturbation will cause the polymer molecules to rearrange to a new conformational state. The rate at which this conformational adaptation occurs depends on the mobility of the polymer chains. At temperatures well above the glass transition, this occurs quite rapidly and the diffusive process resembles that in the liquid state. At temperatures near or below the glass transition, the conformational change does not take place instantaneously. Instead, there is a finite rate of polymer relaxation induced by the... 

JC Wu, NA Peppas. Numerical simulation of anomalous penetrant diffusion in polymers. J Appl Polym Sci 49 1845-1856, 1993. 

GWR Davidson IH, NA Peppas. Solute and penetrant diffusion in swellable polymers. V. Relaxation-controlled transport in P(HEMA-co-MMA) copolymers. J Controlled Release 3 243-258, 1986. 

JC Wu, NA Peppas. Modeling of penetrant diffusion in glassy polymers with an integral sorption Deborah number. J Polym Sci Polym Phys Ed 31 1503-1518,... 

PMMA) film is quenched by permeation of methyl ethyl ketone (MEK), a good solvent for PMMA. A steady-state MEK concentration profile has been estimated from quenching data with existing sorption and light scattering data. The profile contains all the features of Case II diffusion the Fickian precursor, the solvent front, and the plateau region. However, the solvent front is not so steep as those observed in systems where penetrant diffusion is much slower. 

The relation between the resin reaction and the booster biocide release process e.g. water penetration, diffusion through the binder phase... 

Lustig, S.R. and Peas, N.A. (1987). Solute and penetrant diffusion in swellable polymers. 7. A free volume based model with mechanical relaxation. J. Alied Polymers Sci., 43, 533-549. 

In their study of the NMR T2 and T2 of crosslinked cis-polyisoprene sheets under extension, von Meerwall and Ferguson 65) found that T2 of the rubber had much smaller anisotropy ( magic angle effect) than that of trace penetrants at the same extension ratio X < 3. However, the penetrant diffusion (referred to the strained dimensions) was within experimental error isotropic these findings are equally valid for C6F6 and n-hexadecane as penetrant. The authors concluded that segment orien-... 

Matrix Diffusion. Historically, the most popular diffusion-controlled delivery system has been the matrix system, such as tablet and granules, where the drug is uniformly dissolved or dispersed, because of its low cost and ease of fabrication. However, the inherent drawback of the matrix system is its first-order release behavior with continuously diminishing release rate. This is a result of the increasing diffusional resistance and decreasing area at the penetrating diffusion front as matrix diffusion proceeds. 

One possible solution to this problem is to develop microscopic diffusion models for glassy polymers, similar to those already presented for rubbery polymers. Ref. (90) combines some of the results obtained with the statistical model of penetrant diffusion in rubbery polymers, presented in the first part of Section 5.1.1, with simple statistical mechanical arguments to devise a model for sorption of simple penetrants into glassy polymers. This new statistical model is claimed to be applicable at temperatures both above and below Tg. The model encompasses dual sorption modes for the glassy polymer and it has been assumed that hole"-filling is an important sorption mode above as well as below Tg. The sites of the holes are assumed to be fixed within the matrix... 

The problem of diffusion modeling in polymers changes to some degree when one envisages to develop a really atomistic model, with trully predictive capabilities and without making any ad hoc assumption on the molecular behaviour and/or motions in the polymer penetrant system. In principle, a possibility to develop such diffusion modelings, is to simulate theoretically the process of penetrant diffusion in a polymer matrix by computer calculations. 

The first attempts in the direction of simulating theoretically at an atomistic level the diffusion of simple gas molecules in a polymer matrix were made more than two decades ago (100). But, the systematic development of ab initio computer simulations of penetrant diffusion in polymeric systems dates only from the late 80 s (101-104). At the beginning of the 90 s it was achieved to simulate some qualitative aspects such as the diffusion mechanism, temperature, and pressure dependence of diffusion coefficients (105-109). The polymers chosen for investigation mainly fell into two categories either they were easily described (model elastomers or polyethylene) or they were known to have, for simple permanent gases like H2, 02, N2, H20 or CH4,... 

Because time is explicitly present in the formulations of MD, this technique is the most straightforward way of computer simulating the motion of penetrant molecules in amorphous polymer matrices (97-99). The MD method allows one to look at a truly atomistic level within the system as it evolves in time. Recently, excellent reviews on the use of MD for simulating penetrant diffusion in polymers have been published (96-99). A summary of the basic concepts and some relevant results obtained so far with MD will be presented bellow. 

In Table 5-2 a comparison between diffusivities obtained with the TSA method and experimental D is presented. From this table one can see that, in all cases computed D agree with experimental data to within an order of magnitude. Moreover most of these D are considerably smaller than the 5 10-7 cm2/s lower threshold assumed to be in reach of nowadays MD simulations Section 5.2.1. This is an encouraging sign that computer simulations of diffusional processes are already able to predict, with a reasonable accuracy and for small and simple penetrants, diffusion coefficients around 10-10 cm2/s. From the point of view the packaging sector it would be interesting to learn if and when further theoretical developments of the TSA method will be able to simulate (predict) such slow diffusional processes for organic penetrants with a much more complex structure, see Chapter 3 and Appendix I. 

The Element of Air is penetrating, diffuse, moveable—the wet and hot properties. Psychologically, air represents the Selfconscious Mind. The Element of Water relates to coolness, contraction, mutability or change—the properties of wet and cold. Water is the... 

There is no fundamental qualitative difference in mechanisms of low molecular weight (MW) penetrant diffusion in polymers above and below glass transition temperature, Tg, of the polymers [5,6]. The difference lies only in the fact that the movement of structural units of the macromolecule that are responsible for the transfer of penetrant molecules takes place at different supermolecular levels of the polymer matrix. At T > Tg the process of diffusion takes place in a medium with equilibrium or near-equUibrium packing of chains, and the fractional free volume, P(, in the polymer is equal to the fractional free volume in the polymer determined by thermal mobUity of strucmral units of macromolecules V((T), i e., V(= vut). At r< Tg the process of diffusion comes about under nonequihbrium packing conditions, although there exists a quasi-equilibrium structural organization of the matrix, where Vf> It is assumed that in this case Vf= where is the fractional free volume... 

The measurement of lipophilicity value for all three families of 5-thio-carbopeptides is essential for their potential affinity effect to cell membrane and the level of penetration/diffusion through membrane. The detailed values of measured lipophilicity calculated as log P via molecular modeling will be published separately as collaborative work effort. These particular data are essential for preliminary biological screening for all thioglycomimetics for selective in vitro cell viability assays as reported by us earlier (27)... 

Many food processes, which affect food quality and stability, are diffusion controlled (Karel et al., 1994 Roos, 1995). Transport of key penetrants such as water into or out of a polymeric food matrix can play a critical role in food quality and stability. Water is one of the major components and a very good plasticizer in foods. The quality and stability of dehydrated products, multi-domain foods, and the performance of biofilms and encapsulation and controlled release technologies are affected by moisture transport. The rates of molecular mobility and diffusion-limited reactions strongly depend on the factors surrounding the food. Temperature and water activity (fl ) pl y significant roles in penetrant diffusion. The physical state of the carrier matrix, chemistry, size, and structure of diffusing molecule and specific... 

Using another electrical analog approach, Klute (26,27) arrived at a similar expression in which the impedance factor was termed the "transmission function." In both cases, however, the properties of the conducting phase are considered not to be influenced by the crystalline phase. Although this was found to be true for sorption, Michaels et al asserted that the crystallites would reduce the mobility of the chains in the amorphous phase and, thus, further reduce penetrant diffusion rates. The "chain... 

Figure 5. Effect of temperature and transitions on penetrant diffusion coefficients. Left cyclopropane in high-density polyethylene to illustrate effect of melting point. Right CO2 in AN/MA copolymer to show effect of glass transition. Note reversed 1/T scale is used.

Case 11 diffusion The rate of penetrant diffusion is higher than the relaxation rate of polymer chains. Case 11 diffusion is characterized by a mass uptake that is proportional to the time, Q t. ... 

Butanoic acid has a powerful, penetrating, diffusive sour odor, reminiscent of rancid butter (Arctander, 1967). It is in the list of potent odorants in raw arabica with a sweaty odor description (Czerny and Grosch, 2000). An odor threshold of 240 xg/l (0.24 ppm) in water is quoted by Teranishi (1971). A flavor threshold of 6.8 ppm in water is given by Patton (1964), and 6.2 ppm by Siek et al. (1969). 

It has a very powerful and penetrating, diffusive, acid odor, pungent when undiluted, but more unpleasant when diluted. In fact it becomes more animal- and perspiration-like in dilution. Only in extreme dilution does the odor become again more pleasant, fruity, warm. Below 10 ppm, the taste is rather fruity, but at higher concentrations, the odor develops and it becomes more unpleasant (Arctan-der, 1967). For Czerny and Grosch (2000), it is one of the potent odorants in green coffee with a sweaty odor description. 

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