A new method for the prediction of diffusion coefficients in poly(ethylene terephthalate)

Poly(ethylene terephthalate) (PET) is used in several packaging applications, especially for beverages. Due to the low concentration of potential chemical compounds like polymer additives or monomers leached out of the polymers and found in food or beverages, the compliance of a PET packaging material is shown often by use of migration modeling. Diffusion coefficients for migrants, however, are rare in the scientific literature. The aim of the study was to develop an equation for the prediction of diffusion coefficients in PET on the basis of activation energies of diffusion for possible migrants in PET. As a result, a correlation between experimentally determined activation energies of diffusion E_A and the volume of the migrant V was established for PET. In addition, a correlation of the pre‐exponential factor D₀ with the activation energy E_A was found. Combining both correlations lead to an equation where the diffusion coefficients D_P are predictable from the molecular volume V of the migrant. The equation might be useful for migration prediction and consumer exposure estimations. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Functional barriers in PET recycled bottles. Part I. Determination of diffusion coefficients in bioriented PET with and without contact with food simulants

A major outcome for recycled plastics consists of making food packaging materials. However, any contamination of collected plastics with chemicals may then be of concern for public health. A solution to mind migration is to use a layer of virgin polymer, named functional barrier, intercalated between the recycled layer and the food. This article aims to provide experimental values of diffusion coefficients (D) of model pollutants (surrogates) in poly(ethylene terephthalate) (PET) to be used for modeling migration through functional barriers. Diffusion coefficients of a large set of surrogates at low concentrations in PET were measured in various conditions. A solid‐to‐solid diffusion test was designed to avoid the use of a solvent that may induce plasticizing of the material and partitioning effects at the interface. Using [Log D = f(molecular weight)] correlations, the values of diffusion coefficients and activation energies of the surrogates measured by this method were shown to be consistent with the literature data obtained for gases, in permeation experiments, where no plasticization occurred. Migration from PET into food simulants was then studied. Migration into an aqueous medium is largely influenced by the solubility of the surrogates, the less soluble ones being not detected, despite high D values. With ethanol solvent, there were no partitioning effects, and the high plasticization effect of PET by ethanol considerably increases the apparent diffusion coefficients. The effects of temperature and plasticization on the relationship between diffusion coefficients and molecular weight are discussed. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 2845–2858, 2004     

Functional barriers in PET recycled bottles. Part II. Diffusion of pollutants during processing

Recycled plastics may be polluted by various chemicals available to consumers. When such materials are used to manufacture packaging materials intended to be in direct contact with food, these pollutants may migrate into food. The use of multilayer structures with a virgin polymer layer as a functional barrier may prevent such migration. This work deals with the possible diffusion of pollutants into and through the virgin layer during processing at high temperatures. A test is designed to measure diffusion coefficients in elastomeric and glassy polymers, in their molten state; 2.5‐dimethoxyacetophenone was used as a surrogate pollutant, and its concentration profiles are monitored by UV microscopy. Based on diffusion coefficients and on activation energies, glassy polymers appear to be much better barriers than polyolefins, even in their molten state. We then focus on poly(ethylene terephthalate) (PET) bottle preforms, processed by injection molding. In a first approach, a worst case situation was simulated by numerical analysis, using both overestimated diffusion coefficient values and very low values of activation energy. It appears that migration into foodstuffs through functional barriers can only be observed with unrealistic high diffusion coefficients and low activation energies. These results were confirmed by experimental determination of the concentration gradients of model pollutants in multilayer structures. It appears that little diffusion occurs, despite at a very high temperature. The effects of temperature and thickness of the functional barrier are discussed. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 2859–2870, 2004     

Water sorption in poly(ethylene furanoate) compared to poly(ethylene terephthalate). Part 2: Kinetic sorption

Diffusion coefficients for water in amorphous poly(ethylene furanoate) (PEF) and poly(ethylene terephthalate) (PET) were studied at 35 °C over the entire water activity range. PEF exhibits a ∼5× reduction in diffusion coefficient averaged over the entire concentration interval compared to PET. Fickian diffusion was observed for water in both polyesters up to ∼0.6 activity, after which the presence of non-Fickian relaxations required treatment using the Berens–Hopfenberg modeling framework. Penetrant plasticization at high activity was found for both PEF and PET, as evidenced by a positive correlation between diffusion coefficient and increasing water concentration. Arrhenius interpretation of diffusion coefficients measured at 15, 25, 35, and 45 °C allowed calculation of the activation energies of diffusion for PEF and PET, which were similar at 47.1 ± 2.8 kJ/mol and 46.4 ± 3.0 kJ/mol, respectively. This study complements prior work pertaining to the equilibrium water sorption properties in both polyesters, and subsequently provides a detailed investigation of the water diffusion process in these materials.     

无定形PET中小分子扩散系数的分子动力学模拟

采用分子动力学模拟研究了相对分子质量在32～339范围内小分子在无定形PET中的扩散过程。基于Einstein关系式计算了扩散系数,讨论了模拟时间、密度对扩散系数的影响。结果表明：在较高的温度下,较短的模拟时间内就能观察到均方位移曲线的线性区;而在较低的温度下,需更长的模拟时间。扩散系数随密度增加而降低,聚合物密度越大,所需的模拟时间越长。通过比较扩散系数的计算值与实验值,发现两者的比值在一个数量级范围内,表明建立的聚合物模型可接受且能正确描述小分子在无定形PET中的扩散过程, 为获得迁移模型中关键参数——扩散系数提供了一种近似的计算方法。     

纸塑复合包装材料纸中化学物迁移预测模型

基于一维Fick扩散理论,考虑了纸和塑料涂层界面处的分配系数及纸和塑料涂层中不同的扩散系数,建立了迁移预测模型,得到了其解析解。分析了各参数如分配系数、扩散系数、纸中化学污染物初始浓度和量纲1时间对迁移行为的影响。结果表明,随纸塑界面处分配系数k_CP的增大,从纸中迁移入功能阻隔层塑料中的化学污染物量和通过功能阻隔层塑料迁移进入食品中的化学污染物量明显增多;塑料中扩散系数D_C的变化显著影响了塑料和食品中化学污染物的量,而纸中扩散系数D_P的改变对迁移的影响不显著。     

Concentration Dependence of the Diffusion Coefficients of Disperse Dyes in Polyethylene Terephthalate

Diffusion coefficients of disperse dyes have been calculated by Matano's method from diffusion profiles in polyethylene terephthalate(PET). The diffusion coefficients (D_c) clearly indicate concentration-dependence. It has been found, from the densities of the dyed PET and the dye, that there is no overall change in the volume of the PET and dye in dyeing. The instrinsic diffusion coefficients have been calculated from D_c and the volume fraction (φ₁) of penetrant in the amorphous region. From these values, thermodynamic diffusion coefficients (χ?) were obtained. It has been found that the relation between 1/log (χ?/χo) and 1/φ₁ is a straight line, and it therefore seems reasonable to assume that the diffusion of disperse dyes in PET can be described by Fujita's ‘free volume theory’ for the diffusion of low molecular-weight organic compounds in an amorphous high-polymer.     

Kinetic migration of PBS and PBSA biopolymers prepared by cast film extrusion and biaxial stretching: A combined experimental and modeling approach

The kinetic migration of poly(butylene succinate) (PBS) and poly(butylene succinate-co-adipate) (PBSA) biopolymers, prepared by cast film extrusion (thin film) and biaxial stretching (biaxially oriented [BO] film) techniques, were investigated based on experimental and mathematical modeling. MATLAB coding was used to fit the migration data to a diffusion model. BO films significantly reduced the migration rate compared with thin films, with reductions of 29% and 41% for BO-PBS and BO-PBSA, respectively, due to the increased degree of molecular crystallinity. Higher ethanol content increased the quantity of substance diffusing from plastic film. PBS and PBSA are more suitable for packaging hydrophilic foods than alcoholic beverages. PBS exhibited a lower migration rate than PBSA due to its more rigid polymer matrix. Remarkably, BO-films exhibited 31% and 41% lower diffusion coefficients (D) compared with thin films, but significantly higher partition coefficients (K_P,F) by 44% and 267% for BO-PBS and BO-PBSA, respectively. This suggests a stronger affinity of migrant for BO film matrix. However, at 70°C, PBSA films may be hydrolyzed with a high ethanol, resulting in an inadequate diffusion model. The diffusion–reaction concept should be implemented for a better fit. These findings provide valuable insights for selecting appropriate packaging materials and predicting migration under diverse conditions, ultimately promoting consumer safety.     

Estimation of Diffusion Coefficients Based on Adsorption Measurements in Model Extraction Systems

The drop volume technique has been used to measure the equilibrium and dynamic interfacial tension at the liquid/liquid interfaces of selected hydroxyoximes, as examples of chelating type hydrophobic metal ion extractants. The measurements for the kinetics of adsorption enable the calculation of diffusion coefficients. In this paper, new methods for the estimation of the diffusion coefficient by Fick's and the Maxwell‐Stefan equations are presented. The calculated values of the diffusion coefficient were compared with the values obtained from the short and long time approximation models of the Ward‐Tordai equation. The influence of the organic phase and the addition of non‐organic electrolyte to the aqueous phase on the estimated values of the diffusion coefficients were investigated.     

塑料食品包装材料化学物迁移的数值模拟

基于有限差分方法数值模拟了塑料食品包装材料化学物向食品（模拟物）的迁移及迁移物在食品内的不稳定性。结果表明,扩散系数DP决定了迁移的动力学过程,分配系数KP,F表征平衡时化学物在包装材料和食品内的浓度比值,平衡时食品内的化学物浓度随化学物在包装材料内的初始浓度Cin的增加而增加。对于多层复合包装,阻隔层可显著减缓污染物层内化学物向食品的迁移,从而达到保证食品安全的目的,阻隔层厚度LR影响阻隔功效。化学迁移物在食品内存在不稳定现象,这将导致实验结果低估其向食品的迁移。     

Carrier Dyeing of Polyester Fibre

Aspects of the diffusion of carriers in polyester fibre have been studied using several compounds representative of commercial carriers. The apparent diffusion coefficients, activation energies of diffusion, and entropies of activation of diffusion have been determined. The apparent diffusion coefficients were found to be several orders of magnitude greater than those of disperse dyes, whilst the apparent activation energies and entropies of activation of diffusion were lower. A major difference in the diffusion behaviour of carriers, compared with that of disperse dyes, is the concentration–dependence of the diffusion coefficients of the former class of compound.     

纸塑复合包装材料中化学物迁移的改进预测模型及其通用性

以真实纸塑包装-化学物-食品体系为依据,基于一维Fick扩散理论,考虑化学物在纸和塑料涂层内具有不同的扩散系数及纸的厚度为有限厚,引入纸和塑料涂层界面处的分配系数,给出初始条件和边界条件,建立迁移预测模型,得到解析解。同时,对模型进行简化处理,分析其用于双层同种塑料-化学物-食品体系的使用通用性,并与Laoubi-Vergnaud模型进行对比分析,结果发现所建模型不仅可用于纸塑复合包装材料中化学物的迁移预测,同时还可用于双层同种塑料包装材料中化学物的迁移预测。     

Nonisothermal crystallization kinetics of poly(ethylene terephthalate)/clay nanocomposites prepared by melt processing

In this study, cold and melt crystallization behaviors of amorphous poly(ethylene terephthalate) (PET)/clay nanocomposites were investigated. Two nanocomposite samples with the same amount of inorganic content were prepared by melt processing using natural montmorillonite (Na‐MMT) and organo‐modified montmorillonite (org‐MMT). Depending on the clay structure, clay dispersion into PET and crystallization behavior of the samples were studied using X‐ray diffraction and differential scanning calorimetry methods, respectively. Effects of clay structure and organic groups between clay layers in org‐MMT on the melt crystallization kinetics of the samples were analyzed with various kinetic models, namely, the Ozawa, Avrami modified by Jeziorny, and Liu‐Mo. Crystallization activation energies of the samples were also determined by the Kissinger and Augis–Bennett models. Exfoliated structures were obtained in the nanocomposite samples prepared with both the Na‐MMT and org‐MMT. From the kinetics study, it was found that the melt‐crystallization rate of the sample prepared with the Na‐MMT was higher than that prepared with the org‐MMT at a given cooling rate. It can be concluded that organic ammonium groups in the org‐MMT decelerate the crystallization rate of PET chains possibly by affecting the chain diffusion and folding. POLYM. COMPOS., 2010. © 2009 Society of Plastics Engineers     

The diffusion of carbon dioxide in organic liquids

Methods of predicting gas-liquid diffusion coefficients are reviewed. A study has been made on the diffusion of carbon dioxide into a range of organic liquids and hydrocarbon mixtures over a sixty fold range of solvent viscosity. All available models for predicting diffusion coefficients were tested. It is shown that the data presented are best fitted by Arnold's equation. Until more exact models to represent the liquid state are available this affords a reliable method for correlating gas-liquid diffusion data.     

Investigation on Ultraviolet Absorption Properties,Migration, and Catalytic Performances of Ferrocene‐Modified Hyper‐Branched Polyesters

The ultraviolet absorption properties of a series of ferrocene‐modified hyper‐branched polyesters (HBPE‐Fcs) were analyzed by Ultraviolet/visible spectrometry. HBPE‐Fcs were used as burning rate catalyst components added into hydroxyl‐terminated polybutadiene (HTPB) based elastomers to investigate their migration behavior. Migration inhibition effects of HBPE‐Fcs in different aging conditions were analyzed. The diffusion coefficients (D) of the migration components were calculated according to Fick’s law of diffusion. The catalytic performances of HBPE‐Fcs for the thermal decomposition of cyclotrimethylenetrinitramine (RDX) were also investigated by non isothermal measurements using Kissinger method. The incorporation of ferrocenes into hyper‐branched polyesters (HBPEs) endows HBPEs with new ultraviolet absorption properties. The migration of HBPE‐Fc was minimized by grafting ferrocene on the hyper‐branched structures compared to that of simple ferrocene derivatives. HBPE‐Fcs present efficient catalytic effects on the thermal degradation of RDX; and, the catalytic reactions were characterized by decreased activation energies and increased rate constants.     

Fundamental studies on solvent dyeing with tetrachloroethylene. I. Diffusion of disperse dyes in poly(ethylene terephthalate)

The diffusion of C.I. disperse Violet 1 and Violet 8 in poly(ethylene terephthalate) (PET) was investigated by the method of cylindrical film roll. The effect of tetrachloroethylene (TCE) on the properties of PET was also studied. The treatment of PET with TCE brought about a strong effect on the thermal properties without degradation of PET. The diffusion of disperse dyes in PET from the TCE dyebath was faster than that from the aqueous dyebath. The activation energies of diffusion in the temperature range of 60° to 95°C from the TCE dyebath were smaller than those from the aqueous dyebath. Some break points were observed in the Arrhenius plots of diffusion coefficients in PET from the TCE dyebath. They were lower than those observed at dry and water-swollen states.     

Adsorption in finite bath and countercurrent flow with systems having a concentration dependant coefficient of diffusion

In many adsorbents surface diffusion is the governing mechanism of transport. The coefficient of surface diffusion may be concentration dependent.A model based on the assumption that the coefficient of diffusion is exponentially dependent on concentration in the adsorbent is used. Filmresistance is included. The model equations for adsorption in finite bath and in countercurrent flow have been solved for some cases for a range of parameter values which may apply for many adsorption systems where activated carbon is used for adsorbing organic compounds from aqueous solution. The results are presented in generalized diagrams. A comparison is made with other models with constant coefficient of diffusion. It is shown that by proper choice of variables most models give very similar results. The very simple model based on pore diffusion and a saturation isotherm approximately describes other cases such as pore diffusion and surface diffusion with and without a concentration dependent coefficient of diffusion. The saturation isotherm model has a simple analytical solution which makes it very simple to use.     

Theoretical Study on Pyrolysis and Sensitivity of Energetic Compounds. Part I: Simple model molecules containing NO2 Group

UHF (Unrestricted Hartree-Fock) Molecular Orbital calculations have been first performed for studying the pyrolysis mechanism of five compounds (nitromethane, methyl nitrate, nitroamine, methyl nitroamine and dimethyl nitroamine) containing NO₂ group as the simple models of organic explosives by using PM3 and AM1 methods. The potential energy curves and activation energies of the five pyrolysis reactions (into radicals) have been obtained. The activation energies are consistent with the experimental impact sensitivity of these three kinds of explosives: C-nitro < N-nitro < O-nitro compounds. It is found that there is a parallel linear relationship between the bond orders of N NO₂ bond in the molecules of three nitroamine compounds and the activation energies of their initiation reactions breaking N NO₂ bond. The obtained correlation coefficients between bond orders and activation energies from PM3 and AM1 calculations are 0.9962 and 0.9999, respectively.     

Diffusion of organic volatile molecules in LDPE/Halloysite nanocomposites

Diffusion behavior of d‐limonene and menthol propylene glycol carbonate were determined in halloysite/Low density polyethylene (LDPE), nanocomposites by a desorption method under nonisothermal conditions. Nanocomposites were prepared by melt mixing and diffusion coefficients of the organic molecules were determined in LDPE without halloysite, in the presence of halloysite, and with halloysite previously impregnated with each molecule. In general, the diffusion coefficient decrease for the molecules studied through the polymeric matrix with the amount of nanoclay loaded. Physical barriers due to halloysite nanoclay dispersed in the matrix give rise to an increase in activation energy for diffusion lowering the diffusion coefficients and desorption rate of the organic molecule through the LDPE matrix. No significant changes in crystallinity that affect the diffusion coefficients were found in the LDPE matrix by the addition of halloysite. The minimum release rate or maximum resistance for molecules to diffusion toward the surface in the halloysite/LDPE nanocomposite was found when the organic molecules were previously impregnated in the halloysite. An indication that impregnation of halloysite with the organic molecule will help to slow, and properly used, to dose their release rate. POLYM. COMPOS. 37:1267–1273, 2016. © 2014 Society of Plastics Engineers     

Fat-simulating and accelerating solvents for polyolefins and MWD of solvent extracts of polyethylenes

Migration kinetics of straight-chain oligomers and antioxidants from several polyolefins at different temperatures into various solvents have been studied by radioactive tracer techniques. Anhydrous ethanol appears to be a well suited food-oil or liquid-fat simulant for extracting different types of migrants from polyolefins. Pure and mixed triglycerides are also good oil or fat simulants, but the triglycerides offer no simpler analytical procedures than the use of oil or fat themselves. n-Octanol may also be considered as a reasonable oil or fat simulant; however, its action depends somewhat on the choice of migrants. The accelerating action of n-heptane over that of oil or simulants is quantitatively demonstrated. The accelerating effects are greater for migration systems with lower diffusion coefficients. The diffusion coefficients for migration into n-heptane are about 20 times greater than the diffusion coefficients into ethanol or oil for otherwise identical migration systems yielding diffusion coefficients of about 10^?7 cm²s^?1 into oil or ethanol. For systems yielding diffusion coefficients into oil or ethanol of about 10^?12 cm²s^?1, the corresponding diffusion coefficients into n-heptane are about 1000 times greater. The molecular weight distributions (MWDs) of the n-heptane and ethanol extracts of polyolefins have been analysed. n-Heptane can not only accelerate the migration of the individual migrant but also remove oligomer species that are slightly soluble or present at low levels in the oil or simulant extracts.