Predicting diffusion coefficients of chemicals in and through packaging materials

References

• Adams, W. A., Xu, Y., Little, J. C., Fristachi, A. F., Rice, G. E. and Impellitteri, C. A. (2011). Predicting the migration rate of dialkyl organotins from PVC pipe into water. Environ. Sci. Technol. 45: 6902–6907.
   PubMed Web of Science ®Google Scholar
• Aichele, M., Gebremichael, Y., Starr, F. W., Baschnagel, J. and Glotzer, S. C. (2003). Polymer-specific effects of bulk relaxation and stringlike correlated motion in the dynamics of a supercooled polymer melt. J. Chem. Phys. 119: 5290–5304.
   Web of Science ®Google Scholar
• Al-Malack, M. H. (2001). Migration of lead from unplasticized polyvinyl chloride pipes. J. Hazard Mater. 82: 263–274.
   PubMed Web of Science ®Google Scholar
• Alexander Stern, S. (1994). Polymers for gas separations: the next decade. J. Membrane Sci. 94: 1–65.
   Web of Science ®Google Scholar
• Alfadul, S. M. and Elneshwy, A. A. (2010). Use of nanotechnology in food processing, packaging and safety - review. Afr. J. Food Agr., Nutr. Dev. 10: 2719–2739.
   Google Scholar
• Alin, J. and Hakkarainen, M. (2011). Microwave heating causes rapid degradation of antioxidants in polypropylene packaging, leading to greatly increased specific migration to food stimulants as shown by ESI-MS and GC-MS. J. Agr. Food Chem. 59: 5418–5427.
   PubMed Web of Science ®Google Scholar
• Alin, J. and Hakkarainen, M. (2012). Migration from polycarbonate packaging to food simulants during microwave heating. Polym. Degrad. Stabil. 97: 1387–1395.
   Web of Science ®Google Scholar
• Anderson, W. A. C. and Castle, L. (2003). Benzophenone in cartonboard packaging materials and the factors that influence its migration into food. Food Addit. Contam. 20: 607–618.
   PubMed Web of Science ®Google Scholar
• Arnold, J. C. (2010). A free-volume hole-filling model for the solubility of liquid molecules in glassy polymers 1: Model derivation. Eur. Polym. J. 46: 1131–1140.
   Web of Science ®Google Scholar
• Arnould, D. and Laurence, R. L. (1992). Size effects on solvent diffusion in polymers. Ind. Eng. Chem. Res. 31: 218–228.
   Web of Science ®Google Scholar
• Arora, A. and Padua, G. W. (2010). Review: nanocomposites in food packaging. J. Food Sci. 75: R43–R49.
   PubMed Web of Science ®Google Scholar
• Arvanitoyannis, I. S. and Bosnea, L. (2004). Migration of substances from food packaging materials to foods. Crit. Rev. Food Sci. Nutr. 44: 63–76.
   PubMed Web of Science ®Google Scholar
• Aurela, B., Ohra-aho, T. and Soderhjelm, L. (2001). Migration of alkylbenzenes from packaging into food and Tenax (R). Pack. Technol. Sci. 14: 71–77.
   Web of Science ®Google Scholar
• Az, R., Dewald, B. and Schnaitmann, D. (1991). Pigment decomposition in polymers in applications at elevated temperatures. Dyes Pigments. 15: 1–14.
   Web of Science ®Google Scholar
• Azeredo, H. M. C. d. (2009). Nanocomposites for food packaging applications. Food Res. Int. 42: 1240–1253.
   Web of Science ®Google Scholar
• Aznar, M., Rodriguez-Lafuente, A., Alfaro, P. and Nerin, C. (2012). UPLC-Q-TOF-MS analysis of non-volatile migrants from new active packaging materials. Anal. Bioanal. Chem. 404: 1945–1957.
   PubMed Web of Science ®Google Scholar
• Bach, C., Dauchy, X., Chagnon, M.-C. and Etienne, S. (2012). Chemical compounds and toxicological assessments of drinking water stored in polyethylene terephthalate (PET) bottles: A source of controversy reviewed. Water Res. 46: 571–583.
   PubMed Web of Science ®Google Scholar
• Baner, A., Brandsch, J., Franz, R. and Piringer, O. (1996). The application of a predictive migration model for evaluating the compliance of plastic materials with European food regulations†. Food Addit. Contam. 13: 587–601.
   PubMed Web of Science ®Google Scholar
• Barnes, K. A., Sinclair, C. R. and Watson, D. H. (2007). Chemical Migration and Food Contact Materials. Woodhead, Abington, England..
   Google Scholar
• Barrat, J.-L., Baschnagel, J. and Lyulin, A. (2010). Molecular dynamics simulations of glassy polymers. Soft. Matter. 6: 3430–3446.
   Web of Science ®Google Scholar
• Bart, J. C. J. (2006). Polymer Additive Analytics. Industrial Practice and Case Studies. Firenze University Press, Firenze, Italy.
   Google Scholar
• Baschnagel, J., Wittmer, J. P. and Meyer, H. (2004). Monte Carlo simulation of polymers: Coarse-grained models. In: Computational Soft Matter: From Synthetic Polymers to Proteins, pp. 83–140. John von Neumann Institute for Computing, Jülich, Germany.
   Google Scholar
• Batra, T. (2011). Endocrine-disrupting carcinogenic plastic contamination in the food chain: a review. BioSci. BioTechnol. Res. Asia. 8: 597–601.
   Google Scholar
• Battelli, G., Limbo, S., Panseri, S., Chiesa, L., Pellegrino, L., Biondi, P. A. and Noni, I. d. (2011). Wrapping films for cheese packaging: qualitative aspects and migration phenomena. Sci. Tecnica Lattiero-Casearia. 62: 313–326.
   Google Scholar
• Bayer, F. L. (2002). Polyethylene terephthalate recycling for food-contact applications: testing, safety and technologies: a global perspective. Food Addit. Contam. A-Chem. Anal. Control Expo. Risk Assess. 19: 111–134.
   PubMed Web of Science ®Google Scholar
• Begley, T., Castle, L., Feigenbaum, A., Franz, R., Hinrichs, K., Lickly, T., Mercea, P., Milana, M., O'Brien, A., Rebre, S., Rijk, R. and Piringer, O. (2005). Evaluation of migration models that might be used in support of regulations for food-contact plastics. Food Addit. Contam. 22: 73–90.
   PubMed Web of Science ®Google Scholar
• Begley, T. H. and Hollifield, H. C. (1993). Recycled polymers in food packaging: migration considerations. Food Technol. 47: 109–112.
   Web of Science ®Google Scholar
• Berens, A. R. (1981). Vinyl chloride monomer in PVC: from problem to probe. Pure Appl. Chem. 53: 365–375.
   Web of Science ®Google Scholar
• Berg, H. C. (1993). Random Walks in Biology. Princeton University Press, Princeton, NJ, USA.
   Google Scholar
• Berlinet, C., Brat, P. and Ducruet, V. (2008). Quality of orange juice in barrier packaging material. Pack. Technol. Sci. 21: 279–286.
   Web of Science ®Google Scholar
• Biedermann, M., Ingenhoff, J. E., Dima, G., Zurfluh, M., Biedermann-Brem, S., Richter, L., Simat, T., Harling, A. and Grob, K. (2013). Migration of mineral oil from printed paperboard into dry foods: survey of the German market. Part II: advancement of migration during storage. Eur. Food Res. Technol. 236: 459–472.
   Web of Science ®Google Scholar
• Biedermann, M., Uematsu, Y. and Grob, K. (2011). Mineral oil contents in paper and board recycled to paperboard for food packaging. Pack. Technol. Sci. 24: 61–73.
   Web of Science ®Google Scholar
• Boersma, A. (2003). Mobility and solubility of antioxidants and oxygen in glassy polymers. I. Concentration and temperature dependence of antioxidant sorption. J. Appl. Polym. Sci. 89: 2163–2178.
   Web of Science ®Google Scholar
• Boersma, A., Cangialosi, D. and Picken, S. J. (2003a). Mobility and solubility of antioxidants and oxygen in glassy polymers II. Influence of physical ageing on antioxidant and oxygen mobility. Polym. Degrad. Stabil. 79: 427–438.
   Web of Science ®Google Scholar
• Boersma, A., Cangialosi, D. and Picken, S. J. (2003b). Mobility and solubility of antioxidants and oxygen in glassy polymers. III. Influence of deformation and orientation on oxygen permeability. Polymer. 44: 2463–2471.
   Web of Science ®Google Scholar
• Boulougouris, G. C. (2010). Calculation of the chemical potential beyond the first-order free-energy perturbation: from deletion to reinsertion†. J. Chem. Eng. Data. 55: 4140–4146.
   Web of Science ®Google Scholar
• Boulougouris, G. C. (2011). On the estimation of the free energy, from a single equilibrium statistical ensemble, via particle reinsertion. J. Phys. Chem. B. 116: 997–1006.
   Web of Science ®Google Scholar
• Brandrup, J., Immergut, E. H. and Grulke, E. A. (1999). Polymer Handbook. John Wiley & Sons, New York City.
   Google Scholar
• Brandsch, J., Mercea, P., Rüter, M., Tosa, V. and Piringer, O. (2002). Migration modelling as a tool for quality assurance of food packaging. Food Addit. Contam. 19: 29–41.
   PubMed Web of Science ®Google Scholar
• Breiman, L., Friedman, J. H., Olshen, R. A., Stone, C. J. (1984). Classification and Regression Trees. Wadsworth International Group, Monterey, CA, USA.
   Google Scholar
• Brimer, L. and Skaanild, M. T. (2011). Chemical Food Safety. CABI, Cambridge, UK.
   Google Scholar
• Brogioli, D. and Vailati, A. (2000). Diffusive mass transfer by nonequilibrium fluctuations: Fick's law revisited. Phys. Rev. E. 63:012105.
   Web of Science ®Google Scholar
• Brydson, J. A. (1999). Plastics Materials. Elsevier Science Butterworth-Heinemann, Oxford, UK.
   Google Scholar
• Bueche, F. (1968). Diffusion of polystyrene in polystyrene: effect of matrix molecular weight. J. Chem. Phys. 48: 1410–1411.
   Web of Science ®Google Scholar
• Buonocore, G. G., Del Nobile, M. A., Panizza, A., Corbo, M. R. and Nicolais, L. (2003). A general approach to describe the antimicrobial agent release from highly swellable films intended for food packaging applications. J. Control. Release. 90: 97–107.
   PubMed Web of Science ®Google Scholar
• Busolo, M. A. and Lagaron, J. M. (2012). Oxygen scavenging polyolefin nanocomposite films containing an iron modified kaolinite of interest in active food packaging applications. Innovative Food Sci. Emerg. Technol. 16: 211–217.
   Web of Science ®Google Scholar
• Callaghan, P. T. and Pinder, D. N. (1984). Influence of multiple length scales on the behavior of polymer self-diffusion in the semidilute regime. Macromolecules. 17: 431–437.
   Web of Science ®Google Scholar
• Callister, W. D. and Rethwisch, D. G. (2011). Chapter 4. Polymer structures. In: Fundamentals of Materials Science and Engineering: An Integrated Approach. pp. 102–1033.Wiley, New York.
   Google Scholar
• Camacho, W. and Karlsson, S. (2000). Quality-determination of recycled plastic packaging waste by identification of contaminants by CC-MS after microwave assisted extraction (MAE). Polym. Degrad. Stabil. 71: 123–134.
   Web of Science ®Google Scholar
• Caner, C., Hernandez, R. J., Pascall, M., Balasubramaniam, V. M. and Harte, B. R. (2004). The effect of high-pressure food processing on the sorption behaviour of selected packaging materials. Pack. Technol. Sci. 17: 139–153.
   Web of Science ®Google Scholar
• Cao, X.-L. and Corriveau, J. (2008). Migration of bisphenol A from polycarbonate baby and water bottles into water under severe conditions. J. Agr. Food Chem. 56: 6378–6381.
   PubMed Web of Science ®Google Scholar
• CFR (2011). Federal Food, Drug and Cosmetic Act. In: Title 21 - Food and Drugs, pp. 109–113. FDA Ed, US Government Printing Office, Washington D.C.
   Google Scholar
• CFR (2012a). Part 184—Direct food substances affirmed as generally recognized as safe. In: Title 21. Code of Federal Regulations. United States Government Printing Office, Washington, DC.
   Google Scholar
• CFR (2012b). Part 186—Indirect food substances affirmed as generally recognized as safe. In: Title 21. Code of Federal Regulations. United States Government Printing Office, Washington, DC.
   Google Scholar
• CFR (2012c). Section 170.39—Threshold of regulation for substances used in food-contact articles. In: Title 21. Code of Federal Regulations. United States Government Printing Office, Washington, DC.
   Google Scholar
• Chatwin, P. C. and Katan, L. L. (1989). The role of mathematics and physics in migration predictions. Pack. Technol. Sci. 2: 75–84.
   Google Scholar
• Chen, S. P. and Ferry, J. D. (1968). Erratum-the diffusion of radioactively tagged n-hexadecane and n-dodecane through rubbery polymers. effects of temperature, cross-linking, and chemical structure. Macromolecules. 1: 374–374.
   Google Scholar
• Chernikov, A. A., Petrovichev, B. A., Rogal'sky, A. V., Sagdeev, R. Z. and Zaslavsky, G. M. (1990). Anomalous transport of streamlines due to their chaos and their spatial topology. Phys. Lett. A. 144: 127–133.
   Web of Science ®Google Scholar
• Choudalakis, G. and Gotsis, A. D. (2009). Permeability of polymer/clay nanocomposites: A review. Eur. Polym. J. 45: 967–984.
   Web of Science ®Google Scholar
• Cohen, M. H. and Turnbull, D. (1959). Molecular transport in liquids and glasses. J. Chem. Phys. 31: 1164–1169.
   Web of Science ®Google Scholar
• Consolati, G. and Quasso, F. (2001). An experimental study of the occupied volume in polyethylene terephthalate. J. Chem. Phys. 114: 2825–2829.
   Web of Science ®Google Scholar
• Costa, F. R., Dutta, N. K., Choudhury, N. R. and Bhowmick, A. K. (2010). Chapter 5. Thermoplastic Elastomers. In: Current Topics in Elastomers Research. Bhowmick, A. K., Ed., Taylor & Francis, Boca Raton, FL, USA.
   Google Scholar
• Coughlin, C. S., Mauritz, K. A. and Storey, R. F. (1990). A general free volume based theory for the diffusion of large molecules in amorphous polymers above Tg. 3. Theoretical conformational analysis of molecular shape. Macromolecules. 23: 3187–3192.
   Web of Science ®Google Scholar
• Coughlin, C. S., Mauritz, K. A. and Storey, R. F. (1991a). A general free-volume-based theory for the diffusion of large molecules in amorphous polymers above glass temperature. 5. Application to dialkyl adipate plasticizers in poly(vinyl chloride). Macromolecules. 24: 2113–2116.
   Web of Science ®Google Scholar
• Coughlin, C. S., Mauritz, K. A. and Storey, R. F. (1991b). A general free volume based theory for the diffusion of large molecules in amorphous polymers above Tg. 4. Polymer-penetrant interactions. Macromolecules. 24: 1526–1534.
   Web of Science ®Google Scholar
• Courgneau, C., Domenek, S., Guinault, A., Avérous, L. and Ducruet, V. (2011). Analysis of the structure-properties relationships of different multiphase systems based on plasticized poly(lactic acid). J. Polym.s Environment. 19: 362–371.
   Web of Science ®Google Scholar
• Crank, J. (1979). The Mathematics of Diffusion. Clarendon Press, Oxford, UK.
   Google Scholar
• Crawshaw, J. and Windle, A. H. (2003). Multiscale modelling in polymer science. Fibre Diffraction Rev. 11: 52–67.
   Google Scholar
• Crockett, C. and Sumar, S. (1996). The safe use of recycled and reused plastics in food contact materials. II. Nutr. Food Sci.: 34–37.
   Google Scholar
• Crompton, T. R. (2007). Additive Migration from Plastics Into Foods: A Guide for Analytical Chemists. Smithers Rapra Technology, Showbury, UK.
   Google Scholar
• Cruz, J. M., Sanches Silva, A., Sendón García, R., Franz, R. and Paseiro Losada, P. (2008). Studies of mass transport of model chemicals from packaging into and within cheeses. J. Food Eng. 87: 107–115.
   Web of Science ®Google Scholar
• Cruz, S. A., Oliveira, E. C., de Oliveira, F. C. S., Garcia, P. S. and Kaneko, M. L. Q. A. (2011). Recycled polymers for food contact. Polimeros-Ciencia E Tecnologia. 21: 340–345.
   Web of Science ®Google Scholar
• Curtiss, C. F. and Bird, R. B. (1996). Multicomponent diffusion in polymeric liquids. Proc. National Acad. Sci. 93: 7440–7445.
   PubMed Web of Science ®Google Scholar
• Cussler, E. L. (2009). Diffusion: Mass Transfer in Fluid Systems. Cambridge University Press, Cambridge, UK.
   Google Scholar
• D'Hollander, W., de Voogt, P., De Coen, W. and Bervoets, L. (2010). Perfluorinated substances in human food and other sources of human exposure. Rev. Environ. Contam Toxicol. 208: 179–215.
   PubMed Web of Science ®Google Scholar
• De Angelis, M. G., Boulougouris, G. C. and Theodorou, D. N. (2010). Prediction of infinite dilution benzene solubility in linear polyethylene melts via the direct particle deletion method. J. Phys. Chem. B. 114: 6233–6246.
   PubMed Web of Science ®Google Scholar
• De Gennes, P. G. (1971). Reptation of a polymer chain in the presence of fixed obstacles. J. Chem. Phys. 55: 572–579.
   Web of Science ®Google Scholar
• Del Nobile, M. A., Mensitieri, G., Netti, P. A. and Nicolais, L. (1994). Anomalous diffusion in poly-ether-ether-ketone. Chem. Eng. Sci. 49: 633–644.
   Web of Science ®Google Scholar
• Delmaar, J. E., Park, M. V. D. Z. and van Engelen, J. G. M. (2005) ConsExpo 4.0-Consumer Exposure and Uptake Models -Program Manual RIVM report 320104004. National Institute of Public Health and the Environment (RIVM). Bilthoven, The Netherlands.
   Google Scholar
• Deppe, D. D., Miller, R. D. and Torkelson, J. M. (1996). Small molecule diffusion in a rubbery polymer near Tg: Effects of probe size, shape, and flexibility. J. Polym. Sci. Part B: Polym. Phys. 34: 2987–2997.
   Web of Science ®Google Scholar
• Derjaguin, B. (1934). Untersuchungen über die Reibung und Adhäsion, IV. Kolloid-Zeitschrift. 69: 155–164.
   Google Scholar
• Deshpande, S. S. (2002). Handbook of Food Toxicology. Marcel Dekker, Inc., New-York.
   Google Scholar
• Dobiáš, J., Voldřich, M., Marek, M. and Chudáčková, K. (2004). Changes of properties of polymer packaging films during high pressure treatment. J. Food Eng. 61: 545–549.
   Web of Science ®Google Scholar
• Doi, M. and Edwards, S. F. (1978). Dynamics of concentrated polymer systems. Part 1.-–Brownian motion in the equilibrium state. J. Chem. Soc. Faraday T. 2: Mol. Chem. Phys. 74: 1789–1801.
   Web of Science ®Google Scholar
• Dole, P., Feigenbaum, A. E., Cruz, C. D. L., Pastorelli, S., Paseiro, P., Hankemeier, T., Voulzatis, Y., Aucejo, S., Saillard, P. and Papaspyrides, C. (2006a). Typical diffusion behaviour in packaging polymers–application to functional barriers. Food Addit. Contam. 23: 202–211.
   PubMed Web of Science ®Google Scholar
• Dole, P., Voulzatis, Y., Vitrac, O., Reynier, A., Hankemeier, T., Aucejo, S. and Feigenbaum, A. (2006b). Modelling of migration from multi-layers and functional barriers: Estimation of parameters. Food Addit. Contam. 23: 1038–1052.
   PubMed Web of Science ®Google Scholar
• Doolittle, A. K. (1951). Studies in Newtonian flow. I. The dependence of the viscosity of liquids on temperature. J. Appl. Phys. 22: 1031–1035.
   Web of Science ®Google Scholar
• Doong, S. J. and Ho, W. S. W. (1992). Diffusion of hydrocarbons in polyethylene. Ind. Eng. Chem. Res. 31: 1050–1060.
   Web of Science ®Google Scholar
• Dopico-Garcia, M. S., Lopez-Vilarino, J. M. and Gonzalez-Rodriguez, M. V. (2003). Determination of antioxidant migration levels from low-density polyethylene films into food simulants. J. Chromatogr. A. 1018: 53–62.
   PubMed Web of Science ®Google Scholar
• du Yeon, B., Minji, K., Min Ji, K., Bu Young, J., Myung Chan, C., Seul Min, C., Young Woo, K., Seong Kwang, L., Duck Soo, L., Won, A. J., Seung Jun, K., Youngkwan, L., Hyung Sik, K. and Byung Mu, L. (2012). Human risk assessment of endocrine-disrupting chemicals derived from plastic food containers. Compr. Rev. Food Sci. Food Safe. 11: 453–470.
   Web of Science ®Google Scholar
• Dubreuil, A.-C., Doumenc, F., Guerrier, B. and Allain, C. (2003). Mutual diffusion in PMMA/PnBMA copolymer films: influence of the solvent-induced glass transition. Macromolecules. 36: 5157–5164.
   Web of Science ®Google Scholar
• Ducruet, V., Vitrac, O., Saillard, P., Guichard, E., Feigenbaum, A. and Fournier, N. (2007). Sorption of aroma compounds in PET and PVC during the storage of a strawberry syrup. Food Addit. Contam. A-Chem. Anal. Control Expo. Risk Assess. 24: 1306–1317.
   PubMed Web of Science ®Google Scholar
• Durand, M., Meyer, H., Benzerara, O., Baschnagel, J. and Vitrac, O. (2010). Molecular dynamics simulations of the chain dynamics in monodisperse oligomer melts and of the oligomer tracer diffusion in an entangled polymer matrix. J. Chem. Phys. 132: 194904.
   Web of Science ®Google Scholar
• Dutra, C., Pezo, D., Freire, M. T. d. A., Nerín, C. and Reyes, F. G. R. (2011). Determination of volatile organic compounds in recycled polyethylene terephthalate and high-density polyethylene by headspace solid phase microextraction gas chromatography mass spectrometry to evaluate the efficiency of recycling processes. J. Chrom. A. 1218: 1319–1330.
   PubMed Web of Science ®Google Scholar
• EC (2002a). Commission Directive 2002/72/EC of 6 August 2002 relating to plastic materials and articles intended to come into contact with foodstuffs. Off. J. Eur. Communities. L 220: 18–58.
   Google Scholar
• EC (2002b) Evaluation of migration models to be used under directive 90/128/EEC. Final report contract SMT4-CT98–7513. European Commission. Brussels.
   Google Scholar
• EC (2004). Regulation (EC) No 1935/2004 of the European parliament and of the council of 27 October 2004 on materials and articles intended to come into contact with food and repealing Directives 80/590/EEC and 89/109/EEC. Off. J. Eur. Union. L 338: 4–17.
   Google Scholar
• EC (2011). Commission Regulation (EU) No 10/2011 of 14 January 2011 on plastic materials and articles intended to come into contact with food. Off. J. Eur. Union. L 12: 1–89.
   Google Scholar
• EC (2012a). Commission Regulation (EU) No 1183/2012 of 30 November 2012 amending and correcting Regulation (EU) No 10/2011 on plastic materials and articles intended to come into contact with food. Off. J. Eur. Union. L 338: 11–15.
   Google Scholar
• EC (2012b). Corrigendum to Commission Regulation (EU) No 1183/2012 of 30 November 2012 amending and correcting Regulation (EU) No 10/2011 on plastic materials and articles intended to come into contact with food. Off. J. Eur. Union. L 349: 77.
   Google Scholar
• EC (2012c) Practical guidance document on the implementation of diffusion modelling for the estimation of specific migration in support of Regulation (EU) No 10/2011. Joint Research Centre of the European Commission. Ispra, Italy.
   Google Scholar
• EC (2013) Estimation of specific migration by generally recognised diffusion models in support of Regulation (EC) No 10/2011. Joint Research Centre of the European Commission. Ispra, Italy.
   Google Scholar
• Edwards, C. J. C., Rigby, D. and Stepto, R. F. T. (1981). Kirkwood-Riseman interpretation of the diffusion behavior of short polymer chains in dilute solution. Macromolecules. 14: 1808–1812.
   Web of Science ®Google Scholar
• Ehlich, D. and Sillescu, H. (1990). Tracer diffusion at the glass transition. Macromolecules. 23: 1600–1610.
   Web of Science ®Google Scholar
• Einstein, A. (1905a). On the movement of small particles suspended in a stationary liquid demanded by the molecular-kinetic theory of heat. Ann. Phys. (Leipzig). 17: 549–560.
   Web of Science ®Google Scholar
• Einstein, A. (1905b). Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann. Phys. 322: 549–560.
   Google Scholar
• Einstein, A. and Fürth, R. (1956). Investigations on the Theory of the Brownian Movement. Dover Publications, New York.
   Google Scholar
• Eu, B. C. (2006). Transport Coefficients of Fluids. Springer, London.
   Google Scholar
• Fang, X., Domenek, S., Ducruet, V., Réfrégiers, M. and Vitrac, O. (2013). Diffusion of aromatic solutes in aliphatic polymers above glass transition temperature. Macromolecules. 46: 874–888.
   Web of Science ®Google Scholar
• FDA (1999) Guidance for Industry-Preparation of Premarket Notifications for Food Contact Substances: Chemistry Recommendation. FDA. Washington, DC, USA.
   Google Scholar
• FDA (2006). Guidance for Industry: Use of Recycled Plastics in Food Packaging: Chemistry Considerations. Available from http://www.fda.gov/food/guidancecomplianceregulatoryinformation/GuidanceDocuments/FoodIngredientsandPackaging/ucm120762.htm. Date accessed: Feb. 1, 2013.
   Google Scholar
• FDA (2007). Guidance for Industry: Preparation of Premarket Submissions for Food Contact Substances: Chemistry Recommendations. Available from http://www.fda.gov/Food/GuidanceComplianceRegulatoryInformation/GuidanceDocuments/FoodIngredientsandPackaging/ucm081818.htm. Date accessed: Feb. 1, 2013.
   Google Scholar
• FDA (2012a). Food Ingredients and Packaging Guidance for Industry. Available from http://www.fda.gov/Food/GuidanceComplianceRegulatoryInformation/GuidanceDocuments/FoodIngredientsandPackaging/#food. Date accessed: Jan. 4, 2012.
   Google Scholar
• FDA (2012b). Inventory of Effective Food Contact Substance (FCS) Notifications. Available from http://www.accessdata.fda.gov/scripts/fcn/fcnNavigation.cfm?filter=&sortColumn=&rpt equals;fcsListing. Date accessed: Jan. 4, 2013.
   Google Scholar
• Fei, F., Chen, Q., Liu, Z., Liu, F. and Solodovnyk, A. (2012). The application of Nano-SiOx coatings as migration resistance layer by plasma enhanced chemical vapor deposition. Plasma Chem. Plasma Process. 32: 755–766.
   Web of Science ®Google Scholar
• Feigenbaum, A., Dole, P., Aucejo, S., Dainelli, D., Garcia, C. D. L. C., Hankemeier, T., N'Gono, Y., Papaspyrides, C. D., Paseiro, P., Pastorelli, S., Pavlidou, S., Pennarun, P. Y., Saillard, P., Vidal, L., Vitrac, O. and Voulzatis, Y. (2005). Functional barriers: properties and evaluation. Food Addit. Contam. 22: 956–967.
   PubMed Web of Science ®Google Scholar
• Feigenbaum, A., Scholler, D., Bouquant, J., Brigot, G., Ferrier, D., Franz, R., Lillemark, L., Riquet, A. M., Petersen, J. H., Lierop, B. V. and Yagoubi, N. (2002). Safety and quality of food contact materials. Part 1: Evaluation of analytical strategies to introduce migration testing into good manufacturing practice. Food Addit. Contam. 19: 184–201.
   PubMed Web of Science ®Google Scholar
• Feigenbaum, A. E., Ducruet, V. J., Delpal, S., Wolff, N., Gabel, J. P. and Wittmann, J. C. (1991). Food and packaging interactions: penetration of fatty food simulants into rigid poly(vinyl chloride). J. Agr. Food Chem. 39: 1927–1932.
   Web of Science ®Google Scholar
• Felix, J. S., Isella, F., Bosetti, O. and Nerin, C. (2012). Analytical tools for identification of non-intentionally added substances (NIAS) coming from polyurethane adhesives in multilayer packaging materials and their migration into food simulants. Anal. Bioanal. Chem. 403: 2869–2882.
   PubMed Web of Science ®Google Scholar
• Felix, J. S., Manzoli, J. E., Padula, M. and Monteiro, M. (2008). Plastic packaging with polyamide 6 used for meat foodstuffs and cheese: caprolactam migration and effect of irradiation. A review. Ali. Nutr. 19: 19 (13) 361–370.
   Google Scholar
• Ferry, J. D., Landel, R. F. and Williams, M. L. (1955). Extensions of the Rouse theory of viscoelastic properties to undiluted linear polymers. J. Appl. Phys. 26: 359–362.
   Web of Science ®Google Scholar
• Fierens, T., Servaes, K., Van Holderbeke, M., Geerts, L., De Henauw, S., Sioen, I. and Vanermen, G. (2012). Analysis of phthalates in food products and packaging materials sold on the Belgian market. Food Chem. Toxicol. 50: 2575–2583.
   PubMed Web of Science ®Google Scholar
• Fiselier, K. and Grob, K. (2012). Barriers against the migration of mineral oil from paperboard food packaging: experimental determination of breakthrough periods. Pack. Technol. Sci. 25: 285–301.
   Web of Science ®Google Scholar
• Fordham, P. J., Gramshaw, J. W., Crews, H. M. and Castle, L. (1995). Element residues in food contact plastics and their migration into food simulants, measured by inductively‐coupled plasma‐mass spectrometry. Food Addit. Contam. 12: 651–669.
   PubMed Web of Science ®Google Scholar
• Forrest, J. (2007). Coatings and Inks for Food Contact Materials. Rapra Technology, United Kingdom.
   Google Scholar
• Franz, R. and Simoneau, C. (2008) Final report: Modelling migration from plastics into foodstuffs as a novel and cost efficient tool for estimation of consumer exposure from food contact materials. EU Project QLK1-CT2002–2390. Institute for Health and Consumer Protection Luxembourg.
   Google Scholar
• Freire, M. T. D., Castle, L., Reyes, F. G. R. and Damant, A. P. (1998). Thermal stability of polyethylene terephthalate food contact materials: formation of volatiles from retail samples and implications for recycling. Food Addit. Contam. 15: 473–480.
   PubMedGoogle Scholar
• Frenkel, J. (1955). Kinetic Theory of Liquids. Dover Publications, New York.
   Google Scholar
• Geisel, T., Zacherl, A. and Radons, G. (1988). Chaotic diffusion and 1/f-noise of particles in two-dimensional solids. Z. Phys. B Con. Mat. 71: 117–127.
   Google Scholar
• Gillet, G., Vitrac, O. and Desobry, S. (2009a). Prediction of solute partition coefficients between polyolefins and alcohols using a generalized Flory–Huggins approach. Ind. Eng. Chem. Res. 48: 5285–5301.
   Web of Science ®Google Scholar
• Gillet, G., Vitrac, O. and Desobry, S. (2010). Prediction of partition coefficients of plastic additives between packaging materials and food simulants. Ind. Eng. Chem. Res. 49: 7263–7280.
   Web of Science ®Google Scholar
• Gillet, G., Vitrac, O., Tissier, D., Saillard, P. and Desobry, S. (2009b). Development of decision tools to assess migration from plastic materials in contact with food. Food Addit. Contam. A-Chem. Anal. Control Expo. Risk Assess. 26: 1556–1573.
   PubMed Web of Science ®Google Scholar
• Goetz, N. v., Wormuth, M., Scheringer, M. and Hungerbuehler, K. (2010). Bisphenol A: how the most relevant exposure sources contribute to total consumer exposure. Risk Anal. 30: 473–487.
   PubMed Web of Science ®Google Scholar
• Goujot, D. and Vitrac, O. (2013). Extension to nonlinear adsorption isotherms of exact analytical solutions to mass diffusion problems. Chem. Eng. Sci. 99: 2–22.
   Web of Science ®Google Scholar
• Goulas, A. E., Riganakos, K. A., Badeka, A. and Kontominas, M. G. (2002). Effect of ionizing radiation on the physicochemical and mechanical properties of commercial monolayer flexible plastics packaging materials. Food Addit. Contam. 19: 1190–1199.
   PubMed Web of Science ®Google Scholar
• Granda-Restrepo, D. M., Soto-Valdez, H., Peralta, E., Troncoso-Rojas, R., Vallejo-Cordoba, B., Gamez-Meza, N. and Graciano-Verdugo, A. Z. (2009). Migration of alpha-tocopherol from an active multilayer film into whole milk powder. Food Res. Int. 42: 1396–1402.
   Web of Science ®Google Scholar
• Gryn'ova, G., Ingold, K. U. and Coote, M. L. (2012). New insights into the mechanism of amine/nitroxide cycling during the hindered amine light stabilizer inhibited oxidative degradation of polymers. J. Am. Chem. Soc. 134: 12979–12988.
   PubMed Web of Science ®Google Scholar
• Guart, A., Bono-Blay, F., Borrell, A. and Lacorte, S. (2011). Migration of plasticizersphthalates, bisphenol A and alkylphenols from plastic containers and evaluation of risk. Food Addit. Contam. A-Chem. Anal. Control Expo. Risk Assess. 28: 676–685.
   PubMed Web of Science ®Google Scholar
• Guillard, V., Mauricio-Iglesias, M. and Gontard, N. (2010). Effect of novel food processing methods on packaging: structure, composition, and migration properties. Crit. Rev. Food Sci. Nutr. 50: 969–988.
   PubMed Web of Science ®Google Scholar
• Hakkarainen, M. (2008). Solid phase microextraction for analysis of polymer degradation products and additives. In: Chromatography for Sustainable Polymeric Materials: Renewable, Degradable and Recyclable, pp. 23–50. Albertsson, A. C. and Hakkarainen, M., Eds., Springer-Verlag Berlin.
   Google Scholar
• Halden, R. U. (2010). Plastics and health risks. Annual Review of Public Health, 31:179–194.
   Google Scholar
• Haldimann, M., Alt, A., Blanc, A., Brunner, K., Sager, F. and Dudler, V. (2013). Migration of antimony from PET trays into food simulant and food: determination of Arrhenius parameters and comparison of predicted and measured migration data. Food Addit. Contam. Part A Chem Anal Control Expo Risk Assess.30: 587–598.
   PubMed Web of Science ®Google Scholar
• Hall, D. B., Hamilton, K. E., Miller, R. D. and Torkelson, J. M. (1999). Translational and rotational diffusion of probe molecules in polymer films near Tg: effect of hydrogen bonding. Macromolecules. 32: 8052–8058.
   Web of Science ®Google Scholar
• Han, J. H. (2003). Chapter 4. Antimicrobial food packaging. In: Novel Food Packaging Techniques, pp. 50–70. Ahvenainen, R., Ed., Woodhead, Abington, UK.
   Google Scholar
• Hanggi, P. and Marchesoni, F. (2005). Introduction: 100 years of Brownian motion. Chaos: Int. J. Nonlinear Sci. 15: 026101.
   PubMed Web of Science ®Google Scholar
• Hansen, C. M. (2007). Hansen Solubility Parameters: A User's Handbook, 2nd ed. Taylor & Francis, Boca Raton, FL, USA.
   Google Scholar
• Harmandaris, V. A., Doxastakis, M., Mavrantzas, V. G. and Theodorou, D. N. (2002). Detailed molecular dynamics simulation of the self-diffusion of n-alkane and cis-1,4 polyisoprene oligomer melts. J. Chem. Phys. 116: 436–446.
   Web of Science ®Google Scholar
• Hatzigrigoriou, N. B., Papaspyrides, C. D., Joly, C. and Dole, P. (2010). Effect of migrant size on diffusion in dry and hydrated polyamide 6. J. Agr. Food Chem. 58: 8667–8673.
   PubMed Web of Science ®Google Scholar
• Haw, M. D. (2002). Colloidal suspensions, Brownian motion, molecular reality: a short history. J. Phys.: Con. Mat. 14: 7769.
   Web of Science ®Google Scholar
• Haward, R. N. (1970). Occupied volume of liquids and polymers. J. Macromol. Sci., C. 4: 191–242.
   Web of Science ®Google Scholar
• Heath, V. (2010). The perils of plastic. Nat. Rev. Endocrinol. 6: 237.
   PubMed Web of Science ®Google Scholar
• Hedenqvist, M., Angelstok, A., Edsberg, L., Larsson, P. T. and Gedde, U. W. (1996). Diffusion of small-molecule penetrants in polyethylene: free volume and morphology. Polym. 37: 2887–2902.
   Web of Science ®Google Scholar
• Hedenqvist, M. and Gedde, U. W. (1996). Diffusion of small-molecule penetrants in semicrystalline polymers. Prog. Polym. Sci. 21: 299–333.
   Web of Science ®Google Scholar
• Helmroth, E., Rijk, R., Dekker, M. and Jongen, W. (2002a). Predictive modelling of migration from packaging materials into food products for regulatory purposes. Trends Food Sci. Technol. 13: 102–109.
   Web of Science ®Google Scholar
• Helmroth, E., Varekamp, C. and Dekker, M. (2005). Stochastic modelling of migration from polyolefins. J. Sci. Food Agr. 85: 909–916.
   Web of Science ®Google Scholar
• Helmroth, I. E., Dekker, M. and Hankemeier, T. (2002b). Influence of solvent absorption on the migration of Irganox 1076 from LDPE. Food Addit. Contam. 19: 176–183.
   PubMed Web of Science ®Google Scholar
• Hess, B., Peter, C., Ozal, T. and van der Vegt, N. F. A. (2008). Fast-growth thermodynamic integration: calculating excess chemical potentials of additive molecules in polymer microstructures. Macromolecules. 41: 2283–2289.
   Web of Science ®Google Scholar
• Hess, B. and van der Vegt, N. F. A. (2008). Predictive modeling of phenol chemical potentials in molten bisphenol A—polycarbonate over a broad temperature range. Macromolecules. 41: 7281–7283.
   Web of Science ®Google Scholar
• Himmelsbach, M., Buchberger, W. and Reingruber, E. (2009). Determination of polymer additives by liquid chromatography coupled with mass spectrometry. A comparison of atmospheric pressure photoionization (APPI), atmospheric pressure chemical ionization (APCI), and electrospray ionization (ESI). Polym. Degrad. Stabil. 94: 1213–1219.
   Web of Science ®Google Scholar
• Hoekstra, E. J. and Simoneau, C. (2011). Release of bisphenol A from polycarbonate—a review. Crit. Rev. Food Sci. Nutr. 53: 386–402.
   Web of Science ®Google Scholar
• Hsu, Y.-D. and Chen, Y.-P. (1998). Correlation of the mutual diffusion coefficients of binary liquid mixtures. Fluid Phase Equilibria. 152: 149–168.
   Web of Science ®Google Scholar
• INRA (2010). EU/FP6 Migresives closing conference. Available from sfpp3.agroparistech.fr/SFPP3/SFPP3_migresives./ Date accessed: 3, March, 2013.
   Google Scholar
• INRA (2011). Safe food packaging portal: research server. Available from modmol.agroparistech.fr./ Date accessed: 18 Feb, 2013.
   Google Scholar
• Ito, T., Seta, J. and Urakawa, H. (1987). Effects of pressure and solvent on the diffusion of aromatic compounds through polymers. Colloid Polym. Sci. 265: 557–573.
   Web of Science ®Google Scholar
• IUPAC (2007). Compendium of Chemical Terminology, 2nd ed, Vol 79. Blackwell Scientific Publications, Oxford.
   Google Scholar
• Jain, R. K., Gupta, R. N. and Nanda, V. S. (1975). Crystallinity, relaxational transitions, and free volume in high-density polyethylene. J. Macromol. Sci. B. 11: 411–417.
   Web of Science ®Google Scholar
• Jamshidian, M., Tehrany, E. A. and Desobry, S. (2012). Release of synthetic phenolic antioxidants from extruded poly lactic acid (PLA) film. Food Control. 28: 445–455.
   Web of Science ®Google Scholar
• Janes, D. W. and Durning, C. J. (2013). Sorption and diffusion of n-alkyl acetates in poly(methyl acrylate)/silica nanocomposites. Macromolecules. 46: 856–866.
   Web of Science ®Google Scholar
• Jiang, C., Driffield, M., Bradley, E. L., Oldring, P. K. T., Cooke, P., Castle, L. and Guthrie, J. T. (2009). Studies of the aging effect on the level of isocyanate residues in polyester-based can coating systems. J. Coatings Technol. Res. 6: 437–444.
   Web of Science ®Google Scholar
• Johns, S. M., Jickells, S. M., Read, W. A. and Castle, L. (2000). Studies on functional barriers to migration. 3. Migration of benzophenone and model ink components from cartonboard to food during frozen storage and microwave heating. Pack. Technol. Sci. 13: 99–104.
   Web of Science ®Google Scholar
• Juliano, P., Koutchma, T., Sui, Q., Barbosa-Cánovas, G. and Sadler, G. (2010). Polymeric-based food packaging for high-pressure processing. Food Eng. Rev. 2: 274–297.
   Web of Science ®Google Scholar
• Jung, T., Simat, T. J. and Altkofer, W. (2010). Mass transfer ways of ultraviolet printing ink ingredients into foodstuffs. Food Addit. Contam. Part a-Chem. Analysis Control Exposure Risk Assessment. 27: 1040–1049.
   PubMed Web of Science ®Google Scholar
• Kappenstein, O., Vieth, B., Luch, A. and Pfaff, K. (2012). Toxicologically relevant phthalates in food. Exs. 101: 87–106.
   PubMedGoogle Scholar
• Karayiannis, N. C., Mavrantzas, V. G. and Theodorou, D. N. (2001). Diffusion of small molecules in disordered media: study of the effect of kinetic and spatial heterogeneities. Chem. Eng. Sci. 56: 2789–2801.
   Web of Science ®Google Scholar
• Kawamura, Y., Mutsuga, M., Yamauchi, T., Ueda, S. and Tanamoto, K. (2009). Migration tests of cadmium and lead from paint film of baby toys. Shokuhin Eiseigaku Zasshi. 50: 93–96.
   PubMedGoogle Scholar
• Keffer, D. J., Edwards, B. J. and Adhangale, P. (2004). Determination of statistically reliable transport diffusivities from molecular dynamics simulation. J. Non-Newtonian Fluid Mech. 120: 41–53.
   Web of Science ®Google Scholar
• Kirkwood, J. G. and Riseman, J. (1948). The intrinsic viscosities and diffusion constants of flexible macromolecules in solution. J. Chem. Phys. 16: 565–573.
   Web of Science ®Google Scholar
• Klopffer, M. H. and Flaconneche, B. (2001). Transport properties of gases in polymers: Bibliographic review. Oil Gas Sci. Technol.—Revue D Ifp Energies Nouv. 56: 223–244.
   Google Scholar
• Kontogeorgis, G. M. and Folas, G. K. (2009). Thermodynamic Models for Industrial Applications: From Classical and Advanced Mixing Rules to Association Theories. Wiley, Chichester, UK.
   Google Scholar
• Koszinowski, J. (1986). Diffusion and solubility of hydroxy compounds in polyolefines. J. Appl. Polym. Sci. 31: 2711–2720.
   Web of Science ®Google Scholar
• Kotelyanskii, M. and Theodorou, D. N. (2004). Simulation Methods for Polymers. Marcel Dekker, New York City.
   Google Scholar
• Kovarski, A. L. (1997). Molecular Dynamics of Additives in Polymers. VSP, Zeist, Netherlands.
   Google Scholar
• Krishna, R. and Wesselingh, J. A. (1997). The Maxwell-Stefan approach to mass transfer. Chem. Eng. Sci. 52: 861–911.
   Web of Science ®Google Scholar
• Kwan, K. S., Subramaniam, C. N. P. and Ward, T. C. (2003). Effect of penetrant size and shape on its transport through a thermoset adhesive: I. n-alkanes. Polym. 44: 3061–3069.
   Web of Science ®Google Scholar
• Lakes, R. (1993). Materials with structural hierarchy. Nature. 361: 511–515.
   Web of Science ®Google Scholar
• Lambert, Y., Demazeau, G., Largeteau, A., Bouvier, J. M., Laborde-Croubit, S. and Cabannes, M. (2000). Packaging for high-pressure treatments in the food industry. Pack. Technol. Sci. 13: 63–71.
   Web of Science ®Google Scholar
• Langevin, P. (1908). Sur la théorie du mouvement brownien. C. R. Acad. Sci. (Paris). 146: 530–533.
   Google Scholar
• Laoubi, S. and Vergnaud, J. M. (1996). Theoretical treatment of pollutant transfer in a finite volume of food from a polymer packaging made of a recycled film and a functional barrier. Food Addit. Contam. 13: 293–306.
   PubMedGoogle Scholar
• Lau, O.-W. and Wong, S.-K. (2000). Contamination in food from packaging material. J. Chrom. A. 882: 255–270.
   PubMed Web of Science ®Google Scholar
• Le-Bail, A., Hamadami, N. and Bahuaud, S. (2006). Effect of high-pressure processing on the mechanical and barrier properties of selected packagings. Pack. Technol. Sci. 19: 237–243.
   Web of Science ®Google Scholar
• Lemons, D. S. and Gythiel, A. (1997). Paul Langevin's 1908 paper “On the Theory of Brownian Motion” “Sur la théorie du mouvement brownien,” C. R. Acad. Sci. (Paris) [bold 146], 530–533 (1908)]. Am. J. Phys. 65: 1079–1081.
   Web of Science ®Google Scholar
• Lewis, H., Verghese, K. and Fitzpatrick, L. (2010). Evaluating the sustainability impacts of packaging: the plastic carry bag dilemma. Pack. Technol. Sci. 23: 145–160.
   Web of Science ®Google Scholar
• Li, T., Kildsig, D. O. and Park, K. (1997). Computer simulation of molecular diffusion in amorphous polymers. J. Control. Release. 48: 57–66.
   Web of Science ®Google Scholar
• Liang, Y., Hilal, N., Langston, P. and Starov, V. (2007). Interaction forces between colloidal particles in liquid: Theory and experiment. Adv. Colloid Interface Sci. 134–135: 151–166.
   PubMed Web of Science ®Google Scholar
• Lide, D. R. (2009). Handbook of Chemistry and Physics. CRC Press, Boca Raton, FL, USA.
   Google Scholar
• Limm, W. and Hollifield, H. C. (1996). Modelling of additive diffusion in polyolefins. Food Addit. Contam. 13: 949–967.
   PubMedGoogle Scholar
• Linssen, J. P. H., Rijnen, L., Legger-Huiysman, A. and Roozen, J. P. (1998). Combined GC and sniffing port analysis of volatile compounds in rubber rings mounted on beer bottles. Food Addit. Contam. 15: 79–83.
   PubMedGoogle Scholar
• Lipscomb, G. G. (1990). Unified thermodynamic analysis of sorption in rubbery and glassy materials. Aiche J. 36: 1505–1516.
   Web of Science ®Google Scholar
• Llorens, A., Lloret, E., Picouet, P. A., Trbojevich, R. and Fernandez, A. (2012). Metallic-based micro and nanocomposites in food contact materials and active food packaging. Trends Food Sci. Technol. 24: 19–29.
   Web of Science ®Google Scholar
• Lodge, T. P. (1999). Reconciliation of the molecular weight dependence of diffusion and viscosity in entangled polymers. Phys. Rev. Lett. 83: 3218–3221.
   Web of Science ®Google Scholar
• Lorenzini, R., Fiselier, K., Biedermann, M., Barbanera, M., Braschi, I. and Grob, K. (2010). Saturated and aromatic mineral oil hydrocarbons from paperboard food packaging: estimation of long-term migration from contents in the paperboard and data on boxes from the market. Food Addit. Contam. A-Chem. Anal. Control Expo. Risk Assess. 27: 1765–1774.
   PubMed Web of Science ®Google Scholar
• MAPP 5015.5, R. (2011). CMC Reviews of Type III DMFs for Packaging Materials. Office of Pharmaceutical Science Washington D.C., USA.
   Google Scholar
• Mark, J. E. (1999). Polymer Data Handbook. Oxford University Press, Oxford, UK.
   Google Scholar
• Mark, J. E. (2007). Physical Properties of Polymer Handbook. Springer, New York City.
   Google Scholar
• Marque, D., Feigenbaum, A., Dainelli, D. and Riquet, A. M. (1998). Safety evaluation of an ionized multilayer plastic film used for vacuum cooking and meat preservation. Food Addit. Contam. 15: 831–841.
   PubMedGoogle Scholar
• Marqué, D., Feigenbaum, A. and Riquet, A. (1996). Repercussions of the ionization of plastic packaging on the compatibility with packaged foodstuffs. J. Chimie Phys. Phys.-Chimie Biologique. 93: 165–168.
   Google Scholar
• Masaro, L. and Zhu, X. X. (1999). Physical models of diffusion for polymer solutions, gels and solids. Progress Polym. Sci. 24: 731–775.
   Web of Science ®Google Scholar
• Mattozzi, A., Serralunga, P., Hedenqvist, M. S. and Gedde, U. W. (2006). Mesoscale modelling of penetrant diffusion in computer-generated polyethylene–spherulite-like structures. Polym. 47: 5588–5595.
   Web of Science ®Google Scholar
• Mauritz, K. A. and Storey, R. F. (1990). A general free volume based theory for the diffusion of large molecules in amorphous polymers above Tg. 2. Molecular shape dependence. Macromolecules. 23: 2033–2038.
   Web of Science ®Google Scholar
• Mauritz, K. A., Storey, R. F. and George, S. E. (1990). A general free volume-based theory for the diffusion of large molecules in amorphous polymers above the glass temperature. I. Application to di-n-alkyl phthalates in PVC. Macromolecules. 23: 441–450.
   Web of Science ®Google Scholar
• McKeen, L. W. (2008). Effect of Temperature and other Factors on Plastics and Elastomers. Elsevier Science, Watham, MA, USA.
   Google Scholar
• Meerwall, E. v., Beckman, S., Jang, J. and Mattice, W. L. (1998). Diffusion of liquid n-alkanes: Free-volume and density effects. J. Chem. Phys. 108: 4299–4304.
   Web of Science ®Google Scholar
• Mehrer, H. (2010). Diffusion in Solids: Fundamentals, Methods, Materials, Diffusion-Controlled Processes. Springer, Heidelberg.
   Google Scholar
• Mensitieri, G., Apicella, A., Nobile, M. A. and Nicolais, L. (1991). Solvent mixtures sorption in amorphous peek. Polym. Bulletin. 27: 323–330.
   Web of Science ®Google Scholar
• Mercea, P. (2008). Chapter 5 Models for diffusion in polymers. In: Plastic Packaging: Interactions with Food and Pharmaceuticals. Piringer, O. and Baner, A., Eds., Wiley, Weinheim, Germany.
   Google Scholar
• Mercea, P. (2009). Physicochemical processes involved in migration of bisphenol A from polycarbonate. J. Appl. Polym. Sci. 112: 579–593.
   Web of Science ®Google Scholar
• Metois, P., Scholler, D., Bouquant, J. and Feigenbaum, A. (1998). Alternative test methods to control the compliance of polyolefin food packaging materials with the European Union regulation: the case of aromatic antioxidants and of bis(ethanolamine) antistatics based on H-1-NMR and UV-visible spectrophotometry. Food Addit. Contam. 15: 100–111.
   PubMedGoogle Scholar
• Miller-Chou, B. A. and Koenig, J. L. (2003). A review of polymer dissolution. Progress Polym. Sci. 28: 1223–1270.
   Web of Science ®Google Scholar
• Miltz, J., Ram, A. and Nir, M. M. (1997). Prospects for application of post-consumer used plastics in food packaging. Food Addit. Contam. 14: 649–659.
   PubMed Web of Science ®Google Scholar
• Möller, K. and Gevert, T. (1994). An FTIR solid-state analysis of the diffusion of hindered phenols in low-density polyethylene (LDPE): The effect of molecular size on the diffusion coefficient. J. Appl. Polym. Sci. 51: 895–903.
   Web of Science ®Google Scholar
• Morrissey, P. and Vesely, D. (2000). Accurate measurement of diffusion rates of small molecules through polymers. Polym. 41: 1865–1872.
   Web of Science ®Google Scholar
• Mu, M., Clarke, N., Composto, R. J. and Winey, K. I. (2009). Polymer diffusion exhibits a minimum with increasing single-walled carbon nanotube concentration. Macromolecules. 42: 7091–7097.
   Web of Science ®Google Scholar
• Mu, M., Seitz, M. E., Clarke, N., Composto, R. J. and Winey, K. I. (2010). Polymer tracer diffusion exhibits a minimum in nanocomposites containing spherical nanoparticles. Macromolecules. 44: 191–193.
   Web of Science ®Google Scholar
• Mueller, F., Krueger, K.-M. and Sadowski, G. (2012). Non-Fickian diffusion of toluene in polystyrene in the vicinity of the glass-transition temperature. Macromolecules. 45: 926–932.
   Web of Science ®Google Scholar
• Muller-Plathe, F. (1991). Diffusion of penetrants in amorphous polymers: A molecular dynamics study. J. Chem. Phys. 94: 3192–3199.
   Web of Science ®Google Scholar
• Muncke, J. (2009). Exposure to endocrine disrupting compounds via the food chain: Is packaging a relevant source? Sci. Total Environment. 407: 4549–4559.
   PubMed Web of Science ®Google Scholar
• Muncke, J. (2011). Endocrine disrupting chemicals and other substances of concern in food contact materials: An updated review of exposure, effect and risk assessment. J. Steroid BioChem. Mol. Biol. 127: 118–127.
   PubMed Web of Science ®Google Scholar
• Munro, C., Hlywka, J. J. and Kennepohl, E. M. (2002). Risk assessment of packaging materials. Food Addit Contam. 19 Suppl: 3–12.
   PubMedGoogle Scholar
• Narasimhan, B. (2001). Mathematical models describing polymer dissolution: consequences for drug delivery. Adv. Drug Deliver. Rev. 48: 195–210.
   PubMed Web of Science ®Google Scholar
• Narasimhan, B. and Peppas, N. A. (1996). On the importance of chain reptation in models of dissolution of glassy polymers. Macromolecules. 29: 3283–3291.
   Web of Science ®Google Scholar
• Nauman, E. B. and He, D. Q. (2001). Nonlinear diffusion and phase separation. Chem. Eng. Sci. 56: 1999–2018.
   Web of Science ®Google Scholar
• Neethirajan, S. and Jayas, D. (2011). Nanotechnology for the food and bioprocessing industries. Food Bioprocess Technol. 4: 39–47.
   PubMed Web of Science ®Google Scholar
• Neogi, P. (1996). Diffusion in Polymers. Marcel Dekker, New York City.
   Google Scholar
• Nerin, C., Albinana, J., Philo, M. R., Castle, L., Raffael, B. and Simoneau, C. (2003a). Evaluation of some screening methods for the analysis of contaminants in recycled polyethylene terephthalate flakes. Food Addit. Contam. 20: 668–677.
   PubMed Web of Science ®Google Scholar
• Nerin, C., Canellas, E., Aznar, M. and Silcock, P. (2009). Analytical methods for the screening of potential volatile migrants from acrylic-base adhesives used in food-contact materials. Food Addit. Contam. A-Chem. Anal. Control Expo. Risk Assess. 26: 1592–1601.
   PubMed Web of Science ®Google Scholar
• Nerin, C., Fernandez, C., Domeno, C. and Salafranca, J. (2003b). Determination of potential migrants in polycarbonate containers used for microwave ovens by high-performance liquid chromatography with ultraviolet and fluorescence detection. J. Agr. Food Chem. 51: 5647–5653.
   PubMed Web of Science ®Google Scholar
• Nguyen, P.-M., Goujon, A., Sauvegrain, P. and Vitrac, O. (2013). A computer-aided methodology to design safe food packaging and related systems. AICHE J. 59:1183–212.
   Web of Science ®Google Scholar
• Nichols, D. (2004). Biocides in Plastics. Rapra, Shawbury, UK.
   Google Scholar
• Nilsson, F., Gedde, U. W. and Hedenqvist, M. S. (2009). Penetrant diffusion in polyethylene spherulites assessed by a novel off-lattice Monte-Carlo technique. Eur. Polym. J. 45:3409–3417.
   Web of Science ®Google Scholar
• Noguerol-Cal, R., Lopez-Vilarino, J. M., Fernandez-Martinez, G., Gonzalez-Rodriguez, M. V. and Barral-Losada, L. F. (2010). Liquid chromatographic methods to analyze hindered amines light stabilizers (HALS) levels to improve safety in polyolefins. J. Sep. Sci. 33: 2698–2706.
   PubMed Web of Science ®Google Scholar
• Özal, T. A., Peter, C., Hess, B. and van der Vegt, N. F. A. (2008). Modeling solubilities of additives in polymer microstructures: single-step perturbation method based on a soft-cavity reference state. Macromolecules. 41: 5055–5061.
   Web of Science ®Google Scholar
• Page, B. D. and Lacroix, G. M. (1992). Studies into the transfer and migration of phthalate esters from aluminium foil-paper laminates to butter and margarine. Food Addit. Contam. 9: 197–212.
   PubMed Web of Science ®Google Scholar
• Pandey, S. K. and Kim, K.-H. (2011). An evaluation of volatile compounds released from containers commonly used in circulation of sports beverages. Ecotoxicol. Environ. Safe. 74: 527–532.
   PubMed Web of Science ®Google Scholar
• Paquette Kristina, E. (2004). Irradiation of prepackaged food: Evolution of the U.S. food and drug administration's regulation of the packaging materials. In: Irradiation of Food and Packaging, pp. 182–202. American Chemical Society, Washington, DC, USA.
   Google Scholar
• Pastor, R. W. and Karplus, M. (1988). Parametrization of the friction constant for stochastic simulations of polymers. J. Phys. Chem. 92: 2636–2641.
   Web of Science ®Google Scholar
• Pastorelli, S., Sanches-Silva, A., Manuel Cruz, J., Simoneau, C. and Paseiro Losada, P. (2008). Study of the migration of benzophenone from printed paperboard packages to cakes through different plastic films. Eur. Food Res. Technol. 227: 1585–1590.
   Web of Science ®Google Scholar
• Patrick, S. G. R. T. (2005). Practical Guide to Polyvinyl Chloride. Rapra Technology, Shawbury, UK.
   Google Scholar
• Paul, W. and Smith, G. D. (2004). Structure and dynamics of amorphous polymers: computer simulations compared to experiment and theory. Rep. Prog. Phys. 67: 1117.
   Web of Science ®Google Scholar
• Peltzer, M., Wagner, J. and Jimenez, A. (2009). Migration study of carvacrol as a natural antioxidant in high-density polyethylene for active packaging. Food Addit. Contam. Part A-Chem. Anal. Control Expo. Risk Assess. 26: 938–946.
   PubMed Web of Science ®Google Scholar
• Pennarun, P. Y., Dole, P. and Feigenbaum, A. (2004a). Functional barriers in PET recycled bottles. Part I. Determination of diffusion coefficients in bioriented PET with and without contact with food simulants. J. Appl. Polym. Sci. 92: 2845–2858.
   Web of Science ®Google Scholar
• Pennarun, P. Y., Ngono, Y., Dole, P. and Feigenbaum, A. (2004b). Functional barriers in PET recycled bottles. Part II. Diffusion of pollutants during processing. J. Appl. Polym. Sci. 92: 2859–2870.
   Web of Science ®Google Scholar
• Perez-Palacios, D., Angel Fernandez-Recio, M., Moreta, C. and Teresa Tena, M. (2012). Determination of bisphenol-type endocrine disrupting compounds in food-contact recycled-paper materials by focused ultrasonic solid-liquid extraction and ultra performance liquid chromatography-high resolution mass spectrometry. Talanta. 99: 167–174.
   PubMed Web of Science ®Google Scholar
• Petersen, J. H. and Jensen, L. K. (2010). Phthalates and food-contact materials: enforcing the 2008 European Union plastics legislation. Food Addit. Contam. Part A Chem. Anal. Control Expo. Risk Assess. 27: 1608–1616.
   PubMed Web of Science ®Google Scholar
• Pezo, D., Fedeli, M., Bosetti, O. and Nerin, C. (2012). Aromatic amines from polyurethane adhesives in food packaging: The challenge of identification and pattern recognition using Quadrupole-Time of Flight-Mass Spectrometry(E). Anal. Chim. Acta. 756: 49–59.
   PubMed Web of Science ®Google Scholar
• Piergiovanni, L., Fava, P. and Schiraldi, A. (1999). Study of diffusion through LDPE film of Di-n-butyl phthalate. Food Addit. Contam. 16: 353–359.
   PubMedGoogle Scholar
• Pinte, J., Joly, C., Dole, P. and Feigenbaum, A. (2010). Diffusion of homologous model migrants in rubbery polystyrene: molar mass dependence and activation energy of diffusion. Food Addit. Contam.: Part A. 27: 557–566.
   Web of Science ®Google Scholar
• Pinte, J. r. m., Joly, C., Plé, K., Dole, P. and Feigenbaum, A. (2008). Proposal of a set of model polymer additives designed for confocal FRAP diffusion experiments. J. Agr. Food Chem. 56: 10003–10011.
   PubMed Web of Science ®Google Scholar
• Piringer, O. G. and Baner, A. L. (2000). Plastic Packaging Materials for Food: Barrier Function, Mass Transport, Quality Assurance, and Legislation. Wiley-VCH, Weinheim, Germany.
   Google Scholar
• Piringer, O. G. and Baner, A. L. (2008). Plastic Packaging: Interactions with Food and Pharmaceuticals. Wiley.
   Google Scholar
• Plazek, D. J., Schlosser, E., Schonhals, A. and Ngai, K. L. (1993). Breakdown of the Rouse model for polymers near the glass transition temperature. J. Chem. Phys. 98: 6488–6491.
   Web of Science ®Google Scholar
• Poças, M. d. F. and Hogg, T. (2007). Exposure assessment of chemicals from packaging materials in foods: a review. Trends Food Sci. Technol. 18: 219–230.
   Web of Science ®Google Scholar
• Poças, M. d. F., Oliveira, J. C., Pereira, J. R., Brandsch, R. and Hogg, T. (2011). Modelling migration from paper into a food simulant. Food Control. 22: 303–312.
   Web of Science ®Google Scholar
• Poças, M. F., Oliveira, J. C., Brandsch, R. and Hogg, T. (2010). Feasibility study on the use of probabilistic migration modeling in support of exposure assessment from food contact materials. Risk Anal. 30: 1052–1061.
   PubMed Web of Science ®Google Scholar
• Poças, M. F., Oliveira, J. C., Oliveira, F. A. R. and Hogg, T. (2008). A critical survey of predictive mathematical models for migration from packaging. Crit. Rev. Food Sci. Nutr. 48: 913–928.
   PubMed Web of Science ®Google Scholar
• Poole, A., van Herwijnen, P., Weideli, H., Thomas, M. C., Ransbotyn, G. and Vance, C. (2004). Review of the toxicology, human exposure and safety assessment for bisphenol A diglycidylether (BADGE). Food Addit. Contam. 21: 905–919.
   PubMed Web of Science ®Google Scholar
• Prince E., Rouse, J. (1953). A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J. Chem. Phys. 21: 1272–1280.
   Web of Science ®Google Scholar
• Psillos, S. (2011). Moving molecules above the scientific horizon: on Perrin's case for realism. J. Gen. Philos. Sci. 42: 339–363.
   Web of Science ®Google Scholar
• Queyroy, S. and Monasse, B. (2012). Effect of the molecular structure of semicrystalline polyethylene on mechanical properties studied by molecular dynamics. J. Appl. Polym. Sci. 125: 4358–4367.
   Web of Science ®Google Scholar
• Rahman, S. (2007). Handbook of Food Preservation, 2nd ed. Taylor & Francis, Boca Raton, FL, USA.
   Google Scholar
• Ranjit, N., Siefert, K. and Padmanabhan, V. (2010). Bisphenol-A and disparities in birth outcomes: a review and directions for future research. J. Perinatol. 30: 2–9.
   PubMed Web of Science ®Google Scholar
• Reid, R. C., Sidman, K. R., Schwope, A. D. and Till, D. E. (1980). Loss of adjuvants from polymer films to foods simulants. Effect of the external phase. Ind. Eng. Chem. Product Res. Dev. 19: 580–587.
   Web of Science ®Google Scholar
• Reynier, A., Dole, P. and Feigenbaum, A. (2001a). Additive diffusion coefficients in polyolefins. II. Effect of swelling and temperature on the D = f(M) correlation. J. Appl. Polym. Sci. 82: 2434–2443.
   Web of Science ®Google Scholar
• Reynier, A., Dole, P., Humbel, S. and Feigenbaum, A. (2001b). Diffusion coefficients of additives in polymers. I. Correlation with geometric parameters. J. Appl. Polym. Sci. 82: 2422–2433.
   Web of Science ®Google Scholar
• Rhee, C.-K., Ferry, J. D. and Fetters, L. J. (1977). Diffusion of radioactively tagged penetrants through rubbery polymers. II. Dependence on molecular length of penetrant. J. Appl. Polym. Sci. 21: 783–790.
   Web of Science ®Google Scholar
• Riquet, A. M., Wolff, N., Laoubi, S., Vergnaud, J. M. and Feigenbaum, A. (1998). Food and packaging interactions: Determination of the kinetic parameters of olive oil diffusion in polypropylene using concentration profiles. Food Addit. Contam. 15: 690–700.
   PubMed Web of Science ®Google Scholar
• Roduit, B., Borgeat, C. H., Cavin, S., Fragniere, C. and Dudler, V. (2005). Application of Finite Element Analysis (FEA) for the simulation of release of additives from multilayer polymeric packaging structures. Food Addit. Contam. 22: 945–955.
   PubMed Web of Science ®Google Scholar
• Romao, W., Spinace, M. A. S. and De Paoli, M. A. (2009). Poly(ethylene terephthalate), PET. A review on the synthesis processes, degradation mechanisms and its recycling. Polimeros-Ciencia E Tecnologia. 19: 121–132.
   Web of Science ®Google Scholar
• Romdhane, I. H., Danner, R. P. and Duda, J. L. (1995). Influence of the glass transition on solute diffusion in polymers by inverse gas chromatography. Ind. Eng. Chem. Res. 34: 2833–2840.
   Web of Science ®Google Scholar
• Saby-Dubreuil, A. C., Guerrier, B., Allain, C. and Johannsmann, D. (2001). Glass transition induced by solvent desorption for statistical MMA/nBMA copolymers—Influence of copolymer composition. Polym. 42: 1383–1391.
   Web of Science ®Google Scholar
• Sadler, G., Chappas, W. and Pierce, D. E. (2001). Evaluation of e-beam, gamma- and X-ray treatment on the chemistry and safety of polymers used with pre-packaged irradiated foods: a review. Food Addit. Contam. 18: 475–501.
   PubMed Web of Science ®Google Scholar
• Sadler, G., Pierce, D., Lawson, A., Suvannunt, D. and Senthil, V. (1996). Evaluating organic compound migration in poly(ethylene terephthalate): A simple test with implications for polymer recycling. Food Addit. Contam. 13: 979–989.
   PubMedGoogle Scholar
• Sagiv, A. (2001). Exact solution of mass diffusion into a finite volume. J. Membr. Sci. 186: 231–237.
   Web of Science ®Google Scholar
• Sagiv, A. (2002). Theoretical formulation of the diffusion through a slab-theory validation. J. Membr. Sci. 199: 125–134.
   Web of Science ®Google Scholar
• Sanches-Silva, A., Andre, C., Castanheira, I., Manuel Cruz, J., Pastorelli, S., Simoneau, C. and Paseiro-Losada, P. (2009). Study of the migration of photoinitiators used in printed food-packaging materials into food simulants. J. Agr. Food Chem. 57: 9516–9523.
   PubMed Web of Science ®Google Scholar
• Sanches Silva, A., Cruz Freire, J. M. and Paseiro Losada, P. (2010). Study of the diffusion coefficients of diphenylbutadiene and triclosan into and within meat. Eur. Food Res. Technol. 230: 957–964.
   Web of Science ®Google Scholar
• Sanches Silva, A., Cruz, J. M., Sendón Garcı´a, R., Franz, R. and Paseiro Losada, P. (2007). Kinetic migration studies from packaging films into meat products. Meat Sci. 77: 238–245.
   PubMed Web of Science ®Google Scholar
• Schmidt-Rohr, K. and Spiess, H. W. (1991). Chain diffusion between crystalline and amorphous regions in polyethylene detected by 2D exchange carbon-13 NMR. Macromolecules. 24: 5288–5293.
   Web of Science ®Google Scholar
• Seta, J., Ogino, T. and Ito, T. (1984). Activation volume for the diffusion of disperse dye in nylon 6. Sen'i Gakkaishi. 40: T263–T268.
   Google Scholar
• Shanklin, A. P. and Sánchez, E. R. (2005). Regulatory report: FDA's food contact substance notification program. October/November 2005, reprinted from Food Safety Magazine. Available at http://www.fda.gov/Food/IngredientsPackagingLabeling/PackagingFCS/ucm064161.htm
   Google Scholar
• Sharpe, R. M. (2010). Is it time to end concerns over the estrogenic effects of bisphenol A? Toxicol. Sci. 114: 1–4.
   PubMed Web of Science ®Google Scholar
• Silva, A. S., García, R. S., Cooper, I., Franz, R. and Losada, P. P. (2006). Compilation of analytical methods and guidelines for the determination of selected model migrants from plastic packaging. Trend. Food Sci. Technol. 17: 535–546.
   Web of Science ®Google Scholar
• Simal-Gandara, J., Damant, A. P. and Castle, L. (2002). The use of LC-MS in studies of migration from food contact materials: A review of present applications and future possibilities. Crit. Rev. Anal. Chem. 32: 47–78.
   Web of Science ®Google Scholar
• Simal-Gandara, J., Sarria-Vidal, M., Koorevaar, A. and Rijk, R. (2000). Tests of potential functional barriers for laminated multilayer food packages. Part I: Low molecular weight permeants. Food Addit. Contam. 17: 703–711.
   PubMed Web of Science ®Google Scholar
• Simha, R. and Boyer, R. F. (1962). On a general relation involving the glass temperature and coefficients of expansion of polymers. J. Chem. Phys. 37: 1003–1007.
   Web of Science ®Google Scholar
• Siva, N. (2012). Controversy continues over safety of bisphenol A. Lancet. 379: 1186.
   PubMed Web of Science ®Google Scholar
• Smirnova, V. V., Krasnoiarova, O. V., Pridvorova, S. M., Zherdev, A. V., Gmoshinskii, I. V., Kazydub, G. V., Popov, K. I. and Khotimchenko, S. A. (2012). Characterization of silver nanoparticles migration from package materials destined for contact with foods. Voprosy pitaniia. 81: 34–39.
   PubMedGoogle Scholar
• Solovyov, S. and Goldman, A. (2007). Mass Transport and Reactive Barriers in Packaging: Theory, Applications And Design. DEStech Pub, Lancaster, PA, USA.
   Google Scholar
• Spearot, D. E., Sudibjo, A., Ullal, V. and Huang, A. (2012). Molecular dynamics simulations of diffusion of O2 and N2 penetrants in polydimethylsiloxane-based nanocomposites. J. Eng. Mater. Technol. 134: 021013.
   Web of Science ®Google Scholar
• Stachel, J. (2005). Einstein's Miraculous Year: Five Papers That Changed The Face Of Physics. Princeton University Press, Princeton, NJ, USA.
   Google Scholar
• Stastna, J. and De Kee, D. (1995). Transport Properties in Polymers. Technomic Publishing Company, Boca Raton, FL, USA.
   Google Scholar
• Störmer, A. (2010) Final activity report: Research programme on migration from adhesives in food packaging materials in support of European Legislation and Standardisation. COLL-CT-2006–030309. MIGRESIVES. Available at http://www.migresives.eu/internal_documents/Project_reports/Final_activity_Migresives_rev2.pdf. Accessed 29 June 2016.
   Google Scholar
• Sunderrajan, S., Hall, C. K. and Freeman, B. D. (1996). Estimation of mutual diffusion coefficients in polymer/penetrant systems using nonequilibrium molecular dynamics simulations. J. Chem. Phys. 105: 1621–1632.
   Web of Science ®Google Scholar
• Tacker, M. (2011). Endocrine disrupting components and packaging. Ernahrung. 35: 308–313.
   Google Scholar
• Tehrany, E. A. and Desobry, S. (2004). Partition coefficients in food/packaging systems: a review. Food Addit. Contam. A-Chem. Anal. Control Expo. Risk Assess. 21: 1186–1202.
   PubMed Web of Science ®Google Scholar
• Teraoka, I. (2002). Polymer Solutions: An Introduction to Physical Properties. Wiley, New York City.
   Google Scholar
• Till, D., Schwope, A. D., Ehntholt, D. J., Sidman, K. R., Whelan, R. H., Schwartz, P. S. and Reid, R. C. (1987). Indirect food additive migration from polymeric food packaging materials. Crit. Rev. Toxicol. 18: 215–243.
   PubMed Web of Science ®Google Scholar
• Tonge, M. P. and Gilbert, R. G. (2001a). Testing free volume theory for penetrant diffusion in rubbery polymers. Polymer. 42: 1393–1405.
   Web of Science ®Google Scholar
• Tonge, M. P. and Gilbert, R. G. (2001b). Testing models for penetrant diffusion in glassy polymers. Polymer. 42: 501–513.
   Web of Science ®Google Scholar
• Tosa, V., Kovacs, K., Mercea, P. and Piringer, O. (2008). A finite difference method for modeling migration of impurities in multilayer Systems. Numer. Anal. Appl. Math. 1048: 802–805.
   Google Scholar
• Triantafyllou, V. I., Karamani, A. G., Akrida-Demertzi, K. and Demertzis, P. G. (2002). Studies on the usability of recycled PET for food packaging applications. Eur. Food Res. Technol. 215: 243–248.
   Web of Science ®Google Scholar
• Trier, X., Granby, K. and Christensen, J. H. (2011). Polyfluorinated surfactants (PFS) in paper and board coatings for food packaging. Env. Sci. Pollut. Res. 18: 1108–1120.
   PubMed Web of Science ®Google Scholar
• Trier, X., Okholm, B., Foverskov, A., Binderup, M. L. and Petersen, J. H. (2010). Primary aromatic amines (PAAs) in black nylon and other food-contact materials, 2004–2009. Food Addit. Contam. A-Chem. Anal. Control Expo. Risk Assess. 27: 1325–1335.
   PubMed Web of Science ®Google Scholar
• Van Alsten, J. G., Lustig, S. R. and Hsiao, B. (1995). Polymer diffusion in semicrystalline polymers. 2. atactic polystyrene-d transport into atactic and isotactic polystyrene. Macromolecules. 28: 3672–3680.
   Web of Science ®Google Scholar
• van Krevelen, D. W. and te Nijenhuis, K. (2009). Properties of Polymers: Their Correlation with Chemical Structure; their Numerical Estimation and Prediction from Additive Group Contributions. Elsevier Science, Amsterdam.
   Google Scholar
• van Leeuwen, C. J. and Vermeire, T. G. (2007). Risk Assessment of Chemicals: An Introduction. Springer, Dordrecht, The Netherlands.
   Google Scholar
• Vandenberg, L. N., Maffini, M. V., Sonnenschein, C., Rubin, B. S. and Soto, A. M. (2009). Bisphenol-A and the great divide: a review of controversies in the field of endocrine disruption. Endocrine Rev. 30: 75–95.
   PubMed Web of Science ®Google Scholar
• Veniaminov, A. V. and Sillescu, H. (1999). Polymer and dye probe diffusion in poly(methyl methacrylate) below the glass transition studied by forced rayleigh scattering. Macromolecules. 32: 1828–1837.
   Web of Science ®Google Scholar
• Vera, P., Aznar, M., Mercea, P. and Nerin, C. (2011). Study of hotmelt adhesives used in food packaging multilayer laminates. Evaluation of the main factors affecting migration to food. J. Mater. Chem. 21: 420–431.
   Web of Science ®Google Scholar
• Vergnaud, J. M. (1998). Problems encountered for food safety with polymer packages: chemical exchange, recycling. Adv. Colloid Interface Sci. 78: 267–297.
   PubMed Web of Science ®Google Scholar
• Vergnaud, J. M. and Rosca, I. D. (2006). Assessing Food Safety of Polymer Packaging. Rapra Technology Shawbury, UK.
   Google Scholar
• Vettorel, T., Meyer, H., Baschnagel, J. and Fuchs, M. (2007). Structural properties of crystallizable polymer melts: Intrachain and interchain correlation functions. Phys. Rev. E. 75.
   Web of Science ®Google Scholar
• Vieth, W. R. (1991). Diffusion in and Through Polymers: Principles and Applications. Carl Hanser GmbH, Shawbury, UK.
   Google Scholar
• Vignes, A. (1966). Diffusion in binary solutions. variation of diffusion coefficient with composition. Ind. Eng. Chem. Fund. 5: 189–199.
   Web of Science ®Google Scholar
• Vitrac, O. (2012). FMECAENGINE: a seamless tool to chain migration simulations and perform related sensitivity analysis. Available from https://github.com/ovitrac/FMECAengine. Accessed 30 June 2016
   Google Scholar
• Vitrac, O. and Gillet, G. (2010). An off-lattice Flory–Huggins approach of the partitioning of bulky solutes between polymers and interacting liquids. Int. J. Chem. Reactor Eng. 8:1–32.
   Web of Science ®Google Scholar
• Vitrac, O. and Hayert, M. (2005). Risk assessment of migration from packaging materials into foodstuffs. Aiche J. 51: 1080–1095.
   Web of Science ®Google Scholar
• Vitrac, O. and Hayert, M. (2006). Identification of diffusion transport properties from desorption/sorption kinetics: An analysis based on a new approximation of fick equation during solid-liquid contact. Ind. Eng. Chem. Res. 45: 7941–7956.
   Web of Science ®Google Scholar
• Vitrac, O. and Hayert, M. (2007a). Design of safe food packaging under uncertainty. In: New Trends in Chemical Engineering Research, pp. 251–292. Berton, P., Ed., Nova Science Publishers, New York.
   Google Scholar
• Vitrac, O. and Hayert, M. (2007b). Effect of the distribution of sorption sites on transport diffusivities: A contribution to the transport of medium-weight-molecules in polymeric materials. Chem. Eng. Sci. 62: 2503–2521.
   Web of Science ®Google Scholar
• Vitrac, O. and Leblanc, J.-C. (2007). Consumer exposure to substances in plastic packaging. I. Assessment of the contribution of styrene from yogurt pots. Food Addit. Contam. 24:194–215.
   Google Scholar
• Vitrac, O., Lezervant, J. and Feigenbaum, A. (2006). Decision trees as applied to the robust estimation of diffusion coefficients in polyolefins. J. Appl. Polym. Sci. 101: 2167–2186.
   Web of Science ®Google Scholar
• Vitrac, O., Mougharbel, A. and Feigenbaum, A. (2007). Interfacial mass transport properties which control the migration of packaging constituents into foodstuffs. J. Food Eng. 79: 1048–1064.
   Web of Science ®Google Scholar
• Vollmer, A., Biedermann, M., Grundboeck, F., Ingenhoff, J.-E., Biedermann-Brem, S., Altkofer, W. and Grob, K. (2011). Migration of mineral oil from printed paperboard into dry foods: survey of the German market. Eur. Food Res. Technol. 232: 175–182.
   Web of Science ®Google Scholar
• von Goetz, N., Fabricius, L., Glaus, R., Weitbrecht, V., Gunther, D. and Hungerbuhler, K. (2013). Migration of silver from commercial plastic food containers and implications for consumer exposure assessment. Food Addit. Contam. Part A Chem. Anal. Control Expo. Risk Assess. 30: 612–620.
   PubMed Web of Science ®Google Scholar
• Von Meerwall, E. and Ferguson, R. D. (1979). Diffusion of hydrocarbons in rubber, measured by the pulsed gradient NMR method. J. Appl. Polym. Sci. 23: 3657–3669.
   Web of Science ®Google Scholar
• von Meerwall, E. D., Lin, H. and Mattice, W. L. (2007). Trace diffusion of alkanes in polyethylene:  spin-echo experiment and Monte Carlo simulation. Macromolecules. 40: 2002–2007.
   Web of Science ®Google Scholar
• Vrentas, J. S. and Duda, J. L. (1977). Diffusion in polymer—solvent systems. I. Reexamination of the free-volume theory. J. Polym. Sci.: Polym. Phys. Edition. 15: 403–416.
   Web of Science ®Google Scholar
• Vrentas, J. S., Duda, J. L. and Huang, W. J. (1986). Regions of Fickian diffusion in polymer-solvent systems. Macromolecules. 19: 1718–1724.
   Web of Science ®Google Scholar
• Vrentas, J. S., Duda, J. L. and Ling, H. C. (1985a). Free-volume theories for self-diffusion in polymer–solvent systems. I. Conceptual differences in theories. J. Polym. Sci.: Polym. Phys. Edition. 23: 275–288.
   Web of Science ®Google Scholar
• Vrentas, J. S., Duda, J. L., Ling, H. C. and Hou, A. C. (1985b). Free-volume theories for self-diffusion in polymer–solvent systems. II. Predictive capabilities. J. Polym. Sci.: Polym. Phys. Edition. 23: 289–304.
   Web of Science ®Google Scholar
• Vrentas, J. S. and Vrentas, C. M. (1994). Solvent self-diffusion in rubbery polymer-solvent systems. Macromolecules. 27: 4684–4690.
   Web of Science ®Google Scholar
• Vrentas, J. S. and Vrentas, C. M. (1995). Determination of free-volume parameters for solvent self-diffusion in polymer-solvent systems. Macromolecules. 28: 4740–4741.
   Web of Science ®Google Scholar
• Vrentas, J. S. and Vrentas, C. M. (1998). Predictive methods for self-diffusion and mutual diffusion coefficients in polymer–solvent systems. Eur. Polym. J. 34: 797–803.
   Web of Science ®Google Scholar
• Vrentas, J. S., Vrentas, C. M. and Faridi, N. (1996). Effect of solvent size on solvent self-diffusion in polymer−solvent systems. Macromolecules. 29: 3272–3276.
   Web of Science ®Google Scholar
• Wagner, M. and Oehlmann, J. (2009), Endocrine disruptors in bottles mineral water: total estrogenic burden and migration from plastic bottles. Environ. Sci. Pollut. Res., 16: 278–286.
   PubMed Web of Science ®Google Scholar
• Walsh, B. (2010). How dangerous is plastic?. Time Magazine, 2010, 30–36.
   Google Scholar
• Welle, F. and Franz, R. (2010). Migration of antimony from PET bottles into beverages: determination of the activation energy of diffusion and migration modelling compared with literature data. Food Addit. Contam.: Part A. 28: 115–126.
   Google Scholar
• Wesselingh, J. A. and Krishna, R. (2006). Mass Transfer in Multicomponet Mixtures. VSSD Delft, The Netherlands.
   Google Scholar
• Widen, H. (1998). Recycled plastics for food packaging - a literature review. SIK Rapport Number 646, 60 pgs. Sveriges Tekniska Forskningsinstitut, Borås, Sweden.
   Google Scholar
• Wijmans, J. G. and Baker, R. W. (1995). The solution-diffusion model: a review. J. Membr. Sci. 107: 1–21.
   Web of Science ®Google Scholar
• Wittassek, M. and Angerer, J. (2008). Phthalates: metabolism and exposure. Int. J. Androl. 31: 131–138.
   PubMed Web of Science ®Google Scholar
• Wong, C.-P., Schrag, J. L. and Ferry, J. D. (1970). Diffusion of radioactively tagged 1,1-diphenylethane and n-hexadecane through rubbery polymers: Dependence on temperature and dilution with solvent. J. Polym. Sci. Part A-2: Polym. Phys. 8: 991–998.
   Web of Science ®Google Scholar
• Yamakawa, H. (1971). Modern Theory of Polymer Solutions. Harper & Row.
   Google Scholar
• Yang, L., Chen, X. and Jing, X. (2008a). Stabilization of poly(lactic acid) by polycarbodiimide. Polym. Degrad. Stabil. 93: 1923–1929.
   Web of Science ®Google Scholar
• Yang, S.-l., Wu, Z.-H., Yang, W. and Yang, M.-B. (2008b). Thermal and mechanical properties of chemical crosslinked polylactide (PLA). Polym. Test. 27: 957–963.
   Web of Science ®Google Scholar
• Zeliger, H. (2011). Human Toxicology of Chemical Mixtures. Elsevier Science.
   Google Scholar
• Zhang, J. and Wang, C. H. (1987). Application of the laser-induced holographic relaxation technique to the study of physical aging of an amorphous polymer. Macromolecules. 20: 683–685.
   Web of Science ®Google Scholar
• Zhu, J., Chen, L.-Q., Shen, J. and Tikare, V. (2001). Microstructure dependence of diffusional transport. Comput. Mater. Sci. 20: 37–47.
   Web of Science ®Google Scholar
• Zielinski, J. M. (1996). An alternate interpretation of polymer/solvent jump size units for free-volume diffusion models. Macromolecules. 29: 6044–6047.
   Web of Science ®Google Scholar