Introduction to Migration Modelling

Transcription

1 Introduction to Migration Modelling

2 Content Historical Context Scope and condition of use Migration model for monolayer materials Migration from multilayer packaging Regulatory context Modelling for compliance purpose JRC Guideline on migration modelling

3 Historical Context

4 Short History Adolf Fick: - Physiologist employed at the University of Zurich published in 1855 in "Poggendorf's Annalen der Physik an article titled: About Diffusion". - investigated diffusion of water through membranes. - theoretical / phenomenological approach today we would call it linear-response theory.

5 Short History Albert Einstein: - Investigations on Theory of Brownian Movement (1926). - Thermal induced random walk of molecules. - Driving force is a difference in the chemical potential between two adjacent media.

6 Short History scientific work world wide in the 80 th and 90 th - FDA: Limm and Holifield - EU: Zweifel, Piringer - others various EU projects - Migration Modelling - Recyclability - Certified Reference Materials - Foodmigrosure - Migresives various national projects - Multilayer Modelling (DE) - others

7 Scope and conditions of use

8 Scope and conditions of use to predict migration processes - conservative, upper bound migration values for compliance purposes - realistic migration values for packaging development and exposure estimation for monolyer plastics - defined boundary conditions - limited to monolyer in contact with a well mixed liquid - "simple" mathematics for multilayer plastics - defined boundary conditions - complex packaging structures - complex numerical mathematics

9 Migration model for - monolayer and - multilayer materials

10 Migration - mass transfer Diffusion Convection Reaction Evaporation Reaction Convection Evaporation Partitioning c t Diffusion Partitioning >>> change of concentration with time...

11 Mass transfer Migration ~ Diffusion simplifying assumption

12 Migration process (Mass transfer) Migration ~ Diffusion Diffusion process is the rate determining step Diffusion process is determined by: - mobility of the polymer (A P, polymer specific constant) - size of the migrant (M r, molecular weight) - temperature (T, temperatur)

13 Mass transfer ~ diffusion P M Fick's 2 nd law of diffusion (one dimensional): c 2 c t D x 2 P - polymeric material M - contacting medium c - concentration t - time x - distance D - diffusion coefficient

14 Diffusion models P M K P,M» monolayer materials (monolayer) D/K» multilayer materials (multilayer) D P migrant (D/K) n D,K - mass transfer constants

15 Diffusion models polymeric materials in contact with... general diffusion model: D/K/.../D D/K D/K/D D/K/D/K... (D/K) n /D - polymer/liquid - polymer/solid - polymer/coating/liquid - general

16 Diffusion coefficient (how fast is the migration) P M D D 0 e RT E A K P,M D - diffusion coefficient [cm²/s] D P migrant D 0 - pre-exponential factor E A - activation energy [J] R - gas constant [8,314 J/mol K] T - temperature [K]

17 Partitioning Partition coefficient, K P,F Packstoff Füllgut c P,0 t = 0 migration t = K P, F c c P, F, c P,0 c F,0 = 0 c P, c F,

18 Partition coefficient (how far goes the migration) P M K P, M c c P, M, K P,M K - partition coefficient D P migrant c - concentration P - polymeric material M - contacting medium - at equilibrium

19 Solution of the diffusion equation»» analytical solution - only monolayer - only mean concentration in the contacting medium and the polymeric material (no concentration profile available) - no exchange cycles can be simulated D/K see J. Crank ("Mathematics of Diffusion")

20 Solution of the diffusion equation H.S.Carslaw & J.C.Jaeger: Conduction of heat in solid J. Crank: The Mathematics of Diffusion

21 Analytical solution of the diffusion equation m U, t A c P,0 d P P q exp D 2 n 2 Pt 2 1 n1 n dp q VU / V K P, U P m U,t /A in [µg/cm 2 ] t in [s] A in [cm 2 ] c P,0 in [mg/kg = ppm] P and F in [g/cm 3 ] d P in [cm] D P in [cm 2 /s] V P and V F in [cm 3 ] K P,F = c P, P / c F, F tan q n = - q n, - Migration - contact time - contact area - initial concentration of the migrant in the plastic - density of plastic and food or simulant - thickness of plastic - diffusion coefficient of the migrant in the plastic - volume of plastic and food or simulant - partition coefficient (condentration relation of migrant (w/v) in plastic and food at equilibrium) - q n positive roots of the trigonometric equation

22 Solution of the diffusion equation (D/K) n»» numerical solution - for multilayer materials - concentration profile available - exchange cycles can be simulated see standard textbooks for Numerical Mathematics e.g. Finite Elements und Finite Differences algorithms

23 Software Tools must solve the diffusion equation numerically (partial differential equation, PDE) the analytical solution of the diffusion equations serves as reference for validation validation required, i.e. experimental examples must be reproduced correctly

24 Estimation of mass transfer constants D P - diffusion coefficient D 0 - pre-exponential factor (Arrhenius) E A - activation energy (Arrhenius) T - temperature [K] A P ' - polymer specific constant (Piringer) tau - polymer specific temperature constant (Piringer) M - molecular weight [g/mol] M r - relative molecular weight T g, - glass temperature of polymer K P,M - partition coefficient V P - volume of polymer V W - volume of medium p - vapour pressure of migrant S W - water solubility of migrant P O/W - octanol/water- partition coefficient of migrant» Diffusion coefficients (D P ) Arrhenius Piringer Brandsch D P =f(d 0,E A,T) D P =f(a P ',tau,m r,t) D P =f(t g,m,t) - new» Partition coefficients (K P,M ) worst case K=1, (V P <<V M ) Piringer K=f(p, M a, W a, G F ) Brandsch K=f(S W ) K=f(P O/W ) - new

25 Estimation of diffusion coefficients

26 Migration process (Mass transfer) Migration ~ Diffusion Diffusion process is the rate determining step Diffusion process is determined by: - mobility of the polymer (A P, polymer specific constant) - size of the migrant (M r, molecular weight) - temperature (T, temperatur)

27 Diffusion coefficient P M D D 0 e RT E A K P,M D - diffusion coefficient [cm²/s] D P migrant D 0 - pre-exponential factor E A - activation energy [J] R - gas constant [8,314 J/mol K] T - temperature [K]

28 Estimation of diffusion coefficients (Piringer) D P D 0 exp A P M 2/3 r M r R10454 RT D P A P = A P -/T M r T E A - Diffusion coefficient (D 0 = 10 4 cm²/s) - material specific constant ( - material specific temperature constant) - relative molar mass of migrant in Dalton - temperature in K - reference activation energy (= R = 86,9 kj, R = 8,314 J/K mol)

29 Upper limit A P *-values (polyolefines) Polymer A P T [ C] c P,0 [%] LDPE < 80 < 1 LLDPE < 100 < 1 HDPE < 90 < 1 PP(homo) < 120 < 1 PP(random) < 120 < 1 PP(rubber) < 100 < 1 FOOD CONTACT MATERIALS PRACTICAL GUIDE A PRACTICAL GUIDE FOR USERS OF EUROPEAN DIRECTIVES

30 Upper limit A P *-values (non-polyolefines) Polymer A P T [ C] c P,0 [%] PS 0 0 < 70 < 1 HIPS 1 0 < 70 < 1 PET < 175 < 1 PEN < 175 < 1 PA 6,6 2 0 < 100 < 1 FOOD CONTACT MATERIALS PRACTICAL GUIDE A PRACTICAL GUIDE FOR USERS OF EUROPEAN DIRECTIVES

31 conditions Other Polymers (EU-Project Migration Modeling) Polymer A P s A P (max) A P (min) N t A P * LDPE HDPE PP PET PEN PS HIPS PA (6,6) A P = A P '-/T Food Additives and Contaminants, 2005; 22(1): 73 90

32 Migration process (Mass transfer) Diffusion properties of different polymers can be compared based on their A P -value, i.e. mobility of the polymer high A P -values account for high mobility of the polymer (flexible polymers) and high diffusion coefficients respectively low A P -values account for low mobility of the polymer (rigid polymers) and low diffusion coefficients respectively

33 Diffusion coefficients (at T=20 C, M r =300 g/mol) D P [cm²/s] gases ~ 10-1 liquids ~ viscous liquids ~ soft PVC ~ Polymere T > T g LDPE ~ HDPE ~ PP ~ Polymere T < T g PA ~ PS ~ PET ~ rigid PVC ~ (T g - glas temperature) A P

34 Regulatory context

35 EU legislation (FCM 2002/72/EC, Article 8)

36 Legal requirements for A P -values real diffusions coefficient: D P <--> A P upper limit diffusion coefficient : D P * <--> A P * - an upper limit diffusions coefficient D P * gives a worst case migration estimation

37 Functional barrier concept Article 7a» Only glass and some metals may ensure complete blockage of migration. (absolute barrier)» Plastics may be partial functional barriers with properties and effectiveness to be assessed and may help reducing the migration of a substance below a SML or a limit of detection.

38 Functional barrier concept FB consists of one or several layers, FB assures that the migration of positively listed substances does mot exceed the specific migration limit FB assures that the migration of substances not listed does not exceed the limit of 0,01 mg/kg food (including set-off) not allowed are substances classified as proved or suspect "carcinogenic", mutagenic or toxic to reproduction, substances in Annex I to Council Directive 67/548/EEC FB prevents the migration of "not intentionally added substances" (NIAS = impurities, decomposition products, etc.), i.e. keeps their migration not detectable (detection limit 0,01 mg/kg food).

39 Direct and indirect contact contact medium

40 Functional barrier concept Food contact layer two data points: C C m F, t A concave I > 0 t 2d 10d

41 Functional barrier concept printing ink two data points: C C m F, t A concave I > 0 convex I < 0 2d 10d t

42 Theoretical understanding "lag time" Migrant Migrant Migrant Migrant D P D P D P D P K FB,F K FB,F K FB,F K FB,F Kunststoff FB Simulanz / Lebensmittel Kunststoff FB Simulanz / Lebensmittel Kunststoff FB Simulanz / Lebensmittel Kunststoff FB Simulanz / Lebensmittel 1 6 dfb - thickness d 2 FB D FB K P,FB D FB - diffusions coefficient - "lag time" D FB

43 Migration [µg/dm²] Functional barrier migration kinetic one sided migration test food simulant (D) substitute: 95% ethanol temperature: 20 C migrant: DEHA DEHA, Verbund 1 (NC/20µmOPP/Adh/30µmOPP) 21Tage bei 20 C, Ethanol95% multilayer structure: (from left to right) ink(1µm) OPP(20µm) adh.(2,5µm) OPP(30µm) O O CH 3 CH 3 H 3 C O O CH 3 exp. calc. N time Zeit [Tage] [days]

44 Migration [µg/dm²] Functional barrier migration kinetic one sided migration test food simulant (D) substitute: 95% ethanol temperature: 40 C migrant: DEHA DEHA, Verbund 1 (NC/20µmOPP/Adh/30µmOPP) 10 Tage bei 40 C, Ethanol95% multilayer structure: (from left to right) ink(1µm) OPP(20µm) adh.(2,5µm) OPP(30µm) O O CH 3 CH 3 H 3 C O O CH 3 calc. N exp. time Zeit [days] [Tage]

45 Migration [µg/dm²] Functional barrier migration kinetic one sided migration test food simulant (D) substitute: 95% ethanol temperature: 60 C migrant: DEHA DEHA, Verbund 1 (NC/20µmOPP/Adh/30µmOPP) 7 Tage bei 60 C, Ethanol95% multilayer structure: (from left to right) ink(1µm) OPP(20µm) adh.(2,5µm) OPP(30µm) O O CH 3 CH 3 H 3 C O O CH 3 exp. calc. N time Zeit [days] [Tage]

46 JRC Guideline on Migration Modelling

47