Introduction to Migration Modelling - European Commission · JRC Guideline on migration modelling...

Introduction to

Migration Modelling

► 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

Content

► Historical Context

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”.

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.

► scientific work world wide in the 80th and 90th

- 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

Short History

► 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

Scope and conditions of use

► Migration model for

- monolayer and

- multilayer materials

Diffusion

Convection

Evaporation

Reaction

Partitioning

Migration - mass transfer

>>> change of concentration

with time

t

c

Diffusion

Convection

Reaction

Evaporation

Partitioning

. . .

Migration ~ Diffusion

Mass transfer

simplifying assumption


Migration process (Mass transfer)

● Diffusion process is the rate

determining step

● Diffusion process is determined

by:

- mobility of the polymer

(AP, polymer specific constant)

- size of the migrant

(Mr, molecular weight)

- temperature

(T, temperatur)

2

2

x

cD

t

c

Fick's 2nd law of diffusion

(one dimensional):

c - concentration

t - time

x - distance

D - diffusion coefficient

D

P - polymeric material

M - contacting medium

P M

Mass transfer ~ diffusion

Diffusion models

» monolayer materials

(monolayer)

D/K

» multilayer materials

(multilayer)

(D/K)n

D,K - mass transfer constants

P M

migrant

DP

KP,M

general diffusion model:

D/K/.../DD/K - polymer/liquid

D/K/D - polymer/solid

D/K/D/K - polymer/coating/liquid

...

(D/K)n/D - general

Diffusion models

polymeric materials in contact with ...

D - diffusion coefficient [cm²/s]

D0 - pre-exponential factor

EA - activation energy [J]

R - gas constant [8,314 J/mol K]

T - temperature [K]

RT

EA

eDD

0D RT

EA

eDD

0D

Diffusion coefficient (how fast is the migration)

P M

migrant

DP

KP,M

FüllgutPackstoff

cP,0

t = 0

migration

t =

cP,0 cF,0 = 0 cP, cF,

,

,

,

F

P

FPc

cK

Partitioning

Partition coefficient, KP,F

K - partition coefficient

c - concentration

P - polymeric material

M - contacting medium

- at equilibrium

Partition coefficient (how far goes the migration)

,

,

,

M

P

MPc

cK

P M

migrant

DP

KP,M

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

→ see J. Crank

("Mathematics of Diffusion")

D/K

H.S.Carslaw &

J.C.Jaeger: Conduction of heat in solid

J. Crank: The Mathematics of Diffusion


12

2

220,

,exp

1

121

1 n P

nP

n

PPP

tU

d

qtD

qdc

A

m

UP

PU

K

VV

,

/

Analytical solution of the diffusion equation

mU,t/A in [µg/cm2] - Migration

t in [s] - contact time

A in [cm2] - contact area

cP,0 in [mg/kg = ppm] - initial concentration of the migrant in the plastic

P and F in [g/cm3] - density of plastic and food or simulant

dP in [cm] - thickness of plastic

DP in [cm2/s] - diffusion coefficient of the migrant in the plastic

VP and VF in [cm3] - volume of plastic and food or simulant

KP,F = cP,P / cF,F - partition coefficient (condentration relation of migrant

(w/v) in plastic and food at equilibrium)

tan qn = - qn, - qn positive roots of the trigonometric 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


► 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

Software Tools

Estimation of mass transfer constants

» Diffusion coefficients (DP)

Arrhenius DP=f(D0,EA,T)

Piringer DP=f(AP',tau,Mr,T)

Brandsch DP=f(Tg,M,T) - new

» Partition coefficients (KP,M)

worst case K=1, (VP<<VM)

Piringer K=f(p, Ma, Wa, GF)

Brandsch K=f(SW)

K=f(PO/W) - new

DP - diffusion coefficient


(Arrhenius)

EA - activation energy (Arrhenius)

T - temperature [K]

AP' - polymer specific constant

(Piringer)

tau - polymer specific temperature

constant (Piringer)

M - molecular weight [g/mol]

Mr - relative molecular weight

Tg, - glass temperature of polymer

KP,M - partition coefficient

VP - volume of polymer

VW - volume of medium

p - vapour pressure of migrant

SW - water solubility of migrant

PO/W - octanol/water- partition

coefficient of migrant

► Estimation of diffusion

coefficients



● Diffusion process is the rate

determining step

● Diffusion process is determined

by:

- mobility of the polymer

(AP, polymer specific constant)

- size of the migrant

(Mr, molecular weight)

- temperature

(T, temperatur)

D - diffusion coefficient [cm²/s]


EA - activation energy [J]

R - gas constant [8,314 J/mol K]

T - temperature [K]

RT

EA

eDD

0D RT

EA

eDD

0D

Diffusion coefficient

P M

migrant

DP

KP,M

DP - Diffusion coefficient (D0 = 104 cm²/s)

AP= AP„-/T - material specific constant

( - material specific temperature constant)

Mr - relative molar mass of migrant in Dalton

T - temperature in K

EA - reference activation energy

(= R·10454 = 86,9 kJ, R = 8,314 J/K·mol)

TR

RMMADD rrPP

10454003.01351.0exp

3/2

0

Estimation of diffusion coefficients (Piringer)

Polymer AP´ T [°C] cP,0 [%]

LDPE 11.5 0 < 80 < 1

LLDPE 11.5 0 < 100 < 1

HDPE 14.5 1577 < 90 < 1

PP(homo) 13.1 1557 < 120 < 1

PP(random) 13.1 1557 < 120 < 1

PP(rubber) 11.5 0 < 100 < 1

FOOD CONTACT MATERIALS

PRACTICAL GUIDE

“A PRACTICAL GUIDE FOR USERS OF EUROPEAN DIRECTIVES ”

Upper limit AP*-values (polyolefines)

Polymer AP´ T [°C] cP,0 [%]

PS 0 0 < 70 < 1

HIPS 1 0 < 70 < 1

PET 6 1577 < 175 < 1

PEN 5 1557 < 175 < 1

PA 6,6 2 0 < 100 < 1

FOOD CONTACT MATERIALS

PRACTICAL GUIDE

“A PRACTICAL GUIDE FOR USERS OF EUROPEAN DIRECTIVES ”

Upper limit AP*-values (non-polyolefines)

Table 6 Statistical validation of AP’-values for migration modelling under ’worst case’

conditions

Polymer

AP’

s

AP’(max)

AP’(min)

N

t

AP’*

LDPE 10.0 1.0 11 7.0 27 1.7 11.7 0

HDPE 10.0 1.9 12.6 5.0 49 1.68 13.2 1577

PP 9.4 1.8 12.9 6.2 53 1.68 12.4 1577

PET 2.2 2.5 7.2 -4.3 58 1.67 6.35 1577

PEN -0.34 2.4 3.8 -5.5 38 1.7 3.7 1577

PS -2.8 1.25 0.0 -6.5 32 1.7 -0.7 0

HIPS -2.7 1.67 0 -6.2 33 1.7 0.1 0

PA (6,6) -1.54 2.0 2.3 -7.7 31 1.7 1.9 0

Other Polymers (EU-Project Migration Modeling)

AP= AP'-/T Food Additives and Contaminants, 2005; 22(1): 73–90

Diffusion properties of different

polymers can be compared

based on their AP-value,

i.e. mobility of the polymer

► high AP-values account for high

mobility of the polymer (flexible

polymers) and high diffusion

coefficients respectively

► low AP-values account for low

mobility of the polymer (rigid

polymers) and low diffusion

coefficients respectively


DP AP

[cm²/s]

gases ~ 10-1

liquids ~ 10-5 20

viscous liquids ~ 10-6 18

soft PVC ~ 10-7 16

Polymere T > Tg

LDPE ~ 10-9 11

HDPE ~ 10-10 9

PP ~ 10-11 7

Polymere T < Tg

PA ~ 10-13 2

PS ~ 10-14 0

PET ~ 10-15 -2

rigid PVC ~ 10-16 -4(Tg - glas temperature)

Diffusion coefficients (at T=20°C, Mr=300 g/mol)

► Regulatory context

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

real diffusions coefficient: DP <--> AP

„upper limit“ diffusion coefficient : DP* <--> AP*

- an „upper limit“ diffusions coefficient DP* gives a „worst

case“ migration estimation

Legal requirements for AP-values

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.

► 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).


contact

medium

Direct and indirect contact

t

A

m tF ,

2d 10d

concave

I > 0

Food contact

layer

two data points:

2d@60°C

10d@60°C


t

A

m tF ,

2d 10d

convex

concave

I > 0

I < 0

two data points:

2d@60°C

10d@60°C

printing ink


FB

FB

D

d 2

6

1

dFB - thickness

DFB - diffusions coefficient

- "lag time"

Simulanz /Lebensmittel

Migrant

Kunststoff

DP

KFB,F

FBSimulanz /

Lebensmittel

Migrant

Kunststoff

DP

KFB,F

FBSimulanz /

Lebensmittel

Migrant

Kunststoff

DP

KFB,F

FBSimulanz /

Lebensmittel

Migrant

Kunststoff

DP

KFB,F

FBSimulanz /

Lebensmittel

Migrant

Kunststoff

DP

KFB,F

FBSimulanz /

Lebensmittel

Migrant

Kunststoff

DP

KFB,F

FB

KP,FB

DFB

"lag time"

Theoretical understanding

DEHA, Verbund 1 (NC/20µmOPP/Adh/30µmOPP)

21Tage bei 20°C, Ethanol95%

0

100

200

300

400

500

600

700

0 5 10 15 20 25 30 35 40

Zeit [Tage]

Mig

rati

on

[µ

g/d

m²]

exp.

calc. N

Functional barrier

multilayer structure:(from left to right)

ink(1µm)

OPP(20µm)

adh.(2,5µm)

OPP(30µm)

time [days]

one sided migration test

food simulant (D) substitute: 95% ethanol

temperature: 20°C

migrant: DEHA

migration kinetic

O

O

O

O

CH3

CH3

CH3 CH3


10 Tage bei 40°C, Ethanol95%

0

500

1000

1500

2000

2500

0 5 10 15 20 25 30 35 40 45

Zeit [Tage]

Mig

rati

on

[µ

g/d

m²]

calc. N

exp.

time [days]



temperature: 40°C

migrant: DEHA


ink(1µm)

OPP(20µm)

adh.(2,5µm)

OPP(30µm)

Functional barrier

migration kinetic

O

O

O

O

CH3

CH3

CH3 CH3


7 Tage bei 60°C, Ethanol95%

0

500

1000

1500

2000

2500

0 1 2 3 4 5 6 7 8

Zeit [Tage]

Mig

rati

on

[µ

g/d

m²]

exp.

calc. N

time [days]



temperature: 60°C

migrant: DEHA


ink(1µm)

OPP(20µm)

adh.(2,5µm)

OPP(30µm)

Functional barrier

migration kinetic

O

O

O

O

CH3

CH3

CH3 CH3

► JRC Guideline on

Migration Modelling

Introduction to Migration Modelling - European Commission · JRC Guideline on migration modelling...

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