Migrants Diffusion

The fraction of migrant diffused from F into P up to time t, from mpo = VpCpo and the fraction migrated from P into F up to time t, from mpo = FpCpo are ... 

Migration is the result of diffusion and equilibrium processes involving the transfer of low molecular mass compounds from a plastic package into a food or food simulant. The migrants diffuse through the amorphous portion of the polymer matrix toward the interface where they are partitioned between the two media until their chemical potential values in both the polymer and the food reach equilibrium. Migration can be mathematically described by Pick s second law (Equation 13.1) ... 

Equation 11.63 still overestimates the amount of migrant in the contacting phase, since it is assumed that all migrant diffuses only in the direction of contacting phase, which is perfectly mixed. 

In order to use the migration equations, especially the generally accepted equation (7-51), values for the partition coefficient K of the migrant between P and L and the diffusion coefficient DP of the migrant in P are needed. For migrants with a high solubility in the foodstuff or simulant, the value K = 1 can be used and a worst case estimation is obtained in this way. 

Here the migration rate of i in the food is determined by the value of the diffusion coefficient in the food as well as by the partition coefficient. The concentration cL,t of migrants that are poorly dissolved in the food (K > 1) increases more slowly than when they are more easily dissolved. 

The use of these diffusion models to progress the evaluation process of a food packaging plastic will be discussed shortly. In those cases where assessment by mass balance considerations under equilibrium conditions, including partitioning effects, does not provide a clear picture of the plastics conformity status, then the different diffusivities of polymer types and the influence of the migrant molecule size or its molecular weight on its mobility within a plastic can be taken into account to achieve more distinguished views on QM/SML ratios. 

In this respect one solution for the estimation of a Dp-value is to correlate the diffusion coefficient with the relative molecular mass, Mr, of the migrant and with matrix specific parameters at a given temperature T in Kelvin. This approach has already been successfully used (Piringer 1993,1994 Limm and Hollifield 1996). The estimation of the diffusion coefficient can be achieved for example using the following heuristic correlation (Piringer 1994 Baner et al. 1996) ... 

The parameter AP accounts for a specific contribution of the plastic material to the diffusion process. Phenomenologically speaking AP has the role of a conductance of the polymer matrix towards the diffusion of the migrant (Chapter 6). Higher values of AP in such polymers as PE lead to increased DP-values while in stiff chain polymers such as polyesters and polystyrenes lower AP-values account for smaller diffusion coefficients for the same migrant. The parameters b and c account for the specific contributions of the migrant and the diffusion activation energy respectively. 

Recently Reynier et al. (1999) measured diffusion coefficients by the film to film method for a series of compounds in polyolefins at 40 °C An advantage of this method lies in the absence of possible interaction (swelling) processes produced from a liquid phase in contact with the polymeric sample. Moreover, using the same procedure and the same sample for a series of migrants, some sources for scatter of results could be avoided. Such scatter of experimental data often results when one compares results obtained in different laboratories with different samples and different experimental methods. The results obtained by Reynier et al. (1999) for HDPE and PP are compared in Fig. 15-3 with... 

The considerable influence of the food simulant can be observed in many cases for non-polyolefins. For example, the migration of an additive with Mr = 549 from IPS into 50 % ethanol in water in Table 15-4 shows a decrease of the migration amount measured at 49 °C after an initial contact temperature of 66 °C This phenomenon cannot be explained by changes in diffusion. The decrease in migration must be a consequence of a strong increase of the partition coefficient, KPR with decreasing temperature that shifts the equilibrium concentration of the migrant to the plastic phase. 

Dp upper bond" value of the diffusion coefficient which is larger than any possible real DP for the migrant 15.1.1... 

The temperatures to which the polymers are exposed must be below certain limits because above these (which are unique for each type of polymer) the diffusion behaviour of the migrant changes and cannot be calculated using the migration models. 

One of the most important migration problems occurs if a liquid food or food simulant F with the volume Vp and density pp comes in contact with a plastic layer P of thickness dp and density pp. The mass transfer takes place across an interface with area A between two different media with different characteristics, e.g., with different diffusion coefficients Dp and Z>p of the migrant. If the value of a quantity is desired, for example, the concentration of the substance transported across the interface in one of the two media, then a mass balance must be considered that takes into account the ratio of the contact surface area and the volume of the corresponding medium. The model describing this process is based on the following assumptions ... 

A component distributed homogeneously in the matrix P with an initial concentration Cpo is dissolved in F at the contact interface between P and F and subsequently diffuses into the liquid. It is assumed that there is no boundary resistance for the transfer of the migrant between P and F. In so doing there is a decrease in concentration in the region of the contact... 

The second important quantity influencing the mass transport is the diffusion coefficient Dp of the migrant in P. For relatively low concentration ranges Dp is assumed to be constant. 

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