Model based design of barrier coatings for paper based materials : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Bioprocess Engineering at Massey University, Manawatu campus, New Zealand
Paper based materials have limited vapour barrier properties. Several techniques have been developed to overcome this limitation. One of such technique is the use of barrier dispersion coatings. These barriers are continuous and solid layers normally applied on the surface of paper materials. Dispersion coatings are normally composed of two materials; a latex binder and filler particles. The interaction between these materials creates tortuous pathways that reduce the diffusion of the permeant. The main objective of this study was to develop an understanding of how the dispersion coatings can be designed to optimise the barrier properties of paper materials. In particular, the aim was to comprehend the effect of fillers added into dispersion coatings on the permeability with the purpose of developing of a model for predicting permeability.
A number of models have been developed to predict the permeability of barrier films such as thermoplastic composites but none have been applied or developed for use on barrier dispersion coatings. These models are normally based on idealised geometries, where the fillers are arranged in either oriented or random ways. The heterogeneous characteristics of the barrier dispersion coatings, such as uneven coating thickness, particle size and the lower elongation of the fillers used in dispersion coatings limit the use of the existing models for the prediction of dispersion coating barrier performance.
To develop a predictive model, the characterisation of aspects such as shape, size distribution and volume fraction of fillers in barrier coatings and their effect on the barrier performance were studied. The analysis of the geometry of fillers was carried out by image analysis from microscopy (scanning electron and light microscopes). This was carried out on three types of kaolin clays. The shapes, Feret diameters, and thicknesses of the clays were characterised. The filler shapes were elongated with an average ratio between the major and minor diameter being no larger than two. The Fourier series descriptor approximates the filler shape at the second harmonic. The Feret diameter and thickness were fitted to distribution curves. These distributions were used to define the fillers for generation of particle populations required for modelling. The particle populations can be based on either assuming representative filler shapes such as rectangular or elliptical plates or by the Fourier series descriptor.
Characterisation of dispersion coatings were also carried out. The dispersion coatings were formulated by styrene-butadiene latex and mixed with the selected clays at several filler volume fractions and applied on 160 𝑔∙𝑚−2 linerboards. The characterisation was based on the measurement of water vapour transmission rate (WVTR) and oxygen transmission rate (O2TR).
The coating thickness was also measured by scanning electron microscopy image analysis. The WVTR and O2TR were shown to be sensitive to the type of filler, volume fraction of filler, and thickness of the coatings. Both the WVTR and O2TR tended to be lower as the filler size, filler volume fraction, and coating thickness increased. The thickness of the coating was found to be dependent on the coating process (coated rod), coating formulation, and its variability on the linerboard topography.
The proposed model predicted the relative permeability based on the estimation of permeant flux by the Fick’s first law through three dimensional coating geometries. The coatings were filled with rectangular plates randomly located. These plates were defined by distribution curves of maximum Feret diameter, elongation, and thickness of the selected clays. The amount of fillers in the coating was determined by part of filler volume fractions used for measurements of WVTR and O2TR. The sizes of the geometries were defined by the representative elemental volume estimated from the filler volume fraction and the variation of the predictions. The geometries were generated by programming in Matlab under particular conditions of coating formulation and exposure.
The mathematical solution of the model was carried out by finite element method and solved by Comsol Multiphysics. As expected from the experimental characterisation of the coatings, the predictions indicated that the relative permeability reduced as the volume fraction of filler and the size of the clay increased; however, overestimation of the barrier properties were predicted. To understand the reasons for the discrepancy, several factors, that were not included in the conceptual model, were analysed. It was observed that the filler agglomeration and uncoated areas was the most significant factor that may affect the prediction of the relative permeability. Other factors such the uniformity of coating profile, and filler shape were found to have an effect on the prediction. Despite the discrepancy, the model was suitable for prediction of how to improve barrier performance trend. Thus, it was possible to evaluate different factors related to the barrier performance to find their best combination.
In order to optimise the formulation of barrier dispersion coatings, sensitivity analyses were carried out based on factors that affect the permeability. Filler settling in the coating or coatings with two layers were found to provide a reduction of relative permeability. This technique also may reduce the material used for coating preparation and the occurrence of uncoated areas. However, these effects were smaller than the effect of filler agglomeration on the barrier performance. For this reason, future studies should be focused on the improvement of dispersion of fillers in the coating binder. The application of the model in other coating formulations must consider the definitions of the concepts used in the study in order to apply the correct
information for running simulations.
Because this model was the first approach developed for dispersion coatings, several aspects were fully not explored in this study. In future research may be focused on the improvement of filler geometry characterisation, dispersion of fillers in the coating binder, incorporation of coating irregularities in the conceptual model, and incorporation of commercial coatings additives in the model. These points may increase the complexity of the model; however, it is expected that such complexity will be practical to be included in the model in the near future due to advances in computing capability for FEM simulations.