The transport of water molecules through solids is commonplace and of significance to diverse industries. The interest lies in preventing ingress of water vapour and the associated product protection. Equally there are applications dependent on the transport of water vapour where a controlled release of water vapour is required. Dr M Mercer and Dr M J Benham report.
Molecular transport through solids is termed permeation or transmission and can either be due to absorption where molecules diffuse in the solid or due to adsorption where molecules diffuse through the pore structure of the solid.
The permeation or transmission rate F, is a function of three parameters: The solid dimensions, particularly the thickness, the temperature and the concentration gradient. Net transport requires a difference in the concentration of molecules across the solid so that there will be a correspondingnet rate of transfer from the region of high concentration.
By changing the climate around the film, the entire sample is exposed to water vapour and transport properties are calculated from the change in uptake resulting from the change in concentration with time following a change in humidity (Fig. 1). The simplest treatment of transport is based on Fick's Law where, by definition, in steady state, the rate of transfer, F, is given as: F = -D dC/dx Equ .
Which defines the fundamental rate constant, D, (the macroscopic or chemical diffusion coefficient) for a concentration gradient dC/dx. This definition has a fundamental form since the behaviour is expressed solely in terms of two physical properties, diffusivity and concentration. Classic measurements of the transmission or permeation rate alone do not discriminate between these two contributions.
Isothermal uptake studies performed using the IGAsorp moisture sorption analyser can simultaneously determine both quantities as illustrated in Fig. 2 and 3. The concentration is measured from the equilibrium uptake and the sorption-time curve is a function of the diffusivity. The mathematical models of this behaviour depend on the geometry and transport process(es) involved. In these experiments the film of known dimensions is directly suspended from the IGAsorp balance and one or more isotherms are measured at a series of fixed humidity set-points.
This method is identical to that used for characterisation of water-solid interactions with the IGAsorp and differs only in that uptake is expressed in terms of mass of water per unit volume of solid (eg mg/cc) and that additional kinetic analysis can be applied using the software after the measurement. An example is shown in Fig. 2 where uptake is plotted versus time 1/2 and directly compared to the Fickian model by curve fitting to determine the diffusion coefficient.
This analysis is repeated for the varioussorption-time curves and the final results are then plotted as an overlay of two trends, the equilibrium concentration and the calculated diffusion coefficient as a function of relative humidity (Fig. 3).
The experimental determination of diffusivity by this method will rarely be used to predict MVTR (moisture vapour transport rates) since real-world materials are not ideal Fickian systems. Concentration-dependence of diffusivity is common which means that a single calculated coefficient would be at best an average value over themeasured range.
The IGAsorp in comparison to the classic methods allows the concentration-dependence to be studied. In systems with non-Fickian behaviour that cannot be simply modelled the diffusion coefficient is replaced by an equilibration time calculated by the IGAsorp. However, in all cases the trends of behaviour are important when comparing materials given that extremes of variation of the diffusivity as a function of concentration can give rise to anomalous MVTRs and transmission rates.
The in situ measurement and characterisation of water vapour transport has been reviewed in terms of the sorption/diffusivity method offered by the IGAsorp instrument. This method provides the means to accurately assess transport properties as a function of climatic conditions.
ENQUIRY No 63
Dr M Mercer and Dr M J Benham are with Hiden Analytical Ltd, Warrington, UK. www.HidenAnalytical.com
