The transport of water molecules through solids is significant to a diverse range of industries. The key interest lies in preventing entry of water vapor and protecting the associated products. There are also applications that depend on water vapor transport i.e. release of water vapor in a controlled manner. All these applications require an in-depth understanding of the physical properties that govern the transport rate in various climatic conditions.
Permeation or transmission is defined as the process of molecular transportation through solids. This can either be as a result of adsorption, where molecules diffuse through the porous structure of a solid, or due to absorption, where molecules diffuse in the solid. Figure 1 shows the permeation of water vapor through a film. The permeation or transmission rate, F, is a function of the following three parameters:
- Temperature, T: Molecular diffusion in solids is an activated process that overcomes a potential barrier with sufficient energy. The rise in temperature will assist diffusion.
- The solid dimensions (i.e. the ratio of area, A, to thickness, t, for a film)
- Concentration gradient, ΔC: A difference in the concentration of the molecules across the solid is required for net transport. There will be a corresponding net rate of transfer from the high concentration region.
Figure 1. Schematic showing the permeation of water vapor through a film
A concentration gradient will exist if the solid is not in equilibrium. In practice this can be achieved in two controlled ways, which correspond to the experimental methods described in this article.
Determination of Direct Transmission Rate
This method replicates packaging applications where there is a rate of transfer when the humidity inside and outside the package is not the same. The method uses the film to seal an impermeable chamber.
At constant temperature, % RH1 and % RH2, a steady state will be achieved with a net rate of transfer, known as the transmission rate. In most experiments with this configuration, the measurement is carried out by placing a desiccant (% RH2~0) in a container, sealing this with the film then placing it within a humidity controlled enclosure. At high humidity, the transfer rate can be determined by weighing the container periodically.
This process is commonly expressed in terms of a moisture vapor transmission rate (MVTR) calculated from:
The MVTR values vary based on the previously discussed operating conditions. The in-situ measurement of MVTR can be performed using the IGAsorp moisture sorption analyzer by continuous weighing of a special container, as shown in the Figure 2. The temperature and external humidity of a special film holder can be set using the climate controls of the instrument.
A circular section of the film under test is housed in the holder and compressed between two aluminium flanges. The base flange serves as a well for a saturated salt solution which sets the humidity, while the upper flange is sealed with a thin aluminium foil to assess the seal integrity independently in the different operating conditions required. The puncturing of foil is followed by recording the actual experimental data.
Figure 2. Permeation Cell with calibration salt solutions
Continuous in situ weighing gives a direct recording of the approach towards steady state that is followed by the linear trend as a result of water vapor transmission without an operator intervening. The linearity of the trend demonstrates that the measurement is in steady state and shows the quality of the climate control measurement performed by the IGAsorp. MVTR measurement can be determined from very small weight changes, and it can be repeated under various operating conditions. Figure 3 shows an example of the data collected from such a measurement.
Figure 3. Results of a MVTR study at 35°C of a film using the permeation container
Determination of Simultaneous Sorption-Diffusivity
By changing the climate around the film the entire sample is exposed to water vapour at the same humidity. The change in uptake with time following the humidity change is used to calculate the transport properties. A steady state rate is not achieved, and transport differs in two ways as shown in the Figure 4:
- The surfaces are exposed, and the concentration gradient is from the centre plane to the surface over the thickness l/2.
- The concentration gradient is not constant — it varies from a maximum upon when humidity is changed to zero at equilibrium.
Figure 4. Distribution of water molecules during a sorption study (i) at equilibrium t = 0, (ii) during the uptake phase resulting from a step in RH 0 < t < ∞ and (iii) at the new equilibrium concentration t = ∞.
The simplest transport treatment is based on Fick’s law, which is given as follows. By definition, the rate of transfer, F, in steady state, is given as:
which defines the fundamental rate constant, D, (the macroscopic or chemical diffusion coefficient) for a concentration gradient δC/δx. This definition is expressed solely in terms of two physical properties, diffusivity and concentration.
Therefore measurement of the transmission or permeation rate alone does not discriminate between these two contributions.
Both the quantities can be determined by the direct determination of isothermal uptake as given below. The concentration is measured from the equilibrium uptake and the sorption time and the sorption-time curve is a function of diffusivity. Fickian diffusion in a thin film is the simplest case where diffusivity is not a function of concentration. The uptake as a function of time, m(t), is given by:
where l is the thickness of the specimen, D is the chemical diffusion coefficient and M∞ is the asymptotic uptake. Fickian characteristics are not always observed in experimentally determined sorption-time curves, this can be assessed by plotting fractional uptake versus t1/2, as shown in the Figure 5. The IGAsorp moisture sorption analyzer also provides the means to directly determine the equilibrium concentration and sorption-time curves. In such 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.
Figure 5. The classification of sorption time curves
The method is identical to that used for characterizing water-solid interactions using the IGAsorp, differing only in that the uptake is expressed in terms of mass or water per unit volume of solid, and that additional kinetic analysis can be used after the measurement. Figure 6 shows an example where uptake-time is plotted verus time, t1/2, and compared against the Fickian model by curve fitting to determine the diffusion coefficient.
The analysis is repeated for different sorption-time curves, the final results are plotted as an overlay of two trends, the calculated diffusion coefficient as a function of the relative humidity, and the equilibrium concentration as shown in the Figure 6.
Figure 6. Sorption isotherm and diffusion coefficients as a function of relative humidity for a polymer film
As real-world materials are not ideal Fickian systems, experimental determination of diffusivity by this method is rarely used to predict MVTR. Concentration-dependence of diffusivity ensures that appropriate average value of a single calculated coefficient can be achieved over the measured range. The IGAsorp facilitates new studies on the concentration-dependence. The equilibration time calculated by the IGAsorp is substituted for the diffusion coefficient to model systems with non-Fickian characteristics.
This article demonstrates the in situ measurement and characterization of water vapor transport through two different methods using the IGAsorp instrument. Both the methods are used for determining the physical properties as a function of the climatic conditions.
This information has been sourced, reviewed and adapted from materials provided by Hiden Isochema.
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