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# Vapour permeation measurements and DVS

## WVTR measurements and Water Vapour Permeance

The terms Moisture Vapour Transmission Rate (MVTR) and Water Vapour Transmission Rate (WVTR), both refer to the rate of transfer of water across a unit area of a sheet or membrane. Both of these terms are widely used.

Many methods are used to measure transport of water vapour through membranes, films and sheets of material.

Some of the simplest and most direct methods measure the weight of water passing through a sample of the material where each face is exposed to a different humidity.

### Gravimetric MVTR measurement

Typical gravimetric MVTR methods are defined in the standards for building materials such as “ASTM E96” and the european “EN ISO 12572:2016 Hygrothermal performance of building materials and products - Determination of water vapour transmission properties”

In these gravimetric MVTR or WVTR measurements, a protocol usually involves :

• A cup-shaped cell which is partially filled with a dessicant or a saturated salt solution which will give a fixed humidity inside the cup
• Sealing of the opening of the cup with the test material
• Storage in a humidity and temperature controlled chamber
• Periodic measurement of the weight of the cup
• Calculation of the net flux of water through the sample, in units of weight per unit time.

With knowledge of the surface area of the sample, the rate of gain or loss of water per unit area can be calculated. This value is the Moisture Vapour Transmission Rate or MVTR for the conditions used, and has dimensions of Weight/(Time × Area).

$MVTR = \frac{flux}{Area} = \frac{(weight/time)}{Area}$

In practice, measurement methods are divided into two main groups:

• Dry cup methods, where a dessicant is placed inside the cup, with a regulated source of fixed humidity outside. The dessicant gains weight during the experiment.
• Wet Cup methods, where either pure water or a saturated salt solution are placed inside the cup. Outside the cup, it is possible to use either a dessicant or a regulated humidity source.

### Water Vapour Permeance

In many practical applications, the parameter being sought is the Permeance, $$W$$, which is a property of a specific configuration of a material, or of a composite, in the form of a sheet or membrane. The Permeance is calculated by normalising the MVTR of the membrane to the partial pressure difference across the membrane:

$W = \frac{MVTR}{ \Delta P} = \frac{(flux/Area)}{ \Delta P }$

$$W$$ is typically stated in kg/(m² s Pa).

## Corrections to MVTR data

As is commonly the case, it is necessary to take instrumental factors into account, when using the data obtained from the simple measurement described above.

The simple model of a perfect infinite film, with perfectly parallel surfaces, and an exactly defined humidity on each face, does not always represent the true experimental configuration.

When the membrane has a significant permeability, gradients of humidity are established in the air around the membrane, and between the membrane and the material inside the cup, introducing vapour resistances in series with that of the membrane. The limited rate of evaporation in wet-cup methods or the rate of absorption in dry-cup methods give a source term, which must also be taken into account. In addition, the edge effects at the border of the membrane can be significant, particularly for thick samples, or where sealing is difficult.

Most standardised measurement methods specify the geometry and the other conditions of the test to limit the variability in the results. For example, the method may require:

• particular values of internal and external humidity. This gives a constant driving force for the vapour tranport. Often 50 %RH is used for the external humidity.
• to fix the relative area of membrane and salt solution or water to standardise the ratio between the source term and the other resistances.
• to fix the gap between the water or salt surface and the membrane (for the air layer resistance)
• to define the air circulation velocity above the membrane (for the external air boundary layer).

In addition, or instead of standardising the experimental configuration, calculated corrections may be applied:

• for the air resistance between the salt solution and the test sample (Annex G, EN ISO 12572:2001)
• for the masked edge effect (Annex F, EN ISO 12572:2001)
• for the air resistance of the layer above the sample.

In effect, the vapour pressures at the membrane surfaces can be far from the nominal values defined by the chamber controls and the desiccant or salt solution. The measured values of vapour flux are characteristic of those pressures, and not of the known, nominal values. The magnitude of these effects is particularly large for samples with high permeability - use of a DVS instrument can help to eliminate some of these problems.

For membranes where the thickness can be varied, it is possible to eliminate some of the airgap and surface resistance effects by measuring several different samples, and then extrapolating to infinite thickness. (for example: NT BUILD 265)

## Why measure MVTR in a DVS instrument?

Gravimetric MVTR measurements depend on maintaining a perfectly constant humidity and temperature inside a chamber, with periodic weighing of the cup/sample assembly. Dedicated MVTR instruments and climatic chambers help the experimenter by assuring this constant environment, depending on manual or (more rarely) automatic transfer to a balance.

DVS instruments have an additional feature, which is that they must be able to give rapid changes and stable control across the full range of humidity, to permit measurement of full sorption isotherms.

This capability allows more detailed experiments. For example:

### Fast, automated and more accurate measurements

The automated weighing is more frequent, and often more reproducible in a DVS instrument. This makes it far quicker to determine that a steady rate of weight change or flux has been reached. The larger number of samples improves the precision of the value obtained.

### Variable driving force

When using a wet-cup method, with a saturated salt inside the cup, it is possible to vary the external humidity over a range of values above and below the value inside the cup. By fitting the curve of flux against external humidity or partial pressure of vapour, it is possible to interpolate to find the point corresponding to zero flux. The slope of the curve at this point is effectively the value of permeance at the humidity set inside the cell. Because only small humidity differences are used, this method is particularly adapted to very high permeability materials, where the large vapour flux values obtained in standard tests using two fixed humdities cause large errors from air layer and other resistances.

### Direct Solubility measurement

The DVS instrument is able to measure the sorption isotherm of the membrane material directly, by using the bare membrane as the sample in a standard DVS measurement.

The sorption isotherm gives the value of Solubility, $$S$$, which can be used with Permeability values obtained from the MVTR measurement to calculate the Diffusion coefficient, $$D$$, for the substance. See below for more details..

### Diffusion coefficient measurement

For some samples, where the time constant of the absorption is sufficiently slow and the membrane is a relatively homogeneous material, it is also possible to treat the kinetic curve of absorption versus time in order to obtain the Diffusion coefficient at each point on the isotherm. If you would like more information about this, please contact us.

## Representation and application of the data.

### Vapour resistance

The vapour resistance, $$Z$$, is the reciprocal of $$W$$

$Z = \frac{1}{W}$

Resistance values are very useful, because they can be added together to obtain the resistance for a stack or composite of multiple parallel sheets.

### Permeability

Permeability, $$P$$, is a property of a substance, and does not depend on the form of the material. Typical units for permeability are: mol/(m･s･Pa), Barrer, perm

From a measurement of permeance, which gives a value of $$W$$ for a sheet of pure material, it is possible to calculate the Permeability :

$P= W \times l$

where $$l$$ is the thickness of the sheet.

Permeability can also be obtained from knowledge of the solubility, $$S$$, and the diffusion coefficient, $$D$$, of the vapour in the material :

$P = S \times D$

For simple geometries, it is possible to obtain the values of $$D$$ and $$S$$ from DVS measurements, by treatment of the kinetic and isotherm curves respectively.