Water sorption by hygroscopic materials

The water sorption of materials is primarily controlled by the relative humidity, with only a small influence by temperature.

Figure xx shows a typical sorption curve. The lower black line describes the sorption process. The desorption curve follows a higher trajectory. This imperfect reversibility of the sorption curve is known as hysteresis. It looks a large effect on the graph, but in a room with relative humidity varying between 40% and 60%, the sorption cycle is much narrower, as shown by the red curves. The sorption behaviour of any material within a narrow RH range can be approximated by a straight line - the dashed red curve.

The sorption, expressed as the gradient of this line, can be regarded as a single number defining the moisture available in the material for buffering RH in the indoor range suitable for museum exhibits. Even if the line has a steep gradient, the actual performance of the material depends on its density and on the diffusion rate of water vapour through it.

The steep portion of the curve towards high RH is useful in moderating the RH in extreme indoor situations, such as in a shower cubicle or kitchen, where intermittent episodes of steam generation occur, followed by long periods where the wall can re-equilibrate with the indoor air of the house. Materials with a steep sorption curve at high RH provide a comforting protection against accidental rise in RH above the specified moderate range.

The water vapour sorption is usually expressed in weight percent of water based on the dry weight of the material. The sorption curves of cellulose are shown in figure xx.

Notice that the curves for different temperatures are close together, indicating that RH, rather than water vapour concentration, is the controlling factor in water sorption.

For our purpose, it is useful to convert the sorption curve to units of weight per unit volume. Wool insulation has a high sorption by weight, but a negligible sorption when calculated by volume.

Water vapour in air

Water vapour in the space around hygroscopic materials follows different rules. Water vapour does not dissolve in air, in an analogous way to the reaction between water molecules and the reactive surfaces of absorbent materials. The concentration of water vapour in air in an enclosed space is in equilibrium with the concentration of water in the adjacent porous materials. However, air contains very little water vapour at normal temperature, compared with the exchangeable water in hygroscopic materials, so the RH in a poorly ventilated room is mainly determined by the walls and furnishings. The relationship between relative humidity and water vapour concentration in space is described in the diagram below.

From figs xx and xx one can calculate that 500 g of paper, about a 10 mm stack of A4 printing paper, will contain about 25 g of exchangeable water, while one cubic metre of air will contain 8.5 g of water vapour. If this air were suddenly to be replaced by completely dry air, the paper would release water vapour to restore the equilibrium, which would result in about 6 g of water evaporating from the paper, giving a final RH at 35%. This is the process known as humidity buffering. In reality, it will take some time for the water to move from the bulk of the paper through the surface to enter the air but it will eventually happen.

The well established practice and theory of showcase buffering is based on the presumption of instant equilibrium, because the air exchange is in practice very slow, so the absorbent material has ample time to react. However, in an inhabited room with an air exchange of twice per hour, the rate of permeation of water vapour through the material becomes important: it is the limiting factor in passive buffering of whole rooms. Even if there is ample water in the depth of the wall, it cannot diffuse to the surface fast enough significantly to influence the water content of the air moving in from outside.

The rate of movement of water vapour through porous materials exposed to a dynamic air environment with ever changing temperature and water vapour content has long been studied by building physicists, starting from the assumption that diffusion rate is proportional to the instantaneous water vapour concentration gradient within the material. This is known as Fick's law. There are materials, such as wood, which do not obey it. They are described as non-Fickian, though one can speculate that Fick's law, derived by analogy with Fourier's law of heat transfer, is naive in its neglect of the molecular processes governing sorption and desorption within materials.

The amount of water that is exchangeable between wall and room air in a given time depends on the sorptive capacity, which can be defined as the weight of water that moves between one cubic metre of material and the air space when the RH changes by 100%. It also depends on the diffusion rate of water vapour through the material.

This multiple dependency is shown graphically in figure xx.

One can use these data to model the expected change of RH in a room, buffered only by the wall material and exposed to a flux of water vapour, imitating leakage of air from outside.

This diagram predicts the course of the RH in a room buffered by clay walls and subjected to constant leakage of outside air with an annual RH cycle. The actual variation in RH in northern Europe is much less than this but this diagram imitates the variation in RH of outside air leaking into the room and acquiring the room temperature before being allowed to interact with the walls. Working at constant temperature considerably simplifies the arithmetic yet gives realistic predictions for inhabited rooms, which scarcely alter temperature through the year.

The influence of air exchange rate is shown in figure xx, which shows the decay in room RH caused by a constant leakage of air at 20% RH. It is evident that a slow air exchange rate is essential to humidity buffering by walls. However, this is mainly because of the slow diffusion of water to the surface rather than exhaustion of the water capacity of the buffer material.

This theoretical analysis is supported by Padfield's [1998] experimental studies of process of humidity buffering by absorbent materials exposed at constant temperature to a varying water content in the adjacent air (figure xx). His work suggested the practicality of buffering whole rooms but showed also that the available materials have such slow diffusion rates for water vapour that only the few surface mm can participate in buffering the daily cycle of water vapour flux typical of a human dwelling, or a museum gallery.

Figure xx The blue trace is the measured RH in a chamber in which water vapour is added and removed in a daily cycle. The chamber contains panels of wood cut across the cell direction, exposing about 0.4 m^2 per m^3 of chamber. The RH predicted for the empty chamber is the red curve. The other curves show the RH measured in small cavities within the thickness of the wood panels.

The subject of this article is how to increase the rate of movement of water between material and room air, using materials that are already available in large quantities, or novel materials and structures that can easily be manufactured in bulk.