3.3 Moisture sorption isotherms and their applications

Moisture Sorption Processes

Adsorption and Desorption

Adsorption is the process where water molecules bind to the surface of a food material. It occurs when the vapor pressure of the food is lower than the surrounding environment, causing water molecules to accumulate on the food's surface and form a thin layer. Adsorption is exothermic, meaning it releases heat as water molecules bind to the surface.

Desorption is the reverse: water molecules leave the surface of a food material. This happens when the food's vapor pressure is higher than the surrounding environment, reducing the food's moisture content. Desorption is endothermic, requiring heat input to break the bonds between water and the food surface.

Think of it this way: a dry cracker left on a humid countertop adsorbs moisture from the air and goes stale. A moist piece of bread left in a dry environment loses water through desorption and dries out.

Hysteresis and Moisture Content

Hysteresis is the phenomenon where the adsorption and desorption curves on a sorption isotherm don't overlap. At any given relative humidity, the moisture content during desorption is higher than during adsorption. This happens because the food's internal structure changes during wetting and drying. Capillary condensation and swelling of the food matrix alter how water is held, so the path "back" doesn't retrace the path "forward."

Two moisture thresholds are especially important:

• Monolayer moisture content is the amount of water tightly bound to specific sites on the food surface. This water is essentially locked in place and isn't available for chemical reactions or microbial growth. For dehydrated foods, keeping moisture at or below the monolayer value is a primary strategy for maximizing shelf life.
• Critical moisture content is the point where significant changes in physical and chemical properties begin. It marks the transition from monolayer to multilayer moisture. Above this threshold, foods become much more susceptible to spoilage, caking, and clumping.

Moisture Sorption Models

BET Equation

The Brunauer-Emmett-Teller (BET) equation describes water adsorption on food surfaces. It assumes the food surface is homogeneous and that adsorbed water molecules don't interact with each other.

The equation is:

$\frac{a_w}{(1-a_w)m} = \frac{1}{m_0 C} + \frac{C-1}{m_0 C}a_w$

where $a_w$ is water activity, $m$ is moisture content, $m_0$ is the monolayer moisture content, and $C$ is an energy constant related to the heat of adsorption.

To use the BET equation, you plot $\frac{a_w}{(1-a_w)m}$ on the y-axis against $a_w$ on the x-axis. The result should be a straight line in the valid range. From the slope and intercept, you can calculate $m_0$ and $C$:

1. The y-intercept equals $\frac{1}{m_0 C}$
2. The slope equals $\frac{C-1}{m_0 C}$
3. Solve these two equations simultaneously for $m_0$ and $C$

The main limitation: the BET equation is only reliable at low water activities, roughly $a_w$ = 0.05 to 0.45. Beyond that range, its assumptions break down and predictions become inaccurate.

GAB Model

The Guggenheim-Anderson-de Boer (GAB) model extends the BET equation by accounting for multilayer adsorption. It introduces a third parameter, $K$, which relates to the heat of adsorption in the multilayer region.

The GAB equation is:

$\frac{m}{m_0} = \frac{CKa_w}{(1-Ka_w)(1-Ka_w+CKa_w)}$

Because of that extra parameter, the GAB model fits experimental data over a much wider range of water activities (0.05 to 0.90). This makes it the more practical choice for most food science applications. It's widely used across the industry to describe sorption behavior of cereals, fruits, vegetables, and many other products.

Applications

Food Packaging Design

Moisture sorption isotherms directly inform how food packaging is designed. The core goal is to maintain the desired water activity inside the package and prevent quality loss.

Here's how sorption data feeds into packaging decisions:

• Barrier selection: Sorption isotherms tell you how much moisture a food will gain or lose at different humidities. From this, you can calculate the required water vapor permeability of the packaging material. A product like dried fruit needs a high-barrier film to prevent moisture uptake, while a fresh baked good might need a film that limits moisture loss.
• Desiccant use: Desiccants like silica gel packets are placed inside packages to absorb excess moisture and keep the internal humidity low. Sorption data helps determine how much desiccant is needed and how long it will remain effective.
• Humectant use: Humectants like glycerol can be incorporated into food formulations or packaging systems to control moisture loss and prevent the product from drying out.

Choosing the right combination of barrier material, desiccants, and humectants based on a product's sorption isotherm can significantly extend shelf life. For example, pairing a moderate-barrier film with a calibrated desiccant sachet for crackers keeps $a_w$ low enough to prevent both microbial growth and textural changes like softening.