The Science of Toast

A Study of Heat and Chemistry

The scent of buttered toast, according to Bertie Wooster, is part of the general atmosphere of leisured coziness. What better way to start a day than a cup of hot coffee and a piece of warm toast with golden crust? We will explore the science of this winning combination of breakfast. We will look into coffee in a future article. Here we focus on how to make a good toast.

We will follow the model we have established to unravel a cooking problem:

1. Define “What is good?” We want our toast to have just the right shade of golden crust, with a warm and soft crumb.
2. Find out what “good” means in terms of chemical and physical changes and under what conditions those changes happen.
3. How to control the cooking process for the food to get to the desired temperature profile.

From bread to toast

In a way, toasting is reviving stale bread. The simplest bread only needs three ingredients: flour, yeast, and water. The two main ingredients of wheat flour are protein and starch. Technically, wheat flour does not contain gluten. It contains two proteins: glutenin and gliadin. In the presence of water, these proteins bond to each other and form gluten networks. The growth of the network just requires water. That’s why no-knead bread recipes work. There is a fascinating picture in Modernist Bread that shows the proteins growing branches in water. Kneading speeds up the development of the gluten network and strengthens it. Other flours (rye, rice) don’t have the same kind of proteins, so gluten networks do not form when they are mixed with water, no matter how much they are kneaded.

Another result of kneading is the even distribution of yeast. Yeast cells are living, single-celled fungi. They serve two functions in the making of bread:

1. They generate carbon dioxide as a product of their metabolism. These carbon dioxides are trapped by the elastic gluten network. That’s why dough size grows during proofing. In the oven, yeast activities accelerate by the higher temperature and a last burst of carbon dioxide is generated, resulting in what’s known as the “oven spring”. Eventually, the yeats die at around 60⁰C.
2. Yeast cells also generate flavor. As a byproduct of the microbes’ metabolic processes, they produce many aromatic compounds. The longer the dough ferments, the more complex flavors are produced. However, you can not ferment the dough forever because the yeast will run out of food and stop generating gas. The existing gas will slowly leak out of the dough and you will not have an airy crumb. Most commercial baker’s yeasts are a single strain of Saccharomyces cerevisiae, while levains typically contain a mix of different species of yeasts and lactic acid bacteria. So in theory sourdough bread has a richer flavor. But it’s harder to achieve consistency and some people are turned off by the sour taste.

The food for yeast is sugar, which comes from the hydrolysis of the starch in wheat flour. Yeast cells can not consume starch directly. It depends on the enzyme amylase to catalyze the hydrolysis (the splitting of compounds by the addition of water) of starch molecules. The resulting simple sugar not only feeds the yeast but also reacts with proteins during the Maillard reactions that brown the crust during baking. The aromatic compounds generated by the Maillard reaction and the yeast cells are why fresh bread smells so good.

To make the dough easier to handle before putting them into the oven, people spread dry flour. These flour particles don’t mix enough with water and the starch molecules in them do not decompose into sugar. That’s where the white dust on top of the brown crust of baked bread comes from. They are cooked flour that did not participate in the browning Maillard reactions.

It takes time for the flour to absorb water. Novice bakers often make the mistake of thinking their dough is too wet and rush to add flour. They should trust the recipe and give it time. When starch is heated up in the presence of water, a process called gelatinization happens. The starch granules absorb water and swell. Water molecules break into the crystalline structure and intermolecular bonds between starch molecules break down. The whole thing becomes viscous. Eventually, new bonds form between starch molecules. When the bread cools down, the new network becomes a gel that sets, which prevents the crumb from collapsing.

During baking, water moves both inwards and outwards. On the surface of the dough, water boils first and evaporates. This allows the surface temperature to rise above 100⁰C and accelerates the Maillard reactions. The browned outer layer is the crust of the bread. In professional deck ovens, steam is injected at the beginning of baking. The steam condenses on the surface of the cold bread, it dumps a lot of heat (the specific latent heat of water vaporization). This gelatinizes the starch and causes the formation of a thin skin, the pellicle. This thin skin seals the moisture below. The bread ends up with a thinner and more crispy crust. If steam is present throughout the process, as in steamed Chinese Bao, we will see the pellicle as a shiny, peel-able layer.

In the other direction, as heat propagates into the dough, water boils in the high-temperature region on the outer layer and condenses in the low-temperature region on the inner layer, acting like a heat pipe. That’s why bread bakes so fast even though the airy crumb actually makes it a nice insulator. When freshly baked bread is taken out of the oven, the moisture in the middle of the bread starts migrating out. Like steaks, you should wait for the bread to cool down before tasting it.

As the bread cools, the gelatinized starch molecules rearrange themselves and return to the crystalline form. This is called retrogradation. Retrogradation is the reason stale bread gets hard. Retrogradation is slower at room temperature than at low temperature (fridge temperature), but completely stops under -20⁰C. Putting bread in the fridge is the worst way to preserve it. You should either leave them out and eat them quickly or freeze them.

The retrogradation process is partially reversed in the temperature range between 60⁰C and 80⁰C. Another effect of the reversal is more water molecules are bonded to the starch molecules at the hydrogen bonding sites so the bread tastes moist.

Toasts are sliced bread where:

1. The top and bottom sides used to be the internal crumb of bread.
2. It’s slightly stale. Retrogradation has happened.
3. The surface-to-volume ratio is large, which means there is a relatively small window of time to maintain a temperature gradient.

So this is what we need to get our ideal toast:

1. The surface needs to dry out and reach a high enough temperature to accelerate Maillard reactions, which give us the golden crust and the aroma.
2. The Interior should reach around 75⁰C to reverse retrogradation, but not so high that too much water evaporates. If retrogradation is not reversed, the interior will not become soft.

This concludes the second step of our investigation. Let’s move on to the third step: the cooking process.

Radiation

The main form of heat transfer in toasters is radiation. In thermal radiation, the energy is transferred in the form of electromagnetic waves, at the speed of light. It’s the fastest way of heat transfer and it doesn’t require any medium.

Figure 1 Spectrum of electromagnetic radiation

Figure 1 shows the complete spectrum of electromagnetic radiation. From approximately 0.1 to 100 micrometer, the radiation is called thermal radiation because it’s both caused by and affects the thermal state, or temperature, of matter.

The Stefan-Boltzmann law shows how to calculate the power of the radiation from a surface.

Fgiure 2. The Stefan-Botlamann Law

Where ε is emissivity, σ is the Stefan–Boltzmann constant. Tₛ is the absolute temperature of the surface.

Some observations about radiation that are relevant to the toaster oven are:

1.The radiated power is proportional to the 4th power of the temperature. If we could increase the temperature of the heating element in the toaster just a little bit, we could significantly increase its cooking power.

2. When the emissivity is 1, we have a black body, which is an ideal surface that emits the most energy at any prescribed temperature and wavelength. Many real-life heat sources (like the sun) have a similar radiation profile to the blackbody. Figure 3 shows that the shape and distribution of the emitted energy are related to the temperature. That’s why the color temperature of light bulbs has such weird numbers like 5800K or 3000K. They correspond to what the visible light spectrum of a blackbody looks like at those temperatures. In the kitchen, we see the heating element of the toaster oven grows red when it heats up. That’s because more energy is emitted in the visible light frequency range as the surface temperature rises.

Figure 3 Black Body Radiation

3. The Stefan-Boltzmann law calculates the total power leaving the surface. At a distance, the incident radiation on unit surface area decreases in proportion to the square of the distance. It’s not due to any mysterious quantum mechanical mechanism. It’s just that the surface area of a sphere is proportional to the square of the radius. If your bread is twice the distance from the heating element, you are only getting a quarter of the cooking power. Or if the bread is close to the heating element, and its size is relatively large compared to the dimension of the hearting element, different parts of the bread will receive significantly different radiative heat.

4. In addition to emitting radiation, all surfaces also reflect and absorb radiation. Bread in the toaster heats up because it absorbs radiation. Absorptivity is a surface characteristic and it changes when the surface changes. White bread reflects more and absorbs less. The bread might take a long time to brown. But when it’s browned, its absorptivity increases and it could burn in a hurry. Consequently, if different parts of the bread receive different amounts of radiation, over time the color difference of different parts will become more pronounced.

5. Infrared thermometers work by collecting radiation from the surface being measured. It has to make an assumption about the emissivity of the surface. As far as I know, most of them assume a value between 0.9 and 1. That works for most of the organic food ingredients, water, and oil. However, it doesn’t work for shiny stainless steel surfaces because their emissivity is less than 0.2. If you want to check if a stainless sauté pan is hot enough, pointing at the bare metal will give you a very low temperature. You need to pour some oil into it and aim the IR thermometer at the oil. By the way, high-end griddles and stainless pans are deliberately shiny. They retain more heat by emitting less.

6. Transparent materials not only reflect and absorb radiation, but also let some radiation pass. So some thermal radiation will leak out through the glass door of your toaster oven.

7. Radiation absorptivity is mostly a surface phenomenon. However, the wavelength of the radiation and the water content of the bread have some impact on the penetration depth.

8. The moisture level of the bread changes how much radiation is reflected. NIR(Near InfraRed) moisture meter takes advantage of this.

Advice for making better toasts in home toaster ovens.

1. If you slice your own bread, consider how thick it should be. If the slice is too thick, there is the danger that the internal is not warm while the surface is burned.
2. If you use a toaster oven and don’t like the browning pattern on your toast, experiment with different positions inside the oven.
3. Humidity inside the toaster oven has some effect on the internal temperature of the bread. As the surface of the bread dries out, the moisture inside starts to migrate out and takes energy away, effectively cooling down the interior of the bread. The speed water evaporates is determined by the relative humidity of the oven air. You could put a bowl of boiled water inside the oven as a crude way to control the humidity. But I don't’ see much of a difference in my own experiments. I suspect in the short time the toast is made, it’s more effective to control the heat input to the bread.

Ideas for a better toaster oven

A conventional toaster oven controls two things in the toasting process: output power and timing. They actually don’t even seem to exercise much control over the output power, other than ramping it up as quickly as possible. This will get us warm bread with somewhat unpredictable crust, but to get what we want (even golden crust with a soft interior), we need to have better control of the surface temperature of, and the heat dumped into the bread.

The first thing to fix is that we can not operate in an open loop. Every piece of bread is different, and every person’s idea of doneness level number 4 is different. Some sensors to collect information about the bread and the heating processes could be:

1. Infrared thermometer. To measure the surface temperature of the bread. To minimize error caused by reflection from the bread surface, the heating element of the oven should be turned off (blocked) during the temperature measurement.
2. Camera. Take pictures to determine the color of the crust. Users should be able to choose the shade of brown they desire in the final product, instead of an arbitrary number of doneness. To get controlled color measurement, the oven should not have a glass window, which leaks heat and causes cold spots inside the oven anyway.
3. The Scale and shape sensor. The shape sensor could work with Radar or structured light. With the weight and density of the bread, we can simulate how much heat input will bring the bread to the desired temperature. With knowledge of the shape and location of the bread, we can calculate the irradiation that actually arrives at the bread, instead of the radiation leaving the heating element.
4. Heat flux sensor. It will be good to know how much heat actually goes into the bread. It’s probably impractical to get an accurate overall number, but maybe data from a sample area can help.
5. Moisture meter. The moisture, surface temperature, and weight change over time will give us a better idea of the true state of the bread.

To fully take advantage of these data, we need more precise and flexible control:

1. The heating control should support multi-step, multi-level programs. The heating process should support a specific temperature profile over time, just like the reflow oven for PCB assembly. For instance, maybe the best way to make toast is to bring up the overall temperature of the bread slices before browning the surface, as in the reverse sear of steaks.
2. In general, the penetration depth of infrared radiation varies with the wavelength and the moisture content of the thread. It would be desirable to be able to control the radiation spectrum of the heating element over time.
3. To support the above two control characteristics, the heating elements should have low latency.
4. The heating on either side of the bread should be controlled separately. We don’t always want the two sides to heat up the same way.
5. The heating should have a finer spatial resolution so we can adapt to and remedy uneven browning.

Finally, to tie everything together we need to have good simulation models. It’s probably better to host them in the cloud so an improved model can be easily deployed. To that end, the oven needs a wireless datalink. It solves another problem: I really don’t want to put a big display on the oven. It feels like a mockery of the concept of smart appliances. Now those pictures captured by the camera can be sent to any of the myriad screens we already have in the house.

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