My reviewers commenters on yesterday’s post on chocolate chip cookie deformation had some great points. (Some of them also seem to have been very hungry. For those who want me to experiment more, and to get to analyze the results: looks like I’ve got something that I can promise once the Donors Choose challenge rolls around.)

Key criticism #1, from DDeden:

First the cookies puffed up, and then they collapsed. While they puffed up, their surface area increased [No, it decreased!], so the cookie crust was pulled apart. When the cookies collapsed, the surface area decreased again [No, it increased!], and the cookie crust wrinkled as the dome tried to fit itself into a pancake.

The point is that a sphere has the lowest possible surface area for a given volume, a pancake (like the final cookies, alas) has a much larger surface area, and a dome shape has a surface area between the two.

And that analysis makes sense… but only if the volume is constant.

As two other commenters pointed out, there was also metamorphism going on. I ignored it, because I’m not great with non-silicate systems (especially C-H-O-Na-Cl- whatever is in eggs). But, yeah, there’s definitely some metamorphism going on, and it ultimately involves the loss of volatiles (probably H20 and CO2 in this case). But before the volatiles are lost, I think they are temporarily trapped in the dough. (Isn’t that what causes the rising? That’s the whole point of the baking soda, right? The baking soda that I need to decrease?) So the reaction

flour + egg + vanilla + sugar + salt + baking soda + butter -> cookie + H2O + CO2

appears to involve a positive change in volume. (My Inner Metamorphic Petrologist would like to note that this implies that the products should be more stable at lower pressures, which probably has implications for baking at elevation.)

If the volume changes, then that messes up all the calculations of surface area. (A more voluminous sphere has a larger surface area than a littler sphere, right?) But I think I’ve got some other constraints on the geometry.

So, here’s a new try at my structural interpretation:

1) The dough started out as irregular, mishapen blobs. I am not going to try to estimate their volume or surface area.

2) However, when the cookie began to bake, the dough spreaded out (to make a larger footprint on the cookie sheet), and also rose. This may have involved primarily a change from a spheroid to a dome shape, but I suspect it also involved an increase in volume as the metamorphic cookie-forming reactions liberated water and carbon dioxide. Either case should have resulted in an increase in surface area, because a dome shape has a larger surface area than a sphere (which I suspect the baking dough smoothed into, except for the parts with the chocolate chips, which I will ignore because they add complications as well as deliciousness), and a larger volume spheroid should have a larger surface area than a smaller spheroid.

3) When the volatiles (water + CO2) started to escape, the dome collapsed. The bottom of the cookie became stuck to the pan, so the radius of the syn-cooking dome was equal to that of the post-cooking pancake-like cookie. If I approximate the syn-cooking dome as a hemisphere, and the final cookie as a cylindar, and leave out the area of the bottom (because they’re the same), then the surface areas should be:

dome-shape area = 1/2*4 π r^2 = 2 π r^2

and

final cookie = π r^2 + 2 π r h (with h = height of the cookie)

The relative surface areas depend on the height of the final cookie. For heights less than half the radius of the cookie, the dome has a larger surface area. (I can’t do the actual measurement, because we’ve eaten all the cookies, but they were pretty flat. And I watched them deflate after I took them out of the oven, so I’m pretty sure there was a volume loss involved.)

So in the case of my cookies, there should really have been a decrease in surface area as the cookies lost their volatiles. And that would explain the concentric folds around the edges of my cookies.

Clearly, more experimentation is needed. If I increase the strength of my dough at baking temperatures (by adding more flour and less sugar), perhaps I will not get a collapse at the end. And if I use less baking soda, I’ll decrease the amount of CO2 that’s released, and that should keep the volume from increasing as much. And then there’s the effect of heat conduction through the cookie sheet, and the relative timing of metamorphism and deformation.

I can see that I’m going to be eating a lot more chocolate before this research is publishable.