All of My Faults Are Stress Related

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.

Comments

  1. #1 peter
    April 14, 2009

    you can go for that second degree in applied biochemistry…

    btw, while you’re at it, there are differences in opinion as to whether or not creaming the sugar into the butter before adding the flour helps or hinders. tradition claims it is important to take that step, “cook’s illustrated” magazine appears to have experimented and found otherwise. I haven’t tried since I read that tidbit, so I’m on the fence there…

    out of curiosity, what sort of mixer are you using?

  2. #2 A life-long scholar
    April 14, 2009

    It seems to me that baked goods which collapse after baking nearly always do so when they are taken out of the oven (or, sometimes, just opening the oven door at the wrong time), so clearly sudden changes in temperature can be a factor, as can sudden changes in pressure (the air inside the oven will be at a different pressure than that outside of the oven, simply due to the change in temperature). Cookies are very sensitive to subtle changes in P and T. The geothermobarometers I’m using are often only good to +/- 1000 bars or 150 C, but I think if you could calibrate a cookietherombarometer you’d find it was good to +/- 1 bar or 5 C…

  3. #3 DDeden
    April 14, 2009

    Yay! waiting for S’more research, that’d be tasty too!

  4. #4 abb3w
    April 14, 2009

    You’re trying for an IgNobel prize, aren’t you?

  5. #5 peter
    April 14, 2009

    cakes and cookies fall when exposed to temperature drops because parts of them are still uncooked. unless the food is cooked long enough for the starch structure to become rigid, then the food will collapse when the expanded air and liquid in the food contract.

    the general difficulty is that frequently the surface will cook much faster than the interior. the easiest way to mitigate that particular problem is to cook thin things. I’m curious now whether bakeries in the rockies tend towards having more layers in a cake of a given size…

  6. #6 Mary Fitz...
    April 14, 2009

    Have you taken into account that the various ingredients in the dough are not mixed into a 100% homogeneous mix? Most Chocolate Chip Cookie dough is supposed to be a little lumpy.

    as far as the pursuit of the perfect cookie…

    Are you using butter or margarine? I’ve found that margarines often makes for flatter cookies than butter.

    You might try using 3/4 to 1/2 the sugar the recipe calls for (1/2 cup brown and 1/4 cup white) You can also sub milled flax seed for 1/4 of the flour and 1/4 of the oil/butter/shortening the recipe calls for. At least at Midwestern altitudes this makes for a soft but not damp cookie that stays soft even after it cools.

  7. #7 Lab Lemming
    April 15, 2009

    1. The expension takes place in a fully (except for the chips) ductile regime, so you won’t see brittle movement morphologies.

    2. CO2 escape is governed by the viscosity of the molten cookie. Your dough needs more SiO2 polymerization. Add sand.

    Alternatively, the diffusion of CO2 out of the dough depends on the pCO2 in the surrounding air. Si if you spray your cookies with a CO2 fire extinguisher after pulling them out, the ambient fugasity will be higher, and the gas might be trapped by cooling before it can escape.

  8. #8 Kim Hannula
    April 15, 2009

    Lab Lemming: doesn’t it depend on whether the top of the dough crusts over early in the baking process? I think that the top of the cookie is analogous to the crust that forms on a lava lake: a thin brittle layer on top of something ductile.

  9. #9 Lab Lemming
    April 23, 2009

    You’re heating from the outside…

  10. #10 Chrissl
    April 28, 2009

    On the geology of cookies: I once accidentally dropped a cookie sheet full of chocolate chip cookies that had just that moment come out of the oven. The result was a rather spectacular set of deformations that resulted in totally scrambled cookies. (I ate them rather than analyzing them, though.)