Cryonics, January 1985

How Cold Is Cold Enough?

by Hugh Hixon

Why don't you store people: (pick one)

  • In your freezer at home?
  • In a low temperature laboratory freezer?
  • In the permafrost in Alaska?
  • On the Greenland icecap?
  • On the Antarctic icecap?
  • In Siberia?
  • Packed in dry ice?
  • Other?
How cold is cold enough?
After all, it's really cold there, and all this fooling around with liquid nitrogen seems like a lot of unnecessary hassle. And besides, it's (free/costs less)(circle appropriate words).

                       — various people, some of them ostensibly with scientific educations.

Misapprehensions concerning why we use liquid nitrogen for cryonic storage fall into roughly three classes: 1) Economic considerations; 2) Legitimate bafflement caused by the use of a simple arithmetic temperature scale where a more complex scale is much more appropriate; 3) Disnumeria, or disability to deal with numbers. This may range from reluctance to use a calculator to inability to count above five, because you need the other hand for counting. The temperature scale for people so afflicted goes something like: very hot-hot-warm-comfortable-cool-cold-very cold-freezing. I will attempt to answer 2) and 3) together, with an explanation and examples, and then treat the economic aspect in a short afterword.

For a suspension patient, the object of cryonics is to arrest time. It is never possible to do this completely, but as we will see, our best is remarkably good. We cannot affect nuclear processes, such as radioactive decay, but for the period of time we are concerned with, radioactivity and its attendant problems are largely irrelevant. Our primary focus is on chemical processes. The human body is a dynamic structure, with creation and destruction of the chemical compounds essential to life going on in it simultaneously and continually. A good analogy would be a powered airplane, lifted by the efforts of its engines and pulled down by gravity. When the engine quits, sooner or later you're going to get to the bottom. When we die, only the destructive functions remain. Fortunately, these are all chemical processes, and proceed in such a fashion that they are well described by the Arrhenius equation.

STOP!!! DO NOT GO INTO SHOCK OR ADVANCE THE PAGE!!! The elements of the Arrhenius equation have familiar counterparts that you see every day, and while it cranks out numbers beyond the comprehension of even your Congressperson, beyond a certain point they are either so large or so small that we can safely ignore them.

To continue. The Arrhenius equation takes the form:

          k = A exp(-E/RT)


  • k is the rate of a given chemical reaction
  • A is a fudge factor to make the numbers come out right
  • exp is the symbol for a particular arithmetic operation, like +, -, X, or /
  • E is the Energy of Activation of the reaction, like the push it takes to start a car when the battery is dead (small for VW's, large for Cadillacs)
  • R is the Ideal Gas Constant. Another fudge factor, but a well defined one, like a dollar bill. Here, its value is 1.9872 calories/degree-mole.
  • T is the Absolute Temperature in degrees Kelvin (K). Which is just the Celsius (centigrade) temperature + 273.16. I should remark that the Absolute Temperature Scale is a rather arbitrary definition of a real property, and that R is used to make things come out right.

By itself, k isn't very useful so I will relate it to itself at some other temperature. For the purposes of this article, I will pick two temperatures, 77.36°K and 37°C. These are, of course, liquid nitrogen temperature and normal body temperature, respectively.

Dividing the rate at some given temperature by the rate at liquid nitrogen temperature will give ratios which will have some meaning. At the given temperature, chemical reactions will occur so many times faster or slower than they would at liquid nitrogen temperature. I will then invert the process and divide the rate ratio at 37°C by the rate ratio at the other temperatures, and say that if the reaction proceeds so far in one second at 37°C, then it will take so many seconds, minutes, days, or years to proceed as far at some lower temperature.

Now, if you'll just close your eyes while I use this page to perform a simple algebraic manipulation:

                              A exp(-E/RT)
          k[T]/k[77.36°K] = ----------------------
                              A exp(-E/R(77.36°K))

A is the same in both cases and cancels itself out. The rest of the right side of the equation also contains several identical terms (E and R), and I will simplify it by rearranging,

          k[T]/k[77.36°K] = exp(-E/R(1/T - 1/(77.36°K)))

Now, R is a constant and we will not worry ourselves more about it. E we will select later, and give reasons for doing so. The rest of the equation, we will examine to understand its properties better.

"exp" is the operation for an exponential function. A familiar example of this is to take a number and add zeros to it, thus:

          5   50   500   5,000   50,000   500,000   5,000,000   50,000,000   etc.

this is called exponentiating 10. With the "exp" operation a similar thing occurs, but the number is not 10, but 2.71828..., a number with useful mathematical properties, but not of interest to us otherwise.

The other important part of the equation is:

                    1           1
                  -----  -  ----------
                    T       (77.36°K)


              -------------  =  0.0129265..

1/T is called a reciprocal function, and its particular property is that when T is larger than 1, 1/T is less than 1, and the larger T gets, the more slowly 1/T gets small. It does not, however, ever become zero.

Thus, the behavior for

          1/T - 0.0129265...

is that at high temperatures, it approaches the value -0.0129265.. closely, but at temperatures much below 77.36°K, it get larger fairly rapidly, and then extremely rapidly.

Putting the equation back together again, we can predict that far above 77.36°K, say at 37°C, the rate ratio will change relatively slowly, but that as the temperature drops, the rate ratio will change increasingly rapidly. That is, we will see that the change from 0°C to 20°C is about 2.4, the change from -100°C to -80°C is about 8.6, and the change from -200°C to -180°C (around liquid nitrogen temperature) is about 31,000. >From -240°C to -220°C, the change is a factor of 227,434,000,000,000,000. As I mentioned at the beginning of this explanation, the temperature scale that we normally use can be very misleading.

Now. Somewhere in the distant past, I was actually taught to do this kind of calculation with pencil, paper, a slide rule, and a book of tables. But I have a computer now, and I'm going to give it a break from word processing and let it go chase numbers. Some of them were bigger than it was.

One last question remains before I turn the computer loose. What should my value for E, the Energy of Activation of the reaction be, or rather, since each chemical reaction has its own E, what reaction should I choose?

I am going to be pessimistic, and choose the fastest known biological reaction, catalase. I'm not going to get into detail, but the function of the enzyme catalase is protective. Some of the chemical reactions that your body must use have extraordinarily poisonous by-products, and the function of catalase is to destroy one of the worst of them. The value for its E is 7,000 calories per mole-degree Kelvin. It is sufficiently fast that when it is studied, the work is often done at about dry ice temperature. My friend Mike Darwin remarks that he once did this in a crude fashion and that even at dry ice temperature things get rather busy. Another reason to use it is that it's one of the few I happen to have. E's are not normally tabulated.

I had never specifically done this calculation before, and I confess that I was a bit startled by the size of some of the numbers. Enough to check my procedure fairly carefully. I am reasonably confident of the picture that they show.

Degrees Degrees                    Rate relative      Time to equal
Celcius Kelvin    1/T    Exponent  to LN2 (77.36°K)   1 sec. at 37°C
 37     310.16   0.0322   34.1173  776,682,000,000,000      1 second
        (Body temperature)
 20     293.16   0.003411 33.5817  360,555,000,000,000     2.154 sec

  0     273.16   0.003660 32.6389  149,588,000,000,000     5.192 sec
        (Water freezes)
-20     253.16   0.003950 31.6201  54,007,200,000,000     14.381 sec

-40     233.16   0.004289 30.4266  16,371,100,000,000     47.439 sec

-60     213.16   0.004468 29.0091  3,967,220,000,000       3.263 min

-65     208.16   0.004804 28.6122  2,667,460,000,000       4.853 min
        (Limit of simple mechanical freezers)
-79.5   193.66   0.005164 27.3451  751,335,000,000        17.229 min
        (Dry ice)
-100    173.16   0.005775 25.1917  87,222,100,000          2.474 hrs

-120    153.16   0.006529 22.5353  6,123,060,000          1.468 days

-128    145.16   0.006889 21.2678  1,723,820,000          5.213 days
        (CF4, lowest boiling Freon)
-140    133.16   0.007510 19.0810  193,534,000           46.448 days

-160    113.16   0.008837 14.4056  1,804,070            13.652 years

-164    109.16   0.009169 13.2649  576,591              42.714 years
        (Methane boils)
-180    93.16    0.010734  7.7227  2,259               10.9 thousand
-185.7  87.46    0.011434  5.2584  192               128.16 thousand
        (Argon boils)                                          years
-195.8  77.36    0.012926  0.0     1                  24.628 million
        (Liquid nitrogen)                                      years
-200    73.16    0.013669 -2.6141  0.07324           336.285 million
-220    53.16    0.018811 -20.728  0.00000000099    24760.5 trillion
-240    33.16    0.030157 -60.694  0.[26 zeros]44     5,390,000,000,
                                            000,000,000 trillion yrs
-252.8  20.36    0.049116 -127.48  0.[54 zeros]22        Long enough
        (Liquid hydrogen)
-260    13.16    0.075988 -222.14  0.[95 zeros]29        Even longer

-268.9  4.26     0.234741 -781.35  0.[338 zeros]19       Don't worry
        (Liquid helium)                                     about it

The first thing to notice about the table is that somewhere slightly below -240°C, the computer gave up. I did say that the equation goes rather fast at low temperatures. The last three numbers in the "Rate relative... " column I did by hand. You can see what the computer was attempting to do in the "exponent" column, trying to perform the "exp" operation. As noted, the relative rate at liquid helium temperature would be about 0.0.... (eight and a quarter lines of zeros)....19. The next thing to notice is that a reaction that would take one second at body temperature takes 24,000,000 years at liquid nitrogen temperature. This is clearly a case of extreme overkill, and seems to support advocates of storage at higher temperatures.

However, note how fast things change as the temperature drops closer to 77°K. At dry ice temperature, "only" 115 degrees higher, 100 years is about equal to 40 days dead on the floor. Clearly unacceptable.

So what is acceptable? Here is my opinion. People have fully recovered after being dead on the floor for one hour, when the proper medical procedure was followed. [Note: This was based on some work by Dr. Blaine White, of Detroit, that was reported in the January 18, 1982 issue of Medical World News. It was not subsequently reproduced. However, the current record for drowning in ice water with subsequent resuscitation is now over one hour. -HH (1992)] There are reasonable arguments to support the idea that brain deterioration is not significant until somewhere in the range of 12 to 24 hours, although changes in other organs of the body probably make revival impossible. Say 12 hours at 37°C is a limit. How long can we have to expect to store suspension patients before they can be revived? Again I guess. Biochemistry is advancing very fast now, but I do not see reanimation as possible in less than 25 years, with 40-50 years being very likely. If we cannot be reanimated in 100 years, then our civilization has somehow died, by bang or whimper, and probably neither liquid nitrogen, nor dry ice, nor even refrigeration may be available, and our plans and these calculations become irrelevant. Let us set a maximum storage period of 100 years.

Thus: In 100 years there are about 876,600 hours. In 12 hours, there are 43,200 seconds. The temperature must be low enough that each 20 hours is equal to one second at 37°C. (The ratio is about 73,000 to 1). From the table, the storage temperature should be no higher than -115°C. Add to this additional burdens, all eating into your 12 hours: time between deanimation and discovery; time to get the transport team on location; transport time; time for perfusion; time to cool to the storage temperature. -115°C is for when things go right.

There is one bright spot. Below -100°C, the water in biological systems is finally all frozen, and molecules can't move to react. We use cryoprotectants that have the effect of preventing freezing, but somewhere around -135°C they all have glass transition points, becoming so viscous that molecules can't move and undergo chemical change. While the table indicates that staying below -150°C is safe from a rate of reaction standpoint, in fact any temperature below -130°C to -135°C is probably safe due to elimination of translational molecular movement as a result of vitrification.

Okay, you say, why not use a mechanical system to hold a temperature of -135°C? First problem: They don't hold a temperature. They cycle between a switch-on temperature and a switch-off temperature. This causes expansion and contraction, and mechanical stresses. Cracking. We don't know what is acceptable yet. This problem can probably be eliminated by the application of sufficient money. Second problem: If the power goes, you start to warm up. Immediately. Emergency generator? Sure, but you'll need at least 8 kilowatts, and it has to reliably self-start within minutes, unattended. Expensive. Third problem: Have you priced a mechanical system? $20,000 up front, and then you start paying the electric bill. Small units like this are rather inefficient so the electric bill is not a minor consideration. Fourth problem: Eventually, the system is going to die on you. Next year. Next month. Next week. Tomorrow. Read the warranty. It doesn't say a thing about a loaner within five minutes. Buy another one for backup. You may get a deal for buying two at once.

How about using some other compound with a boiling point above that of nitrogen? With careful examination of the HANDBOOK OF CHEMISTRY AND PHYSICS I came up with 30 compounds with boiling points below -80°C. When you eliminate the ones that boil above -115°C, the mildly poisonous ones, the very poisonous ones, the corrosive ones, the oxidizers, the explosively flammable ones and the very expensive ones, you're left with nitrogen and the rather expensive ones. To retain the rather expensive ones, you either need a mechanical system, with all the problems mentioned before except that you are much more tolerant to power-outs and breakdowns, or you use a liquid nitrogen condenser. If you use a condenser, you may as well use liquid nitrogen directly and save the cost of the special gas and the condenser system.

How about moving to the arctic, and using the low temperatures there to assist the refrigeration? This is a potentially good idea, but there are severe problems of cost and logistics. It's nice of you to volunteer to go up there, though.

THAT'S why we use liquid nitrogen.

As a footnote to all the above arguments, it is worth noting that Alcor (in Riverside, CA) is in an unusually favorable position with respect to liquid nitrogen. Los Angeles is a major industrial center, and liquid nitrogen is a major industrial chemical, particularly in the aerospace industry. As a result, there are at least two major liquid nitrogen plants in the LA area; one out at Fontana, about 30 miles northeast of us, and one on the Long Beach Harbor area, about 30 miles to the southwest. Each plant is several acres in size, and as efficient as only a plant that size can be. Our delivered cost for liquid nitrogen is about $0.31/liter. A short calculation will show that at that price, you can get a lot of years of liquid nitrogen for just the buy-in price of the schemes mentioned above. This does not mean that we will always use LN2, however. If our further studies on the cracking problems we have reported here previously (CRYONICS, September 1984), we will certainly have to consider storage temperatures above 77°K. As I have indicated though, the economic penalties may be severe.