From: kqb@cbnewsl.cb.att.com (kevin.q.brown)
Subject:  How Cold Is Cold Enough?
Organization: AT&T Bell Laboratories
Date: Tue, 21 Jul 1992 23:33:54 GMT

> From: alcor@cup.portal.com
> Message-Subject: How Cold Is Cold Enough?
> Date: Mon, 20 Jul 92 00:35:35 PDT

How Cold Is Cold Enough?
by Hugh Hixon

Reprinted from *Cryonics* magazine, January, 1985.


     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?

     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)

     where
                    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.
                       
     To summarize, E is what we're stuck with for the reaction, and k is 
the reaction rate at any given T(emperature).

     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 2.17828..., 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)

     where

                    1
              -------------  =  0.0129265..
                (77.36*K)

     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.

------------------------------------------------------------------------------
Degrees  Degrees                             Rate relative      Time to equal
Celsius  Kelvin   Remarks    1/T   Exponent  to LN2 (77.36*K)   1 sec. at 37*C
------------------------------------------------------------------------------
 37       310.16  Body temp. 0.0322 34.1173  776,682,000,000,000   1 second

 20       293.16           0.003411 33.5817  360,555,000,000,000   2.154 sec

  0       273.16  Water    0.003660 32.6389  149,588,000,000,000   5.192 sec
                  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  Limit,   0.004804 28.6122  2,667,460,000,000    4.853 min
                  simple mechanical freezers

-79.5     193.66  Dry ice  0.005164 27.3451  751,335,000,000     17.229 min

-100      173.16           0.005775 25.1917  87,222,100,000     2.474 hours

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

-128      145.16  CF4      0.006889 21.2678  1,723,820,000      5.213 days
                  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  Methane  0.009169 13.2649  576,591           42.714 years
                  boils

-180      93.16            0.010734  7.7227  2,259             10.9 thousand
                                                                      years

-185.7    87.46   Argon    0.011434  5.2584  192              128.16 thousand
                  boils                                               years

-195.8    77.36   Liquid   0.012926  0.0     1                24.628 million
                  nitrogen                                            years

-200      73.16            0.013669 -2.6141  0.07324         336.285 million
                                                                      years

-220      53.16            0.018811 -20.728  0.00000000099   24760.5 trillion
                                                                      years

-240      33.16            0.030157 -60.694  0.<26 zeros>44 5,390,000,000,000,000,000
                                                              trillion years

-252.8    20.36   Liquid   0.049116 -127.48  0.<54 zeros>22   Long enough
                  hydrogen

-260      13.16            0.075988 -222.14  0.<95 zeros>29   Even longer

-268.9    4.26    Liquid   0.234741 -781.35  0.<338 zeros>19  Don't worry
                  helium                                       about it
-----------------------------------------------------------------------------

     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.  

     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.