Gravi-chemistry
DEFINITIONS
Gravi-chemistry (gravi-chem) is chemistry involving a large environmental
acceleration. Gravi-chem is essentially chemistry in a centrifuge. Some
important variables are defined below, along with some initial computations
that are essential to discuss gravi-chem.
Variables:
r = radius in meters
rpm = revolutions per minute of the centrifuge
g = acceleration due to gravity = 9.80665 m/s^2
Mg = acceleration of 1 million g's = 9.80665x10^6 m/s^2
Pi = 3.14159
r_1 = radius of top (innermost) surface of electrolyte in meters
r_2 = radius of bottom (outermost) surface of electrolyte in meters
E_ion1 = anion balanced E_ion for given g, in (V/m)/Mg
E_ion2 = cation balanced E_ion for given g, in (V/m)/Mg
a = acceleration in Mg
U = total voltage drop sustainable in volts
Note: both E_ion1 and E_ion2 were taken from Gravi-chem table below.
>From the given:
a = 10^-6 * r/g * (2 * Pi * rpm / 60)^2
So the incremental potential dU sustained for small radial increment dr is:
dU = [(E_ion1 + E_ion2)/g * 10^-6 * (2 * Pi * rpm / 60)^2] r dr
And integrating for r = r_1 to r_2:
U = [(E_ion1 + E_ion2)/g * 2x10^-6 * (Pi * rpm / 60)^2] [(r_2)^2 - (r_1)^2]
where U is given in volts. Note: if U is negative then hydroxils (OH-) are
concentrated at the bottom of the cell. If U is positive, then hydronium
(H3O+) is concentrated at the bottom of the cell.
THE GRAVI-CHEM TABLE
Gravi-chem Table for Selected Ions
R-ion Vol_ion rho_ion F_b E_ion
Atomic Ionic Ion Ion Bouyancy Balanced E vs g
Atomic Ion Weight Radius Volume Density in water H2O @ 100 C
Number Name q (g/mol) (ang.) (cm^3/mol)(g/cm^3) (g/cm^3) (V/m/mega-g)
3 Li 1 6.941 0.76 1.11 6.27 -5.31 -0.59761
4 Be 2 9.012 0.45 0.23 39.21 -38.25 -0.44680
5 * B 3 10.810 0.30 0.07 158.72 -157.76 -0.36403
6 * C 4 12.011 0.35 0.11 111.05 -110.10 -0.30256
7 * N 5 14.007 0.12 0.00 3213.31 -3212.35 -0.28464
8 O -2 15.999 1.40 6.92 2.31 -1.35 0.47595
9 F -1 18.998 1.33 5.93 3.20 -2.24 1.35288
11 Na 1 22.990 1.02 2.68 8.59 -7.63 -2.07589
12 Mg 2 24.305 0.72 0.94 25.81 -24.86 -1.18931
13 Al 3 26.982 0.54 0.40 67.93 -66.97 -0.90123
14 Si 4 28.086 0.26 0.04 633.47 -632.51 -0.71256
15 P 5 30.974 0.17 0.01 2499.24 -2498.28 -0.62939
16 S -2 32.060 1.84 15.71 2.04 -1.08 0.86390
17 Cl -1 35.453 1.81 14.96 2.37 -1.41 2.14633
19 K 1 39.098 1.51 8.69 4.50 -3.54 -3.12789
20 Ca 2 40.080 1.00 2.52 15.89 -14.93 -1.91398
21 Sc 3 44.956 0.75 1.06 42.24 -41.29 -1.48853
22 Ti 4 47.900 0.61 0.57 83.66 -82.70 -1.20318
23 V 5 50.942 0.54 0.40 128.25 -127.29 -1.02779
24 Cr 3 51.996 0.62 0.60 86.49 -85.53 -1.74208
25 Mn 2 54.938 0.67 0.76 72.41 -71.45 -2.75496
26 Fe 3 55.847 0.55 0.42 133.07 -132.11 -1.87845
27 Co 2 58.933 0.65 0.69 85.07 -84.11 -2.96121
28 Ni 2 58.700 0.69 0.83 70.84 -69.88 -2.94274
29 Cu 2 63.546 0.73 0.98 64.76 -63.80 -3.18158
20 Zn 2 65.380 0.74 1.02 63.96 -63.00 -3.27279
31 Ga 3 69.720 0.62 0.60 115.97 -115.01 -2.34257
32 Ge 4 72.590 0.53 0.38 193.29 -192.33 -1.83534
33 As 3 74.922 0.58 0.49 152.22 -151.27 -2.52233
34 Se -2 78.960 1.98 19.58 4.03 -3.07 3.05900
35 Br -1 79.904 1.96 18.99 4.21 -3.25 6.27117
37 Rb 1 85.468 1.61 10.53 8.12 -7.16 -7.66138
38 SR 2 87.620 1.26 5.05 17.36 -16.41 -4.20703
39 Y 3 88.906 1.02 2.68 33.21 -32.25 -2.92518
40 Zr 4 91.220 0.84 1.50 61.01 -60.05 -2.28146
41 Nb 5 92.906 0.64 0.66 140.50 -139.54 -1.87570
42 Mo 6 95.940 0.59 0.52 185.18 -184.23 -1.61679
44 Ru 3 101.070 0.68 0.79 127.43 -126.47 -3.39846
45 Rh 3 102.906 0.67 0.76 135.64 -134.68 -3.46176
46 Pd 2 106.400 0.64 0.66 160.90 -159.94 -5.37498
47 Ag 1 107.868 1.15 3.84 28.12 -27.16 -10.58986
48 Cd 2 112.410 0.95 2.16 51.98 -51.02 -5.60727
49 In 3 114.820 0.80 1.29 88.90 -87.94 -3.84812
50 Sn 4 118.890 0.45 0.23 517.21 -516.25 -3.01536
51 Sb 3 121.750 0.76 1.11 109.95 -108.99 -4.08889
52 Te -2 127.600 1.07 3.09 41.29 -40.33 6.33405
53 I -1 126.905 2.20 26.86 4.72 -3.77 10.28197
55 Cs 1 132.905 1.74 13.29 10.00 -9.04 -12.21387
56 Ba 2 137.330 1.42 7.22 19.01 -18.06 -6.62724
73 Ta 5 180.948 0.64 0.66 273.64 -272.68 -3.66538
74 W 6 183.850 0.60 0.54 337.42 -336.46 -3.10554
78 Pt 4 195.090 0.63 0.63 309.30 -308.34 -4.94182
79 Au 3 196.967 0.85 1.55 127.14 -126.19 -6.62285
80 Hg 2 200.590 1.02 2.68 74.93 -73.97 -10.06348
82 Pb 2 207.200 1.19 4.25 48.74 -47.78 -10.32274
83 Bi 3 208.980 1.03 2.76 75.81 -74.86 -6.99067
90 Th 4 232.038 1.05 2.92 79.46 -78.50 -5.82491
92 U 6 238.029 0.81 1.34 177.56 -176.60 -4.01040
Notes:
* - means estimated ion radius. (Wildly guessed based on proportions)
1. In equilibrium , the force of acceleration equals the electrostatic force:
Fg = m*a = Fe = q * E
Thus we can compute the field strength corresponding to an acceleration:
E = m*a/q
2. Acceleration is normalized to 10^6 g's in the table, or 9.80665x10^6
m/s^2, a "mega-g" or Mg.
However, m in this case is M_b, bouyant mass:
M_b = F_b * Vol_ion / Na
where Na is Avogadro's number, so we see how the units work out by:
M_b (g/ion) = F_b (in g/cm^3) * Vol_ion (cm^3/mol)
/(6.0221367x10^23 ions/mol)
3. The density of water used in computing bouyancy, 0.9584, is the value
for water at 100 C at 1 Bar.
4. Warning: There may be typos and other errors! Also, there may be
significant errors in the source data, especially for ionic radius.
Posting of corrections is encouraged!
SAMPLE COMPUTATION
Now that the gravi-chem computation method is available, lets compute what
might actually be a feasible test of principle.
Assume cesium chloride as the electrolyte, a rotation of 20,000 rpm. Assume
r_1 (radius at top of electrolyte) is 30 percent of r_2 (radius at bottom
of electrolyte.) We want r_1 and r_2 so that we obtain -1.6 volts.
Looking at the Gravi-chem table we see:
17 Cl -1 35.453 1.81 14.96 2.37 -1.41 2.14633
55 Cs 1 132.905 1.74 13.29 10.00 -9.04 -12.21387
=========
-10.06754 V/m/Mg
Now, using the Gravi-chem formula:
U = [(E_ion1 + E_ion2)/g * 2x10^-6 * (Pi * rpm / 60)^2] [(r_2)^2 - (r_1)^2]
or with variables in unitless values:
U = [(E_ion1 + E_ion2) * 5.591x10^-10 * (rpm)^2] [(r_2)^2 - (r_1)^2]
we have:
U = [(-10.06754) * 5.591x10^-10 * (20,000)^2] [(r_2)^2 - (0.3*r_2)^2]
U = -2.252 * (1-.09) (r_2)^2
but we want U = -1.6 volts so:
-1.6 = -2.052 (r_2)^2
(r_2)^2 = 0.7797
r_2 = .883 m
r_1 = 0.3 r_2 = .265 m
and we have the answer of r_2 = 88.3 cm and r_1 = 26.5 cm.
If the above is correct, then this is pretty tough to pull off.
Bumping to 30,000 rpm we have:
-1.6 = -5.0658 r^2
(r_2)^2 = .3158
r_2 = .562 m
r_1 = 0.3 r_2 = .169 m
which is still very difficult.
GENERAL DISCUSSION
There is a lot of information still needed to do any serious
gravi-chemistry. Most important is to develop an experimental
understanding of how hydronium and protons in particular react in a
gravi-electrolytic environment. Similarly, information needs to be
developed for the hydroxil and other radicals.
One thing it seems to me is clear. High g force, well under 1 Mg (a
"mega-g") can significantly and selectively change ion concentrations in
inner and outer volumes of the centrifuge. This means that reaction
equilibriums can be shifted and manipulated by the addition of ions or
molecules of differing densities and charge. There could be very
significant breakthroughs of a practical kind just waiting for discovery.
Gravichemistry also provides an opportunity for pure science and
engineering to grind forth in its usual lumbering manner.
Precipitation rates can be enhanced significantly for selected compounds,
though removing precipitates in a continuous process could require
significant engineering. By selectively increasing ion pair
concentrations, reactions can be catalyzed even without a catalyst.
Crystal growing might be accelerated.
The proton is interesting because its density is practically infinite.
However, it ionically binds to the negative end of the water molecule to
form the hydronium ion, H3O+. It does not seem possible to break the
hydronium bond with any high-g field. The excess proton can tunnel between
water molecules, but the relative orientation must be right to do so. The
proton's migration rate is slowed down due to the need for the water
molecules to rotate relative to each other. However, even though the
proton only moves at few percent of a cm per second in typical
electrolytes, that rate is significantly faster than other radicals. It is
important to measure that rate over a range of electrolyte accelerations.
High-g forces should affect the tunneling ability of the proton.
An electrolyte is a conductor. The huge electrostatic fields that result
from even a tiny charge imbalance will overwhelm the small electrostatic
fields generated by gravitational means. We thus can expect the electrolyte
to remain neutral. The potential generated at the electrodes will be due
to ion concentration differences at the anode and cathode, and can in fact
determine which is the anode and cathode.
Consider an NaF electrolyte. The Gravi-chem table entries are:
9 F -1 18.998 1.33 5.93 3.20 -2.24 1.35288
11 Na 1 22.990 1.02 2.68 8.59 -7.63 -2.07589
We thus see that as Na+ and F- ions are pushed to the periphery of the
centrifuge, they will create a gradient of 1.35288 V/m/Mg - 2.07589 V/m/Mg
= -0.723 V/m/Mg. (Note that the 5 digit accuracy implied in the table is
way overstated. I should have cut down the field size on the spread
sheet.) Does this mean that the periphery of the electrolyte will be
negative? This does not seem to make sense. This gradient will likely be
neutralized by hydronium ions, which should have nearly zero buoyancy. As
to which electrode is anode or cathode, and which ions are oxidized or
reduced, that is decided by the electronegativites of the ions and the
electrodes.
Looking at the entry for bromine:
35 Br -1 79.904 1.96 18.99 4.21 -3.25 6.27117
We see that NaBr electrolyte will produce a positive gradient toward the
outer regions of the centrifuge: 6.27117 V/m/Mg - 2.07589 V/m/Mg = 4.2
V/m/Mg. This gradient should be neutralized by hydroxil radicals, which
should also have nearly neutral buoyancy. This makes one think that
possibly multiple or stacked centrifuge rotors might be electrically
connected in series to generate a battery of sorts.
Well, all that is musing and somewhat speculative, but I think it
establishes a basis for thinking that gravi-chemistry has a genuine future.
CONSERVATION OF ENERGY
The most remarkable thing about gravi-chem is that it seems to violate
conservation of energy. More thinking is required in this area.
The following seems to be a reasonable proposition.
Proposition 1: Mass flow outward in a centrifuge requires energy, in the
form of torque times radius, in order to accelerate the mass in a
tangential fashion, i.e to bring it up to speed at the radius occupied.
Similarly, mass flow inward supplies torque to the centrifuge shaft. If
the *net* mass flow at every radius is maintained at zero, the centrifuge
requires no energy other than that required to overcome friction of
rotation.
If this is correct, then we next have to examine:
Proposition 2: Centrifuges can change chemical equilibrium, and thus energy
balances.
Proposition 3. Differing chemical balances in the vicinity of two
identical electrodes can result in current flow and thus useful energy
production.
Proposition 4. Chemical processes can be sustained in a centrifuge while
maintaining the condition that net mass flow at every radius is zero.
Proposition 5: Chemical energy obtained from centrifuge modified chemical
balances is free energy.
Of the 5 propositions, it looks like 3 is the most suspicious, or at least
2 and 3 combined.
It is interesting that a series of isolated cells could be arranged around
a rotor, or organized in stacked rotors, and electrodes placed in series,
so as to accomplish complex chemical processes.
Gravi-chem is most interesting because, if the effect is real, it is highly
engineerable. A normal slow process of technology development should bring
it to fruition. The source of free energy, assuming there is such, is
basically understood and formalized, quantified. If an experimental proof
of principle works as already quantified, then things do not require any
miracle to proceed. Further, many applications exist that have nothing to
do with energy production, only shifting chemical energy balances.
Regards,
Horace Heffner
