The State of Matter

{Keith Dixon-Roche © 17/04/18}

This webpage provides the evidence that the Newton-Coulomb atomic model can be used to predict the properties of same-element matter.

Sources: Planck's Atom; Newton's Atom; Laws of Motion; Physical Constants
Related Books: Philosophiæ Naturalis Principia Mathematica Rev. IV; The Atom; The Mathematical Laws of Natural Science
Related Calculators: Atomic Elements; Orbital Motion; Atoms; Physics
CalQlata comment: This is the only study we (at CalQlata) know on this subject that manifestly works.

Introduction

The purpose of this study is to answer the following question:
1) Can the Newton-Coulomb atomic model be used to predict the properties of elemental matter using mathematics?

Conclusion

The answer to the above question is yes.
An online calculator for this subject is now available on this website.

The relationship between gas transition temperature and density of matter
Fig 1. Gas Transition Temperature and Density

The Model

Matter is a collection of atoms.
In its basic form, it is a crystal lattice of same-element atoms, the properties of which can be easily predicted using mathematics.

Viscous vs Gaseous

The state of matter refers to its condition; viscous or gaseous, which is governed by the relationship between its temperature and its density, both of which are governed by the neutronic ratio (ψ) of its atoms. It appears therefore, that an element's characteristics are defined by its neutrons. If it was based upon its protons (Z), the plots in Fig 1 would be linear.

This study of elemental matter was sparked by the discovery that their densities (ρ) and gas transition temperatures (Ṯg) are directly related by their neutronic ratio, which is clearly revealed in Fig 1. Because the plots in Fig 1 are based upon documented data, it is understood that there will be minor discrepancies due to experimental error. However, as we now know how atoms work, we can apply this information to how same-element atoms interact; as matter.

Atomic Separation Forces

The transition between viscous and gaseous matter
Fig 2. Viscous vs Gaseous Matter

For example; all adjacent atoms are attracted by the magnetic field generated by their proton-electron pairs, and repulsed by their electrical charges, exactly as Coulomb explained. Therefore, magnetism must be responsible for an element's viscosity and electricity must define its gaseous properties.
And because magnetism is not affected by temperature, this inter-atomic attraction never changes in viscous matter#. But the electrical charge collected by an atom's protons does vary with temperature; therefore, as temperature rises so too does inter-atomic repulsion. When the collective electrical charge in an atom's protons exceeds its magnetic attraction, the matter will exist as a gas.
# apart from minor variations due to changes in crystal structure.

Fig 2 shows how this viscous/gaseous relationship applies to oxygen atoms:
The magnetic attraction force is calculated thus: Fₘ = hₚ².mₐ / R³ = (Rₙ.c)²/ξₘ . mₐ / R³
The electrical repulsion force is calculated thus: Fₑ = Ṯ.KB.N / R = PE₁.N / R.Y

Where:
mₐ is the atomic mass
R is the inter-atomic radial separation
N is the number of atoms in the gaseous molecule (1 or 2)
PE₁ is the potential energy in the atom's innermost shell (shell number 1) proton-electron pairs

Lattice Constant 'ζ'

We can define this constant using the atomic constants 'Z' and 'RAM' for each atom:
Atomic Number: Z; 1 to 92
Relative Atomic Mass: RAM
Neutronic Ratio: Ψ = RAM/Z – 1
Neutronic Factor: Γ = 9.(Ψ - 1)

The relationship between the lattice factor and the atoms properties
Fig 3. Lattice Factor vs Atomic Properties

Lattice Constant: ζ is the temperature:density ratio (Fig 3)
Where Tg is the gas-transition temperature of the atom, and ρ is its viscous density. The formula used to establish its value is:
ζ = ³√[ Ṯg.A.(Ψ-1) / ρ.R ]
radius 'R' was calculated from; Ṯg = Mₐ / N.A.R²
It should be understood that this constant has been set here using documented values for ρ & Tg, both of which are subject to experimental error; some mismatch is therefore expected. But as can be seen in Fig 3, the relationship is clearly identified (see Discussion below).

Inter-Atomic Separation Radius 'R'

This radius may be calculated as follows:
R = √[ mₐ / N.Ṯg.A ]
and the following formulas:
g = mₐ / N.R².A & ρ = Ṯg.A.(ψ-1) / ζ³.R
may be used to define the values for gas transition temperature and viscous density, both of which are plotted in Figs 4a & 4b#
# both graphs include two plots, one blue and one red. The blue plot is hidden behind the red plot

The relationship between calculated and documented values for the gas transition temperature of matter
Fig 4a. Gas Transition Temperature; Calculated vs Documented

It is important to understand that the gas transition temperature (Ṯg) can only occur when the magnetic and electrical forces (Fₘ and Fₑ) are equal (Fig 2) at the same atomic separation radius. In other words, whilst the separation radii between adjacent atoms will always be identical whether viscous or gaseous, at temperatures above and below 'Ṯg', these forces will not be equal.

The Properties of Same-Element Matter

The relationship between calculated and documented values for the density of matter
Fig 4b. Density; Calculated vs Documented

Using the above values; Z, RAM, ψ, Γ & R, we can now calculate the properties of any and all same-elemental matter.

Specific Heat Capacity

The relationship between calculated and documented values for the specific heat capacity of matter
Fig 5. Specific Heat Capacity; Calculated vs Documented

The specific heat capacity of any atom may be calculated for any temperature using the following formula:
SHC = KET / Y.mₐ.Ṯ
where Ṯ is the measured temperature of the atoms; i.e. that of the proton-electron pairs whose electrons are orbiting in the atoms innermost shell (shell-1), and KET is the sum of all of the kinetic energies in all the atom's electrons.
Fig 5 shows quite clearly that the calculated values match those extracted from various document sources.

Potential Acceleration

Potential acceleration is the magnetic [field] attraction and electrical [charge] repulsion between adjacent atoms, which can be calculated as follows:
gₘ = G.mₐ / φ.R²
gₑ = Fₘ.R / μ.e²
gₘ must equal gₑ at all times, whether the elements are in viscous or gaseous state.

Fₘ vs Fₑ (viscous or gaseous)

It is possible to determine the state of matter using the atomic separation force formulas (provided above); i.e. it will be gaseous if Fₑ is greater (than Fₘ) otherwise it will be viscous.

The calculated values for viscous and gaseous condition of matter
Fig 6. The calculated Condition for Matter

As can be seen in Fig 6, where the electrical and magnetic forces have been plotted together at a temperature of 2500K, the atomic elements exist as gaseous matter where the red line is above the blue line, and as viscous matter where the blue line is higher.

Dynamic Viscosity (μ)

Viscosity is the frictional resistance between adjacent atoms and only applies to viscous matter.

Dynamic viscosity is the difference between the magnetic and electrical forces (at a particular temperature) and may be calculated as follows:
μ = (Fₘ-Fₑ)/hₚ {N.s/m²}
If the result is negative, i.e. electrical repulsion (Fₑ) is greater than magnetic attraction (Fₘ), the matter will be gaseous and offer no viscous resistance.

Tensile Modulus (E)

The tensile modulus is a reflection of the pressure exerted between adjacent atoms due to their magnetic [field] force (Fₘ). However, as temperature rises, so too does the electrical [charge] repulsion. This not only reduces viscosity in viscous matter, but also reduces the attractive pressure holding the atoms together in the form of viscous matter.
The tensile modulus of a pure and perfect crystal of any elemental matter can be calculated from its dynamic viscosity:
E = μ.ƒ / √ζ (N.s/m² . 1/s = N/m²)
where 'ƒ' is the orbital frequency of the electrons in shell-1 of the elemental atoms, which may be calculated as follows:
ƒ = √[XR / X.R₁] / (2πR₁) = √[Ṯ/X] / (2πR₁)
'R₁' is the orbital radius of the electrons in shell-1 and 'Ṯ' is the measured temperature of the matter.

Mathematical prediction of the tensile modulus of viscous matter
Fig 7. Mathematical Prediction of Tensile Modulus

Atmospheric Drag

The current method for calculating the resistance (force) generated in a body travelling through a gas was established by J. R. Morrison et. al.

However, the above atomic model can also be used to determine this same force.

We know from above that magnetism (magnetic field) holds atoms together and electrical charge forces them apart (Fig 2).
Therefore, the drag induced in a body travelling through a gas (e.g. our atmosphere) is almost certainly caused by the magnetic field generated between adjacent gas and body atoms.

Morison equation
drag force: F = ½.Cd.ρ.A.v²
KDR's equation
atomic radial separation: R = ³√[ 3.mM / 4π.ρ ] { ³√[kg / kg/m³] = m } #
inter-atomic attraction [magnetic] force: Fₘ = (Rₙ.c)²/ξₘ . mₐ/R³ { m⁴/s² . kg/m³ = kg.m/s² = N } #
number of gas-atoms in contact with the surface of the body: Nº = A / (2π.R)²
total attraction force between gas and body: Fₜ = Fₘ.Nº
drag force: F = F.v² / 1.g { N . (m/s)² / (m.m/s²) = N }
The above formuas accumulate to; F = mₐ.(Rₙ.c)²/ξₘ . A . v²/(2π)²/g/[ 3.mM / 4π.ρ ]5/3
# The Mathematical Laws of Natural Science

The following Table lists a 'force' comparison between the two above calculation options based upon the following variables:
surface area: A = 3 m²
coefficient of drag: Cd = 0.75

velocity (m/a) KDR equation (N) Morison equation (N) error
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
1.18679
4.74717
10.68113
18.98868
29.66981
42.72453
58.15283
75.95471
96.13018
118.67924
143.60188
170.89810
200.56791
232.61131
267.02829
303.81885
342.98300
384.52073
428.43205
474.71696
523.37544
574.40752
627.81317
683.59242
741.74524
802.27166
865.17165
930.44523
998.09240
1068.11315
1.10808
4.43233
9.97273
17.72931
27.70204
39.89094
54.29600
70.91723
89.75461
110.80817
134.07788
159.56376
187.26580
217.18401
249.31837
283.66890
320.23560
359.01846
400.01748
443.23266
488.66401
536.31152
586.17520
638.25504
692.55104
749.06320
807.79153
868.73602
931.89668
997.27349
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
1.07103
Atomspheric Drag Force; equation comparison

Whether or not inter-atomic magnetism is the cause of atmospheric drag, the above calculation makes this argument extremely compelling; yet again validating this atomic model.

Atomic Separation Radii; verification

The relationship between actual and calculated values for inter-atomic radial separation
Fig 8. Radial Separation Values; Actual vs Calculated

Finally we need to identify a relationship between the radial separation as calculated using the formula provided above, and another using the lattice constant (ζ):
actual radius as calculated above         calculated radius (excluding ρ & Ṯg): R = π.aₒ.³√Γ / ζ

As can be seen in Fig 8, there exists an unmistakeable relationship between the two. In order to match the two plots exactly, we simply need to vary (correct) the solid/liquid densities and gas transition temperatures (ρ and Ṯg) for each of the elements to identify their true values. The differences (±<5%) will be due to experimental errors in the documented values.

PVRT

The most important validation of this atomic and elemental model is the accurate prediction of the properties of any gas at any temperature using the potential energy of an atom's electron kinetic energy; replacing the need for the ubiquitous PVRT formula.

But when considered together with the accurate prediction of the specific heat capacity of any and all atoms (Fig 5), there can no longer be any doubt that the Newton-Coulomb atom is the correct model.

The Neutron

It is interesting to note that the noble gases are directly related to 'Γ' (Fig 9).

Given that together with its neutronic ratio (ψ) we can define an element's density, radial separation and the rate at which its atoms eject its neutrons (radioactive fission), it is highly likely that neutrons - not protons - govern the behaviour of elements and thereby define their characteristics.

Mathematical prediction of the noble gases using the neutronic ratio
Fig 9. Mathematical Prediction of the Noble Gases

Note: Γ = 9.(ψ -1)
where ψ is the neutronic ratio

And because neutrons also store all of the universe's energy, they play a far more important part in the workings of the universe - and everything within it - than with which they are currently credited.

Discussion

It could be argued that, because lattice constant 'ζ' and radial separation radii (R) were originally established from documented data, that the above results were contrived. However, all of the properties calculated above use 'R' in different forms:
Tg (1/R²); ρ (1/R); Fₘ (1/R³); Fₑ (1/R); gₘ (1/R²); gₑ (.R); E (1/R²)
If this radius is altered, at least three of these calculated properties are incorrect.
Many different radii have been tried during this study, but the above values are the only ones found that ensure full compliance.

Further Reading

You will find further reading on this subject in reference publications(69, 70, 71 & 73)