The State of Matter

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?

For example:
The density of matter is a balance between magnetic field attraction and electrical charge repulsion forces. The factor defining this balance is calculated as follows:
Fₑ = k.(eꞌ/d)² {kg.m/s²}
Fₘ = μ.I² {kg.m/s²}
F = Fₑ:Fₘ
where:
      d = the average atomic spacing {m}
      μ = mₚ.Rₛ/e² {kg.m/C²}
      I = e.a/v {C/s}
      Rₛ = the outermost shell electron orbital radius {m}
      a = potential acceleration in the proton-electron pair at Rₛ {m/s²}
      v = electron orbital velocity at Rₛ {m/s}

Boiling point and gas transition temperature are not the same.
Gas transition temperature (Fig 1c) occurs when the electrical charge force between adjacent nucleic protons exceeds the magnetic field force holding them together. The gas transition factor (F) is calculated thus:
Fₑ = k.(eꞌ/d)²
Fₘ = μ.I² . √Z {kg.m/s²}
F = Fₑ:Fₘ
where:
      d = the average atomic spacing {m}
      μ = mₚ.Rₛ/e² {kg.m/C²}
      I = e.a/v {C/s}
      Rₛ = the outermost shell electron orbital radius {m}
      a = potential acceleration in the proton-electron pair at Rₛ {m/s²}
      v = electron orbital velocity at Rₛ {m/s}

Boiling point is the temperature at which matter vapourises. It remains in a viscous state; globules suspended in atmospheric gases. Vapourisation requires the presence of an atmosphere.

Gas transition temperature is that at which atoms repel each other; every atom (or molecule) exists as an individual entity.

The predictive pattern from the above factors (Figs 1b & 1c) which were derived from the properties of the Newton/Coulomb atom is unmistakable.
It is important to point out, however, that matter properties calculated as above - based upon the atom - presume perfect crystals in outer-space; i.e. with no ambient effects (e.g. temperature, gravitational acceleration, atmosphere, etc.), whereas the test conditions and matter purity of documented values are at best variable, and rarely (if ever) defined.

Conclusion

It is now evident that the state of matter in all its forms and its properties^#, may be calculated mathematically at any temperature and/or pressure simply from an element's atomic number and its neutronic ratio (Fig 2).
# Tensile modulus, yield strength, tensile strength, elongation, shear modulus, bulk modulus, Poisson's ratio, expansivity, thermal conductivity, electrical, etc.

All that is required to verify this work is a comprehensive database of accurately defined elemental matter densities at gas transition temperature established in a vacuum. But the facts are plain for all to see: the Newton-Coulomb atomic model has, at last, been further authenticated by applying it to the properties of matter.

CalQlata's consequential conclusions have been allocated to a dedicated webpage, reserving this page for the scientific facts alone.

States of Matter

In this context, 'Matter' is the term used to describe a collection of pure elements in their natural state at any temperature and/or pressure; viscous or gaseous, the only states in which they can exist.
Same-element matter refers to that in which all the atoms have the same atomic number. All these calculations refer to same-element matter.

But before we begin;
it has become clear that very little we see, hear and read concerning the state of matter is either accurate or true; for example;
1) The term "fluid" is a misnomer as it unifies two disparate states of matter "viscous" and "gaseous". Liquid is viscous and gas is not. In fact, all matter exists either as viscous or gaseous, dependent upon temperature.
2) When trying to identify a particular property of matter, such as its 'boiling temperature', not only do all sources disagree⁽¹⁾, they do not state the conditions under which the property is defined.
3) The gas-transition temperature of matter occurs whilst liquid, and whilst the density of liquidous matter may be similar to its solid state, it is rarely identical. Density tends to reduce with increasing temperature⁽²⁾. Therefore, the densities stated here for solid matter are likely to be [significantly in some cases] higher than that of the matter concerned at its gas-transition temperature.
4) The gas transition temperature of atmospheric matter, such as nitrogen or oxygen, is dependent upon atmospheric pressure. The gas transition temperatures calculated below apply to matter in a perfect vacuum.
5) Hydrogen, either as a single proton or as a proton-electron pair, cannot exist in viscous form due to their positive [proton] charges, which can only repel. Only as deuterium or tritium (containing one or two neutrons respectively) can this occur⁽³⁾.

The highest energies (e.g. temperature {Ṯ} or electro-magnetic {EME}) in any atom occur in the proton-electron pairs whose electrons are orbiting in shell-1. All the following calculations are therefore based upon the performance of the proton-electron energies in these proton-electron pairs, whose electrons are orbiting in shell-1, and designated in the calculations with the sub-script '1'; e.g. PE₁, KE₁, etc.

Definition

The force (Fₘ) holding adjacent atoms together is the magnetic field generated by their proton-electron pairs. This force is constant because the magnetic charge (currently referred to as mass) responsible, is constant.
The force (Fₑ) repelling adjacent atoms is due to the positive electrical charge collected by their [nucleic] protons. This charge (e') varies linearly with the EME collected by the orbiting electrons from their surroundings and transferred to - and held by - their proton partners.

If the electrical force is less than the magnetic force, the matter will exist in a viscous state.
If the electrical force is greater than the magnetic force, the matter will exist in a gaseous state.
The gas transition temperature occurs when these two forces are equal (Fₘ = Fₑ).
This relationship is the fundamental cause of the 'State of Matter' (Fig 2).

Viscous

The term 'viscosity' describes all and/or any matter when adjacent atoms are attracted to each other in solid or liquid form, and refers to the resistance in adjacent atoms to slip - plastically, as in plastic stress - relative to each other.
Liquid matter is no different to solid but the inter-atomic electrical separation force (Fₑ), which varies with temperature, is sufficient to reduce the attractive magnetic force (Fₘ) whereby slip between adjacent atoms occurs with little resistance (low viscosity). What we understand as 'solid' matter is simply that with a very high viscosity, you can still cause its atoms to slip by applying greater (than for liquid matter) force.
Liquidity refers to a body's ability to maintain its shape under the prevalent ambient conditions; gravitational acceleration, atmospheric pressure, etc. It will differ in all matter, for example, here on Earth and and on our moon.
Magnetism remains constant at any temperature (Fig 2), which is why the attraction force (Fₘ) between atoms is constant.

Gaseous

Gaseous matter describes adjacent atoms that repel each other.
This condition occurs when the electrical separation force (Fₑ) between adjacent atoms at elevated temperatures is sufficient to overcome (exceed) the attractive magnetic force (Fₘ).
This electrical force (Fₑ) is due to the positive electrical charge held in the nucleic protons, which varies with temperature (Fig 2).

As a gas, the force between adjacent atoms (F = Fₘ-Fₑ) is negative because Fₑ is greater than Fₘ, therefore, viscosity should not exist. However, at very low temperatures, just above gas transition, magnetic attraction (Fₘ) is still evident and responsible for the resistance in bodies travelling through an atmosphere.

Gas-Transition Temperature

Gas transition temperature occurs when the electrical and magnetic forces are equal (Fₑ=Fₘ) (Fig 2)
The temperature at which this condition occurs here on Earth, depends upon the partial pressure of same-elemental atoms in the atmosphere.

Lattice Structure

Same element atoms always attract and repulse in a similar pattern to that held by the protons in an atom's nucleus. This pattern is what we today refer to as a lattice structure that depends upon the atom's neutronic ratio.
We designate these lattice structures as; face-centre cubic, body-centre cubic, tetrahedra, close-packed hexagonal, etc. but they are not quite so simple. Whilst a particular group of atoms may resemble a single structure, they will not be identical; every lattice structure differs from every other.
This pattern applies to all same-element matter in both viscous and gaseous form, and is therefore responsible for partial pressure (gas) theory.

Partial Pressure

At first sight, Dalton's law and partial pressure theory appear to conflict.
If as Dalton states; each gas in a mixture of gases should be treated independently, the pressure in a container of mixed gases should be the maximum individual pressure. But this is not the case; partial pressure theory tells us that the total pressure is the sum of the individual gases. This anomaly may be explained as follows:
The positive electrical charge in all atomic protons (e') will repel all other atoms, irrespective of atomic number, but such repulsion is random.
All same-element atoms will repel each other equally according to their respective lattice structures, and because all energies (and forces) try to settle at their minimum condition, they will distribute evenly and equally throughout their container, maximising their relative distances (Dalton).
This is why; the total pressure in a container of mixed gases is the sum of all the individual pressures and same-elemental gases must be treated individually.

Dalton's Law

Dalton stated that each individual gas in a container of mixed gases, distributes independently.
It is also true that same-element atoms coalesce as a liquid.
These phenomena occurs because an atom's treatment of its neighbouring atoms is defined by its nucleic arrangement.
e.g., if an elemental atom's nucleic protons are arranged in, say, a face-centre cubic pattern, this will be replicated in the arrangement of neighbouring same-element atoms in both gaseous and viscous condition.

In other words ...
In viscous state (below the gas transition temperature), each elemental atom will attract same-element atoms arranging themselves in the same pattern as its nucleic protons. I.e. the lattice structure of the viscous matter will also be face-centre cubic.
In gaseous state (above the gas transition temperature), each elemental atom will repel same-element atoms according to the same pattern as its nucleic protons. I.e. same-element gaseous atoms in a container will be organised [repulsed] in a face-centre cubic pattern, causing all same-element atoms to fill the container independently.
It is their unique gas transition temperatures and nucleic structures that ensure same-element atoms coalesce (as a liquid) and repel evenly (as a gas).

Partial pressure theory states that the total pressure inside a container of mixed gases is the sum of all individual same-element [partial] gas pressures.
It is also true that the internal [core] pressure of a solid comprising numerous elemental atoms, is the sum of their individual core pressures.
Irrespective of its nucleic structure, an elemental atom will always attract or repel neighbouring atoms according to their respective gas transition temperatures and nucleic arrangements.

In other words ...
Dalton's Law applies to all elements in both gaseous and viscous conditions.

Neutronic Ratio

The neutronic ratio used in these calculations is calculated thus; ψ = RAM/Z - 1
where; RAM is the relative atomic mass and Z is the atomic number.
The relationship between atomic spacing - and therefore density - and neutronic ratio for any same-element matter can be clearly seen in Fig 3.

Inter-Atomic Forces

It has now been demonstrated that the well-known and accepted 'PVRT' formula can be replaced with a formula based upon the potential energy in the True Atom;
p = ρ.PE₁ / Y.mₐ = kB.Ṯ / d³ both of which give exactly the same value;
where the density (ρ) applies to matter both in viscous and gaseous states and 'd' represents inter-atomic separation; d = ³√[mₐ/ρ]
These forces are defined by the properties of the proton-electron pairs, the electrons of which orbit in an atom's innermost shell.
And the formulas used to define these conditions are listed as follows:

Electrical (repulsion); Fₑ = kB.Ṯ/d = -PE₁ / Y.d = k'.e'₁² / Y.d.Rₙ̱ = V.e'/d . √[Ṯₓ/Ṯ] = K.mₚ.v²/d
all of which give exactly the same result, and all of which break down to⁽⁴⁾;
Fₑ = mₑ.c² . (Ṯ/Tₙ) / Y.d = PEₙ/(Y.Tₙ) . (Ṯ/d) = kB/d . Ṯ {kg.m²/s² / m = kg.m/s²}

Magnetic (attraction); Fₘ = hₑ² . mₚ . (ψ/d)³

The viscous/gaseous condition for each element may be defined mathematically at any temperature (Ṯ) as shown in Fig 4

Gas Transition Temperature

Fig 4 reveals an undeniable relationship between the magnetic and electrical inter-atomic forces and the gas transition temperature of the elements.
That the gas-transition values calculated using these forces are not the same as the documented boiling temperatures Fig 5 can be explained due to;
a) the problems with documented values, and;
b) there are other factors affecting the calculated values, such as;
the boiling point of matter (@ ambient pressure and temperature) is not the same as gas transition temperature (in a vacuum), and this relationship takes no account of of the fact that condensation occurs between boiling-point and gas-transition.

Gas-transition temperature occurs when both magnetic and electrical forces are equal; Fₘ = Fₑ:
kB.Ṯg/d = hₑ².mₚ . (ψ/d)³
Ṯg = hₑ².mₚ/kB . (ψ³/d²)
The boiling point of all matter declines with reducing ambient pressure and temperature.
And gas-transition temperature (in a vacuum) is greater than the boiling-point of the same matter; in a vacuum or otherwise.

Specific Heat Capacity (SHC)

The specific heat capacity for all atoms, may be calculated thus; SHC = ΣKE / Ṯ.Y.mₐ
where ΣKE is the sum of the kinetic energies in all the proton-electron pairs in any atom, and mₐ is the atomic mass (Fig 6).

Fig 6 confirms the Newton-Coulomb atomic model with two electrons per orbital shell.

Viscosity

The dynamic viscosity (μ) of all elements - at a specified temperature - can be calculated thus;
μ = (Fₘ-Fₑ) / Z.hₚ
Note: the kinematic viscosity (ν) may be derived thus; ν = μ/ρ

Young's Modulus

Young's modulus (E) for each element at a specified temperature may be determined thus;
E = Fₘ / ν³.Rₛ²
The unmistakeable relationship between documented values at room-temperature and those calculated here may be seen in Fig 7

Noble gases

Fig 8 reveals the noble gases based upon the neutronic ratio, which may be calculated thus;
Γ = 9.(ψ -1)
the noble gases occur when Γ is at or close to an integer; 1 to 5

Properties

These forces (Fₘ & Fₑ) can now be used to predict various properties of matter, which when taken along with the relationship between neutronic ratio (ψ) and matter density (ρ) (Fig 3), it is evident that all the physical properties of matter can be predicted from an atom's neutronic ratio and its atomic mass. For example:

Radial separation: Rₛ = ³√[mₐ/ρ]
Viscosity: μ = (Fₘ-Fₑ) / Z.hₚ
Gas pressure: p = Fₑ/Rₛ²
Tensile stress: σ = ν.(Fₘ-Fₑ)/Rₛ²
Tensile (Young’s) modulus: Fₘ / R².ν³
Specific heat capacity: SHC = ΣKE / Ṯ.Y.mₐ
Atmospheric drag: F_d = hₑ.ρ.ψ . N° . (v_d/vₐ)² . (PEₙ/-PE₁)

In fact, it is highly likely that viscosity and gas pressure are the only genuine properties we need to consider when describing the behaviour of elemental matter given their dependence on temperature; along with the fact that viscous and gaseous are its only possible states.

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, because the magnetic [attraction] force (Fₘ) between adjacent atoms is responsible for the drag on bodies passing through an atmosphere, the Newton-Coulomb atomic model can now be used to determine this resistance based upon relative velocities and energies thus:

F = hₑ.ρ.ψ . N° . (v_d/vₐ)² . (PEₙ/-PE₁)
where;
A = cross-sectional area
ρ = gas (e.g. air) density
N° = number of atoms in contact with the body (= A / π.Rₛ²)
v_d = relative velocity between body and gas
v₁ = electron velocity in shell-1 (gas-atom)
PE₁ = potential energy proton-electron pair in shell-1 (gas-atom)

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.

The Molecule

The molecule (and atomic bonding) is the next step, which can also be solved mathematically using the same atomic forces.

Whilst Keith Dixon-Roche knows how to solve this problem,
due to the responses he has received as a result of his scientific discoveries and their possibilities, he has decided to leave this work up to you,
but he is willing to give you a hint:

'atomic and matter densities react differently with varying temperature;
e.g. the density of an iron atom @ 300K is 0.007533336 kg/m³ but the density of its matter is 7870 kg/m³.
That atomic density increases with rising temperature as matter density decreases, is a clue as to the functioning of chemical bonding; electron charge sharing.'

He wishes you luck.

Notes

1. The temperatures are in Kelvin, and the references can be found on our references page or '⁽ꜞ⁾' which refers to an internet source. For example; the boiling temperature of Rhodium: 4000⁽¹⁵⁾, 3980⁽¹⁾, 4755⁽³⁾, >2773⁽¹²⁾, 3968⁽ꜞ⁾, 2219⁽ꜞ⁾, 3915 (Elements), 3300 (CalQlata).
   Note: the value included in Elements was taken from the most reliable documented source at the time. However, whilst CalQlata's calculated value may not be exact, it clearly demonstrates that none of the documented values can be counted upon.
2. The density of solid boron is said to be 2320 kg/m³, but a reliable technical source (page 5) states that the specific gravity of liquid boron varies between 1.32 and 1.36 but does not state the associated temperatures or pressures.
3. H⁺, which represents about 99.997% of all atmospheric hydrogen, can never coalesce as a liquid because it possesses a positive charge and generates no magnetic field. However, the inability of hydrogen atoms (H) to attract other hydrogen atoms (H) in viscous form is currently hypothesis, based upon their positive proton electrical charges. If, however, at a sufficiently low temperature, their attractive magnetic forces (Fₘ) are greater than their repulsive electrical forces (Fₑ), a liquid state may exist.
4. Fₑ = ...
   ... kB.Ṯ/R = c².mₑ / Y.Tₙ . Ṯ/R = mₑ.c² . (Ṯ/Tₙ) / Y.R
   ... -PE₁/Y/R = mₑ.(Ṯ/X) / Y.R = mₑ.(Ṯ/X) / Y.R = mₑ.(Ṯ.c²/Ṯₙ) / Y.R = mₑ.c² . (Ṯ/Ṯₙ) / Y.R
   ... k'/Y . e'²/R/Rₙ = mₑ.c².Rₙ/(mₚ.e/mₑ)² . (mₚ.e/mₑ/c . √[Ṯ.c²/Ṯₙ])² / (Y.R.Rₙ) = mₑ.c² . (Ṯ/Ṯₙ) / Y.R
   ... V.e'/R . √[Ṯᵪ/Ṯ] = (-PE₁/e) . (mₚ.e/mₑ . v/c)/R . √[Ṯₓ/Ṯ] = mₑ.(Ṯ.c²/e)/e . mₚ.e/mₑ . √[Ṯ.c²/e]/c / R . √[Ṯₓ/Ṯ] = Ṯ.c²/e² . mₚ.e / √e / R . √Ṯₓ = mₑ.c² . (Ṯ/Ṯₙ) . / Y.R
   ... mₚ.v²/R . √[Ṯᵪ/Ṯₙ] = mₚ.(Ṯ/X)/R . mₑ/mₚ/Y = mₚ.(Ṯ.c²/Tₙ)/R . mₑ/mₚ./Y = mₑ.c² . (Ṯ/Tₙ) / Y.R.

Further Reading

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