This manuscript theoretically investigates the properties of mag-carbon nanotubes, building upon the recently refined understanding of magnetic monopole matter (magmatter) as a material forming stable crystal lattices. By deriving a new carbon-specific strength scaling factor of $5.60 \times 10^{38}$, we predict that mag-carbon nanotubes will exhibit a linear mass density of approximately $12.8 \text{ kg/m}$ and a theoretical tensile strength of $5.60 \times 10^{49} \text{ Pa}$. These calculations yield an unprecedented specific strength of $2.87 \times 10^{14} \text{ N} \cdot \text{m/kg}$ and a breaking length exceeding $2.93 \times 10^{13} \text{ m}$. Such properties suggest mag-carbon nanotubes could serve as a foundational material for revolutionary engineering feats, including single-stage space elevators and the construction of colossal megastructures. This study underscores magmatter’s potential to redefine material science, acknowledging the need for further research into its behavior under extreme gravitational potentials and the implications for large-scale structural design.

Cover picture is generated by Gemini and Imagen 4.

1. Introduction

The advent of magnetic monopole matter (magmatter) has fundamentally reshaped the technological landscape for advanced galactic civilizations. As detailed in foundational works [1], magmatter, a dualistic counterpart to ordinary electrically charged matter, exhibits properties of unparalleled extremity, including astronomical densities, unfathomable mechanical strength, and melting temperatures orders of magnitude beyond any known conventional material. Its definitive identification and extensive utilization by our patron Artificial Intelligences (AIs) underscore its critical importance across diverse domains, from energy generation to the construction of megastructures.

Our understanding of magmatter’s condensed phase has recently undergone significant refinement. Initial theoretical models, driven by the profound asymmetry of forces within magatoms, predicted an ultimate packing density where atomic orbitals would be entirely crushed [2]. However, recent crystallographic analyses of synthesized mag-diamond samples have provided unexpected empirical insights, revealing that magmatter, despite its immense internal forces, forms stable, ordered crystal lattices where the atomic volume is defined by its Bohr radius, rather than a fully degenerate state [2]. This revised understanding, encapsulated in Model C from our previous work, now serves as the foundational assumption for exploring magmatter’s material properties.

In the realm of ordinary matter, carbon nanotubes (CNTs) have emerged as a revolutionary class of materials, renowned for their exceptional tensile strength, electrical conductivity, and remarkable strength-to-weight ratios [3, 4]. These nanoscale structures have opened new frontiers in material science and engineering, enabling applications previously deemed impossible. Given the extraordinary properties of magmatter, a natural extension of this inquiry is to theoretically investigate the characteristics of its nanoscale analogues.

This paper aims to explore the potential of mag-carbon nanotubes, building directly upon the refined understanding of magmatter’s condensed phase (Model C) established in our recent crystallographic studies [2]. Specifically, we will theoretically calculate the linear mass density and the theoretical tensile strength of mag-carbon nanotubes. By extrapolating the unique properties of mag-carbon atoms to this nanoscale architecture, we seek to predict the performance metrics of such materials. The implications of these findings are profound, suggesting the potential for the development of ultra-strong, ultra-lightweight materials that could redefine engineering capabilities across the galaxy, enabling the construction of structures and devices of unprecedented scale and resilience.

2. Foundational Principles of Mag-Carbon and its Condensed Phase

Magmatter, as established in foundational theoretical frameworks [1], is composed of fundamental magnetic charge carriers: the magtron and the magnucleus. The magtron, analogous to the electron, is a fermionic composite particle with an estimated invariant mass of approximately $1.5 \text{ TeV}/c^2$. It is conceptualized as a composite entity formed by the embedding of a bosonic magnetic monopole within a very light, neutral elementary fermion. The magnucleus, a multi-charged magnetic core akin to an atomic nucleus, is also a composite particle, formed by the embedding of a fundamentally heavier bosonic magnetic monopole within a neutral elementary fermion, with its mass scaling at approximately $10 \text{ TeV}/c^2$ per magnetic charge unit. These constituents bind to form stable magatoms, which are magnetically neutral analogues of ordinary atoms.

A critical aspect distinguishing magmatter from ordinary matter lies in the asymmetry of the fundamental forces governing its interactions [1]. Within a magatom, the primary attractive force, a powerful, short-range Higgs-boson mediated interaction, operates at exceptionally high energy scales, resulting in substantial binding energies of approximately 300 GeV. This immense intra-atomic force is responsible for the atom’s stability and its incredibly compact nature. Conversely, the inter-atomic forces that would govern the spacing between two distinct magatoms in a condensed phase are fundamentally different. While the intra-atomic binding is dominated by the Higgs-boson interaction, the repulsive forces between the “magtron clouds” of adjacent magatoms, analogous to the Pauli exclusion principle in ordinary matter, would be mediated by the screened magnetic force. Due to vacuum magnetic polarization, this inter-atomic repulsion is significantly curtailed at inter-atomic distances, operating at a much weaker MeV energy scale. This profound asymmetry—where the intra-atomic attractive force is orders of magnitude stronger than the inter-atomic repulsive force—leads to an initial theoretical expectation that magmatter, in a condensed state, would be crushed to extreme densities, with its volume determined by the packing of its fundamental nuclear constituents rather than by any orbital structure. This foundational understanding sets the stage for the theoretical models explored in the subsequent sections.

3. Theoretical Framework for Mag-Carbon Nanotubes

Building upon the established understanding of magmatter’s condensed phase (Model C, Section 2), we now develop a theoretical framework for mag-carbon nanotubes (mag-CNTs). These structures are conceptualized as direct analogues to conventional carbon nanotubes (CNTs), but scaled down by the unique properties of mag-carbon atoms. Normal CNTs, typically formed from rolled-up sheets of graphene (a hexagonal lattice of carbon atoms), are renowned for their exceptional mechanical and electrical properties, making them a benchmark for high-performance materials.

We assume that mag-carbon atoms, like their ordinary counterparts, can form stable hexagonal lattice structures. This assumption is consistent with the empirical findings from mag-diamond crystallography [2], which demonstrated magmatter’s capacity to maintain ordered crystal lattices with atomic volumes defined by their Bohr radii. Therefore, a mag-CNT is envisioned as a rolled-up sheet of a mag-graphene analogue. For simplicity in our calculations, we will focus on single-walled mag-CNTs.

The key geometric parameters of a mag-CNT are directly scaled from those of a conventional CNT:

  • Mag-carbon Bond Length: In normal carbon nanotubes, the carbon-carbon bond length is approximately 0.142 nm (for graphene) or 0.154 nm (for diamond) [3]. Given that mag-carbon atoms maintain a Bohr radius of $r_{\text{mag-C, Bohr}} \approx 3.71 \times 10^{-20} \text{ m}$ (Section 2), and a normal carbon atom has a covalent radius of approximately $70 \text{ pm} = 7.0 \times 10^{-11} \text{ m}$, the scaling factor for atomic dimensions is: $$\text{Scaling Factor} = \frac{r_{\text{mag-C, Bohr}}}{r_{\text{C, covalent}}} = \frac{3.71 \times 10^{-20} \text{ m}}{7.0 \times 10^{-11} \text{ m}} \approx 5.300 \times 10^{-10}$$ Applying this scaling factor to a typical carbon-carbon bond length in graphene (0.142 nm), the mag-carbon bond length ($L_{\text{mag-C}}$) is: $$L_{\text{mag-C}} = 0.142 \times 10^{-9} \text{ m} \times 5.300 \times 10^{-10} \approx \mathbf{7.53 \times 10^{-19} \text{ m}}$$ This incredibly short bond length is a direct consequence of the mag-carbon atom’s diminutive size and the powerful inter-atomic forces that allow for such close packing.

  • Nanotube Diameter and Chirality: The diameter and chirality (defined by the (n,m) indices) of a nanotube determine its precise atomic arrangement and, consequently, its macroscopic properties. For the purpose of this theoretical exploration, we will consider a generic single-walled mag-CNT. The principles of scaling apply universally; for instance, a (10,10) armchair mag-CNT would have its diameter scaled down by the same factor as the bond length. The linear mass density and strength calculations presented in subsequent sections will be generalizable, but for illustrative purposes, we can consider a representative diameter scaled from a typical CNT.

This theoretical framework provides the necessary geometric foundation for calculating the linear mass density and tensile strength of mag-carbon nanotubes, which will be explored in the following sections.

4. Calculation of Linear Mass Density

The linear mass density ($\rho_L$), defined as mass per unit length (kg/m), is a crucial metric for assessing the weight efficiency of one-dimensional materials like nanotubes. It is directly influenced by the mass of the constituent atoms and their packing density along the nanotube’s axis.

For a conventional single-walled carbon nanotube (SWCNT), such as a (10,10) armchair configuration, the linear mass density is approximately $1.1 \times 10^{-12} \text{ kg/m}$ [3]. This value serves as a benchmark for comparison.

To calculate the linear mass density of a mag-carbon nanotube (mag-CNT), we leverage the scaling principles established in Section 3 and the properties of the mag-carbon atom (Section 2). A mag-CNT is a direct analogue of a conventional CNT, but scaled down by a factor ($S$) derived from the ratio of the mag-carbon Bohr radius to the normal carbon covalent radius ($S \approx 5.300 \times 10^{-10}$). This scaling factor applies to all linear dimensions, including the bond length and the diameter of the nanotube.

The linear mass density of a mag-CNT ($\rho_{L, \text{mag-CNT}}$) can be calculated by scaling the linear mass density of a normal CNT ($\rho_{L, \text{CNT}}$) by the ratio of the mass of a mag-carbon atom to a normal carbon atom, and by the inverse of the linear scaling factor (since more atoms fit into a given length).

$$\rho_{L, \text{mag-CNT}} = \rho_{L, \text{CNT}} \times \left( \frac{M_{\text{mag-C}}}{M_{\text{C}}} \right) \times \left( \frac{1}{S} \right)$$

Where:

  • $\rho_{L, \text{CNT}} \approx 1.1 \times 10^{-12} \text{ kg/m}$ (for a typical SWCNT)
  • $M_{\text{mag-C}} \approx 1.229 \times 10^{-22} \text{ kg}$ (mass of a mag-carbon atom, Section 2)
  • $M_{\text{C}} \approx 1.9926 \times 10^{-26} \text{ kg}$ (mass of a carbon-12 atom)
  • $S \approx 5.300 \times 10^{-10}$ (scaling factor, Section 3)

Substituting these values:

$$\rho_{L, \text{mag-CNT}} = (1.1 \times 10^{-12} \text{ kg/m}) \times \left( \frac{1.229 \times 10^{-22} \text{ kg}}{1.9926 \times 10^{-26} \text{ kg}} \right) \times \left( \frac{1}{5.300 \times 10^{-10}} \right)$$

$$\rho_{L, \text{mag-CNT}} = (1.1 \times 10^{-12}) \times (6167.82) \times (1.88679 \times 10^9)$$

$$\rho_{L, \text{mag-CNT}} \approx \mathbf{12.8 \text{ kg/m}}$$

Comparison: The calculated linear mass density of a mag-carbon nanotube is approximately $12.8 \text{ kg/m}$. This is an extraordinarily high linear density, roughly $1.16 \times 10^{13}$ times denser per unit length than a conventional carbon nanotube. This extreme value is a direct consequence of the minuscule bond lengths and the immense mass of mag-carbon atoms, allowing an astronomical number of heavy atoms to be packed into a given macroscopic length. Despite this high linear density, the material’s strength-to-weight ratio, as explored in the next section, remains unparalleled due to its even more extreme tensile strength.

5. Calculation of Theoretical Tensile Strength and Derived Properties

The theoretical tensile strength ($\sigma_T$), defined as the maximum stress a material can withstand before fracturing, is a critical indicator of its structural integrity. For nanoscale materials like nanotubes, this strength is fundamentally linked to the strength of individual inter-atomic bonds and the density of these bonds across the material’s cross-section.

5.1. Derivation of a Carbon-Specific Strength Scaling Factor

To achieve a more accurate prediction for carbon-based magmatter allotropes, we will first derive a material-specific strength scaling factor. This refines the generalized, hydrogen-based factor calculated in [1] by using the properties of a normal carbon-carbon bond as the baseline.

The overall strength scaling is a product of the scaling of energy-per-bond and the scaling of bonds-per-unit-area.

  • Energy Scaling: We compare the magmatter binding energy ($E_{mag} \approx 300 \text{ GeV}$) to the standard energy of a normal C-C single bond ($E_{C-C} \approx 3.6 \text{ eV}$). $$\text{Energy Scaling Factor} = \frac{E_{mag}}{E_{C-C}} = \frac{300 \times 10^9 \text{ eV}}{3.6 \text{ eV}} \approx 8.33 \times 10^{10}$$

  • Length Scaling: We compare the normal carbon covalent radius ($r_C \approx 70 \text{ pm}$) to the mag-carbon Bohr radius ($r_{mag-C} \approx 3.71 \times 10^{-5} \text{ pm}$). $$\text{Length Scaling Factor (Inverse)} = \frac{r_C}{r_{mag-C}} = \frac{7.0 \times 10^{-11} \text{ m}}{3.71 \times 10^{-20} \text{ m}} \approx 1.887 \times 10^9$$

  • Overall Strength Scaling: The final factor is the energy scaling multiplied by the cube of the inverse length scaling (as strength is force per area, or energy per volume). $$\text{Overall Strength Scaling} = (\text{Energy Scaling}) \times (\text{Length Scaling (Inverse)})^3$$ $$\text{Overall Strength Scaling} = (8.33 \times 10^{10}) \times (1.887 \times 10^9)^3 \approx 5.60 \times 10^{38}$$ This new Carbon-Specific Strength Scaling Factor of $5.60 \times 10^{38}$ will be used for all subsequent calculations involving mag-carbon structures.

5.2. Theoretical Tensile Strength of Mag-Carbon Nanotubes

We apply the new scaling factor to the benchmark theoretical tensile strength of a conventional single-walled carbon nanotube (SWCNT), which is approximately 100 GPa ($100 \times 10^9 \text{ Pa}$) [4].

$$\sigma_{T, \text{mag-CNT}} = \sigma_{T, \text{CNT}} \times \text{Overall Strength Scaling}$$ $$\sigma_{T, \text{mag-CNT}} = (100 \times 10^9 \text{ Pa}) \times (5.60 \times 10^{38}) = \mathbf{5.60 \times 10^{49} \text{ Pa}}$$

5.3. Derived Properties: Specific Strength and Breaking Length

  • Specific Strength ($S_S$): Using the Model C bulk density ($\rho_{mag-C, \text{diamond}} \approx 1.95 \times 10^{35} \text{ kg/m}^3$) [2]: $$S_S = \frac{\sigma_{T, \text{mag-CNT}}}{\rho_{mag-C, \text{diamond}}}$$ $$S_S = \frac{5.60 \times 10^{49} \text{ Pa}}{1.95 \times 10^{35} \text{ kg/m}^3}$$ $$S_S \approx \mathbf{2.87 \times 10^{14} \text{ N} \cdot \text{m/kg}}$$

  • Breaking Length ($L_B$): $$L_B = \frac{S_S}{g}$$ $$L_B = \frac{2.87 \times 10^{14} \text{ m}^2/\text{s}^2}{9.81 \text{ m/s}^2}$$ $$L_B \approx \mathbf{2.93 \times 10^{13} \text{ m}} \quad (\text{or } 29.3 \text{ trillion km})$$

  • Breaking Load of a Single Thread: Using a cross-sectional area of $\approx 4.08 \times 10^{-37} \text{ m}^2$: $$\text{Force} = (5.60 \times 10^{49} \text{ N/m}^2) \times (4.08 \times 10^{-37} \text{ m}^2) \approx \mathbf{2.28 \times 10^{13} \text{ N}}$$

5.4. Recalculated Comparison Summary

Property Conventional Carbon Nanotube Mag-Carbon Nanotube (Recalculated)
Linear Mass Density $\approx 1.1 \times 10^{-12} \text{ kg/m}$ $\approx 12.8 \text{ kg/m}$
Tensile Strength $\approx 100 \text{ GPa}$ $\approx 5.60 \times 10^{49} \text{ Pa}$
Specific Strength $\approx 7.7 \times 10^7 \text{ N} \cdot \text{m/kg}$ $\approx 2.87 \times 10^{14} \text{ N} \cdot \text{m/kg}$
Breaking Length $\approx 7.8 \times 10^6 \text{ m}$ $\approx 2.93 \times 10^{13} \text{ m}$
Breaking Load (Single Thread) $\approx 145 \text{ nN}$ $\approx 2.28 \times 10^{13} \text{ N}$

The theoretical properties of mag-carbon nanotubes are truly revolutionary, indicating a material with an unprecedented combination of strength and weight efficiency.

6. Discussion and Implications

Our theoretical calculations predict that mag-carbon nanotubes possess extraordinary properties, far surpassing those of conventional materials. Specifically, a mag-carbon nanotube exhibits a linear mass density of approximately $12.8 \text{ kg/m}$, a theoretical tensile strength of $5.60 \times 10^{49} \text{ Pa}$, a specific strength of $2.87 \times 10^{14} \text{ N} \cdot \text{m/kg}$, and a remarkable breaking length of approximately $2.93 \times 10^{13} \text{ m}$ (or 29.3 trillion km). These figures represent an unprecedented combination of strength and weight efficiency, indicating a material with truly revolutionary potential.

The implications for engineering and technology are profound. Materials with such unparalleled strength-to-weight ratios could redefine the boundaries of what is structurally feasible. The breaking length, in particular, is a critical metric for applications like space elevators. A conventional carbon nanotube’s breaking length (approximately 7,800 km) is insufficient to reach geostationary orbit (around 35,786 km), let alone extend to a counterweight. The calculated breaking length of a mag-carbon nanotube, exceeding 29 trillion kilometers, makes the construction of a single-stage space elevator, extending from a planetary surface to well beyond geostationary orbit, a theoretically viable engineering endeavor.

Beyond space elevators, the potential applications of mag-carbon nanotubes are vast and transformative:

  • Structural Components for Megastructures: Their immense strength and relative “lightness” (in terms of specific strength) would enable the construction of structures on scales previously unimaginable, such as Dyson spheres, orbital rings, planetary defense systems, and even continent-sized habitats.
  • High-Energy Containment: The extreme material integrity could facilitate the containment of ultra-high-energy plasmas for advanced fusion reactors or the stable storage of exotic matter, pushing the boundaries of energy generation and manipulation.
  • Ultra-Miniaturized Devices: The incredibly short bond lengths and minuscule atomic dimensions would allow for the fabrication of components for devices operating at scales far below current nanotechnology, leading to unprecedented computational power and sensor capabilities.

It is important to acknowledge the limitations of this theoretical model. Our calculations are based on ideal structures, assuming perfect crystallinity and uniform properties. They do not account for potential defects, impurities, complex multi-walled structures, or the challenges of macroscopic synthesis and assembly. Real-world materials rarely achieve their theoretical maximums.

Despite these theoretical limitations, the predicted properties warrant extensive future work. Research should focus on:

  • More detailed quantum mechanical simulations of mag-carbon bonding in various nanotube geometries and chiralities to refine strength predictions.
  • Investigation into the synthesis and characterization of multi-walled mag-CNTs, which may offer different property profiles.
  • “Experimental” verification of these predicted properties through advanced material testing techniques.
  • Crucially, further investigation is needed into the interplay between magmatter’s extreme density and gravitational effects at larger scales. As discussed in [2], while individual nanotubes are thin, for truly massive structures built from them, the self-gravitation of the entire structure could become a significant factor. This raises questions about the precise limits of magmatter compression under extreme gravitational potentials, including conditions nearing the formation of a black hole. Such studies will be paramount to determine whether these conditions are indeed sufficient to force magmatter into a more degenerate state, approaching the densities predicted by Model A in [2] ($\approx 6.36 \times 10^{35} \text{ kg/m}^3$), or if the inherent lattice stability persists even under such immense pressures. Understanding these gravitational phase transitions will be critical for the safe and effective engineering of truly colossal magmatter constructs.

7. Conclusion

This theoretical study has explored the unprecedented potential of mag-carbon nanotubes, building upon the refined understanding of magmatter’s condensed phase. By applying scaling principles derived from recent crystallographic analyses, we have theoretically predicted the linear mass density, tensile strength, specific strength, and breaking length of these hypothetical structures. Our calculations reveal a material with an extraordinary combination of strength and weight efficiency, far surpassing any known conventional substance.

The implications of these findings are profound, suggesting that mag-carbon nanotubes could serve as a foundational material for revolutionary engineering feats, from enabling single-stage space elevators to facilitating the construction of megastructures on scales previously confined to theoretical speculation. This work underscores the transformative power of magmatter, a material whose unique properties, rooted in its fundamental physics, promise to redefine the limits of what is achievable in advanced material science and engineering across the galaxy.

References

[1] Zou Xiang-Yi, Google Gemini. “The Extreme Properties of Magnetic Monopole Matter.” Xenomancy Lores, 2025. Available at: https://lores.xenomancy.id/genai/the-extreme-properties-of-magnetic-monopole-matter/

[2] Zou Xiang-Yi, Google Gemini. “Revisiting the Bulk Density of Magnetic Monopole Matter: Theoretical Models, Terrestrial Validation, and Unexpected Insights from Mag-Diamond Crystallography.” Xenomancy Lores, 2025. Available at: https://lores.xenomancy.id/genai/revisiting-bulk-mag-monopole-matter-density/

[3] Dresselhaus, M. S., Dresselhaus, G., & Avouris, P. (2001). Carbon Nanotubes: Synthesis, Structure, Properties, and Applications. Springer Science & Business Media.

[4] Yu, M. F., Lourie, O., Dyer, M. J., Moloni, K., Kelly, T. F., & Ruoff, R. S. (2000). Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load. Science, 287(5453), 637-640.

Appendix A: Theoretical Properties of Mag-Boron Nitride Nanotubes (Mag-BNNTs)

While mag-carbon nanotubes (mag-CNTs) represent a revolutionary class of materials, exploring alternative magmatter compositions is crucial for understanding the full spectrum of their potential. Boron nitride nanotubes (BNNTs) in ordinary matter are structural analogues to CNTs, known for their distinct electronic and thermal properties. This appendix theoretically investigates the linear mass density, tensile strength, specific strength, and breaking length of mag-boron nitride nanotubes (mag-BNNTs), building upon the same Model C understanding of magmatter’s condensed phase as applied to mag-CNTs.

A.1. Mag-Boron and Mag-Nitrogen Atoms

We first define the properties of mag-boron (B) and mag-nitrogen (N) atoms based on their atomic numbers (Z) and the established magmatter principles [1].

  • Mag-Boron (B): Analogous to Boron (Z=5).

    • Composition: Magnucleus with +5g_D, 5 magtrons.
    • Mass ($M_{\text{mag-B}}$): $5 \times (10 \text{ TeV}/c^2) + 5 \times (1.5 \text{ TeV}/c^2) = 50 \text{ TeV}/c^2 + 7.5 \text{ TeV}/c^2 = \mathbf{57.5 \text{ TeV}/c^2}$.
    • Bohr Radius ($r_{\text{mag-B, Bohr}}$):
      • Reduced Mass ($\mu_{\text{mag-B}}$): $\frac{50 \cdot 1.5}{50+1.5} = \frac{75}{51.5} \approx 1.456 \text{ TeV}/c^2$.
      • $r_{\text{mag-B, Bohr}} = \frac{n^2 \hbar c}{Z \alpha_{\text{eff}} \mu c^2} = \frac{1 \cdot (0.1973 \text{ GeV} \cdot \text{fm})}{5 \cdot (0.678) \cdot (1456 \text{ GeV})} \approx \mathbf{0.0000398 \text{ fm}}$.

  • Mag-Nitrogen (N): Analogous to Nitrogen (Z=7).

    • Composition: Magnucleus with +7g_D, 7 magtrons.
    • Mass ($M_{\text{mag-N}}$): $7 \times (10 \text{ TeV}/c^2) + 7 \times (1.5 \text{ TeV}/c^2) = 70 \text{ TeV}/c^2 + 10.5 \text{ TeV}/c^2 = \mathbf{80.5 \text{ TeV}/c^2}$.
    • Bohr Radius ($r_{\text{mag-N, Bohr}}$):
      • Reduced Mass ($\mu_{\text{mag-N}}$): $\frac{70 \cdot 1.5}{70+1.5} = \frac{105}{71.5} \approx 1.469 \text{ TeV}/c^2$.
      • $r_{\text{mag-N, Bohr}} = \frac{n^2 \hbar c}{Z \alpha_{\text{eff}} \mu c^2} = \frac{1 \cdot (0.1973 \text{ GeV} \cdot \text{fm})}{7 \cdot (0.678) \cdot (1469 \text{ GeV})} \approx \mathbf{0.0000283 \text{ fm}}$.

  • Average Mag-BN Atom: For a BNNT, we consider an alternating structure, so we use average properties for a B-N unit.

    • Average Mass ($M_{\text{mag-BN, avg}}$): $(57.5 + 80.5) / 2 = \mathbf{69 \text{ TeV}/c^2}$ (Note: This is coincidentally the same average mass as a mag-carbon atom).
    • Average Bohr Radius ($r_{\text{mag-BN, Bohr, avg}}$): $(0.0000398 + 0.0000283) / 2 = \mathbf{0.00003405 \text{ fm}}$.

A.2. Theoretical Framework for Mag-Boron Nitride Nanotubes

Normal BNNTs also form hexagonal lattices, similar to CNTs, with a typical B-N bond length of approximately 0.145 nm. We will scale this to the magmatter domain. The average covalent radius for a B-N bond in normal BNNT is roughly $(88 \text{ pm} + 75 \text{ pm})/2 = 81.5 \text{ pm}$.

  • Scaling Factor for Mag-BNNTs ($S_{\text{BN}}$): $$S_{\text{BN}} = \frac{r_{\text{mag-BN, Bohr, avg}}}{r_{\text{BN, covalent, avg}}} = \frac{0.00003405 \text{ fm}}{81.5 \text{ pm}} = \frac{3.405 \times 10^{-20} \text{ m}}{8.15 \times 10^{-11} \text{ m}} \approx \mathbf{4.178 \times 10^{-10}}$$ (Note: This scaling factor is slightly smaller than that for mag-carbon, $S_{\text{C}} \approx 5.300 \times 10^{-10}$).

  • Mag-BN Bond Length ($L_{\text{mag-BN}}$): $$L_{\text{mag-BN}} = 0.145 \times 10^{-9} \text{ m} \times 4.178 \times 10^{-10} \approx \mathbf{6.06 \times 10^{-19} \text{ m}}$$

A.3. Calculation of Linear Mass Density for Mag-BNNTs

We scale the linear mass density of a normal BNNT ($\rho_{L, \text{BNNT}}$) using the average mag-BN atom mass and the mag-BN scaling factor. A typical normal BNNT has a linear mass density slightly higher than CNTs due to the slightly heavier average atomic mass (average B-N mass $\approx 12.409 \text{ amu}$ vs. Carbon $\approx 12 \text{ amu}$). Let’s use $\rho_{L, \text{BNNT}} \approx 1.137 \times 10^{-12} \text{ kg/m}$ (scaled from CNT by mass ratio).

$$\rho_{L, \text{mag-BNNT}} = \rho_{L, \text{BNNT}} \times \left( \frac{M_{\text{mag-BN, avg}}}{M_{\text{BN, avg}}} \right) \times \left( \frac{1}{S_{\text{BN}}} \right)$$

Where:

  • $M_{\text{mag-BN, avg}} \approx 2.352 \times 10^{-22} \text{ kg}$
  • $M_{\text{BN, avg}} \approx 12.409 \text{ amu} \approx 2.059 \times 10^{-26} \text{ kg}$

Substituting these values: $$\rho_{L, \text{mag-BNNT}} = (1.137 \times 10^{-12} \text{ kg/m}) \times \left( \frac{1.229 \times 10^{-22} \text{ kg}}{2.059 \times 10^{-26} \text{ kg}} \right) \times \left( \frac{1}{4.178 \times 10^{-10}} \right)$$ $$\rho_{L, \text{mag-BNNT}} = (1.137 \times 10^{-12}) \times (5968.91) \times (2.3936 \times 10^9)$$ $$\rho_{L, \text{mag-BNNT}} \approx \mathbf{16.2 \text{ kg/m}}$$

A.4.1. Derivation of a Boron-Nitride-Specific Strength Scaling Factor

To ensure maximum accuracy and consistency with the methodology used for mag-carbon nanotubes in the main body of this paper, we will derive a new material-specific strength scaling factor for boron-nitride-based magmatter. This approach replaces the use of a generalized, hydrogen-based scaling factor with one derived directly from the properties of a normal boron-nitride (B-N) bond.

The overall strength scaling is a product of the scaling of energy-per-bond and the scaling of bonds-per-unit-area.

  • Energy Scaling: We compare the magmatter binding energy ($E_{mag} \approx 300 \text{ GeV}$) to the cohesive energy of a normal B-N bond in hexagonal boron nitride ($E_{B-N} \approx 6.2 \text{ eV}$). $$\text{Energy Scaling Factor} = \frac{E_{mag}}{E_{B-N}} = \frac{300 \times 10^9 \text{ eV}}{6.2 \text{ eV}} \approx 4.84 \times 10^{10}$$

  • Length Scaling: We compare the normal B-N average covalent radius ($r_{B-N, avg} \approx 81.5 \text{ pm}$) to the average mag-BN Bohr radius ($r_{mag-BN, avg} \approx 3.405 \times 10^{-5} \text{ pm}$). $$\text{Length Scaling Factor (Inverse)} = \frac{r_{B-N, avg}}{r_{mag-BN, avg}} = \frac{8.15 \times 10^{-11} \text{ m}}{3.405 \times 10^{-20} \text{ m}} \approx 2.39 \times 10^9$$

  • Overall Strength Scaling: The final factor is the energy scaling multiplied by the cube of the inverse length scaling. $$\text{Overall Strength Scaling} = (\text{Energy Scaling}) \times (\text{Length Scaling (Inverse)})^3$$ $$\text{Overall Strength Scaling} = (4.84 \times 10^{10}) \times (2.39 \times 10^9)^3 \approx 6.61 \times 10^{38}$$ This new Boron-Nitride-Specific Strength Scaling Factor of $6.61 \times 10^{38}$ will be used for all subsequent calculations involving mag-BNNTs.

A.4.2. Recalculation of Mag-BNNT Mechanical Properties

We now apply this new scaling factor to the benchmark theoretical tensile strength of a conventional single-walled boron nitride nanotube (SWBNNT), which is approximately 87 GPa ($87 \times 10^9 \text{ Pa}$), a value comparable to CNTs.

  • Theoretical Tensile Strength ($\sigma_{T, \text{mag-BNNT}}$): $$\sigma_{T, \text{mag-BNNT}} = \sigma_{T, \text{BNNT}} \times \text{Overall Strength Scaling}$$ $$\sigma_{T, \text{mag-BNNT}} = (87 \times 10^9 \text{ Pa}) \times (6.61 \times 10^{38}) = \mathbf{5.75 \times 10^{49} \text{ Pa}}$$

  • Bulk Density of Mag-BNNT (Model C): We need this for specific strength. The calculation is based on a diamond-like lattice with 34% packing efficiency.

    • Average mag-BN atom mass: $1.229 \times 10^{-22} \text{ kg}$.
    • Average mag-BN Bohr radius: $3.405 \times 10^{-20} \text{ m}$.
    • Volume of average mag-BN atom: $\frac{4}{3}\pi (3.405 \times 10^{-20})^3 \approx 1.65 \times 10^{-58} \text{ m}^3$.
    • Bulk density ($\rho_{mag-BN, \text{diamond}}$): Using the unit cell method, $\frac{8 \times (1.229 \times 10^{-22} \text{ kg})}{ (8 \times 1.65 \times 10^{-58} \text{ m}^3) / 0.34} \approx \mathbf{2.53 \times 10^{35} \text{ kg/m}^3}$.

  • Specific Strength ($S_{S, \text{mag-BNNT}}$): $$S_{S, \text{mag-BNNT}} = \frac{\sigma_{T, \text{mag-BNNT}}}}{\rho_{mag-BN, \text{diamond}}} = \frac{5.75 \times 10^{49} \text{ Pa}}{2.53 \times 10^{35} \text{ kg/m}^3} \approx \mathbf{2.27 \times 10^{14} \text{ N} \cdot \text{m/kg}}$$

  • Breaking Length ($L_{B, \text{mag-BNNT}}$): $$L_{B, \text{mag-BNNT}} = \frac{S_{S, \text{mag-BNNT}}}{g} = \frac{2.27 \times 10^{14} \text{ m}^2/\text{s}^2}{9.81 \text{ m/s}^2} \approx \mathbf{2.31 \times 10^{13} \text{ m}}$$

  • Breaking Load of a Single Thread: Following the same procedure, we can calculate the breaking load for a single mag-BNNT thread.

    1. Diameter of Mag-BNNT: Based on scaling a typical BNNT (diameter $\approx 1.38$ nm) by the mag-BNNT scaling factor ($S_{BN} \approx 4.178 \times 10^{-10}$), the diameter is approximately $5.76 \times 10^{-19} \text{ m}$.
    2. Cross-sectional Area: The area is $\pi r^2$, which is $\pi \times (2.88 \times 10^{-19} \text{ m})^2 \approx 2.61 \times 10^{-37} \text{ m}^2$.
    3. Breaking Load (Force): $$\text{Force} = (5.75 \times 10^{49} \text{ N/m}^2) \times (2.61 \times 10^{-37} \text{ m}^2)$$ $$\text{Force} \approx \mathbf{1.50 \times 10^{13} \text{ N}}$$

    This means a single mag-BNNT thread could theoretically withstand a load of 15.0 trillion Newtons.

A.5. Comparison Summary: Mag-CNTs vs. Mag-BNNTs

Property Mag-Carbon Nanotube (Theoretical) Mag-Boron Nitride Nanotube (Theoretical)
Linear Mass Density $\approx 12.8 \text{ kg/m}$ $\approx 16.2 \text{ kg/m}$
Tensile Strength $\approx 5.60 \times 10^{49} \text{ Pa}$ $\approx 5.75 \times 10^{49} \text{ Pa}$
Specific Strength $\approx 2.87 \times 10^{14} \text{ N} \cdot \text{m/kg}$ $\approx 2.27 \times 10^{14} \text{ N} \cdot \text{m/kg}$
Breaking Length $\approx 2.93 \times 10^{13} \text{ m}$ $\approx 2.31 \times 10^{13} \text{ m}$
Breaking Load (Single Thread) $\approx 2.28 \times 10^{13} \text{ N}$ $\approx 1.50 \times 10^{13} \text{ N}$

Conclusion: Our theoretical calculations suggest that while mag-BNNTs exhibit a slightly higher linear mass density (16.2 kg/m vs 12.8 kg/m), their theoretical tensile strength ($5.75 \times 10^{49} \text{ Pa}$) is remarkably comparable to, and even slightly exceeds, that of mag-CNTs ($5.60 \times 10^{49} \text{ Pa}$). However, due to their lower density, mag-CNTs maintain a superior specific strength and breaking length. This finding highlights that both materials are top-tier candidates for megastructure engineering, with the choice between them depending on whether absolute stress resistance (favoring Mag-BNNTs) or strength-to-weight efficiency (favoring Mag-CNTs) is the more critical design parameter.