This manuscript investigates the theoretical properties of one-dimensional mag-carbon polymers, specifically mag-carbyne, as a lighter-weight alternative to the previously studied mag-carbon nanotubes (mag-CNTs). While mag-CNTs exhibit unparalleled absolute strength, their substantial linear mass density ($\approx 12.8 \text{ kg/m}$) presents a challenge for mass-critical applications. This work explores if a 1D polymer analogue can offer a superior strength-to-weight ratio. By applying a rigorously derived, carbon-specific scaling methodology to carbyne, theoretically the strongest 1D material, we calculate the properties of its magmatter counterpart.

Our results predict that a mag-carbyne chain possesses a theoretical tensile strength of $1.12 \times 10^{51} \text{ Pa}$ and a specific strength of $5.74 \times 10^{15} \text{ N} \cdot \text{m/kg}$, both approximately 20 times greater than those of a mag-CNT. Most critically, its linear mass density is found to be only $1.78 \times 10^{-3} \text{ kg/m}$, over 7,000 times lighter than a mag-CNT, yielding a breaking length of 585 trillion kilometers. While the absolute breaking load of a single chain is lower than that of a single, more massive nanotube, we conclude that mag-carbyne’s phenomenal specific strength and flexibility make it the ideal foundational thread for creating woven macro-scale structures. It represents a revolutionary material for applications where minimal mass per unit length is the most critical design parameter, such as tethers for space elevators and the construction of planetary-scale infrastructure.

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, 2], magmatter, a dualistic counterpart to ordinary electrically charged matter, exhibits properties of unparalleled extremity. Its fundamental constituents—the fermionic magtron and magnucleus—are bound by powerful Higgs-boson mediated interactions, resulting in a material with astronomical densities, unfathomable mechanical strength, and melting temperatures orders of magnitude beyond any known conventional substance.

Subsequent research has extended these foundational principles to explore the properties of specific magmatter allotropes, most notably mag-carbon nanotubes (mag-CNTs) [3]. Rigorous theoretical modeling, using a carbon-specific scaling factor, predicts that these structures possess an immense tensile strength on the order of $5.60 \text{ } \times 10^{49} \text{ Pa}$. However, these same studies revealed that the extreme mass of mag-carbon atoms, combined with their dense packing in a nanotube lattice, results in a substantial linear mass density of approximately $12.8 \text{ kg/m}$.

While mag-CNTs represent a pinnacle of absolute strength, their significant mass per unit length may be a limiting factor for applications where the strength-to-weight ratio (specific strength) is the most critical design parameter. Grand-scale engineering projects, such as space elevators, planetary rings, and interstellar tethers, demand materials that are not only strong but also exceptionally lightweight to minimize the immense challenge of supporting their own mass against gravitational forces. This necessity motivates the current investigation into one-dimensional (1D) mag-carbon polymers as a potentially lighter, more efficient alternative.

This paper will focus on mag-carbyne, the theoretical magmatter analogue of carbyne. In ordinary matter, carbyne—a 1D chain of carbon atoms—is predicted to be the strongest material known, surpassing even graphene and carbon nanotubes [4]. By modeling mag-carbyne, we aim to establish a theoretical upper bound for the performance of any mag-carbon polymer. We will apply the same carbon-specific scaling methodology used in the revised mag-CNT study [3] to calculate its geometric properties, linear mass density, and mechanical strength, ultimately comparing its performance profile directly with that of mag-CNTs to evaluate the trade-offs between absolute strength, flexibility, and mass efficiency.

2. Benchmarking Real-World Carbon Polymers

To construct a credible theoretical model for a mag-carbon polymer, it is essential to first identify the most appropriate real-world analogue. The world of polymers is vast, but for the purpose of modeling a pure -(magC-magC)-n chain, a crucial distinction must be made between two categories of high-strength polymers.

The first category includes commercial high-strength hydrocarbon polymers, such as Zylon (PBO), Kevlar (an aramid), and Dyneema (UHMWPE). While these materials exhibit exceptional tensile strength (up to 5.8 GPa for Zylon), their molecular structure consists of a carbon backbone intricately bonded with other elements like hydrogen, oxygen, and nitrogen. These additional elements and the complex intermolecular forces (like hydrogen bonding) play a critical role in their bulk properties. As such, they are not direct structural analogues for a pure, one-dimensional chain of mag-carbon atoms.

The second category, which provides a far more accurate foundation for our study, consists of pure carbon allotropes. These materials are composed solely of carbon atoms, with their properties dictated entirely by the nature of the carbon-carbon bonds. This group includes well-known structures like diamond (3D), graphene (2D), and carbon nanotubes (quasi-1D). Within this category, the ideal analogue for a true one-dimensional polymer is carbyne.

Carbyne is a 1D chain of carbon atoms linked by alternating single and triple bonds ((-C≡C-)n) or by consecutive double bonds ((=C=C=)n). Although its synthesis in long, stable chains remains a significant experimental challenge, theoretical calculations have consistently predicted it to be the strongest material known. Its theoretical tensile strength is estimated to be in excess of 200 GPa [4], a value roughly double the intrinsic strength of graphene or carbon nanotubes (~100 GPa). This immense strength is derived from the powerful covalent bonds forming the chain’s backbone.

Given its one-dimensional nature and its status as the theoretical pinnacle of material strength, carbyne is the ideal benchmark for our mag-polymer investigation. By scaling the properties of carbyne, we can model a “mag-carbyne” chain, thereby establishing a credible upper bound for the performance of any conceivable 1D mag-carbon polymer. This approach ensures that our comparison to mag-CNTs is based on the most potent polymer analogue possible.

3. Theoretical Framework for Mag-Carbyne

To theoretically model the properties of a mag-carbyne chain, we must first establish the foundational assumptions and geometric parameters that govern its structure. This framework directly extends the “Model C” (Diamond-like Lattice) approach used in the successful analysis of mag-diamond and mag-carbon nanotubes [2, 3], which posits that magmatter forms stable, scaled-down analogues of ordinary matter’s crystalline and molecular structures.

3.1. Foundational Assumptions

Our calculations are built upon a consistent set of physical parameters for both mag-carbon and its ordinary matter counterpart. This ensures that our scaling methodology is applied uniformly and comparably with previous work.

  • Scaling Methodology: We will employ the “Model C” scaling principle, where the geometric properties of the magmatter structure are scaled from its ordinary matter analogue based on the ratio of their fundamental atomic radii.

  • Mag-Carbon Atom Properties (from [1, 2]):

    • Mass ($M_{\text{mag-C}}$): $\approx 1.229 \times 10^{-22} \text{ kg}$
    • Bohr Radius ($r_{\text{mag-C, Bohr}}$): $\approx 3.71 \times 10^{-20} \text{ m}$

  • Normal Carbon Atom Properties (for scaling):

    • Covalent Radius ($r_{\text{C, covalent}}$): $\approx 7.0 \times 10^{-11} \text{ m}$ (a standard value for carbon in covalent bonds).

3.2. Geometry of a Mag-Carbyne Chain

The geometry of the mag-carbyne chain is derived by applying the scaling factor to the known geometry of a normal carbyne chain.

  • Normal Carbyne Bond Length: The average bond length in a stable carbyne chain (-C≡C-) is approximately $L_{\text{carbyne}} \approx 0.130 \text{ nm}$ ($1.30 \times 10^{-10} \text{ m}$). This represents the distance occupied by a single carbon atom in the 1D chain.

  • Linear Scaling Factor ($S$): The scaling factor is the ratio of the mag-carbon Bohr radius to the normal carbon covalent radius. This dimensionless quantity dictates how much smaller the magmatter structure is. $$ S = \frac{r_{\text{mag-C, Bohr}}}{r_{\text{C, covalent}}} = \frac{3.71 \times 10^{-20} \text{ m}}{7.0 \times 10^{-11} \text{ m}} \approx 5.30 \times 10^{-10} $$

  • Mag-Carbyne Bond Length ($L_{\text{mag-carbyne}}$): We calculate the bond length of the mag-carbyne chain by scaling down the normal carbyne bond length by the factor $S$. $$ L_{\text{mag-carbyne}} = L_{\text{carbyne}} \times S $$ $$ L_{\text{mag-carbyne}} = (1.30 \times 10^{-10} \text{ m}) \times (5.30 \times 10^{-10}) \approx 6.89 \times 10^{-20} \text{ m} $$ This incredibly short bond length of approximately $6.89 \times 10^{-20} \text{ m}$ is a direct consequence of the mag-carbon atom’s minuscule size and the powerful inter-atomic forces that allow for such extreme proximity. This value forms the geometric basis for all subsequent calculations of the chain’s properties.

4. Calculation of Linear Mass Density ($\rho_L$)

The linear mass density ($\rho_L$), defined as mass per unit length, is a fundamental property for evaluating the efficiency of one-dimensional materials like a carbyne chain. A lower linear mass density is highly desirable for applications where weight is a critical constraint, such as in the construction of space tethers.

The calculation for the linear mass density of a mag-carbyne chain is direct and follows from the geometric and mass properties established in the previous section. It is determined by the mass of a single mag-carbon atom ($M_{\text{mag-C}}$) and the effective length that atom occupies within the one-dimensional chain ($L_{\text{mag-carbyne}}$).

The formula is given by: $$ \rho_{L, \text{mag-carbyne}} = \frac{M_{\text{mag-C}}}{L_{\text{mag-carbyne}}} $$

Using the values from our theoretical framework:

  • Mass of a Mag-Carbon Atom ($M_{\text{mag-C}}$): $\approx 1.229 \times 10^{-22} \text{ kg}$
  • Mag-Carbyne Bond Length ($L_{\text{mag-carbyne}}$): $\approx 6.89 \times 10^{-20} \text{ m}$

We can now substitute these values into the formula: $$ \rho_{L, \text{mag-carbyne}} = \frac{1.229 \times 10^{-22} \text{ kg}}{6.89 \times 10^{-20} \text{ m}} $$ $$ \rho_{L, \text{mag-carbyne}} \approx 1.78 \times 10^{-3} \text{ kg/m} $$

The resulting theoretical linear mass density for a single mag-carbyne chain is approximately $1.78 \times 10^{-3} \text{ kg/m}$, or 1.78 grams per meter.

This value is remarkably low, especially when contrasted with the calculated linear mass density of a mag-carbon nanotube, which was approximately $12.8 \text{ kg/m}$ [3]. The mag-carbyne chain is, therefore, over 7,000 times lighter per unit length than its nanotube counterpart. This dramatic reduction in mass is a direct result of its purely one-dimensional structure, which contains the absolute minimum number of atoms required to span a given length, highlighting its potential as an ultra-lightweight structural material.

5. Calculation of Theoretical Tensile Strength and Derived Properties

Having established the geometry and linear mass density of mag-carbyne, we now turn to its mechanical properties. This section calculates the theoretical tensile strength ($\sigma_T$) and derives key performance metrics such as specific strength ($S_S$), breaking length ($L_B$), and the breaking load of a single chain ($F_{\text{break}}$).

5.1. Theoretical Tensile Strength ($\sigma_T$)

The tensile strength of a material is its ultimate resistance to being pulled apart. For magmatter, this value is determined by scaling the strength of its ordinary matter analogue by a rigorously derived, material-specific scaling factor.

  • Benchmark Strength: As established in Section 2, the theoretical tensile strength of normal carbyne ($\sigma_{T, \text{carbyne}}$) is approximately 200 GPa ($200 \times 10^9 \text{ Pa}$), making it the strongest known 1D material.

  • Carbon-Specific Strength Scaling: For maximum accuracy, we use the carbon-specific strength scaling factor of $5.60 \times 10^{38}$, which was derived in [3] by comparing the properties of a mag-carbon atom to a normal carbon-carbon bond.

  • Mag-Carbyne Tensile Strength Calculation: We find the theoretical tensile strength of mag-carbyne by applying this carbon-specific scaling factor to the benchmark strength of normal carbyne. $$ \sigma_{T, \text{mag-carbyne}} = \sigma_{T, \text{carbyne}} \times (\text{Carbon-Specific Strength Scaling}) $$ $$ \sigma_{T, \text{mag-carbyne}} = (200 \times 10^9 \text{ Pa}) \times (5.60 \times 10^{38}) $$ $$ \sigma_{T, \text{mag-carbyne}} = 1.12 \times 10^{51} \text{ Pa} $$ The theoretical tensile strength of mag-carbyne is an astronomical $1.12 \times 10^{51} \text{ Pa}$. This value is approximately 20 times greater than the recalculated, immense theoretical strength of mag-CNTs, a direct result of carbyne’s superior intrinsic strength as a base material.

5.2. Derived Properties

From the tensile strength and density, we can derive metrics that better describe the material’s performance in practical applications.

  • Specific Strength ($S_S$): This is the crucial strength-to-weight ratio, calculated by dividing the tensile strength by the material’s bulk density. For consistency, we use the bulk density of mag-diamond ($\rho_{\text{mag-C, diamond}} \approx 1.95 \times 10^{35} \text{ kg/m}^3$) as a proxy for the intrinsic density of condensed mag-carbon matter [2]. $$ S_S = \frac{\sigma_{T, \text{mag-carbyne}}}{\rho_{\text{mag-C, diamond}}} = \frac{1.12 \times 10^{51} \text{ Pa}}{1.95 \times 10^{35} \text{ kg/m}^3} \approx 5.74 \times 10^{15} \text{ N} \cdot \text{m/kg} $$

  • Breaking Length ($L_B$): This is the maximum length a material can support its own weight. It is calculated by dividing the specific strength by the acceleration due to gravity ($g \approx 9.81 \text{ m/s}^2$). $$ L_B = \frac{S_S}{g} = \frac{5.74 \times 10^{15} \text{ N} \cdot \text{m/kg}}{9.81 \text{ m/s}^2} \approx 5.85 \times 10^{14} \text{ m} $$ This corresponds to a length of approximately 585 trillion kilometers.

  • Breaking Load of a Single Chain ($F_{\text{break}}$): This is the absolute force a single 1D chain can withstand. This calculation requires an assumption for the chain’s cross-sectional area. A reasonable approximation is a circle with a radius equal to the mag-carbon Bohr radius ($r_{\text{mag-C, Bohr}} \approx 3.71 \times 10^{-20} \text{ m}$). $$ A \approx \pi r_{\text{mag-C, Bohr}}^2 = \pi (3.71 \times 10^{-20} \text{ m})^2 \approx 4.32 \times 10^{-39} \text{ m}^2 $$ The breaking force is the tensile strength multiplied by this area: $$ F_{\text{break}} = \sigma_{T, \text{mag-carbyne}} \times A $$ $$ F_{\text{break}} = (1.12 \times 10^{51} \text{ N/m}^2) \times (4.32 \times 10^{-39} \text{ m}^2) \approx 4.84 \times 10^{12} \text{ N} $$ A single mag-carbyne chain can theoretically withstand a force of approximately 4.84 trillion Newtons, equivalent to the weight of about 493 million metric tons on Earth.

6. Comparative Analysis: Mag-Carbyne vs. Mag-CNT

To fully appreciate the distinct advantages and trade-offs of mag-carbyne, a direct comparison with the recalculated properties of mag-carbon nanotubes (mag-CNTs) from [3] is essential. While both materials represent the pinnacle of theoretical performance, their differing dimensionalities lead to significant differences in their key properties. The following table summarizes the recalculated theoretical values for both materials.

Property Mag-Carbyne (Theoretical) Mag-CNT (Theoretical, Recalculated) Ratio (Carbyne/CNT)
Linear Mass Density $\approx 1.78 \times 10^{-3} \text{ kg/m}$ $\approx 12.8 \text{ kg/m}$ $\approx 1.4 \times 10^{-4}$
Tensile Strength $\approx 1.12 \times 10^{51} \text{ Pa}$ $\approx 5.60 \times 10^{49} \text{ Pa}$ $\approx 20$
Specific Strength $\approx 5.74 \times 10^{15} \text{ N} \cdot \text{m/kg}$ $\approx 2.87 \times 10^{14} \text{ N} \cdot \text{m/kg}$ $\approx 20$
Breaking Length $\approx 5.85 \times 10^{14} \text{ m}$ $\approx 2.93 \times 10^{13} \text{ m}$ $\approx 20$
Breaking Load (per strand) $\approx 4.84 \times 10^{12} \text{ N}$ $\approx 2.28 \times 10^{13} \text{ N}$ $\approx 0.21$

The analysis reveals several critical insights:

  1. Mass Efficiency: The most striking difference remains in the Linear Mass Density. Mag-carbyne is approximately 7,200 times lighter per unit length than a mag-CNT. This makes it an overwhelmingly superior material for any application where minimizing mass is the primary objective.

  2. Superior Intrinsic and Specific Strength: Mag-carbyne exhibits a Tensile Strength and Specific Strength that are both roughly 20 times greater than that of mag-CNTs. This is a direct consequence of using the intrinsically stronger carbyne (200 GPa) as the structural analogue compared to the graphene sheet of a nanotube (100 GPa). This translates to a Breaking Length that is also 20 times longer, making it far more capable of supporting its own weight over astronomical distances.

  3. The Trade-off: Absolute Load per Strand: The only metric where the mag-CNT appears superior is the Breaking Load per strand. A single mag-CNT can withstand a force about five times greater than a single mag-carbyne chain. This is not because the carbyne is weaker—its material strength is far higher—but because the nanotube is a much larger structure with a significantly greater cross-sectional area, composed of many more atoms per unit length. It is, in essence, a pre-fabricated, hollow rope, whereas the carbyne chain is a single, ultra-strong thread.

This comparison clearly establishes mag-carbyne as the pre-eminent material for strength-to-weight performance. While a single nanotube is stronger than a single carbyne chain, the carbyne’s vastly lower mass and higher specific strength make it the ideal building block for creating macroscopic structures, a concept that will be explored in the following discussion.

7. Discussion and Implications

The comparative analysis between mag-carbyne and mag-carbon nanotubes reveals a clear and compelling picture of material trade-offs at the extreme edge of theoretical physics. The results indicate that mag-carbyne is not merely an incremental improvement over mag-CNTs, but represents a fundamentally different class of material optimized for weight efficiency. Its linear mass density is over 7,000 times lower, while its specific strength and breaking length are approximately two times greater.

This identifies a distinct application sweet spot for mag-carbyne. It is unequivocally the superior choice for any engineering project where the primary design constraint is minimizing mass while maximizing tensile strength over vast distances. The most prominent example is the construction of a space elevator. The calculated breaking length of 585 trillion kilometers far exceeds the requirement for reaching geostationary orbit (approx. 36,000 km), providing a safety margin so vast as to render the tether’s own weight a negligible factor in the design. Other applications, such as the construction of planetary ring systems, Dyson swarm tethers, or interstellar solar sails, would similarly benefit from a material that is almost massless relative to its strength.

The one metric where mag-CNTs appear superior—the absolute breaking load of a single strand—is misleading from a practical engineering standpoint. A single mag-CNT is a pre-formed, hollow tube with a larger cross-section, making it inherently stronger than a single 1D atomic chain. However, this is akin to comparing the strength of a steel pipe to a single fiber of Zylon. The true engineering potential lies in the ability to combine these fundamental threads into larger structures.

This leads to the concept of mag-carbyne “yarns” or “ropes.” To overcome the lower breaking load per individual chain, countless parallel strands of mag-carbyne could be woven or bundled into macroscopic cables. By doing so, a cable of any desired total breaking strength could be fabricated, while the overall structure would retain the phenomenal specific strength of the base material. A cable made from 7,200 mag-carbyne chains would have the same mass per meter as a single mag-CNT but would be approximately 14,400 times stronger (7,200 chains $\times$ 2 times the specific strength).

Furthermore, a 1D polymer chain offers a critical advantage that a rigid nanotube lacks: flexibility. A rope woven from mag-carbyne chains would be exceptionally pliable, allowing it to be spooled, stored, deployed, and repaired in a way that a rigid nanotube structure could not. This makes it far more practical for dynamic applications like tethers and cables that must withstand flexing and torsion.

In essence, the mag-CNT can be viewed as a high-strength, rigid building beam, while mag-carbyne is the ultimate high-tensile, flexible thread. For the grandest scales of structural engineering, where building materials must be lifted against gravity and support their own colossal weight, the ultra-lightweight, ultra-strong, and flexible nature of mag-carbyne makes it the undisputed material of choice.

8. Conclusion

This theoretical investigation has systematically evaluated the properties of mag-carbyne, the one-dimensional polymer analogue of magmatter, as a potential alternative to the previously studied mag-carbon nanotubes. Our findings, derived by applying a consistent scaling methodology to the strongest known 1D material, demonstrate that mag-carbyne not only complements but, in several critical aspects, surpasses the performance of its nanotube counterpart.

The calculations reveal that a mag-carbyne chain possesses a theoretical tensile strength of $1.12 \times 10^{51} \text{ Pa}$ and a specific strength of $5.74 \times 10^{15} \text{ N} \cdot \text{m/kg}$, both approximately 20 times greater than those of mag-CNTs. Most significantly, its linear mass density is over 7,000 times lower, resulting in a theoretical breaking length of 585 trillion kilometers. This establishes mag-carbyne as the pre-eminent material for applications where an extreme strength-to-weight ratio is the most critical design parameter.

While a single mag-carbyne chain has a lower absolute breaking load than a single, more massive mag-CNT, this is a superficial limitation. The true engineering potential of mag-carbyne lies in its role as a fundamental thread. By weaving these ultra-strong, ultra-lightweight, and inherently flexible chains into macroscopic cables and textiles, structures of any desired strength can be fabricated.

In conclusion, mag-carbyne represents a revolutionary material that redefines the theoretical limits of what is possible. Its unparalleled combination of lightness, strength, and flexibility makes it the ideal candidate for the most ambitious engineering projects imaginable, from single-stage space elevators to the foundational tethers of stellar-scale megastructures, solidifying magmatter’s role as the cornerstone of advanced galactic engineering.

References

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[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] Zou Xiang-Yi, Google Gemini. “Theoretical Strength and Linear Mass Density of Mag-Carbon Nanotubes: Extending the Magmatter Crystallographic Model.” Xenomancy Lores, 2025. Available at: https://lores.xenomancy.id/genai/theoretical-strength-and-linear-mass-density-of-mag-carbon-nanotubes/

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