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Surface Curvature-Quantized Energy and Forcefield in Geometrochemical Physics

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Surface Curvature-Quantized Energy and Forcefield in Geometrochemical Physics Title: Surface curvature-quantized energy and forcefield in geometrochemical physics Author: Z. R. Tian, Univ. of Arkansas, Fayetteville, AR 72701, USA, (Email) [email protected]. Text: Most recently, simple-shape particles’ surface area-to-volume ratio has been quantized into a geometro-wavenumber (Geo), or geometro-energy (EGeo) hcGeo, to quantitatively predict and compare nanoparticles (NPs), ions, and atoms geometry- quantized properties1,2. These properties range widely, from atoms’ electronegativity (EN) and ionization potentials to NPs’ bonding energy, atomistic nature, chemical potential of formation, redox potential, surface adsorbates’ stability, and surface defects’ reactivity. For countless irregular- or complex-shaped molecules, clusters, and NPs whose Geo values are uneasy to calculate, however, the EGeo application seems limited. This work has introduced smaller surfaces’ higher curvature-quantized energy and forcefield for linking quantum mechanics, thermodynamics, electromagnetics, and Newton’s mechanics with Einstein’s general relativity. This helps quantize the gravity, gravity-counterbalancing levity, and Einstein’s spacetime, geometrize Heisenberg’s Uncertainty, and support many known theories consistently for unifying naturally the energies and forcefields in physics, chemistry, and biology. Firstly, let’s quantize shaper corners’ 1.24 (keVnm). Indeed, smaller atoms’ higher and edges’ greater surface curvature (1/r) into EN and smaller 0-dimensional (0D) NPs’ a spacetime wavenumber (ST), i.e. Spacetime lower melting point (Tm) and higher (i.e. Energy (EST) = hc(ST) = hc(1/r) (see the Fig. more blue-shifted) optical bandgap (EBG) (see 3 below), where the r = particle radius, h = the Supplementary Table S1)3-9 are linearly Planck constant, c = speed of light, and hc governed by their greater (1/r) i.e. (EST/hc) 1 6 a) 3 CdTe 0D-NPs EBG vs. (1/r) f) 4 2 2 y = 1.5595x + 1.3038, R² = 0.98 EN (eV) 1 y = 0.169x - 0.013, R² = 0.99 0 BG E 0.1 0.3 0.5 0.7 0.9 3 7 11 15 19 23 27 1/r (nm-1) 1/r (nm-1) 4 b) 4 CdSe 0D-NPs EBG vs. (1/r) g) 3 2 2 EN (eV) y = 0.843x + 1.7011, R² = 0.98 1 y = 0.2947x - 0.739, R² = 0.98 BG 0 E 0 0.6 1.2 1.8 3 6 9 12 15 1/r (nm-1) 1/r (nm-1) 4 c) 5 CdS 0D-NPs EBG vs. (1/r) h) 4 2 (eV) 3 y = 0.6404x + 2.502, R² = 0.94 EN 2 y = 0.3298x - 0.629, R² = 0.99 BG 0 E 0 0.8 1.6 2.4 3.2 3 6 9 12 1/r (nm-1) 1/r (nm-1) 4 d) 2 PbSe 0D-NPs EBG vs. (1/r) i) 1 2 (eV) y = 1.7179x + 0.1643, R² = 1.00 EN y = 0.3169x - 0.3703, R² = 0.97 BG 0 0 E 0.3 0.5 0.7 0.9 3 5 7 9 11 1/r (nm-1) 1/r (nm-1) e) Au 0D-NPs Tm vs. (1/r) j) 3 ) 1500 K 2 o 1000 ( 500 y = -651.54x + 1367.8, R² = 0.99 EN 1 m y = 0.3244x - 0.3442, R² = 0.98 T 0 0 0 0.2 0.4 0.6 0.8 3 4 5 6 7 8 1/r (nm-1) 1/r (nm-1) Fig. 1. The generalized linear fits of spherical particles’ 3(1/r) i.e. 3(EST/hc). With 0D- NPs EBG (a)-(d), with Au 0D-NPs Tm (e), and with main-group atoms’ EN values (f)-(j). -6 10 (Fig. 1). Since a spherical particle’s Geo = For a nucleon (r ≈ 0.4 × 10 nm) , 2 3 -6 4πr /(4πr /3) = 3(1/r), i.e. EGeo hcGeo = for instance, its EST = 1.24/(0.4 × 10 ) = 3.1 hc3(1/r), or EST = EGeo/3, the non-spherical (GeV), contrasting the E(Nuclear Binding) 10 11 structure’s EGeo simply averages all surface- (MeV) (see the Supplementary curvatures’ EST. The EST, proving the Surface Information). In a spherical particle’s total Curvature−Energy Equivalence (SCEE), energy, the E(surface) (= EST = hc/r) unites the 2 supports minute facet-, edge- and corner- E(potential) (= moc , i.e. Einstein’s mass- 12 energy ) with the E(kinetic) (= pc, i.e. de surfaces’ dangling bonds, and the EST-based 13 chemical physics below. Broglie’s matter-wave energy i.e. QM), 2 where the mo = particle rest mass, and p = charge’s inward forcefield). The repulsing particle momentum. FST(convex) couples with the attracting By the energy−force relation, the FST(concave) (like that between opposite point- Spacetime Force (FST) = EST/d (see the Fig. charges, see the Supplementary Fig. S1), 3), where the d = distance to the curving pushing a freestanding smaller S-shaped surface. Thus, the convex surfaces’ positive string (Fig. 2a) (or spiral, e.g. DNA- and/or curvature-quantized repulsing FST(convex) > 0 -helices) to rotate faster. (like a positive charge’s outward forcefield), Given a nanoshell’s inner concave and concave surfaces’ negative curvature- surface’s negative (−1/r)-based attracting based attractive FST(concave) < 0 (like a negative force F⃑ ST(A) = −hc/(rd), thickness y, and outer Atom a) b) c) Acceleration FST(R) Spin Deceleration Nanoshell FST(A) F F A R FST(R) F F R Deceleration A F Spin Earth ST(A)(gravity) Acceleration d) FR e) FA FR FA Particle FA FA Planet FR FR N S F FR FR F Point Point A A + - charge S charge N FA F Magnetic fields FR A FR Fig. 2. Schematics of FST interaction, migration, rotation, vibration and oscillation. In between the S-shaped string’s convex and concave surfaces (a), Earth, nanoshell, and atom (b), migrating particles (c), thermally vibrating and oscillating string’s and membrane’s curving surfaces (d), and spinning particle, planet, and point-charges (d). 3 convex surface’s positive {1/(r + y)}-based of Motion and Wheeler’s Geometrodynamic 14,15 repulsing force F⃑ ST(R) = hc/{d(r + y)}, the Gravitation . 2 Countering bigger planets’ greater FA F⃑ ST(nanoshell) = (F⃑ ST(R) + F⃑ ST(A)) = −hcy/(r d + that pulls the planets closer (Supplementary ryd). Symmetrically, the F⃑ ST(nanoshell) should Fig. S2), smaller particles’ surface greater couple with the atom’s F⃑ ST(R) and Earth’s FST(R) repel the particles farther apart each F⃑ ST(A) (Fig. 2b). other (Fig. 2c). This supports smaller Between close-packed smaller particles greater incapability of collision particles, the smaller void’s greater (F⃑ ST(shell)- (matching the Ideal Gas Law, and a particle like) F⃑ ST(A) should pull the particles closer. collider’s need of high energy-input), faster This can help quantify self-assemblies’ Brownian motion (i.e. nonstop acceleration, F⃑ -based bonding to expand the Chemical ST(A) deceleration, and rotation), lower boiling and 3 Bonding Theory , and attribute a planet’s freezing points, and greater chaosity (or mass-induced gravity to the voids (or Boltzmann entropy i.e. thermodynamics). ⃑ ⃑ vacuums) of all sizes, i.e. F(gravity) = FST(void) So, smaller particles in faster rotation, (Supplementary Information). acceleration and deceleration should interact Accordingly, a particle can migrate more using their greater FST, emitting waves steadily (or stay still) when the surrounding in stronger diffractions upon passing through 16 net F⃑ ST(Net) = 0, acceleratively when the two thinner and closer slits (i.e. four matter- F⃑ ST(Net) > 0, deceleratively when the F⃑ ST(Net) < vacuum interfaces). This supports the EST in 0, and rotate when passing by another particle governing the QM’s wave−particle dualism17 18 (Fig. 2c). This supports the FST-based and quantum entanglement . mechanics and dynamics in Newton’s Laws 4 Further, thinner and longer wires and considering the EST and EST-spun ФST. Thus, membranes can use their edge’s and curving on thinner strings and membranes in higher surface’s higher EST(Levity) to energize nearby thermal vibration or oscillation (Fig. 2d), the smaller particles to migrate in a higher speed greater EST(Surface) should support the Tribo- (or momentum) over a longer mean free path energy Nanogenerators21, String Theory22, 23 on the edge and surface. This supports the FST and M-Theory . in motor proteins’ quicker migration on Thus, a spinning particle’s rotating 19 thinner nanowires and rapid charge transfer FST can couple with an oppositely spinning on thousands of topological insulators20. particle’s and with a spinning planet’s, as Logically, the DNA- and -helices spinning point-charges do (Fig. 2e). This can 24 edges’ EST should energize nearby molecules help expand Maxwell Equations , e.g. and ions to spiral rapidly along the edge to ∮ E⃑⃑ STdA⃑⃑ ST -dФST/dt, where the A⃑⃑ ST = E⃑⃑ ST activate countless chemical changes. This flux area, and ФST = FST-rotated magnetics helps expand the chemical bonding theory3 to n ) n n ) ) 1 100 200 Cl 1 Br 60 I - - 1 R² = 0.999 - R² = 0.9637 100 R² = 0.9883 50 30 1/r (nm 1/r 1/r (nm 1/r 0 0 (nm 1/r 0 -1 1 3 5 7 -1 1 3 5 7 -1 1 3 5 7 () Charge () Charge () Charge ) ) ) n n 60 ) n n 1 60 60 1 1 160 1 S Se - - N - Te - 30 R² = 0.9999 30 R² = 0.9975 30 R² = 0.9598 80 R² = 0.9975 1/r (nm 1/r 1/r (nm 1/r 1/r (nm 1/r 0 (nm 1/r 0 0 0 -2 0 2 4 6 8 -2 0 2 4 6 8 -2 0 2 4 6 8 -3 -1 1 3 5 7 () Charge () Charge () Charge () Charge +n +n +n +n ) ) +n ) ) V 60 Cr ) Mn 60 Mo 60 60 1 1 100 1 1 Ru 1 - - - - - R² = 0.983 R² = 0.9581 30 R² = 0.9632 30 R² = 0.9996 50 R² = 0.9714 30 30 0 1/r (nm 1/r 1/r (nm 1/r 0 0 (nm 1/r 1/r (nm 1/r 0 (nm 1/r 0 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 (+) Charge (+) Charge (+) Charge (+) Charge (+) Charge +n +n +n +n +n ) ) 40 ) 40 60 Re 60 Os ) 60 U Np Pu 1 1 1 1 1) - - - - - 30 R² = 0.9823 30 R² = 0.9228 30 R² = 0.9654 20 R² = 0.9647 20 R² = 0.9639 1/r (nm 1/r 1/r (nm 1/r 0 0 1/r (nm 1/r 0 (nm 1/r 0 0 1/r (nm 1/r 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 3 4 5 6 7 8 (+) Charge (+) Charge (+) Charge (+) Charge (+) Charge Fig.
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