On the radiative and multiple reflection corrections of the van der Waals force between two particles/atoms: dipolar contribution
DOI:
https://doi.org/10.31349/RevMexFis.69.040403Keywords:
Van der Waals force; Casimir force; electromagnetic fluctuationsAbstract
We present a theoretical formalism based on fluctuational electrodynamics and the Maxwell-stress tensor for describing the impact of radiative and multiple reflections corrections on the van der Waals force between two nanoscale spherical particles and a pair of atoms in the dipolar approximation. Particularly, we examine the van der Waals forces for two metallic particles whose dielectric constant is represented by the Drude model, for two dielectric particles in which their material response has phononic resonances, and for two atoms with dynamic polarizabilities containing a single resonant frequency. For the metallic particles, in relation to the case in which the aforementioned effects are omitted, the van der Waals force is unchanged by the radiative corrections of the polarizabilities, whereas the mechanism of multiple reflections perturbs force about a few percentage points when the spheres nearly touch each other. In contrast to the the metallic case, the radiative corrections of the polarizabilities of the dielectric particles modify peculiarly the van der Waals force in comparison to the case where such corrections are neglected; there is a critical interparticle separation that divides two regimes: when the interparticle separation is smaller (larger) than this critical distance the force with radiative corrections is smaller (greater) than that without these corrections. Moreover, the van der Waals force is practically unchanged when effect of multiple reflections is taken into account. For the atomic case, the deviation of the van der Waals force due to multiple reflections is about a few percentage points when the interatomic separation corresponds to twice the van der Waals radius, and this deviation can reach about seventeen percent at a separation of 2.5 times the atomic radius. This work might have implications concerning the fine-tuning between theoretical and experimental outcomes of the van der Waals forces.
References
F. London, The general theory of molecular forces, Trans. Faraday Soc. 33 (1937) 8b.
H. G. B. Casimir, On the attraction between two perfectly conducting plates, Proc. Kon. Ned. Akad. Wetensch. B 51 (1948) 793.
C. Kittel, Introduction to Solid State Physics, chap. 3, pp. 49– 60, 8th ed. (John Wiley & Sons, Hoboken, NJ, 2005).
G.-X. Zhang, A. Tkatchenko, J. Paier, H. Appel, and M. Scheffler, Van der Waals interactions in ionic and semiconductor solids, Phys. Rev. Lett. 107 (2011) 245501.
D. Leckband and S. Sivasankar, Forces controlling protein interactions: theory and experiment, Colloid Surf. B 14 (1999) 83.
B. Kollmitzer, P. Heftberger, R. Podgornik, J. F. Nagle, and G. Pabst, Bending rigidities and interdomain forces in membranes with coexisting lipid domains, Biophys. J. 108 (2015) 2833.
F. M. Serry, D. Walliser, and G. J. Maclay, The role of the Casimir effect in the static deflection and stiction of membrane strips in microelectromechanical systems (MEMS), J. Appl. Phys. 84 (1998) 2501.
C. Henkel and K. Joulain, Casimir force between designed materials: What is possible and what not, Europhys. Lett. 72 (2005) 929.
J. F. Dobson, T. Gould, and G. Vignale, How many-body effects modify the van der Waals interaction between graphene sheets, Phys. Rev. X 4 (2014) 021040.
W. Nie, R. Zeng, Y. Lan, and S. Zhu, Casimir force between topological insulator slabs, Phys. Rev. B 88 (2013) 085421.
J. H. Wilson, A. A. Allocca, and V. Galitski, Repulsive Casimir force between Weyl semimetals, Phys. Rev. B 91 (2015) 235115.
M. F. Maghrebi, S. J. Rahi, T. Emig, N. Graham, R. L. Jaffe, and M. Kardar, Analytical results on Casimir forces for conductors with edges and tips, P. Natl. Acad. Sci. USA 108 (2011) 6867.
M. Levin, A. P. McCauley, A. W. Rodriguez, M. T. Homer Reid, and S. G. Johnson, Casimir repulsion between metallic objects in vacuum, Phys. Rev. Lett. 105 (2010) 090403.
M. Antezza, Surface-atom force out of equilibrium and its effect on ultra-cold atoms, J.Phys. A: Math. Gen. 39 (2006) 6117.
M. Krüger, T. Emig, and M. Kardar, Nonequilibrium electromagnetic fluctuations: Heat transfer and interactions, Phys. Rev. Lett. 106 (2011) 210404.
V. A. Parsegian, Van der Waals Forces (Cambridge University Press, New York, NY, 2006).
D. Dalvit, P. Milonni, D. Roberts, and F. da Rosa, eds., Casimir Physics, Lecture Notes in Physics (Springer, Berlin, 2011).
L. M. Woods, D. A. R. Dalvit, A. Tkatchenko, P. Rodriguez-Lopez, A. W. Rodriguez, and R. Podgornik, Materials perspective on Casimir and van der Waals interactions, Rev. Mod. Phys. 88 (2016) 045003.
J. Herman, R. A. DiStasio Jr., and A. Tkatchenko, Firstprinciples models for van der Waals interactions in molecules and materials: Concepts, theory, and applications, Chem. Rev. 117 (2017) 4714.
P. J. van Zwol, G. Palasantzas, and J. Th. M. De Hosson, Influence of dielectric properties on van der Waals/Casimir forces in solid-liquid systems, Phys. Rev. B 79 (2009) 195428.
M. M. Gudarzi and S. H. Aboutabelu, Self-consistent dielectric functions of materials: Toward accurate computation of Casimir-van der Waals forces, Sci. Adv. 7 (2021) eabg2272.
P. J. van Zwol, G. Palasantzas, and J. Th. M. De Hosson, Influence of random roughness on the Casimir force at small separations, Phys. Rev. B 77 (2008) 075412.
W. Broer, G. Palasantzas, J. Knoester, and V. B. Svetovoy, Significance of the Casimir force and surface roughness for actuation dynamics of MEMS, Phys. Rev. B 87 (2013) 125413.
S. Kawai et al., Van der Waals interactions and the limits of isolated atom models at interfaces, Nat. Comm. 7 (2016) 11559.
M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, and M. R. Querry, Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W, Appl. Opt. 24 (1985) 4493.
W. J. Choyke and E. D. Palik, Handbook of Optical Constants of Solids, chap. Silicon Carbide (SiC), pp. 587–595 (Academic Press, San Diego, 1985).
L. Novotny and B. Hecht, Principle of Nano-optics, 1st ed. (Cambridge University Press, Cambridge, UK, 2006).
WebElements, https://www.webelements.com, (last accessed September 6th, 2022).
J. Tao, J. P. Perdew, and A. Ruzsinszky, Accurate van der Waals coefficients from density functional theory, P. Natl. Acad. Sci. (USA) 109 (2012) 18.
T. Ooura and M. Mori, The double exponential formula for oscillatory functions over the half infinite interval, J. Comput. Appl. Math. 38 (1991) 353.
M. Mori and M. Sugihara, The double-exponential transformation in numerical analysis, J. Comput. Appl. Math. 127 (2001) 287.
A. D. Yaghjian, Electric dyadic Green’s functions in the source region, Proc. IEEE 68 (1980) 248.
G. S. Agarwal, Quantum electrodynamics in the presence of dielectrics and conductors. I. Electromagnetic-field response functions and black-body fluctuations in finite geometries, Phys. Rev. A 11 (1975) 230.
W. Eckhardt, First and second fluctuation-dissipation theorem in electromagnetic fluctuation theory, Opt. Commun. 41 (1982) 305.
K. Joulain, J.-P. Mulet, F. Marquier, R. Carminati and J.-J. Greffet, Surface electromagnetic waves thermally excited: Radiative heat transfer, coherence properties and Casimir forces revisited in the near field, Surf. Sci. Rep. 57 (2005) 59.
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