Volume 18 Issue 1
May  2020
Article Contents

Vladimir M. Mostepanenko, Elena N. Velichko, Maksim Aleksandrovich Baranov. Role of Electromagnetic Fluctuations in Organic Electronics[J]. Journal of Electronic Science and Technology, 2020, 18(1): 52-58. doi: 10.1016/j.jnlest.2020.100023
Citation: Vladimir M. Mostepanenko, Elena N. Velichko, Maksim Aleksandrovich Baranov. Role of Electromagnetic Fluctuations in Organic Electronics[J]. Journal of Electronic Science and Technology, 2020, 18(1): 52-58. doi: 10.1016/j.jnlest.2020.100023

Role of Electromagnetic Fluctuations in Organic Electronics

doi: 10.1016/j.jnlest.2020.100023
Funds:  This work was partly supported by the Russian Foundation for Basic Research under Grant No. 19-02-00453 A
More Information
  • Author Bio:

    Vladimir M. Mostepanenko was born in St. Petersburg in 1947. He obtained the Ph.D. degree from St. Petersburg State University, St. Petersburg in 1974 and the degree of doctor in physical and mathematical sciences from Moscow State University, Moscow in 1981. He obtained the academic status of full professor in 1986. For many years, he worked with several universities in Brazil, Germany, and USA. Now he is working with the Institute of Physics, Nanotechnology and Telecommunications, Peter the Great St. Petersburg Polytechnic University (SPbPU), St. Petersburg and also with Central Astronomical Observatory at Pulkovo of the Russian Academy of Sciences, St. Petersburg. His research interests include the Casimir effect, graphene, quantum effects in strong fields, gravitation, and cosmology. He is the author of about 300 papers and several books, two of which are published by the Oxford University Press. He also took part as an invited speaker in about 100 scientific conferences

    Elena N. Velichko was born in St. Petesburg in 1982. She received the B.S. and M.S. degrees from SPbPU in 2005 and 2007, respectively. And she obtained the Ph.D. degree from Saint Petersburg Electrotechnical University, St. Petersburg in 2010. Now she is working with SPbPU as the Director of the Higher School of Applied Physics and Space Technologies at the Institute of Physics, Nanotechnology and Telecommunications. Her research interests include biomolecular electronics and the study of biomolecular processing by laser technologies

    Maksim Aleksandrovich Baranov was born in Lipetsk in 1993. He received the B.S. and M.S. degrees from SPbSTU in 2015 and 2017, respectively. Now he is pursing the Ph.D. degree with the Higher School of Applied Physics and Space Technologies, Institute of Physics, Nanotechnology and Telecommunications, SPbSTU. His research interests include self-organization processes in biological systems, image processing, and other programming for medical purposes

  • Corresponding author: V. M. Mostepanenko is with the Institute of Physics, Nanotechnology and Telecommunications, Peter the Great St. Petersburg Polytechnic University, St. Petersburg 195251 and also with Central Astronomical Observatory at Pulkovo of Russian Academy of Sciences, St. Petersburg 196140 (e-mail: vmostepa@gmail.com).
  • Received Date: 2019-08-14
  • Rev Recd Date: 2019-09-08
  • Available Online: 2020-05-06
  • Publish Date: 2020-03-01
  • Thin organic films find expanding applications in electronic and optoelectronic devices, biotechnology, food packing, and for many other purposes. Among other factors, the stability of films with a thickness below a micrometer is determined by the zero-point and thermal fluctuations of the electromagnetic field. These fluctuations result in the van der Waals and Casimir free energy and forces between a film and a substrate. The fluctuation-induced force may be both attractive and repulsive making the film either more or less stable, respectively. Here, we review recently obtained results for the Casimir free energy of both freestanding and deposited on the metallic and dielectric substrates peptide films. We also perform computations for the free energy of the peptide films deposited on a silica glass substrate in the region of parameters where this free energy vanishes. Possible applications of the obtained results are discussed.
  • 加载中
  • [1] C. D. Dimitrakopoulos and P. R. L. Malenfant, “Organic thin film transistors for large area electronics,” Advanced Materials, vol. 14, no. 2, pp. 99-117, Jan. 2002. doi:  10.1002/1521-4095(20020116)14:2<99::AID-ADMA99>3.0.CO;2-9
    [2] C.-Y. Lee, J.-C. Hwang, Y.-L. Chueh, T.-H. Chang, Y.-Y. Cheng, and P.-C. Lyu, “Hydrated bovine serum albumin as the gate dielectric material for organic field-effect transistors,” Organic Electronics, vol. 14, no. 10, pp. 2645-2651, Oct. 2013. doi:  10.1016/j.orgel.2013.07.004
    [3] M.-C. Ma, X.-J. Xu, L.-L. Shi, and L.-D. Li, “Organic field-effect transistors with a low driving voltage using albumin as the dielectric layer,” RSC Advances, vol. 4, no. 102, pp. 58720-58723, Oct. 2014. doi:  10.1039/C4RA11833B
    [4] B. Zheng, D. T. Haynie, H. Zhong, et al., “Design of peptides for thin films, coatings and microcapsules for applications in biotechnology,” Journal of Biomaterials Science, Polymer Edition, vol. 16, no. 3, pp. 285-299, Apr. 2005. doi:  10.1163/1568562053654103
    [5] M. Natesan and R. G. Ulrich, “Protein microarrays and biomarkers of infectious disease,” Intl. Journal of Molecular Sciences, vol. 11, no. 12, pp. 5165-5183, Dec. 2010. doi:  10.3390/ijms11125165
    [6] E. Velichko, M. Baranov, E. Nepomnyashchaya, A. Cheremiskina, and E. Aksenov, “Studies of biomolecular nanomaterials for application in electronics and communications,” in Internet of Things, Smart Spaces, and Next Generation Networks and Systems, S. Balandin, S. Andreev, and Y. Koucheryavy, Eds. Cham: Springer, 2015, pp. 786-792.
    [7] A. Fang and M. Haataja, “Crystallization in organic semiconductor thin films: A diffuse-interface approach,” Physical Review E, vol. 89, no. 2, pp. 022407:1-9, Feb. 2014.
    [8] H. Chandra, P. J. Reddy, and S. Srivastava, “Protein microarrays and novel detection platforms,” Expert Review of Proteomics, vol. 8, no. 1, pp. 61-79, Jan. 2011. doi:  10.1586/epr.10.99
    [9] M. A. Baranov, E. N. Velichko, and E. T. Aksenov, “Self-assembled biomacromolecular films as a basis for nonlinear optical devices,” in Proc. of Intl. Conf. on Laser Optics, New York, 2018, p. 356.
    [10] A. Tretiakov, V. Kapralova, N. Sudar, O. Gryshkov, and B. Glasmacher, “Dielectric properties of PVDF based thin films and electrospun mats,” Journal of Physics: Conf. Series, vol. 1236, no. 1, pp. 012009:1-4, Jul. 2019.
    [11] A. Nayak and K. A. Suresh, “Conductivity of Langmuir-Blodgett films of a disk-shaped liquid-crystalline molecule-DNA complex studied by current-sensing atomic force microscopy,” Physical Review E, vol. 78, no. 2, pp. 021606:1-8, Aug. 2008.
    [12] A. Ulman, An Introduction to Ultrathin Organic Films: From Langmuir-Blodgett to Self-Assembly, Boston: Academic Press, 1991, pp. 1-442.
    [13] M. A. Baranov, E. N. Velichko, and E. T. Aksenov, “Methods of non-destructive testing in studies of self-organization processes in protein films,” Journal of Physics: Conf. Series, vol. 917, no. 6, pp. 062059:1-4, Nov. 2017.
    [14] A. Laschitsch, B. Menges, and D. Johannsmann, “Simultaneous determination of optical and acoustic thicknesses of protein layers using surface plasmon resonance spectroscopy and quartz crystal microweighing,” Applied Physics Letters, vol. 77, no. 14, pp. 2252-2254, Sept. 2000. doi:  10.1063/1.1315338
    [15] V. M. Kapralova, I. Y. Sapurina, and N. T. Sudar’, “Variation in the conductivity of polyaniline nanotubes during their formation,” Semiconductors, vol. 52, no. 6, pp. 816-819, Jun. 2018. doi:  10.1134/S1063782618060076
    [16] V. M. Kapralova, D. D. Karov, and A. I. Slutsker, “New 3D cross-linked copolymers with variable mechanical properties and high durability,” Solid State Phenomena, vol. 265, pp. 553-557, Sept. 2017. doi:  10.4028/www.scientific.net/SSP.265.553
    [17] O. V. Stepanenko, G. S. Bublikov, I. M. Kuznetsova, V. V. Verkhusha, and K. K. Turoverov, “Stabilization of structure in near-infrared fluorescent proteins by binding of biliverdin chromophore,” Journal of Molecular Structure, vol. 1140, pp. 22-31, Jul. 2017. doi:  10.1016/j.molstruc.2016.10.095
    [18] S. Sharma, R. W. Johnson, and T. A. Desai, “Evaluation of the stability of nonfouling ultrathin poly(ethylene glycol) films for silicon-based microdevices,” Langmuir, vol. 20, no. 2, pp. 348-356, Jan. 2004. doi:  10.1021/la034753l
    [19] L. Boinovich and A. Emelyanenko, “Wetting and surface forces,” Advances in Colloid and Interface Science, vol. 165, no. 2, pp. 60-69, Mar. 2011. doi:  10.1016/j.cis.2011.03.002
    [20] M. Bordag, G. L. Klimchitskaya, U. Mohideen, and V. M. Mostepanenko, Advances in the Casimir Effect, Oxford: Clarendon Press, 2015, pp. 1-750.
    [21] G. L. Klimchitskaya and V. M. Mostepanenko, “Casimir free energy of metallic films: Discriminating between Drude and plasma model approaches,” Physical Review A, vol. 92, no. 4, pp. 042109:1-11, Oct. 2015.
    [22] G. L. Klimchitskaya and V. M. Mostepanenko, “Casimir and van der Waals energy of anisotropic atomically thin metallic films,” Physical Review B, vol. 92, no. 20, pp. 205410:1-7, Nov. 2015.
    [23] G. L. Klimchitskaya and V. M. Mostepanenko, “Casimir free energy and pressure for magnetic metal films,” Physical Review B, vol. 94, no. 4, pp. 045404:1-9, Jul. 2016.
    [24] G. L. Klimchitskaya and V. M. Mostepanenko, “Characteristic properties of the Casimir free energy for metal films deposited on metallic plates,” Physical Review A, vol. 93, no. 4, pp. 042508:1-9, Apr. 2016.
    [25] G. L. Klimchitskaya and V. M. Mostepanenko, “Low-temperature behavior of the Casimir free energy and entropy of metallic films,” Physical Review A, vol. 95, no. 1, pp. 012130:1-9, Jan. 2017.
    [26] G. L. Klimchitskaya and V. M. Mostepanenko, “Casimir free energy of dielectric films: Classical limit, low-temperature behavior and control,” Journal of Physics: Condensed Matter, vol. 29, no. 27, pp. 275701:1-25, May 2017.
    [27] S. Nir, “Van der Waals interactions between surfaces of biological interest,” Progress in Surface Science, vol. 8, no. 1, pp. 1-58, Feb. 1977. doi:  10.1016/0079-6816(77)90007-7
    [28] C. M. Roth, B. L. Neal, and A. M. Lenhoff, “Van der Waals interactions involving proteins,” Biophysical Journal, vol. 70, no. 2, pp. 977-987, Feb. 1996. doi:  10.1016/S0006-3495(96)79641-8
    [29] V. A. Parsegian and B. W. Ninham, “Application of the Lifshitz theory to the calculation of van der Waals forces across thin lipid films,” Nature, vol. 224, no. 5225, pp. 1197-1198, Dec. 1969. doi:  10.1038/2241197a0
    [30] B.-S. Lu and R. Podgornik, “Effective interactions between fluid membranes,” Physical Review E, vol. 92, no. 2, pp. 022112:1-15, Aug. 2015.
    [31] M. A. Baranov, G. L. Klimchitskaya, V. M. Mostepanenko, and E. N. Velichko, “Contribution of electromagnetic fluctuations to the free energy of protein films,” in Proc. of IEEE Intl. Conf. on Electrical Engineering and Photonics, St. Petersburg, 2018, pp. 240-243.
    [32] M. A. Baranov, G. L. Klimchitskaya, V. M. Mostepanenko, and E. N. Velichko, “Fluctuation-induced free energy of thin peptide films,” Physical Review E, vol. 99, no. 2, pp. 022410:1-10, Feb. 2019.
    [33] E. M. Lifshitz, “The theory of molecular attractive forces between solids,” Soviet Physics JETP, vol. 2, pp. 73-83, Jan. 1956.
    [34] G. L. Klimchitskaya and V. M. Mostepanenko, “Observability of thermal effects in the Casimir interaction from graphene-coated substrates,” Physical Review A, vol. 89, no. 5, pp. 052512:1-7, May 2014.
    [35] D. B. Hough and L. R. White, “The calculation of Hamaker constants from Liftshitz theory with applications to wetting phenomena,” Advances in Colloid and Interface Science, vol. 14, no. 1, pp. 3-41, Dec. 1980. doi:  10.1016/0001-8686(80)80006-6
    [36] G. Löffler, H. Schreiber, and O. Steinhauser, “Calculation of the dielectric properties of a protein and its solvent: Theory and a case study,” Journal of Molecular Biology, vol. 270, no. 3, pp. 520-534, Jul. 1997. doi:  10.1006/jmbi.1997.1130
    [37] P. Adhikari, A. M. Wen, R. H. French, et al., “Electronic structure, dielectric response, and surface charge distribution of RGD (1FUV) peptide,” Scientific Reports, vol. 4, pp. 5605:1-7, Jul. 2014.
    [38] L. Bergström, “Hamaker constants of inorganic materials,” Advances in Colloid and Interface Science, vol. 70, pp. 125-169, Jul. 1997. doi:  10.1016/S0001-8686(97)00003-1
  • 加载中
  • [1] Ching-Ta Lu, Jia-An Lin, Chia-Yi Chang, Chia-Hua Liu, Ling-Ling Wang, Kun-Fu Tseng. Recognition of Film Type Using HSV Features on Deep-Learning Neural Networks. Journal of Electronic Science and Technology, 2020, 18(1): 31-41. doi: 10.11989/JEST.1674-862X.90904223
    [2] Elena N. Velichko, Galina L. Klimchitskaya, Elina N. Nepomnyashchaya. Casimir Effect in Optoelectronic Devices Using Ferrofluids. Journal of Electronic Science and Technology, 2020, 18(1): 76-82. doi: 10.1016/j.jnlest.2020.100024
    [3] Bernd Teufel, Anton Sentic, Mathias Barmet. Blockchain Energy: Blockchain in Future Energy Systems. Journal of Electronic Science and Technology, 2019, 17(4): 317-331. doi: 10.1016/j.jnlest.2020.100011
    [4] Li-Bo He, Dong-Jie Yan, Hu Xiong, Zhi-Guang Qin. Pairing-Free Certificateless Key-Insulated Encryption with Provable Security. Journal of Electronic Science and Technology, 2018, 16(1): 50-56. doi: 10.11989/JEST.1674-862X.6052718
    [5] Xin Tong, Zhiming M. Wang. Ferroelectric Properties and Applications of Hybrid Organic-Inorganic Perovskites. Journal of Electronic Science and Technology, 2017, 15(4): 326-332. doi: 10.11989/JEST.1674-862X.70909051
    [6] Stephanie Teufel. Special Section on Energy-Efficient Technologies: Crowd Energy Applications. Journal of Electronic Science and Technology, 2015, 13(3): 193-194. doi: 10.11989/JEST.1674-862X.507291
    [7] Guo-Bin Zhu, Hu Xiong, Zhi-Guang Qin. Pairing-Free ID-Based Key-Insulated Signature Scheme. Journal of Electronic Science and Technology, 2015, 13(1): 33-38. doi: 10.3969/j.issn.1674-862X.2015.01.007
    [8] Stephanie Teufel, Bernd Teufel. The Crowd Energy Concept. Journal of Electronic Science and Technology, 2014, 12(3): 263-269. doi: 10.3969/j.issn.1674-862X.2014.03.005
    [9] Jian Liao, Guang-Zhong Xie, Hui-Ling Tai, Ya-Dong Jiang, Wei-Zhi Li, Yong Zhou, Fang Xu. Toluene Sensing Properties of P4VP/Multi-Walled Carbon Nanotubes Multi-Layer Film Sensors. Journal of Electronic Science and Technology, 2013, 11(3): 317-321. doi: 10.3969/j.issn.1674-862X.2013.03.015
    [10] Chin-Chen Chang, Thai-Son Nguyen, Chia-Chen Lin. Distortion-Free Data Embedding Scheme for High Dynamic Range Images. Journal of Electronic Science and Technology, 2013, 11(1): 20-26. doi: 10.3969/j.issn.1674-862X.2013.01.005
    [11] Jun-Sheng Yu, Zhao-Lin Yuan, Guang-Zhong Xie, Ya-Dong Jiang. Preparation, Properties, and Applications of Low-Dimensional Molecular Organic Nanomaterials. Journal of Electronic Science and Technology, 2010, 8(1): 3-9. doi: 10.3969/j.issn.1674-862X.2010.01.001
    [12] Mao-Yan Fan, Sheng-Lin Jiang. Influence of La-Mn-Al Co-Doping on Dielectric Properties and Structure of BST Thick Film. Journal of Electronic Science and Technology, 2009, 7(3): 281-285.
    [13] Cheng Zeng, Zheng-Xiang Luo, Qi-Shao Zhang, Kai Yang. Design of TE01Δ Test Probe for Measuring the Microwave Surface Resistance of HTS Thin Film. Journal of Electronic Science and Technology, 2008, 6(2): 212-215.
    [14] Jia Du, Cathy P. Foley, Keith L. Leslie. Superconducting Electronics Research at CSIRO Australia-20 Years after Discovery of HTS. Journal of Electronic Science and Technology, 2008, 6(2): 216-224.
    [15] Jun-Sheng Yu, Lu Li, Ya-Dong Jiang, Xing-Qiao Ji, Tao Wang. Luminescent Enhancement of Heterostructure Organic Light-Emitting Devices Based on Aluminum Quinolines. Journal of Electronic Science and Technology, 2007, 5(2): 183-186.
    [16] WANG Zhi-hong, CHEN Kun, ZHOU Yu, SHEN Bo-kan. MFM Study: the Air Damping Effect on Magnetic Imaging of CoNbZr Thin Film. Journal of Electronic Science and Technology, 2007, 5(1): 50-52.
    [17] Zhe-Sheng Feng, Ying-Jie Xia, Jia Ding, Jin-Ju Chen. Formation of Al-Si Composite Oxide Film by Hydrolysis Precipitation and Anodizing. Journal of Electronic Science and Technology, 2007, 5(4): 289-292.
    [18] HE Zheng, LI Shi-ming. Product Innovation in High-tech SMEs: A Case Study of Weili Electronics Co., Ltd. Journal of Electronic Science and Technology, 2006, 4(4): 328-332.
    [19] LIU Bao-yuan, SHI Yu, WEN Qi-ye. Design and Simulation of the Thin Film Pulse Transformer. Journal of Electronic Science and Technology, 2005, 3(1): 48-51.
    [20] LIU Bao-yuan, SHI Yu, WEN Qi-ye. Study of the Thin Film Pulse Transformer. Journal of Electronic Science and Technology, 2005, 3(2): 161-163.

通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Figures(3)

Article Metrics

Article views(76) PDF downloads(1) Cited by()

Related
Proportional views

Role of Electromagnetic Fluctuations in Organic Electronics

doi: 10.1016/j.jnlest.2020.100023
Funds:  This work was partly supported by the Russian Foundation for Basic Research under Grant No. 19-02-00453 A
  • Author Bio:

  • Corresponding author: V. M. Mostepanenko is with the Institute of Physics, Nanotechnology and Telecommunications, Peter the Great St. Petersburg Polytechnic University, St. Petersburg 195251 and also with Central Astronomical Observatory at Pulkovo of Russian Academy of Sciences, St. Petersburg 196140 (e-mail: vmostepa@gmail.com).

Abstract: Thin organic films find expanding applications in electronic and optoelectronic devices, biotechnology, food packing, and for many other purposes. Among other factors, the stability of films with a thickness below a micrometer is determined by the zero-point and thermal fluctuations of the electromagnetic field. These fluctuations result in the van der Waals and Casimir free energy and forces between a film and a substrate. The fluctuation-induced force may be both attractive and repulsive making the film either more or less stable, respectively. Here, we review recently obtained results for the Casimir free energy of both freestanding and deposited on the metallic and dielectric substrates peptide films. We also perform computations for the free energy of the peptide films deposited on a silica glass substrate in the region of parameters where this free energy vanishes. Possible applications of the obtained results are discussed.

Vladimir M. Mostepanenko, Elena N. Velichko, Maksim Aleksandrovich Baranov. Role of Electromagnetic Fluctuations in Organic Electronics[J]. Journal of Electronic Science and Technology, 2020, 18(1): 52-58. doi: 10.1016/j.jnlest.2020.100023
Citation: Vladimir M. Mostepanenko, Elena N. Velichko, Maksim Aleksandrovich Baranov. Role of Electromagnetic Fluctuations in Organic Electronics[J]. Journal of Electronic Science and Technology, 2020, 18(1): 52-58. doi: 10.1016/j.jnlest.2020.100023
  • During the last few years, thin organic films were used in field-effect transistors, light-emitting diodes, solar cells, biomarkers, and many other devices and technologies[1]-[10]. This progress has been made possible due to the beneficial mechanical, electrical, and optical properties of these films[11]-[17]. In doing so, some applications of protein and peptide films are related to organic microdevices[5],[18] where the thickness of a film may be below a micrometer. In this case, one should take into account the roles of zero-point and thermal fluctuations of the electromagnetic field, which contribute to the free energy of a film and respective pressure. It is well known that electromagnetic fluctuations may play both a positive and negative role in respect to the film stability[19].

    It is common knowledge that electromagnetic fluctuations result in the van der Waals and Casimir free energy and forces[20]. This effect arises not only for two closely spaced bodies but also for freestanding in vacuum thin films or films deposited on a substrate. Recently it was investigated for thin films made of various inorganic materials including nonmagnetic and magnetic metals and dielectrics[21]-[26]. Although the van der Waals and Casimir forces between the organic and, specifically, peptide films have been investigated over a period of years[27]-[30], the effects of electromagnetic fluctuations on the free energy and pressure of organic films became the subject of study only recently[31],[32]. In these papers, the fluctuation-induced free energy was computed at room temperature for the modeled peptide films, both freestanding and deposited on dielectric (SiO2) or metallic (Au) substrates. The free energy was investigated as a function of the film thickness and the fraction of water contained in the film. It was shown that for a freestanding film the fluctuation-induced (Casimir) free energy is negative which corresponds to the attractive pressure favorable for the film stability. For the peptide films deposited on an Au substrate, both the free energy and respective pressure turned out to be positive, which corresponds to Casimir repulsion. This makes the peptide coating less stable. The free energy of the peptide films deposited on a dielectric substrate (SiO2) was found to be a non-monotonous function of the film thickness, but the region of the thickness where it vanishes and changes its sign was not investigated.

    In this paper, we investigate the free energy of the modeled peptide films with different fractions of water deposited on a SiO2 substrate in the region of the film thickness where the Casimir free energy per unit area of the film vanishes or takes the minimum value. In the latter region, the Casimir pressure changes its sign from positive to negative with increasing the film thickness, which makes the film more stable. Possible applications of this result are discussed.

    The paper is organized as follows. In Section 2, the Lifshitz formula for the free energy of a film deposited on a substrate is presented, as well as the dielectric permittivities of the used materials along the imaginary frequency axis. Section 3 contains our computational results. In Section 4, several conclusions are formulated.

  • The fundamental theory of the van der Waals and Casimir forces was developed by Lifshitz[33]. In the framework of this theory, the free energy and pressure caused by the electromagnetic fluctuations are expressed via the frequency-dependent dielectric permittivities of interacting bodies. Here we consider a peptide film with the thickness of a below a micrometer deposited on a thick dielectric substrate plate which can be treated as a semispace in our computations. It has been shown[34] that, in the computations of the fluctuation-induced free energy and forces, this assumption is valid if the thickness of a substrate exceeds 2 μm. The dielectric permittivities of a peptide film and of a substrate plate are denoted as ${\epsilon _f}\!\left(\omega \right)$ and ${\epsilon _s}\!\left(\omega \right)$, respectively.

    According to the Lifshitz theory, the fluctuation-induced free energy of a film is expressed via the reflection coefficients of the boundary surfaces between the film and vacuum, $r_\alpha ^{\left({f,v} \right)}\!\left({{\rm{i}}{\xi _l},{k_ \bot }} \right)$, and between the film and substrate plate, $r_\alpha ^{\left({f,s} \right)}\!\left({{\rm{i}}{\xi _l},{k_ \bot }} \right)$. These reflection coefficients are different for two independent polarizations of the electromagnetic field, transverse magnetic (α=TM) and transverse electric (α=TE). They depend on the magnitude of the projection of the wave vector on the plane of a film, ${k_ \bot }$, and, through the dielectric permittivities, on the pure imaginary Matsubara frequencies (${\xi _l} \!=\! 2\pi{k_B}Tl/\hbar $, where kB is the Boltzmann constant, T is the temperature, $l \!=\! 0,\;1,\;2,\; \cdots $, and $\hbar$ is the Planck constant divided by 2π). In fact, these reflection coefficients are the well-known Fresnel coefficients with the only difference that they are calculated along the imaginary frequency axis. The explicit expressions for them are shown as the followings:

    where

    Another pair of reflection coefficients is given by

    where

    With these notations, the Lifshitz formula for the Casimir free energy per unit area of a film is written as[20],[24],[33]

    where the prime on the summation sign in l means that the term with l=0 should be divided by 2.

    To calculate the Casimir free energy in (5), one needs to know the dielectric permittivity of a peptide film εf and that of a substrate plate εs over a wide range along the imaginary frequency axis. For specific materials used in computations, these permittivities are presented in Section 3. Here we only note that the peptide films usually contain some volume fractions of water Φ. Because of this, the dielectric permittivity of a film, εf, should be obtained as a combination of the dielectric permittivity of water, εw, and of the peptide itself, εp. Taking into account that the peptide molecules are randomly distributed in water and have an irregular shape, the dielectric permittivity of the peptide film can be found from the following combination law[35]:

    In the next section, (1) to (6) are used in numerical computations of the fluctuation-induced Casimir free energy of the peptide films.

  • We perform numerical computations for the model peptide which combines the dielectric properties of 18-residue zinc finger peptide found for the frequencies up to the microwave frequency region[36] with that of cyclic tripeptide RGD-4C calculated in the ultraviolet frequency region[37]. Using these data, the dielectric permittivity of the model peptide along the imaginary frequency axis εp was found in [32]. It is shown by the bottom line in Fig. 1 as a function of the imaginary frequency normalized to the first Matsubara frequency.

    Figure 1.  Dielectric permittivities of water and peptide as functions of the imaginary frequency normalized to the first Matsubara frequency.

    In the same figure, the dielectric permittivity of water, which has been much studied in the literature, is shown by the top line[38]. At the zero frequency, the values of the dielectric permittivities are equal to εp(0)=15.0 and εw(0)=81.2, respectively.

    Using the dielectric permittivity of peptide εp and that of water εw, the dielectric permittivities of peptide films εf containing different volume fractions Φ of water are calculated with the help of (6). The obtained permittivity values for the films with Φ=0.10, 0.25, and 0.40 are shown in Fig. 2, as the functions of the imaginary frequency normalized to the first Matsubara frequency by three black lines, plotted from bottom to top, respectively.

    Figure 2.  Dielectric permittivities of silica glass (the gray line) and peptide films with 0.10, 0.25, and 0.40 volume fractions of water (the black lines plotted from bottom to top, respectively) as functions of the imaginary frequency normalized to the first Matsubara frequency.

    The gray line in Fig. 2 shows the well-known dielectric permittivity ${\epsilon _s}$ of a SiO2 substrate plate[35]. At the zero Matsubara frequency, one has εs(0)=3.801.

    The dielectric permittivities εf and εs have been substituted in (1) to (5) in order to compute the fluctuation-induced Casimir free energy per unit area of the peptide films deposited on a SiO2 plate as functions of the film thickness. Computations have been performed at room temperature T=300 K for the peptide films containing Φ=0.10, 0.25, and 0.40 volume fractions of water. The computational results are shown in Fig. 3 as functions of the film thickness by the lines 1, 2, and 3 plotted for the peptide films with Φ=0.10, 0.25, and 0.40 volume fractions of water, respectively.

    Figure 3.  Casimir free energy per unit area of the peptide films with Φ=0.10, 0.25, and 0.40 volume fractions of water as a function of the film thickness by the lines 1, 2, and 3, respectively.

    As shown in Fig. 3, the Casimir free energy of the peptide films deposited on a SiO2 plate is non-monotonous and changes its sign from positive to negative with increasing the film thickness. For the films with the volume fractions of water Φ=0.10, 0.25, and 0.40, the Casimir free energy takes the zero value for the film thickness equal to a=87.4 nm, 84.1 nm, and 75.7 nm, respectively. With increasing the film thickness, the Casimir free energy reaches its minimum value. For the films with Φ=0.10, 0.25, and 0.40, this happens for the thickness of a=135.0 nm, 127.5 nm, and 115.0 nm, respectively.

    With further increasing the film thickness, the Casimir free energy approaches to zero remaining negative. At the points of minimum free energy, the Casimir pressure,

    changes its sign from positive to negative. This means that for the films thinner than 135.0 nm, 127.5 nm, and 115.0 nm, the Casimir pressure is repulsive and, thus, makes these films less stable, whereas for thicker films the Casimir pressure is attractive and contributes to their stability.

  • In the foregoing, we have calculated the Casimir free energy of thin peptide films with different volume fractions of water deposited on a silica glass plate. This was done in the framework of fundamental Lifshitz theory describing the van der Waals and Casimir forces. Taking into account that the Casimir free energy may contribute from 5% to 20% of cohesive energy of the thin peptide films[32], the problem of its calculation is not of entirely academic character, but is important for creating new electronic microdevices exploiting thin organic films.

    According to our results, the Casimir free energy of the peptide film deposited on a SiO2 substrate decreases, remaining positive with increasing the film thickness, takes zero value, reaches some minimum (negative) values, and then increases to zero with further increasing the film thickness. The value of the film thickness, at which the free energy vanishes and reaches its minimum value, depends on the volume fraction of water contained in a peptide film. For the films with minimum Casimir free energy, the Casimir pressure is equal to zero. Thus, for thinner films, electromagnetic fluctuations make these films less stable and contribute to their stability for thicker films. This effect may be useful to ensure the film stability in the next generation of organic-based electronic microdevices with further decreased dimensions.

Reference (38)

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return