Abstract
In almost all works done up to now on proton dynamics in hydrogen-bonded systems, dipole–dipole interactions have been overlooked. Here, we examine the role of these interactions on the dynamics and statistical properties of ions transfer and bonding defects in those systems. A one-dimensional model for hydrogen-bonded chains is investigated by including dipole–dipole interactions created by protons and heavy ion charge movement, generalizing thus the original Antonchenko–Davydov–Zolotaryuk model. The inclusion of dipole–dipole interactions is not only interesting from a physical point of view; it also provides an extraordinary mathematical model, a new class of differential equations possessing several key parameters and many singular straight lines. The dynamics around these singularities gives new information of great interest, such as to better explain analytically the formation of cracks resulting from dislocations observed in semiconductor heterostructures. Despite major individual differences in initial models, our results can generalize the results previously established in DNA, in the wave diffusion by static localized inhomogeneities or by generic time-dependent potentials, in nonlinear discrete electrical transmission lines and many others. Therefore, this work comes, among other things, to present a method of analytical resolution of these new equations. We use dynamic system methods to first determine the crucial parameters of the system (among them is the dipole–dipole interaction coefficient), and then we discuss on bifurcations of phase portraits and vector fields defined by the singular system. These dipole–dipole interactions have crucial effects on the response of nonlinear excitations that can propagate along these hydrogen-bonded systems. For each orbit of phase portraits with corresponding conditions, highlighting the importance of each component in the hydrogen-bonded system with dipole–dipole interactions on the dynamics, we compute all possible exact parametric representations of solutions. Our findings show that, under given parameter conditions, there are smooth solitary wave solutions, periodic wave solutions, periodic peaks, pseudo-peaks, compacton families and obviously kink and antikink solitons, specially interesting in systems with hydrogen bonds.
Similar content being viewed by others
Data availability
The data used to support the findings of this study are included within the article.
References
Jeffrey, G.A.: An Introduction to Hydrogen Bonding. Oxford Univ Press, Oxford (1997)
Dingley, A.J., Grzesiek, S.: Direct observation of hydrogen bonds in nucleic acid base pairs by internucleotide (2)J(NN) couplings. J. Am. Chem. Soc. 120, 8293 (1998)
Mukherjee, S., Majumdar, S., Bhattacharyya, D.: Solvation dynamics in the water pool of an aerosol-OT microemulsion. Effect of sodium salicylate and sodium cholate. J. Phys. Chem. B 109, 10484 (2005)
Pan, Z., Chen, J., Lü, G., Geng, Y.-Z., Zhang, H., Ji, Q.: An ab initio molecular dynamics study on hydrogen bonds between water molecules. J. Chem. Phys. 136, 164313 (2012)
Horowitz, S., Trievel, R.C.: Carbon-oxygen hydrogen bonding in biological structure and function. J. Biol. Chem. 287, 41576 (2012)
Zou, Y., Guo, J., Yin, S.-W., Wang, J.-M., Yang, X.-Q.: Pickering emulsion gels prepared by hydrogen-bonded zein/tannic acid complex colloidal particles. J. Agric. Food Chem. 63, 7405 (2015)
Norimatsu, Y., Hasegawa, K., Shimizu, N., Toyoshima, C.: Protein-phospholipid interplay revealed with crystals of a calcium pump. Nature 545, 193 (2017)
Li, P., He, Y., Zhao, Y., Weng, Y., Wang, H., Krishna, R., Wu, H., Zhou, W., O’Keeffe, M., Han, Y., Chen, B.: A rod-packing microporous HB organic framework for highly selective separation of \(C_{2}H_{2}=CO_{2}\) at room temperature. Angew. Chem. Int. Ed. 54, 574–577 (2014)
Wang, H., Li, B., Wu, H., Hu, T.-L., Yao, Z., Zhou, W., Xiang, S., Chen, B.: A flexible microporous hydrogen-bonded organic framework for gas sorption and separation. J. Am. Chem. Soc. 137, 9963 (2015)
Karmakar, A., Illathvalappil, R., Anothumakkool, B., Sen, A., Samanta, P., Desai, A.V., Kurungot, S., Ghosh, S.K.: Hydrogen-bonded organic frameworks (HOFs): a new class of porous crystalline proton-conducting materials. Angew. Chem. Int. Ed. 55, 10667 (2016)
Jakešovaá, M., Apaydin, D.H., Sytnyk, M., Oppelt, K., Heiss, W., Sariciftci, N.S., lowacki, E.D.G.: Hydrogen-bonded organic semiconductors as stable photoelectrocatalysts for efficient hydrogen peroxide photosynthesis. Adv. Funct. Mater. 26, 5248 (2016)
Lin, Y., Jiang, X., Kim, S.T., Alahakoon, S.B., Hou, X., Zhang, Z., Thompson, C.M., Smaldone, R.A., Ke, C.: An elastic hydrogen-bonded cross-linked organic framework for effective iodine capture in water. Am. Chem. Soc. 139, 7172 (2017)
Li, S.-S., Huang, C.-Y., Hao, J.-J., Wang, C.-S.: A polarizable dipole-dipole interaction model for evaluation of the interaction energies for N-H\(\Delta \Delta \Delta \)O: C and C-H\(\Delta \Delta \Delta \)O: C hydrogen-bonded complexes. J. Comput. Chem. 35, 415 (2013)
Melchor, J.P., McVoy, L., Nostrand, W.E.V.: Charge alterations of E22 enhance the pathogenic properties of the amyloid \(\beta \)-protein. J. Neurochem. 74, 2209 (2008)
Lemkul, J.A., Huang, J., MacKerell, A.D.: Induced dipole–dipole interactions influence the unfolding pathways of wild-type and mutant amyloid \(\beta \)-peptides. J. Phys. Chem. B 119, 15574 (2015)
Zhang, Y., Li, Y., Liu, W.: Dipole–dipole and H-bonding interactions significantly enhance the multifaceted mechanical properties of thermoresponsive shape memory hydrogels. Adv. Funct. Mater. 25, 471 (2014)
Hu, Y., Miao, K., Peng, S., Zha, B., Xu, L., Miao, X., Deng, W.: Structural transition control between dipole–dipole and hydrogen bonds induced chirality and achirality. CrystEngComm 18, 3019 (2016)
Antonchenko, V.Y., Davydov, A.S., Zolotariuk, A.V.: Solitons and proton motion in ice-like structures. Phys. Status Solidi (b) 115, 631 (1983)
Zolotaryuk, A.V.: One-dimensional lattice dynamics of hydrogen bonded systems. Theor. Math. Phys. 68, 916 (1986)
Hochstrasser, D., Büttner, H., Desfontaines, H., Peyrard, M.: Solitons in hydrogen-bonded chains. Phys. Rev. A 38, 5332 (1988)
Bountis, T. (ed.): Proton Transfer in Hydrogen-Bonded Systems. NATO ASI Series (Series B: Physics), vol. 291. Plenum Press, New York (1992)
Peyrard, M.: Nonlinear Excitations in Biomolecules, edited by S.-V. B. H. GmbH. Springer, Berlin (1995)
Tsironis, G.P., Pnevmatikos, S.: Proton conductivity in quasi-one-dimensional hydrogen-bonded systems: nonlinear approach. Phys. Rev. B 39, 7161 (1989)
Kashimori, Y., Chien, F., Nishimoto, K.: Theoretical study of soliton dynamics of a finite one-dimensional hydrogen-bonded system. Chem. Phys. 107, 389 (1986)
Xun-Ling, Y., Rui-Xin, D., Xiao-Feng, P.: Dynamic properties of proton transfer in the anharmonic-interaction hydrogen bond systems. Commun. Theor. Phys. 35, 615 (2001)
Tchakoutio Nguetcho, A.S., Kofane, T.C.: Soliton patterns and breakup thresholds in hydrogen-bonded chains. Eur. Phys. J. B 57, 411 (2007)
Li, J., Chen, F., Tchakoutio Nguetcho, A.S.: Bifurcations and exact solutions in a model of hydrogen-bonded-chains. Int. J. Bifurc. Chaos 25, 1550062 (2015)
Karpan, V.M., Zolotaryuk, Y., Christiansen, P.L., Zolotaryuk, A.V.: Discrete kink dynamics in hydrogen-bonded chains: the one-component model. Phys. Rev. E 66, 066603 (2002)
Goryainov, S.: A model of phase transitions in double-well Morse potential: application to hydrogen bond. Phys. B 407, 4233 (2012)
Stépán, G.: Nonlinear modelling of shimmying wheels. In: Christiansen, P.L., Eilbeck, J.C., Parmentier, R.D. (eds.) Future Directions of Nonlinear Dynamics in Physical and Biological Systems. NATO ASI Series (Series B: Physics), vol. 312. Springer, Boston (1993)
Hobbs, P.V.: Ice Physics (Oxford Classic Texts in the Physical Sciences). Oxford University Press, Oxford (2010)
Christiansen, P.L., Eilbeck, J.C., Parmentier, R.D.: Future Directions of Nonlinear Dynamics in Physical and Biological Systems, edited by L. NATO ASI Series. Springer, Berlin (1993)
Yu, P.Y., Cardona, M.: Fundamentals of Semiconductors. Springer, Berlin (2010)
Chochliouros, I., Pouget, J.: Transport properties in a hydrogen-bonded chain model including dipole–dipole interactions. J. Phys.: Condens. Matter 7, 8741 (1995)
Braun, O.M., Kivshar, Y.S.: The Frenkel–Kontorova Model. Springer, Berlin (2004)
Han, H.B., Li, H.J., Dai, C.Q.: Wick-type stochastic multi-soliton and soliton molecule solutions in the framework of nonlinear Schrödinger equation. Appl. Math. Lett. 120, 107302 (2021)
Chen, Y.X., Xu, F.Q., Hu, Y.L.: Excitation control for three-dimensional Peregrine solution and combined breather of a partially nonlocal variable-coefficient nonlinear Schrödinger equation. Nonlinear Dyn. 95, 1957 (2019)
Dai, C.Q., Wang, Y.Y.: Coupled spatial periodic waves and solitons in the photovoltaic photorefractive crystals. Nonlinear Dyn. 102, 1733 (2020)
Tchakoutio Nguetcho, A.S., Nkeumaleu, A.S., Bilbault, J.M.: Behavior of gap solitons in anharmonic lattices. Phys. Rev. E 96, 022207 (2017)
Wamba, E., Tchakoutio Nguetcho, A.S.: Generation of localized patterns in anharmonic lattices with cubic-quintic nonlinearities and fourth-order dispersion via a variational approach. Phys. Rev. E 97, 052207 (2018)
Kivshar, Y.S., Kivshar, Y.S.: Optical Solitons : From Fibers to Photonic Crystals. Elsevier, Amsterdam (2003)
Govind-Agrawal, P.: Nonlinear Fiber Optics (Optics and Photonics), 4th edn. Elsevier, Amsterdam (2006)
Nail Akhmediev, A.A.: Solitons: Non-linear Pulses and Beams. Springer US, New York (1997)
Zaviyalov, A., Iliew, R., Egorov, O., Lederer, F.: Multi-soliton complexes in mode-locked fiber lasers. Appl. Phys. B 104, 513 (2011)
Grelu, P., Akhmediev, N.: Dissipative solitons for mode-locked lasers. Nat. Photonics 6, 84 (2012)
Zhao, X., Gorbach, A.V., Skryabin, D.V.: Dispersion of nonlinearity in subwavelength waveguides: derivation of pulse propagation equation and frequency conversion effects. J. Opt. Soc. Am. B 30, 812 (2013)
Gorbach, A., Zhao, X., Skryabin, D.: Dispersion of nonlinearity and modulation instability in subwavelength semiconductor waveguides. Opt. Express 19, 9345 (2011)
Tchakoutio Nguetcho, A.S., Ndjoko, P.B., Kofane, T.C.: Mobility and conductivity of ionic and bonded defects in hydrogen-bonded chains with nonlinear interactions. Eur. Phys. J. B 62, 7 (2008)
Whalley, E.: The distortion of a water molecule in ice. J. Glaciol. 21, 13 (1978)
Joyeux, M., Buyukdagli, S., Sanrey, M.: \(1/f\) fluctuations of DNA temperature at thermal denaturation. Phys. Rev. E 75, 061914 (2007)
Gninzanlong, C.L., Ndjomatchoua, F.T., Tchawoua, C.: Taming intrinsic localized modes in a DNA lattice with damping, external force, and inhomogeneity. Phys. Rev. E 99, 052210 (2019)
Tchakoutio Nguetcho, A.S., Li, J., Bilbault, J.M.: Bifurcations of phase portraits of a singular nonlinear equation of the second class. Commun. Nonlinear Sci. Numer. Simul. 19, 2590 (2014)
Malomed, B.A., Milchev, A.: Interaction of dislocations with a local defect in an atomic chain with a nonconvex interparticle potential. Phys. Rev. B 41, 4240 (1990)
Paturej, J., Milchev, A., Rostiashvili, V.G., Vilgis, T.A.: Thermal degradation of unstrained single polymer chain: non-linear effects at work. J. Chem. Phys. 134, 224901 (2011)
Li, J., Dai, H.: On the Study of Singular Nonlinear Traveling Wave Equations: Dynamical System Approach. Science Press, Beijing (2006)
Tchakoutio Nguetcho, A.S., Li, Jibin, Bilbault, J.M.: Global dynamical behaviors in a physical shallow water system. Commun. Nonlinear Sci. Numer. Simul. 36, 285 (2016)
Tchakoutio Nguetcho, A.S., Nkeumaleu, G.M., Bilbault, J.M.: Anharmonic effects on the dynamic behavior’s of Klein Gordon model’s. Appl. Math. Comput. 403, 126136 (2021)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no relevant financial or non-financial interests to disclose. The authors have no conflicts of interest to declare that are relevant to the content of this article. All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript. The authors have no financial or proprietary interests in any material discussed in this article.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Tchouadji Ndjike, M.B., Tchakoutio Nguetcho, A.S., Li, J. et al. Interplay role between dipole interactions and hydrogen bonding on proton transfer dynamics. Nonlinear Dyn 105, 2619–2643 (2021). https://doi.org/10.1007/s11071-021-06723-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-021-06723-6