TẠP CHÍ KHOA HỌC − SỐ 18/2017 65 SIMPLE CORECORE-SHELL MODEL FOR A SOFT NANO PARTICLES AND VIRUS WITH ANALYTICAL SOLUTION Phung Thi Huyen1, Luong Thi Theu1, Dinh Thi Thuy2, Dinh Thi Ha3, Nguyen Ai Viet4 Hanoi Pedagogical University 2 Thai Binh University of Medicine and Pharmacy Hanoi National University of Education Institute of Physics Abstract: Abstract In some recently experiments with virus, their core part are DNA tightly packed with very high charge density The contribution of this highly charged part to the electrical field outside virus now cannot be easily neglected in general case In this work we propose a simple core-shell model for this type of soft particles and virus The soft particles consider consisted from the two parts: a charged hard core with a high charge density and a charged outer layer We assume that the core part is tightly condensed, so the charge carriers of DNA can be partly bounded and partly moved With this consideration, the core part now is very look like the outside solution The corresponding Poisson-Boltzmann equations for this new model can be solved analytically These analytical solutions would be useful in the investigation the problem of virus with charged core, such as in bacteriophage MS2 Keywords: Keywords Soft nano, virus, core-shell structure, charge density of AND, PoissonBoltzmann equation, analytical solutions Email: phunghuyen.9xhpu2@gmail.com Received 20 June 2017 Accepted for publication 10 September 2017 INTRODUCTION In the last years, nanotechnology has a rapid advancement and opened up novel wide range of applications in life science and material science [1-3] Because the complexity of biological structures and the variation of solvents, despite many effort to theoretical investigation to understand the properties of soft particles [1, 4-7], the theoretical models still face a variety of problematic issues and challenges Thus, the construction of simple physics models to explain new observed phenomena and experimental data are important to the understanding of these complex systems 66 TRƯỜNG ĐẠI HỌC THỦ ĐÔ H NỘI One of such simple models for soft nano particles was introduced in the works of Ohshima [5-8] The Oshima’s model provides a powerful tool for investigating the behavior of biocolloidal particles, also viruses and bacteria In Oshima’s model, the soft particles are described as a non-penetrable neutral hard core coated by an ion permeable polyelectrolyte soft layer with negative constant volume density charge The electric potential distribution of this system then is obtained by solving the Poisson-Boltzmann equations At present, improved Oshima models of soft nano particles are found much application in the works [9-14] In many present investigations, charge of the core part of virus has been rarely taken into account In most cases, a core charge is assumed to be neglected, so the electrical potential outside the core remains unchanged A theoretical study mentioned the charge of the virus core in general cases to calculate the nonspecific electrostatic interactions in virus systems Recently, experiment data of the case of bacteriophage MS2 [15] have shown that the ratio between the volume charge density of the core and that of the surface layer is measured to be half of that found suggesting that the effect of the core charge on the electrostatic, so electrokinetic properties of the particle should be re-examined For explanation this observed phenomenon, a new core-shell model for soft nano particles was proposed in the work [16] with the consideration that soft particle consists from two parts: a charged hard core with a volume charge density and a charged outer layer Using this model, the contribution of the core parameters, such as the core charge and the core dielectric constant are studied The model still complicated and can be solved by numerical method only In this work we propose a simple core-shell model for a soft particles and virus, based on the assumption the core part is tightly condensed that the charge carriers of DNA can be partly bounded and partly moved [17] With this assumption, the core part now is very look like the outside solution The corresponding Poisson-Boltzmann equations for this new model can be solved analytically Our calculations provide the one of the first theoretical analytical investigations about the effects of temperature and salt concentration on the electrostatic properties, and could be applied to the case of virus with highly charged hard cores, such as bacteriophage MS2 [15] OSHIMA MODEL FOR SOFT-PARTICLES In the figure we present our core-shell model for nano soft particles We consider a soft particle with radius b immersed in an electrolyte solution The soft particle is assumed to contain a hard core of radius a coated by an ion-penetrable surface charge layer of TẠP CHÍ KHOA HỌC − SỐ 18/2017 67 polyelectrolyte with thickness (b − a) Identified with the Ohshima model, the volume charge density of the soft shell is ZNe, where e is an electron charge, Z and N are the valence and the charge density of the polyelectrolyte ions, respectively The theoretical model of a soft particle including a hard core with the charge density ρcore and the dielectric constant εcore, and an ion-penetrable surface layer of polyelectrolyte coated around The soft particle is immersed in an electrolyte solution with the charge density ρel and the permittivity εr (see in Fig 1) The electric potential distribution obeys the Poisson- Boltzmann equations [6, 15] ρel , ∆ψ = − ε ε r ρel + ZNe , ∆ψ = − ε ε r ρ ∆ψ = − core , εcoreε0 b ≤ r