**1.4 Electrorheological complex dusty plasma**

CDPs have electrorheological characteristics like conventional electrorheological fluids when an external ac electric field is applied. The dust particles respond quickly to the external applied electric field and make a chain (string) sheet-like as conventional ERFs so-called electrorheological CDPs (ER-CDPs). The first time ER-CDPs were observed by Ivlev A. V. et al., in 2008 during the microgravity experiments (PK-3 plus laboratory) and MD simulation. They show the phase transition of CDPs from isotropic to anisotropic with increasing the external applied electric field [20]. Under the influence of electric field dc mode, attractive attractions between charged dust particles are introduced by ions streaming. In this way, wake potential behind the dust grains produced, which make particles strings (sheet), in the dc discharge plasma sheath, where charged dust particles levitated against the electric field's gravity force. Such a type of system is non-Hamiltonian, and wake potential is asymmetric. The ac electric fields have a much smaller frequency than ion plasma frequency, but larger than dust plasma frequency was applied to the complex plasma. In this way, the wake potential is symmetric, and a system known as Hamiltonian due to the electric field, dipole–dipole attractions increased in ER-CDPs, particles arrange themselves in sheet, string, or crystalline structure same as conventional ERFs. The phase transition in ER-CDPs has studied experiments and simulations method [20–23].

After discovering ER-CDPs, it opens up new dimensions of research for plasma science and technologies communities. There is little literature available to understand the macroscopic phenomena of ER-CDPs. Ivlev A. V. et al., done a PK-3 plus experiments under microgravity conditions and molecular dynamics simulations, observed phase transition from an isotropic to string with increasing external ac electric field [24]. Later they have done *PK*-4 dc discharge experiment and observed an anisotropic structure under the influence of an external ac electric field [22]. Yaroshenko V. V. theoretically studied the propagations of dust lattice waves along the electric field in a one-dimensional string. He found the instability leads to spontaneous excitations of compressional waves [25]. Rosenberg *M*. theoretically studied the formation and excitation of waves in one-dimensional ER-CDPs under the ac electric field [26]. Kana *et al*. explored the phase transition in ER-CDPs using MD simulation and observed the anisotropic structure under the influence of ac electric field and did not find the anisotropic structure for the dc electric field mode [21]. Sukhinin *et al*. used a Monte Carlo (MC) simulation of plasma polarization around dust particles in an external applied electric field. They mentioned that due to induced dipole potential, the formation of dust particles alignment, chain (string) multi-layered structure, and coagulation of charged dust particles [27]. A self-consistent model was developed for plasma anisotropy (string) of charged dust particles under the external electric field's action by Sukhinin *et al*. [28]. No evidence has been found of thermophysical properties in ER-CDPs. In the future, for precise tailoring, new materials may be modeled with the help of ER-CDPs. The ER-CDPs can play a significant role in modeled new smart materials. It is also be used to generate negative dipolar interparticle interactions [24].

*Studies of Self Diffusion Coefficient in Electrorheological Complex Plasmas… DOI: http://dx.doi.org/10.5772/intechopen.98854*
