Motivated by our recent work,in this work,we present the numerical study of the anchoring effect on the Frederiks threshold field in a nematic liquid crystal doped with ferroelectric colloidal nanoparticles.Assuming w...Motivated by our recent work,in this work,we present the numerical study of the anchoring effect on the Frederiks threshold field in a nematic liquid crystal doped with ferroelectric colloidal nanoparticles.Assuming weak anchoring conditions,we employ the relaxation method and Maxwell construction to numerically solve the Euler–Lagrangian differential equation for the total free energy together the Rapini–Papoular surface energy to take into account anchoring of nematic liquid crystal molecules at the substrates.In this study,we focus our attention on obtaining the phase diagrams of Frederiks transition for different values of anchoring strength which have been not computed in our previous work.In this way,the effect of nanoparticle radius,nanoparticle volume fraction,nanoparticle polarization,and cell thickness on the Frederiks transition for different values of anchoring conditions are summarized in the phase diagrams.The numerical results show that by increasing the nanoparticles size and nanoparticle volume fraction in the ferronematic system,the Frederiks threshold field is strongly reduced.展开更多
In this paper,we visit the thermodynamic criticality and thermodynamic curvature of the charged AdS black hole in a new phase space.It is shown that when the square of the total charge of the charged black hole is con...In this paper,we visit the thermodynamic criticality and thermodynamic curvature of the charged AdS black hole in a new phase space.It is shown that when the square of the total charge of the charged black hole is considered as a thermodynamic quantity,the charged AdS black hole also admits a van der Waals-type critical behavior without the help of thermodynamic pressure and thermodynamic volume.Based on this,we study the fine phase structures of the charged AdS black hole with fixed AdS background in the new framework.On the one hand,we give the phase diagram structures of the charged AdS black hole accurately and analytically,which fills up the gap in dealing with the phase transition of the charged AdS black holes by taking the square of the charge as a thermodynamic quantity.On the other hand,we analyse the thermodynamic curvature of the black hole in two coordinate spaces.The thermodynamic curvatures obtained in two different coordinate spaces are equivalent to each other and are also positive.Based on an empirical conclusion under the framework of thermodynamic geometry,we speculate that when the square of charge is treated as an independent thermodynamic quantity,the charged AdS black hole is likely to present a repulsive between its molecules.More importantly,based on the thermodynamic curvature,we obtain a universal exponent at the critical point of phase transition.展开更多
基金the support of Shiraz University of Technology Research Council
文摘Motivated by our recent work,in this work,we present the numerical study of the anchoring effect on the Frederiks threshold field in a nematic liquid crystal doped with ferroelectric colloidal nanoparticles.Assuming weak anchoring conditions,we employ the relaxation method and Maxwell construction to numerically solve the Euler–Lagrangian differential equation for the total free energy together the Rapini–Papoular surface energy to take into account anchoring of nematic liquid crystal molecules at the substrates.In this study,we focus our attention on obtaining the phase diagrams of Frederiks transition for different values of anchoring strength which have been not computed in our previous work.In this way,the effect of nanoparticle radius,nanoparticle volume fraction,nanoparticle polarization,and cell thickness on the Frederiks transition for different values of anchoring conditions are summarized in the phase diagrams.The numerical results show that by increasing the nanoparticles size and nanoparticle volume fraction in the ferronematic system,the Frederiks threshold field is strongly reduced.
基金The financial supports from the National Natural Science Foundation of China(Grant Nos.11947208 and 11947301)China Postdoctoral Science Foundation(Grant No.2020M673460)are gratefully acknowledged.This research was also supported by The Double First-class University Construction Project of Northwest University.
文摘In this paper,we visit the thermodynamic criticality and thermodynamic curvature of the charged AdS black hole in a new phase space.It is shown that when the square of the total charge of the charged black hole is considered as a thermodynamic quantity,the charged AdS black hole also admits a van der Waals-type critical behavior without the help of thermodynamic pressure and thermodynamic volume.Based on this,we study the fine phase structures of the charged AdS black hole with fixed AdS background in the new framework.On the one hand,we give the phase diagram structures of the charged AdS black hole accurately and analytically,which fills up the gap in dealing with the phase transition of the charged AdS black holes by taking the square of the charge as a thermodynamic quantity.On the other hand,we analyse the thermodynamic curvature of the black hole in two coordinate spaces.The thermodynamic curvatures obtained in two different coordinate spaces are equivalent to each other and are also positive.Based on an empirical conclusion under the framework of thermodynamic geometry,we speculate that when the square of charge is treated as an independent thermodynamic quantity,the charged AdS black hole is likely to present a repulsive between its molecules.More importantly,based on the thermodynamic curvature,we obtain a universal exponent at the critical point of phase transition.
