The Study On Viscoelastic Relaxation Time Of Lennard-Jones System

Viscoelastic relaxation time is an important concept to characterize the viscoelastic response of materials,which is one of the keys to establish viscoelastic models and directly related to the interactions among the microscopic atoms of materials.How to characterize and obtain the viscoelastic relaxation time is of great significance for the establishment of viscoelastic calculation model.At present,there are three characterization methods of viscoelastic relaxation time.The viscoelastic characteristic relaxation time is most consistent with the concept of material viscoelastic response,but it needs to calculate the storage modulus and loss modulus at different frequencies,which requires long calculation time and complicated calculation process.Maxwell relaxation time is simple to calculate,but its description is limited by the Maxwell model so that it cannot be applied to a wider range of materials.The lifetime of the state of local atomic connectivity can explain the cause of shear stress relaxation from a microscopic perspective,but its calculation process requires a lot of calculation resources to calculate the trajectory of the atom.Therefore,it is of great significance to study the method of calculating the viscoelastic relaxation time of materials further.In this paper,molecular dynamics simulations(MD simulations)was applied to explore the viscoelastic relaxation time in the monoatomic Lennard-Jones system.The prediction method of viscoelastic relaxation time,based on the analysis of the arrangement of atoms in the system and the dissociation and association processes between atoms,was proposed and applied in the mixed diatomic Lennard-Jones system.The work in this paper can provide a reference for the research on the characterization of the relaxation time of viscoelasticity.First,the viscoelastic relaxation time of the monoatomic Lennard-Jones system is studied.The viscoelastic relaxation time of the monoatomic Lennard-Jones system on 22 conditions in the range of T*=0.85-5,?*=0.85?1,?=0.97?1,?=0.8?1.3 were discussed from a microscopic perspective by the equilibrium molecular dynamics methods.Static viscoelasticity(viscosity?*,high-frequency shear modulus G_?*)was calculated by Green-Kubo formula,and Fourier transform was applied to the calculation of dynamic viscoelasticity(storage modulus G'*,loss modulus G"*).On these basis,viscoelastic characteristic relaxation time(?_MD*),Maxwell relaxation time(?Maxwell*)and the lifetime of the state of local atomic connectivity(?_LC*)were calculated.In addition,according to the arrangement of atoms,a method for predicting the viscoelastic relaxation time of monoatomic Lennard-Jones system was proposed based on the equilibrium theory and Kramers' rate theory.The results show that,T_Maxwell*cannot predict?_MD*accurately at low temperatures in the monoatomic Lennard-Jones system.Compared to?Maxwell*,?_LC*is closer to ?_MD*.But the calculation of ?_LC* should count the trajectories of all atoms at a certain time step,which requires a lot of time and computing resources.The relaxation time ?_model*calculated by the method we proposed is closer to ?_MD*.The prediction method of viscoelastic relaxation time proposed in this paper has certain accuracy and reliability.Second,we carried out a study on the viscoelastic relaxation time of KA model,a typical mixed diatomic Lennard-Jones system.In order to verify the applicability of the prediction method of the viscoelastic relaxation time which was proposed in this paper,the mixed diatomic Lennard-Jones system was simulated with a temperature in the range of T*=2?5.Viscoelastic characteristic relaxation time(?_MD*),Maxwell relaxation time(T_Maxwell*),the lifetime of the state of local atomic connectivity and the relaxation time of the prediction method(?_model*)were calculated and analyzed.At the same time,all types of viscoelastic relaxation under different A atom ratio conditions were also studied.The results show that,T_Maxwell* and ?_MD* are obviously different,while the difference between and is smaller.Tmodel*is closest to ?_MD*.There were multiple types of RDF curves(A-A,B-B,A-B)in the KA model,which corresponded to different types of dissociation and association processes.When multiple RDF curves existed,it was found that the relaxation time of the prediction method calculated by the process with the fastest rate could well predict ?_MD* in the KA model.