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چكيده انگليسي :

AbstractHard core potentials including the Hard Sphere HS Square Well SW Sutherland ST Hard core double Yukawa HCDY and Hard Core Lennard Jones HCLJ are ofgreat importance in the liquid state theories because HS potential is used as a referencestate in the perturbation theory of simple liquids HS SW and HCDY potential modelsare used as reference system for modeling of various molecular fluids in the statisticalassociating fluid theory equations of state the behavior of all simple liquids tends tobecome similar to the behavior of hard core fluids when the temperature and densityincrease and above all we will show that we can derive analytical expressions for theirradial distribution functions RDF at least at low density limit hence all their propertiesmay be expressed and calculated analytically So in the first step we derive a generalanalytical solution to the integral equations of liquid state theories Born Green Yvon Hyper Netted Chain and Percus Yevick Equations at low density limit for potentialswith a hard core For the specific case of the Lennard Jones potential with a hard core wehave derived an analytical function for the radial distribution function at high temperatureand low density We have noted that this function has two humps which is thecharacteristic feature of the radial distribution function at low densities In addition thisfunction has been used to calculate the third virial coefficient for such a fluid exactly Inorder to use the derived RDF for real fluids one of the potential parameters is chosen insuch a way that the RDF behaves more like that for a real fluid Hence we have been ableto calculate all thermodynamic properties of a simple fluid analytically We have thenapplied our procedure to a Lennard Jones fluid and compared the results with simulationdata The agreement is good up to moderate densities We have also applied our methodto a real fluid i e argon We supposed that argon is an example of a Lennard Jonesfluid The calculated results are in good agreement with experimental data for gaseousstate of argon Despite useful features of hard core potentials they have an unwillingbehavior that must be improved For instance while these potential models correctlypredict the behavior of the second virial coefficient B T at low temperature region theyshow however a significant deviation from experimental data at high temperatures specifically they do not predict any maximum value for B T versus T at any temperature which is called inversion temperature observed experimentally This behavior is due toexistence of a hard core diameter in such potential models Because the moleculardiameter becomes smaller when temperature increases we introduced a new expressionfor the variation of molecular diameter with temperature that incorporates this effect Thetemperature dependence of the diameter was used in both ST and SW potential models tomodify the second virial coefficients Then we have shown that the experimental secondvirial coefficient fits into the modified ST and modified SW quite well for the entiretemperature range for which experimental data are reported including the inversiontemperature Then we have calculated the non equilibrium properties of real fluids i e viscosity thermal conductivity and self diffusion coefficients When these calculationswere performed we found that the obtained results were in a closer agreement withexperimental data that is there is no need to have two sets of potential parameters for theequilibrium and non equilibrium properties of real fluids when the temperaturedependence of the molecular parameter are taken into account correctly

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اصلاح پتانسيل هاي با مغز سخت به منظور كاربرد آنها در سيالات واقعي

خواص ماكروسكوپي سيالات , مغز سخت , لنارد- جونز , ضريب دوم ويريال , ساترلند , آرگون