The Monte Carlo Simulation Of The Polydisperse Hard Sphere Colloids

The hard sphere colloid is the most simple and representative colloidal sys-tem. The interaction between particles is the excluded-volume interaction, how-ever, the simple system possess very rich physical phenomena. Under di?erentconditions, the system can respectively be in the ?uid state, solid state, coexist-ing state and even glass state. As the density increases, the system undergoesan entropy-driven first-order transition from the ?uid phase to solid state. Thesystem has been investigated extensively by the experiment, theory and simu-lation, which is very important for us to understand the properties of the morecomplicated colloids. But the true colloids are size-polydisperse(i.e., the sizes ofparticles are not completely equal.), which is essential in the course of the productof colloidal particles. Therefore, the investigation of the e?ect of polydispersityto the properties of colloids is crucial for us to understand the true colloids. Inthe thesis, we use Monte Carlo simulation to study extensively and intensivelythe thermodynamic behaviors of the polydisperse hard-sphere colloid, and findsome novel phenomena which don't exist in the monodisperse system.The thesis is organized as follows, there are eight chapters in the thesis. Thebackground of the thesis is presented in chapter 1; in chapter 2 we introduce thebasic theories and methods used in the research; from chapter 3 to chapter 7, weprovide the details of our investigation; in the last chapter we give the conclusionand outlook.In the third chapter, by extending the nonequilibrium potential refinementalgorithm(NEPR) and lattice switch(LW) method to the semigrand ensemble,the free energy of the fcc and hcp structure of polydisperse hard sphere crystalsare calculated. The result shows that the fcc structure is more stable than the hcpstructure for polydisperse hard sphere crystals below the terminal polydispersity, which is the same as the monodisperse case. In chapter 4, a general Monte Carlosimulation method of calculating the elastic constants of polydisperse colloidalcrystal was developed. The elastic constants of a size polydisperse hard spherefcc crystal is calculated by using the method. The pressure and three elasticconstants(C11, C12 and C44) increase significantly with the polydispersity. It wasalso found from extrapolation that there is a mechanical terminal polydispersityabove which a fcc crystal will be mechanically unstable. In chapter 5, a newMonte Carlo approach is proposed to investigate the ?uid-solid phase transitionof the polydisperse system. By using the extended ensemble, a reversible pathwas constructed to link the monodisperse and corresponding polydisperse system.Once the ?uid-solid coexistence point of the monodisperse system is known, the?uid-solid coexistence point of the polydisperse system can be obtained from thesimulation. The validity of the method is checked by the simulation of the ?uid-solid phase transition of a size-polydisperse hard sphere colloid. The results are inagreement with the previous studies. In chapter 6, the solid-solid coexistence of apolydisperse hard sphere system is studied by using the Monte Carlo simulation.The results show that for large enough polydispersity the solid-solid coexistencestate is more stable than the single-phase solid. The two coexisting solids havedi?erent composition distributions but the same crystal structure. Moreover,there is evidence that the solid-solid transition terminates in a critical point asin the case of the ?uid-?uid transition. In the first part of chapter 7, we proposea simple Monte Carlo method to calculate the interfacial free energyγbetweenthe substrate and the material. Using this method we investigate the interfacialfree energies of the hard sphere ?uid and solid phases near a smooth hard wall.According to the obtained interfacial free energies of the coexisting ?uid and solidphases and the Young equation we are able to determine the contact angle withhigh accuracy, cosθ= 1.010(31), which indicates that a smooth hard wall can bewetted completely by the hard sphere crystal at the interface between the walland the hard sphere ?uid. In the second part, the method is extended to thepolydisperse system. By the extended method we calculate the interfacial freeenergy between the polydisperse hard-sphere colloid and smooth hard wall. Theresults indicate that as the polydispersity increases the ?uid-wall interfacial freeenergy is almost unchanged, but the solid-wall interfacial free energy increases significantly. Further, we find that the hard wall can be wetted partially by thepolydisperse hard-sphere crystal.