Study on glass transition by saturated square well network model

Abstract

Glass and glass formation have long been the interest of chemist, physicists and material scientists in its application to polymer, biology and metallic alloys. Glassy transition phenomenon in laboratory observation is the rapid increase of heat capacity when the glassy material is warmed. The relaxation time, which is the time the system need to recover from a temperature perturbation, is too long below the glass transition temperature that we can not observe it in the experiment time scale. The concept of inherent structure is used to explain process of freezing and glass transition from the potential of packing configurations. The total potential of the system is illustrated in a (3N+1) dimensional diagram that consists of many basins and saddle points. Each basin, the potential minimum, represents an inherent structure. Inherent structure focus on the static point of view in understanding the nature of glass, which is often smear by the vibration of the component particles. This thesis focuses on Molecular Dynamics studies on glass properties of a two dimensional square well model. Since the well depth e/kT is set to be zero, the dominant interaction between molecules is the hard core repulsive potential. This is similar to hard disk models for study of melting and freezing. However, when studying properties of glass and glass transition, hard disks model is not so promising, simply because the system is easy to freeze Square well model with no triangle constrain and valency constriction, especially by mixture valency constriction, may help to reduce the chance of freeze. We choose the square well depth to be zero in our experiment by the following considerations: (1) for high density glasses, very few bonds are able to break and form, therefore, the well depth has little effect to the property of glass. (2) because this model has not energy stored in bonds, it will be convenient to compare the equation of state of low density fluid to that of hard disk model, Second virial coefficients for hard disk can also used in the equation of state for fluid. (3) This will make the simulation programming easier, as when a bond is broken or formed, there is no need to re-scale the total temperature for all particles in (N,V,E) or (N, V,T) simulation. Another advantage of square well model is that this model clearly defines bonds. This is suitable to study properties of network topology of configurations by using the inherent structure formalism. To avoid the fluid to freeze into crystal, fast compression on equilibrium fluid is necessary to make glass samples. Glass transition density is determined by the intersection of extrapolation of equation of state for fluid and that of the glass. The thermal entropy of the glass is calculated by integration of the equation of state using ideal gas at the same density as the reference. The change of heat capacity at glass transition, calculated from the equation of state, has analogue to the characteristics of "fragile" fluid whose structure is sensitive to temperature. By annealing glass samples in high density,local re-arrangement of bond patterns is possible. Statistical entropy of a glass sample is calculated from the configurational integral for the particular topology of the sample. For a equilibrate system, it is the same as the thermal entropy. However, when the system is trapped in one of many glass configurations, its value is below the thermal entropy at the same temperature. The difference between two kinds of entropy, for a system with no potential, is related to the number of inherent structures. Tether method, which has been used to measure the melting and freezing of regular crystals, is applied to the present system to measure the statistical entropy of glasses. For a system consisting N particles, the number of distinct glass configurations is huge. A particular glass is very unlikely to be made twice. Properties of different glass configurations may differ. Thus, the basins of inherent structure will have different depth. In molecular dynamics experiment, slow compression rate may let the fluid find a path to a more relaxed glass configuration. Squash procedure is designed to assign a configuration of fluid, along the steepest-descent path, to its unique inherent structure basin. Since the procedure moves a pair of molecules at a time by limited distance, the process is regarded as to instantly solidify the given configuration without relaxation. Mixture valency glasses seem to be more stable to allow accurate measurement. The limiting density of mixture glasses seems to have a distribution, which is assumed to be a Gaussian function. Since the configurational integral of a fluid is the sum of that of all possible glasses the equilibrated fluid can sample, the property of fluid is thus calculated by the property of glass through a group of simple equations. This calculation leads to some concepts in discussion of properties of fluid represented by that of glasses (Chapter 4). z m is the limiting density for most of inherent structures of a fluid. Another quantity z o' is the maximum limiting density calculated from the Gaussian equation. This is a unique value that may represent an ideal glass. For an equilibrium fluid, the system preferentially samples inherent structures with limiting density z o, which is a function of the fluid density itself. Squash experiment results support this calculation. Heat capacity decrease at glass transition is also explained. In conclusion, the square well model with no triangle and valency constrictions provides a better model to study properties of glass and glass transition.