Lattice models basic principles

Even though the basic idea of the Widom model is certainly very appealing, the fact that it ignores the possibihty that oil/water interfaces are not saturated with amphiphiles is a disadvantage in some respect. The influence of the amphiphiles on interfacial properties cannot be studied in principle in particular, the reduction of the interfacial tension cannot be calculated. In a sense, the Widom model is not only the first microscopic lattice model, but also the first random interface model configurations are described entirely by the conformations of their amphiphilic sheets. 

But in terms of these fundamentals, we would dare to say that an important progress had been achieved over the last several years. Previously, at the time of Anfinsen, protein folding seemed a fundamental physics mystery. People could not imagine how it could be happening even in principle. Now, there is at least an overall understanding of the basic physics behind folding, as we tried to outline in the present chapter. There are lattice models, which are very much unlike proteins in many respects (too many and too obvious to list) — but which are like proteins in two most important aspects they have the same fundamental difficulties, such as Levinthal paradox, and they do fold. And we understand this model pretty well But, of course, the study continues in many directions... 

He, X.Y. and Luo, L.S., 1997. Lattice Boltzmann Model for the Incompressible Navier-Stokes Equation. Journal of Statistical Physics, 88(3-4) 927-944. Himmelblau, D.M., 1974. Basic Principles and Calculations in Chemical Engineering. Prentice Hall, New Jersey, 542 pp. 

The infortnation provided in this chapter can be divided into four parts 1. introduction, 2. thermodynamic theories of polymer blends, 3. characteristic thermodynamic parameters for polymer blends, and 4. experimental methods. The introduction presents the basic principles of the classical equilibrium thermodynamics, describes behavior of the single-component materials, and then focuses on the two-component systems solutions and polymer blends. The main focus of the second part is on the theories (and experimental parameters related to them) for the thermodynamic behavior of polymer blends. Several theoretical approaches are presented, starting with the classical Flory-Huggins lattice theory and, those evolving from it, solubility parameter and analog calorimetry approaches. Also, equation of state (EoS) types of theories were summarized. Finally, descriptions based on the atomistic considerations, in particular the polymer reference interaction site model (PRISM), were briefly outlined. 

NMR observations basically contain spin relaxation processes which are associated with molecular motions with different specific frequencies in a given system. For quantitative measurements to determine the compositions of the system or selective measurements of particular components with different relaxation parameters, it is essential, therefore, to understand the principle of the relaxation mechanism. When our interest is focused on molecular motions, spin relaxation parameters such as spin-lattice relaxation time T, spin-spin relaxation time T2, and the nuclear Overhauser enhancement (NOE), are directly measured as a function of temperature or field frequency by using appropriate pulse sequences. Such temperature or frequency dependencies of the spin relaxation parameters are analyzed in terms of appropriate models to obtain detailed information of molecular motions with frequencies of Hz in the system. In this chapter, the basic theories and analyses... 

---