Statistical mechanics teaching

There are two basic approaches to the computer simulation of liquid crystals, the Monte Carlo method and the method known as molecular dynamics. We will first discuss the basis of the Monte Carlo method. As is the case with both these methods, a small number (of the order hundreds) of molecules is considered and the difficulties introduced by this restriction are, at least in part, removed by the use of artful boundary conditions which will be discussed below. This relatively small assembly of molecules is treated by a method based on the canonical partition function approach. That is to say, the energy which appears in the Boltzman factor is the total energy of the assembly and such factors are assumed summed over an ensemble of assemblies. The summation ranges over all the coordinates and momenta which describe the assemblies. As a classical approach is taken to the problem, the summation is replaced by an integration over all these coordinates though, in the final computation, a return to a summation has to be made. If one wishes to find the probable value of some particular physical quantity, A, which is a function of the coordinates just referred to, then statistical mechanics teaches that this quantity is given by... 

There are other topics that might be considered, such as solid state theory and classical statistical mechanics. You must decide how much time to spend on each of your chosen topics. You can identify subtopics that you might omit or to which you can give only an introduction. One of the difficult decisions involves how much to teach about your own research area. You are obviously excited about this area, and will be tempted to spend too much class time on it. Another difficult decision is how much time to spend on topics of current interest such as nanomaterials and environmental chemistry. Your decisions should be guided by the composition of your class. If the class has a lot of premedical students and biochemistry majors in it, they are probably well served by a thorough treatment of thermodynamics and dynamics, and perhaps less well served by a thorough treatment of quantum mechanics and statistical mechanics. If the class is mostly composed of future chemistry graduate students, quantum mechanics and statistical mechanics are more important. 

We have been teaching physical chemistry with a kinetics-first orientation for 13 years. Over the course of this past decade we have also examined our students using the ACS Comprehensive Standardized Exam. Form 1995 (16) was used from 1996 through 2003 and Form 2002 (17) was used in 2004 and 2005. This comprehensive exam has been administered at the end of physical chemistry II covering quantum chemistry and spectroscopy. Both versions divide the 60 multiple choice questions into the three canonical areas, T, Q, and D, with the 1995 version assigning 20 questions each to the three areas. The 2002 version assigns 15 questions to the dynamics section and 25 to the quantum section. A few statistical mechanics questions are also scattered among these sections. 

Distribution of institutions teaching Statistical Mechanics as part of a typical physical chemistry class ... 

Equilibrium statistical mechanics may still have something useful to teach us in this problem. At that same discussion at Cooperstown in 1958 Flory made the perspicacious remark (the crystal) surface presents an impenetrable barrier to the random coil, and this restricts the statistical possibilities of the coil. The problem resembles that encountered in treating the surface tension of a dilute polymer solution . I do not believe the consequences of that remark have been sufficiently followed up. 

The VUB offered a compulsory course on basic quantum mechanics and an introduction to quantum chemistry firom the start of the chemistry curriculum in the early sixties. These lectures were given by Andre Bellemans, a former student of Nobel Laureate Ilya Prigogine at the ULB and still one of his collaborators at that time, specialist in statistical mechanics. In 1974 when Bellemans resigned firom his VUB charge, Henk Lekkerkerker was appointed for teaching the complete range of theoretical physical chemistry courses (including thermodynamics and quantum... 

The extent to which statistical concepts enter the picture as we go from the micro- to the macroworld is not at all at our disposal. For example, quantum mechanics as we know it today teaches us that it is impossible in principle to obtain complete information about a microscopic entity (i.e., the precise and simultaneous knowledge of an electron s location and momentum, say) at any instant in time. On account of Heisenberg s Uncertainty Principle, conjugate quantities like, for instance, position and momentum can only be known with a certain maximum precision. Quantum mechanics therefore already deals with averages only (i.e., expectation values) when it comes to actual measurements. 

Unfortunately, not enough time is spent teaching students to think critically about the models they are using. Most mathematics and statistics classes focus on the mechanics of a calculation or the derivation of a statistical test. When a model is used to illustrate the calculation or derivation, little to no time is spent on why that particular model is used. We should not delude ourselves, however, into believing that once we have understood how a model was developed and that this model is the true model. It may be in physics or chemistry that elementary equations may be true, such as Boyle s law, but in biology, the mathematics of the system are so complex and probably nonlinear in nature with multiple feedback loops, that the true model may... 

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