统计热力学(英文).ppt

Then the Rb achieved in walks of N steps is N : number of steps ri : the vector position of the i-th link in the chain, ?ri? = ri = b P(Rb) : the probability distribution of Rb ? For each Rb there exists astronomical variety of possible configurations ? the full sequence of ri is virtually unknowable ? the statistical approach becomes both necessary and valid. Fig. 2.1. Distribution functions for the Rb of an assembly of ideal chains Gaussian distribution ? Rrms = ?Rb2?1/2 = N1/2?b movements of atoms from their equilibrium position ? result strain Stretch a material ? do work on the system ? ? exhibit a limited elastic region crystalline solids amorphous glasses elastic limits: atomic adjustments are localized. 1% ? Elastomers ? natural or synthetic polymeric materials ? can be stretched to several times its original length without breaking ? constituent polymeric chains can rotate about the chain bonds most widely studied elastomer Natural rubber deformation is reversible instantaneous almost no creep ?? = 1/kT S = kN lnZ + U/ T F = U ? TS = ?nRT lnZ Z function of each energy mode depends in turn upon the allowed energy levels for that mode. 2.3 Energy Mode and Energy Levels ? = ?e + ?v + ?rt + ?n + ?t Different energy Different modes of motion electronic vibrational rotational nuclear translational result in General method of attacking a problem is to set up and solve an Schr?dinger’s equation r = (x,y,z): the particle?s position in a three-dimensional space ?(r,t): the wave function, which is the amplitude for the particle at a given position r at any given time t m: the mass of the particle V(r): the potential energy of the particle at the position r. ?(r,t) = f(t)?(r). ? Particles are restrained to certain regions of the space. ? Set up time-independent standing waves Depend on t alone Depend on r only Equal the