By Prof. Toshihiro Kawakatsu (auth.)
This textbook presents senior undergraduate and graduate scholars with an creation to the fundamental suggestions used the statistical physics of polymers. tools of Gaussian chain information are mentioned intimately. functions to varied fascinating phenomena starting from the microscopic (chain conformations, biopolymers, etc.) to the macroscopic (phase separations, rheology, etc.) are defined. Readers are assumed to have taken straight forward classes on statistical physics, quantum physics and mathematical physics, yet past wisdom of polymer technological know-how isn't really required. The booklet includes many illustrations and diagrams in addition to routines, to be able to support readers to simply and intuitively comprehend the options defined within the text.
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Additional resources for Statistical Physics of Polymers: An Introduction
Sample text
This is because the spring of the bead- spring model originates from the change in the conformation entropy. 29) Therefore, we can identify b as the average bond length of the coarse-grained model. This quantity b is often called the effective bond length. Now let us define the Hamiltonian of the bead- spring model. 28). We number each segment i = 0, 1, ... , N from one end to the other. We assume that the solvent is so viscous that the kinetic energy can be neglected. Then the Hamiltonian of this polymer chain is given by N= 3kB T 2b2 L N-l i=O Iri - ri+ll 2 _ + W(rO , rl, .
9. This property of the ideal chain will be used in the self-consistent field theory introduced in Chap. 3. Scaling of the End-to-End Distance One of the measures of the spatial extension of a polymer chain is the distance between the two end segments of the chain. As shown in Fig. 7) is called the end-to-end distance. Here, note that the quantity (R) is not suitable for the definition of the end-to-end distance because the average of any odd power of a vector quantity vanishes due to the isotropy of the system.
The wave function of the scattered beam at a certain steric angle consists of a superposition of scattered waves from different points. This is expressed by the convolution of the segment density fluctuation and the plane waves as J drB¢(r; r)e- iq . 44) where q is the difference in the wave vectors between the incident beam and the scattered beam. This expression means that the scattered wave function is the Fourier transformation of the density fluctuation B¢(r; r). 3 Statistical Mechanical Theory of Equilibrium Conformations 47 The scattering intensity is the probability of detecting the scattered beam in the direction specified by q.