枝分れのある鎖状分子の統計

抄録

The most elemental quantity with appears in the Debye's theory of the viscosity of high polymer solution, is the mean square deviation of each segment from the center of gravity of a chain, σ2.There are many theorie's about a linear chain polymer whichever Markoffian or not, and the viscosity varies proportionally with the degree of polymerization by some theorie's, but does not by others.Zimon and Stockmayer discussed the branched polymers having special types exactly, but for the general type, they gave only the approxcimate results.
There will be studied the theory for the general type of branching polymer, except containg ring, and cosiderablly simple but exact formula to calculate σ2 is obtained.The result is as follows.
σ2 is not proportional to the degree of the polymerization but shows complex dependency on it. However, if we take appropriate average treatment about σ2, get
σ²=K·N
where N is the degree of polymerization, and K is a proportional constant. which is get the function depending on the branching type.