Internal distances in short polyelectrolytes: A Monte Carlo study

The new critical phenomenon of a coil-rod transition that was studied in our previous papers [J. Chem. Phys. 92, 4468 (1990); 93, 2736 (1990); 94, 3213 (1991); 97, 2119 (1992); J. Phys. Chem. 96, 5553 (1992)] is investigated further. The family of physical statistical bonds is expanded. An important additional bond, the linear statistical bond, is introduced. Parameters based on internal distance investigations are proposed and these are used to analyze the Monte Carlo data. One of the most important parameters is the average probability for a linear statistical bond at a site on the chain, ${\mathit{P}}_{\mathit{l}}$. Indications are reported that scaling behavior in polyelectrolyte chains exists only for chain lengths having the same kink fraction g. An important relation is shown between the average number of kinks, 〈${\mathit{n}}_{\mathrm{kink}}$〉, and D(2), the mean-square distance between the end beads of three adjacent beads in a cubic lattice: g=〈${\mathit{n}}_{\mathrm{kink}}$〉/N-2=1-[D(2)-2]/2=1-${\mathit{P}}_1$. In a previous article [J. Chem. Phys. 97, 2119 (1992)] we found that for a self-avoiding-walk chain, g is constant and equal to 0.77. This relation leads to new constants, ${\mathit{P}}_1$=0.23 and D(2)=2.46 squared cell units in addition to the constant mean straight length 〈${\mathit{l}}_{\mathit{s}}$〉=1.29 cell units, found in the above reference, to be connected to g.