Abstract
Recent calculations on the change in radial dimensions of reacting (growing) polyethylene in the gas phase experiencing Lennard Jones and Kihara type potentials revealed that a single reacting polyethylene molecule does not experience polymer collapse. This implies that a transition that is the converse of what happens when molten polyethylene crystallizes, i.e. it transforms from random coil like structure to folded rigid rod type structure, occurs. The predicted behaviour of growing polyethylene was explained by treating the head of the growing polymer chain as myopic whereas as the whole chain (i.e. when under equilibrium conditions) being treated as having normal vision, i.e. the growing chain does not see the attractive part of the LJ or Kihara Potentials. In this paper we provide further proof for this argument in two ways. Firstly we carry forward the exact enumeration calculations on growing self avoiding walks reported in that paper to larger values of number of steps by using Monte Carlo type calculations. We thereby assign physical significance to the connective constant of self avoiding walks, which until now was treated as a purely abstract mathematical entity. Secondly since a reacting polymer molecule that grows by addition polymerisation sees only one step ahead at a time, we extend this calculation by estimating the average atmosphere for molecules, with repulsive potential only (growing self avoiding walks in two dimensions), that look at two, three, four, five ...steps ahead. Our calculation shows that the arguments used in the previous work are correct.
Highlights
While developing a theory for the kinetics of polymerization it was assumed that the rate constant for the polymerization process at each step of the polymerization was the same
The basis of this assumption was that the reaction occurs between the head of the reacting polymer and the monomer and between the head of one reacting polymer molecule and the tail of another reacting polymer molecule and that the rapid segmental motion of the head of the reacting polymer is much faster than the slow motion of the rest of the polymer molecule.[1]
The term self avoiding walk as applied to the configurational statistical mechanics of polymer molecules in dilute solution was latter proposed.[5,6,7]. This term refers to Non Markovian chains only. In these Refs. 4–7 equilibrium statistical mechanics of the polymer molecule was studied by increasing the number of monomer units in an arbitrary manner when plotting against the mean square end to end distance or the mean square radius of gyration
Summary
While developing a theory for the kinetics of polymerization it was assumed that the rate constant for the polymerization process at each step of the polymerization was the same (i.e. constant). The term self avoiding walk as applied to the configurational statistical mechanics of polymer molecules in dilute solution was latter proposed.[5,6,7] This term refers to Non Markovian chains only. One can think of three scenarios for necklaces made up of beads, whose size increases in three different ways:
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