Statistics of copolymer sequences obtained by polymeranalogous reactions of homopolymer globules

Abstract

For the first time the macrokinetics of polymeranalogous reaction in a homopolymer globule is considered theoretically. Using mathematical apparatus of the theory of markovian stochastic processes we examined the statistical characteristics of the chemical structure of the emerging copolymers. It is shown that when the reaction is kinetically-controlled the sequence distribution of monomeric units in copolymer chains follows Bernoullian statistics. In the opposite regime, when the reaction is diffusion-controlled it is proved that the resulting primary structure is described by the Levy flight distribution. Such copolymers with nonmarkovian character of the alteration of units in macromolecules can not be synthesized in the bulk or in concentrated solutions by means of standard synthetic polymerization procedures.

Polymer Globule as a Nanoreactor

“…This obviously deteriorates the efficiency of the nanoreactor. So, for the set of parameters, corresponding to the largest value of K in Figure 1, the change of 31 LP from 2 to 0.75 reduces K from 13 to 7 and Φ from 0.74 to 0.49.…”

“…22 The macrokinetics of such PARs has been theoretically studied in papers. 30,31 Second, in line with ref 21 we considered only homogeneous heteropolymer globules in "volume approximation", ignoring their narrow surface layer. This approximation is known to work rather well outside the immediate vicinity of the coil-globule transition point.…”

“…For the vast majority of pairs of solvents, reagents and monomeric units the values of the Flory parameters fall within the interval (0, 2), although in some cases large and even negative values are known. 28 An example of these latter is the solution of poly(ethyl methacrylate) in toluene, where 31 LP ≈ -1. 29 Positive and negative values of the Flory interaction parameter for every pair of (quasi)components correspond respectively to the loss and gain in the free energy at the contact between the constituents of this pair.…”

“…The type of the conformational state of the macromolecule in dilute solution is primarily controlled by the value of parameter 31 LP . For this state to be globular, inequality 31 LP J 0.5 should necessarily hold, provided the remaining Flory parameters (4) fall within the interval (0, 2).…”

“…For this state to be globular, inequality 31 LP J 0.5 should necessarily hold, provided the remaining Flory parameters (4) fall within the interval (0, 2). Note, the value of 23 LL tangibly affecting coefficient K just slightly influences the volume fraction Φ of monomeric units in the globule.…”