Theory of formation of polymer crystals with folded chains in dilute solution

Abstract

A detailed interpretation of the kinetics of homogeneous nucleation and growth of crysLals or a linear homopolymer from dilute solution is given. The probability of forming both nuclei with fold ed chains, and conventional bundlelike nuclei, from dilute solution is analyzed. It is predicted that at sufficiently high dilution, critical nuclei of length 1: will be formed from single polym er molecules by sharp folding of the chain backbone. The step height of the nucleus is given approximately by 1:=4O' ,/A f. Here fI , is the fr ee energy requ ired to form a unit area of the loop-containing end surfaces, and Af is the free energy d ifference per unit volum e of crystal between the crystalline and solution states. The quantity Af is approxim ately proportional to the degree of s upercooling AT. The growth of thesc nuclci is then analyzcd. After growth, the resulting crystal is flat and platelike, the loops formed by the chain folds being on the upper and lower surfaces Kinetic factors d etermine that the distance between the flat slll'faces in the grown crystal will vary over only a narrow range about a value that is in the vicinityofl *=4O' ./Af. (NeglectingefTects du e to edge free encrgies, the theoretical upper and lower limits are l *= 40' ,/ Af and I *= 2O' ,/Af, respccLi vely.) In so me cases the predicted temperature dependence of the step height of the grown crystal, I*= const./ AT, may be modified by the existence of a constant tcrm resulting from thc presence of an edge fr ce cnergy E". A grown loop-type cry tal is predicted to be stable in comparison with a bundlclike crystal of the same shape and volume in a sufficiently diluLe olution. The logarithm of the nucleation rate is approximately proportional to 1/ (A T )2 near the m elting point. The cxponent n in the free growth rate law is predicted under various ass umption s. To the extent that compariso n is possibl e, the predictions givcn agree with the experimental r es ults obtained by K eIJ er and O'Connor an d others on single crystals of unbranched polyethylene grown from dilute solution.A su rvey is given of homogeneo us ll!..! cleaiion in bulk polymers, where the conventional bundlelik e nucleus containing segmenLs from many different molecules is v alid, and the essential results comparcd with thosc calculated for the dilu te solution case.The theory given for loop nuclei is both general and precise enough at the critical points to s uggest that, on crystallization from sufficiently dilute solution, crystals of a definite step height arc commonly to be expect()d for other crystalli zable linear polymers than polyethylene, provid ed loop formation is sterically possible.

Phase behavior of a lattice protein model

“…We have not observed spontaneous formation of ''extended chain'' crystals. The absence of extended chain crystals could either be due to kinetic factors ͑as in the case of homopolymers 30 ͒, or to finite size effects. However, in larger system we also did not observe the spontaneous formation of extended-chain crystals.…”

Drying of semicrystalline polymers: mathematical modeling and experimental characterization of poly(vinyl alcohol) films

“…The assumption of volume fraction proportionality is at its simplest form. The folding rate, k i ; proposed by Lauritzen and Hoffman [33], can be calculated for the polymer in the presence of each solvent.…”

Fabrication of Hollow Silica Particles Using a Self-Assembled Polyethylene Granule as a Template

“…Self-assembly process of polyethylene (PE) crystallization has been known since the 1960s [30]. Spherulite structure with few tens micron in size can be obtained from its melt state by a cooling process which originated from stacking of lamellae with interlamellar thickness of~12 nm [31].…”