Theory of flow-induced fibril formation in polymer solutions

Abstract

A treatment of the formation of a basic core fibril (shish) of the type that is ge nerated by fl ow-indu ced crystallization of a polymer from solution is given that features the concept of cu mulative strain. Multiple nucleation acts by flow-elongated molecules produce an e mbryonic fibril that is a connec ted set of bundlelike nucle i. Surface s tress resulting from repu ls ion of the quasi-random coil c hains in the amorphous zone between the nucle i or c rystallit es builds up at the bundl e e nds as the nucle i mature, lead ing ultimately to a high e nd surface free e nergy, and to volume strain in th e crysta llit es compri sing the core fibril. The theory leads to a s table (or meta sta ble) fibril diameter as and mea n c haracteri sti c length i s with a fix ed ax ial ratio, a nd pred icts why the diameter does not grow further even in a med ium that is supersaturated with polymer. Th e pred ic ted dependence of a s, ls, and th e axia l ratio, on und ercoo ling is ill approximate agreement with expe riment. The latti ce expa nsion in the crystal resulting from volume s tra in is a lso in fair accord with ex perim e nt. The effect of a nn ea ling, including the commonl y e ncou ntered case whe re the volume strain relaxes to give normal la tti ce dimensions, but with a high end surface energy still remaining, is not ed. The effect of vo lume strain and the distribution of core fibril lengths about is on the melting be havior is calculated. The theory ca n reprod uce c rys tallinity versus te mperature data on polye thylene fibrils. Thi s procedure yields an indepe nde nt value of i8 • The ove rall treatment implies that the core fibril is a set of concatenated and substantially exte nded-c hain crystallites with bundlelike ends and a somewhat expanded lattice when una nnealed and under te nsion, the molec ular co nnections between the crystallites consisting of short amorphous ci liary bridges. It is s uggested that pro longed annealing at high temperatures ca n remove a substantial numbe r of the amorphous zones .Key words: Core fibril ; c umulative stress; fl ow-indu ced c rys talli zalion; nucl eation Iheory; polye thyle ne; polymer fiber ; shi sh; vo]um e strain.

X-ray investigations of the formation of core-fibrils crystallized out of the oriented melt

“…Davis et al [18] showed that the cross-sectional area occupied by each chain is inversely proportional to the fold period of the axial surface of the crystal. Hoffman demonstrated that then the cross-sectional area of the strained chain is inversely proportional to the thickness of the core-fibril [10]. This means that the thinner fibril should exhibit a larger lattice expansion.…”

“…This can lead to relatively uniform expansion effects in the crystals [10,16]. In particular, an expansion effect can be expected arising from the ciliary bridges.…”

“…The second model we will discuss is that of Hoffman [10]. Induced by the flow field, the polymer chains are statistically elongated, the longer chains being more ready extended, representing sites for the formation of nuclei.…”

“…While the morphology of the fibrils seems to be relatively well known [6][7][8], nucleation and crystal growth is still controversial. Several authors have developed crystallization models which predict a number of morphological features [9][10][11][12][13].…”

Phase field modelling of strain induced crystal growth in an elastic matrix

“…In a study of the formation of fibrils in polymer solutions, Hoffman 54 proposed a similar mechanism to explain the formation of stable crystallites when a shear stress is applied to the fluid. The origin of such a stress accumulation around the crystallite was in this case a consequence of the cumulative strain resulting in an expansion of the chains at the surface of the crystallites.…”