No abstract

A new method of estim ati ng t he eq uiIibrium melting tem perature, T m, of a poIy mer is descr,lbed, and appli ed to polychIorotnfiuoroethylene (P CTFE) , Experim entall y determll1~d values of the sO,-called obser ved melting point, T ~ C obs), a re plotted as a function of t he Isother,mal crystalIl zatlOn temperat ure, 'l'x. , . \'\Then frced of scconda ry effects, s uch as recrystaIIIzatlOll, the data ~t a s t ra lgh t lille of posit ive s lope on a T~(obs) versus T x plot, '1', be~n g t~e abscIssa. This 1m? I~ t hen extrap o~~ted ~o ,its intersection wi th t he line '1'~ (obs) = T x , ~he te mperat ure at t hi s In te rsectIOn IS 7 m' 1hls Intersection is at 224°C for PCTF E a nd T m IS quoted as 224 ± 1°C, (The hi ghest melti ng po i nt act ua lI y attain ed for a speci m e l~ was 218,2 00.,) The v,alue of '1'", estim ated usin g t he extrapolation procedure is co mpa rcd WIth t hat estll;, ated USll1 g th e customary method of slow st epwise warming, A theorctlcal Just lfi catlOll IS gIven [or making t he type o f plot mentioncd abo\'e, The most Imp or~an t ass ump t Ion used in the theo ry is t hat on(' of the dim e nsions of the growin g crystal retains a val,ue r ather close to t hat of t ho app ropri ate growth llu cleus during a n isot hermal ~r y s ta lll zatlOn, the other two dimenSion s bCll1g Ia rge in comparison, Combin ation of th IS WIth the fact t hat t hc r cleva nt dimension of th e growth nu cle us will var v as the reciprocal of t he d egree, of s upcrcooIing lead s to the prediction of melting points t llat inc rease 1ll1early With crystallizatIOn te mperat ure, The ass ump tion t hat ono of the dimension s of the crystal retains a valu e fairly cIose t

No 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.

The kinetic theory of the rate of growth G and the initial lamellar thickness lg* of chain-folded crystals is extended so that it is applicable at high undercoolings. Attention is centered on the details of how the first step element and the first fold are put down on the substrate. A parameter φ that varies between zero and unity, which apportions the free energy of attachment of the step element between the forward and backward reactions, is used to denote variations in this process. Expressions for G are derived from flux equations for two limiting cases: regime I, single surface nucleation act with rapid substrate completion and regime II, numerous surface nucleation acts with very slow substrate completion. Data from the literature on G for isotactic polystyrene (regime II) and polyethylene single crystals (regime I) are analyzed to obtain surface free energies, and these are used with the revised theory for lg* to predict the lamellar thickness of these polymers. Good agreement between lg* and published data is found for 1 > φ > 0. Values of φ below unity imply that the molecules are physically adsorbed onto the substrate prior to actual crystallographic attachment. A discussion is given of the segmental transport effects that dominate the behavior of G at high undercoolings in bulk polymers.