Th e growth rate C of th e cr ys tallin e bodi es a pp ea rin g in eac h of a se t of 35 c haracte rize d po ly. e th ylen e fracti ons ra ngin g from 3600 to 807 ,000 in molec ular we ight ha s been meas ured as a fun ction of th e unde rcoolin g tJ.T. In isoth e rmal c rys tallization, only ax ial ites we re found from M",= 3600 to 18 ,000.(For th ese run s, tJ.T < 17.5 °C.) From M".= 18 ,000 to M". "" 115,000 coa rse·grain ed non ·band e d s phe ru · lit es we re fo und for tJ.T > 17. 5 °C , and axialites for tJ.T < 17.5 °C : a rathe r s ha rp brea k occ urre d in th e log .o C ve r sus T data at tJ.T "" 17.5 0c. Th e morphologi ca l changes we re more gradual. Above Mil' "" 115,-000, only nea rly s tru ctureless " irregular" s ph erulit es we re found a t all und e rcoolin gs corres pondin g to isothermal growth. Typica l rin ged sphe rulites were o btain ed only on quenching. Wid e·a ng le x·ray data s howed that th e usu al orthorhombi c subce ll predominat ed in all th e morph ologies e ncount e re d. Lo w· angle x·ray data showed tha t th e s pec ime ns ex hibit e d lam e llar crystallization irres pectiv e of th e particular gross morphology involv ed. Th e growth rat e data on eac h fra c tion we re analyzed us in g /T (tJ.T )/]where / "" I to obtain va lu es of K" a nd Co. Th e va lue of Y in K,,= Ybuue/ (tJ.hj )k was obta ined fo r eac h morphology by a ppl ying th e "Z" test of La uritze n. Y = 4 for regim e I cr ys talli zation (s in gle s urface nucl eus leads to co mpl etio n of s ubs trat e) and Y =2 for regim e II cr ys talli za tio n (num e rous s urface nu c lei involve d in s ubstra te co mp letion). It wa s found that the axia lites obeyed regim e I kin e tics (Y=4), th e coarse·grain e d s phe rulit es regime II kin etics (Y = 2), and th e irregular s ph e r ulit es " mix e d " kineti cs (Y -3). Th e ass umpti on that th e sub strat e le ngth L in Laurit ze n's regim e theory was -5 I'-m led to the prediction of a rath e r s harp regim e 1 ..... regime II tran sition (corresponding to a break in the 10glO C versus T dat a) a t tJ.T "" 17 .5 °C, in accord with ex pe riment. Th e UUe value ca lc ulat ed fro m K" and Y for M". ;;. 20 ,000 was ap proxim ate ly co nst a nt with molec ular we ight and indep end e nt of morphology; th e limiting value of uU e from kineti c meas ure me nt s was about 1285 e rg'/c m 4 • corre· s ponding to Ue(x)=90.5 erg/e m ' and u= 14.2 erg/c m ' . (This valu e of Ut'{x) co mpare s favorably with u dcQ)= 93 ± 8 e rg/ cm ' from me ltin g point expe riment s.) T he in c rease of uUe and U e that too k place at low mol ec ul ar we ight s on up to -20 ,000 was treat e d usin g an expression given by Hoffman , viz , Ue=Udx) [(,.,+/3;) / (,.,+1)] where v=number of fo ld s per molecule, /3; = U"c;lIum)/Ud x) , I ntermittent hi gh and low values of U e were found ex p erim entally in thi s regio n , s howin g that j3 ; varied with in creas· in g mol ec ular we ight between 0.15 and -0.7. Theore tic al estimates of these upper and lowe r bound s for /3; are give n . Th e ...

Th e drop let tec hniqu e wa s used to o btain es tim a tes of th e isoth e rm a l ra te of hom oge neo us cr yst al nu c leation in hi ghl y s upe rc oo led m e lts of 8 c ha racte rize d fraction s of lin ear po lye th yle ne (we ight a ve rage molec ular weights from 3,100 to 249 ,000). Th e da ta obta in e d from th ese e xpe rim e nt s we re a na lyzed in acco rd with c urre nt th eori es of hom oge neou s nu cl eatio n of c ha in folded c r ys ta ls . Valu es fo r th e quantity a 2 a ", wh e re U a nd U e are th e la tc ra l a nd e nd· s urfa ce free e ne rgies of th e c rys ta l, were es tim a ted a s a fun c ti o n of mo lec ular we ig ht.Sa mpl e 3.2 K was fo und to be a noma lo us in its nu cle ation be havior. When we a ss um c tha t thi s sa m ple c rys tallizes in th e e xte nded c ha in form a nd ca lc ul a te cfl in s tead of a 2u e th e va lu e for a is found to be lO.57 ergs/c m 2 which is in reas o nab le a gree me nt with th e va lu c 9.6 e rgs/c m' fo und by oth e r inv es ti ga tors for lin ea r h ydroca rbon s . How ev e r, th e re re main s th e que sti o n as to wh e th e r s a mpl e 3.2 K e ve r und erwent homoge neo us nu c le ation.For samp les 9.70, 11.74 , a nd 23.0 K, a 2Ue was fo und t o in c rea se rapidl y du e to a decrea se in th e numbe r of cili a per c hain fold as th e mo lec ul ar we ight in c re ases. Fo r hi ghe r molec ul a r wei ghts th e va lu e for a 2 a e le ve ls off and th e ave ra ge va lu e of a 2a e for sa mpl es 23.0 to 249 K wa s fou nd to be 19,000 e rgs"/c m"-Th e expe rim e nta l valu e of th e ab s olute nu c lea ti o n fre qu e nc y 10 , was fo und to diffe r fro m th e th eore ti ca l value by approximate ly :I X 10". If one ass um es th at th e s urfa ce free e ne rgi es a re t emperature d e pe nd e nt [i.e., a = a, (l + x 6.1' ) a nd Ue = a e , (1 + )'6.1' ) wh e re x = -0.0073 and Y= 0.0141 th e av e rage valu e of a 2 a e c ha nges o nl y sli ghtl y (to 19,800 e rgs"/c m") du e to th e compe ns atin g e ffects in th e signs of th e te mperature co rrectio ns and 10 is c lose to the th eoreti cal va lu e , 1 X 1034 nu c lei/c m3/s . Ke y word s : C hai n fold s ; fra c tion s; homo ge neo us nu c le a ti o n; mo lec ul a r weight ; nu c leat io n theo ry ; polyethy len e ; s urface free ene rgi es.

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The droplet technique was utilized to obtain estimates of the isothermal rate of homogeneous crystal nucleation in highly supercooled melts of unfractionated linear polyethylene. In a typical experiment a cell containing a suspension of several hundred micron‐size spherical droplets of the polymer was placed on a microscope hot stage and quenched from a temperature well above the melting point of polyethylene to the desired crystallization temperature. When viewed between crossed polarizers, the droplets were initially invisible but, upon freezing, they appeared as visible birefringent spheres. The time dependence of the process was followed by time‐lapse photography. Half times (T1/2) for the freezing of those droplets remaining unfrozen by the time the crystallization temperature was attained were thus obtained at a series of undercoolings and related to the desired nucleation rate constant I (nuclei cm.−1 sec.−1) by the equation I = In 2/T1/2/v, where v is the droplet volume. The temperature dependence of I, as obtained by the above procedure, was analyzed in accord with current theories of homogeneous nucleation of chain‐folded polymer crystals. From this analysis, an estimate, 14,960 ergs3 cm.−6 was made of the quantity (%sG2%sGe), where %sG and %sGe are, respectively, the lateral and end‐surface free energies of the crystal.

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