Isothermal spherulite growth rates were measured over a sufficient range of undercoolings, DeltaT, for a narrow linear polyethylene fraction M = 70 300 (70.3K), polydispersity 1.12, such that the fraction exhibited all three growth regimes as crystallized from the subcooled melt. The I-II transition occurred at DeltaT(I-II) = 15.8 degreesC and the II-III transition at DeltaT(II-III) = 23.8 degreesC. (Neither transition was fully abrupt.) The nucleation constants K-g and preexponential factors G(0) that described the absolute growth rates for each regime were determined, thus quantifying key parameters for all three regimes for a single specimen measured in the same apparatus. The K-g's for 70.3K conformed to the predicted relationship K-g(III) congruent to K-g(I) = 2K(g(II)). Theoretical relationships for the preexponential factors were employed using the observed Go's to investigate the nature of the transport of chain segments to the growth front. It was reconfirmed that this process was forced "near-ideal" reptation for an M congruent to 30K fraction. For M = 70.3K. it was found that the reptational transport mechanism in regimes II and III was perturbed and thereby slowed beyond that attributable to "near-ideal" forced reptation; the additional retardation was taken to be the result of labile chain attachments on a surface some distance from the site where the dangling chain was being drawn onto the substrate. In another test, the expression S-k/a(0). for the stem separation between primary surface nuclei in regime II was employed to calculate DeltaT(I-II) and DeltaT(II-III). This was successful for both M congruent to 30K (near-ideal reptation) and M = 70.3K (perturbed reptation). In this test, earlier estimates of quantities of importance to nucleation theory, such as C-0, n(III), and the substrate length L, were found to be either identical or only slightly modified. The treatment leads to satisfactory numerical estimates of the absolute substrate completion rate g and the nucleation rate i, and is consistent with the crystal morphology present in melt-crystallized PE, including the lenticular crystal --> truncated lozenge transformation associated with the I --> II regime transition. In general, this work provides significant additional support for the "three regime" concept in narrow PE fractions crystallized from the melt through a consideration of nucleation, regime, and reptation concepts.

The rate of growth of chain-folded lamellar crystals from the subcooled melt of polyethylene fractions is treated in terms of surface nucleation theory with the objective of illuminating the origin of the chain folding phenomenon and associated kinetic effects in molecular terms. An updated version of flux-based nucleation theory in readily usable form is outlined that deals with the nature of polymer chains in more detail than previous treatments. The subjects covered include: (i) the origin of regimes I, II, III, and III-A and the associated crystal growth rates, including the effect of forced steady-state reptation and reptation of ‘slack’ in the subcooled melt; (ii) the variation of the initial lamellar thickness with undercooling; (iii) the origin of the fold surface free energy σe and the lateral surface free energy σ; (iv) the generation and effect of nonadjacent events (such as tie chains) on the crystallinity and growth rates; and (v) ‘quantized’ chain folding at low molecular weight. The topological limitation on nonadjacent re-entry and the value of the apportionment factor ψ are discussed. Key experimental data are analysed in terms of the theory and essential parameters determined, including the size of the substrate length L involved in regime I growth. The degree of adjacent and/or ‘tight’ folding that obtains in the kinetically-induced lamellar structures is treated as being a function of molecular weight and undercooling. New evidence based on the quantization effect indicates a high degree of adjacent re-entry in regime I for the lower molecular weight fractions. The quality of the chain folding at higher molecular weights in the various regimes is discussed in terms of kinetic, neutron scattering, i.r., and other evidence. Application of the theory to other polymers is discussed briefly.

The expression σ = constant × C∞−1 is proposed for the lateral surface free energy that appears in polymer crystallization theory; C∞ is the characteristic ratio of the polymer molecules in the melt and the constant consists of known parameters. Given C∞, the theory predicts an accurate value of σ for polyethylene. It is shown that C∞ for polyethylene in the melt state can be obtained directly from the nucleation rate constant Kg and the fold surface free energy σe (C∞(theor.) = 6.53 for melt, C∞(expt) = 6.7 from chain dimensions in dilute θ solvents). The corresponding results for i-polystyrene are C∞(theor.) = 10.45 for the melt and C∞(expt) = 10.5 from chain dimensions. The treatment clarifies the meaning of the empirical α parameter and shows prospects for being applicable to other polymers.

The expression sigma = constant x C(infinity)-1 is proposed for the lateral surface free energy that appears in polymer crystallization theory; C(infinity) is the characteristic ratio of the polymer molecules in the melt and the constant consists of known parameters. Given C(infinity), theory predicts an accurate value of sigma for polyethylene. It is shown that C(infinity) for polyethylene in the melt state can be obtained directly from the nucleation rate constant K(g) and the fold surface free energy sigma(e) (C(infinity)(theor.) = 6.53 for melt, C(infinity)(expt) = 6.7 from chain dimensions in dilute theta-solvents). The corresponding results for i-polystyrene are C(infinity)(theor.) = 10.4(5) for the melt and C(infinity)(expt) = 10.5 from chain dimensions. The treatment clarifies the meaning of the empirical alpha-parameter and shows prospects for being applicable to other polymers.

A theory is presented for the lateral surface free energy parameter-sigma in the nucleation constant K(g) in the relation G is-proprotational-to exp[-K(g)/T(DELTA-T)f] that describes the growth rate of polymer crystals from the melt at low-to-moderate undercoolings DELTA-T. The theory forms a connection between nucleation theory and the statistics of polymer chain dimensions and provides a new approach to the determination of the characteristic ratio C(infinity). It is predicted that sigma-varies as const x C(infinity)-1, where the constant involves known quantities. The effect of chain structure resides principally in C(infinity. The theory was tested for polyethylene, isotactic polystyrene, and poly(L-lactic acid) by employing known values of sigma obtained from melt crystallization studies to calculate C(infinity) and then comparing these with the C(infinity) values cited in the literature as determined from chain dimensions in dilute THETA-solvents. The agreement is satisfactory, showing the theory for sigma to be valid in these cases, with the further implication that these polymers possessed a close approximation to unperturbed chain dimensions in the melt. Support was provided by data for isotactic polypropylene, poly(pivalolactone), and poly(epsilon-caprolactone), some of this deriving from a method of finding C(infinity) for the melt state without direct reference to sigma. The C(infinity)-dependent "segmental" character induced by the crystal surface in the section of chain comprising the activated complex is discussed. The theory for sigma provides strong support for polymer nucleation theory as there is now a predictive molecular picture for all the nucleation parameters in K(g). The treatment casts new light on the empirical formulas commonly employed to estimate sigma.

The nucleation-based theory of polymer crystal growth has been extended to apply to the growth rate and morphology of polyethylene (PE) single crystals with curved edges. The treatment is employed to analyse in detail the data of Organ and Keller on PE crystals formed from n-hexadecane and n-tetradecanol, which possess both {1 1 0} and {2 0 0} sectors; the subordinate {2 0 0} sectors exhibit the curved edge. The theory (1) introduces the concept of lattice strain in the {2 0 0} sectors through a parameter σs (which has an independent justification), (2) takes a {2 0 0} growth front to have the energetics associated with its being ‘serrated’ on a molecular level in addition to being strained, and (3) treats the dominant {1 1 0} growth front in terms of the energetics of the customary Lauritzen-Hoffman ‘flat-surface’ nucleation model. For the correct σs, the theory accurately predicts the aspect ratio and curvature as a function of crystallization temperature for each solvent. The treatment provides insights relating to (1) the different melting points, fold surface energies, angles of tilt and fold surface regularities of the {1 1 0} and {2 0 0} sectors, (2) the prediction of an upper limit Tmax above which such crystals will not form, (3) the occurrence of a regime I → H transition on the {1 1 0} growth front and its absence on the {2 0 0} front, and (4) the reason that both melt- and solution-crystallized PE exhibit a preference for b axis growth. The proposed treatment removes an objection to nucleation theory and, with appropriate modifications, is potentially useful in treating morphological problems in other systems.

Nucleation theory is applied to extended-chain crystallization as background to the extended-chain to once-folded transition problem and certain unusual effects found in recent experiments. In the ‘partial stem attachment’ model employed, the activated complex leading to stem addition involves most of the length of the molecule, but only in the form of occasional contacts with the substrate. Here the lateral surface free energy σ is of mostly entropic origin. With a normal σ, the model gives the main features of the striking maximum in the extended-chain growth rate found by Ungar and Keller for n-C246H494. Complete register of the chain ends is not attained during nucleation, resulting in a transient layer of cilia on the crystal (‘kinetic ciliation’). This layer leads to an end surface free energy σ′, which is deduced from the growth rate data and used to estimate the initial thickness la of the unstable ciliated surface layer for n-C246H494. Shrinkage of la through annealing is discussed, with special reference to its effect on increasing the melting point toward its equilibrium value. This leads to an interpretation of the remarkable T′ versusTx plot for extended-chain n-C192H386 given by Stack and co-workers. Nucleation theory is employed to predict the temperature T∗1 at which once-folding begins in n-C246H494. With a normal value of the fold surface free energy (acting in a ‘mean field’ to account for chain end effects) the theory predicts both T∗1 and a marked increase in the growth rate of the once-folded species relative to that of the extended-chain at T∗1. This explains the extended-chain to once-folded transition in n-C246H494, and also accounts for the previously unexplained minimum in the overall growth rate at T∗1 observed by Ungar and Keller. The treatment of the onset of once-folding is supported by data on other systems. The disordered nature of the initially-formed once-folded structure and its fate on annealing are discussed.

Solutions of crystallizable polymers subjected to orientation crystallize in a fibrillar morphology if the polymer is solidified rapidly. The central core of the polymer fibers consists of thin, extended chain crystallites interspersed with disordered regions. The extended chain crystals are small fibrils having diameters generally less than a few hundred angstroms, while the lengths are usually not more than 5000 Å. These dimensions are limited by an unknown mechanism, because even in a saturated solution, the fibril crystal size is limited. Hoffman's theory of flow-induced crystallization predicts that cumulative strain limits the growth of the central core fibril such that the diameter and length of the fibril are an inverse function of undercooling. This study was undertaken to obtain data to test the theory. The dependence of the fibril dimensions on undercooling at the time of orientation has been studied. Polyethylene fibrils were made by shearing a dilute solution between two slides under isothermal conditions at an elevated temperature, and the dimensions of the resulting fibrils were measured with transmission electron microscopy. The fibril diameter appeared to be a function of undercooling, while the fibril length was constant and not a function of undercooling.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTDetermination of the fold surface free energy and the equilibrium melting temperature for .alpha.-phase poly(pivalolactone) crystalsHerve Marand and John D. HoffmanCite this: Macromolecules 1990, 23, 15, 3682–3687Publication Date (Print):July 1, 1990Publication History Published online1 May 2002Published inissue 1 July 1990https://pubs.acs.org/doi/10.1021/ma00217a023https://doi.org/10.1021/ma00217a023research-articleACS PublicationsRequest reuse permissionsArticle Views453Altmetric-Citations37LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose Get e-Alerts

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTKinetics of crystallization and morphology of poly(pivalolactone): regime II .fwdarw. III transition and nucleation constantsDaniel B. Roitman, Herve Marand, Robert L. Miller, and John D. HoffmanCite this: J. Phys. Chem. 1989, 93, 19, 6919–6926Publication Date (Print):September 1, 1989Publication History Published online1 May 2002Published inissue 1 September 1989https://doi.org/10.1021/j100356a009RIGHTS & PERMISSIONSArticle Views228Altmetric-Citations55LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (2 MB) Get e-Alerts

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTSurface nucleation theory for chain-folded systems with lattice strain: curved edgesJohn D. Hoffman and Robert L. MillerCite this: Macromolecules 1989, 22, 7, 3038–3054Publication Date (Print):July 1, 1989Publication History Published online1 May 2002Published inissue 1 July 1989https://doi.org/10.1021/ma00197a027RIGHTS & PERMISSIONSArticle Views182Altmetric-Citations49LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (2 MB) Get e-Alerts Get e-Alerts

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTResponse to criticism of nucleation theory as applied to crystallization of lamellar polymersJohn D. Hoffman and Robert L. MillerCite this: Macromolecules 1989, 22, 8, 3502–3505Publication Date (Print):August 1, 1989Publication History Published online1 May 2002Published inissue 1 August 1989https://pubs.acs.org/doi/10.1021/ma00198a055https://doi.org/10.1021/ma00198a055research-articleACS PublicationsRequest reuse permissionsArticle Views272Altmetric-Citations40LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose Get e-Alerts

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTTest of the reptation concept: crystal growth rate as a function of molecular weight in polyethylene crystallized from the meltJohn D. Hoffman and Robert L. MillerCite this: Macromolecules 1988, 21, 10, 3038–3051Publication Date (Print):October 1, 1988Publication History Published online1 May 2002Published inissue 1 October 1988https://pubs.acs.org/doi/10.1021/ma00188a024https://doi.org/10.1021/ma00188a024research-articleACS PublicationsRequest reuse permissionsArticle Views698Altmetric-Citations172LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose Get e-Alerts

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTOnset of chain folding in low-molecular-weight poly(ethylene oxide) fractions crystallized from the meltJohn D. HoffmanCite this: Macromolecules 1986, 19, 4, 1124–1128Publication Date (Print):April 1, 1986Publication History Published online1 May 2002Published inissue 1 April 1986https://pubs.acs.org/doi/10.1021/ma00158a032https://doi.org/10.1021/ma00158a032research-articleACS PublicationsRequest reuse permissionsArticle Views201Altmetric-Citations35LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose Get e-Alerts

The ACR-NEMA Digital Imaging and Communications Standards Committee has published its Standard for an interface to medical imaging equipment. Various groups are now working on implementing this Standard, and the need for an exchange medium other than the electrical one of the Standard was forseen as necessary for software development. Working Group V was formed to examine this issue, and proposed to work first on a magnetic tape standard as magnetic tape drives are present on many imaging devices. The message format of the Standard was felt to be readily adaptable to magnetic tape. The physical specification has been chosen to conform to the ANSI standards for unrecorded and recorded magnetic tape, The logical specification is being developed with an attempt to adhere to the ANSI Standard for Magnetic Tape Labels and File Structure (1). This paper will discuss the reasons for developing a new format instead of using existing image interchange standards, explain the need for, and problems raised by tape directories, and explain the tape Standard as it currently exists.

The concept of a substrate length L is essential in the understanding of the regime I→II growth rate transitions in melt-crystallized lamellar polymers. The present work deals with the actual magnitude of L in polyethylene fractions as determined strictly from the kinetics of crystallization. With the help of an improved value of the activation energy of transport in the melt, and a more precise method of analysis than was employed heretofore, it is found from published growth rate measurements on polyethylene fractions that L is within about a factor of two of 0.77 μm at the regime I→II transition. The value of L is independent of the equilibrium melting temperature T0m(∞) assumed in the analysis. It is shown that L is much larger than a just stable surface nucleus. A brief summary is given of what is known about L from a kinetic point of view, and possible correlations with morphological features are mentioned. It is conjectured that L may relate to the mean distance between surface defects that have the capacity to terminate strip completion. In the course of the study, better values of the pre-exponential factors N0 and C0 that govern the absolute growth rates in regimes I and II, respectively, are obtained. A revised numerical value is given for the pre-exponential factor in the Lauritzen ‘Z’ test. This is based partly on the new value of C0, and partly on a reformulation of the problem.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTGrowth rate of extended-chain crystals: the lateral surface free energy of pure n-C94H190 and a fraction .apprx.C207H416John D. HoffmanCite this: Macromolecules 1985, 18, 4, 772–786Publication Date (Print):April 1, 1985Publication History Published online1 May 2002Published inissue 1 April 1985https://pubs.acs.org/doi/10.1021/ma00146a032https://doi.org/10.1021/ma00146a032research-articleACS PublicationsRequest reuse permissionsArticle Views123Altmetric-Citations29LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose Get e-Alerts