Crystallization Process Of Polymers Research Articles

What can polymer crystal structure tell about polymer crystallization processes?

Contrary to most or all other materials, crystallization of chiral but racemic polymers such as isotactic polypropylene is accompanied by a conformational rearrangement which leads to helical geometries: the building units of the crystal are helical stems, \(\)-20nm long, which can be either right-handed or left-handed. Helical hand cannot be reversed within the crystal structure: it is therefore a permanent marker and an indicator of molecular processes (in particular segregation/selection of helical hands) which take place during crystal growth, and more precisely during the crucial step of “efficient” helical stem deposition. The issue of proper helical hand selection during polymer crystal growth is mainly illustrated with isotactic polypropylene. Its various crystalline polymorphs (\(\), \(\), \(\) and smectic) display virtually all possible combinations of helical hands, azimuthal settings and even non-parallel orientation of helix axes in space. Furthermore, a specific homoepitaxy which generates a lamellar branching in the \(\) phase “quadrites” and \(\) composite structures makes it possible a) to determine the helical hand and associated azimuthal setting of every stem in the crystalline entities and b) to determine the impact on the crystal structure and morphology of “mistakes” in helical hand of the depositing stem. Analysis of these morphologies demonstrates that the crystallization of isotactic polypropylene (and by implication of other achiral, helical polymers) is a highly sequential and “substrate-determined” process, i.e. that the depositing stem probes the topography of the growth face prior to attachment. These observations appear difficult to reconcile with crystallization schemes in which molecules (helical segments) are prearranged in a kind of pseudo-crystalline bundle (and as such, are not subjected to the high constraints of crystal symmetry) before deposition as a preassembled entity on the substrate.

Simultaneous measurements of small angle x-ray scattering, wide angle x-ray scattering, and dielectric spectroscopy during crystallization of polymers

A novel experimental setup is described which allows one to obtain detailed information on structural and dynamical changes in polymers during crystallization. This technique includes simultaneous measurements of small angle-wide angle x-ray scattering and dielectric spectroscopy (SWD). The capabilities of the technique have been probed by following in real time the crystallization process of a model crystallizable polymer: poly(ethylene terephthalate). By performing these experiments, simultaneous information from both, the amorphous and the crystalline phase is obtained providing a complete description of changes occurring during a crystallization process. The SWD technique opens up new promising perspectives for the experimental study of the relation between structure and dynamics in materials science.

A Direct Observation of the Formation of Nuclei and the Development of Lamellae in Polymer Spherulites

Since polymer spherulites were observed using optical microscopy and single polymer crystals were prepared from solution,1,2 the internal structure of polymer spherulites has been investigated widely with electron microscopy.3-9 For most crystalline polymers, it is generally accepted that spherulites are developed from a single crystal through unidirectional growth, and the spherical shape is attained through continuous splaying apart and occasional branching of lamellae,5 though there are ongoing debates concerning the details of the branching in the literature. More recently, atomic force microscopy (AFM) has been utilized to study the organization of spherulites and the crystallization process of polymers.10,11 A copolymer, poly(bisphenol A-co-octane),12 was synthesized with the following structure:

Inverse problems related to crystallization of polymers

This paper is devoted to identification problems in polymer crystallization processes. As a first step the identification of nucleation and growth rates from boundary measurements will be discussed in the case of one-dimensional crystallization. This leads to an identification problem in a coupled system of a hyperbolic and a parabolic equation. An algorithm for the solution of this inverse problem will be developed using Landweber iteration as a regularization method. The behaviour of the algorithm will be studied both numerically and mathematically on the basis of the recently developed convergence theory for iterative regularization methods for nonlinear inverse problems.

Dynamics of α-Relaxation and Structure Formation during Crystallization Process of Polymers: Dielectric Relaxation and Small-Angle X-Ray Scattering on PET

Dynamics of α-Relaxation and Structure Formation during Crystallization Process of Polymers: Dielectric Relaxation and Small-Angle X-Ray Scattering on PET

Empirical Estimation of Distribution Quantiles of Random Closed Sets

Previous article Next article Empirical Estimation of Distribution Quantiles of Random Closed SetsI. S. MolchanovI. S. Molchanovhttps://doi.org/10.1137/1135085PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] G. Matheron, Random sets and integral geometry, John Wiley & Sons, New York-London-Sydney, 1975xxiii+261 52:6828 0321.60009 Google Scholar[2] A. A. Borovkov, Statistique mathématique, Mir, Trad. Francais, Moscow, 1987 Google Scholar[3] William F. Eddy, R. Ambartzumian and , W. Weil, Set-valued orderings for bivariate dataStochastic geometry, geometric statistics, stereology (Oberwolfach, 1983), Teubner-Texte Math., Vol. 65, Teubner, Leipzig, Germany, 1984, 79–90 794 870 0557.62050 Google Scholar[4] I. S. Molchanov, Uniform laws of large numbers for empirical associated functionals on random closed sets, Theory Probab. Appl., 32 (1987), 556–560 10.1137/1132086 0644.60028 LinkGoogle Scholar[5] I. S. Molchanov, Nonparametric estimation of functionals of random sets and its applications, The 1st World Congress of the Bernoulli Society, Abstracts, Vol. 2, Nauka, Moscow, 1986 Google Scholar[6] N. Bourbaki, Elements de mathématique, Livre III, Topologie generale, Hermann, Paris, 1958 Google Scholar[7] Ronald Pyke, A uniform central limit theorem for partial-sum processes indexed by setsProbability, statistics and analysis, London Math. Soc. Lecture Note Ser., Vol. 79, Cambridge Univ. Press, Cambridge, 1983, 219–240 84g:60043 0497.60030 CrossrefGoogle Scholar[8] I. S. Molchanov, Masters Thesis, Construction and estimation of distributions for some classes of random sets, Thesis Cand. Degree, Kiev, USSR, 1986, (In Russian.) Google Scholar[9] Patrick Billingsley, Convergence of probability measures, John Wiley & Sons Inc., New York, 1968xii+253 38:1718 0172.21201 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Solution manifold and its statistical applicationsElectronic Journal of Statistics, Vol. 16, No. 1 Cross Ref Quantile regression with interval data5 August 2021 | Econometric Reviews, Vol. 40, No. 6 Cross Ref Drone Ground Impact Footprints with Importance Sampling: Estimation and Sensitivity Analysis25 April 2021 | Applied Sciences, Vol. 11, No. 9 Cross Ref Density Level Sets: Asymptotics, Inference, and Visualization7 August 2017 | Journal of the American Statistical Association, Vol. 112, No. 520 Cross Ref Topological consistency via kernel estimationBernoulli, Vol. 23, No. 1 Cross Ref Random Closed Sets and Capacity Functionals10 November 2017 Cross Ref Expectations of Random Sets10 November 2017 Cross Ref Minkowski Sums10 November 2017 Cross Ref Unions of Random Sets10 November 2017 Cross Ref Random Sets and Random Functions10 November 2017 Cross Ref Level sets estimation and Vorob’ev expectation of random compact setsSpatial Statistics, Vol. 2 Cross Ref Plug-in estimation of d -dimensional density minimum volume set of a rare event in a complex system21 November 2011 | Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, Vol. 226, No. 3 Cross Ref Generalization of Portmanteau Theorem with Respect to the Pseudoweak Convergence of Random Closed SetsT. Grbić and E. Pap17 February 2012 | Theory of Probability & Its Applications, Vol. 54, No. 1AbstractPDF (223 KB)Kernel estimation of density level setsJournal of Multivariate Analysis, Vol. 97, No. 4 Cross Ref The stochastic geometry of polymer crystallization processes 1Stochastic Analysis and Applications, Vol. 15, No. 3 Cross Ref A Consistent Estimate of Parameters of Boolean Models of Random Closed SetsI. S. Molchanov17 July 2006 | Theory of Probability & Its Applications, Vol. 36, No. 3AbstractPDF (836 KB)Random Closed Sets Cross Ref Volume 35, Issue 3| 1991Theory of Probability & Its Applications History Submitted:26 May 1988Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1135085Article page range:pp. 594-600ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Study of crystallization process of polymer from melt by a real-time pulsed NMR measurement

Crystallization process of polymer [poly(ε-caprolactone)] has been studied by a real-time pulsed NMR measurement. The temporal change of both the spin–spin relaxation time T2 and the spin-lattice relaxation time in the rotating frame T1ρ were obtained. The growth behavior of crystalline lamellae and interface has been detected successfully by T2 measurement. It becomes clear that the real-time pulsed NMR measurement is a very powerful tool for studying crystallization dynamics. The crystallization dynamics of polymers has been discussed based on the results.

Real-time measurement of crystallization process of polymers by pulsed nuclear magnetic resonance

Real-time measurement of the crystallization process of polymers [poly(ε-caprolactone) and its blend with poly(vinyl methyl ether) and polystyrene] by pulsed nuclear magnetic resonance has been made. The measurements on both the spin-spin relaxation time T2 and the spin-lattice relaxation time in the rotating frame T*1 ρ have been performed for the first time. From the data, we can obtain information on the temporal change of the crystallinity as well as the change of the mobility in each phase. Furthermore, the temporal change of the intermediate phase corresponding to the interface between crystalline and amorphous part has been successfully detected.

General treatment of polymer crystallization kinetics—Part 1. A new macrokinetic equation and its experimental verification

AbstractA new macrokinetic equation of the autocatalytic type is proposed to describe the polymer crystallization process. The derived equation is compared with the known Avrami equation. It is shown to be consistent with the results of isothermal experiments.

Polymer crystallization: Proper accounting of a wider class of paths to crystallization—variations on a theme of Point

Point has suggested that during the polymer crystallization process, individual stems form by zippering of monomer segments onto the substrate and that at any time during the zippering process the stem can fold over, thus initiating a new stem. We augment the treatment of Point analytically by allowing each of the subsequent stems to fold any stage in the zippering process rather than only during the forming of the first stem. The problem is isomorphic to the mathematical problem of the growth of a Cayley Tree with infinite branching! Although there is net growth, the rules of growth (crystallization) are such that branches of the tree can be resorbed. By use of a simple renormalization technique, formulae are obtained both for the steady state growth rate and for the lamellar thickness, which for special cases reduce to the Point results. Classical nucleation theory remains valid at low to moderate supercoolings.

Lamellar structure and plasticity micromechanisms in bulk crystalline polymers. Communication 1

It is shown by electron microscopy that the lamellar structure typical of bulk crystalline polymers is identical in its structural-morphological characteristics with the typical products of martensite transformations in metal systems. It is also established that the polymer crystallization process has the typical characteristics of transformations governed by the shear (martensite) mechanism. These conclusions are used as a basis for an examination of the principal factors controlling the formation of the real structure of bulk polymers. The thermodynamic conditions under which bulk polymers crystallize require that the lamellar-spherulitic structure be formed in accordance with a self-consistent shear mechanism. In accordance with the new model, the spherulites represent an organization of the martensite lamellae in which the structural stress fields are mutually compensated. The proposed model underlines the fact that polycrystalline polymers and metal systems in the martensitic state are structurally similar materials.

Fibrillar Growth of Amylose Acetate and Other Polymers

AbstractFibrillar crystals of amylose acetate have been grown in different conditions of growth using film formation method of crystal growth. For generalization of fibrillar growth conditions, crystals of cellulose triacetate, polyoxymethylene and polyacrylonitrile have been grown and compared with the fibrillar crystal growth habit of amylose acetate. The type of fibrillar aggregation is dependent on type of solvent, concentration of polymer and crystallization temperature. Various growth stages of features are shown in order to understand their growth mechanismus. It is proposed that the fibrils are the fundamental units of most polymer crystallization processes and fibrous crystal growth is as common as the frequently observed lamellar growth of polymer crystals. The most common features of the fibres are the twisting and branching habit which can be compared with the morphology of fibres of natural polymers.

Orientation Effects in Filled Plastics Bearing Materials

The development of antifriction materials based on lamellar solid lubricants dispersed as fillers in thermoplastic compounds is briefly reviewed. Experimental evidence is offered to account for the wide variations in friction and wear properties reported, in terms of flow orientation and cross-flow migration of the filler particles. These findings confirm the importance of finish machining operations on the rubbing surfaces. Preliminary evidence is also offered for the disruption of particle orientation by polymer crystallization processes where the particles are small. Experimental methods used are: image analyzing microscopy, X-ray diffraction, and a specially developed friction testing machine for molded plastics samples. Presented at ASLE International Conference on Solid Lubrication, held in Denver, Colorado, August 24–27, 1971

Effect of external pressure on the physicochemical and mechanical properties of polymers

The behavior of crystalline polymers obtained by molding at high pressures has been investigated. External pressure can promote or retard polymer crystallization processes, depending on its intensity. Comparison of various physicochemical and mechanical properties of specimens obtained at different external pressures shows that the corresponding curves have two maxima: one at 200–800 kgf/cm2 and another on the narrower interval between 1300 and 1500 kgf/cm2. The position of the first maximum is associated with the molecular weight distribution and the flexibility of the polymer chain, and position of the second is determined by the chemical nature of the polymer. The data obtained help to make possible a rational choice of polymer processing methods in which pressure is involved.

Pressure‐induced crystallization in polyethylene

AbstractThe kinetics of crystallization of a high density polyethylene melt under hydrostatic pressure have been studied dilatometrically. The isotherms for the crystallization thus found are not superimposable by a shift along the logarithmic time axis. A mathematical model for the crystallization process of polymers has been developed by modifying the existing theory of kinetics of phase transition in nonpolymeric materials. The comparison of the experimental results with the above model shows that the two are in very good agreement.