Crystallization in melts of semi-flexible hard polymer chains: An interplay of entropies and dimensions

T. Shakirov, W. Paul

Institut für Physik, Martin Luther Universität Halle-Wittenberg, 06099 Halle 

Stochastic Approximation Monte Carlo simulations [1] are employed to obtain the complete thermodynamic equilibrium information for a melt of short, semi-flexible polymer chains with purely repulsive intermolecular interactions. Thermodynamics is obtained based on the density of states of our simple coarse-grained model, which varies by up to 5000 orders of magnitude. We show that our polymer melt undergoes a first-order crystallization transition upon increasing the chain stiffness at fixed density [2]. The lyotropic three-dimensional orientational ordering transition drives the crystallization and is accompanied by a two-dimensional hexagonal ordering transition in the plane perpendicular to the chains. While the three-dimensional ordering can be understood in terms of Onsager theory, the two-dimensional transition is similar to the liquid-hexatic transition of hard disks. Due to the domination of lateral two-dimensional translational entropy over the one-dimensional translational entropy connected with columnar displacements, the chains form a lamellar phase. The tilt of the chain axis with respect to the lamella surface makes this a rotator II phase.

[1] B. Werlich, T. Shakirov, M. P. Taylor, W. Paul, Comput. Phys. Commun. 186, 65, (2015) (link)
[2] T. Shakirov, W. Paul, preprint

Crystallization of Supramolecular Polymers Linked by Multiple Hydrogen Bonds

Pengju Pan, Jianna Bao, Xiaohua Chang, Ruoxing Chang, Guorong Shan, Yongzhong Bao

State Key Laboratory of Chemical Engineering, College of Chemical and Biological Engineering, Zhejiang University, 38 Zheda Road, Hangzhou 310027, P. R. China.

Supramolecular polymers (SMPs) have different crystallization behavior from conventional polymers. Crystallization of SMPs occurs in a “confined” and “dynamic” manner. Because of the reversible and stimuli-responsive natures of non-covalent bonds in SMPs, crystalline structure and crystallization kinetics of SMPs depend strongly on crystallization conditions (e.g., crystallization temperature, Tc). This offers a feasible way to tune the physical properties and functions of SMPs in processing. We first selected the 2-ureido-4[1H]-pyrimidione (UPy)-bonded poly(L-lactic acid) (PLLA) as a model SMP and investigated the crystallization kinetics, polymorphic crystalline structure, and phase transition of supramolecular PLLAs (SM-PLLAs). Crystallization rate and crystallinity of SM-PLLAs were strongly depressed as compared to the non-functionalized PLLA precursors. Crystalline structure of SM-PLLAs was sensitive to Tc. A low Tc (80~100 °C) facilitated the formation of metastable β crystals of PLLA in SM-PLLAs. The β crystals formed in SM-PLLAs transformed into the more stable α crystals in the following heating process. We further studied the stereocomplex crystallization between UPy-functionalized PLLA and poly(D-lactic acid) (PDLA). It was found that the stereocomplexation ability of PLLA and PDLA was highly improved after UPy end functionalization; this was ascribed to the enhanced interchain interaction.

[1] Chang, R. X., Pan, P. J., et al. Macromolecules 2015, 48, 7872. (link)
[2] Bao, J. N., Pan, P. J., et al. Polym. Chem. 2016, 7, 4891. (link)
[3] Bao, J. N.; Pan, P. J., et al. Cryst. Growth Des. 2016, 16, 1502. (link)

Structure and Morphology Orientation of Comb-like Polymers with Rigid Backbones

V. Danke1,2, G. Gupta1,2, and M. Beiner1,2

1Fraunhofer-Institut für Mikrostruktur von Werkstoffen und Systemen IMWS, Walter-Hülse-Straße 1, 06120, Halle, Germany
2Institut für Chemie, Martin Luther Universität Halle-Wittenberg, 06120, Halle, Germany

Comb-like polymers with rigid backbones and flexible side chains are an important class of functional materials with applications in various fields like organic semiconductors and light weight components in high performance composite materials. A common feature of such polymers is the formation of layered structures with typical spacing in the 1-3 nm range wherein the side chains (long methylene sequences) aggregate to form alkyl nanodomains [1]. Crystallographic analysis in poly (1,4-phenylene-2,5-n-didecyloxy terephthalate) (PPDOT) and poly (2,5-didecyloxy-1,4-phenylene vinylene) (DOPPV) each having 10 alkyl carbons per side chain shows that PPDOT exhibits an orthorhombic unit cell, whereas the DOPPV is characterized by a monoclinic unit cell. The interplay between backbone and side chain packing within the alkyl nanodomain leading to different crystallographic states is discussed. Investigations on molecular orientation in extruded fibers of poly (1,4-phenylene-2,5-n-dialkyloxy terephthalate)s (PPAOT) and poly (2,5-dialkyloxy-1,4-phenylene vinylene)s (AOPPV) show that the backbones in case of PPAOT align along the shear direction whereas in AOPPV they align preferentially perpendicular to the shear direction [2]. Potential reasons for the differences in the preferred orientations for PPAOT and AOPPV are considered.

[1] About different packing states of alkyl groups in comb-like polymers with rigid backbones. T. Babur, G. Gupta and M. Beiner, Soft Matter, 2016, 12, 8093-8097 (link)
[2] Interrelations Between Side Chain and Main Chain Packing in Different Crystal Modifications of Alkoxylated Polyesters. G. Gupta, V. Danke, T. Babur, and M. Beiner. J. Phys. Chem. B, 2017, 121, 4583-45. (link)

Transition from Ring- to Chain-Dominated Phases in Supramolecular Polymer Networks

E. Lee, T. Shakirov, and W. Paul

Institut für Physik, Martin-Luther Universität Halle-Wittenberg, 06099 Halle (Saale), Germany

Rheological properties of supramolecular polymers depend on their structures including the size, the number, and the topology of aggregates. A linear polymer with hydrogen bonding units at both ends is one of widely used precursors to build the supramolecular polymer networks. Due to complex interplay between chain stiffness, hydrogen bonding interaction, and polymer conformational entropy it is difficult to theoretically predict the structure of the supramolecular polymer. In this work, we investigate structures of supramolecular polyethylene glycol and polybutylene glycols whose ends are capable of the hydrogen bond using a coarse-grained (CG) model via stochastic approximation Monte Carlo simulation (SAMC) method. Our CG force field is constructed by Boltzmann inversion of the probability distributions of all-atom polymer conformations. SAMC provides all the thermodynamic information of the system, which allows one to investigate supramolecular structures in a wide temperature range. This work especially focuses on the transition from ring- to chain-dominated phases since the contaminant of rings in a melt is known to significantly influence its rheology. In a limit of dilute concentration, the transition temperature (T*) shows non-monotonous behavior as molecular weight of the precursor increases due to competition between chain stiffness and hydrogen bonding. We also investigate the polymer concentration (c) dependence on T* to construct a c-T phase diagram.

The Isothermal Crystallization of Polyamide 11 Investigated from Low to High Supercooling by Simultaneous Fast Scanning (Chip) Calorimetry (FSC) and Synchrotron SAXS/WAXD

D. Baeten1, V.B.F. Mathot1, M.F.J. Pijpers1, O. Verkinderen1, P. Van Puyvelde2, B. Goderis1

1Polymer Chemistry and Materials, KU Leuven, Heverlee, Belgium
2Soft Matter, Rheology and Technology, KU Leuven, Heverlee, Belgium

An in-situ FSC-SAXS/WAXD approach was used to study the isothermal crystallization of polyamide 11 (PA11) at different degrees of supercooling in order to elucidate its bimodal crystallization rate behavior with temperature [1]. Time resolved WAXD analyses over the complete range of supercoolings revealed that mesomorphic material was produced in less than a second at high supercooling, whereas at very low supercooling crystals were obtained [2]. The crystalline to mesomorphic ratio was found to increase gradually with increasing crystallization temperature. Analysis of the SAXS data supported the existence of a crystallization temperature dependent semicrystalline morphology composed of alternating solid and liquid-like layers with the solid layers made from crystalline, mesomorphic and rigid amorphous patches. Moreover, the crystalline or mesomorphic patches alternate with rigid amorphous patches in neighboring solid layers. The relation between details of this peculiar morphology and the crystallization rate as a function of the crystallization temperature will be discussed.

[1] A. Mollova, R. Androsch, D. Mileva, C. Schick, A. Benhamida, Macromolecules 46, 828–835 (2013) (link)
[2] D. Baeten, V.B.F. Mathot, M.F.J. Pijpers, O. Verkinderen, G. Portale, P. Van Puyvelde, B. Goderis, Macromol. Rapid Commun. 36, 1184–1191 (2015) (link)

Morphology–Density Relations in Polyamide 12

O. Verkinderen1, P. Adriaensens2, P. Van Puyvelde3 and B. Goderis1

1Polymer Chemistry and Materials, KU Leuven, Heverlee, Belgium
2Applied and Analytical Chemistry, UHasselt, Diepenbeek, Belgium
3Soft Matter, Rheology and Technology, KU Leuven, Heverlee, Belgium

A two-phase model consisting of alternating amorphous and crystalline layers is often used to describe the morphology of semi-crystalline polymers. However, this simple model – at least in the case of polyamide 12 (PA12) – does not allow rationalizing the outcome of different techniques which are sensitive to particular features of the semicrystalline morphology. Therefore, several authors argued for the existence of a third phase [1], [2]. This third phase is the rigid amorphous fraction (RAF) and is in fact a phase with a higher density and lower mobility than the amorphous fraction but without the order of the crystalline. Although the existence of this RAF seems beyond dispute, there clearly is no consensus on its topology. Based on a combination of temperature dependent WAXD, SAXS, solid state NMR, and density measurements a new morphological model is proposed for PA12, which consists of alternating solid and mobile (liquid) amorphous layers. The solid layers are in turn composed of crystalline and rigid amorphous patches with the density of the latter being intermediate between that of mobile amorphous and crystalline matter. This morphology, which includes a clear picture of the RAF topology, leads to a similarity in the WAXD and SAXS based crystallinity as well as to matching SAXS based dense and NMR based rigid fractions. The model adequately describes the SAXS patterns and produces overall densities that are identical to experimentally observed ones.

[1] B. Goderis, P. G. Klein, S. P. Hill, and C. E. Koning, Prog. colloid Polym. Sci., 130, 40 (2005). (link)
[2] C. Hedesiu, D. E. Demco, R. Kleppinger, G. Vanden Poel, W. Gijsbers, B. Blümich, K. Remerie, and V. M. Litvinov, Macromolecules, 40, no. 11, 3977 (2007). (link)

Synthesis, aggregation and crystallization of precision polymers with repetitive folding elements

M. B. Canalp, J. Freudenberg, S. Reimann and W. H. Binder

Martin Luther University Halle-Wittenberg, Faculty of Natural Sciences II, Chair of Macromolecular Chemistry, Von-Danckelmann-Platz 4, D-06120 Halle

The investigation of ordering phenomena in biological and synthetic macromolecules still presents an interesting and promising field of research. Biological macromolecules form stable secondary or higher structures via inter- and intramolecular ordering processes, which are based on the interaction of their precisely placed amino-acids and the rotational constraints resulting from the peptide bonds. [1] Especially the understanding of the secondary structure formation from polypeptides is essential as it depends strongly on their (bio)chemical environment.
We investigate the aggregation and crystallization behavior of different precision polymers, which are characterized by repeating sequences of synthetic polyolefins and different biomimetic structure-elements. Constraints like 2,6-diaminopyridine and urea induce a conformational restriction while poly(amino acids) like poly-L-glutamic acid, poly-L-aspartic acid, poly-L-lysine and poly-L-leucine display a large conformational variability and dynamic α-helical-to-coil-transition. [2] All included moieties additionally interact with each other via supramolecular interactions influencing the crystallization behavior of the polyethylene chain. Therefore, acyclic diene metathesis (ADMET) polymerization was used to achieve a periodic incorporation of the constraint into the polymer backbone, resulting in precision polymers, which were analyzed via DSC and WAXS measurements. [3]

[1] C. B. H. Anfinsen, E., J. Biol. Chem. 1961, 236, 1361. (link)
[2] P. Novotná, M. Urbanová Vib. Spectrosc. 2013, 66, 1. (link)
[3] S. Reimann, U. Baumeister, W. H. Binder, Macromol. Chem. Phys. 2014, 215, 1963. (link)

Small polyethylene systems: On the ground state of single chains and few chain aggregates

T. Shakirov, W. Paul

Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle (Saale), Germany

The phase behavior of polyethylene has been under investigation for the last six decades. Investigation of single-chain crystallization in solution is a technically difficult problem, because in molecular dynamics simulations as well as in experiments, it is not so easy to distinguish kinetic and thermodynamic effects on chain folding. The general picture, however, is, that single polyethylene chains in solution fold into lamellar crystals. We present results of a Stochastic Approximation Monte Carlo (SAMC) simulation, which gives a possibility to analyze thermodynamical equilibrium properties of a system. Our simulation study of relatively short polyethylene chains is based on a chemically realistic united atom model [1]. Simulational results for low-energy states of single chains of different lengths demonstrate a set of various ground-state configurations: from stretched and hairpin-like configurations of short chains to a helix-like structure reeled round one of the chain’s ends. Aggregates of a few short polyethylene chains exhibit another set of ground states, depending on chain length and number of aggregated chains. However, with increasing chain length, single chain and aggregate morphologies become more similar.

[1] W. Paul, D.Y. Yoon, and G.D. Smith, J. Chem. Phys. 103, (1995) 1702 – 1709. (link)

SAXS Study on Density Fluctuations in Crystallization Process of Poly(trimethylene terephthtalate)

T. Konishi1, D. Tadokoro1, Y. Kawahara1, K. Fukao2 and Y. Miyamoto2

1Graduate School of Human and Environmental Studies, Kyoto University, Kyoto 606-8501, Japan
2Department of Physics, Ritsumeikan University, Noji-Higashi 1-1-1, Kusatsu 525-8577, Japan

Polymer crystallization mechanism especially at large supercooling has not been fully understood yet. Kaji et al. found that the density fluctuations occur in the early stage of crystallization in poly(ethylene terephthalate). [1] Research on such a fluctuations have been done from both theoretical [2] and experimental [3] aspects. But an interpretation for the fluctuations has not been fully obtained. Recently the strong density fluctuations are reported in the early stage of glass-crystallization process for poly(trimethylene terephthalate) (PTT)[4]. In order to clarify the density fluctuations in PTT, we have studied the crystallization processes of PTT from the glass and the melt by small-angle X-ray scattering (SAXS) and wide-angle X-ray diffraction (WAXD).
The density fluctuations of several hundred Å have been obtained in the SAXS results in the early stage of crystallization process both from the glass and the melt. The fluctuations appear simultaneously with the generation of the nodular crystals of several tens Å. From the results we conclude that the fluctuations is due to the nodular crystals heterogeneously aggregated in space.

[1] K. Kaji et al., Adv. Polym. Sci. 191, 187 (2005). (link)
[2] A. J. Ryan et al., Faraday Discuss. 112, 13 (1999). (link)
[3] P. D. Olmsted et al., Phys. Rev. Lett. 81, 373–376 (1998). (link)
[4] W.T. Chuang et al., Macromolecules 44, 1140 (2011). (link)

NMR investigations of dynamics in the different phases of semicrystalline polymers

M. Schäfer, R. Kurz, A. Seidlitz, T. Thurn-Albrecht and K. Saalwächter

Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle (Saale), Germany

The melt-crystallized morphology of semicrystalline polymers strongly depends on the diverse dynamics in the amorphous and crystalline region. The connections between structure formation and dynamics of polymer chains are investigated with SAXS and NMR spectroscopy, respectively, comparing polymers with and without intracrystalline dynamics (crystal-mobile and crystal-fixed). Proton time-domain techniques enable the analysis of the phase components, the intracrystalline and the amorphous phase dynamics. The intracrystalline motion displays only a weak dependence on morphology [1]. SAXS results show, that the morphology of the crystal-fixed polymer, poly-ε-caprolactone (PCL), and the crystal-mobile polymer, polyethylene oxide (PEO), are qualitatively different [2]. The crystal thicknesses in PCL are well-defined, whereas in PEO a crystal reorganization process caused by the intracrystalline dynamics leads to a uniform amorphous region [2].
To investigate the impact of the crystalline growth and reorganization process on the morphology separately, polymers with slower intracrystalline mobility, e.g. polyoxymehtylene (POM), will be investigated. Further investigations address the relationship between morphology and entangled dynamics in the amorphous phase.

[1] R. Kurz, A. Achilles, W. Chen, M. Schäfer, A. Seidlitz, Y. Golitsyn, J.  Kressler, W. Paul, G. Hempel, T. Miyoshi, T. Thurn-Albrecht, and K. Saalwächter. Macromolecules 2017, 50, 3890-3902.  (link)
[2] A. Seidlitz. 2016. “Einfluss von Kristallisationskinetik und Dynamik im Kristall und in der Schmelze auf die Strukturbildung teilkristalliner Polymere.” Dissertation, Martin-Luther-Universtität Halle-Wittenberg.  (link)