Review: The physics of polymer chain-folding
Review: The physics of polymer chain-folding
Why do proteins have beta-folding? Why are polymer materials tougher than metals and ceramics? Why polymers become stronger in fibers, thin films and bottles?
Hu, W.-B. The physics of polymer chain-folding. Physics Reports 747, 1-50 (2018). Journal link
1. The discovery of chain-folding
2. The origin of chain-folding
3. Crystal growth with chain-folding
4. Polymer unfolding
5. Protein folding, misfolding and unfolding
Integer folding of short-chains
Hu, W.-B. Chain folding in polymer melt crystallization studied by dynamic
[ABSTRACT] The morphological metastability of spontaneous crystallization from the melt of short-chain semiflexible homopolymers was studied through dynamic Monte Carlo simulations of a lattice multiple-chain system. Frictional hindrance for the sliding diffusion of the chains in the crystallites was employed to enhance the metastability of folded-chain crystallites, and distinguish the polymer crystallite from its mesophase, though their phase transitions have the similar driving forces. The integral folding of short chains in the crystallites and the constant linear crystal growth rate were identified with the actual polymers. In addition, the roughness of the local growth front accompanied with the occasional reversals and jumplike advancing was observed, which cannot be explained by current models. The crowding of the dangling ends on the fold surface seems to be the main reason for suppressing the lateral growth front, and the mechanism of chain folding was proposed. Its implications to the special behaviors of polymer meltcrystallization, such as the semicrystalline state, the effect of the chain rigidity and molecular weight to crystal growth, the reversible premelting, and molecular segregation are briefly discussed.
Sectorization of fold-end orientations in the single lamellar crystal
Hu, W.-B.; Frenkel,D.; Mathot,V.B.F. Sectorization of a lamellar polymer crystal studied by dynamic
Communication to the Editor
Hu, W.-B.; Frenkel, D.; Mathot, V. B. F. Shish-kebab crystallites induced by a single pre-aligned macromolecule. Macromolecules 35, 7172-7174(2002).Journal link
Communication to the editor.
Free energy calculation of single-chain crystallization
Hu, W.-B.; Frenkel,D.; Mathot,V.B.F. Free energy barrier to melting of single-chain polymer crystallite. J. Chem. Phys. 118, 3455-3457(2003).Journal link
[ABSTRACT] We report Monte Carlo simulations of the melting of a single-polymer crystallite. We find that, unlike most atomic and molecular crystals, such crystallites can be heated appreciably above their melting temperature before they transform to the disordered “coil” state. The surface of the superheated crystallite is found to be disordered. The thickness of the disordered layer increases with super-heating. However, the order–disorder transition is not gradual but sudden. Free-energy calculations reveal the presence of a large free-energy barrier to melting.
[ABSTRACT] We report a numerical study of the free energy barrier for crystallization and melting of a single homopolymer chain. The simulations show that the free energy barrier separating the crystalline and molten states at the same free energy level strongly depends on the chain length. However, at a fixed temperature the barrier for single-chain crystallization is independent of chain length. This observation is in agreement with recent experiments on multichain bulk-polymer systems and can be understood theoretically if we assume that the primary nucleation of polymer crystals is determined by intramolecular nucleation. If we further assume that the subsequent growth of polymer crystals is controlled by two-dimensional intramolecular nucleation on the growth front, we can even account for the experimentally observed molecular segregation during crystal growth as well as the chain-length independence of the free energy barrier for secondary nucleation.
Hu, W.-B. Intramolecular crystal nucleation, an invited chapter in the book Lecture Notes in Physics: Progress in Understanding of Polymer Crystallization , Edited by G. Strobl and G. Reiter, Springer-Verlag, Vol. 714, 47-63(2007). Journal link
[ABSTRACT] We review how the nucleation mechanism of polymer crystallization could be assigned to intramolecular processes and what are the preliminary benefits for understanding some fundamental crystallization behaviors. The speculative concept of molecular nucleation and the theoretical model of intramolecular nucleation have been elucidated in a broad context of classical nucleation theory. The focus is on explaining the phenomenon of molecular segregation caused by polymer crystal growth.
We review how the nucleation mechanism of polymer crystallization could be assigned to intramolecular processes and what are the preliminary benefits for understanding some fundamental crystallization behaviors. The speculative concept of molecular nucleation and the theoretical model of intramolecular nucleation have been elucidated in a broad context of classical nucleation theory. The focus is on explaining the phenomenon of molecular segregation caused by polymer crystal growth.
Crystallization fractionation of molecular weights
Hu, W.-B. Molecular segregation in polymer melt crystallization: simulation evidence and unified-scheme interpretation. Macromolecules 38, 8712-8718(2005). Journal link
[ABSTRACT] The segregation of the low-molecular-weight fractions on the crystal growth of polydisperse polymers has been identified as a general phenomenon by means of dynamic Monte Carlo simulations of lattice polymer systems. Its mechanism was elucidated on the basis of the intramolecular nucleation model. A unified scheme has been proposed to interpret all three scenarios of molecular segregation according to the location of the crystallization temperature Tc demarcated by two melting points of short chain fractions, namely Tm0 for the bulk extended-chain crystals and Tm2D for two-dimensional single folded-chain crystals on a smooth crystal-growth front. In the first scenario, Tc > Tm0 , and short-chain fractions are thermodynamically forbidden in crystallization, like the small solvents in conventional monotectic polymer solutions. In the second scenario, Tm0 > Tc > Tm2D, and short-chain fractions are fully excluded by their failures on the intramolecular secondary nucleation for folded-chain crystal growth. In the third scenario, Tc ≤ Tm2D, and short-chain fractions are partially segregated due to their much less free energy gains in the intramolecular secondary nucleation than long-chain fractions. When Tc « Tm2D, both short-chain and long-chain fractions cocrystallize without any molecular segregation. In addition, an upper limit of molecular weights in crystallization fractionation has been explained.
Regime transitions of temperature dependence of the growth rates
[ABSTRACT] We report dynamic Monte Carlo simulations of polymer crystal growth induced by a template layer in the melt and semidilute solutions. The molecular simulations evidenced intrinsic regime transitions in the temperature dependence of crystal growth rates, which have been interpreted on the basis of the Lauritzen−Hoffman model, a specific model among the diverse points of view on the general mechanism of polymer crystallization in the literature. We found that, corresponding to the regime II−III transition, there exists a morphological transition from single to multiple lamellar crystal growth, implying the style of spherulite formation changing from a sequential filling to a completed inner filling at low temperatures. Meanwhile, stem-length distributions in the crystallites also exhibit a shift. Dilution makes more perfect chain-folding upon crystal growth, in accord with experimental observations. However, we could not observe the predicted smooth crystal growth front in regime I. In addition, contradictory to the previous expectation, the probability of adjacent chain folding increases slightly at low temperatures. We proposed a new interpretation of regime transitions on the basis of the intramolecular-crystal-nucleation model for a better understanding of both experimental and simulation observations.
Effect of molecular-weight polydispersity on the co-growth rate
Cai, T.; Ma, Y.; Yin, P.-C.; Hu, W.-B.* Understanding the growth rates of polymer co-crystallization in the binary mixtures of different chain lengths. J. Phys. Chem. B 112, 7370-7376(2008). Journal link
[ABSTRACT] Polymer materials often contain a polydispersity of molecular lengths. We studied the linear growth rates of polymer lamellar crystals in the binary mixtures of different chain lengths by means of dynamic Monte Carlo simulations. Both chain lengths were chosen large enough to perform chain folding upon crystal growth but not very large to avoid the effect of chain entanglement in the bulk phase. We found that the crystal growth rates exhibit a linear dependence upon the compositions of mixtures. This linear relation implies that the overall crystal growth rates are integrated by the separate contributions of variable-length single polymers, supporting the model of intramolecular crystal nucleation. In each event of crystal growth of single polymers, long chains yield more crystallinity than short chains. This high efficiency explains higher crystal growth rates of long chains than that of short chains, and the explanation is quite different from the traditional view on the basis of their different melting points. In addition, with a partial release of sliding diffusion for crystal thickening, a new dependence of crystal growth rates occurs near the dilute end of long-chain compositions at high temperatures, which can be attributed to the preference of integer-number chain folding at the crystal growth front. The preferred fold lengths may vary with chain lengths and thus influence the crystal growth rates.
Jiang, X.-M.; Li, T.-X.; Hu, W.-B.* Understanding the growth rates of polymer co-crystallization in the binary mixtures of different chain lengths: Revisited. J. Phys. Chem. B 119(30), 9975–9981(2015). Journal link
[ABSTRACT] Polymers often contain a polydispersity of chain lengths, which brings a complicated influence on crystallization behaviors. In our previous publication (J. Phys. Chem. B 2008, 112, 7370), we reported dynamic Monte Carlo simulations of co-crystallization in the binary mixtures of long (32-mer) and short (16-mer) homologue chains. We observed a linear dependence of crystal growth rates on the volume fractions of the long-chain component at low temperatures. In this article, with new confirming data, we further observed that the mole fractions also give linear dependence to the crystal growth rates, but split into two regimes. We attributed the phenomenon of two regimes to the variation between two thicknesses of lamellar crystals. The small thickness in the regime of low mole fractions is dominated by the metastable integer-number folding of 16-mers, which causes the “self-poisoning” effect on the crystal growth rates.
Semi-crystalline texture due to the difficulty of chain-folding
Ren, Y. J.; Zha, L. Y.; Ma, Y.; Hong, B. B.; Qiu, F.; Hu, W.-B.* Polymer semi-crystalline texture made by interplay of crystal growth. Polymer 50, 5871-5875(2009). Journal Link
[ABSTRACT] Chain-folded lamellar crystal growth of polymers typically makes a semicrystalline texture, which exhibits a layer-by-layer, alternating assembly of crystalline and amorphous phases. We performed dynamic Monte Carlo simulations of lamellar crystal growth in a row structure. We found that parallel growth of lamellar crystals appears staggered at high temperatures, and those loops and cilia on the fold-end crystal surfaces interfere with the in-between lagging growth of the third crystal. This mechanism produces an intrinsic amorphous layer between two crystals, with its thickness comparable with coil sizes of single polymers. The results may facilitate our better understanding about the low crystallinity of high-molecular-weight polyethylenes, and the scaling law of their amorphous thickness on chain lengths.
Chain-folding on the roughening growth/melting front
Gao, H.-H.; Wang, J.; Schick, C.; Toda, A.; Zhou, D.-S.; Hu, W.-B.* Combining fast-scan chip-calorimeter with molecular simulations to investigate superheating behaviors of lamellar polymer crystals. Polymer 55, 4307-4312(2014). Journal Link
[ABSTRACT] We studied the power-law heating-rate dependence of superheating for the melting of alpha- and beta-crystals of isotactic polypropylene by means of chip-calorimeter, and expanded our parallel observation to higher heating rates by means of molecular simulations. We observed that, at low heating rates, the melting of lamellar crystals after thickened via melting-recrystallization exhibits no power-law-dependent superheating; at medium heating rates, the melting of crystals after thickened via chain-sliding diffusion exhibits the power-law-dependent superheating with the power indexes sensitive to chain mobility in the crystals; while at high heating rates, the zero-entropy-production melting of crystals without further thickening maintains the power-law-dependent superheating but with the power indexes uniform at an upper-limit 0.375. We attributed the index 0.375 to a result combining local intramolecular nucleation and global roughening growth at the lateral surface of lamellar crystals, which dominate the kinetics of crystal growth and melting of polymer crystals at high temperatures.
Transition from intramolecular to intermolecular nucleation
Nie, Y.-J.; Gao, H.-H.; Yu, M.-H.; Hu, Z.-M.; Reiter, G.; Hu, W.-B.* Competition of crystal nucleation to fabricate the oriented semi-crystalline polymers. Polymer 54, 3402-3407(2013) Journal Link
[ABSTRACT] The mechanical performance of many polymeric materials, such as natural rubber tires, plastic bottles and bags, and textile fibers, depends crucially on the stretch-induced alignment of crystalline molecules in the course of processing. However, the underlying molecular mechanism to solidify the alignment is still poorly understood. We employed dynamic Monte Carlo simulations to unveil how at temperatures close to the melting point a homogeneous stretch of bulk polymers can affect crystal nucleation and leads to aligned crystalline molecules. We observed that upon the molecular strain increasing beyond a critical value, the emerging crystallites suddenly decrease their probability of chain-folding, corresponding to a transition from intramolecular chain-folding nuclei to intermolecular fringed-micelle nuclei. On the basis of the classical nucleation theory, the transition can be predicted well by the competition in the free energy barriers for these two coexisting nucleation mechanisms.
Chain-folding reveals the habits of shish-kebabs and plastic necking
Nie, Y.-J.; Gao, H.-H.; Hu, W.-B.* Variable trends of chain-folding in separate stages of strain-induced crystallization of bulk polymers. Polymer 55, 1267-1272(2014). Journal Link
[ABSTRACT] We performed dynamic Monte Carlo simulations of isothermal crystallization of bulk polymers at a high temperature, which was induced by a homogeneous stretching with a constant strain rate over a wide range of strains. We observed that the crystallites exhibit variable trends of chain folding in three sequential regions of strains, revealing hierarchical mechanisms of strain-induced polymer crystallization: in the first region, sporadic stretched segments initiate intermolecular crystal nucleation with less chain folding at higher strains; in the second region, massive less-stretched segments perform crystal growth with more chain folding at higher strains; in the third region, those folded chains extend via a melting-recrystallization process, again with less chain folding at higher strains. Different trends of chain-folding between crystal nucleation and growth appear intrinsic and ultimately lead to shish-kebab crystals. Our observations provided a molecular-level rationale to understand various experimental phenomena upon the processing for oriented semi-crystalline polymers.
Linear concentration dependence of crystal growth rates in solutions
Zhou, Y.-J.; Hu, W.-B.* Kinetic analysis of quasi-one-dimensional growth of polymer lamellar crystals in dilute solutions. J. Phys. Chem. B 117, 3047-3053(2013). Journal Link
[ABSTRACT] Flexible polymers are featured with two-dimensional growth of metastable chain-folded lamellar crystals in quiescent dilute solutions. Recently, a massive cylindrical micelle with quasi-one-dimensional (quasi-1D) growth driven by confined crystallization of diblock copolymers in dilute solutions raised a new challenge. We performed dynamic Monte Carlo simulations to investigate the kinetics of quasi-1D growth of lamellar crystals in two typical cases of dilute but not very dilute polymer solutions. We found that in both cases the growth kinetics is dominated by the surface-nucleation-controlled mechanism. Moreover, in the first case corresponding to few and small crystals grown under almost constant polymer concentrations in the huge bulk of solutions, the driving-force term in the kinetic equation dominates a linear concentration dependence of crystal growth rates in the high-concentration region, and the nucleation-barrier term dominates their nonlinear deviation in the low-concentration region. In the second case corresponding to massive crystals grown under depleting polymer concentrations in a limited volume of solutions, the crystal growth rates decay with time, but at the early stage, they follow exactly with the linear-concentration-dependent growth rates of the first case. Therefore, the growth size at the early stage of the second case can be described as an exponential-decay function of time, which provides a theoretical model to the data analysis of corresponding experimental observations.
Linear concentration dependence of crystal growth rates under nano-confinement
Shu, R.-F.; Zha, L.-Y.; Eman, A.; Hu, W.-B.* Fibril crystal growth in diblock copolymer solutions studied by dynamic Monte Carlo simulations. J. Phys. Chem. B 119, 5926-5932(2015) Journal Link.
[ABSTRACT] Quasi-one-dimensional fibril crystal growth of diblock copolymers is a fundamental issue in the investigation of nanotechnology and neurodegenerative diseases. We performed dynamic Monte Carlo simulations of lattice polymers to study the crystallization-driven fibril crystal growth of diblock copolymers under two circumstances of solutions: sporadic crystals with the feeding mode of constant polymer concentrations, and massive crystals with the depleting mode of decaying polymer concentrations. We confirmed anisotropic driving forces as a prerequisite of steady growth of fibril crystals. The lamellar crystal width is confined by the noncrystalline block below a critical concentration that shifts down with the decrease of the noncrystallizable block fractions. In the depleting mode, the long-axis sizes at the early stage of fibril crystal growth can be fitted well by an exponential-decay function of time, and the growth rates decrease linearly with polymer concentrations by following the growth rates in the feeding mode, appearing as consistent with our previous simulation results of homopolymer solutions.
Evidence of intramolecular nucleation preferred in crystal growth
Zhang, R.; Zha, L.-Y.; Hu, W.-B.* Intramolecular crystal nucleation favored by polymer crystallization: A Monte Carlo simulation evidence. J. Phys. Chem. B 120(27), 6754-6760(2016). Journal link
[ABSTRACT] We performed dynamic Monte Carlo simulations of half–half binary blends of symmetric (double and mutual) crystallizable polymers. We separately enhanced the driving forces for polymer-uniform and polymer-staggered crystals. Under parallel enhancements, polymer-uniform crystals exhibit faster nucleation and growth, with more chain folding and less lamellar thickening, than those in polymer-staggered crystals. We attributed the results to intramolecular crystal nucleation, ruined by enhanced polymer-staggered crystallization. Our observations provide direct molecular-level evidence to support the fact that intramolecular crystal nucleation is favored by polymer crystallization in quiescent solutions and melt, which yields chain folding for the characteristic β-sheet or lamellar morphology of macromolecular crystals.
Competition between secondary nucleation and lamellar thickening decides the nascent fold-length
Jiang, X.-M.; Reiter, G.; Hu, W.-B.* How chain-folding crystal growth determines thermodynamic stability of polymer crystals. J. Phys. Chem. B 120(3), 566-571(2016). Journal link
[ABSTRACT] Chain-folding is a habit of polymer crystallization, which yields limited lamellar thickness of polymer crystals and thus determines their thermodynamic stability. We performed dynamic Monte Carlo simulations of a lattice polymer model with chain-folded lamellar crystal growth stopped by a critical spacing of two parallel-oriented bars. We confirmed the critical spacing as minimum lamellar thickness (lmin) proposed previously in the Lauritzen–Hoffman (LH) model; however, the temperature dependence of excess lamellar thickness beyond lmin appears opposite to the prediction of the LH model. Moreover, it reproduces Strobl et al.’s experimental observations, but our lattice-model approach rules out any mesophase hypothesis. We proposed a kinetic model combining intramolecular secondary nucleation and stem elongation to explain this temperature-dependence behavior, which reconciles the controversial arguments on the microscopic mechanism of lamellar crystal growth of polymers.
Further extension of fold-length is slow or even retarded by integer folding
Wang, M.-Q.; Gao, H.-H.; Zha, L.-Y.; Chen, E.-Q.; Hu, W.-B.* Systematic kinetic analysis on monolayer lamellar crystal thickening via chain-sliding diffusion of polymers. Macromolecules 46, 164-171(2013). Journal Link
[ABSTRACT] Lamellar polymer crystals are metastable due to their limited lamellar thickness. We performed dynamic Monte Carlo simulations of lattice linear polymers to investigate the kinetics of isothermal thickening via chain-sliding diffusion in single lamellar crystals of polyethylene and poly(ethylene oxide). We sorted out three typical cases for controversial experimental observations. The basic case is a continuous increase of lamellar thickness for heavily folded long chains, with a logarithmic time dependence typical at the lateral growth front. Its kinetics is dominated by the activation energy barrier for sliding diffusion with higher speeds at higher temperatures. For integer-folded short chains, however, the lamellar thickness increases discontinuously, and its kinetics is dominated by a free energy barrier for surface nucleation. The latter can be further split into two cases: the thickening in the melt is mainly driven by the bulk free energy, with lower speeds at higher temperatures due to a temperature-sensitive barrier; while the thickening on a solid substrate is mainly driven by the surface free energy, with higher speeds at higher temperatures due to a temperature-insensitive barrier. The simulations facilitate our systematic understanding to the case-by-case microscopic mechanisms for the thickening of monolayer lamellar crystals via sliding diffusion of polymers.
Fold-length variation makes the cloning seed
Xu, J.-J.;* Ma, Y.; Hu, W.-B.;* Rehahn, M.; Reiter, G. Cloning polymer single crystals via self-seeding. Nature Materials 8, 348-353(2009). Journal Link.
[ABSTRACT] In general, when a crystal is molten, all molecules forget about their mutual correlations and long-range order is lost. Thus, a regrown crystal does not inherit any features from an initially present crystal. Such is true for materials exhibiting a well-defined melting point. However, polymer crystallites have a wide range of melting temperatures, enabling paradoxical phenomena such as the coexistence of melting and crystallization. Here, we report a self-seeding technique that enables the generation of arrays of orientation-correlated polymer crystals of uniform size and shape ('clones') with their orientation inherited from an initial single crystal. Moreover, the number density and locations of these cloned crystals can to some extent be predetermined through the thermal history of the starting crystal. We attribute this unique behaviour of polymers to the coexistence of variable fold lengths in metastable crystalline lamellae, typical for ordering of complex chain-like molecules.
Integer folding is a poison to the growth rates
Ma, Y.; Qi, B.; Ren, Y. J.; Ungar, G.; Hobbs, J. K.; Hu, W.-B.* Understanding self-poisoning phenomenon in crystal growth of short-chain polymers. J. Phys. Chem. B 113, 13485-13490(2009). Journal Link
[ABSTRACT] Flexible polymers crystallize with chain folding, which shows a unique phenomenon called self-poisoning. As a result, minima in crystal growth rates of strictly monodisperse short-chain polymers are observed near the temperatures of transitions from extended-chain to once-folded-chain growth, from once-folded to twice-folded growth, etc. We employed dynamic Monte Carlo simulation of lattice polymers to visualize such transitions in molecular details. We observed a rate crossover between chain extension and lateral growth of polymer lamellar crystals at the wedge-shaped growth front, resulting in a rate minimum around the melting point of the metastable once-folded lamellar crystal. The rate minimum can be interpreted as due to the dependence of crystal growth rates on the excess crystal thickness beyond the minimum stable thickness. Furthermore, during crystal thickening, numerous molten chains are shown to be sucked into the lamellar crystals through the basal planes, demonstrating an important source of crystallinity from secondary crystallization lagging behind the crystal growth front.
Melting as a kinetic mirror of lamellar growth
Ren, Y. J.; Ma, A. Q.; Li, J.; Jiang, X. M.; Ma, Y.; Toda, A.; Hu, W.-B.* Melting of polymer single crystals studied by dynamic Monte Carlo simulations. Eur. Phys. J. E 33, 189-202(2010) Journal link.
[ABSTRACT] We report dynamic Monte Carlo simulations of lattice polymers melting from a metastable chain-folded lamellar single crystal. The single crystal was raised and then melted in an ultrathin film of polymers wetting on a solid substrate, mimicking the melting observations made by using Atomic Force Microscopy. We observed that the thickness distribution of the single crystal appears quite inhomogeneous and the thickness increases gradually from facetted edges to the center. Therefore, at low melting temperatures, melting stops at a certain crystal thickness, and melting-recrystallization occurs when allowing crystal thickening; at intermediate temperatures, melting maintains the crystal shape and exhibits different speeds in two stages; at high temperatures, fast melting makes a melting hole in the thinnest region, as well as a saw-tooth-like pattern at the crystal edges. In addition, the linear melting rates at low temperatures align on the curve extrapolated from the linear crystal growth rates. The temperature dependence of the melting rates exhibits a regime transition similar to crystal growth. Such kinetic symmetry persists in the melting rates with variable frictional barriers for c -slip diffusion in the crystal as well as with variable chain lengths. Visual inspections revealed highly frequent reversals upon melting of single chains at the wedge-shaped lateral front of the lamellar crystal. We concluded that the melting kinetics is dominated by the reverse process of intramolecular secondary crystal nucleation of polymers.
Thinfilm confinement to fold-length
Ren, Y.-J.; Gao, H.-H.; Hu, W.-B. Crystallization kinetics of lamellar crystals confined in polymer thin films. J. Macromol. Sci., Part B: Phys. 51, 1548-1557(2012). Journal Link
[ABSTRACT] We used dynamic Monte Carlo simulations to investigate the crystallization kinetics of flat-on lamellar polymer crystals in variable thickness films. We found that the growth rates linearly reduced with decreasing film thickness for the films thinner than a transition thickness dt , while they were constant for the films thicker than dt . Moreover, the mean stem lengths (crystal thickness) we calculated decreased with film thickness in a similar way to the growth rates, and the intramolecular crystallinities we calculated confirmed the film thickness dependence of the crytsal thickness. Besides, the crystal melting rates in thin films were calculated and increased with decreasing film thickness. We proposed a new interpretation on the film thickness dependence of the crystal growth rate in thin films, suggesting that it is dominated by the crystal thickness in terms of the driving force term (l–l min) expressed by Sadler, rather than the chain mobility based on experiments. The crystal thickness can determine whether a crystal grows or melts in a thin film at a fixed temperature, indicating the reversibility between the crystal growth and melting.
Thinfilm confinement to fold-spreading
Ren, Y.-J.; Huang, Z.; Hu, W.-B. Growth rates of edge-on lamellar crystals confined in polymer thin films. J. Macromol. Sci., Part B: Phys. 51, 2341-2351(2012). Journal Link
[ABSTRACT] The growth rates of edge-on lamellar polymer crystals in variable thickness films were investigated in terms of dynamic Monte Carlo (MC) simulations. The growth rates linearly decreased with decreasing film thickness for the thinner films and were nearly constant for the thicker films. The mean stem lengths (crystal thickness) were also constant in different thickness films. The crystal widths parallel to the film thickness increased more slowly with increasing film thickness in the thinner films than that in the thicker films, indicating they were restrained by the film thickness. We propose that the growth rate of edge-on lamellar crystals in thin films is dominanted by the crystal width in the thinner films and by the crystal thickness in the thicker films; the variation of the film thickness can change the three-dimensional shape of the crystal growth front, also affecting the growth rate of the edge-on lamellar crystal.
Reversible breathing of fold-length
Hu, W.-B.; Albrecht, T.; Strobl, G. Reversible premelting of PE and PEO crystallites indicated by TMDSC. Macromolecules 32, 7548-7554(1999).Journal link
[ABSTRACT] Quasi-isothermal temperature-modulated differential scanning calorimetry was employed in a study of thermoreversible structural changes in the melting range of semicrystalline polymers. The results indicated a reversible melting and crystallization process occurring at the fold surfaces of crystallites of polyethylene and poly(ethylene oxide). For polyethylene, good agreements were found with reported small-angle X-ray scattering data and Fischer's theory. Surface melting and crystallization depend on the ability of the chains in the crystals to carry out a sliding diffusion. This was shown by a comparison of polyethylene and poly(ethylene oxide) with other polymers such as poly(ethylene terephthalate), polycaprolactone, isotactic polypropylene, and syndiotactic polypropylene. When the longitudinal chain mobility in the crystals is much reduced or completely absent, only a small or no excess reversing heat capacity is observed. The special performance of short-chain poly(ethylene oxide) is indicative for the metastability of the crystals built of once-folded chains.
Jiang, X.-M.; Li, Z.-L.; Wang, J.; Gao, H.-H.; Zhou, D.-S.; Hu, W.-B.* Combining TMDSC measurements between chip-calorimeter and molecular simulation to study reversible melting of polymer crystals. Thermothimica Acta 603, 79-84(2015). Journal Link
[ABSTRACT] Reversible melting is a phenomenon unique to polymer crystals, which raises an excess reversing heat capacity near their melting points. By means of temperature-modulated differential scanning calorimetry (TMDSC) measurements with an expanded frequency range in chip-calorimeter, we studied reversing heat capacities of alpha- and beta-form crystals of isotactic polypropylene. We attributed their differences at high temperatures and low frequencies to variable chain mobility in these two crystals. We further performed parallel dynamic Monte Carlo simulations of lattice polymers with variable chain mobility in the crystals to confirm this attribution. Our observations provide the first evidence on the role of chain mobility in the microscopic mechanism of reversible melting at the fold-end surfaces of lamellar polymer crystals.