In block or statistical copolymers
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Parallel-packing interaction model
Hu, W.-B. The melting point of chain polymers. J. Chem. Phys. 113, 3901(2000). Journal link
[ABSTRACT] Based upon a consideration of the similarity in the driving force of polymer crystallization to the mesophase formation from the melt state, the equilibrium melting point of chain polymers relating to the details of molecular structure and the impure environment of crystallites was studied by classical lattice statistics and dynamic Monte Carlo simulations. The compact packing energy change of local chains during crystallization can be represented as an orientation-dependent attraction in the lattice model. The results as a function of driving force, chain length, content of random comonomers, and content of the diluent like small molecules or non-crystalline chains were compared with the semi-empirical expressions that have been verified for several polymers. Good agreements were obtained. As a result, the classical lattice statistics can predict a disorder–order phase transition as well as a phase separation behavior in a mixture system containing polymers, and supply the thermodynamic background to explore details of these behaviors in computer simulations.
A review
Hu, W.-B.; Frenkel, D. Polymer crystallization driven by anisotropic interactions. Advances in Polymer Science 191, 1-35(2005). Journal link
[ABSTRACT] In this review, we consider a variety of aspects of polymer crystallization using a very simple lattice model. This model has three ingredients that give it the necessary flexibility to account for many features of polymer crystallization that have been observed experimentally. These ingredients are (1) a difference in attraction between neighboring (nonbonded) components, (2) attraction between parallel bonds, and (3) temperature-dependent flexibility due to the energy cost associated with kinks in the polymer chain. We consider this model using both dynamic Monte Carlo simulations and a simple mean-field theory. In particular, we focus on the interplay of polymer crystallization and liquid–liquid demixing in polymer solutions. In addition, we study the factors that are responsible for the characteristic crystal morphologies observed in a variety of homopolymer and statistical-copolymer crystals. Finally, we consider how the freezing of polymers in the bulk can be related to the crystallization of a single polymer chain.
Calculating phase diagrams
Hu, W.-B.; Mathot,V.B.F.; Frenkel,D. Lattice model study of the thermodynamic interplay of polymer crystallization and liquid-liquid demixing. J. Chem. Phys. 118, 10343-10348(2003).Journal link
Reviews
Hu, W.-B. Statistical thermodynamics of polymer crystallization. Frontiers of Chemistry in China 5,29-32(2010). Journal link (Feature Article)
[ABSTRACT] A survey was made on the recent development of the mean-field lattice theory of polymer solutions to predict the properties of equilibrium melting points of bulk polymers. The interaction parameters were identified for several real polymers.
Hu, W.-B. Interplay of liquid-liquid demixing and polymer crystallization. Understanding Soft Condensed Matter via Modeling and Computation, edited by W. Hu and A. Shi, World Scientific Publisher: Singapore, 2010. p179. Book link
Controlling either pore sizes in membranes or crystal sizes in solutions
Hu, W.-B.; Frenkel, D. Effect of metastable liquid-liquid demixing on the morphology of nucleated polymer crystals. Macromolecules 37, 4336-4338(2004). Journal link
[ABSTRACT]
Zha, L.-Y.; Hu, W.-B.;* Homogeneous crystal nucleation triggered by spinodal decomposition in polymer solutions. J. Phys. Chem. B 111, 11373-11378(2007). Journal link.
[ABSTRACT] We report dynamic Monte Carlo simulations of polymer crystal nucleation initiated by prior spinodal decomposition in polymer solutions. We observed that the kinetic phase diagrams of homogeneous crystal nucleation appear horizontal in the concentration region below their crossovers with the theoretical liquid−liquid spinodal. When the solution was quenched into the temperature beneath this horizontal boundary, the time evolution of structure factors demonstrated the spinodal decomposition at the early stage of crystal nucleation. In comparison with the case without a prior liquid−liquid demixing, we found that the prior spinodal decomposition can regulate the nanoscale small polymer crystallites toward a larger population, more uniform sizes, and a better spatial homogeneity, whereas chain folding in the crystallites seems little affected.
Competition between entropy and enthalpy at interface
Zha, L.; Hu, W.-B.* Understanding crystal nucleation in solution-segregated polymers. Polymer 50, 3828-3834(2009). Journal Link
[ABSTRACT] We report dynamic Monte Carlo simulations of crystal nucleation in polymer bulk phase segregated from solutions. We found that poorer solvent enhances crystal nucleation in the concentrated phase of polymers. In addition, when the solvent becomes poor enough, crystal nucleation prefers to occur at the diffuse interfaces. The results are consistent with the predictions from theoretical phase diagrams, but something different from immiscible polymer blends. The surface-enhanced crystallization may explain the bowl-shaped crystal aggregates observed experimentally in poor solvent.
Tuning the nascent structure of spun fiber
Liu, Q.; Gao, H.-H.; Zha, L.-Y.; Hu, Z.-M.; Ma, Y.; Yu, M.-H.; Chen, L.; Hu, W.-B.* Tuning bio-inspired skin-core structure of nascent fiber via interplay of polymer phase transitions. Physical Chemistry Chemical Physics 16 (29), 15152-15157(2014). Journal Link
[ABSTRACT] The properties of polymer fibers are determined by their inner structures. We performed dynamic Monte Carlo simulations of early-stage solidification in the fluid filaments of stretched polymer solutions after extrusion into a coagulation bath upon fiber spinning. We observed that the radial temperature gradient dominates polymer crystallization to form an oriented crystalline skin (from single to multiple layers), while the radial non-solvent influx dominates phase separation to form a concentrated but less oriented core. The skin–core structure offers fibers a balanced performance between strength and toughness similar to plant stems, which can be tuned by the interplay of phase transitions. Our molecular-level observations facilitate a systematic understanding of the microscopic mechanism of fiber-spinning, which will pave a way towards making excellent polymer fibers.
Fundamental for the fast path of protein folding
Hu, W.-B. Structural transformation in the collapse transition of the single flexible homopolymer model. J. Chem. Phys. 109, 3686-3690(1998).Journal link
[ABSTRACT] The structural transformation in the coil-globule transition of a single flexible lattice chain has been investigated using dynamic Monte Carlo simulations. The results based upon ensemble averaging illustrated that for the homopolymers with limited chain length, an intermediate state with a dense-core and molten-shell structure reversibly occurs in the transition region. It was attributed to a special microphase separation behavior in an isolated coil, performing with densifying the dense core and contracting the thin shell. The continuous appearance of the size transition and its tendency to discontinuity at the theta temperature with the chain length approaching infinity were illustrated by the coexistence curves of the monomers with limited chain length. A possible explanation and its implications to the general mechanism of protein folding are also discussed.
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.
Hu, W.-B.; Frenkel, D. Effect of the coil-globule transition on the free-energy barrier for intra-chain crystal nucleation. J. Phys. Chem., B 110, 3734-3737(2006). Journal link
[ABSTRACT] The rate of crystal nucleation of colloids and globular proteins can be enhanced by critical density fluctuations. It has been argued that a closely related phenomenon influences the rate of intramolecular “crystallization” of single-chain polymers. We report Monte Carlo simulations of the free-energy barrier that separates the crystalline state of a homopolymer chain from the disordered state. The simulations show that the barrier for nucleation of the ordered state is drastically lowered as the disordered state changes from a coil to a globule. We discuss the relation of the present findings to intramolecular nucleation of heteropolymers, such as proteins.
Hidden driving force for demixing
Hu, W.-B.; Mathot,V.B.F. Liquid-liquid demixing in a polymer blend driven solely by the component-selective crystallizability. J. Chem. Phys. 119, 10953-10957(2003). Journal link
[ABSTRACT] On the basis of an extended Flory-Huggins expression for the mixing free energy of the long-chain binary polymer blend, we showed that liquid–liquid demixing can be driven solely by the propensities of crystallization differing with respect to components. Demixing prior to crystallization on cooling was demonstrated by dynamic Monte Carlo simulations of the lattice model for a symmetric polymer blend where only one component is crystallizable. We discussed the implications of this principle to several experimental observations including the (in)compatibility of polymer chains with different stereochemical compositions, the memory effect of polymer crystallization, and the spinodal decomposition at an early stage of polymer crystallization.
Something new near critical
Ma, Y.; Hu, W.-B.;* Wang, H. Polymer immiscibility enhanced by thermal fluctuations toward crystalline order. Phys. Rev. E 76, 031801(2007). Journal link.
[ABSTRACT] We report dynamic Monte Carlo simulations of binary polymer blends. The blends exhibit liquid-liquid phase separation influenced by the nearby crystallization of one component. We found that both binodal and spinodal boundaries of liquid-liquid phase separation shift up above the predictions of the mean-field lattice theory. The enhancement of immiscibility can be assigned to the thermal fluctuations toward better parallel order of the crystallizable chains in the blends, which has been neglected in the mean-field theory. This result serves as a theoretical background to explain the related experimental observations.
Melting point higher at interface
Ma, Y.; Zha, L.-Y.; Hu, W.-B.;* Reiter G.; Han, C. C. Crystal nucleation enhanced at the diffuse interface of immiscible polymer blends. Phys. Rev. E 77, 061801(2008). Journal link
[ABSTRACT] We report dynamic Monte Carlo simulations of immiscible binary polymer blends, which exhibit weakly enhanced crystal nucleation near interfaces between two phase-separated polymers. We found that this enhancement is not accompanied by any preferred crystal orientation, implying its origin is mainly of enthalpic rather than entropic nature. Mean-field theory of polymer blends predicts that for immiscible polymers the melting point of the crystallizable component increases upon dilution in the other component, while it normally decreases for miscible blends. A local dilution is forced to occur at the diffuse interface of immiscible polymers; therefore the melting point of crystallizable polymers rises, which, in turn, enhances the thermodynamic driving force for crystal nucleation near the interface.
In block or statistical copolymers
Molecular junction changes everything
Ma, Y.; Li, C.; Cai, T.; Li, J.; Hu, W.-B.* Role of block junctions in the interplay of phase transitions of two-component polymeric systems. J. Phys. Chem. B 115, 8853-8857(2011). Journal Link
[ABSTRACT] Block junctions are the topological constraints of connecting two homopolymers of different species to form diblock copolymers, which make the phase transition behaviors of diblock copolymers deviate from that of parallel polymer blends. We performed dynamic Monte Carlo simulations of these two parallel polymeric systems to compare their behaviors in the interplay of phase transitions. The results showed the lowered melting point of one component in symmetric diblock copolymers, as well as their enhanced critical segregation strength for demixing prior to crystallization. Furthermore, prior microphase separation in symmetric diblock copolymers produces a template for parallel stacking of lamellar crystals, which is of practical importance in the barrier properties of polymeric materials. Our observations may facilitate a better understanding to the phase transition behaviors of copolymer systems.
Chemical confinement to polymer crystallization (statistical copolymers)
Hu, W.-B.; Mathot,V.B.F.; Frenkel,D. Phase transitions of bulk statistical copolymers studied by dynamic
such as temperature rising elution fractionation (TREF).
A Review
Hu, W.-B.; Mathot, V. B. F.; Alamo, R. G.; Gao, H.-H.; Chen, X.-J. Crystallization of statistical copolymers. Advances in Polymer Science Published online. Journal link
Sequence-length segregation in the crystallization of statistical copolymers
Hu, W.-B.; Mathot,V.B.F. Sequence-length segregation during crystallization and melting of a model homogeneous copolymer. Macromolecules 37, 673-675(2004). Journal link
Communication to the editor.
Strong memory effect due to sequence-length segregation
Reid, B. O.; Vadlamudi, M.; Mamun, A.; Janani, H.; Gao, H.-H.; Hu, W.-B.; Alamo, R.* Strong memory effect of crystallization above the equilibrium melting point of random copolymers. Macromolecules 46, 6485-6497(2013). Journal Link
Gao, H.-H.; Vadlamudi, M; Alamo, R.; Hu, W.-B.* Monte Carlo simulations of strong memory effect of crystallization in random copolymers. Macromolecules 46, 6498-6506(2013). Journal Link
Guan, X.-C.; Zha, L.-Y.; Wu, Y.-X.; Hu, W.-B.* Strong memory of strain-induced copolymer crystallization revealed by Monte Carlo simulations. Polymer 98, 282-286(2016). Journal link
Different comonomer sizes bring variable chemical confinements
Hu, W.-B.; Karssenberg, F. G.; Mathot, V. B. F. How a sliding restriction of comonomers affects crystallization and melting of homogeneous copolymers. Polymer 47, 5582-5587(2006). Journal link
[ABSTRACT] In ethylene-based copolymers, large comonomers/branches make the sliding diffusion difficult in the crystalline regions constituted by small monomers. We studied the influence of such a restricted sliding diffusion on the mechanisms of crystallization and melting of homogeneous copolymers, by means of dynamic Monte Carlo simulations. Comparing two extreme cases—no restriction and a hard restriction—we found that the hard restriction increases both temperatures of crystallization and melting on the temperature scanning. Moreover, during crystallization, the restriction weakens segregation of sequence lengths and decreases the lamellar-crystal thickness. These results can be attributed to a switch of the dominant crystal growth mode from longitudinal thickening to lateral growth due to the presence of a hard restriction.
Secret in toughening iPP
Yang, F.; Gao, H.-H.; Hu, W.-B.* Monte Carlo simulations of crystallization in heterogeneous copolymers: The role of copolymer fractions with intermediate comonomer content. Journal of Materials Research 27, 1383-1388(2012). Journal link