Interplay between Polymer Crystallization and Liquid-Liquid Demixing

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In polymer solutions

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

[ABSTRACT] We report Monte Carlo simulations of a lattice-polymer model that can account for both polymer crystallization and liquid–liquid demixing in solutions of semiflexible homopolymers. In our model, neighboring polymer segments can have isotropic interactions that affect demixing, and anisotropic interactions that are responsible for freezing. However, our simulations show that the isotropic interactions also have a noticeable effect on the freezing curve, as do the anisotropic interactions on demixing. As the relative strength of the isotropic interactions is reduced, the liquid–liquid demixing transition disappears below the freezing curve. A simple extended Flory–Huggins theory accounts quite well for the phase behavior observed in the simulations.

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] Communication to the editor.

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.

In polymer blends

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] Onthe basis of an extended Flory-Huggins expression for the mixingfree energy of the long-chain binary polymer blend, we showedthat liquid–liquid demixing can be driven solely by the propensitiesof crystallization differing with respect to components. Demixing prior tocrystallization on cooling was demonstrated by dynamic Monte Carlo simulationsof the lattice model for a symmetric polymer blend whereonly one component is crystallizable. We discussed the implications ofthis principle to several experimental observations including the (in)compatibility ofpolymer chains with different stereochemical compositions, the memory effect ofpolymer crystallization, and the spinodal decomposition at an early stageof 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 Monte Carlo simulations. Macromolecules 36, 2165-2175(2003).Journal link

[ABSTRACT] We report a numerical study of crystallization and melting in bulk statistical homogeneous (random), homogeneous (slightly alternating), and heterogeneous (produced in a batch reaction) copolymers formed by crystallizable monomers and noncrystallizable comonomers. In our dynamic Monte Carlo simulations of lattice chains, the current model further assumes that the comonomers cannot move into crystalline regions by sliding diffusion of the chains. We find that both the overall composition and the statistical distribution of the monomers affect the phase-transition temperature, the resulting relative crystallinity, and the crystal morphology. However, the final absolute crystallinity of homogeneous copolymers seems insensitive to these parameters. Intramolecular segregation between monomers and comonomers is accompanied by crystallization, demonstrating the concept of sequence segregation or nanophase separation of statistical copolymers with assembling structures like in thermoplastic elastomers. Moreover, if crystallization of homogeneous copolymers has started but not yet completed on cooling, subsequent heating will show cold crystallization before melting, which can be attributed to insertion-mode lamellar growth. For heterogeneous copolymers, intermolecular segregation occurs on cooling before crystallization. On the basis of our observations, a pair of master melting and crystallization curves for the crystallinity of a statistical copolymer as a function of temperature are suggested to reflect the characteristic of the monomer-sequence-length distribution. This suggestion facilitates the clarification to the kinetic disturbance in local temperature regions and to the principle of some fractionation methods,
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

[ABSTRACT] We report the effect of molecular weight and comonomer content on melt crystallization of model random ethylene 1-butene copolymers. A large set of narrowly distributed linear polyethylenes (PE) was used as reference of unbranched molecules. The samples were crystallized from a melt state above the equilibrium melting temperature and cooled at a constant rate. The exothermic peaks of the melt-solid transition are reported as the crystallization temperatures (T_c). Following expectations, the T_c of unbranched PE samples was constant and independent of the initial melt temperature. The same independence was observed for copolymers (2.2 mol % ethyl branches) with molar mass below 4500 g/mol. Moreover, the T_c of copolymers with higher molar mass depends on the temperature of the initial melt, T_c increases as the temperature of the melt decreases. We attribute the increase in T_c to a strong crystallization memory in the melt above the equilibrium melting, and correlate this phenomenon with remains in the melt of the copolymer’s crystallizable sequence partitioning. Albeit molten, long crystallizable sequences remain in the copolymer’s melt at a close proximity, lowering the change in free energy barrier for nucleation. The residual sequence segregation in the melt is attributed to restrictions of the copolymer crystalline sequences to diffuse upon melting and to reach the initial random topology of the copolymer melt. Erasing memory of the prior sequence selection in copolymer melts requires much higher temperatures than the theoretical equilibrium value. The critical melt temperature to reach homogeneous copolymer melts (T_onset), and the comonomer content at which melt memory above the equilibrium melting vanishes are established. The observed correlation between melt memory, copolymer crystallinity and melt topology offers strategies to control the state of copolymer melts in ways of technological relevance for melt processing of LLDPE and other random olefin copolymers.

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

[ABSTRACT] Recently, experiments reported a strong memory effect of crystallization in model ethylene-based homogeneous random copolymers after being annealed at temperatures higher than the equilibrium melting point of copolymers. By means of dynamic Monte Carlo simulations of random copolymers, we reproduced this phenomenon in the similar model copolymer systems. We attributed this phenomenon to the sequence-length segregation upon first-time crystallization. The resulting heterogeneous melt of copolymers survives upon annealing below the critical demixing point that could be much higher than the equilibrium melting point of copolymers. Therefore, the local high concentration of long sequences raises the local melting point to accelerate primary crystal nucleation upon second-time crystallization. This source of memory effects demonstrates how crystallization can be influenced by the substantial trend of demixing between different sequences in homogeneous random copolymers.

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

[ABSTRACT] We performed dynamic Monte Carlo simulations of strain-induced crystallization of homopolymer and random copolymers under cyclic loading of strains. We found that since the second loading random copolymers shift down the onset strain of crystallization and raise up the crystallinity, in contrast to homopolymer. We attributed the strong memory to the remaining of sequence-length segregation raised by copolymer crystallization during the first loading of strains. The mechanism is consistent with that for the strong memory of copolymer crystallization under cyclic cooling, as revealed by previous experiments and simulations. Our results showed a new effect of chain-sequence defects on the cyclic loading performance of rubbers.

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

[ABSTRACT] Heterogeneous copolymers contain diverse comonomer contents among copolymers, and the extremely diverse case becomes a binary polymer blend. We report a numerical study of crystallization in two series of heterogeneous copolymers that are separated with strong and weak heterogeneities of comonomer distributions, and both of which are composed of crystallizable monomers and noncrystallizable comonomers with various compositions. A comparison of simulation results between these two series of samples demonstrates that, something like a compatibilizer in an incompatible polymer blend, copolymer fractions with intermediate comonomer contents between two compositional extremities depress the prior liquid–liquid demixing on cooling, and hence weaken the subsequent crystallization behaviors. However, we found that in these intermediate fractions, comonomers distribute quite homogeneously on each chain and the amphiphilicity occurs on multiple short sequences, rather than like on a diblock copolymer.

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Interplay between Polymer Crystallization and Liquid-Liquid Demixing

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