Predicting Nematic Phases of Semiflexible Polymers

Three/Four-Dimensional Printed PLA Nano/Microstructures: Crystallization Principles and Practical Applications

Compared to traditional methods, three/four-dimensional (3D/4D) printing technologies allow rapid prototyping and mass customization, which are ideal for preparing nano/microstructures of soft polymer materials. Poly (lactic acid) (PLA) is a biopolymer material widely used in additive manufacturing (AM) because of its biocompatibility and biodegradability. Unfortunately, owing to its intrinsically poor nucleation ability, a PLA product is usually in an amorphous state after industrial processing, leading to some undesirable properties such as a barrier property and low thermal resistance. Crystallization mediation offers a most practical way to improve the properties of PLA products. Herein, we summarize and discuss 3D/4D printing technologies in the processing of PLA nano/microstructures, focusing on crystallization principles and practical applications including bio-inspired structures, flexible electronics and biomedical engineering mainly reported in the last five years. Moreover, the challenges and prospects of 3D/4D printing technologies in the fabrication of high-performance PLA materials nano/microstructures will also be discussed.

What Is the Assembly Pathway of a Conjugated Polymer From Solution to Thin Films?

The hierarchical assembly of conjugated polymers has gained much attention due to its critical role in determining optical/electrical/mechanical properties. The hierarchical morphology encompasses molecular-scale intramolecular conformation (torsion angle, chain folds) and intermolecular ordering (π-π stacking), mesoscale domain size, orientation and connectivity, and macroscale alignment and (para)crystallinity. Such complex morphology in the solid state is fully determined by the polymer assembly pathway in the solution state, which, in turn, is sensitively modulated by molecular structure and processing conditions. However, molecular pictures of polymer assembly pathways remain elusive due to the lack of detailed structural characterizations in the solution state and the lack of understanding on how various factors impact the assembly pathways. In this mini-review, we present possible assembly pathways of conjugated polymers and their characteristics across length scales. Recent advances in understanding and controlling of assembly pathways are highlighted. We also discuss the current gap in our knowledge of assembly pathways, with future perspectives on research needed on this topic.

The interplay of interfaces, supramolecular assembly, and electronics in organic semiconductors

Organic semiconductors, which include a diverse range of carbon-based small molecules and polymers with interesting optoelectronic properties, offer many advantages over conventional inorganic semiconductors such as silicon and are growing in importance in electronic applications. Although these materials are now the basis of a lucrative industry in electronic displays, many promising applications such as photovoltaics remain largely untapped. One major impediment to more rapid development and widespread adoption of organic semiconductor technologies is that device performance is not easily predicted from the chemical structure of the constituent molecules. Fundamentally, this is because organic semiconductor molecules, unlike inorganic materials, interact by weak non-covalent forces, resulting in significant structural disorder that can strongly impact electronic properties. Nevertheless, directional forces between generally anisotropic organic-semiconductor molecules, combined with translational symmetry breaking at interfaces, can be exploited to control supramolecular order and consequent electronic properties in these materials. This review surveys recent advances in understanding of supramolecular assembly at organic-semiconductor interfaces and its impact on device properties in a number of applications, including transistors, light-emitting diodes, and photovoltaics. Recent progress and challenges in computer simulations of supramolecular assembly and orientational anisotropy at these interfaces is also addressed.

A metastable nematic precursor accelerates polyethylene oligomer crystallization as determined by atomistic simulations and self-consistent field theory

Using PYS, TraPPE, OPLS-L, and Flexible-Williams (FW) force field models, atomistic simulations at temperatures ranging from 450 K to 600 K are performed to predict the melt density ρ, the persistence length N_p, the nematic coupling constant α, and crystallization dynamics for pentacontane (C50). The coupling constant α arises from packing entropy of rodlike Kuhn segments and increases with increasing ρ and N_p. Together with a self-consistent field theory, N_p and α are then used to predict the isotropic-to-nematic (IN) transition temperature for polyethylene (PE) oligomers as a function of chain length. The nematic phase is found to be metastable since the IN transition temperature lies below the crystal melting temperatures for C50 in simulations using different force fields. Finally, isothermal simulations of crystallization for PE C50 oligomers and C1000 polymers show that crystal nucleation may be much accelerated by quenching below the IN transition temperature, where chains in the isotropic state first rapidly form nematic ordered domains, within which crystalline order then grows. We also find that the PYS, TraPPE, and FW models overpredict the melting temperature for C50 by around 50 K, while the most flexible OPLS-L model gives a melting temperature within around 10 K of the experimental value. Although giving a more accurate melting temperature, the slow crystallization kinetics of the OPLS-L model may limit its application in direct simulations of PE crystallization.

Thermal Fluctuations Lead to Cumulative Disorder and Enhance Charge Transport in Conjugated Polymers

All conjugated polymers examined to date exhibit significant cumulative lattice disorder, although the origin of this disorder remains unclear. Using atomistic molecular dynamics (MD) simulations, the detailed structures for single crystals of a commonly studied conjugated polymer, poly(3-hexylthiophene-2,5-diyl) (P3HT) are obtained. It is shown that thermal fluctuations of thiophene rings lead to cumulative disorder of the lattice with an effective paracrystallinity of about 0.05 in the π-π stacking direction. The thermal-fluctuation-induced lattice disorder can in turn limit the apparent coherence length that can be observed in diffraction experiments. Calculating mobilities from simulated crystal structures demonstrates that thermal-fluctuation-induced lattice disorder even enhances charge transport in P3HT. The mean inter-chain charge transfer integral is enhanced with increasing cumulative lattice disorder, which in turn leads to pathways for fast charge transport through crystals.

Tension-Induced Nematic Phase Separation in Bidisperse Homopolymer Melts

We use an analytical mean-field theory and all-atom molecular dynamics (MD) simulations to predict that external tension, together with the nematic coupling interactions, can drive phase separation of long chains from short ones in bidisperse homopolymer melts. The nematic coupling parameter α for polyethylene (PE) oligomers under applied tension is extracted from the MD simulations and used in the mean-field free energy to predict the phase boundary for bidisperse melts in which the longer chains are stretched by uniaxial tension. The predicted phase diagram is validated by direct MD simulations. We also show that extensional flow, and possibly even shear flow, may lead to nematic phase separation in molten PE oligomers, because the flow can impose a stronger tension on the longer chains than the short ones.

Crystallization in melts of short, semiflexible hard polymer chains: An interplay of entropies and dimensions

What is the thermodynamic driving force for the crystallization of melts of semiflexible polymers? We try to answer this question by employing stochastic approximation Monte Carlo simulations to obtain the complete thermodynamic equilibrium information for a melt of short, semiflexible polymer chains with purely repulsive nonbonded interactions. The thermodynamics is obtained based on the density of states of our coarse-grained model, which varies by up to 5600 orders of magnitude. We show that our polymer melt undergoes a first-order crystallization transition upon increasing the chain stiffness at fixed density. This crystallization can be understood by the interplay of the maximization of different entropy contributions in different spatial dimensions. At sufficient stiffness and density, the three-dimensional orientational interactions drive the orientational ordering transition, which is accompanied by a two-dimensional translational ordering transition in the plane perpendicular to the chains resulting in a hexagonal crystal structure. While the three-dimensional ordering can be understood in terms of Onsager theory, the two-dimensional transition can be understood in terms of 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. Based on this physical understanding, orientational ordering and translational ordering should be separable for polymer melts. A phenomenological theory based on this understanding predicts a qualitative phase diagram as a function of volume fraction and stiffness in good agreement with results from the literature.

Nematic Order Imposes Molecular Weight Effect on Charge Transport in Conjugated Polymers

Nematic order, in the bulk or at interfaces, is ubiquitous for semiflexible conjugated polymers. Nevertheless, the effect of liquid crystalline order on charge transport remains unclear. Using an analytical model, we demonstrate that nematic order leads to an enhancement in charge mobilities when compared to isotropic chains. Furthermore, we predict a quadratic dependence of the charge mobility on molecular weight of the chains. Analysis of the probability of forming hairpin defects also shows how the persistence length affects charge transport in conjugated polymers. We speculate that the prevalence of nematic order in conjugated polymers explains the reported increase in charge mobilities with molecular weight.

Demixing by a Nematic Mean Field: Coarse-Grained Simulations of Liquid Crystalline Polymers

Liquid crystalline polymers exhibit a particular richness of behaviors that stems from their rigidity and their macromolecular nature. On the one hand, the orientational interaction between liquid-crystalline motifs promotes their alignment, thereby leading to the emergence of nematic phases. On the other hand, the large number of configurations associated with polymer chains favors formation of isotropic phases, with chain stiffness becoming the factor that tips the balance. In this work, a soft coarse-grained model is introduced to explore the interplay of chain stiffness, molecular weight and orientational coupling, and their role on the isotropic-nematic transition in homopolymer melts. We also study the structure of polymer mixtures composed of stiff and flexible polymeric molecules. We consider the effects of blend composition, persistence length, molecular weight and orientational coupling strength on the melt structure at the nano- and mesoscopic levels. Conditions are found where the systems separate into two phases, one isotropic and the other nematic. We confirm the existence of non-equilibrium states that exhibit sought-after percolating nematic domains, which are of interest for applications in organic photovoltaic and electronic devices.

Thermodynamics of a Compressible Maier-Saupe Model Based on the Self-Consistent Field Theory of Wormlike Polymer

This paper presents a theoretical formalism for describing systems of semiflexible polymers, which can have density variations due to finite compressibility and exhibit an isotropic-nematic transition. The molecular architecture of the semiflexible polymers is described by a continuum wormlike-chain model. The non-bonded interactions are described through a functional of two collective variables, the local density and local segmental orientation tensor. In particular, the functional depends quadratically on local density-variations and includes a Maier–Saupe-type term to deal with the orientational ordering. The specified density-dependence stems from a free energy expansion, where the free energy of an isotropic and homogeneous homopolymer melt at some fixed density serves as a reference state. Using this framework, a self-consistent field theory is developed, which produces a Helmholtz free energy that can be used for the calculation of the thermodynamics of the system. The thermodynamic properties are analysed as functions of the compressibility of the model, for values of the compressibility realizable in mesoscopic simulations with soft interactions and in actual polymeric materials.

Chain conformations and phase behavior of conjugated polymers

Conjugated polymers may play an important role in various emerging optoelectronic applications because they combine the chemical versatility of organic molecules and the flexibility, stretchability and toughness of polymers with semiconducting properties. Nevertheless, in order to achieve the full potential of conjugated polymers, a clear description of how their structure, morphology, and macroscopic properties are interrelated is needed. We propose that the starting point for understanding conjugated polymers includes understanding chain conformations and phase behavior. Efforts to predict and measure the persistence length have significantly refined our intuition of the chain stiffness, and have led to predictions of nematic-to-isotropic transitions. Exploring mixing between conjugated polymers and small molecules or other polymers has demonstrated tremendous advancements in attaining the needed properties for various optoelectronic devices. Current efforts continue to refine our knowledge of chain conformations and phase behavior and the factors that influence these properties, thereby providing opportunities for the development of novel optoelectronic materials based on conjugated polymers.

Maier-Saupe model of polymer nematics: Comparing free energies calculated with Self Consistent Field theory and Monte Carlo simulations

Self Consistent Field (SCF) theory serves as an efficient tool for studying mesoscale structure and thermodynamics of polymeric liquid crystals (LC). We investigate how some of the intrinsic approximations of SCF affect the description of the thermodynamics of polymeric LC, using a coarse-grained model. Polymer nematics are represented as discrete worm-like chains (WLC) where non-bonded interactions are defined combining an isotropic repulsive and an anisotropic attractive Maier-Saupe (MS) potential. The range of the potentials, σ, controls the strength of correlations due to non-bonded interactions. Increasing σ (which can be seen as an increase of coarse-graining) while preserving the integrated strength of the potentials reduces correlations. The model is studied with particle-based Monte Carlo (MC) simulations and SCF theory which uses partial enumeration to describe discrete WLC. In MC simulations the Helmholtz free energy is calculated as a function of strength of MS interactions to obtain reference thermodynamic data. To calculate the free energy of the nematic branch with respect to the disordered melt, we employ a special thermodynamic integration (TI) scheme invoking an external field to bypass the first-order isotropic-nematic transition. Methodological aspects which have not been discussed in earlier implementations of the TI to LC are considered. Special attention is given to the rotational Goldstone mode. The free-energy landscape in MC and SCF is directly compared. For moderate σ the differences highlight the importance of local non-bonded orientation correlations between segments, which SCF neglects. Simple renormalization of parameters in SCF cannot compensate the missing correlations. Increasing σ reduces correlations and SCF reproduces well the free energy in MC simulations.

Phase Behavior of Poly(3-hexylthiophene-2,5-diyl)

The phase behavior of many conjugated polymers is rich with both crystalline and liquid crystalline phases. Recent computational efforts have identified the isotropic-to-nematic transition temperature for polymers such as poly(3-hexylthiophene-2,5-diyl) (P3HT). Herein, model predictions are combined with experimentally determined values of the equilibrium melting temperature as a function of chain length to provide the complete phase behavior for P3HT. Additionally, because a full description of the phase behavior requires proper accounting for the regioregularity of the chain, a thermodynamic relationship is derived to predict this behavior as a function of both chain length and regioregularity and the impact of regioregularity on the expected phase diagram is discussed.

A new insight into the isotropic-nematic phase transition in lyotropic solutions of semiflexible polymers: density-functional theory tested by molecular dynamics

Semiflexible polymers in solution are studied for a wide range of both contour length L and persistence length lp as a function of monomer concentration under good solvent conditions. Both density-functional theory (DFT) and molecular dynamics (MD) simulation methods are used, and a very good agreement between both techniques is observed for rather stiff polymers. Evidence for a new mechanism of order parameter fluctuations in the nematic phase is presented, namely collective deformations of bundles of wormlike chains twisted around each other, and the typical wavelengths and amplitudes of these modes are estimated. These long wavelength fluctuations cause a reduction of the order parameter in comparison with the DFT prediction. It is also found that DFT becomes unreliable for rather flexible polymers in predicting that the transition from the isotropic (I)-phase to the nematic (N)-phase still exists at very high monomer concentrations (which in reality does not occur). However, under conditions when DFT is accurate, it provides reliable predictions also for the width of the I-N two-phase coexistence region, which are difficult to obtain from MD in spite of the use of very large systems (up to 500 000 monomers) by means of graphics processing units (GPU). For short and not very stiff chains, a pre-transitional chain stretching is found in the isotropic phase near the I-N-transition, not predicted by theories. A comparison with theoretical predictions by Khokhlov-Semenov, Odijk, and Chen reveals that the scaled transition densities are not simply functions of L/lp only, as these theories predict, but depend on d/lp (where d is the chain diameter) as well. Chain properties in the nematically ordered phase are compared to those of chains confined in tubes, and the deflection length concept is tested. Eventually, some consequences for the interpretation of experiments are spelled out.