Analysis of Phase Separation in Compressible Polymer Blends and Block Copolymers

Critical role of lattice vacancies in pressure-induced phase transitions of baroplastic diblock copolymers

Baroplastic diblock copolymers exhibit order-disorder transitions and melt upon compression at low temperatures, in some cases even at ambient temperatures. Their unique low-temperature processability makes them promising candidates for sustainable polymeric materials. Despite their potential, however, the molecular mechanisms governing the pressure-induced phase transitions of these copolymers remain largely unexplored. This study develops a compressible self-consistent field theory for baroplastic copolymers based on a simple lattice vacancy model that explicitly incorporates voids to account for compressibility. The theory shows that the selective presence of voids in compressible domains stabilizes the ordered phase, while a reduction of voids under compression leads to the order-disorder transition. In addition, this work demonstrates for the first time the critical role of gas absorption rates in each segment in the pressure-induced order-disorder transition of baroplastic diblock copolymers. These findings have significant implications for the rational design of baroplastic polymers with tailored low-temperature processability.

Effect of Disparity in Self Dispersion Interactions on Phase Behaviors of Molten A-b-B Diblock Copolymers

Phase behaviors of molten A-b-B diblock copolymers with disparity in self dispersion interactions are revisited here. A free energy functional is obtained for the corresponding Gaussian copolymers under the influence of effective interactions originating in the localized excess equation of state. The Landau free energy expansion is then formulated as a series in powers of A and B density fluctuations up to 4th order. An alternative and equivalent Landau energy is also provided through the transformation of the order parameters to the fluctuations in block density difference and free volume fraction. The effective Flory χ is elicited from its quadratic term as the sum of the conventional enthalpic χH and the entropic χS that is related to energetic asymmetry mediated by copolymer bulk modulus. It is shown that the cubic term is balanced with Gaussian cubic vertex coefficients in corporation with energetics to yield a critical point at a composition rich in a component with stronger self interactions. The full phase diagrams with classical mesophases are given for the copolymers exhibiting ordering upon cooling and also for others revealing ordering reversely upon heating. These contrasting temperature responses, along with the skewness of phase boundaries, are discussed in relation to χH and χS. The pressure dependence of their ordering transitions is either barotropic or baroplastic; or anomalously exhibits anomalously both at different stages. These actions are all explained by the opposite responses of χH and χS to pressure.

Polyacrylonitrile-b-Polystyrene Block Copolymer-Derived Hierarchical Porous Carbon Materials for Supercapacitor

The use of block copolymers as a sacrificial template has been demonstrated to be a powerful method for obtaining porous carbons as electrode materials in energy storage devices. In this work, a block copolymer of polystyrene and polyacrylonitrile (PS-b-PAN) has been used as a precursor to produce fibers by electrospinning and powdered carbons, showing high carbon yield (~50%) due to a low sacrificial block content (f_PS ≈ 0.16). Both materials have been compared structurally (in addition to comparing their electrochemical behavior). The porous carbon fibers showed superior pore formation capability and exhibited a hierarchical porous structure, with small and large mesopores and a relatively high surface area (~492 m²/g) with a considerable quantity of O/N surface content, which translates into outstanding electrochemical performance with excellent cycle stability (close to 100% capacitance retention after 10,000 cycles) and high capacitance value (254 F/g measured at 1 A/g).

Phase Transitions in Poly(vinylidene fluoride)/Polymethylene-Based Diblock Copolymers and Blends

The crystallization and morphology of two linear diblock copolymers based on polymethylene (PM) and poly(vinylidene fluoride) (PVDF) with compositions PM23-b-PVDF77 and PM38-b-PVDF62 (where the subscripts indicate the relative compositions in wt%) were compared with blends of neat components with identical compositions. The samples were studied by SAXS (Small Angle X-ray Scattering), WAXS (Wide Angle X-ray Scattering), PLOM (Polarized Light Optical Microscopy), TEM (Transmission Electron Microscopy), DSC (Differential Scanning Calorimetry), BDS (broadband dielectric spectroscopy), and FTIR (Fourier Transform Infrared Spectroscopy). The results showed that the blends are immiscible, while the diblock copolymers are miscible in the melt state (or very weakly segregated). The PVDF component crystallization was studied in detail. It was found that the polymorphic structure of PVDF was a strong function of its environment. The number of polymorphs and their amount depended on whether it was on its own as a homopolymer, as a block component in the diblock copolymers or as an immiscible phase in the blends. The cooling rate in non-isothermal crystallization or the crystallization temperature in isothermal tests also induced different polymorphic compositions in the PVDF crystals. As a result, we were able to produce samples with exclusive ferroelectric phases at specific preparation conditions, while others with mixtures of paraelectric and ferroelectric phases.

Pressure Effects on Self-Assembly in Mixtures Containing Zwitterionic Amphiphiles

To understand the responses of self-assembly in mixtures containing zwitterionic amphiphilic chains to high pressure, we introduce a self-consistent field theory in combination with a molecular equation-of-state model for them in a primitive way. The free energy density for those in the bulk state is first formulated. Its locally equilibrated excess part is then incorporated into Edwards Hamiltonian along with the electrostatic energy contributions to elicit the saddle point approximation to the partition function with proper self-consistent field equations. It is shown that charge-charge correlations enhance self-assembling tendency for the amphiphiles with the opposite charges on one component side, as the medium dielectric constant ε_r decreases. Those with the opposite charges at the two chain ends respond in a more complicated way to ε_r. Densification by applied pressure strengthens the self-assembly for both at a moderate ε_r, similar to typical phospholipids, but pressure effects are strongly dependent on the position of charges along the chains at a lower ε_r. It is argued that the manipulation of the dielectric environment and disparity in component dispersion interactions can yield useful materials exhibiting various types of baroresponsivity or thermoresponsivity with re-entrant self-assembly.

Phase Behaviors in Compressible Polymer Blends

We study phase behaviors in compressible polymer blends by using an equation of state in the framework of classical density-functional theory. The phase behaviors are explored by decomposing the compressible mixing of polymers into two steps: incompressible mixing as holding the volume and density relaxation at the given pressure. There exists both upper consolute pressure (UCP) and lower consolute pressure (LCP). LCP-type behaviors are driven by the entropy effect of asymmetric size of molecules, while UCP-type behaviors are driven by energetic interactions. The value of LCP follows a scaling of O(N^-2), which can be improved to O(N^-1.8) by taking into account the effects of random chain conformation. The volume of LCP-type polymers expands upon mixing, while that of UCP-type polymers contracts. A closed-loop phase coexisting curve may appear because of the interplay between UCP- and LCP-type behaviors. At the UCP/LCP boundary, the mixing free energy of density relaxation is much smaller than that of both UCP- and LCP-type behaviors. The contribution from incompressible mixing step always dominates the phase behaviors, while that from density relaxation step could distinguish UCP-type between LCP-type behaviors.

Identification of Some New Triply Periodic Mesophases from Molten Block Copolymers

Using field-theoretic simulations based on a self-consistent field theory (SCFT) with or without finite compressibility, nanoscale mesophase formation in molten linear AB and ABC block copolymers is investigated in search of candidates for new and useful nanomaterials. At selected compositions and segregation strengths, the copolymers are shown to evolve into some new nanostructures with either unusual crystal symmetry or a peculiar morphology. There exists a holey layered morphology with Im3 symmetry, which lacks one mirror reflection compared with Im3m symmetry. Also, a peculiar cubic bicontinuous morphology, whose channels are connected with tetrapod units, is found to have Pn3m symmetry. It is shown that there is another network morphology with tripod connections, which reveals P432 symmetry. The optimized free energies of these new mesophases and their relative stability are discussed in comparison with those of double gyroids and double diamonds.

MOLECULAR MODELING OF THERMAL AND MECHANICAL PROPERTIES OF ELASTOMERS: A REVIEW

Elastomers have varied applications from adhesives, sealants, encapsulants, and coatings to specialty usage in electronics, aviation, optical, and communications industries due to their high structural stability. In addition, more and more biological applications of elastomeric compounds are gaining ground, particularly in mimetic architecture. Modeling and simulation provide tools by which the interactions leading to various structure–property relationships can be explored at the micro level. An understanding of these processes could cut down on the extensive and expensive trial-and-error experiments as well as provide a benchmark for material design. This review article explores the work done by different groups, especially at the molecular level, to model the properties of both thermoplastic and thermoset elastomers. Each presents its own challenges and solutions: from microphase separation to network building and force field parameterization. The results of these modeling efforts along with the challenges are presented in this review work.

Superposition in Flory-Huggins χ and Interfacial Tension for Compressible Polymer Blends

We investigate theoretically the response of interfacial tension γ for compressible polymer blends to thermodynamic variables. Helfand's self-consistent field theory is first extended to be combined with an off-lattice equation-of-state model to describe compressibility. Typical incompatible blends reveal that the effects of temperature and pressure (T-P) on γ are superposed into a single curve by a dimensionless pressure variable through the superposition in Flory-Huggins χ and density. In the case of polymer blends with strong compressibility difference, γ shows an anomaly upon pressurization with no T-P superposition, even though χ still follows the superposition.

Concentration fluctuation effects on the phase behavior of compressible diblock copolymers

A Hartree analysis has been performed for compressible diblock copolymers of incompatible pairs to investigate the concentration fluctuation effects on their microphase separation behavior. The free energy in the Hartree analysis is obtained from the self-consistent correction to its mean-field cousin, which was recently formulated for such copolymer systems. The mean-field phase diagram is shown to be significantly affected by the fluctuation effects as the copolymer chain size N is lowered. An effective interaction chi(cRPA), which carries not only the change in contact interactions but also the compressibility difference between block components, plays a key role in understanding of the phase behavior and the pressure responses of various thermodynamic transitions for the copolymers with finite sizes. In particular, a symmetric copolymer at disorder-to-lamella transition is found to satisfy Nchi(cRPA)(q*)=10.495+41.022N(-1/3) when evaluated at a characteristic wave number q* for ordered microphases.

Effect of hydrostatic pressure on closed-loop phase behavior of block copolymers

The effect of hydrostatic pressure (P) on closed-loop phase behavior of deuterated polystyrene-block-poly(n-pentyl methacrylate) copolymers [dPS-PnPMA] was investigated by using small-angle neutron scattering and birefringence. For P<20.7 bar, dPS-PnPMA exhibited a lower disorder-to-order transition temperature (T(LDOT)) at 175 degrees C, and then an upper order-to-disorder transition temperature (T(UODT)) at 255 degrees C. With increasing pressure both T(LDOT) and T(UODT) were markedly changed, where dT(LDOT)/dP was 725 degrees C/kbar and dT(UODT)/dP was -725 degrees C/kbar. These are consistent with predictions by the Clausius-Clapeyron equation using measured values of the volume and enthalpy changes of both transitions. The large pressure coefficients imply that the closed-loop phase behavior observed for PS-PnPMA is an entropic-driven phase transition.