Nematic-isotropic phase behaviours of polydisperse polymer/liquid crystal systems: Applicability of continuous thermodynamics

Phase behaviours of polydisperse polystyrene (PS)/nematic liquid crystals (LCs) P-ethoxy-benzylidene-p-n-butylaniline (EBBA) are investigated by thermo-optical analysis (TOA) technique. In this study, to describe nematic-isotropic transition of the polydisperse PS/EBBA systems, a continuous distribution function to obtain the composition of polydisperse polymers is considered precisely. We apply these molar mass distributions to the extended Flory–Huggins model. The proposed semi-empirical model gives a remarkable agreement with experimental data for the model systems.     

Phase diagrams of poly(dimethylsiloxane) and 5CB blends

The phase diagrams of poly(dimethylsiloxane) (PDMS) and 4‐cyano‐4′‐n‐pentyl‐biphenyl (5CB) mixtures are studied for two systems of different molecular weights of the polymer. The experimental diagrams are established by polarized optical microscopy (POM), and analyzed using a combination of the Flory–Huggins theory of isotropic mixing and the Maier–Saupe theory of nematic order. The results are compared with those of polystyrene (PS) and 4‐cyano‐4′‐n‐octyl‐biphenyl (8CB) with analogous molecular weight of the polymer. This investigation could be useful for the choice of systems in electro‐optical devices. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 581–588, 2001     

Organizing thermodynamic data obtained from multicomponent polymer electrolytes: Salt‐containing polymer blends and block copolymers

The objective of this review is to organize literature data on the thermodynamic properties of salt‐containing polystyrene/poly(ethylene oxide) (PS/PEO) blends and polystyrene‐b‐poly(ethylene oxide) (SEO) diblock copolymers. These systems are of interest due to their potential to serve as electrolytes in all‐solid rechargeable lithium batteries. Mean‐field theories, developed for pure polymer blends and block copolymers, are used to describe phenomenon seen in salt‐containing systems. An effective Flory–Huggins interaction parameter, χ_eff , that increases linearly with salt concentration is used to describe the effect of salt addition for both blends and block copolymers. Segregation strength, χ_effN , where N is the chain length of the homopolymers or block copolymers, is used to map phase behavior of salty systems as a function of composition. Domain spacing of salt‐containing block copolymers is normalized to account for the effect of copolymer composition using an expression obtained in the weak segregation limit. The phase behavior of salty blends, salty block copolymers, and domain spacings of the latter systems, are presented as a function of chain length, composition and salt concentration on universal plots. While the proposed framework has limitations, the universal plots should serve as a starting point for organizing data from other salt‐containing polymer mixtures. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1177–1187     

Phase behaviors of partially ionized hydrogels in aqueous salt solutions: Applicability of the modified double‐lattice model

We investigated the effect of charge densities of the gel network and ionic strength of solution on swelling behaviors of ionized gels. We used the modified double‐lattice model, Flory–Erman's elastic model, and the ideal Donnan theory to describe swelling behaviors of the electrolyte bounded hydrogels. Energy parameters (?/k, δ?/k) were obtained from fitting liquid–liquid equilibria data of the linear poly‐N‐isopropylacrylamide/water system and two adjustable model parameters obtained from a nonelectrolyte hydrogel system. Calculated values agreed with experimental data for the given systems. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2333–2338, 2002     

Temperature‐induced spontaneous sol–gel transitions of poly(D,L‐lactic acid‐co‐glycolic acid)‐b‐poly(ethylene glycol)‐b‐poly(D,L‐lactic acid‐co‐glycolic acid) triblock copolymers and their end‐capped derivatives in water

The spontaneous hydrogel formation of a sort of biocompatible and biodegradable amphiphilic block copolymer in water was observed, and the underlying gelling mechanism was assumed. A series of ABA‐type triblock copolymers [poly(D,L ‐lactic acid‐co‐glycolic acid)‐b‐poly(ethylene glycol)‐b‐poly(D,L ‐lactic acid‐co‐glycolic acid)] and different derivatives end‐capped by small alkyl groups were synthesized, and the aqueous phase behaviors of these samples were studied. The virgin triblock copolymers and most of the derivatives exhibited a temperature‐dependent reversible sol–gel transition in water. Both the poly(D,L ‐lactic acid‐co‐glycolic acid) length and end group were found to significantly tune the gel windows in the phase diagrams, but with different behaviors. The critical micelle concentrations were much lower than the associated critical gel concentrations, and an intact micellar structure remained after gelation. A combination of various measurement techniques confirmed that the sol–gel transition with an increase in the temperature was induced not simply via the self‐assembly of amphiphilic polymer chains but also via the further hydrophobic aggregation of micelles resulting in a micelle network due to a large‐scale self‐assembly. The coarsening of the micelle network was further suggested to account for the transition from a transparent gel to an opaque gel. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 1122–1133, 2007     

Synthesis and characterization of mesogen‐jacketed liquid‐crystal polymers based on 2,5‐bis(4′‐alkoxyphenyl)styrene

A series of novel mesogen‐jacketed liquid‐crystal polymers, poly[2,5‐bis(4′‐alkoxyphenyl)‐styrene] (P‐n, n = 1–11), were prepared via free‐radical polymerization of newly synthesized monomers, 2,5‐bis(4′‐alkoxyphenyl)styrene (M‐n, n = 1–11). The influence of the alkoxy tail length on the liquid‐crystalline behaviors of the monomers and the polymers was investigated with differential scanning calorimetry (DSC), thermogravimetry, polarized optical microscopy (POM), and wide‐angle X‐ray diffraction (WAXD). The monomers with n = 1–4, 9, and 11 were monotropic nematic liquid crystals. All other monomers exhibited enantiotropic nematic properties. Their melting points (T_m's) decreased first as n increased to 6, after which T_m increased slightly at longer spacer lengths. The isotropic–nematic transition temperatures decreased regularly with increasing n values in an odd–even way. The glass‐transition temperatures (T_g's) of the polymers first decreased as the tail lengths increased and then leveled off when n ≥ 7. All polymers were thermally stable and entered the mesophase at a temperature above T_g. Upon further heating, no mesophase‐to‐isotropic melt transition was observed before the polymers decomposed. WAXD studies indicated that an irreversible order–order transition for the polymers with short tails (n ≤ 5) and a reversible order–order transition for those with elongated tails (n ≥ 6) occurred at a temperature much higher than T_g. However, such a transition could not be identified by POM and could be detected by DSC only on heating scans for the polymers with long tails (n ≥ 7). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1454–1464, 2003     

Preparation of block copolymers via Diels Alder reaction of maleimide‐ and anthracene‐end functionalized polymers

A number of diblock copolymers were successfully prepared by Diels–Alder reaction, between maleimide‐ and anthracene‐end functionalized poly (methyl methacrylate) (PMMA), polystyrene (PS), poly(tert‐butyl acrylate) (PtBA), and poly(ethylene glycol) (PEG) in toluene, at 110 °C. For this purpose, 2‐bromo‐2‐methyl‐propionic acid 2‐(3,5‐dioxo‐10‐oxa‐4‐azatricyclo[5.2.1.02,6]dec‐8‐en‐4‐yl)‐ethyl ester, 2 , 9‐anthyrylmethyl 2‐bromo‐2‐methyl propanoate, 3 , and 2‐bromo‐propionic acid 2‐(3,5‐dioxo‐10‐oxa‐4‐azatricyclo[5.2.1.02,6]dec‐8‐en‐4‐yl)‐ethyl ester, 4 , were used as initiators in atom transfer radical polymerization, in the presence of Cu(I) salt and pentamethyldiethylenetriamine (PMDETA), at various temperatures. On the other hand, PEG with maleimide‐ or anthracene‐end functionality was achieved by esterification between monohydroxy PEG and succinic acid monoathracen‐9‐ylmethyl ester, 1 , or 4‐maleimido‐benzoyl chloride. Thus‐obtained PMMA‐b‐PS, PEG‐b‐PS, PtBA‐b‐PS, and PMMA‐b‐PEG block copolymers were characterized by ¹H NMR, UV, and GPC. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1667–1675, 2006     

Isotropic–nematic phase separation and demixing in mixtures of spherical nanoparticles with length‐polydisperse nanorods

An extension of Onsager theory is developed to simulate isotropic–nematic phase separation in a mixture of spheres with length‐polydisperse system of rods. This work is motivated by recent experimental data on nanorod liquid crystals. Prior theoretical investigations indicate that both polydispersity and the presence of spheres should increase the biphasic–nematic phase transition, that is, the nematic cloud point. Results indicate that the phase diagrams undergo drastic changes depending upon both particle geometry and rod length polydispersity. The key geometric factor is the ratio between the sphere diameter and the rod diameter. In general, length fractionation is enhanced by the addition of spheres, which may be experimentally advantageous for separating short nanorods from a polydisperse population. Simulation results also indicate that the nematic cloud and shadow curves may cross one another because of the scarcity of spheres in the shadow phase. In general, these results do indicate that the nematic cloud point increases as a function of sphere loading; however, in certain areas of phase space, this relationship is nonmonotonic such that the nematic cloud point may actually decrease with the addition of spheres. This work has application to a wide range of nanoparticle systems, including mixtures of spherical nanoparticles with nanorods or nanotubes. Additionally, a number of nonspherical particles and structures may behave as spheres, including crumpled graphene and tightly coiled polymers. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Phase behaviors of nematic liquid crystal/linear polymer systems: Effect of specific interactions

A new model has been proposed that takes into account the specific interaction between nematic liquid crystal and polymer. A generalized lattice fluid model was employed to describe the specific interaction between liquid crystal and polymer. The proposed model postulates that a specific interaction between dissimilar components in a mixture has both an energetic and an entropic component. A degeneracy parameter and an interaction parameter are also discussed, followed by a comparison of the experimental data to the model. The results show that that a specific interaction plays an important role in the phase behaviors of the given systems. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 4128–4136, 2000     

Modeling structural recovery in glasses: An analysis of the peak‐shift method

Amorphous polymers below their glass‐transition temperature are inherently not at equilibrium. As a result, their structures continuously relax in an attempt to reach the equilibrium state. The current models of structural recovery can quantitatively describe the process. One of the parameters needed for the models is the nonlinearity parameter x. It has been proposed that x can be obtained from experimental data with the so‐called peak‐shift method. In this work, we use the Tool–Narayanaswamy–Moynihan model to identify the factors that determine the accuracy of the peak‐shift method and to quantify the errors in the value of x obtained from the peak‐shift method. In addition, we determine the influence of the error in x on the evaluation of the nonexponential model parameter β. Finally, the peak‐shift method is compared with the traditional curve‐fitting method for model parameter determination. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2027–2036, 2002     

Influence of molecular weight on the phase behaviors of comb‐like polymers with long n‐alkyl side chains based on mesogen‐jacketed liquid crystalline polymers

A series of comb‐like polymers, poly{2,5‐bis[(4‐octadecyloxyphenyl)oxycarbonyl]‐styrenes{ (P‐OC18s) with different molecular weights (M_n) and low molecular weight distributions have been successfully synthesized via atom transfer radical polymerization. The phase behaviors have been investigated by a combination of techniques including differential scanning calorimetry, polarized optical microscopy, wide‐angle X‐ray diffraction, and temperature‐variable FTIR spectroscopy. One hand, phase behaviors of the alkyl tails were strongly influenced by the mesogens of polymers, leading to the poor packing of the alkyl tails and the low melting. The other hand, the liquid crystalline phase structures of polymers were found to be strongly M_n dependent. The samples with M_n ≤ 4.6 × 10⁴ formed a smectic phase in low temperature and an isotropic phase in high temperature. The samples with M_n ≥ 5.2 × 10⁴ displayed a reentrant isotropic phase, which was separating the smectic phase and columnar nematic phase. Meantime, the experiment results showed that the glass temperature and the transition temperature from smectic phase to isotropic phase both slightly increased with the increase of M_nS; however, the transition temperature from isotropic phase to columnar phase sharply decreased with the M_nS improved. The reappearance of isotropic phase is due to the competing between the driving force of the enthalpy and the driving force of the entropy. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Anionic copolymerization of styrenic‐tipped macromonomers: A route to novel triblock–comb copolymers of styrene and isoprene

The following triblock–comb copolymers of isoprene (I) and styrene (S)—PS‐b‐(PI‐g‐PI)‐b‐PS, PS‐b‐[PI‐g‐(PI‐b‐PS)]‐b‐PS, and (PS‐g‐PS)‐b‐(PI‐g‐PI)‐b‐(PS‐g‐PS) (where PS is polystyrene and PI is polyisoprene)—with PS contents of 20–30% were synthesized with high‐vacuum techniques and the anionic copolymerization of styrenic‐tipped macromonomers with I and S. The macromonomers, prepared by the reaction of living PI or PS with 4‐(chlorodimethylsilyl) styrene, were used without isolation. Molecular characterization by size exclusion chromatography, size exclusion chromatography/two‐angle laser light scattering, and NMR spectroscopy indicated that the triblock–comb copolymers had high molecular and compositional homogeneity. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4030–4039, 2005     

Synthesis and characterization of side‐chain liquid crystalline ABC triblock copolymers with p‐methoxyazobenzene moieties by atom transfer radical polymerization

A series of novel side‐chain liquid crystalline ABC triblock copolymers composed of poly(ethylene oxide) (PEO), polystyrene (PS), and poly[6‐(4‐methoxy‐4′‐oxy‐azobenzene) hexyl methacrylate] (PMMAZO) were synthesized by atom transfer radical polymerization (ATRP) using CuBr/1,1,4,7,7‐pentamethyldiethylenetriamine (PMDETA) as a catalyst system. First, the bromine‐terminated diblock copolymer poly(ethylene oxide)‐block‐polystyrene (PEO‐PS‐Br) was prepared by the ATRP of styrene initiated with the macro‐initiator PEO‐Br, which was obtained from the esterification of PEO and 2‐bromo‐2‐methylpropionyl bromide. An azobenzene‐containing block of PMMAZO with different molecular weights was then introduced into the diblock copolymer by a second ATRP to synthesize the novel side‐chain liquid crystalline ABC triblock copolymer poly(ethylene oxide)‐block‐polystyrene‐block‐poly[6‐(4‐methoxy‐4′‐oxy‐azobenzene) hexyl methacrylate] (PEO‐PS‐PMMAZO). These block copolymers were characterized using proton nuclear magnetic resonance (¹H NMR) and gel permeation chromatograph (GPC). Their thermotropic phase behaviors were investigated using differential scanning calorimetry (DSC) and polarized optical microscope (POM). These triblock copolymers exhibited a smectic phase and a nematic phase over a relatively wide temperature range. At the same time, the photoresponsive properties of these triblock copolymers in chloroform solution were preliminarily studied. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 4442–4450, 2008     

N‐band Hubbard models. III. Boson–fermion and interaction–boson models for high‐Tc superconductivity

In this series of articles (I, II), N‐band Hubbard models have been considered for strongly correlated electron systems, which are realized in d–p, π–d, π–R, and σ–R conjugated systems. The magnetism and superconductivity of these systems have been elucidated in terms of effective exchange integrals (J), which are calculated by first‐principle methods. In part III of this series, the BCS–BEC crossover theory, has been introduced to elucidate the physical foundation of our J and JP model for the high‐T_c superconductivity (HTSC). The boson–fermion (BF) model for this theory is found useful for a reasonable explanation of the experimental phase diagrams of HTSC. The underlying physics of the BF model is different from that of the slave boson field‐theoretical model assuming spinon–holon condensations in the low dimension. The interaction boson model (IBM) for nuclear matter is also employed to describe the cooperative mechanisms of electron–phonon (EP), spin fluctuation (SF), charge fluctuation (CF), and many‐bands (MB) effects. This phenomenological model is useful for pictorial understanding and for the theoretical explanation of the cooperative mechanisms: (EP + SF), (SF + CF), (EP + SF + MB), etc. These are also investigated in analogy to BF model of fermionic gases, where the Feshbach resonance between boson and fermion is responsible for their coupling. The implications of these theoretical results are discussed in relation to recent ALPES and STM experiments for HTSC, which suggest the contributions of SF (J) and EP (P) interactions. The recently discovered superconductivity of boron‐doped diamond is examined as an example of two‐band sigma‐radical (σ–R) conjugated systems. Finally, the bipolaron model is briefly discussed in relation to boson–fermion model via EP interaction to superconductivity. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Heteroarm H‐shaped terpolymers through the combination of the Diels–Alder reaction and controlled/living radical polymerization techniques

Heteroarm H‐shaped terpolymers (PS)(PtBA)–PEO–(PtBA)(PS) and (PS)(PtBA)–PPO–(PtBA)(PS) [where PS is polystyrene, PtBA is poly(tert‐butyl acrylate), PEO is poly(ethylene oxide), and PPO is poly(propylene oxide)], containing PEO or PPO as a backbone and PS and PtBA as side arms, were prepared via the combination of the Diels–Alder reaction and atom transfer radical and nitroxide‐mediated radical polymerization routes. Commercially available PEO or PPO containing bismaleimide end groups was reacted with a compound having an anthracene functionality, succinic acid anthracen‐9‐yl methyl ester 3‐(2‐bromo‐2‐methylpropionyloxy)‐2‐methyl‐2‐[2‐phenyl‐2‐(2,2,6,6‐tetramethylpiperidin‐1‐yloxy)ethoxycarbonyl]propyl ester, with a Diels–Alder reaction strategy. The obtained macroinitiator with tertiary bromide and 2,2,6,6‐tetramethylpiperidin‐1‐oxy functional end groups was used subsequently in the atom transfer radical polymerization of tert‐butyl acrylate and in the nitroxide‐mediated free‐radical polymerization of styrene to produce heteroarm H‐shaped terpolymers with moderately low molecular weight distributions (<1.31). The polymers were characterized with ¹H NMR, ultraviolet, gel permeation chromatography, and differential scanning calorimetry. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3947–3957, 2006     

Ordered nanostructures at two different length scales mediated by temperature: A triphenylene‐containing mesogen‐jacketed liquid crystalline polymer with a long spacer

A mesogen‐jacketed liquid crystalline polymer (MJLCP) containing triphenylene (Tp) moieties in the side chains with 12 methylene units as spacers (denoted as PP12V) was synthesized. Its liquid crystalline (LC) phase behavior was studied with a combination of solution ¹H NMR, solid‐state NMR, gel permeation chromatography, thermogravimetric analysis, polarized light microscopy, differential scanning calorimetry, and one‐ and two‐dimensional wide‐angle X‐ray diffraction. By simply varying the temperature, two ordered nanostructures at sub‐10‐nm length scales originating from two LC building blocks were obtained in one polymer. The low‐temperature phase of the polymer is a hexagonal columnar phase (Φ_H, a = 2.06 nm) self‐organized by Tp discotic mesogens. The high‐temperature phase is a nematic columnar phase with a larger dimension (a′ = 4.07 nm) developed by the rod‐like supramolecular mesogen—the MJLCP chain as a whole. A re‐entrant isotropic phase is found in the medium temperature range. Partially homeotropic alignment of the polymer can be achieved when treated with an electric field, with the polymer in the Φ_H phase developed by the Tp moieties. The incorporation of Tp moieties through relatively long spacers (12 methylene units) disrupts the ordered packing of the MJLCP at low temperatures, which is the first case for main‐chain/side‐chain combined LC polymers with MJLCPs as the main‐chain LC building block to the best of our knowledge. The relationship of the molecular structure and the novel phase behavior of PP12V has implications in the design of LC polymers containing nanobuilding blocks toward constructing ordered nanostructures at different length scales. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 295–304     

Theoretical simulation of thermally induced phase separation in a main‐chain liquid‐crystalline polymer solution

Phase diagrams of main‐chain liquid‐crystalline polymer (MCLCP) solutions have been calculated self‐consistently on the basis of a simple addition of the Flory–Huggins free energy for isotropic mixing, the Maier–Saupe free energy for nematic ordering, and the Flory free energy for chain rigidity of the MCLCP backbone. The calculated phase diagram is an upper critical solution type overlapping with the nematic–isotropic transition. The phase diagram consists of liquid–liquid, liquid–nematic, and pure nematic regions. Subsequently, the dynamics of thermally induced phase separation and morphology development have been investigated by the incorporation of the combined free energy density into the coupled time‐dependent Ginzburg–Landau (model C) equations, which involve conserved compositional and nonconserved orientational order parameters. The numerical calculations reveal a variety of the morphological patterns arising from the competition between liquid–liquid phase separation and nematic ordering of the liquid‐crystalline polymer. Of particular interest is the observation of an inflection in the growth dynamic curve, which may be attributed to the nematic ordering of the MCLCP component, which leads to the breakdown of the interconnected domains. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 913–926, 2003     

Solution behavior of polyimide‐graft‐polystyrene copolymers in selective solvents

A polyimide‐graft‐polystyrene (PI‐g‐PS) copolymer with a polyimide backbone and polystyrene side chains was synthesized by the “grafting from” method using styrene polymerization on a polyimide multicenter macroinitiator via ATRP mechanism. The side chain grafting density z = 0.86 of PI‐g‐PS is rather high for graft‐copolymers synthesized by the ATRP method. Molecular characteristics and solution behavior of PI‐g‐PS were studied in selective solvents using light scattering and viscometry methods. In all solvents, the backbone tends to avoid contact with a poor solvent. To describe the conformation and hydrodynamic properties of PI‐g‐PS macromolecules in thermodynamically good solvents for side chains and PI‐g‐PS, the wormlike spherocylinder model is used. Macromolecules of the studied graft‐copolymer are characterized by high equilibrium rigidities (Kuhn segment length >20 nm). In Θ‐conditions, PI‐g‐PS macromolecules may be modeled by a rigid prolate ellipsoid of revolution with a low asymmetry form and a collapsed backbone as the ellipsoid core. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1539–1546     

Fracture toughness and fracture mechanism of liquid‐crystalline epoxy resins with different polydomain structures

Liquid‐crystalline (LC) epoxy resins were cured at different temperatures to obtain polydomain LC phase–cured resins. The cured resins had polydomain structures with a nematic LC phase and their domain diameters differed depending on the curing temperatures. The relationship between the domain diameter and fracture toughness of the diglycidyl ether of terephthalylidene‐bis‐(4‐amino‐3‐methylphenol) (DGETAM)/m‐phenylenediamine (m‐PDA) systems with the nematic phase and the previously reported smectic LC phase structures was investigated. It was clarified that the highly ordered LC structure (smectic phase) in each domain could improve the fracture toughness. In addition, the changes in the network orientation of the DGETAM/m‐PDA systems were evaluated by a mapping of the microscopic infrared dichroism in the fracture process and their toughening mechanism was suggested. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010