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     

Morphology development of main‐chain liquid crystalline polymer fibers during solvent evaporation

A nonequilibrium thermodynamic approach has been developed for describing the emergence of fiber morphologies from a liquid crystalline polymer solution undergoing solvent evaporation, including fibrillar structures, concentric rings, and spiral structures. We utilized Matsuyama–Kato free energy for main‐chain liquid crystalline polymer (MCLCP) solutions, which is an extension of Maier–Saupe theory for nematic ordering and incorporates a chain‐stiffening, combined with Flory‐Huggins free energy of mixing. Temporal evolution of the concentration and nematic order parameters pertaining to the above free energy density of liquid crystalline polymer solution was simulated in the context of time‐dependent Ginzburg–Landau theory coupled with the solvent evaporation rate equation under the quasi‐steady state assumption. The emerged morphological patterns are discussed in relation to the phase diagram of the MCLCP solution and the rate of solvent evaporation. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 429–435, 2007     

Phase transitions in mixtures of a side-on-side chain liquid crystalline polymer and low molar mass nematic liquid crystals

Miscibility phase diagrams of mixtures of side-on side chain liquid crystalline polymers (s-SCLCP) and low molar mass liquid crystals (E48 and E44) have been established by means of polarized optical microscopy and light scattering. E48 and E44 are cyanobiphenyl-based eutectic nematic liquid crystal (LC) mixtures with nematic-isotropic transition temperatures of 93 and 105 C, respectively. The phase diagram of the s-SCLCP/E48 system reveals the coexistence of an isotropic nematic region and a single nematic phase in order of descending temperature. The single nematic phase suggests that the pair is miscible in the nematic region. On the other hand, the s-SCLCP/E44 mixture shows liquid liquid and nematic nematic coexistence phases, suggestive of the immiscibility character of the pair. These nematic phase diagrams of the s-SCLCP/E48 and s-SCLCP/E44 have been analysed in the context of the combined Flory-Huggins (FH) free energy for isotropic mixing and the Maier-Saupe (MS) free energy for nematic ordering of the mesogens. This combined FH/MS theory is capable of predicting the observed nematic phase diagrams consisting of liquid liquid, liquid nematic, nematic nematic, and the pure nematic regions. The change of colour accompanying the appearance and disappearance of the inversion walls may be attributed to the temperature dependence of birefringence.     

Phase diagrams of binary crystalline-crystalline polymer blends

A thermodynamically self-consistent theory has been developed to establish binary phase diagrams for two-crystalline polymer blends by taking into consideration all interactions including amorphous-amorphous, crystal-amorphous, amorphous-crystal, and crystal-crystal interactions. The present theory basically involves combination of the Flory-Huggins free energy for amorphous-amorphous isotropic mixing and the Landau free energy of polymer solidification (e.g., crystallization) of the crystalline constituents. The self-consistent solution via minimization of the free energy of the mixture affords determination of eutectic, peritectic, and azeotrope phase diagrams involving various coexistence regions such as liquid-liquid, liquid-solid, and solid-solid coexistence regions bound by liquidus and solidus lines. To validate the present theory, the predicted eutectic phase diagrams have been compared with the reported experimental binary phase diagrams of blends such as polyethylene fractions as well as polycaprolactone/trioxane mixtures.     

Nematic–isotropic phase behaviors of polydisperse polymer/liquid‐crystal systems: Chain‐length‐dependent interaction parameter

Phase behaviors of polydisperse polystyrene (PS)/nematic liquid‐crystal systems [P‐ethoxy ‐ benzylidene ‐ p ‐ n‐butylaniline (EBBA)] are investigated with a thermo‐optical analysis technique. We also develop a thermodynamic framework to describe the phase behaviors of polydisperse PS/EBBA systems. The proposed model is based on a modified double‐lattice model to describe isotropic mixing and Maier–Saupe theory for anisotropic ordering. To correlate the polymer chain length and energy parameters in a nematic–isotropic biphasic region and to apply the primary interaction parameter in an isotropic–isotropic phase‐transition behaviors of polydisperse PS/EBBA systems. The proposed model shows remarkable agreement with experimental data for the model systems in comparison with an existing model. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1031–1039, 2006     

Phase equilibria and photopolymerisation-induced phase transitions of mesogenic diacrylate monomer and low molecular mass liquid crystal mixture

Experimental phase diagrams of binary mesogenic mixtures of reactive mesogenic diacrylate (RM257) monomer and low molar mass liquid crystals (E7) were determined by means of differential scanning calorimetry and optical microscopy. The combined free energy densities of Flory–Huggins for liquid–liquid demixing, Maier–Saupe for nematic ordering, and phase field free energy for crystal solidification was proposed to describe the phase diagrams of the starting E7/RM257 mixtures. The phase diagram thus constructed is an ideal mixing type, exhibiting a narrow loop of isotropic + nematic (I + N) coexistence region followed by the crystal + nematic (Cr1 + N) region in descending order of temperature. Of particular interest is the permanent fixation of the mesophase structures upon photopolymerisation of neat RM257 in the corresponding nematic and crystalline phases. Upon photopolymerisation of a low RM257 content mixture in both isotropic and nematic states, the nematic–isotropic transition of E7 was found to persist. The permanent structural anchoring is seen upon photo-curing of the 90/10 RM257/E7 mixture in the crystalline state.     

Liquid phase demixing in ferroelectric/semiconducting polymer blends: An experimental and theoretical study

This article describes a combined experimental and theoretical study on nanophase structure development as a result of liquid phase demixing in solution‐cast blends of the organic semiconductor poly(9,9′‐dioctyl fluorene) (PFO) and the ferroelectric polymer poly(vinylidene fluoride‐co‐trifluoroethylene) (P(VDF‐TrFE)). Blend layers (200 nm) are prepared by spin coating a 1:9 (w/w) PFO:P(VDF‐TrFE) blend solution in a common solvent on a poly(ethylenedioxy thiophene)/poly(styrene sulfonate) substrate. Owing to the pronounced incompatibility between the two polymers, a strong phase‐separated morphology is obtained, characterized by disk‐like nanodomains of PFO embedded in a P(VDF‐TrFE) matrix, as revealed by scanning electron microscopy. By varying the processing conditions, we find the average domain size and standard deviation to increase with spinning time. The considerable increase in domain size suggests the coarsening process not to be impeded by a steep rise in viscosity. This indicates solvent evaporation to be only moderate within the experimental time frame. The evolution of the observed phase morphology is modeled using ternary diffuse interface theory integrated with a modified Flory–Huggins (FH) treatment of the homogeneous (bulk) free energy of mixing, to account for significant molecular differences between the active blend components. Using calculated FH interaction parameters, the model confirms the phase separation to occur via spinodal decomposition of the blend solution during spin coating, as suggested by experimental observations. The simulated phase morphologies as well as the modeled trends in domain growth and standard deviation compare favorably with the experimental data. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1255–1262, 2011     

On the phase behavior of blends of polymers and nematic liquid crystals

The phase behavior of mixtures of polymers and nematic liquid crystals (LC) is investigated. Two types of systems are examined. The first one deals with blends in which the polymer is made of linear chains. In this case, a systematic study of the effects of various parameters on the phase diagrams is performed. In particular, it is shown how increasing the polymer size and/or the LC molecule size increases the miscibility gap of the mixture. It also reduces the region where a single nematic phase is observed in the presence of a tiny amount of polymer. Likewise, the relative effects of the isotropic and the nematic interaction parameters on the phase diagrams are examined. The second part of this investigation deals with blends involving crosslinked polymers. Here, substantial differences are observed as compared to the case where the polymer components are made of linear chains. These differences are illustrated by showing the phase diagrams in similar conditions for both blends. Unlike the case of a linear polymer matrix, it is observed that the single nematic phase and the nematic-isotropic spinodal branches are absent from the phase diagram of crosslinked polymers. This results into significant distortions of the phase diagram. In order to highlight all these effects, examples representing hypothetical blends are considered. These examples are chosen for illustration of the results in which the choice of numerical parameters is made consistently with the existing values in the literature which makes comparison with published data possible.     

Multivariable structural characterization of semicrystalline polymer blends by small‐angle light scattering

A new multi‐variable‐measurement approach for characterizing and correlating the nanoscale and microscale morphology of crystal‐amorphous polymer blends with melt‐phase behavior is described. A vertical small‐angle light scattering (SALS) instrument optimized for examining the scattering and light transmitted from structures ranging from 0.5 to 50 μm, thereby spanning the size range characteristic of the initial‐to‐late stages of thermal‐phase transitions (e.g., melt‐phase separation and crystallization) in crystal‐amorphous polymer blends, was constructed. The SALS instrument was interfaced with differential scanning calorimetry (DSC), and simultaneous SALS/DSC/transmission measurements were performed. We show that the measurement of transmitted light and SALS under H_V (cross‐polarized) optical alignments during melting can be used to reliably measure the thermodynamic (e.g., crystal melting and melt‐phase separation temperatures) and structural variables (e.g., crystalline fraction within the superstructures and volume fraction of superstructures) necessary for describing the multiphase behavior of crystal‐amorphous blends in one combined measurement. We also evaluate the orientation correlations of crystalline volume elements within the superstructures. Our results indicate that simultaneous measurement of transmitted light can provide a reliable estimate of the total scattering from density and orientation fluctuations and the melt‐phase separation temperature of polymer blends. For solution‐cast poly(?‐caprolactone)/poly(D,L‐lactic acid) blends, our multivariable measurements during melting provide the parameters necessary to generate a crystal–liquid and liquid–liquid phase diagram and characterize the solid‐state morphology. This opens up the challenge to explore use of our vertical SALS instrument as a rapid and convenient method for developing structure–property relationships for crystal‐amorphous polymer blends. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2714–2727, 2002     

Phase behavior of polystyrene acrylonitril copolymer and polymethylmethacrylate blends under shear

Polymer blends undergo external stresses such as pressure and shear in course of processing cycles. The knowledge of their phase behavior at each step of these cycles is crucial for understanding their physical properties and eventually improves their performance in practical applications. The effects of shear on the phase diagram of binary polymer blends are considered. A theoretical formulism is used upon which the free energy is the sum of two terms. The first term is modeled with the Flory–Huggins free energy of mixing and describes the thermodynamic behavior of the system in the quiescent state. The second term represents the excess free energy stored during flow. In the presence of shear flow, the excess free energy is expressed in terms of the viscosity and the shear modulus. Both quantities depend on composition and shear rate. The curvature of the variation of viscosity versus composition has a tremendous impact upon the nature of phase separation. Phase diagrams are described by the spinodal curves and show for the case considered here miscibility enhancement with increasing shear rate. A good correlation is found with experimental data of the literature on blends of polystyrene acrylonitril copolymer and polymethylmethacrylate. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Miscibility and morphology of poly(ethylhexylacrylate)/liquid crystal blends prepared under different conditions

A comparative study of the phase diagrams and morphology of blends of poly(2‐ethylhexylacrylate) and low molecular weight liquid crystals (LCs) prepared under different conditions is presented. Two LCs are used; one is the 4‐cyano‐4′‐n‐pentyl‐biphenyl and the other is the eutectic mixture of cyanoparaphenylenes known as E7. Two series of blends are prepared under different conditions. The first series is obtained by the polymerization induced phase separation (PIPS) process under UV‐curing starting from a monomeric mixture, while the second series is prepared by a combination of the solvent induced phase separation and the thermally induced phase separation process starting from a mixture containing a commercial polymer with known molecular weight. Using gel permeation chromatography, it is found that the polymer molecular weight of the UV‐cured systems decreases with the concentration of LC in the precursor mixture. The experimentally obtained phase diagrams of these two series of systems show a miscibility shift at the composition where the molar mass of the polymer in the PIPS/UV blend exceeds that of the commercial polymer. Data are rationalized in terms of the Flory‐Huggins theory of isotropic mixing and the Maier‐Saupe theory of nematic order. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 18–27, 2007     

Model phase diagrams of binary nematic mixtures. A comparative study between linear and crosslinked polymers

Model calculations of phase diagrams of side chain liquid crystal polymers (SCLCP) and low molecular weight liquid crystals (LMWLC) are presented. The polymer is assumed to have grafted side chain units characterized by a nematic‐isotropic transition temperature T_{NI 2}, and the LMWLC presents also a similar transition at a temperature T_{NI 1} . The model calculations can accommodate for the cases where the latter two temperatures are comparable or widely different. For the sake of illustration, the case T_{NI 1} = 60°C and T_{NI 2} = 80°C is adopted here. The main point of interest here is to perform a comparative study of the equilibrium phase diagrams of SCLCP made either of linear free chains or crosslinked chains forming a single network. To our knowledge this is the first comparative study of the phase behavior of binary nematic mixtures involving linear and crosslinked polymer matrices which permits to clearly identify the effects of crosslinks present in the polymer matrix. The crosslinks attribute elasticity to the polymer constituent which induces important distortions in the phase diagram. To highlight these distortions, examples of hypothetical binary nematic mixtures are chosen involving both linear and crosslinked polymers with side chain mesogen units. The quadrupole interaction parameter between the two nematogens is related to individual parameters via a geometric average ν²₁₂ = κν₁₁ν₂₂ with a coupling parameter κ. Different values of this parameter are considered and the impact of coupling strength on the phase diagram is discussed for crosslinked and linear polymers.     

Mixtures of liquid-crystalline polymers

A density-functional expansion method is used to derive the free energy of a polymer mixture. The expression obtained includes the entropy of mixing, the entropy of configuration of the chains and the interactions (both isotropic and anisotropic ones). The chains are modelled as interacting elastic lines (bend curvature). The method is very general, and we only focus our attention on binary mixtures. The phase diagram and the order parameters are calculated. We show some results for two types of mixtures: a nematic polymer in a non-mesomorphic particle (polymer or solvent) and in another nematic liquid crystal (small-molecule or polymer). We discuss the influence of the molecular weights, the persistence length and the interactions on the phase separation.     

The phase diagram of a single polymer chain: New insights from a new simulation method

We present simulation results for the phase behavior of a single chain for a flexible lattice polymer model using the Wang-Landau sampling idea. Applying this new algorithm to the problem of the homopolymer collapse allows us to investigate not only the high temperature coil–globule transition but also an ensuing crystallization at lower temperature. Performing a finite size scaling analysis on the two transitions, we show that they coincide for our model in the thermodynamic limit corresponding to a direct collapse of the random coil into the crystal without intermediate coil–globule transition. As a consequence, also the many chain phase diagram of this model can be predicted to consist only of gas and crystal phase in the limit of infinite chain length. This behavior is in agreement with findings on the phase behavior of hard-sphere systems with a relatively short-ranged attractive square well. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2542–2555, 2006     

Induced smectic phases in phase diagrams of binary nematic liquid crystal mixtures

To elucidate induced smectic A and smectic B phases in binary nematic liquid crystal mixtures, a generalized thermodynamic model has been developed in the framework of a combined Flory-Huggins free energy for isotropic mixing, Maier-Saupe free energy for orientational ordering, McMillan free energy for smectic ordering, Chandrasekhar-Clark free energy for hexagonal ordering, and phase field free energy for crystal solidification. Although nematic constituents have no smectic phase, the complexation between these constituent liquid crystal molecules in their mixture resulted in a more stable ordered phase such as smectic A or B phases. Various phase transitions of crystal-smectic, smectic-nematic, and nematic-isotropic phases have been determined by minimizing the above combined free energies with respect to each order parameter of these mesophases. By changing the strengths of anisotropic interaction and hexagonal interaction parameters, the present model captures the induced smectic A or smectic B phases of the binary nematic mixtures. Of particular importance is the fact that the calculated phase diagrams show remarkable agreement with the experimental phase diagrams of binary nematic liquid crystal mixtures involving induced smectic A or induced smectic B phase.     

Phase diagrams of poly(siloxane)/liquid crystal blends

Phase diagrams of blends of poly(methylphenylsiloxane) in short PMPS and two low molecular weight liquid crystals (4‐cyano‐4′‐n‐pentyl‐biphenyl and an eutectic mixture of paraphenylenes) are reported. Two polymers with very different weight‐average molar masses are considered in an evaluation of the loss of miscibility resulting from a known increase in the weight‐average molar mass. The experimental diagrams have been constructed via polarized optical microscopy and are rationalized in terms of the Flory–Huggins theory of isotropic mixtures and the Maier–Saupe theory of nematic order. The results show a good agreement between the theory and experiments and reveal a remarkable enhancement of miscibility with respect to similar systems involving poly(dimethylsiloxane). Variations of the interaction parameter with the temperature are compared for different systems of polysiloxanes. The effects of the nature of the liquid crystal and the polymer molar mass on the χ parameter are evaluated. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 39–43, 2003     

Theory of a helicoidal cholesteric phase induced by an external field

We present a mean field theory to describe a helicoidal cholesteric phase for mixtures of a chiral nematic liquid crystal (LC) and a polymer chain as well as for pure chiral nematic LC molecules in the presence of a longitudinal external field parallel to the pitch axis of a cholesteric (Ch) phase. The free energy of the helicoidal Ch phase (Ch_H) is derived as a function of a usual orientational order parameter and an order parameter of the Ch_H phase. On increasing the strength of the external field, we find that the Ch phase changes to the nematic (N) phase through the Ch_H phase. Depending on the temperature and the strength of the external field, we find the second-order N–Ch_H and Ch_H–Ch phase transitions and the first-order paranematic (pN)–N, pN–Ch_H and pN–Ch phase transitions. We also predict phase diagrams in mixtures of a flexible polymer and a Ch LC molecule under the external field.     

Poly(ethylene oxide)/poly(methyl methacrylate) (semi-)interpenetrating polymer networks: Synthesis and phase diagrams

Interpenetrating polymer networks (IPNs) of poly(ethylene oxide) (PEO) and poly(methyl methacrylate) (PMMA) were prepared by simultaneous network formation. The PEO network was produced by acid-catlayzed self-condensation of α,ω-bis(triethoxysilane)-terminated PEO in the presence of small amounts of water. The PMMA network was formed by free radical polymerization of MAA in the presence of divinylbenzene as crosslinker. The reaction conditions were adjusted to obtain similar crosslinking kinetics for both reactions. An attempt was made to construct a phase diagram of the IPNs by measuring the composition of the IPNs at the moment of the appearance of the phase separation, as indicated by the onset of turbidity. This composition could be determined because the siloxane crosslinks of the PEO network could be hydrolyzed in aqueous NaOH with the formation of linear, soluble PEO chains. The phase diagram was compared with phase diagrams of blends of linear polymers and of semi-IPNs (crosslinked PMMA and linear PEO), obtained under similar conditions, i.e. polymerization of MMA in the presence of varying amounts of PEO. It was observed that the form of the phase diagrams of the linear polymers is similar to that of the IPNs, but is quite different from that of the semi-IPNs. Thus, homogeneous transparent materials containing up to 60% of PEO could be prepared in the blends and the IPNs, but in the semi-IPNs, phase separation occurred with PEO contents as low as 10%.     

Binary versus ternary interactions in a completely miscible three‐polymer blend system: Poly(ϵ‐caprolactone) with two different methacrylic polymers

A truly miscible ternary miscible blend consisting of poly(?‐caprolactone) (PCL), poly(phenyl methacrylate), and poly(benzyl methacrylate) (PBzMA) was discovered. The three‐polymer blend system was completely miscible within the entire composition range at ambient temperature up to about 150 °C, and ternary phase diagrams at increasing temperatures were characterized and interpreted. A ternary‐interaction model based on the modified Flory–Huggins expression was used to describe the phase diagrams with the individual binary interaction strengths. The model fitted well with the experimental‐phase diagram for the ternary blend system at T = 250 °C, where the binary PCL‐PBzMA blend system is on the critical points of phase separation. Interpretation of discrepancy between the model and experimental at other temperatures was handled with an empirical approach. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 747–754, 2002