Phase separation in mixtures of thermotropic liquid crystals and flexible polymers

The spinodal equation and the concentration-induced anisotropic-isotropic transition equation of the mixtures of thermotropic liquid crystals and flexible polymers have been studied by using the molecular field theory The calculations of the phase diagrams of this system show that,besides the isotropic classic spinodal curve,there ex ists an anisotropic spinodal curve which has not been reported in literature.These two spinodal curves can be linked up by the concentration-induced anisotropic-isotropic transition line.In the various phase regions,demixing may take place due to different phase separation mechanisms.The phase equilibrium curve cannot always join the.spinodal curve at a critical point.These results are considered very meaningful for the understanding of the special properties of liquid crystal/polymer composites and very useful for controlling the morphology and the performance of PDLC materials     

A Computational Study into Thermally Induced Phase Separation in Polymer Solutions under a Temperature Gradient

The influence of spatial temperature gradients on the morphological development in polymer solutions undergoing thermally induced phase separation was studied using mathematical modeling and computer simulation. The one‐dimensional mathematical model describing this phenomenon incorporates the nonlinear Cahn‐Hilliard theory for spinodal decomposition (SD), the Flory‐Huggins theory for polymer solution thermodynamics, and the slow‐mode theory and Rouse law for polymer diffusion. The resulting governing equation and auxiliary conditions were solved using the Galerkin finite element method. The temporal evolution of the spatial concentration profile from the computer simulation illustrates that an anisotropic morphology (see Figure) results when a temperature gradient is maintained along the polymer solution sample. The final anisotropic morphology depends on the overall phase separation time. If phase separation is terminated at very early stages, smaller (larger) droplets are formed in the lower (higher) temperature regions due to the deep (shallow) quench effect. On the other hand, if phase separation is allowed to proceed for a long period of time, then larger droplets are formed in the low‐temperature regions, whereas smaller droplets are developed at higher temperatures. This is due to the fact that the low‐temperature regions have entered the late stage of SD, while the high temperature regions are still in the early stage of SD. The presence of a temperature gradient during thermally induced phase separation introduces spatial variations in the change of chemical potential, which is the driving force for phase separation. These numerical results provide a better understanding of the control and optimization during the fabrication of anisotropic polymeric materials using the thermally induced phase separation technique.

     

A Computational Study of the Polymerization‐Induced Phase Separation Phenomenon in Polymer Solutions under a Temperature Gradient

This paper studied the polymerization‐induced phase separation phenomenon (spinodal decomposition) in a model binary polymer solution under a linear spatial temperature gradient for the purpose of fabricating anisotropic polymeric materials by using mathematical modeling and computer simulation. Reaction kinetics were incorporated with the non‐linear Cahn‐Hilliard theory and the Flory‐Huggins free energy expression in the model. Moreover, the slow mode theory and Rouse law were used to account for polymer diffusion. It was found that an anisotropic morphology was obtained when a temperature gradient was imposed along the polymer solution sample. The direction of the structural anisotropy, however, depended significantly on the overall phase separation time. The presence of a temperature gradient along the polymer solution sample generated a spatial variation in polymerization rate, which resulted in a spatial variation of quench depth. Consequently, at a given instant, the phase separation at different locations of the polymer solution was at different stages of spinodal decomposition. The droplet size formed along the polymer solution was therefore dependent on the polymerization rate, the quench depth and the stage of spinodal decomposition. Furthermore, the spatial temperature gradient produced a spatial variation in the process induction time, which contains the polymerization induction time and phase separation induction time. It was also found that the polymerization induction time played a significant role on the spatial variation in the overall process induction time.

     

Phase separation in mixtures of ionic liquids and water

The phase separation of ionic liquids (ILs) in water is studied by laser light scattering (LLS). For the ILs with longer alkyl chains, such as [C(8)mim]BF(4) and [C(6)mim]BF(4) (mim = methylimidazolium), macroscopic phase separation occurs in the mixture with water. LLS also reveals the coexistence of the mesoscopic phase, the size of which is in the order of 100-800 nm. In aqueous mixtures of ILs with shorter alkyl chains, such as [C(4)mim]BF(4), only the mesoscopic phase exists. The mesoscopic phase can be effectively removed by filtration through a 0.22 μm filter. However, it reforms with time and can be enhanced by lowering the temperature, thus indicating that it is controlled by thermodynamics. The degree of mesoscopic phase separation can be used to evaluate the miscibility of ILs with water. This study helps to optimize the applications of ILs in related fields, as well as the recycling of ILs in the presence of water.     

Phase equilibria and phase separation dynamics in a polymer composite containing a main-chain liquid crystalline polymer

Various topological phase diagrams of blends of main-chain liquid crystalline polymer (MCLCP) and flexible polymer have been established theoretically in the framework of Matsuyama–Kato theory by combining Flory–Huggins (FH) free energy for isotropic mixing, Maier–Saupe (MS) free energy for nematic ordering in the constituent MCLCP, and free energy pertaining to polymer chain-rigidity. As a scouting study, various phase diagrams of binary flexible polymer blends have been solved self-consistently that reveal a combined lower critical solution temperature (LCST) and upper critical solution temperature (UCST), including an hourglass phase diagram. The calculated phase diagrams exhibit liquidus and solidus lines along with a nematic–isotropic (NI) transition of the constituent MCLCP. Depending on the strengths of the FH interaction parameters and the anisotropic (nematic–nematic) interaction parameters, the self-consistent solution reveals an hourglass type phase diagram overlapping with the NI transition of the constituent MCLCP. Subsequently, thermodynamic parameters estimated from the phase diagrams hitherto established have been employed in the numerical computation to elucidate phase separation dynamics and morphology evolution accompanying thermal-quench induced phase separation of the MCLCP/polymer mixture. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3621-3630, 2006     

Phase separation and glass transition point versus composition diagrams of binary mixtures with covalent bond between components

The geometric thermodynamics approach has been used for investigation of the possible glass transition point versus composition curves and their dependence on various parameters for both mixtures and systems with covalent bond between the components (block-, graftand star-polymers) in which phase separation is possible. Predicted relationships are compared with the experiment. Conditions have been determined under which glass transition hinders the liquid-liquid separation.List of principle symbols and abbreviations T _ps phase separation (or annealing) temperature - T _ps1,T _ps2... two-phase region annealing temperature - T _{ps 0} one-phase region annealing temperature - T _g1,T _g2 glass transition temperature of the first and second component - T _g,T _g glass transition temperature of phases with the compositionx andx - T _g ⁰ glass transition temperature of one-phase system - T _b temperature bordering the two-phase region at which the glass transition affects the phase separation - T_bin temperature of the liquid-liquid phase transition - M ₁,M ₂ molecular mass of 1st (rigid) and 2nd (soft) components, correspondingly - x, x compositions (fraction of the second component) in the first and second phases - x_trunc the value of the fraction of the second component at which the concentration profile is truncated by the glass transition - x _ent,M _ent the composition and molecular mass of the entrance beneath the binodal surface - x _cr,M _cr the critical composition and molecular mass - x _ent,x _ent the compositions of the first and second phases at the point of the entrance of the composition curve beneath the binodal surface - x_ex M _ex the composition and molecular mass of the composition curve exit from under the binodal surface - volume fraction - CPC cloud point curve - GTD glass transition diagram - GTCSS glass transition curve of a single phase system - LCP lower critical point - UCP upper critical point     

Phase separation kinetics in mixtures of polymers and liquid crystals

Light scattering has been used to study phase separation kinetics in mixtures containing liquid crystals and epoxy resins. In the samples studied, phase separation was induced by the polymerization of the resins with an appropriate curing agent. Experiments were carried out at different compositions and at different temperatures. The results show that the kinetic mechanism of phase separation is composition dependent. For high liquid crystal content the data are in qualitative agreement with existing theories describing spinodal decomposition; at lower concentrations the mechanism is different. The physical properties of the resulting materials are independent of the decomposition mechanism. The data have also been analysed considering the scaling behaviour expected for late stages of phase separation in polyinduced meric mixtures. Samples obtained in a narrow concentration range, where the two kinetic mechanisms overlap, exhibit peculiar physical properties.     

RMC_POT: A computer code for reverse monte carlo modeling the structure of disordered systems containing molecules of arbitrary complexity

An approach has been devised and tested for preserving the molecular dynamics molecular geometry taking into account energetic considerations during Reverse Monte Carlo (RMC) modeling. Instead of the commonly used fixed neighbor constraints, where molecules are held together by constraining distance ranges available for the specified atom pairs, here molecules are kept together via bond, angle, and dihedral potential energies. The scaled total potential energy contributes to the measure of the goodness‐of‐fit, thus, the atoms can be prevented from drifting apart. In some of the calculations (Lennard‐Jones and Coulombic) nonbonding potentials were also applied. The algorithm was successfully tested for the X‐ray structure factor‐based structure study of liquid dimethyl trisulfide, for which material now significantly more sensible results have been obtained than during previous attempts via any earlier version of RMC modeling. It is envisaged that structural modeling of a large class of materials, primarily liquids and amorphous solids containing molecules of up to about 100 atoms, will make use of the new code in the near future. © 2012 Wiley Periodicals, Inc.     

Phase separation and the kinetics of phase coarsening in commercial impact polypropylene copolymers

The phase segregation and subsequent minor phase coarsening of a commercial impact polypropylene copolymer was studied. The major components of the impact polypropylene copolymer studied were 82.4 wt % polypropylene homopolymer and 17.6 wt % ethylene-propylene rubber (EPR). The system was artificially manipulated to ensure homogeneity by precipitation from solution with a nonsolvent. This ensured that the initial system did not exhibit large-scale phase segregation. The homogeneous initial system was subjected to storage in the melt at 193°C for a series of times. The two-phase morphology of commercial impact polypropylenes was generated in the melt state by storage in the melt for various periods of time from 5 s to 1 h. Small nuclei of particles appeared at short time and increased in volume with increasing time in the melt state. The coarsening of the minor phase EPR component was shown to follow the theoretically predicted d ～ t^1/3 and N ～ t^?1 (where d = diameter, N = number of particles, and t = time in the melt) relationships to a close approximation in accord with Ostwald ripening theory. At short times these relationships were not obeyed. The indication was that the long-time coarsening regime was not entered until several minutes elapsed in the melt state. The particle size distribution was initially quite narrow and exhibited a trend of broadening at longer times of coarsening. This may be due to a shift from the short-time regime to the long-time coarsening regime. The initial polymer, which was precipitated from solution, was shown not to have undergone large-scale phase segregation in that it exhibited a one-phase morphology (i.e., no particles with > 0.1 μm diameter) as determined by ¹²⁹Xe NMR spectroscopy. The precipitated blend produced incipient particle nuclei (> 0.1 μm diameter) after a very short time (5 s) in the melt state. © 1994 John Wiley & Sons, Inc.     

Scattering properties,stability analysis,and phase separation of polyelectrolyte mixtures

The conditions of stability for weakly charged polyelectrolyte mixtures are analyzed from a scattering theory developed previously. In the thermodynamic limit of zero wave vector q = 0, it is found that electrostatic interaction induces a compatibility enhancement which is discussed for various cases of charge distributions. The condition of microphase separation transition at the wave vector for which the scattering is a maximum is also discussed. © 1993 John Wiley & Sons, Inc.     

Phase separation,porous structure,and cure kinetics in aliphatic epoxy resin containing hyperbranched polyester

Thermosetting blends of an aliphatic epoxy resin and a hydroxyl‐functionalized hyperbranched polymer (HBP), aliphatic hyperbranched polyester Boltorn H40, were prepared using 4,4′‐diaminodiphenylmethane (DDM) as the curing agent. The phase behavior and morphology of the DDM‐cured epoxy/HBP blends with HBP content up to 40 wt % were investigated by differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA), and scanning electron microscopy (SEM). The cured epoxy/HBP blends are immiscible and exhibit two separate glass transitions, as revealed by DMA. The SEM observation showed that there exist two phases in the cured blends, which is an epoxy‐rich phase and an HBP‐rich phase, which is responsible for the two separate glass transitions. The phase morphology was observed to be dependent on the blend composition. For the blends with HBP content up to 10 wt %, discrete HBP domains are dispersed in the continuous cured epoxy matrix, whereas the cured blend with 40 wt % HBP exhibits a combined morphology of connected globules and bicontinuous phase structure. Porous epoxy thermosets with continuous open structures on the order of 100–300 nm were formed after the HBP‐rich phase was extracted with solvent from the cured blend with 40 wt % HBP. The DSC study showed that the curing rate is not obviously affected in the epoxy/HBP blends with HBP content up to 40 wt %. The activation energy values obtained are not remarkably changed in the blends; the addition of HBP to epoxy resin thus does not change the mechanism of cure reaction of epoxy resin with DDM. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 889–899, 2006     

Phase separation in thin films of polymer blends: The influence of symmetric boundary conditions

Using nuclear reaction analysis composition‐depth profiling, we investigate the influence of symmetric/asymmetric confining walls on the equilibrium configuration of thin films of phase‐separated polymer blends. Depth profiles of samples annealed under symmetric boundary conditions show a laterally averaged concentration, while samples confined by nonsymmetric walls show (as in earlier studies) clear separation into two thin layers of coexisting phases. This suggests that for phase separation under symmetric boundary conditions the interface between the two phases is orthogonal to the sample plane, in line with recent theoretical discussion. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 831–837, 2000     

Self‐assembly of nanorod/nanoparticle mixtures in polymer brushes

The aggregation behavior and phase separation of nanorod (NR)/nanoparticle (NP) nanoinclusions immersed in semiflexible polymer brushes (PBs) are investigated by using molecular dynamics simulations. A variety of phases are formed by varying the size ratio q = σ_r/σ_p, where σ_r and σ_p are the diameters of NR and NPs, respectively, and the attractive interactions ε_M between NR/NP nanoinclusions and PBs. Ordered structures of NRs surrounded by large NPs are observed for the small size ratio q, and a dispersed mixture phase appears for the moderate size ratio q at weak attractive interaction. Meanwhile, the crystallization of NRs occurs at strong attractive interaction for the large size ratio q and a main face‐centered cubic (fcc) structure combined with a small amount of hexagonal‐closed packed (hcp) structure is observed. This investigation can provide some insights into the self‐assembly of complex nanoinclusions and promise a new approach for controlling the self‐assemble behavior of NPs. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 299–309     

Phase separation time/temperature dependence of some thermoplastics-modified thermosetting systems

The phase separation processes of various thermoplastics-modified thermosetting systems which show upper critical solution temperature (UCST) or lower critical solution temperature (LCST) were studied with emphasis on the temperature dependency of the phase separation times. It was found that the phase separation time-temperature relationship follows the Arrhenius equation. The cure-induced phase separation activation energy E _a (ps) generated from the equation is independent of the method used to measure phase separation time. In our experimental ranges it is found that E _a (ps) is independent of the thermoplastic (TP) content, TP molecular weight and curing rate but it varies with the cure reaction kinetics and the chemical environments of the systems. __________ Translated from Acta Polymerica Sinica, 2007, 8: 725–730 [译自: 高分子学报]     

Effect of Concentration Gradient on the Morphology Development in Polymer Solutions Undergoing Thermally Induced Phase Separation

Anisotropic porous polymeric materials fabricated from the phase separation method via spinodal decomposition are used in various practical engineering applications. We studied the formation of anisotropic porous polymeric materials numerically, by imposing an initial linear concentration gradient across a model polymer solution. The initial concentration gradient is placed at three different regions of the polymer sample for comparison purposes. All the simulation results are in good agreement with published experimental observations, which are reported from the applications of porous polymeric membranes. The structure development shows that an anisotropic porous morphology forms when an initial linear concentration gradient is applied to the model polymer solution.

     

Small-angle neutron scattering studies of dynamics and hierarchical pattern formation in binary mixtures of polymers and small molecules

We present the dynamics of the composition fluctuations and pattern formation of two-component systems in both single-phase and two-phase states as studied by time-resolved small-angle neutron scattering and light scattering. Two-component systems to be covered here include not only dynamically symmetric systems, in which each component has nearly identical self-diffusion coefficients, but also dynamically asymmetric systems, in which each component has different self-diffusion coefficients. We compare the dynamic behaviors of the two systems and illuminate their important differences. The scattering studies presented for dynamically asymmetric systems highlight that stress–diffusion coupling and viscoelastic effects strongly affect the dynamics and pattern formation. For dynamically symmetric systems, we examine the universality existing in both polymer systems and small-molecule systems as well as new features concerning the time evolution of hierarchical structures during phase separation via spinodal decomposition over a wide range of wave numbers (up to four orders of magnitude). For both systems, we emphasize that polymers provide good model systems for studying the dynamics and pattern formation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3027–3062, 2004     

Phase separation by continuous quenching: similarities between cooling experiments in polymer blends and reaction-induced phase separation in modified thermosets

Small angle light scattering (SALS) has been applied to study the phase separation kinetics in a binary polymer mixture of poly(ethyl methyl siloxane) (PEMS) and poly(dimethyl siloxane) (PDMS). The phase separation was induced by cooling an initially homogeneous mixture with well defined cooling rates. The results have been compared to time resolved SALS and microscopy in the course of reaction-induced phase separation in mixtures of an epoxy resin and polysulfone (PSU). For the critical PEMS/PDMS mixture with an upper critical point it was found in a continuous quenching experiment that the time evolution of the scattered light intensity I(q,t) scales with the cooling rate. The similarity to the scaling behavior of I(q,t) in isothermal experiments after fast quenches (scaled by the quench depth) is discussed. A secondary phase separation was found and has been explained by the competition between the growth of the two phase structure during cooling and the mutual diffusion without the assumption of gelation or vitrification. For the epoxy/PSU mixture with 15% PSU, after the appearance of a bicontinuous structure a secondary phase separation was observed. Mixtures with higher PSU-contents formed epoxy-rich droplets in the PSU-rich matrix by nucleation and growth mechanism. The frustration of the structure growth can be explained by approaching vitrification of one or both phases. The similarity between continuous cooling experiments in blends and the reaction-induced phase separation have been discussed in the generalized χN vs. composition phase diagram (N: degree of polymerization, χ: Flory-Huggms interaction parameter).     

Phase separation kinetics in mixtures of flexible polymers and low molecular weight liquid crystals

A dynamic Monte Carlo (MC) simulation is performed to investigate the phase behavior of mixtures of flexible polymers and low molecular weight thermotropic liquid crystals (LCs). The polymer is represented by three‐dimensional self‐avoiding lattice chains, while the LC is described by the Lebwohl‐Lasher nematogen model. The initially homogeneous rod‐coil mixture is, following a deep quench, separated into an isotropic phase rich in coils and a nematic phase rich in rods. The underlying spinodal decomposition (SD) process is then simulated and studied extensively. This is the first simulation of SD in a rod‐coil mixture where the nematic ordering is included. Concentration fluctuations with a conserved order parameter are thus coupled with orientation fluctuations with a nonconserved order parameter. It is found that the early stage SD in the rod‐coil mixture still exhibits the dominant spatial wavelength and that the scalar scattering functions in the late stage of SD obey the Furukawa scaling law. The kinetic difference between the so‐called isotropic and anisotropic SD regions is, however, much less pronounced than predicted recently by the mean‐field theory.     

Inhomogeneous phase separation kinetics in liquid binary mixtures: Sensitivity to initial local composition 2

The kinetics of phase separation subsequent to a finite temperature quench is assumed to be driven by diffusion on the altered free energy surface and is generally assumed to be slow. The situation can be different in phase separating liquid binary mixtures, especially for systems characterized by the large difference in mutual interactions between solute and solvent molecules. In such cases, the phase separation kinetics could be fast and may get completed within a short time (ns) scale. As a result, in these systems, one may observe diverse dynamical features arising out of local heterogeneity leading to the onset of phase separation through pattern formation, spinodal decomposition, nucleation, and growth. By using a coarse-grained analysis, we examine phase separation kinetics in each spatial grid and indeed observe important effects of initial heterogeneity on the subsequent evolution. Interestingly, we observe slower separation kinetics for those regions that correspond to the composition at the minimum of the high-temperature surface. The heterogeneous dynamics has been captured here through the non-linear susceptibility function, which shows a pattern similar to what is observed in the supercooled liquid. Each grid shows somewhat different dynamics in the three-stage (exponential, power-law, and logarithmic regime) phase separation dynamics. The late stage of phase separation kinetics is usually attributed to the coarsening of the phase-separated domains. However, in a liquid binary mixture, the late-stage power-law decay undergoes a further change. A new dynamical regime arises characterized by a logarithmic time dependence, which is due to the “smoothening” of the rough interface of already well-separated phases. This can also be described as opposite to the roughening transition described by Chui and Weeks [Phys. Rev. Lett. 40, 733 (1978)]. This reverse roughening transition can explain the logarithmic time dependence observed in the simulation.