Phase behavior of polymer/nanoparticle blends near a substrate

We use the recent fluids density functional theory of Tripathi and Chapman [Phys. Rev. Lett. 94, 087801 (2005); J. Chem. Phys. 122, 094506 (2005)] to investigate the phase behavior of athermal polymer/nanoparticle blends near a substrate. The blends are modeled as a mixture of hard spheres and freely jointed hard chains, near a hard wall. There is a first order phase transition present in these blends in which the nanoparticles expel the polymer from the surface to form a monolayer at a certain nanoparticle concentration. The nanoparticle transition density depends on the length of the polymer, the nanoparticle diameter, and the overall bulk density of the system. The phase transition is due to both packing entropy effects related to size asymmetry between the components and to the polymer configurational entropy, justifying the so-called "entropic push" observed in experiments. In addition, a layered state is found at higher densities which resembles that in colloidal crystals, in which the polymer and nanoparticles form alternating discrete layers. We show that this laminar state has nearly the same free energy as the homogeneously mixed fluid in the bulk and is nucleated by the surface.     

Molecular modeling of phase behavior of polymer blends

Recent advances in the lattice cluster theory are applied to describe polymer blend miscibilities and variations with pressure. Extensive comparisons are made with experiment.     

Effect of grafting on nanoparticle segregation in polymer/nanoparticle blends near a substrate

Nanoparticles in polymer films have shown the tendency to migrate to the substrate due to an entropic-based attractive depletion interaction between the particles and the substrate. It is also known that polymer-grafted nanoparticles show better dispersion in a polymer matrix. Here, molecular dynamics simulations are employed to study the effect of grafting on the nanoparticle segregation to the substrate. The nanoparticles were modeled as spheres and the polymers as bead-spring chains. The polymers of the grafts and the matrix are identical in nature. For a purely repulsive system, the nanoparticle density near the surface was found to decrease as the length of grafted chains and the number of grafts increased and in the bulk, the nanoparticles are well-dispersed. Whereas, in case of attractive systems with interparticle interactions on the order of thermal energy, the nanoparticles segregated to the substrate even more strongly, essentially forming clusters on the wall and in the bulk. However, due to the presence of grafted chains on the nanoparticles, the clusters formed in the bulk are structurally anisotropic. The effect of grafts on nanoparticle segregation to the surface was found to be qualitatively similar to the purely repulsive case.     

Shear flow effect on phase behavior and morphology in polymer blends

The effect of simple shear flow on the phase behavior and morphology was investigated for both polystyrene/poly(vinyl methyl ether) (PS/PVME) and poly(methyl methacrylate)/poly(styrene‐co‐acrylonitrile) (PMMA /SAN‐29.5) blends, which have LCST (lower critical solution temperature)‐type phase diagram. The measurements were carried out using a special shear apparatus of two parallel glass plates type. The PS/PVME blends showed shear‐induced demixing and shear‐induced mixing at low and high shear rate values, respectively. In addition, the rotation speed and the sample thickness were found to have a pronounced effect on the phase behavior under shear flow. On the‐other hand, PMMA/SAN blend showed only shear‐induced mixing and the magnitudes of the elevation of the cloud points were found to be composition and molecular weight dependent. The morphology of the PMMA/SAN=75/25 blend indicated that shear‐induced mixing occurred at a critical shear rate value, below which the two phases were highly oriented and elongated in the flow direction.     

Ginzburg number and phase behavior of binary polymer blends in pressure fields

In some polymer blends the temperature and pressure dependence of thermal composition fluctuations have been measured with small angle neutron scattering. The Ginzburg number Gi, the Flory‐Huggins parameter Γ, and the phase boundaries were determined for pressure fields up to 150 MPa. In polymer blends the compressibility leads to a strongly increased Gi which could be appreciably larger than in low molecular liquids and which decreases with increasing pressure fields. Usually, the phase boundaries of UCST as well as of LCST blends shift with pressure to higher temperatures. One blend having PDMS as one component, however, shows an abnormal decrease of the phase boundaries with increasing pressure. The Clausius‐Clapeyron equation correctly predict from the experimentally determined Γ and Gi the observed pressure dependence of the phase boundaries.     

Entanglement and phase separation in hyperbranched polymer/linear polymer/solvent ternary blends

Hyperbranched polyethylene (HBPE)/linear polystyrene (PS)/chloroform (CF) solution was selected as a model system to investigate the effect of branching structure on entanglement and phase separation behavior in semi-dilute ternary polymer solutions. All the HBPE materials in this work were found to have similar chain architectures and the critical molecular weight was estimated to be 81.2 kDa. The results obtained by elastic light scattering and intrinsic fluorescence methods suggested that all ternary solutions exhibited UCST transition behavior upon cooling. Also, it was found that the increase in the molecular weight of PS led to increase in the phase separation rate, consistent with de Gennes prediction. However, the increase of molecular weight of HBPE did not monotonously reduce the compatibility of polymer components and the phase separation rate in ternary blends is as follows: medium molecular weight HBPE (HBPE-M) > high molecular weight HBPE (HBPE-H) > low molecular weight HBPE (HBPE-L). This abnormal behavior can be explained by the fact that, (i) for HBPE-L, no entanglements between HBPE chains occurred and the branching effect can be ignored, and (ii) for HBPE-M and HBPE-H, entanglement of HBPE chains can be formed, and the dilution of branches on entanglement of backbones should be taken into consideration, that is, the shorter the branches of HBPE, the higher the possibility of interpenetration of HBPE backbones between neighboring molecules and, consequently, the faster aggregation of HBPE during phase separation. Furthermore, a simple model based on decomposition reaction was proposed to quantitatively describe the phase separation kinetics and the apparent activation energies of phase separation were calculated to be −150.3 and −52.3 kJ/mol for HBPE-M/PS/CF and HBPE-H/PS/CF systems, respectively.     

Thermal behavior and film formation from an organogermanium polymer/nanoparticle precursor

In situ high-resolution transmission electron microscopy (HRTEM) was used to investigate the effect of heating on an organo-Ge polymer/nanoparticle composite material containing 4-8 nm diameter alkyl-terminated Ge nanoparticles. The product was obtained from the reduction of GeCl4 with Na(naphthalide) with subsequent capping of the -Cl surface with n-butyl Grignard reagent. The in situ HRTEM micrographs show that the product undergoes significant changes upon heating from room temperature to 600 degrees C. Two pronounced effects were observed: (i) Ge nanoparticles coalesce and remain crystalline throughout the entire temperature range, and (ii) the organo-Ge polymer acts as a source for the in situ formation of additional Ge nanoparticles. The in situ-formed Ge nanoparticles are approximately 2-3 nm in diameter. These in situ-formed nanoparticles (2-3 nm) are so dense that, together with the original ones, they build up an almost continuous crystalline film in the temperatures between 300 and 500 degrees C. Above 480 degrees C, melting of the in situ formed Ge nanoparticles (2-3 nm) is observed, while nanoparticles greater than 5 nm remain crystalline. After cooling to room temperature, the 2-3 nm Ge nanoparticles recrystallized.     

Correlation of surfactant/polymer phase behavior with adsorption on target surfaces

In this contribution, the phase behavior of a surfactant/polymer mixed system is related to the adsorption of a complex derived from the mixture onto a target surface. The phase map for the system sodium dodecyl sulfate (SDS, a model anionic surfactant)/pDMDAAC (poly(dimethyl diallyl ammonium chloride), a cationic polymer) shows behavior very typical of surfactant/oppositely charged polyelectrolyte mixtures. The predominant feature is a broad, two-phase region in the phase map which lies asymmetrically around the 1:1 stoichiometry of surfactant charge groups to polymer charge units. The overall controlling principle driving the phase separation is charge compensation. Excess of polymer yields an isotropic solution, as does a great excess of surfactant (termed resolubilization). The phase separating in the SDS/pDMDAAC system is characterized by a positive zeta-potential when the polymer is in excess and a negative zeta-potential when the surfactant is in excess. The surface charge properties of the precipitated phases are essentially identical to those of target particles (ground borosilicate glass) dispersed at the same approximate position in the phase map, suggesting that the surfactant/polymer complex at the precipitation boundary is the same as that adsorbing onto the pigment particle. This conclusion is confirmed by depletion studies which allow the polymer adsorption density to be determined. For polymer-rich systems, essentially all of the surfactant adsorbs along with the polymer via a high-affinity isotherm with a plateau coverage of about 0.8 mg polymer/m (2). Surfactant-rich systems adsorb with a similar affinity, despite the mismatch of the complex charge matching that of the particle surface. Once adsorbed, these complexes are not readily removed by rinsing, though complexes adsorbed from SDS-rich systems will lose excess surfactant upon extreme dilution. Over a wide range of surfactant-rich compositions, from 1:1 stoichiometry out toward the resolubilization zone, a chemical analysis reveals that the surfactant/polymer precipitate species consists of a 1:1 charge complex with the addition of about 0.25 mol of surfactant/mol of complex. Resolubilization of these sparingly soluble species is achieved simply by dilution to below their solubility limit.     

The phase behavior of tetramethyl bisphenol-A polyarylate/aliphatic polyester blends

The phase behavior of blends of tetramethyl bisphenol-A polyarylate (TMPAr) with various linear aliphatic polyesters characterized by the ratio of aliphatic carbons to ester groups in the repeating unit, CH₂/COO = 3 ∼ 9, was examined by differential scanning calorimetry and dynamic mechanical analysis. TMPAr/aliphatic polyester blends prepared by solvent casting were found to be miscible when the CH₂/COO ratio of aliphatic polyesters was larger than 4 and up to 9. The thermodynamic interaction parameter, B for the miscible blends was determined by the analysis of the depression of the melting point of polyester using the Hoffman-Weeks method. From the analysis of the heat of mixing data using a binary interaction model, it was concluded that strong unfavorable intramolecular interaction exists between the  CH₂ and  COO units in aliphatic polyesters and that four substituted methyl groups produces more favorable effects on the miscibility TMPAr with aliphatic polyesters. © 1998 John Wiley & Sons, Inc. J Polym Sci 36 : 201–212, 1998     

Shear mixing and phase diagram shift of polymer blends

For a low molecular weight polystyrene/polybutadiene blend, the effect of shear on the suppressing of critical fluctuations and the critical temperature has been studied and is in good agreement with the predictions of Onuki and Kawasaki. By assuming the symmetry of this critical scaling into the two phase region, together with the Taylor theory, the observed (phase separated) droplet break-up and the formation of string pattern can be explained. The exact shear dependence of T_c(γ) can be obtained by the use of the fluorescence microscope under steady shear.     

Self-vertical phase separation study of nanoparticle/polymer solar cells by introducing fluorinated small molecules

A new approach to induce self-vertical phase separation of nanoparticle/polymer hybrid solar cells is reported by introducing fluorinated small molecules into the active layer. The formation of a vertically gradient structure improves not only polymer organization but also charge transport efficiency, thus increasing the photovoltaic cell performance by a factor of 5.     

Kinetics of phase separation in polymer blends for deep quenches

Electro microscopy was used to study the phase separation kinetics of a polystyrene/polyvinylmethylether system subjected to a critical deep quench. The size of the phase-separated domains was found to increase linearly with time, implying that hydrodynamic effects control the rate of growth of the domains in the time scale and temperature range under consideration. From these measurements the growth velocity and approximate diffusion constants can be determined for three different temperatures. Comparison of these results with those obtained by light scattering on other systems and with theoretical predictions is possible by replotting in dimensionless units.     

Coalescence in quiescent polymer blends with a high content of the dispersed phase

Coalescence in molten quiescent polymer blends induced by van der Waals forces is studied theoretically. Interaction between a droplet and its nearest neighbor keeping spherical shape during drainage of the matrix trapped between them is considered. It is assumed that droplets with time dependent radius R or effective droplets with radius R + h_c/2, where h_c is the critical inter-droplet distance for breakup of the matrix trapped between them, are randomly distributed in the blend through the whole course of the coalescence. Various approaches to calculation of the average time of coalescence, t_c (calculation with preaveraged distance between a droplet and its nearest neighbor at the start of coalescence, h₀, direct averaging of t_c and averaging coalescence frequency, 1/t_c) are compared. Calculated dependence of R on the time of coalescence, t, is compared with experimental results for polypropylene/ethylene–propylene rubber (PP/EPR) blends with EPR content from 15 to 30 wt.%. Calculations using average h₀ and direct averaging of t_c lead to more-less linear dependence of R³ on t. Bare averaging of 1/t_c leads to a steeper than linear dependence of R³ on t and to unreasonably high rate of the coalescence; averaging of 1/t_c with exclusion of pairs with elapsed coalescence time leads to decreasing rate of R³ growth but unreasonably low rate of coalescence. Theories based on the concept of effective droplet radius give smaller differences among various methods of calculations of t_c than the theories assuming random distribution of the droplets. Experimental results show decreasing slope of R³ vs. t dependence, especially for a higher content of dispersed EPR. Theories using average h₀ or direct averaging of t_c predict somewhat smaller rate of coalescence than that experimentally determined for PP/EPR blends. Reasons of these differences are discussed.     

Anisotropic phase separation of polymer blends induced by polarization-selective photoisomerization

Anisotropic phase separation of polystyrene/poly(vinyl methyl ether) (PS/PVME) blends was induced by photoisomerization of trans-stilbene moieties labeled on the PS chains (abbreviated hereafter as PSS chains) using linearly polarized light. As temperature increases, the anisotropy becomes weaker and eventually disappears at 10°C above the glass transition of the PSS component. It was concluded that the elastic stress associated with the spatial distribution of the reaction is responsible for this morphological anisotropy.     

Phase behavior of polymer blends under equilibrium and nonequilibrium conditions

This contribution embraces two topics related to phase behavior of polymer blends under equilibrium and nonequilibrium. 1. Polymer blends can undergo different phase changes as liquid-liquid phase transition and crystallization. Coupling of demixing and crystallization may occur at the kinetic stage. This is illustrated by blends of poly(ϵ-caprolactone)(PCL) and poly(styrene-co-acrylonitrile)(SAN). 2. Extension of studies to blend systems under flow is necessary for the better understanding of structure formation in polymer blends outside equilibrium. Polymer molecules will be oriented and stretched when subjected to flow. This may result in flow-induced phenomena. Effects of flow on the phase behavior have been studied only for a few blends, as yet. The primary observation was flow-induced miscibility. Apparent shifts of the phase transition temperatures will be discussed qualitatively in terms of a decoupled mode theory.     

On phase equilibria,interfacial tension and phase growth in ternary polymer blends

A gradient squared free energy functional of the Landau-Ginzburg type is combined with Flory-Huggins theory to calculate minimum domain sizes, concentration profiles and interfacial tensions in ternary polymer blends. The dynamic equations governing spinodal decomposition are linearized to show that the minimum size for growth is identical to the thermodynamic minimum on phase volume. It is shown that unseparated, third components are enriched at the interface, reduce interfacial tension, increase stability and increase the minimum domain sizes. Enrichment of the third component at the interface causes concentrations at the major components to lie outside their binodal limits at a distance from the interface. Although the effects are most pronounced when the third component is a compatibilizer, the general phenomena remain true even when the third component is relatively incompatible. Generalizations to blends of N components are presented, and a robust method for calculating multicomponent phase diagrams is described.     

Phase behavior and photocrosslinking kinetics of semi-interpenetrating polymer networks prepared from miscible polymer blends

Mixtures of polystyrene derivatives (PSCS) and poly(vinyl methyl ether) (PVME) were made photocrosslinkable by chemically labeling PSCS chains with photoreactive anthracene. Miscibility of these anthracene-labeled PSCS/PVME blends was examined by light scattering under several crosslinking conditions in the one-phase region via photodimerization of anthracenes. As the reaction proceeds, the coexistence curve of PSCS/PVME blends shifts toward the low temperature side. By following the changes in concentration of anthracenes with irradiation time, it was found that the crosslinking reaction of PSCS chains in the blends does not follow the mean-field kinetics. However, it can be well expressed by the Kohlrausch–Williams–Watts (KWW) relaxation mechanism, indicating that the crosslinking reaction proceeds inhomogeneously in the blends. By scaling the reaction time with the average reaction rate obtained from the KWW equation modified for the reaction kinetics, all the crosslinking data obtained in the miscible region of the reacted blends fall on a single master curve. These experimental results suggest the universal behavior of the photocrosslinking kinetics obtained under the “shallow quench” conditions in the region far away from the coexistence curve of the reacting blends. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 455–462, 1998