Estimation of interaction energies by the critical molecular weight method: 1. Blends with polycarbonates

The interaction energies between PS, Pα-MS, and PMMA with several bisphenol-A-based polycarbonates were quantitatively determined from oligomer/oligomer, oligomer/homopolymer, and homopolymer/copolymer blends. Interaction energies were calculated from the Flory-Huggins theory and the Sanchez-Lacombe equation of state theory using experimental cloud points or miscibility boundaries. Alkyl addition to the phenyl rings of polycarbonate is favorable for miscibility with polystyrene whereas halogenation of the bisphenol connector unit is favorable for miscibility with poly(methyl methacrylate). Interaction energies are quantitatively ranked and described qualitatively in terms of changes in the electronic charge distribution of the polymer repeat units as calculated by SYBYL software. © 1994 John Wiley & Sons, Inc.     

Miscibility of tetramethyl-hexafluoro copolycarbonates with styrene-methyl methacrylate copolymers

The compositions for which blends of copolycarbonates of tetramethyl bisphenol-A and hexafluoro bisphenol-A (TMPC-HFPC) with styrene-methyl methacrylate copolymers (SMMA) are miscible were determined experimentally. These copolymer compsition boundaries were compared to predictions based on the Flory-Huggins theory combined with the binary interaction model. The theoretical predictions employed interaction energies from the literature for the TMPC/PS, PS/PMMA, and TMPC/PMMA pairs, and values for the TMPC/HFPC, HFPC/PS, and HFPC/PMMA pairs were established or verified using independent experiments. The recommended set of interaction energies predicts that miscibility occurs in two separate regions of copolymer compositions. These predictions agree well with the experimental observations. The theoretical requirements for a single, continuous miscible region versus two disjointed miscible regions when the two limiting homopolymer pairs exhibit miscibility, that is, TMPC-PS and HFPC-PMMA in this example, are described. © 1994 John Wiley & Sons, Inc.     

Theoretical investigation of structures and electronic states of a series of phenyl-capped oligothiophenes

The structures and electronic states of a series of phenyl-capped oligothiophenes (PnTs) and their ionic species were investigated by means of the density functional theory (DFT). The calculations were performed on the oligomers formed by n repeating units, where n ranges from 2 to 6, using the B3LYP/6-31G** level of theory. The results obtained show that the end-substitution plays a fine-tuning effect on the geometries, electronics, and excitation states. It was found that the oligomers in the doped state have more satisfactory structural and electronic characteristics for the conducting polymers. The conjugated system in the doped oligomers has more aromaticity, with expanded and planar chains. The calculated energy gap values between the frontal molecular orbitals for the PnTs indicate that with increasing the oligomer chain length, the conductive band gap decreases. The calculated ?rst excitation energies of the PnTs at the TD-B3LYP/6-31G** level reveal that the doped PnTs have lower excitation energies than the neutral states. The oligomer chains with a phenyl ring as the end-capped group display red shifts in their absorption spectra. The end-caped substituted oligothiophenes display better characteristics than the unsubstituted ones. It could be anticipated that the phenyl-caped substitution would be helpful to charge-carrier hopings between chains, and thereby, enhance the conductivity.     

Controlling effective interactions and spatial dispersion of nanoparticles in multiblock copolymer melts

The microscopic Polymer Reference Interaction Site Model theory is employed to study, for the first time, the effective interactions, spatial organization, and miscibility of dilute spherical nanoparticles in non‐microphase separating, chemically heterogeneous, compositionally symmetric AB multiblock copolymer melts of varying monomer sequence or architecture. The dependence of nanoparticle wettability on copolymer sequence and chemistry results in interparticle potentials‐of‐mean force that are qualitatively different from homopolymers. An important prediction is the ability to improve nanoparticle dispersion via judicious choice of block length and monomer adsorption‐strengths which control both local surface segregation and chain connectivity induced packing constraints and frustration. The degree of dispersion also depends strongly on nanoparticle diameter relative to the block contour length. Small particles in copolymers with longer block lengths experience a more homopolymer‐like environment which renders them relatively insensitive to copolymer chemical heterogeneity and hinders dispersion. Larger particles (sufficiently larger than the monomer diameter) in copolymers of relatively short block lengths provide better dispersion than either a homopolymer or random copolymer. The theory also predicts a novel widening of the miscibility window for large particles upon increasing the overall molecular weight of copolymers composed of relatively long blocks. The influence of a positive chi‐parameter in the pure copolymer melt is briefly studied. Quantitative application to fullerenes in specific copolymers of experimental interest is performed, and miscibility predictions are made. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1098–1111     

Characterization of the interaction energies for polystyrene blends with various methacrylate polymers

The binary interaction energies between styrene and various methacrylates were determined from newly examined phase boundaries with lattice–fluid theory. Because the blends of polystyrene (PS) and poly(cyclohexylmethacrylate) (PCHMA) were only miscible at high molecular weights when the blends were prepared by solution casting from tetrahydrofuran, we examined the miscibility of other blends by changing the molecular weights of PS or methacrylate polymers. On the basis of the phase‐separation temperature caused by the lower critical solution temperature, the miscibility of PS with the various methacrylates appeared to be in the order PCHMA > poly(n‐propyl‐methacrylate) (PnPMA) > poly(ethyl methacrylate) (PEMA) > poly(n‐butyl‐methacrylate) (PnBMA) > poly(iso‐butyl‐methacrylate) > poly(methyl methacrylate) (PMMA) > poly(tert‐butyl methacrylate), and the branching of butylmethacrylate appeared to decrease the miscibility with PS. The interaction energies between PS with various methacrylates obtained from phase boundaries with lattice–fluid theory reached minimum value corresponding to the styrene/n‐propylmethacrylate interaction. They were in the order PnPMA < PEMA < PCHMA < PnBMA < PMMA. The difference in the order of miscibility and interaction energies might be attributed to the terms related to the compressibility. The phase‐separation temperatures calculated with the interaction energies obtained here indicated that the PS/PEMA and PS/PnPMA blends at high molecular weights were miscible, whereas the PS/PnBMA blends were immiscible at high molecular weights. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2666–2677, 2000     

Upper critical solution temperature type phase behavior of poly(styrene‐co‐acrylonitrile) blends with poly(styrene‐co‐n‐phenyl maleimide) and their interaction energies

To enhance the heat resistance of poly(styrene‐co‐acrylonitrile‐co‐butadiene), ABS, miscibility of poly(styrene‐co‐acrylonitrile), SAN, with poly(styrene‐co‐n‐phenyl maleimide), SNPMI, having a higher glass transition temperature than SAN was explored. SAN/SNPMI blends casted from solvent were immiscible regardless of copolymer compositions. However, SNPMI copolymer forms homogeneous mixtures with SAN copolymer within specific ranges of copolymer composition upon heating caused by upper critical solution temperature, UCST, type phase behavior. Since immiscibility of solvent casting samples can be driven by solvent effects even though SAN/SNPMI blends are miscible, UCST‐type phase behavior was confirmed by exploring phase reversibility. When copolymer composition of SNPMI was fixed, the phase homogenization temperature of SAN/SNPMI blends was increased as AN content in SAN copolymer increased. To understand the observed phase behavior of SAN/SNPMI blend, interaction energies of blends were calculated from the UCST‐type phase boundaries by using the lattice‐fluid theory combined with a binary interaction model. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1131–1139, 2008     

Evaluation of the interaction parameter for poly(ε‐caprolactone)/poly(styrene‐co‐acrylonitrile) blends

In this article, the miscibility of poly(ε‐caprolactone) (PCL) with poly(styrene‐co‐acrylonitrile) (SAN) containing 25 wt % of acrylonitrile is studied from both a qualitative and a quantitative point of view. The evidences coming from thermal analysis (differential scanning calorimetry) demonstrate that PCL and SAN are miscible in the whole range of composition. The Flory interaction parameter χ_1,2 was calculated by the Patterson approximation and the melting point depression of the crystalline phase in the blends; in both cases, negative values of χ_1,2 were found, confirming that the system is miscible. The interaction parameter evaluated within the framework of the mean field theory demonstrates that the miscibility of PCL/SAN blends is due to the repulsive interaction between the styrene and acrylonitrile segments in SAN. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

COMPUTER SIMULATION OF MISCIBILITY AND SELF-ASSEMBLY STRUCTURE FOR POLYMER-CONTAINING SYSTEMS WITH SPECIAL INTERACTIONS

The miscibility and structure of A-B copolymer/C homopolymer blends with special interactions were studied by aMonte Carlo simulation in two dimensions. The interaction between segment A and segment C was repulsive, whereas it wasattractive between segment B and segment C. In order to study the effect of copolymer chain structure on the morphologyand structure of A-B copolymer/C homopolymer blends, the alternating, random and block A-B copolymers were introducedinto the blends, respectively. The simulation results indicated that the miscibility of A-B block copolymer/C homopolymerblends depended on the chain structure of the A-B copolymer. Compared with alternating or random copolymer, the blockcopolymer, especially the diblock copolymer, could lead to a poor miscibility of A-B copolymer/C homopolymer blends.Moreover, for diblock A-B copolymer/C homopolymer blends, obvious self-organized core-shell smicture was observed inthe segment B composition region from 20% to 60%. However if diblock copolymer composition in the blends is less than40%, obvious self-organized core-shell structure could be formed in the B-segment component region from 10 to 90%.Furthermore, computer statistical analysis for the simulation results showed that the core sizes tended to increasecontinuously and their distribution became wider with decreasing B-segment component.     

Miscibility of poly(vinyl chloride) with poly(methyl-co-hexyl acrylate) and poly(methyl-co-2 ethyl hexyl acrylate)

The miscibility and phase behavior in blends of PVC with poly(methyl-co-hexyl acrylate)[MHA] and poly(methyl-co-2 ethyl hexyl acrylate)[MEH] were studied. It was found that PVC is miscible with MHA copolymers having a HA volume fraction from 0.30 to 0.92 and MEH copolymers having an EH volume fraction from 0.30 to 0.83 at 100°C. By applying the mean field theory to the phase diagrams of these blend systems, segmental interaction parameters which represent the binary interaction between different monomer units were estimated. The calculated values reflect the fact that the miscibility window observed for PVC/MHA and PVC/MEH blend systems was attributed to the effect of repulsion between different monomer units within the copolymer. To investigate the effect of specific interaction on the miscibility for these blend systems, an attempt was also made to describe the blend interaction parameter as a function of polar group concentration in the acrylate copolymer. The blend interaction parameter values exhibit a u-shaped curve as a function of the weight fraction of C?O group in the copolymer, and the lowest blend interaction parameter value appears at about 0.24 C?O weight fraction.     

Study of hopping transport in long oligothiophenes and oligoselenophenes: dependence of reorganization energy on chain length

Internal reorganization energies for self-exchange hole-transfer process were calculated at the B3LYP/6-31G(d) level of theory for a series of oligothiophenes and oligoselenophenes up to the 50-mers. This is the first study of reorganization energy in very long pi-conjugated systems. We observed a linear correlation between reorganization energy and the reciprocal chain length for these long pi-conjugated heterocyclic oligomers, which can be explained by the changes in bond length that occur between the neutral and cation radical species and by the charge distribution in the cation radicals. In contrast to the saturation behavior observed for the HOMO-LUMO gaps of long pi-conjugated heterocyclic oligomers, the reorganization energy does not show saturation behavior for any length of the oligomers in this study, even up to the 50-mers. Interestingly, the reorganization energy approaches zero for infinite numbers of oligomer units (at the B3LYP/6-31G(d) level of theory), that is, for polythiophene and polyselenophene. The absolute values of the reorganization energies of oligoselenophenes, and the changes that occur in those energies with chain length, are similar to those found for oligothiophenes.     

Miscibility of poly(styrene‐co‐butyl acrylate) with poly(ethyl methacrylate): Existence of both UCST and LCST

A miscible homopolymer–copolymer pair viz., poly(ethyl methacrylate) (PEMA)–poly(styrene‐co‐butyl acrylate) (SBA) is reported. The miscibility has been studied using differential scanning calorimetry. While 1 : 1 (w/w) blends with SBA containing 23 and 34 wt % styrene (ST) become miscible only above 225 and 185 °C respectively indicating existence of UCST, those with SBA containing 63 wt % ST is miscible at the lowest mixing temperature (i.e., T_g's) but become immiscible when heated at ca 250 °C indicating the existence of LCST. Miscibility for blends with SBA of still higher ST content could not be determined by this method because of the closeness of the T_g's of the components. The miscibility window at 230 °C refers to the two copolymer compositions of which one with the lower ST content is near the UCST, while the other with the higher ST content is near the LCST. Using these compositions and the mean field theory binary interaction parameters between the monomer residues have been calculated. The values are χ_ST‐BA = 0.087 and χ_EMA‐BA = 0.013 at 230 °C. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 369–375, 2000     

MISCIBILITY IN COPOLYMER/HOMOPOLYMER BLENDS

In order to study the miscibility of a copolymer with its corresponding homopolymers, varieties of multicomponent polymers including simple graft, muhibranch, diblock, triblock and four-arm block copolymers and so-called ABCPs were synthesized and characterized. The morphologies of the blends comprising the copolymers and the corresponding homopolymers were examined by electron microscopy. It is concluded that besides molecular weight, architecture of a copolypaers has apparent effect on the miscibility, i.e. the more complex is molecular architecture, the greater is conformation restriction in microdomain formation and the less is solubility of homopolymer in corresponding domains. In addition, a density gradient model is suggested for describing the segment distribution of the bound and free chains in block-homopolymer systems. Using this model, Helfand's theory is extended to the blends of copolymer and homopolymer predicting the miscibility which is in good agreement with the experimental results.     

Miscibility of polysulfone blends with poly(1‐vinylpyrrolidone‐co‐styrene) copolymers and their interaction energies

The miscibility of polysulfone (PSf) with various hydrophilic copolymers was explored. Among these blends, PSf gave homogeneous mixtures with poly(1‐vinylpyrrolidone‐co‐styrene) [P(VP–S)] copolymers when these copolymers contained 68–88 wt % 1‐vinylpyrrolidone (VP). Miscible PSf blends with P(VP–S) copolymers underwent phase separation on heating caused by lower critical solution temperature (LCST)‐type phase behavior. The phase behavior depended on the copolymer composition. Changes in the VP content of P(VP–S) copolymers from 65 to 68 wt % shifted the phase behavior from immiscibility to miscibility and the LCST behavior. The phase‐separation temperatures of the miscible blends first increased gradually with the VP content, then went through a broad maximum centered at about 80 wt % VP, and finally decreased just before the limiting content of VP for miscibility with PSf. The interaction energies of binary pairs involved in PSf/P(VP–S) blends were evaluated from the phase‐separation temperatures of PSf/P(VP–S) blends with lattice‐fluid theory combined with a binary interaction model. The decrease in the contact angle between water and the membrane surface with increasing VP content in P(VP–S) copolymers indicated that the hydrophobic properties of PSf could be improved via blending with hydrophilic P(VP–S) copolymers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1401–1411, 2003     

Nonideal behavior of alkylammonium salts in organic solvents at elevated temperatures

Osmometric vapor-pressure-lowering measurements on toluene, butylbenzene, chlorobenzene, and chloronaphthalene solutions of several secondary, tertiary, and quaternary long-chain (at least five carbon atoms per chain) alkylammonium chlorides, bromides, thiocyanates, nitrates, and perrhenates in the temperature range between 50–130°C show an appreciable amount of molecular association. The extent (number of aggregated units) and/or the degree (size of aggregated units) of aggregation decreases with the number of carbon atoms per chain, the polarity of the solvent, and the temperature, but increases with the size of the anions and the solute concentration. The data were treated quantitatively in terms of activity coefficients via the Gibbs-Duhem relation and also in terms of specific oligomer formation. The latter treatment shows the salts to form a dimer and one (exceptionally two) higher oligomer, for which the association constants have been calculated.     

Thermal stability of poly(acryloyl chloride) homopolymer and copolymers of acryloyl chloride with methyl methacrylate

The thermal stabilities of poly(acryloyl chloride) homopolymer and copolymers of acryloyl chloride with methyl methacrylate covering the entire composition range were studied by thermogravimetric analysis. At each extreme of the composition range incorporation of comonomer units results in a copolymer which is less stable than the PMMA homopolymer. The activation energies of the decomposition of the copolymers were calculated using the Arrhenius equation and found to decrease from 32.2 to 12.5 kJ mol^?1 as acryloyl chloride concentration of the copolymer increases, indicating that the copolymers of higher acryloyl chloride concentration should easier decompose than other copolymers. The reactivity ratios of the copolymer were calculated and found to ber ₁(AC)=0.2±0.02 andr ₂(MMA)=0.9±0.1.     

Phase behavior in copolymer blends of poly (p-chlorostyrene-co-o-chlorostyrene) and phenylsulfonylated poly (2,6-dimethyl-1,4-phenylene oxide)

The miscibility of random copolymers of o-chlorostyrene and p-chlorostyrene [P (oClSt-co-pClSt)] with partially phenylsulfonylated poly (2,6-dimethyl-1,4-phenylene oxide) (SPPO) copolymers has been studied, using differential scanning calorimetry (DSC) to establish T_g behavior. It already has been established that the isomeric effect of the chlorine substitution on miscibility is large. Thus the para-chloro-substituted styrenic homopolymer is miscible with all SPPOs containing more than ～ 5 mol % phenylsulfonylation, whereas the ortho-chloro-substituted homopolymer is immiscible with the entire range of SPPO copolymer compositions (and also with the respective homopolymers). As a result of this asymmetric behavior of the homopolymers, the width of the window of miscibility in blends now investigated containing copolymers with high pClSt content and SPPO is much greater than in the corresponding blends containing copolymers with large mole fraction of oClSt. These differences are reflected in the corresponding χ parameters calculated from analysis of the data. It was also found that the miscibility is temperature dependent and that the regime in the copolymer-copolymer composition plane shrank as the equilibrium temperature increased, results indicative of LCST behavior. © 1994 John Wiley & Sons, Inc.     

Prediction and characterization of halogen–hydride interaction in Cu n H n ···ClC2Z and Cu n H···ClC2Z complexes (n = 2–5; Z = H, F, CH3)

Halogen–hydride interactions between the lowest energy structure of Cu _n H _n and Cu _n H clusters (n = 2–5) as halogen acceptor and ClC₂Z (Z = H, F, CH₃) as halogen donor have been investigated at the MP2/6-311++G(d,p) level of theory. Different approaches based on structural parameters, energetic analysis, shift in vibrational frequencies, and molecular electrostatic potential were used to characterize the resultant halogen–hydride bonds. Upon complexation, the Cl–C bonds tend to elongate, concomitant with red shifts of the Cl–C vibrational frequencies. Interaction energies of this type of halogen bonds vary from ?2.34 to a maximum ?7.38 kJ mol^?1. The calculated interaction energies were found to be increased in magnitude with increasing of the negative electrostatic potential at a point on the outer side of hydrogen atom of halogen acceptor units. Moreover, decomposition of the interaction energies reveals that the electrostatic interaction plays a main role in the formation of the complexes. The quantum theory of atoms in molecules analysis has also been applied to provide more insight into the nature and properties of these interactions. Our results indicate pure closed-shell interactions in these systems with similar characteristics to the conventional halogen bonds.     

Interactions in SMA-SAN blends

Styrene/maleic anhydride (SMA) and styrene/acrylonitrile (SAN) copolymers have previously been shown to form miscible blends when the MA and AN contents do not differ too greatly. It is shown here that this is the result of a weak exothermic interaction between the MA and AN units by measuring the heats of mixing for appropriate liquid analogs of the various monomer units. The region of copolymer compositions for miscibility of SMA-SAN blends is predicted from the Sanchez-Lacombe mixture theory using net interaction parameters calculated from the analog calorimetry results via a simple binary interaction model for copolymers. Lower critical solution temperature behavior was observed for blends of copolymers having compositions near the edge of the miscibility region. Various glass transition, volumetric, and FTIR results are discussed in terms of the interactions observed.     

Theoretical study of 1D and 2D fused magnesium porphine oligomers

The structural characteristics, energies, and spectroscopic properties of 1D linear chains and 2D planar sheets of (meso-meso, β-β, β-β)-linked magnesium porphines have been calculated by the density functional theory B3LYP method. The trends in the changes in the ionization potential, electron affinity, relative multiplet energies, and electron and spin density characteristics have been scrutinized as a function of the oligomer size and n in the range 0–8.     

The structures of low molecular weight glycerin propoxylates: An experimental,semi-empirical,and Monte Carlo study

A simple Monte Carlo model has been developed for calculating the structural features and properties of low molecular weight triols produced by the base-catalyzed propoxylation of glycerin. The model computes the probability of a reaction to a specific oligomer from the local site reactivities of model compounds with an adjustment for the molecular weight of the reacting oligomer. The resulting product array is then used to calculate typical polymer properties such as average molecular weight, polydispersity, and average chain length. Trial rate constants were estimated from the activation energies of MNDO-PM3 semi-empirical molecular orbital theory. For the compounds used to model the oligomer chain end groups, the activation enthalpies were found to be within the ranges reported for experimental values. Although the predicted enthalpies of activation were significantly higher for the alkoxylation directly at glycerin, this was found to be attributable to intramolecular hydrogen bonding in the reactants that was disrupted in the transition states. Although the hydrogen bonding energies were higher than what are normally considered typical, comparison tests showed that the calculated energies agreed well with experimental values of alkoxide anion–alcohol systems. The PM3 rate constants, when used to calculate Monte Carlo probabilities, predicted the isomer distribution of the four isomeric monopropoxylates with a error of 4%. Optimization of the model reduced this to 0.5%. However, to accurately predict the oligomer distribution of higher molecular weight adducts and other properties, the correction term (M₀/M_i)^b had to be included, where M₀/M_i is the ratio of the molecular weight of glycerin to the molecular weight of the oligomer undergoing alkoxylation, and b is assigned the value 0.7. Although b is empirical, it is consistent with a simple molecular mechanics (MM2) conformational study of the relative availability of the reactive end groups. When the final model was used to simulate the propoxylation of glycerin for a variety of PO/glycerin ratios, it was found to accurately reproduce properties such as primary hydroxyl content, polydispersity, oligomer distribution, and change in the monopropoxylate isomer ratio as a function of bulk PO/glycerin ratio. © 1995 John Wiley & Sons, Inc.