A Flory–Huggins thermodynamic approach for predicting sorption equilibrium in ternary polymer systems

The Flory–Huggins theory as modified by Pouchlý has been applied to calculate preferential (λ) and total (Y) sorption coefficients for a ternary polymer system. The ternary interaction function (?₁?₂?₃G_T(u₁, ?₃)) is described as the product of three independent binary functions. This expression allows prediction of λ and Y from binary interaction parameters χ, χ, g, g, and g₁₂(?₁₀). Three ternary polymer systems are used to check the validity of the expression. Moreover for polymer systems in which the parameters g and/or g are unknown, a procedure to evaluate them has been developed and verified on systems for which sufficient experimental information is available.     

Entanglement friction and dynamics in blends of starlike and linear polymer molecules

We investigate relaxation dynamics in a series of six‐arm star/linear 1,4‐polybutadiene blends with mechanical rheometry measurements. Blend systems are formulated to systematically probe constraint release and arm relaxation dynamics. Zero shear viscosity and terminal relaxation times of star/linear polymer blends with fixed star arm molecular weights (M_a) and compositions (?_S) are found to follow nonmonotonic dependencies on the linear polymer molecular weight (M_L). At low values of ?_S, at least two scaling regimes are apparent from the data (ξ₀ ～ M and ξ₀ ～ M), where ξ₀ refers to the zero shear viscosity or terminal relaxation time of the blend. The two regimes are separated by a critical linear polymer molecular weight M^* that is more than 20 times larger than the critical molecular weight for entanglements. When the linear polymer contribution to blend properties is removed, a clear transition from dilution dynamics, ξ₀ ～ M, to Rouse‐like constraint‐release dynamics, ξ₀ ～ M, is apparent at low values of ?_S. At higher ?_S values, a new activated constraint‐release dynamic regime is evident in which ξ₀ ～ M and ξ₀ ～ ?, where α changes continuously from approximately 2 to 0.5 as ?_S increases and β varies from 2.0 to 1.0 as M_L increases. The experimental results are compared with theoretical predictions based on a drag coupling model for entangled polymer liquids. All features observed experimentally are captured by this model, including the value of M^* for the transition from dilution to Rouse constraint‐release dynamics. Predictions of the drag coupling model are also compared with published data for the zero shear viscosity and terminal relaxation time in bidisperse linear polymer blends and pure entangled starlike molecules. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2501–2518, 2001     

Intrinsic birefringence of poly(trimethylene terephthalate)

Highly oriented poly(trimethylene terephthalate) (PTT) fiber has a low birefringence that is unexpected for an aromatic polyester with a high refractive index. To explain this observation, the intrinsic birefringence Δn of PTT crystal was calculated from its bond polarizabilities to be 0.029. This Δn is almost an order of magnitude smaller than poly(ethylene terephthalate)'s value at 0.22, although both polymers have nearly identical crystal refractive indices. The small Δn is due to the arrangement of PTT's methylene groups in gauche conformations, causing the chain‐repeating unit to be tilted ～53° away from the c axis toward the basal plane. Because of the small Δn, the crystalline‐phase orientation made only a small contribution to the overall birefringence despite the fiber's high crystallinity and orientation. To understand the effect of the number of methylene groups on polyester optical anisotropy, the Δn's of a series of poly(m‐alkylene terephthalates) with m = 2–5 were compared and correlated with ψ: an angle made by the normal of the benzene ring with the crystal's axis. As ψ′ decreases, Δn of the polyesters diminishes. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1513–1520, 2002     

Zone-resolved mass spectroscopic study on RF plasma polymerization of styrene

The radiofrequency (rf) glow discharge plasma of styrene was investigated by direct sampling mass spectroscopy. Measurements were taken in three regions of the discharge: the plasma column and two dark zones before the electrodes. The plasma-polymerized styrene (PPS) thin films were analyzed by infrared spectroscopy (IR). The effects of monomer pressure and rf power on the ratios of mass peak heights C₄H/C₄H, C₆H/C₆H₅()CH in the three discharge regions, the polymer deposition rate, and the polymeric structure of the PPS films were studied. It was found that in the different discharge regions and under various discharge conditions, a variety of reactive species were formed by electron impact on monomer molecules. The polymer deposition rate was mainly dependent on the total number of the reactive species produced in the discharge. The concentration of phenyl groups in PPS films was proportional to the relative concentration of phenyl ring-containing reactive species in the gas phase plasma. © 1996 John Wiley & Sons, Inc.     

Nonlinear rheology of highly entangled polymer solutions in start‐up and steady shear flow

Orientation angle and stress‐relaxation dynamics of entangled polystyrene (PS)/diethyl phthalate solutions were investigated in steady and step shear flows. Concentrated (19 vol %) solutions of 0.995, 1.81, and 3.84 million molecular weight (MW) PS and a semidilute (6.4 vol %) solution of 20.6 million MW PS were used to study the effects of entanglement loss on dynamics. A phase‐modulated flow birefringence apparatus was developed to facilitate measurements of time‐dependent changes in optical equivalents of shear stress (n₁₂ ≈ Cσ) and first normal stress differences (n₁ = n₁₁ ? n₂₂ ≈ CN₁) in a planar‐Couette shear‐flow geometry. Flow birefringence results were supplemented with cone‐and‐plate mechanical rheometry measurements to extend the range of shear rates over which entangled polymer dynamics are studied. In slow (τ > ) steady shear‐flow experiments using the ultrahigh MW polymer sample (20.6 × 10⁶ MW PS), steady‐state n₁₂ and n₁ results manifest unusual power‐law dependencies on shear rate [n_12,ss ～ ^0.4 and n_1,ss ～ ^0.8]. At shear rates in the range τ < < τ, steady‐state orientation angles χ_SS are found to be nearly independent of shear rate for all but the most weakly entangled materials investigated. For solutions containing the highest MW PS, an approximate plateau orientation angle χ_p in the range 20–24° is observed; χ_p values ranging from 14 to 16° are found for the other materials. In the start‐up of fast steady shear flow (γ˙ ≥ τ), transient undershoots in orientation angle are also reported. The molecular origins of these observations were examined with the help of a tube model theory that accommodates changes in polymer entanglement density during flow. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2275–2289, 2001     

Molecular orientation in biaxially oriented sheets of poly(ethylene terephthalate). I. Characterization of orientation and comparison with models

A study of molecular orientation in a series of five one-way-drawn sheets of poly(ethylene terephthalate) is reported. Five orientation averages P which characterize the benzene-ring orientation were determined directly by Raman spectroscopy. Two further averages P and P were determined from a combination of Raman spectroscopy and refractive index measurements on the basis of two different conformational models. As in a previous publication, the seven averages P were used to estimate all the P up to fourth order for the benzene rings on the assumption that in each case the actual distribution of orientations is close to the most probable distribution. The seven orientation averages P for each drawn sheet were also compared with those calculated on the basis of two simple models for the development of molecular orientation during drawing, the pseudoaffine deformation scheme and the rubber network model. It was shown that the orientation of the chain axes is closer to that predicted by the rubber network model, the pseudoaffine deformation scheme greatly overestimating the degree of chain biaxiality. The results also show that the benzene ring planes are preferentially oriented toward the planes of the sheets. The chain axis orientation is, however, nearly uniaxial and similar to that observed for uniaxially drawn samples, suggesting that there is no direct connection between the processes of chain axis orientation and preferential orientation of the benzene-ring planes.     

Structure and viscoelasticity of matched asymmetric diblock and triblock copolymers in the cylinder and sphere microstructures

A polystyrene–polyisoprene (PS–PI) diblock copolymer (10,000–50,000 g/mol) and a matched PS&ndashPI–PS triblock (10,000–100,000–10,000 g/mol) were employed to study the effect of chain architecture on the rheological response of ordered block copolymer melts. Both samples adopt hexagonal microstructures with PS cylinders embedded in a PI matrix; on further heating, an order–order transition (OOT) into a cubic array of spheres takes place prior to the order–disorder transition. Each morphology was verified by SAXS and TEM. Interestingly, at the OOT the low-frequency elastic modulus of the diblock increased abruptly, whereas that of the triblock decreased. In contrast, the modulus of the cubic phase was roughly independent of chain architecture. Chain relaxation parallel and perpendicular to the cylinders was probed by measuring the elastic modulus of a macroscopically aligned sample in directions parallel G and perpendicular (G) to the cylinder orientation. For both materials G < G < G where G is the elastic modulus of a randomly oriented sample. This result is attributed to the ability of the unentangled PS blocks to move along the direction of the cylinder axis, and thus relax the stress in the PI matrix in the parallel alignment. In each of the three cylindrical orientations the triblock had a larger modulus than the diblock, which is attributed to the presence of bridging PI blocks that connect distinct PS domains. About 20° below the OOT G showed a distinct change in its temperature dependence, which, coupled with SAXS measurements, is indicative of the onset of an undulation in the cylinder diameter that presages the pinching off of cylinders into spheres, as recently predicted by theory. The use of oriented samples also permitted SAXS confirmation of an approximate epitaxial relationship between the cylinder and the sphere unit cells, although a distinct change in the location of the structure factor maximum, q^*, is noted at the OOT. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2811–2823, 1997     

Melt‐state polymer chain dimensions as a function of temperature

The unperturbed chain dimensions (〈R²〉_o/M) of cis/trans‐1,4‐polyisoprene, a near‐atactic poly(methyl methacrylate), and atactic polyolefins were measured as a function of temperature in the melt state via small‐angle neutron scattering (SANS). The polyolefinic materials were derived from polydienes or polystyrene via hydrogenation or deuteration and represent structures not encountered commercially. The parent polymers were prepared via lithium‐based anionic polymerizations in cyclohexane with, in some cases, a polymer microstructure modifier present. The polyolefins retained the near‐monodisperse molecular weight distributions exhibited by the precursor materials. The melt SANS‐based chain dimension data allowed the evaluation of the temperature coefficients [dln 〈R²〉_o/dT(κ)] for these polymers. The evaluated polymers obeyed the packing length (p)‐based expressions of the plateau modulus, G = kT/np³ (MPa), and the entanglement molecular weight, M_e = ρN_anp³ (g mol^?1), where n_t denotes the number (～21) of entanglement strands in a cube with the dimensions of the reptation tube diameter (d_t) and ρ is the chain density. The product np³ is the displaced volume (V_e) of an entanglement that is also expressible as pd or kT/G. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1768–1776, 2002     

Solid‐state nuclear magnetic resonance relaxation times in crosslinked macroporous polymer particles of divinylbenzene homopolymers

Monodisperse porous particles of poly(divinylbenzene) prepared by the activated swelling method have been investigated by solid‐state ¹³C crosspolarization magic‐angle spinning (CPMAS) nuclear magnetic resonance (NMR) relaxation measurements. Homopolymeric combinations of two porogens (toluene and 2‐ethylhexanoic acid) and two monomers (meta‐ and para‐divinylbenzene) were studied. Residual vinyl groups were systematically reacted with increasing amounts of bromine, producing 20 different polymers samples for which we measured crosspolarization times, T_CH, proton rotating frame spin‐lattice relaxation, T, ¹³C spin‐lattice relaxation, T, and proton spin‐lattice relaxation, T. These parameters were chosen to reflect expected changes in a wide range of frequencies of motion as a function of structure. Relative differences in the molecular mobility of the major functional groups (aromatic, vinyl and aliphatic) is related to initial reactants used, vinyl concentration, relative reactivity of vinyl groups, distribution of vinyl groups, pore structure, and degree of crosslinking. Variable temperature ¹H combined rotation and multiple pulse NMR (CRAMPS) was used to derive activation energies for selected samples via measurement of the proton spin‐lattice relaxation time, T. Irreversible thermal effects were observed in ambient temperature relaxation after heating to temperatures in the range of 393–418 K. Simple univariate statistical analyses failed to reveal consistent correlations among the known variables. However, the application of more sophisticated multivariate and neural network analyses allowed excellent structure–property predictions to be made from the relaxation time data. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1307–1328, 1999     

Thermodynamic analysis of polymer‐solid adhesion: Sticker and receptor group effects

Adhesion of dense linear polymer chains containing a small number of randomly distributed sticker groups (?_X) to a solid substrate containing receptor groups (?_Y) has been analyzed by a single‐chain scaling approach. An entanglement sink probability (ESP) model motivated by vector percolation explains the nonmonotonic influences of sticker concentration (?_X), receptor concentration (?_Y), and their interaction strength (χ) on the adhesion strength G_IC of the polymer‐solid interface. The ESP model quantifies the degree of interdigitation between adsorbed and neighboring chains on the basis of the adsorbed chain domain with an extension of the scaling treatment of de Gennes. Here, the adsorbed chain domain changes thermodynamically with respect to the energy of interaction parameter, r = χ?_X?_Y. This model considers the situation of a blend consisting of a small volume fraction of adhesive molecules as a compatibilizer at the interface, where these molecules promote adhesion by adsorbing to the surface via sticker‐receptor interactions. The percolation model scales solely with r = χ?_X?_Y, and this parameter can be related to both the adhesive potential (G_A) and the cohesive potential (G_C). G_A describes adhesive failure between adsorbed chains and the solid surface and linearly behaves as G_A ～ r = χ?_X?_Y. The cohesive strength between adsorbed and neighboring chains corresponds to G_C ～ r^?0.5～?1.0 = (χ?_X?_Y)^?0.5～?1.0. When the fracture stresses for cohesive and adhesive failure are equal, the model predicts maximum adhesion strength at an optimal value of r* = (χ?_X?_Y)*. Thus, for a given χ value, optimal values ? and ? exist for the sticker and receptor groups, above or below which the fracture energy will not be optimized. Alternatively, if the X‐Y interaction strength χ increases, then the number of sticker groups required to achieve the optimum strength decreases. Significantly, the optimum strength is not obtained when the surface is completely covered with receptor groups (?_Y = 1) but is closer to 30%. For polybutadiene, the optimum value of r* was determined experimentally (Lee, I.; Wool, R. P. J Adhesion 2001, 75, 299), and typically ? ≈ 1–3%, ? ≈ 25–30%. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2343–2353, 2002     

Interaction parameters of crystalline/crystalline polypropylene/poly(butene‐1) blends: Effect of molecular fractionation

Compatibility of crystalline/crystalline polypropylene (PP)/poly(butene‐1) (PB‐1) blends was investigated via the method of equilibrium melting temperature depression followed by determining the polymer–polymer interaction parameter (χ) using the Nishi–Wang equation. The composition variation of the equilibrium melting temperatures of blends (T) was determined with the Hoffman–Weeks plot. The T and its variation with the blend composition depended on the crystallization temperature range. The morphological effect of the blend composition was not a contribution factor for the T depressions of PP and PB‐1 in the blends. The interplay of the dilution effect and molecular fractionation effect of the amorphous component on crystallization of the crystalline component in the blends governed the relation of T with the blend composition. The calculated χ values were negative depending on the blend composition. The negative χ values suggested that PP and PB‐1 in the amorphous region were compatible. The composition variation of the χ values was attributed to the molecular fractionation effect during crystallization. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 638–648, 2002; DOI 10.1002/polb.10125     

Determination of the crystallinity of polyethylene/α‐olefin copolymers by thermal analysis: Relationship of the heat of fusion of 100% polyethylene crystal and the density

The heat of fusion measured with differential scanning calorimetry (DSC) is typically divided by a constant value of the heat of fusion of 100% polyethylene (PE) crystal (ΔH) for the estimation of the fraction crystallinity of PE copolymers, regardless of the density [i.e., the short‐chain branching (SCB) concentration]. In this work, values of ΔH of about 288 J/g were determined with a combined DSC and X‐ray diffraction (XRD) method for a series of PE copolymers containing SCB from 0 to 50 Br/1000 C (density = 0.965–0.865 g/cc). There was no systematic change in ΔH observed across this density range. This result supports the suitability of determining the fraction crystallinity of PE of any density by the simple division of the observed heat of fusion determined by DSC by a constant value of ΔH. This DSC method yielded values of PE crystallinity in good agreement with corresponding values determined by XRD for a series of PE copolymers. The determination of ΔH involved a small precision error for higher density (lower SCB) PEs, but the precision error increased for lower density (i.e., higher SCB) PEs. This was due to the difficulty in measuring the heat of fusion for lower density PEs, which exhibited low values of the heat of fusion and melted only slightly above room temperature, and due to the difficulty of measuring lower values of crystallinity by XRD. The crystal thickness measured by small‐angle X‐ray scattering for this series of PE copolymers decreased exponentially from about 280 to 6 Å. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1637–1643, 2002     

Determination of molecular weight and its distribution of rigid‐rod polymers determined by phase‐modulated flow birefringence technique

The phase‐modulated flow birefringence (PMFB) method is widely accepted as one of the most sensitive and accurate techniques suitable for experimental tests on the molecular theory of polymer solutions. The objective of this study is to develop a systematic method to determine molecular weight and distribution of rigid‐rod polymers by the PMFB technique. Using molecular theory for rigid polymers, birefringence Δn and orientation angle χ have been expressed as a function of molecular weight and distribution. Δn has been shown to be proportional to Σc_iM, and cot 2χ turned out to have a linear relationship with Σc_iM/Σc_iM. From the experimental results for PBLG solutions, birefringence and orientation angle data were in some degree matched with the theory presented. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 509–515, 2000     

Properties of iodine complexes of monosubstituted polyacetylenes

Iodine complexes of six monosubstituted polyacetylenes with methyl, ethyl, propyl, pentyl, t-butyl, and phenyl substituents have been characterized by electronic spectroscopy. UV spectra allow the determination of the nature and the amount of active species, and photoelectronic spectra confirm the nature of these species. These measurements indicate the presence of iodine in the I and I₂ forms. The concentration of I is low (0.12–4.0 mol%), and it depends on the nature of the substitutent, but this amount does not decrease when the films are left under vacuum. On the other hand, the adsorption of ε high concentration of iodine is possible; this adsorption is governed by a diffusion mechanism and is reversible. Iodine doping leads to a cis-to-trans isomerization of the polymers, except for poly(3-3-dimethyl-1-butyne), which can be isomerized to the cis or to the trans form, depending on the solvent employed. Electrical properties of polymer I complexes are also reported. Conductivities of about 10^?4 Ω^?1 cm^?1 are obtained for all polymers in the presence of an excess of iodine.     

A fourier-transform infrared spectroscopic study of the surface hydrolysis of polythiazyl

The hydrolysis of (SN)_x, in air at room temperature and 90% relative humidity has been studied using the attenuated total reflectance (ATR) method. Decomposition gave rise to strong bands at 3210 and 3150 cm^–1 [v₃ and v₁ (NH)], 1420 cm^–1 (v_b NH), 1220 cm^–1 (S?O), 1089 and 610 cm^–1 [v₁ and v₃ (SO)]. For the first 3 days, the decay of the 808 and 690 cm^–1 bands of (SN)_x was first order, with a half life of about 30 h. The spectroscopic data were consistent with the rapid formation of ? SO₂? NH₂ and ?S?NH chain end groups with subsequent relatively slow hydrolysis to (NH₄)₂SO₄, sulfur, and fresh hydrolysable chain ends.     

Thermodynamics of miscible polymer blends using a concentration-dependent χ parameter

The Flory equation-of-state theory, as expressed by Patterson and co-workers, has been applied to two miscible polymer blends: poly(vinyl chloride)/poly(ε-caprolactone) and poly(methyl methacrylate)/poly(vinylidene chloride). For both blends, the variation of the polymer-polymer interaction parameter, χ, as a function of composition, is mostly small and can be accounted for by the Flory theory. However, for poly(vinyl chloride)/poly(ε-caprolactone) blends, at high poly(ε-caprolactone content), the large variation of χ as a function of concentration can be explained by a variation of the surface-to-volume ratio of the polymers in the mixture with blend composition. The variations of the surface-to-volume ratios determined in this study agree with those reported in the literature using small-angle x-ray scattering.     

Counterion binding to poly(allylammonium) cation

Chloride ion activity coefficients in aqueous solutions of poly(allylamine) hydrochloride (PAA · HCl) have been determined both in the absence and the presence of simple salts. Without added salt, the activity coefficient depends on the polymer concentration. With added salt, the binding of added counterions by PAAH⁺ is evaluated from the release of chloride ion. The extent of interaction between counterions and PAAH⁺ at a given polymer concentration decreases in the order SO ? ClO > NO > Cl^? > Br^? > I^?. This order of counterion selectivity agrees with the previous estimation of potentiometric titrations. The result shows that the hydration of the counterion, as well as its charge, plays an important part in counterion binding to the polyion.     

Crystal thickness distributions from melting homopolymers or random copolymers

Differential scanning calorimetry (DSC) can be used to infer the distribution of lamellar crystal thickness l. For homopolymers, the relation between melting temperature T and thickness is described by the Gibbs relation. In this case the weight distribution function of thickness g(l) ∝ P(T)(T − T)², where P(T) is DSC power and T is the melting temperature of an infinitely thick crystal. Copolymer melting is affected by the concentration of noncrystallizable comonomer in the melt as well as lamellar thickness. Unknown melt composition in copolymers with nonequilibrium crystallinity makes determination of the correct distribution g(l) from DSC impossible. An approximate distribution g₂(l) ∝ P(T)(T − T)² is proposed, where T is based on Flory's equilibrium crystallization theory. This approximate distribution is most accurate when crystallinity is small, that is, near the upper end of the melting range. Results are reported for polyethylene homopolymer and model ethylene–butene random copolymers. Corrections were not made for distortion of the DSC endotherms by thermal lag or by melting and recrystallization; these experiments are primarily to illustrate the effect of analysis in terms of an incorrect g₃(l) ∝ P(T). Average crystal thicknesses are about 20 nm for polyethylene and 5 nm for the copolymers. Distributions are characterized by l_w /l_n ≤ 1.1 in all cases. Width of the melting range is not a reliable indicator of the breadth of the thickness distribution. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 3131–3140, 1999     

Dicyanmethanido- und Cyanamido-oxoanionen. Untersuchungen zum sauerstoffanalogen Charakter der C(CN)2- und NCN-Gruppen

The equivalence of the C(CN)₂- and the NCN-groups with oxygen in the series of homologous ions C(CN), N(CN), OCN^? and NOC(CN), NO causes us to postulate a more general value of this relation. Arguments for the formulation of a pseudochalkogen series C(CN)₂? NCN? O are discussed. Synthesis, structure and reactivity of some dicyanmethanido- and cyanamido-oxoanions RCOY^?, CO₂Y^2?, COY, NOY^?, NO₂Y^?, PO₃Y^3?, PO₂Y and SO₂Y^2? are described. (Y ? C(CN)₂, NCN.) The preparation of some triorganoleadacyles is reported.