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     

Thermal,morphology, and NMR characterizations on phase behavior and miscibility in blends of isotactic polystyrene with poly(cyclohexyl methacrylate)

The miscibility and phase behavior in a binary blend of isotactic polystyrene (iPS) and poly(cyclohexyl methacrylate) (PCHMA) were investigated by differential scanning calorimetry, optical microscopy (OM), and solid‐state ¹³C cross‐polarity/magic‐angle spinning NMR. The iPS/PCHMA blend was miscible when all compositions showed a single composition‐dependent glass‐transition temperature (T_g) and when the blend went through a thermodynamic phase transition upon heating to above the lower critical solution temperature as determined by OM measurements. The ¹H NMR spin‐relaxation times in the laboratory frame (T) and in the rotating frame (T) for iPS/PCHMA blends with various compositions and neat components were directly measured through solid‐state¹³C NMR. The results of T indicated that the blends are homogeneous, at least on a scale of 75–85 nm, confirming the miscibility of the system. The single decay and composition‐dependent T values for each blend further demonstrated the blends are homogeneous on a scale of 2.5–3.5 nm. The results suggested that iPS and PCHMA are intimately mixed at the molecular level within the blends at all compositions. The tacticity of polystyrene does not seem to adversely influence the miscibility in blends of iPS/PCHMA. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 772–784, 2003     

Miscibility and thermal properties of melt‐mixed poly(trimethylene terephthalate)/amorphous copolyester blends

This work examined the miscibility, crystallization kinetics, and melting behavior of melt‐mixed poly(trimethylene terephthalate) (PTT)/poly(ethylene‐co‐cyclohexane 1,4‐dimethanol terephthalate) (PETG) blends. Differential scanning calorimetry (DSC) and wide‐angle X‐ray diffraction techniques were used to approach the goals. The single composition‐dependent glass‐transition temperatures of the blends and the equilibrium melting temperature (T) depression of PTT in the blends indicated the miscible characteristic of the blend system at all compositions. T of pure PTT, determined with a conventional extrapolative method, was 525.8 K. Furthermore, the Flory–Huggins interaction parameter was estimated to be ?0.38. The dynamic and isothermal crystallization abilities of PTT were hindered by the incorporation of PETG. A complex melting behavior was observed for pure PTT and its blends. The observed complex melting behavior resulted mainly from the recrystallization and/or reorganization of the originally formed crystals during the heating scans. For the samples crystallized under the same conditions, the degree of recrystallization and/or reorganization declined with increasing PETG contents in the blends. The preliminary results obtained from the DSC experiments suggested that untraceable interchange reactions occurred in the studied blends. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2264–2274, 2003     

Phase behavior and crystallization analysis in binary crystalline blends of syndiotactic polypropylene and ethylene—Propylene random copolymer

The effects of liquid–liquid (L–L) phase separation on the crystallization behavior of binary syndiotactic polypropylene (sPP) and ethylene–propylene random copolymer (PEP) mixtures are examined by phase‐contrast microscopy (PCM), differential scanning calorimetry (DSC), and cloud point measurements. The PCM experiments reveal that blends of sPP and PEP exhibit a lower critical solution temperature behavior in the melt. The L–L phase diagram, constructed in terms of temperature (T) and composition by cloud point measurements, follows the prediction of the Flory–Huggins theory with the interaction parameter between sPP and PEP [χ(T) = 0.01153 ? 4.5738/T (K)]. When the blends are melted within the two liquid‐phase (α and β) regions, because of the fact that each phase domain reaches the equilibrium concentration ? and ? as well as the phase volume fraction ν^α and ν^β, the crystallinity of each component obeys the equation X_C,I = ν^α X + ν^β X, I = PEP, sPP. Also, the equilibrium melting temperatures of both components remain constants, slightly lower than those of neat polymers. For the sPP/PEP blends crystallized from one homogeneous phase in the melt, we observe that the crystallizability of the major component is not greatly affected upon blending. However, the crystallization behavior of the minority component in the presence of the major component is strongly dependent on the crystallization temperature (T_c). When T_c is high, because the decreasing degree of the minority mobility is much greater than the increasing degree of the formed nuclei, the crystallizability of the minor component is depressed significantly. On the other hand, the promotion of the minority crystallizability in the intermediate regime of T_c is mainly because of the large increase of the heterogeneous nuclei upon blending with a major component. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2995–3005, 2004     

New simple method of measuring the surface glass transition temperature of polymers

A lap‐shear joint mechanical testing method has been probed to measure the surface glass transition temperature (T) of the thick bulk films of high‐molecular‐weight polymers. As T, the temperature transition “occurrence of autoadhesion–nonoccurrence of autoadhesion” has been proposed. The influence of chain flexibility, of molecular architecture, of polymer morphology, and of chain ends concentration on the T has been investigated. The correlation between the reduction in T with respect to the glass transition temperature of the bulk (T) and the intensity of the intermolecular interaction in the polymer bulk in amorphous polymers has been found. The effect of surface roughness on T has been discussed. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 2012–2021, 2010     

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     

Crystallization mechanism of regioregular poly(3‐alkyl thiophene)s

The crystallization properties of three regioregular poly(3‐alkyl thiophene)s (P3ATs) are studied: poly(3‐hexyl thiophene) (P3HT), poly(3‐octyl thiophene) (P3OT), and poly(3‐dodecyl thiophene) (P3DDT). The morphology of the isothermally crystallized samples is a whisker type. The values of the enthalpy of fusion of ideal crystals (ΔH), determined from the melting point depression in the polymer–diluent system, are 99, 73.6, and 52 J/g for P3HT, P3OT, and P3DDT, respectively. The values of the equilibrium melting point (T), determined from the Hoffman–Weeks extrapolation procedure, are 300, 230, and 180 °C for P3HT, P3OT, and P3DDT, respectively. From the linear extrapolation of the P3AT data, the T and ΔH values of unsubstituted polythiophene are predicted to be 400 °C and 139 J/g, respectively. The crystallization kinetics of these polymers are studied with differential scanning calorimetry, and the Avrami exponents vary between 0.6 and 1.4, indicating one‐dimensional heterogeneous nucleation with linear growth. As the P3AT whiskers are produced from the chain‐folding process, the Lauritzen–Hoffman growth rate theory is applied to analyze the temperature coefficient of the crystallization rate data. Graphical plots indicate a transition from regime I to regime II during isothermal crystallization for all the P3ATs studied. The fold surface energy and the work of chain folding calculated from the slopes of the graphical plots decrease with an increase in the number of carbon atoms of the side chain. The primary crystallization process of the side‐chain crystallization is very fast and is attributed to the zipping effect of the main‐chain crystals. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2073–2085, 2002     

Crystallization studies of poly(trimethylene terephthalate) using thermal analysis and far‐infrared spectroscopy

Crystallization of poly(trimethylene terephthalate) (PTT) by annealing was examined using density measurement, differential scanning calorimetry, and far‐infrared spectroscopy (FIR). Crystallinity, measured by density, increased slowly up to the T_a of 185 °C and increases rapidly once T_a exceeds 185 °C. It was found that thermally induced crystallization is mainly temperature‐dependent above T_a = 185 °C and temperature‐ and time‐dependent below T_a = 60 °C. Two melting transitions, T and T, were observed for those samples annealed above 120 °C. No significant change in T was observed as a function of T_a while T showed strong dependency on T_a. Digital subtraction of the amorphous contribution from the semicrystalline FIR spectra provided characteristic spectra of amorphous and crystalline PTT. The bands at 373, 282, and 92 cm^?1 were assigned to the crystalline phase, while the bands at 525, 406, and 351 cm^?1 were attributed to the amorphous phase. It was shown that FIR spectroscopy can be used as a means to estimate the degree of crystallinity of PTT. The band ratio of 373 and 501 cm^?1 was plotted against crystallinity measured by density and reasonably good correlation was obtained. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1675–1682, 2007     

Thermodynamic and kinetic thermal analyses on dual crystal forms in polymorphic poly(heptamethylene terephthalate)

Thermal analyses were performed for determining the equilibrium melting temperatures T of the respective α‐ and β‐crystal in melt‐crystallized polymorphic poly(heptamethylene terephthalate) (PHepT) using both linear and nonlinear Hoffman‐Weeks (H‐W) methods for comparison of validity. These two crystals in PHepT do not differ much in their melting temperatures. The equilibrium melting temperatures of the α‐ and β‐crystal as determined by the linear H‐W method are 98 °C and 100.1 °C, respectively; but the nonlinear H‐W method yielded higher values for both crystals. The equilibrium melting temperatures of the α‐ and β‐crystal according to the nonlinear H‐W method are 121 °C and 122.5 °C, respectively. Both methods consistently indicate that T of the β‐crystal is only slightly higher than that of the α‐crystal. Such small difference in T between the α‐ and the β‐crystal causes difficulties in judging the relative thermodynamic stability of these two crystals. Thus, kinetics of these two crystals was compared using the Avrami and Ozawa theory. The crystallization produced by quenching from T_max = 110 °C and 150 °C shows a heterogeneous and homogeneous nucleation mechanism, respectively. The lower T_max = 110 °C leads to heterogeneous nucleation and only α‐crystal in PHepT, whose crystallization rates at same T_c are much higher than crystallization rates by quenching from T_max = 150 °C leading to either α‐ or β‐crystal with homogeneous nucleation. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1839–1851, 2009     

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.     

Linear versus nonlinear determinations of equilibrium melting temperatures of poly(trimethylene terephthalate) and miscible blend with poly(ether imide) exhibiting multiple melting peaks

Multiple melting peaks in some semicrystalline polymers such as poly(trimethylene terephthalate) (PTT) have caused some difficulty in estimating accurately the equilibrium melting points. PTT forms a miscible blend with amorphous poly(ether imide) (PEI); for comparison purposes, a miscible system of a fixed composition (PTT/PEI of weight ratio = 9/1) was determined. PTT and its miscible blend both exhibited dual melting peaks (labeled as low and high peaks: T_m,L, T_m,H), and the first peaks (T_m,L), not the second peak (T_m,H), should be used for extrapolation. The equilibrium melting temperatures (T) of neat PTT and its blend PTT/PEI (9/1) were 245.2 and 242.4 °C, respectively, by the linear Hoffman–Weeks treatment using the corrected values of T_m,L (i.e., values obtained using a heating rate close to zero). Linear and nonlinear treatments led to a significant difference in estimated T, and the relative validity of these two methods is discussed. The nonlinear estimate yielded a higher value by about 27.3 °C for neat PTT and 23.1 °C for the PTT/PEI (9/1) blend, respectively (also the correction in T_m,L at the same condition mentioned previously). Results showed melting depression in miscible PTT/PEI (9/1). In addition, the T value of neat PTT was higher than that of PTT/PEI (9/1) owing to much thicker and more‐perfect crystals in neat PTT. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1571–1581, 2002     

Spin probe mobility in relation to free volume and relaxation dynamics of glass‐formers: A series of spin probes in poly(isobutylene)

We present the dynamics of a series of three paramagnetic molecules of different volume, mass, and shape in amorphous glass‐forming polymer poly(isobutylene) (PIB) as investigated by means of electron spin resonance (ESR) technique. The reorientation behavior of spin probes is related to the ortho‐positronium (o‐Ps) annihilation in PIB from positron annihilation lifetime spectroscopy (PALS) and the extracted free volume information. It is also related to the dynamic data of PIB from broadband dielectric spectroscopy (BDS), neutron scattering (NS), and nuclear magnetic resonance (NMR) spectroscopy from literature. In the case of the smallest spin probe, 2,2,6,6‐tetramethyl‐1‐piperidinyloxy (TEMPO), a discontinuous course of the spectral parameter 2A_zz′ versus T dependence was observed and the subsequent phenomenological model‐free analyses of the spectral parameter, 2A_zz′ versus T, as well as of the correlation time, τ_c, versus 1/T plots provided the characteristic ESR temperatures ( , T_50G, ) and (T, T, T). These characteristic ESR temperatures were found to be consistent with the characteristic PALS temperatures: T, T = T from temperature dependences of the mean o‐Ps lifetime, τ₃, or the width of o‐Ps lifetime distribution, σ₃, respectively. In addition, the relationships between the spin probe size, V, and the free volume hole size distributions g_n(V_h) at the characteristic ESR temperatures indicate the significant influence of the free volume fluctuation at the crossover from slow to rapid regime as well as within the rapid motional regime. On the other hand, the two larger spin probes exhibit a rather continuous 2A_zz′–T plots with the respective T_50G's lying in the vicinity of T independently of their volume, mass and shape, suggesting the common origin of underlying process controlling this T_50G transition. Finally, these mutual PALS and ESR findings were compared with the known dynamic behavior of PIB which suggest that the dynamics of the TEMPO and the larger spin probes are related to free volume fluctuation associated with primary α ‐ and secondary β processes, respectively. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1058–1068, 2009     

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     

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     

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     

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.     

Isothermal crystallization behavior of poly(L‐lactide) in poly(L‐lactide)‐block‐poly(ethylene glycol) diblock copolymers

The crystal unit‐cell structures and the isothermal crystallization kinetics of poly(L ‐lactide) in biodegradable poly(L ‐lactide)‐block‐methoxy poly(ethylene glycol) (PLLA‐b‐MePEG) diblock copolymers have been analyzed by wide‐angle X‐ray diffraction and differential scanning calorimetry. In particular, the effects due to the presence of MePEG that is chemically connected to PLLA as well as the PLLA crystallization temperature T_C are examined. Though we observe no variation of both the PLLA and MePEG crystal unit‐cell structures with the block ratio between PLLA and MePEG and T_C, the isothermal crystallization kinetics of PLLA is greatly influenced by the presence of MePEG that is connected to it. In particular, the equilibrium melting temperature of PLLA, T, significantly decreases in the diblock copolymers. When the T_C is high so that the crystallization is controlled by nucleation, because of the decreasing T and thereafter the nucleation density with decreasing PLLA molecular weight, the crystallinity of PLLA also decreases with a decrease in the PLLA molecular weight. While, for the lower crystallization temperature regime controlled by the growth mechanism, the crystallizability of PLLA in copolymers is greater than that of pure PLLA. This suggests that the activation energy for the PLLA segment diffusing to the crystallization site decreases in the diblocks. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2438–2448, 2006     

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     

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