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Individual alkanethiol-functionalized gold nanorods act as morphological seeds that specifically template the growth and direction of large, uniform, cylindrical-phase domains from a polystyrene-block-polyisoprene (PS-b-PI) copolymer solution. Adding less than 0.0001 vol % nanorods switched the preference of domain growth from predominantly spherulitic to almost exclusively single crystalline, with the PI cylinders uniformly aligned in the same direction as each seeding nanorod. Polarized and dark-field optical microscopy on individual domains and small-angle X-ray scattering experiments on bulk material confirmed this specific seeding effect. By contrast, we find that spherical gold nanoparticles and other materials that are commonly used as heterogeneous nucleants in crystallization (e.g., carbon black, talc, and calcium carbonate) failed to promote single-crystalline domain growth in the same material. Mesoscale dynamic modeling of nanorod−copolymer mixtures illustrates these observations in terms of a specific interaction between the surface of the nanorods and the polyisoprene block, which orients the self-assembling polyisoprene cylinders in the nascent domain nucleus.

Amine-terminal polystyrene (PS-NH2) was reacted with an anhydride-terminal poly(methyl methacrylate) (PMMA-anh-pyr) at the interface between quiescent PS and PMMA layers, annealed for various times up to 2 h at 175 °C. The concentration of the PS-NH2 in the PS layer was varied from 10% to 100%. By virtue of pyrene labeling, the PMMA-anh-pyr conversion to copolymer in the early stages of the reaction could be measured with a fluorescence detector coupled to a size exclusion chromatograph. Interfacial morphology development was monitored with both atomic force microscopy (AFM), after washing off the top PS layer, and transmission electron microscopy (TEM), in cross section. It was found that the coupling reaction at the initial stage is rapid. Detectable block copolymer interfacial coverage (Σ) and interfacial roughness were obtained even after only 5 min annealing. Further annealing the samples increased Σ significantly when the PS-NH2 concentration exceeded 25%. In this case Σ exceeded the value expected for a saturated monolayer of copolymer Σ*, suggesting emulsification at the interface. The surface roughness determined by AFM supports this conclusion, as the RMS roughness is low when Σ < Σ* but increases dramatically when Σ > Σ*. After the emulsification transition, however, the AFM roughness no longer increases because the emulsified material is washed away with the PS layer. With TEM, the emulsified region could be observed at the interface directly. Furthermore, the interfacial roughness values from AFM and TEM agree well.

Polycarbonate/poly(ε-caprolactone) (PC/PCL) blends are found to be miscible when extruded samples are studied without any further thermal treatment. PCL crystallizes in blends containing 60% or less polycarbonate, a component that remains amorphous for all blend compositions under these conditions. Single, broad calorimetric glass transitions together with distinct component dynamics determined by thermally stimulated depolarization current experiments indicate the miscibility of the blends and the existence of different average local compositions. The Lodge−McLeish model is applied to the compositional variation of the two effective glass transition temperatures. Quantitative agreement is obtained for both components by adjusting the self-concentration values to best fit the experimental points. The relevant length for PCL is very close to its Kuhn length, whereas for PC the best fit leads to a slightly shorter characteristic length. It is shown that upon annealing at sufficiently high-temperature PC undergoes crystallization and thereby induces phase segregation in the otherwise amorphous regions of the blends.

The phase behavior of symmetric styrene−isoprene (SI) diblock copolymers in selective solvents in the vicinity of the order−disorder transition (ODT) was investigated by small-angle neutron scattering (SANS). Particular emphasis is placed on the region just above the ODT, where a disordered phase of micelles is observed. To understand morphological changes in more detail, one of the blocks is deuterated, i.e., PS−dPI and dPS−PI, and the scattering length density (SLD) of the solvents used were identical to the SLD of the corona chains. Two approaches for the analysis of SANS data were taken:  the generalized indirect Fourier transformation (GIFT) and direct model fitting with relevant form and structure factors. With increasing temperature, the micellar aggregation number decreases, and the core radius is roughly maintained by the increased solvent swelling of the core. The critical micelle temperature (cmt) is experimentally described in the present study by an abrupt decrease in the size, aggregation number, and volume fraction of micelles. The micelles were found to dissociate into free chains approximately 20−30 °C higher than the TODT, and the cmt is found to be quite close to the mean-field spinodal temperature TS. A mean-field temperature, TMF, is located by the crossover temperature from the linear behavior of Imax^-1 vs T^-1 plot, and the structure factor above the experimentally determined TMF is also found to be in good agreement with the Leibler−Landau-type mean-field theory. We examined two different ODTs:  body-centered cubic lattices to disorder and hexagonal cylinders to disorder, with similar results in both cases.

The phase behavior of a symmetric styrene−isoprene (SI) diblock copolymer in a styrene-selective solvent, diethylphthalate, was investigated by in situ small-angle X-ray scattering on isotropic and shear-oriented solutions and by rheology and birefringence. A remarkable new feature in this phase diagram is the coexistence of both body-centered cubic (bcc) and hexagonally close-packed (hcp) sphere phases, in a region between close-packed spheres (cps) and hexagonally packed cylinders (hex) over the concentration range φ ≈ 0.33−0.45. By focusing on the transitions among these various ordered phases during heating and cooling cycles, we observed a strong hysteresis:  supercooled cylinders persisted upon cooling. The stability of these supercooled cylinders is quite dependent on concentration, and for φ ≥ 0.40, the supercooled cylinders do not revert to spheres even after quiescent annealing for 1 month. The spontaneous formation of spheres due to the dissociation of cylinders is kinetically hindered in this case, and the system is apparently not amenable to any pretransitional fluctuations of cylinders prior to the cylinder-to-sphere transition. This contrasts with the case of cylinders transforming to spheres upon heating in the melt. The application of large amplitude shear to the supercooled cylinders is effective in restoring the equilibrium sphere phases.

A single concentration solution (36 vol %) of a symmetric polystyrene-block-polyisoprene, total molecular weight 30 000, in the styrene-selective solvent diethyl phthalate shows a remarkably rich sequence of thermotropic order−order transitions (OOT). A combination of small-angle X-ray scattering measurements both under quiescent conditions and after shear orientation, supplemented with rheology and static birefringence, indicates the following phase sequence. At room temperature the solution adopts a close-packed lattice of spherical micelles, corresponding to a mixture of face-centered-cubic (fcc) and hexagonally close-packed (hcp) phases. At approximately 60 °C the solution undergoes a “partial” OOT, in that the fcc portion transforms to body-centered-cubic (bcc), whereas the hcp domains persist. At approximately 82 °C the hcp/bcc mixture transforms to hexagonally packed cylinders, and finally the cylinder phase undergoes the order−disorder transition at 113 °C. Through the use of two different shear cells, scattering patterns along both shear gradient and vorticity axes were obtained. These data confirmed that all three OOTs (fcc to bcc, bcc to cylinder, and hcp to cylinder) are epitaxial. The first two follow the pathways previously established, whereas the hcp to cylinder is described for the first time in block copolymers. Among the other novel features of this system are the proximity to a triple line (coexistence of hcp, bcc, and cylinders) at 82 °C.

We describe a general procedure for the synthesis of miktoarm star triblock copolymers with a hydrocarbon, a fluoropolymer, and a hydrophilic segment. Several μ-(polyethylethylene)(poly(ethylene oxide))(poly(perfluoropropylene oxide)) [μ-(PEE)(PEO)(PFPO)] star triblock copolymers were prepared using two successive anionic polymerization steps and one polymer−polymer coupling reaction. Initially, living polybutadienyllithium chains were end-capped with 2-methoxymethoxymethyloxirane forming a heterobifunctional 1,2-polybutadiene (PBD) precursor, with a hydroxyl group and a protected hydroxyl group at one chain end. Catalytic hydrogenation of this PBD gave the corresponding polyethylethyene (PEE) while preserving the end group structures. Transformation of the terminal hydroxyl group in the PEE precursor to a potassium alkoxide followed by addition of ethylene oxide and subsequent end-capping with ethyl bromide generated polyethylethylene−poly(ethylene oxide) (PEE−PEO) diblock copolymers with a protected hydroxyl group at the junction. Deprotection of the methoxymethyl group followed by coupling with acid chloride end-capped PFPO yielded well-defined μ-(PEE)(PEO)(PFPO) star triblock copolymers. Detailed molecular characterization of these products and their precursors confirmed the composition and architecture of these new star block copolymers. This modular strategy represents a new, straightforward, and versatile methodology for the preparation of mixed arm star block copolymers.

Self-diffusion measurements have been performed on an ordered asymmetric poly(ethylene-alt-propylene-b-dimethylsiloxane) PEP−PDMS block copolymer (Mn = 30 000, fPEP = 0.79) using forced Rayleigh scattering (FRS). Samples were prepared with three different degrees of macroscopic alignment of the hexagonally packed PDMS cylinders. The diffusion coefficients parallel (Dpar) and perpendicular (Dperp) to the cylinder axes were resolved. For a high degree of macroscopic alignment both Dpar and Dperp were found to be significantly retarded compared to D0, the diffusion coefficient in the absence of any interactions. Dperp follows a hindered diffusion mechanism, while Dpar is consistent with a block retraction mechanism; both of these mechanisms have been described previously in the context of block copolymer spheres and lamellae, respectively. The extracted Dperp was dependent on the degree of alignment, with the apparent Dperp increasing as the degree of alignment deteriorated, whereas Dpar was essentially independent of the degree of alignment. This behavior of Dperp is interpreted in terms of defects in the samples (i.e., both misoriented cylinders and dislocations).

The ordering kinetics of the cylinder phase were characterized using polarizing optical microscopy (POM). Measurements were made on a poly(styrene-b-isoprene) diblock copolymer with block lengths of 15 and 13 kg/mol, respectively, in solution with dibutyl phthalate at a polymer volume fraction of 0.50. Thermal quenches from above the disordering temperature, 39.6 °C, to temperatures ranging from 36.5 to 38.4 °C allowed for direct observation of nucleation and growth. Two modes of grain growth were observed after nucleation:  spherulites and oblate ellipsoids. The ellipsoidal grains had an aspect ratio of 2 and corresponded to single crystals with the cylinders parallel to the minor axis of the ellipsoid. In contrast, the spherulites were polycrystalline, with the cylinder axes predominantly tangential to the spherulite. Ellipsoids and spherulites occurred with comparable frequency at all quench depths. The growth front velocities of individual grains were measured, and the velocities for spherulites and for the major axes of the ellipsoids were approximately twice that along the minor axis of the ellipsoids. The growth front velocities were quantitatively compared to the expression of Goveas and Milner, with good agreement in the temperature dependence. Application of the Avrami equation to the observed ordered fraction yielded parameters in good agreement with those inferred microscopically for heterogeneous nucleation and three-dimensional growth.

The effect of block number on the order−disorder transition (ODT) and viscoelastic properties were studied for linear (AB)n multiblock copolymers. A series of symmetric poly(styrene-b-isoprene)n multiblocks ((SI)n, n = 1−10) were synthesized by anionic polymerization, and their order−disorder transition temperatures (TODT) were located using dynamic mechanical spectroscopy. As n increases, TODT approaches an asymptotic value, consistent with random phase approximation calculations. A systematic difference between the experimental and theoretical results is attributable to the effects of fluctuations, independent of the number of blocks. Addition of up to 20 vol % of a nonselective solvent depresses TODT, independent of n. The interaction parameter at the transition, χODT, decreases with polymer volume fraction φ as χODT ~ φ^-1.3, consistent with previous reports for diblocks (n = 1). In contrast, the viscoelasticity of (AB)n block copolymers depends strongly on block number. A crossover frequency, ωx, demarcating the transition from block/chain- and domain-dominated relaxation, scales as n^-7.5, which is much stronger than the molecular weight dependence of the longest relaxation time for entangled homopolymers. Coherent lamellar grains were imaged for quenched and annealed (SI)n, n = 1, 6, and 10, by transmission electron microscopy. Ellipsoidal lamellar grains, with aspect ratios of 2−3, were recorded, independent of block number, but the grain size decreased with increasing n. These results establish the criteria for designing multiblock copolymers based on χ, N, n, and concentration.

A series of 4,1-polyisoprene-b-1,2-polybutadiene diblock copolymers of differing molecular weights and compositions were prepared by anionic polymerization. The polybutadiene blocks were selectively hydrogenated to poly(ethylethylene) using a homogeneous ruthenium catalyst. The double bonds in the polyisoprene blocks were subsequently modified to varying extents by the addition of difluorocarbene. The precursor polyisoprene−poly(ethylethylene) materials were disordered, but upon difluorocarbene (CF2) addition the effective degree of segregation in these materials increased markedly. Small-angle X-ray scattering was used to characterize the ordered state morphologies and domains spacings. Effective interaction parameters (χeff) were extracted from the temperature- and composition-dependent domain spacings, and these in turn were used to place the various samples on an experimental segregation vs composition phase map. The interaction parameter between poly(ethylethylene) and polyisoprene increases by a factor of 370 upon complete CF2 modification. This large enhancement enables examination of a much wider range of segregation strength than is accessible by varying temperature. A notable feature of these results is that the gyroid phase appears to be stable into the strong segregation regime, in contrast to expectations based on self-consistent-field theory.

The Lodge/McLeish model successfully fits the temperature and composition dependences of the segmental dynamics for both components in disordered styrene−isoprene tetrablock copolymers (SISI). The fitted parameters φself are in good agreement with the values anticipated in the Lodge/McLeish model after accounting for the junction effect. A geometric mean mixing rule was used to average the segmental dynamics of the two components in order to describe tracer diffusion in the SISI matrices. This mixing rule accurately reproduces previously reported experimental results for polyisoprene, polystyrene, and styrene−isoprene diblock tracers. The unusual homogeneity of these matrices, as inferred from tracer diffusion measurements, is discussed in terms of thermodynamic barriers to diffusion.

The kinetics of grain growth during thermally induced phase transitions between two block copolymer ordered phases have been determined by polarized optical microscopy (POM). Measurements were made on poly(styrene-b-isoprene) copolymers, fPS = 0.3−0.6, in solutions with dialkyl phthalates at polymer volume fractions of 0.5−0.7. When these solutions are cooled from a disordered state, they exhibit a transition from the transient metastable hexagonally perforated layer (HPL) phase to the gyroid (G) phase. The HPL to G transition typically occurs through classical nucleation, with radially symmetric grain growth, making it a model system for quantifying the growth front velocities of individual G grains. Temperature jump experiments monitored with POM were used to determine the effect of quench depth on the grain growth rates. Grain growth rates are compared quantitatively to the theoretical predictions of Goveas and Milner, with good agreement observed.

We have examined the effect of monomer structure on amine−anhydride reactions at a polymer−polymer interface. The thermodynamic interaction parameter χ was varied by changing the backbone chemical structure, holding molecular weight constant. To eliminate the effects of mixing, experiments were performed with bilayer thin films of end-functional polymers. Using a combination of size exclusion chromatography with fluorescent labeling, we measured the extent of reaction of anhydride-terminal poly(methyl methacrylate) and polystyrene with amine-functional polystyrene, polybutadiene, poly(ethylene/ethylethylene), and poly(dimethylsiloxane). Interfacial structure was observed by atomic force microscopy. Both the conversion to block copolymer and the degree of interfacial roughening are suppressed with increasing χ. This suppression may be related to reduced solubility of the reactive homopolymers in the formed block copolymer and to decreased interfacial volume for reactions to occur. Viscosity does not play a significant role in these studies. In melt blends of similar polymers prepared in a cup-and-rotor mixer, the rate of reaction and extent of conversion also generally decrease with increasing χ. The rates are up to 100 times faster, suggesting that convection sweeps away block copolymer that forms at the interface. These results indicate that thermodynamic interactions play a significant role in determining rates of reaction at polymer interfaces.

The self-diffusion and tracer diffusion of asymmetric poly(ethylene-alt-propylene-b-dimethylsiloxane), PEP−PDMS, copolymers were measured using forced Rayleigh scattering. Diffusion measurements were made in the disordered state, in disordered micelles, and in the body-centered-cubic (bcc) sphere phase. The FRS intensity decays were fit with a single-exponential function in the disordered state and a stretched exponential function in disordered micelles and bcc spheres. The decays are interpreted as the diffusion of single chains with a broadened distribution of relaxation times when micelles are present, due to the polydispersity of chain lengths. The diffusion coefficients in disordered micelles and bcc spheres are retarded compared to the disordered state. This retardation is consistent with a hindered diffusion process, D ~ D0 exp(−AχNA), where χ is the Flory−Huggins interaction parameter, D0 is the diffusion coefficient as χ approaches zero, and NA is the length of the core block. The parameter A is found to increase as χNA increases. These results are compared with recent experimental and computational work.

The frequency-dependent shear moduli were measured over a range of temperature for polyisoprene (PI, M = 22 000 and 78 000), poly(vinylethylene) (PVE, M = 10 000 and 120 000), and their blends. The longest relaxation times of each component in the blends were extracted by a modified Tsenoglou mixing rule, and converted to monomeric friction factors via the reptation model. Dielectric relaxation and pulsed field gradient NMR were used to follow the terminal relaxation and diffusion, respectively, of a low molecular weight PI (M = 1300) in blends with perdeuterated PVE (M = 2300), for a range of temperature and composition. In this case monomeric friction factors were extracted via the Rouse model. The friction factors for PI via all three techniques agreed quantitatively, and the friction factors for both components were independent of molecular weight. Segmental dynamics of each component in PI/PVE blends by NMR methods, reported in the literature, could be compared directly with the terminal relaxation data. In all cases, the segmental and terminal dynamics exhibited equivalent dependences on temperature and composition. The predictions of the model of Lodge and McLeish were compared to the combined data, by calculating component self-concentrations and effective glass transition temperatures using a single temperature-independent length scale. As anticipated in the original model, this length scale is close to the Kuhn length of the particular component. In the case of PI, the model provides a quantitative description over the entire composition and temperature range studied. For PVE the agreement is not as quantitative, but it is still quite satisfactory.

The phenomenon of “anomalous” micellization is investigated in dilute solutions of two nearly symmetric poly(styrene-b-isoprene) diblock copolymers, via dynamic light scattering. In two polystyrene-selective solvents, diethyl phthalate and dimethyl phthalate, the critical micelle temperatures (cmt) are clearly determined by rather abrupt increases in the hydrodynamic radius and scattered intensity upon cooling; this corresponds to “normal” micellization. In contrast, for the same polymers dissolved in two polyisoprene-selective solvents, tetradecane and squalane, anomalous micellization was consistently observed:  the hydrodynamic radius exceeded 1000 Å and the intensity was unusually large, over a modest temperature interval just above the cmt. We propose that anomalous micellization is due to the incipient phase separation of small amounts of polystyrene homopolymer, resulting from incomplete crossover during the sequential anionic polymerization of styrene and isoprene. In one sample, the presence of homopolymer (ca. 1 wt % of copolymer) was confirmed by chromatography, and removal of this impurity eliminated the anomalous micellization. Addition of similar amounts of polyisoprene homopolymer to the same sample induced anomalous micellization in the polystyrene-selective solvents, with the onset of the effect corresponding to the cloud point for the polyisoprene homopolymer. These observations support the proposed hypothesis; the extent to which this hypothesis may extend to previous reports of anomalous micellization is discussed.

The phase behavior of eight poly(styrene-b-isoprene) diblock copolymers in the neutral solvent dioctyl phthalate (DOP) has been examined over the full concentration (φ) range and from room temperature up to 250 °C. The copolymer compositions (f) ranged from 0.15 to 0.76, and molecular weights were chosen to make the melt order−disorder transition (ODT) accessible, or nearly so. Definitive phase assignments were made on the basis of small-angle X-ray scattering (SAXS). Individual order−order transitions (OOTs) and ODTs were located by a combination of rheology, static birefringence, and SAXS; all three techniques gave equivalent results. The transition temperatures were converted to values of the effective interaction parameter, χ, using an established relation for this system. For all compositions, χODT scales as φ^-α, with α varying from 1.3 to 1.6. These results are in conflict with the mean-field dilution approximation (α = 1.0), as was previously demonstrated for lamellae-forming samples. This result is attributed to the additional fluctuation stabilization of the disordered state in two-component solutions. Three of the samples displayed OOTs:  cylinder to sphere (f = 0.15), gyroid to cylinder (f = 0.31), and lamellae to gyroid (f = 0.33). In each case, χOOT scaled as φ^-1.0, in agreement with the dilution approximation. This result underscores the reliability of mean-field theory for computing relative free energies of the various ordered phases. The domain spacing, d, scales approximately as φ^0.33 and χ^0.25, independent of morphology, in good agreement with both mean-field theory and previous experiments.

Two asymmetric poly(ethylenepropylene-b-dimethylsiloxane) diblock copolymer melts have been examined by rheology, small-angle X-ray scattering (SAXS), and small-angle neutron scattering (SANS). The two copolymers have total molecular weights of 24 400 and 23 900 and PDMS volume fractions of 0.12 and 0.10, respectively. The latter copolymer was obtained by extensive fractionation of the former, the difference in composition arising primarily from the removal of traces of PDMS homopolymer. The order−disorder transition (ODT) is unambiguously identified by rheology and SAXS. Above the ODT the SANS and rheological properties are consistent with the recently proposed disordered micelle regime, whereby the copolymers are associated in micellar aggregates that are not ordered on a lattice. The viscosity of the melt in this regime is greater than that of a poly(ethylenepropylene) homopolymer of the same total molecular weight. The SANS structure factors were analyzed by a generalized inverse Fourier transform and by direct fitting to a model based on the Percus−Yevick structure factor and either a spherical or an ellipsoidal form factor. Both approaches give comparable results, and the average micelle core radius, effective hard-sphere radius, and volume fraction were extracted as a function of temperature. The fitting suggests that as temperature increases the micelles remain relatively unchanged, but their number density and volume fraction decrease steadily. The fractionated copolymer has a significantly smaller micellar core than its precursor and therefore a significantly smaller aggregation number. These differences are attributable to the partitioning of PDMS homopolymer into the micellar cores. For these samples the critical micelle temperature (cmt), where the volume fraction of micelles should become negligible, was not accessed, even 100 deg above the ODT.

Transient rheological measurements are reported for a model polymeric bicontinuous microemulsion. The sample consists of a ternary blend of poly(ethyl ethylene) (PEE) and poly(dimethyl siloxane) (PDMS) homopolymers and a symmetric PEE-PDMS diblock copolymer. Steady-flow rheological data, reported previously, show four regimes as a function of increasing shear rate. Newtonian behavior is observed in regime I, followed by shear thinning in regime II. Flow-induced phase separation is the hallmark of regime III. The microemulsion starts ejecting homopolymer-rich phases, and the shear stress is independent of shear rate. In regime IV, complete phase separation occurs and the sample behaves like an immiscible blend. Transient rheological data on flow inception reveal linear viscoelastic response in regime I, and development of a stress overshoot in regime II. In regime III, a strong stress overshoot is observed, followed by a “shoulder” and a slow decay to the steady, rate-independent value. The normal stress shows a similar response as the shear stress. The transient morphology development has been further characterized using light scattering and microscopy. A “double-streak” pattern develops in light scattering on flow inception, which ultimately evolves into a “single-streak” pattern. Optical microscopy shows development of a string-like morphology, indicating a transition in lengthscale from tens of nanometers to microns. Transient rheological measurements on step changes in shear rate, both within and between regimes III and IV, and also on flow cessation, support the proposed morphologies.

The cylinder-to-gyroid transition in a block copolymer solution has been studied using a combination of rheology and small-angle X-ray scattering (SAXS). A poly(styrene-b-isoprene) diblock copolymer with block molecular weights of 11 000 and 32 000 g/mol, respectively, dissolved in the styrene-selective solvent di-n-butyl phthalate (DBP) at a volume fraction of 0.67 exhibits an order−order transition between hexagonally packed cylinders (C) and the cubic gyroid phase (G) at 74 ± 3 °C. A shear-oriented C phase transforms to G epitaxially, as previously established in melts. For shallow quenches into G, the transition proceeds directly by a nucleation and growth process. For deeper quenches, a metastable intermediate structure appears, with scattering and rheological features consistent with the hexagonally perforated layer (HPL) state. The appearance of the HPL state beyond a certain quench depth is reconciled with previous experiments and theory for the lamellar (L)-to-gyroid transition. The C → G transition follows the same pathways, and at approximately the same rates, even when the initial C phase is not shear-oriented. The transition rates are quantified as a function of quench depth. The reverse G → C transition demonstrates a memory of the initial cylinder orientation that persists even after annealing the G phase for 48 h. The results are discussed and compared with related work in the literature.

The phase behavior of six poly(styrene-b-isoprene) (SI) diblock copolymers has been mapped out in the styrene-selective solvents di-n-butyl phthalate (DBP), diethyl phthalate (DEP), and dimethyl phthalate (DMP). The polymer molecular weights were chosen to make the melt order−disorder transition (ODT) experimentally accessible, and the styrene compositions f ranged from 0.23 to 0.70, to access the full range of melt morphologies. For each polymer a phase diagram was constructed, with polymer volume fractions, φ, ranging from 0.01 to 1.0 and temperatures, T, from 0 to 250 °C. Phase assignments were based on small-angle X-ray scattering (SAXS), and the ODTs and order−order transitions (OOTs) were located by a combination of SAXS, rheology, and static birefringence. The critical micelle temperatures (cmt) in dilute solution were determined by dynamic light scattering. In this manner the full “phase cube” was mapped out in each solvent, enabling generation of phase maps (φ,f) at constant T and (f,T) at constant φ. The solvents range from slightly to strongly selective, in the sequence DBP, DEP, and DMP, and in each case the selectivity diminishes with increasing T. This property gives rise to a plethora of thermally induced OOTs, and several solutions exhibit four distinct equilibrium phases upon heating. In addition to the eight phases well established for SI copolymers in the melt (a body-centered-cubic (bcc) array spheres of styrene or isoprene, hexagonally packed cylinders of styrene or isoprene, gyroid with isoprene or styrene matrix, lamellae, disordered), broad regions of lamellae + cylinder coexistence and face-centered-cubic (fcc) isoprene spheres were observed. The sequence of phases could be broadly understood in terms of changes in spontaneous interfacial curvature arising from differential swelling of the two microdomains. For a given polymer and solvent, the ODT varied smoothly with φ from the melt value down toward the dilute solution critical micelle temperature (cmt); at about φ ≈ 0.2 the ordered phases gave way to a solution of micelles. In some cases solutions near φ ≈ 0.2 exhibit reentrant ODTs, as they evolved from a solution of micelles to an fcc (and/or bcc) lattice, to a solution of chains, upon heating. The origins of these various phenomena are discussed, and the results are compared and contrasted with other measurements on SI copolymers in the literature.

Lamellae forming CEC triblock and CECEC pentablock copolymers located near the order−disorder transition temperature were subjected to reciprocating shear as a function of strain amplitude and thermal history. Both variables strongly influence the mix of perpendicular vs parallel lamellae alignment in the triblock copolymer, while only the strain amplitude significantly affects the pentablock material. Dramatically different responses of CEC vs CECEC to shear are rationalized on the basis of viscoelastic contrast and nonlinear chain stretching, each operating differently on the initially disordered and ordered states.

The cloud-point behavior of fluorinated polyisoprenes (FPI) and fluorinated polybutadienes (FPBD) in supercritical fluid (SCF) CO2 are reported at temperatures from 60 to 170 °C and pressures from 1000 to 3000 bar. These fluorinated polymers were prepared by the addition of difluorocarbene (CF2) to the parent polydienes yielding a gem-difluorocyclopropane repeating unit, a segment containing both fluorine and a significant dipole moment. Neither the unmodified polyisoprene starting material nor the hydrogenated variant dissolves in CO2 up to temperatures of 155 °C and pressures of 2600 bar. Both FPI and FPBD dissolve in CO2, but pressures in excess of 1000 bar are needed to obtain a single phase. The PFI and PFBD cloud-point curves exhibit temperature minima at approximately 60 and 80 °C, respectively, likely due to an increase in CO2−CO2 and polymer−polymer interactions relative to polymer−CO2 interactions. As the amount of CF2 incorporation in FPI samples decreases, the cloud-point curves shift to higher pressures and to higher temperatures. In a series of FPBD samples, an increase in cloud-point pressure with increase in molecular weight is initially large for molecular weights less than 10⁵ and then becomes much less at higher molecular weights, as also observed for other polymer−SCF solvent mixtures. This methodology for incorporation of fluorine into macromolecules leads to significant enhancement of solubility in CO2.

A series of partially fluorinated (C6F13H-modified) polystyrene-b-1,2-polybutadiene (PS-b-1,2-PB) copolymers were prepared by the reaction of a model PS-b-1,2-PB copolymer with n-C6F13I followed by substitution of hydrogen for the iodine by hydrogenolysis. The morphologies and domain spacings of the ordered samples at 120 and 195 °C were determined as a function of C6F13H modification extent using small-angle X-ray scattering (SAXS). From the domain spacings an effective interaction parameter (χeff) between the PS and partially C6F13H-modified 1,2-PB blocks was estimated. The χeff at 120 °C increases significantly with fluorination, from ca. 0.05 (0 mol % C6F13H modification) to ca. 0.75 (80 mol % C6F13H modification). The order−disorder transition temperature (TODT) for a partially C6F13H-modified PS-b-1,2-PB (25 mol %) was determined to be 186 ± 3 °C, using rheology and static birefringence. From self-consistent mean-field theory χeff for this block copolymer is estimated to be 0.16 at TODT, which agrees well with the value of 0.21 estimated from the domain spacing. These estimated interaction parameters demonstrate that a selective perfluoroalkylation approach can strongly enhance the incompatibility of PS-b-1,2-PB copolymers and is a powerful method for examining large regions of the block copolymer phase diagram with a single precursor molecule.

Ternary polymer blends of immiscible homopolymers and the corresponding diblock copolymer are useful models for studying equilibrium and nonequilibrium behavior of self-assembled fluids. We report linear viscoelastic data for a polymeric bicontinuous microemulsion, experiments that are possible due to the comparatively high viscosities of the principal components. After subtracting a viscous background contribution from the pure constituents, the microemulsion exhibits “excess” viscoelastic behavior similar in character to that resulting from the Rouse model of polymer dynamics. The data are compared to the predictions of a time-dependent Landau−Ginzburg model developed by Pätzold and Dawson, using structural parameters derived from neutron scattering as input. This model captures the essential characteristics of the viscoelastic behavior very well. However, using independent dynamic light scattering measurements of the Onsager coefficient for these blends, it appears that the model fails to predict either the magnitude or the temperature dependence of the zero shear viscosity and relaxation time of the microemulsion accurately. Possible origins for these discrepancies are discussed.

The order−disorder transition in a melt of asymmetric micelle-forming diblock copolymers is studied analytically in the strong segregation limit. In contrast to previous calculations by Semenov and by self-consistent mean-field theory, both the translational entropy of the micelles in a disordered micelle regime and the intermicelle free energy are taken into account. This enables us to locate the order−disorder transition, ODT, where the long-range order (or lattice) of micelles disappears. In agreement with some experimental observations, the ODT occurs between body-centered-cubic spheres and disordered micelles. A face-centered-cubic sphere phase remains thermodynamically unstable, as it is superseded by the disordered micelle regime due to the gain in the translational entropy of micelles. The ODT is accompanied by a decrease in the micelle volume fraction and, more importantly, in the number density of micelles. The aggregation number and the average distance between micelles also change at the ODT, but only slightly. At higher temperatures the number of micelles decreases, but some small fraction of micelles may persist to very high temperatures. A “critical micelle temperature” (cmt) may be estimated, which separates the disordered micelle regime (with a finite micelle concentration) from a disordered melt (with exponentially small micelle fraction), but it is not a true phase transition. Thus, the disordered micelle regime is part of the disordered phase. The composition dependence of the ODT is also analyzed. We compare the predictions of this model with experimental data for poly(styrene-b-isoprene) diblock copolymers, with encouraging agreement.

The composition (φ) and temperature dependence (T) of the monomeric friction factor (ζ) has been examined for styrene (S) and methyl methacrylate (MMA) in five SMMA diblock copolymers and the corresponding homopolymers. In all cases the degree of polymerization was approximately 150, sufficiently low to ensure that the chain dynamics follow the Rouse model and that the copolymers are far above the order−disorder transition. The five diblock copolymers had styrene compositions of 91, 70, 39, 19, and 9 wt %. Values of an effective friction factor, ζeff, were obtained from measurements of the steady flow viscosity via the Rouse model, whereby ζeff represents an average over the S and MMA contributions. Values of the component friction factors, ζPS and ζPMMA, were extracted from forced Rayleigh scattering tracer diffusion measurements of dye-labeled PS, PMMA, and SMMA chains. In accord with previous studies, ζPMMA in pure PMMA is significantly greater than ζPS in pure PS, whether compared at equal T or equal T − Tg, an effect attributable to specific details of local relaxation in PMMA. This difference between ζPMMA and ζPS persists in a common SMMA matrix, an effect which can be quantitatively accounted for by the recently introduced concept of self-concentration. The values of ζeff increase monotonically with MMA content at fixed T and with decreasing T at fixed φ. The φ dependence of ζeff is consistent with both “Rouse” and “Arrhenius” mixing rules, utilizing the pure component friction factors as input. The T dependence of ζeff follows the standard Williams−Landel−Ferry relation, but the data for different φ do not collapse to a single curve when plotted against T − Tg. In this respect, the PS/PMMA system is more complicated than the previously studied PS/polyisoprene system.

We have developed a simple and mild method for the fluorination of polybutadiene based on the addition of perfluoroalkyl iodides (RfI) to carbon−carbon double bonds. Triethylborane (Et3B) was utilized to initiate this free radical addition to model polybutadiene (PBD) homopolymers and a polystyrene−polybutadiene block copolymer at room temperature. Optimized reaction conditions led to consumption of more than 95% of the double bonds and preservation of narrow molecular weight distribution after the modification. We propose that the reaction undergoes a cyclization pathway rather than open-chain addition and that five-member ring structures are formed during the addition of RfI to 1,2-PBD. From ¹H NMR spectroscopy, we estimate that 83% of the double bonds in the 1,2-PBD cyclized with their neighbors. This agrees well with a theoretical prediction by Flory for random irreversible cyclization between neighboring polymer repeat units. We also demonstrate the selective fluorination of the 1,2-PBD block in a polystyrene-block-1,2-polybutadiene (PS-b-1,2-PBD) copolymer. In contrast to the fluorinated homopolymers, subsequent hydrogenolysis of this fluorinated PS-b-1,2-PBD copolymer gave a soluble material. The ¹H NMR spectrum and elemental analysis confirmed the complete hydrogenolysis. Preliminary physical characterization was performed by differential scanning calorimetry (DSC), thermal gravimetric analysis (TGA), contact angle measurements, and small-angle X-ray scattering (SAXS). The glass transition temperature (Tg) of the fluorinated 1,2-PBD increases by 75 °C, removal of the iodine in the fluorinated PS-b-1,2-PBD copolymer increases the thermal stability by ca. 100 °C, and all fluorinated polymers exhibit very low critical surface tensions (14−16 mN/m).

In the chromatographic separation of macromolecules with a porous stationary phase, the retention is determined by both size exclusion and interaction mechanisms. At the chromatographic critical condition, the effects due to the two separation mechanisms compensate each other, and the retention of homopolymer molecules becomes independent of molecular weight. Liquid chromatography at the critical condition has attracted much interest for the characterization of block copolymers since it might permit the characterization of individual blocks of a block copolymer by making one block chromatographically “invisible”. In this study, we critically examine this method using two sets of styrene−isoprene block copolymers designed to have one block length constant while varying the other block length. For these block copolymer systems we found that a block cannot be made completely “invisible” at the critical condition of its homopolymer, and the retention of block copolymers is affected to some extent by the length of the “invisible” block under its chromatographic critical condition.

Two experimental techniques, forward recoil spectrometry (FRES) and size exclusion chromatography with fluorescence detection (SEC/fluorescence), have been used to monitor independently the extent of reaction between model end-functional polymers at a PS/PMMA interface. Bilayer samples comprising a polystyrene layer containing ca. 8.4 wt % of amino-terminal deuterated polystyrene (dPS-NH2, M = 22 000 g/mol) on an anhydride-terminal fluorescent poly(methyl methacrylate) (*PMMA-anh, M = 31 200 g/mol) layer were annealed at 174 °C for various periods. An interfacial excess observed in the FRES concentration profiles of the dPS-NH2 in the PS layer was used to determine an interfacial coverage of diblock copolymer and a conversion of dPS-NH2 to diblock copolymer. Similarly, the conversion of the fluorescent *PMMA-anh to diblock copolymer was measured using SEC coupled with a fluorescence detector. Both techniques indicate similar reaction kinetics:  the formation of copolymer in the interfacial region continued over several hours and approached a steady-state value after 24 h. Interfacial coverages determined from both methods typically agreed to within 15−20%. This validation of the fluorescence approach is important for further investigation of polymer−polymer reaction kinetics and interfacial segregation during in situ reactive polymer compatibilization.

The frequency dependent viscoelastic properties and lamellar spacing of three symmetric styrene−isoprene (PS−PI) diblock copolymers are compared to those of their hetero-four-arm star counterparts. The PS and PI arm molecular weights of the three linear and three star samples are 10, 20, and 60 kg/mol, respectively. All six samples were unoriented and had lamellar morphology for temperatures less than TODT, the order−disorder temperature for each molecular weight. The lamellar spacing D at the same temperature was found to scale with overall molecular weight N according to D ~ N^δ, with δ ≈ 0.7 for both linear and stars. However, the star chains were consistently 5−10% more strongly stretched compared to their linear counterparts. For the 10K arm materials, the critical frequency for the onset of mesophase relaxations (ωc) for the stars was found to be about 20 times smaller compared to the linears. This difference correlated very well with quantitative estimates of the inverse layer hopping time of the chains, suggesting that mesophase relaxations for the 10K arm materials may be controlled by layer hopping of chains. For the 10K and 20K arm materials, relaxation of the PS chain deformations are dominant for ω ≫ %@mt;sys@%ω%@sx@%term%@be@%PS%@sxx@%%@mx@% , whereas nonclassical terminal scaling of G‘, G‘ ‘ ~ ω^1/2 was observed for ω ≪ %@mt;sys@%ω%@sx@%term%@be@%PS%@sxx@%%@mx@% and T < TODT due to mesophase relaxations (%@mt;sys@%ω%@sx@%term%@be@%PS%@sxx@%%@mx@% is the PS block terminal relaxation frequency). In addition, the linear rheology of the linear and star analogues coincide for ω ≫ %@mt;sys@%ω%@sx@%term%@be@%PS%@sxx@%%@mx@% , but an additional shoulder emerges in the star materials for ω ≈ %@mt;sys@%ω%@sx@%term%@be@%PS%@sxx@%%@mx@% . By fitting to a simple model incorporating free chain Rouse dynamics and mesophase relaxations, we were able to obtain excellent quantitative fits to the 20K materials across the whole frequency range and conclude that the observed shoulder in the star materials was due to differences in the linear and star mesophase relaxations. The fitted ωc and GM0 (the mesophase modulus) values are in good agreement with Kawasaki−Onuki theory indicating that the mesophase relaxations of the 20K arm materials may be controlled by collective hydrodynamic layer fluctuations rather than layer hopping of chains. For the 60K arm materials, qualitatively different behavior compared to the lower molecular weight samples was observed:  PI rate controlled relaxation with G‘, G‘ ‘ ~ ω^1/2 was observed for ω ≫ %@mt;sys@%ω%@sx@%term%@be@%PS%@sxx@%%@mx@% . We identify this relaxation as a PI controlled mesophase relaxation. Theoretical estimates of ωc for this mechanism using Kawasaki−Onuki theory yield ωc ≫ %@mt;sys@%ω%@sx@%term%@be@%PS%@sxx@%%@mx@% in support of our suggestion.

The effect of the thermodynamic selectivity of a solvent on the self-assembly of a styrene−isoprene (SI) diblock copolymer with block molecular weights of 1.1 × 10⁴ and 2.1 × 10⁴ g/mol is investigated. We explore the phase behavior from the melt state to dilute solution in solvents that are of varying selectivities for the two blocks. Bis(2-ethylhexyl) phthalate (DOP) is a neutral good solvent for SI. Di-n-butyl phthalate (DBP) and diethyl phthalate (DEP) are good solvents for PS but marginal and poor, respectively, for PI. Tetradecane (C14) is utilized as a complementary solvent that is good for PI but poor for PS. Small-angle X-ray scattering (SAXS) and static birefringence are used to locate and identify order−order (OOT) and order−disorder transitions (ODT). Dynamic and static light scattering were used to characterize the dilute solution micellar behavior. The neat polymer forms the gyroid (G1) morphology at low temperature, an OOT to hexagonal-packed cylinders (C1) occurs at 185 °C, and the ODT is located at 238 °C. Dilution with DOP decreases the OOT temperature in agreement with the dilution approximation, i.e., χOOT ~ φ^-1, but the ODT follows a stronger dependence of χODT ~ φ^-1.4. The slightly selective solvent DBP stabilizes the ordered state relative to DOP. Rich lyotropic and thermotropic behavior is observed among regions of lamellae (L), inverted gyroid (G2), inverted hexagonal-packed cylinders (C2), and inverted body-centered-cubic spheres (S2^bcc). Solutions in DEP display similar morphological behavior, along with significantly increased ODT temperatures. Because of the asymmetric block copolymer composition, the phase behavior in the isoprene-selective solvent C14 is markedly different, as only G1, C1, and S1^bcc phases are observed. The overall sequence of phases with dilution and/or heating is rationalized on the basis of diagonal trajectories across the phase map (temperature vs composition) for undiluted block copolymers:  addition of a neutral solvent corresponds to increasing the temperature and thus a “vertical” trajectory, whereas the partitioning between microdomains of a selective solvent amounts to a “horizontal” trajectory to a renormalized block volume composition. However, a variety of novel features are observed in DEP:  the formation of face-centered-cubic packed micelles, a reentrant thermotropic ODT, and a large window of L + C2 coexistence. The dependence of the principal length scale, d*, on φ, T, and structure is also considered. The strongly temperature-dependent selectivity produces a crossover in the scaling of d* vs φ for the lamellar phase:  the addition of a selective solvent increases d*, but as the solvent becomes neutral, d* decreases. This phenomenon is captured by self-consistent mean-field calculations.

An investigation of the ternary phase prism for low molecular weight poly(ethylene oxide), squalane, and poly(ethylene oxide-b-ethylenepropylene) is presented. Comparisons are made between this ternary polymer system and classic water/oil/surfactant mixtures to establish further a universal phase diagram description for amphiphilic systems. A combination of visual isothermal measurements, small-angle X-ray scattering, small-angle neutron scattering, and dynamical mechanical spectrometry was used to characterize phases and determine phase boundaries. A rich phase diagram was revealed, including most of the equilibrium liquid crystalline phases associated with diblock copolymers, regions of two-phase and three-phase coexistence, and a bicontinuous microemulsion. Differences between this polymer phase diagram and those from water/oil/surfactant systems highlight the strong effect of water in the latter.

In a miscible polymer blend the local environment of a monomer of type A will, on average, be rich in A compared to the bulk composition, φ, and similarly for B; this is a direct consequence of chain connectivity. As a result, the local dynamics of the two chains may exhibit different dependences on temperature and overall composition. By assigning a length scale (or volume) to particular dynamic mode, the relevant “self-concentration” φs can be estimated. For example, we associate the Kuhn length of the chain, lK, with the monomeric friction factor, ζ, and thus the composition and temperature dependences of ζ should be influenced by φs calculated for a volume V ~ lK³. An effective local composition, φeff, can then be calculated from φs and φ. As lower Tg polymers are generally more flexible, the associated φ s is larger, and the local dynamics in the mixture may be quite similar to the pure material. The higher Tg component, on the other hand, may have a smaller φs, and thus its dynamics in the mixture would be more representative of the average blend composition. An effective glass transition temperature for each component, Tg^eff, can be estimated from the composition-dependent bulk average Tg as Tg(φeff). This analysis provides a direct estimate of the difference in the apparent Tg's for the two components in miscible blends, in reasonable agreement with those reported in the literature for four different systems. Furthermore, this approach can reconcile other features of miscible blend dynamics, including the asymmetric broadening of the calorimetric Tg, the differing effects of blending on the segmental relaxation times of the two components, and the failure of time−temperature superposition.

A set of polystyrenes of varying molecular weights was synthesized by anionic polymerization under identical conditions, and their molecular weight distributions were critically examined. Polymerization of styrene was initiated with 2-butyllithium in cyclohexane at 45 °C. During the polymerization, seven aliquots of the reaction mixture were taken out at various reaction times using a cannula and terminated. The polymerization time varying molecular weights and molecular weight distributions of the polystyrenes were analyzed by temperature gradient interaction chromatography (TGIC) as well as size exclusion chromatography. The molecular weight distribution of the polystyrene approaches the Poisson distribution in the late stages of the polymerization, in accordance with the early prediction of Flory. We also confirmed that the molecular weight distribution of polystyrenes determined by TGIC is close to the true value.

We report measurements of diffusion (D) and viscosity (η) in hydrogenated polybutadiene (hPB)/alkane solutions. The volume fractions (φ) extend from 0.20 up to the melt and the molecular weights (M) from 4900 up to 440 000; the number of entanglements per chain, M/Me, ranges up to about 450. The temperature dependences of both D and η are similar, consistent with literature values, and independent of φ and M. We thus conclude that the monomeric friction factor is also independent of φ and M. For all samples with M/Me ≥ 3 the data are consistent with the scaling relations D ~ M^-2.4±0.1φ^-1.8±0.2 and η ~ M^3.4±0.1φ^3.8±0.2; within the precision of the data the M exponents do not depend on φ, and the φ exponents do not depend on M. The M exponent for D in solution is consistent with previously reported studies for φ ≤ 0.4 but apparently conflicts with the reptation value of −2.0 in the melt. However, by comparing with the literature melt self-diffusion data for hPB and six other polymers, it is clear that the exponent is, in fact, universally stronger than −2.0. Furthermore, if a single universal exponent is assumed, the best value based on all the data is −2.28 ± 0.05. Our hPB data resolve the longstanding anomaly that the longest relaxation times τ1 based on translation (~Rg²/D) and orientational relaxation (~η) appeared to have different M dependences. The data also indicate that for both solutions and melts the dynamics are determined primarily by the number of entanglements per chain. The data are compared with current models of polymer dynamics, both reptative and nonreptative. In the former case it is clear that a self-consistent theory incorporating both “constraint release” and “contour length fluctuations” is required.

Forward recoil spectrometry (FRES) has been used to monitor the extent of reaction between model end-functional polymers at a PS/PMMA interface. Bilayer samples comprising a high molecular weight polystyrene layer containing ~8.5 wt % of amino-terminal deuterated polystyrene (dPS-NH2) on an anhydride-terminal poly(methyl methacrylate) (PMMA-anh) layer were annealed at 174 °C for various periods. Significant reaction with the PMMA-anh, indicated by an interfacial excess, was observed with three molecular weights (M = 22 000, 37 000, and 92 000 g/mol) of dPS-NH2. The measured growth of the interfacial excess with time for all three molecular weights could not be well described with recent theories of diffusion-controlled interfacial reactions. A model that incorporates polymer chain reactivity fit the data better, with reaction rate constants k = 0.20, 0.055, and 0.042 kg mol^-1 s^-1 for dPS-NH2-22, -37, and -92, respectively. Furthermore, a novel trilayer sample geometry showed that the reactive dPS chains can diffuse throughout the PS matrix and sample the PS/PMMA interface several times before a significant amount of reaction occurs. The results of this study are consistent with other experimental systems where the in situ copolymer formation is limited by reaction rate, rather than the diffusion of reactive chains through the bulk.

The effect of difluorocarbene (CF2) modification on the self-assembly of polystyrene-b-polyisoprene (PS-b-PI) copolymers was investigated. We prepared a set of fully CF2-modified PS-b-PI copolymers (PS-b-FPI) with different molecular weights (8−13 kg/mol) and located their order−disorder transition temperatures (TODT) by rheology and static birefringence. Using both mean-field and fluctuation theory, we determined the temperature dependence of the interaction parameter between the styrene and CF2-modified isoprene segments (χSFI). Two series of polystyrene-b-(partially CF2-modified polyisoprene) (PS-b-(FPI-s-PI)) materials with different levels of CF2 modification were also prepared from the reaction between difluorocarbene and two nearly symmetric PS-b-PI precursors with molecular weights of 18 and 61 kg/mol, respectively. A lamellar morphology was established for all of the PS-b-(FPI-s-PI) copolymers below the TODT by small-angle X-ray scattering (SAXS) and rheology. The effective interaction parameter (χeff) between the PS and FPI-s-PI blocks, calculated from the domain spacing determined by SAXS, passes through a minimum before increasing smoothly by a factor of 4 upon complete CF2 modification. Using the binary interaction model originally developed for homopolymer/copolymer blends, we were able to understand the dependence of the χeff on the CF2-modification extent in a quantitative manner and extracted the three pairwise interaction parameters. Rheology and static birefringence were also used to locate the TODT for the lower molecular weight PS-b-(FPI-s-PI) series. The TODT was found to behave in a manner similar to the χeff:  a decrease was observed at initial CF2 modification, and a sharp increase was observed upon further CF2 modification.

The structure of micelles of an asymmetric polystyrene−polyisoprene (PS−PI) diblock copolymer has been studied in di-n-butyl phthalate (DBP), which is a slightly selective solvent for PS. The polymer has a molecular weight of 11 500 for the fully deuterated d-PS block and 48 500 for the PI block. Contrast variation SANS using mixtures of protonated and deuterated solvent and a polymer volume fraction of 18% at 10 °C were performed to get detailed information on the structure of the micelles. An additional contrast was obtained by performing a small-angle X-ray scattering measurement on a sample in protonated DBP. It was found that micelles are formed with an anisometric PI-rich core surrounded by dissolved d-PS chains. The data were analyzed using model form factors of micelles with, respectively, cylindrical and ellipsoidal cores. It was necessary to include a term to describe the concentration fluctuations within the swollen PI cores. The particle interference effects originating from the high volume fraction were described by a hard-sphere structure factor. Both models fit the data well, however, a cylindrical model which includes size polydispersity gives the best fit.

The thermoreversible gelation of methylcellulose in aqueous solution has been studied by static and dynamic light scattering (DLS), small-angle neutron scattering (SANS), and rheology. At 20 °C, dilute solution light scattering establishes the molecular weight, second virial coefficient, radius of gyration, and hydrodynamic radius of the polymer. Semidilute solutions exhibit two relaxation modes in DLS, one reflecting cooperative diffusion and the other attributable to pregel clusters. Rheological measurements in this regime also suggest a weak supermolecular association. The gelation of semidilute solutions proceeds in two stages with increasing temperature above 20 °C, consistent with previous reports. The first stage is attributable to clustering of chains, driven by hydrophobic association, and extends up to approximately 50 °C. This process is accompanied by an increase in the low-frequency dynamic elastic modulus, G‘, and an increase in both light and neutron scattered intensity. The DLS properties of these solutions, and the angular dependence of the scattered intensity, is not greatly affected by this association. The second stage of gelation occurs rather abruptly above ca. 50 °C and is attributed to phase separation accompanied by gelation. The elastic modulus increases rapidly with temperature, the samples become visibly turbid, and the scattered intensity increases markedly over a wide range of scattering wavevector, q. In contrast, dilute solutions do not gel but give clear evidence of aggregation in the high-temperature regime, consistent with crossing a phase boundary. The SANS structure factor S(q) in the gel state is well described by a sum of two terms, corresponding to two power-law regimes. The lower q regime follows S(q) ~ q^-1.8 in both the pregel and gel states, consistent with chains intermediate between good and Θ solvent conditions. At higher q the exponent evolves from ca. −2.5 to −4 upon gelation. The latter exponent indicates a sharp boundary between the gel structure and the intervening fluid, consistent with liquid−liquid phase separation that is arrested by gelation.

The stability and fluctuations of the cylinder (C) and sphere (S) morphologies in the vicinity of the C and S equilibrium have been examined for a poly(styrene-b-isoprene-b-styrene) triblock copolymer by rheology, small-angle X-ray scattering (SAXS), and transmission electron microscopy (TEM). The spinodal temperatures of the C and S phases, %@mt;sys@%%@ital@%T%@rsf@%%@sx@%s%@be@%C%@sxx@%%@mx@% and %@mt;sys@%%@ital@%T%@rsf@%%@sx@%s%@be@%S%@sxx@%%@mx@% , and the equilibrium (coexistence) temperature, TOOT, have been determined by rheological measurements during thermal cycles over a wide range of heating and cooling rates. In the limit of high heating and cooling rates, %@mt;sys@%%@ital@%T%@rsf@%%@sx@%s%@be@%C%@sxx@%%@mx@% and %@mt;sys@%%@ital@%T%@rsf@%%@sx@%s%@be@%S%@sxx@%%@mx@% were determined as 202 ± 2 and 183 ± 3 °C, respectively. From the transitions at low heating and cooling rates, TOOT was determined as 196 ± 1 °C. The metastability window of the S phase, |%@mt;sys@%%@ital@%T%@rsf@%%@sx@%s%@be@%%@sxx@%%@mx@% ^S − TOOT|, was wider than that of the C phase, |%@mt;sys@%%@ital@%T%@rsf@%%@sx@%s%@be@%S%@sxx@%%@mx@% − TOOT|, due to the osmotic barrier for merging spheres for the S → C transition. Prior to the C → S transition, a rheological signature of the fluctuations in the C phase was observed over a temperature interval 20 °C below TOOT. The elastic shear modulus along the cylinder orientation, %@mt;sys@%%@ital@%G%@rsf@%%@/xs;55;%lnwidth@%‘%@/xs;63;(%lnwidth-x55)@%%@mh;-x63@%%@sb@%∥%@sbx@%%@mx@% , starts to increase with temperature at about 176 °C. This region of %@mt;sys@%d%@ital@%G%@rsf@%%@/xs;55;%lnwidth@%‘%@/xs;63;(%lnwidth-x55)@%%@mh;-x63@%%@sb@%∥%@sbx@%%@mx@% /dT > 0 is attributed to the pretransitional fluctuations in the C phase. TEM on the annealed samples at different temperatures provided real space images of various steps during the transition. TEM images from the sample annealed at 183 °C displayed many grains of undulating cylinders and supported the correlation between the anisotropic fluctuations and the rheological signature of %@mt;sys@%d%@ital@%G%@rsf@%%@/xs;55;%lnwidth@%‘%@/xs;63;(%lnwidth-x55)@%%@mh;-x63@%%@sb@%∥%@sbx@%%@mx@% /dT > 0. The symmetry of the anisotropic fluctuations in the C phase was characterized as twinned body-centered-cubic by SAXS after annealing at 189 °C, where %@mt;sys@%d%@ital@%G%@rsf@%%@/xs;55;%lnwidth@%‘%@/xs;63;(%lnwidth-x55)@%%@mh;-x63@%%@sb@%∥%@sbx@%%@mx@% /dT > 0.

We have identified a channel of bicontinuous microemulsion in three chemically distinct hompolymer/hompolymer/block copolymer (A/B/A−B) ternary bends. Experiments were conducted along the isopleth, defined by equal volumes of homopolymer and varying amounts of block copolymer, as a function of temperature. A symmetric condition was achieved through the use of homopolymers with matched degrees of polymerization (NA ≈ NB = NH) and compositionally symmetric diblock copolymers (f ≈ 0.5) where α ≡ NAB/NH ≈ 0.2. We explored PE−PEP/PE/PEP (EP), PEE−PDMS/PEE/PDMS (EED), and PE−PEO/PE/PEO (EO) ternary systems differing in molecular weight by nearly 2 orders of magnitude. Using a combination of small-angle neutron scattering (SANS), rheology, and cloud point measurements, we mapped the phase diagram along the isopleth for each of these systems. On the block-copolymer-rich side of the phase diagrams, a line of lamellar-disorder transitions was observed. On the homopolymer-rich side of the phase diagrams a line of transitions separating one-phase and phase-separated regions was found. A narrow channel of bicontinuous microemulsion separates these two regimes in all three systems. This bicontinuous microemulsion phase is similar to the analogous bicontinuous phases found in oil/water/surfactant mixtures. We have demonstrated that there is a common region in phase space over which the bicontinuous microemulsion is stable in these polymeric systems and that the general phase behavior is independent of polymer molecular weight. The low molecular weight of the EO system is ideal for fundamental phase behavior studies in polymeric blends, since the kinetic limitations that plague high-molecular-weight mixtures are avoided. Furthermore, the EO system utilizes polyethylene−poly(ethylene oxide) block copolymers that are chemically very similar to well-known nonionic surfactants, and thus, connections to surfactancy can readily be made.

Summary A numerical solution to the parallel processes model for combined reptation and constraint release in polymer melts is presented. The discrete chain solution to the problem exhibits an exponent of 3 in the molecular weight dependence of the viscosity, just as in the strict reptation case; the magnitude of the viscosity is overestimated and no crossover to reptation is observed, as in Graessley's independent processes model. It is shown that linear combinations of reptation and constraint release, as modeled here, cannot describe the viscosity results observed experimentally.

The birefringence relaxation after a step strain S(t), and the oscillatory flow birefringence S* are calculated for disordered block copolymer melts, on the basis of four models for the chain dynamics: the Rouse model, the Doi-Edwards reptation model, the reptation model with constraint release, and the reptation model with orientational coupling. All the calculations are performed in the mechanically-uniform limit, i.e., the average subchain length and friction coefficient are independent of block. The net birefringence is assumed to contain no form contribution, and the approach of Kuhn and Gruen is employed in the computation of the intrinsic birefringence. The most important feature of the results is that the stress-optic relation does not apply in general for block copolymers; therefore, unique information about chain relaxation mechanisms can be obtained from measurements of flow birefringence. It is shown that the phase angle of S* can be particularly sensitive to the lengths and chain locations of the various blocks, with the most striking effects occurring when two (or more) blocks have optical anisotropies of opposite sign. In contrast, in the mechanically-uniform limit the viscoelastic properties are independent of block length and location.

Micellar ordering in semidilute solutions of polystyrene−polyisoprene diblock and triblock copolymers in the slightly selective solvent di-n-butyl phthalate has been studied using rheology and small-angle X-ray scattering (SAXS). Ordering as a function of temperature has been investigated for a range of polymer concentrations 0.1 ≤ φ ≤ 0.4. For φ < 0.2, the rheological response is liquidlike and SAXS shows that there is no intermicellar order in the liquid; however, the solution viscosity shows a strong maximum near 50 °C. Above a crossover concentration φ ≈ 0.2, ordering of micelles is indicated by the presence of a sharp structure factor peak. The ordered micellar structure, identified as hexagonal for 0.2 ≤ φ ≤ 0.3 and lamellar for φ ≥ 0.3, persists up to an order−disorder transition at T ≈ 40 °C for the diblock and T ≈ 50 °C for the triblock solutions studied. The rheological characteristics of the ordered solutions are reminiscent of those found in ordered block copolymer melts. At higher temperatures, for example approximately 20−30 °C above the ODT for the φ = 0.2 solutions, indications of chain aggregation disappear from the rheological properties; however, some evidence of chain association persists to still higher temperatures in the SAXS profiles. The domain spacing, d, in the ordered solutions obtained from the principal structure factor peak position, shows a crossover at φ ≈ 0.2, in agreement with rheology. At high concentrations, d scales as d ~ φ^-1/3, suggesting a three-dimensional contraction of the microstructure, and thus micelles of finite length. This concentration dependence is opposite to that previously observed for ordered block copolymer solutions in neutral solvents, due to the solvent selectivity. The results are gathered in a rather rich phase diagram for this system.

The structural and dynamic properties of a styrene−isoprene−styrene (SIS) triblock copolymer, with block molecular weights of 10⁴, 10⁵, and 10⁴, respectively, and the matching styrene−isoprene (SI) diblock, with block molecular weights of 10⁴ and 5 × 10⁴, respectively, are examined in the selective solvent di-n-butyl phthalate (DBP). DBP is a good solvent for PS, but a very poor solvent for PI; PI/DBP solutions exhibit a critical temperature near 80 °C. In dilute solution, the triblock copolymer forms micelles with a hydrodynamic radius of 260 Å, which melt at 49 °C. In this work, solutions were polymer concentrations near 20% are emphasized. Small-angle X-ray scattering (SAXS) indicates that below 0 °C, the copolymers form elongated micelles, with isoprene-rich cores. Detailed analysis with an ellipsoidal micelle model suggests core minor radii on the order of 150−200 Å and overall average lengths greater than 1000 Å. As the solutions are heated from ca. 10 °C to ca. 40 °C, the dynamic shear moduli, G‘ and G‘‘, increase by as much as 2 orders of magnitude. This is attributed to the swelling of the micelles, as the solvent begins to penetrate the micelle cores, leading to substantial steric interactions between micelles. Upon further heating, the moduli drop sharply, until by about 60 °C they correspond to values for disordered, entangled solutions. The temperature at which the moduli first decrease signals a microphase separation transition (MST), as the micelles disintegrate. The locations of the SAXS structure factor peaks are also consistent with micelle overlap just prior to the MST. Oscillatory flow birefringence measurements indicate the same MST, but below the transition the birefringence is very large, and independent of frequency. This originates from form birefringence, due to the alignment of highly anisotropic micelles. Small-angle neutron scattering under shear also indicates alignment of anisotropic aggregates. In the region between the MST and ca. 60 °C, the strong temperature dependences of the moduli, flow birefringence, and scattering intensities are consistent with loose associations among the chains, reminiscent of the fluctuation regime in diblock copolymer melts.