type-A Dipoles Research Articles

Experimental study of phase separation in dynamically asymmetric unentangled polymer blend.

We examined a phase separation process of a dynamically asymmetric blend of unentangled polyisoprene (PI) and poly(4-ethylstyrene) (PC2St) exhibiting the upper critical solution temperature. PI having the type-A dipole was the dielectrically active fast component, whereas PC2St was the dielectrically inert slow component whose dynamics can be detected by rheological measurements. To precisely model the phase separation process, it is important to estimate the composition dependence of the mobility, which is needed to describe the phase separation dynamics. For that purpose, we conducted dielectric and rheological measurements to determine the friction coefficient of each component in a homogeneous state sufficiently above the phase separation temperature. The temperature dependence of the friction coefficient of each component was reasonably expressed by the Williams-Landel-Ferry equation. Extrapolating this dependence obtained for blends of various compositions to the test temperature T* below the phase separation temperature, we were able to estimate the friction coefficient of the chain at T* as a function of the composition. This friction coefficient was then used to determine the mobility Λ defined for the material fluxes at T*. The time-dependent Ginzburg-Landau (TDGL) equation incorporating this Λ well described the experimentally observed phase separation dynamics. In particular, the 2D TDGL simulation with this Λ qualitatively captured the phase-separated structure observed with the optical microscope as well as broad dielectric mode distribution of the blend at T*.

Rheo-Dielectrics and Diffusion of Type-A Rouse Chain under Fast Shear Flow: Method of Evaluation of Non-Equilibrium Parameters for FENE, Friction-Reduction, and Brownian Force Intensity Variation

Rouse model is the basic molecular model for unentangled linear polymer chains in melts. Recent studies suggest that the Rouse parameters characterizing the unentangled melts, the spring strength κ , the segmental friction coefficient ζ, and the mean-square Brownian force intensity B, change under fast flow thereby providing significant rheological nonlinearities with those melts (Matsumiya et al., Macromolecules, 51, 9710 (2018)). This article theoretically analyzes effects of the flow-induced changes of these parameters on the dielectric and diffusion behavior of the Rouse chain having so-called type-A dipoles parallel along the chain backbone. It turned out that the dielectric behavior under steady shear is determined by non-equilibrium parameters, rκ = κ/κeq and rζ,ij = ζij/ζeq but irrelevant to rB,ij = B ij/Beq, where the subscript “eq” stands for the quantities at equilibrium and the subscripts “ij” denote the spatial direction under shear flow: i and/or j = x, y, and z for the velocity, velocity gradient, and vorticity directions, respectively. Specifically, the complex dielectric permittivity ε* is analytically expressed in terms of the parameters rκ and rζ,ij, which in turn enables us to evaluate these parameters from data of the dielectric relaxation time and intensity under steady shear (obtained in future experiments). In contrast, the advective diffusion behavior under steady shear is determined by rζ,ij and rB,ij but irrelevant to rκ. The mean-square displacement ‹Δr2CM› of the center of mass defined with respect to the known non-diffusive advection point is analytically expressed in terms of rζ,ij and rB,ij, thereby allowing us to evaluate rB,ij from the diffusion data under steady shear and the dielectrically determined rζ,ij. The method of experimental evaluation of the non-equilibrium parameters presented in this article provides us with a complementary basis for analyzing nonlinear rheological behavior of unentangled melts.

Dynamics of Rouse chains undergoing head-to-head association and dissociation: Difference between dielectric and viscoelastic relaxation

Polymer chains having type-A dipoles parallel along the chain backbone exhibit slow dielectric relaxation reflecting their global motion. For monofunctionally head-associative Rouse chains having type-A dipoles, the Rouse equation of motion was combined with the association/dissociation kinetics to calculate the dielectric relaxation function, Φj(t) with j = 1 and 2 for unimer and dimer. Φ1(t) reflects the orientation of the end-to-end vector of the unimer, whereas Φ2(t) detects the orientation of two end-to-center vectors of the dimer (having symmetrical dipole inversion), both being in the direction of the applied electric field. The calculation was made by mapping the conformation of dissociating dimer onto the created unimer and vice versa with the aid of the Rouse eigenmode expansion of the bond vector of segments (Gaussian subchains). It turned out that Φj(t) is not influenced by the association/dissociation reaction. This result makes a striking contrast to the behavior of the viscoelastic relaxation function gj(t): gj(t) is strongly affected by the motional coupling between the unimer and dimer due to the reaction [H. Watanabe et al., Macromolecules 48, 3014–3030 (2015)]. This difference emerged because the dielectric Φj(t) corresponds to the vectorial first-moment average of the segmental bond vector at time t, u(n,t) with n being the segment index, whereas the viscoelastic gj(t) corresponds to the tensorial second-moment average. Because of this difference in the averaging moment, Φj(t) is subjected to cancelation in the conformational mapping but gj(t) is not, so that the reaction effect emerges only for gj(t). The experimental data of head-carboxylated high-cis polyisoprene chains (having the type-A dipoles), confirming this difference, are also presented.

Dielectric and Viscoelastic Behavior of Low-M Linear Polyisoprene Blended in Long Matrix

Cis-polyisoprene (PI) has the type-A dipole parallel along the chain backbone thereby exhibiting slow dielectric relaxation that reflects the global chain motion (end-to-end vector fluctuation). For linear PI probes having the molecular weights M1 in a range between 21.4× 103 and 179 × 103 (M1/Me = 4-36) and being blended with a longer PI matrix (M2 = 1.12 × 106), a recent dielectric experiment revealed that the probe relaxation is moderately retarded on blending and this retardation is enhanced with decreasing M1 in this range; cf. Matsumiya et al., Macromolecules, 46, 6067 (2013). Those dielectric data were analyzed within the context of the tube model to suggest that the probe relaxation in monodisperse bulk occurs through reptation along a partially dilated tube that wriggles in a fully dilated tube. However, this mechanism of relaxation is expected to vanish on a further decrease of M1 because the tube itself loses its sound meaning for small M1. This expectation was examined in this study. Dielectric and viscoelastic tests revealed that the retardation of the probe relaxation on blending becomes minor (though not negligible) on a decrease of M1 to 7.8× 103 (≈ 1.6Me), as expected.

Rheo-Dielectric Responses of Entangled cis-Polyisoprene under Uniform Steady Shear and LAOS

cis-Polyisoprene (PI) has type-A dipoles parallel along the chain backbone so that its large-scale (global) motion over the end-to-end distance activates slow dielectric relaxation. This relaxation was examined for entangled solutions of linear and star-branched PI under steady shear and large-amplitude oscillatory strain. For linear PI, the dielectric relaxation (detecting the end-to-end fluctuation in the shear gradient direction) was hardly affected by the steady shear in a range of Weissenberg number examined, Wi = γ̇τG < 7 with γ̇ and τG being the shear rate and the terminal relaxation time in the linear regime, whereas the viscosity η exhibited considerable thinning at those γ̇. In contrast, for star PI, the dielectric relaxation was moderately accelerated by the steady shear in a similar range of Wi but this acceleration was considerably less significant compared to the thinning of η. These rheo-dielectric features, noted also in a previous study, emerged under uniform shear without shear-banding and/or secondary flow, as confirmed in this study from particle tracking velocimetry. Thus, the rheo-dielectric difference between the linear and star PI suggests an essential difference of the entanglement dynamics of linear and star chains (without disturbance from the flow instability), which possibly reflects, at least partly, the constraint release effect at equilibrium being saturated for linear chains but not for star chains. The rheo-dielectric behavior of the linear and star PI chains was also examined under uniform, large amplitude oscillatory strain (LAOS). The relaxational current Irelax under rectangular electric field exhibited oscillatory decay with the main oscillation period being close to π/Ω (Ω = LAOS angular frequency). This behavior lent support to the previous analysis based on the Green–Kubo theorem (Uneyama et al. J. Polym. Sci. Part B: Polym. Phys. 2009, 47, 1039). The decay of the nonoscillating part of Irelax appeared to be rather insensitive to LAOS, which was in harmony with the behavior observed under steady shear.

Dielectric behavior of Styrene–Isoprene (SI) Diblock and SIIS Triblock Copolymers: Global Dynamics of I Blocks in Spherical and Cylindrical Domains Embedded in Glassy S Matrix

Dielectric behavior was examined for nanodomain-forming styrene–isoprene (SI) diblock and SIIS triblock copolymers, the former having type-A dipoles aligned along its I block, whereas the latter be...

Dielectric Behavior of Guestcis-Polyisoprene Confined in Spherical Microdomain of Triblock Copolymer.

Dielectric behavior was examined for ternary blends of guestcis-polyisoprene (PI) chains, coguest PS chains, and host PS–PI–PS triblock copolymers. The guest PI chains had the molecular weight Mg-PI well below Mb-PI of the PI blocks and were mixed in the spherical PI domains formed in the copolymers. PI has the type-A dipoles parallel along the chain backbone and its end-to-end vector fluctuation activates dielectric relaxation. The dielectric test was conducted at temperatures well below the glass transition temperature of the PS blocks, so that the PI blocks had their ends fixed on the glassy PS matrix and exhibited no end-to-end vector fluctuation. Thus, the slow dielectric response of the systems exclusively detected the global motion of the guest PI chains confined in the spherical PI domain. The dielectric mode distribution of the guest PI chains thus observed was broader than that of the same chains in bulk systems, reflecting the osmotic and spatial constraints on the chain dynamics in the spherical domains. The guest PI chains of different Mg-PI exhibited nearly the same extent of mode broadening, despite their average coil size approached the domain size with increasing Mg-PI. This result suggested that the osmotic constraint was the primary factor affecting (broadening and retarding) the guest chain dynamics. The osmotic constraint appeared to be stronger in the spherical domain than in the lamellar domain, the latter being examined in literature.

Polymer segmental cross correlations from dielectric relaxation spectra of block copolymers

Dielectric relaxation spectra of solutions of block polymers containing sequential type-A dipoles are considered from a theoretical correlation-function standpoint. Spectra of a specific set of block copolymers can be combined to isolate the dynamic cross-correlation between the motions of two distinct parts of the same polymer chain. Unlike past treatments of this problem, no model is assumed for the underlying polymer dynamics.

Dynamics in miscible blends of polyisoprene and poly(p-tert-butyl styrene): thermo–rheological behavior of components

Viscoelastic and dielectric properties were examined for miscible blends of moderately entangled cis-polyisoprene (PI) and poly(p-tert-butyl styrene) (PtBS). The dielectric response exclusively detected the global motion of PI chains having type-A dipoles. In most of the blends, PI and PtBS were the fast and much slower components, respectively. In those blends, the dielectric response of PI was thermo–rheologically complex because the slow PtBS chains quenched the dynamic frictional heterogeneity in the time scale of the PI relaxation. In contrast, the viscoelastic response of PtBS was thermo–rheologically simple because the fast PI chains smeared the heterogeneity. Nevertheless, PtBS exhibited no ordinary entanglement relaxation but retarded Rouse-like relaxation attributable to pseudo-constraint release activated by the PI motion. A simple model based on this molecular picture well described the viscoelastic data of the blends.

Entanglement Dynamics in Miscible Polyisoprene/Poly(p-tert-butylstyrene) Blends

Viscoelastic, dielectric, and rheo-optical behavior was examined for miscible blends of high-M cis-polyisoprene (PI) and poly(p-tert-butylstyrene) (PtBS). The slow dielectric relaxation of the blends was exclusively attributed to the global motion of the PI chains having the type-A dipoles. The PI and PtBS chains behaved as the fast and slow (low- and high-friction) components and were well entangled with each other. The dynamics of these chains changed significantly with temperature T. At high T, the blend exhibited two-step entanglement plateau of the storage modulus G′(ω), and the plateaus at high and low angular frequencies (ω) were attributed, with the aid of the dielectric data, to the entanglement among all component chains and that between the PtBS chains, respectively. The entanglement length a characterizing the high-ω plateau was well described by a simple mixing rule based on the number fraction n of the Kuhn segments of the components, a = nPIaPIbulk + nPtBSaPtBSbulk. This result was consiste...

Dynamics of Polyisoprene-Poly(p-tert-butylstyrene) Diblock Copolymer in Disordered State

Linear viscoelastic and dielectric behavior was examined for a diblock copoly-mer composed of cis-polyisoprene (PI) and poly(p-tert-butylstyrene) (PtBS) blocks of the molecular weights MPI = 52.6 × 103 and MPtBS = 41.8 × 103 (PI weight fraction wPI = 55.7 wt %). These blocks were miscible and the copolymer was in the disordered state at temperatures examined, 20 ≤ T/°C ≤ 120. PI has the type-A dipole parallel along the chain backbone while PtBS does not. Thus, the dielectric response at low frequencies exclusively detected the global motion (end-to-end vector fluctuation) of the PI block, while the viscoelastic response reflected the motion of the copolymer chain as a whole. The dielectric data of the PI block exhibited prominent thermo-rheological complexity. Since the PI and PtBS blocks behaved as the fast and slow blocks at low T and this difference of their relaxation rates decreased at high T, the complexity was related partly to the dynamic frictional heterogeneity for the PI block resulting from th...

Polymer motion as detected via dielectric spectra of 1,4- cis-polyisoprene under large amplitude oscillatory shear (LAOS)

In order to investigate the global polymer chain motion under large amplitude oscillatory shear (LAOS), the dielectric properties under LAOS are measured by a new rheo-dielectric combination. The design of the rheo-dielectric setup including a new fixture and modified oven is explained in detail. For 1,4- cis-polyisoprene, having type-A dipoles parallel to the backbone, the dielectric dipoles can detect the global polymer chain motion via the end-to-end vector. Thus rheological and dielectric (rheo-dielectric) properties reflect the dynamics of the polymer chain motion under LAOS. In this study, we investigate the rheo-dielectric properties under LAOS with 1,4- cis-polyisoprene as model component. As the strain amplitude was increased under LAOS, the relaxation strength from dielectric properties decreased for the whole spectra without changing the shape of the dielectric spectra. These results are analyzed on the basis of the molecular model of dynamic tube dilation (DTD) induced by the convective constraint release (CCR). It is found that the global chain motion under LAOS flow is affected by both rheological frequency and strain amplitude. It is also observed that segmental motion is affected via the oscillatory frequency under LAOS. This result differs from experiments under steady shear.

Component Dynamics in Polyisoprene/Poly(4-tert-butylstyrene) Miscible Blends

Linear viscoelastic and dielectric behavior was examined for blends of cis-polyisoprene (PI-20; MPI = 19.9 × 103) and poly(4-tert-butylstyrene) (PtBS-16; MPtBS = 16.4 × 103) with the PtBS concentration of wPtBS = 30 and 50 wt %. At temperatures examined, T ≤ 120 °C, the PI/PtBS blends were in a statically homogeneous state. Since PI had the type-A dipole while PtBS did not, the dielectric loss of the blends measured at low angular frequencies ω (<105 s−1) was attributed exclusively to the global motion of PI chains. At low T and/or high wPtBS, the dielectric loss data of the PI chains did not obey the time−temperature superposition, despite the static homogeneity in the blends. Comparison of the viscoelastic and dielectric data indicated that in the blends PtBS relaxed more slowly than PI. Thus, PtBS possibly gave an effectively quenched, nonuniform frictional environment in the time scale of the global relaxation of PI, and changes of this frictional nonuniformity with T appeared to result in the failure...

Component Chain Dynamics in a Miscible Blend of Low-M Poly(p-t-butyl styrene) and Polyisoprene

Dielectric and viscoelastic behavior was examined for a 8/2 (wt/wt) blend of a cis-polyisoprene (PI; M = 19.9×103) and a low molecular weight (M) poly(p-t-butyl styrene) (PtBS; M = 16.4×103). In general, PtBS and PI exhibit the LCST-type phase behavior, but the blend examined was in the miscible region at temperatures examined, T = 30-70 °C. The dielectric loss e of the blend at low frequencies was exclusively attributable to the large-scale motion of the PI chains having type-A dipoles. The e data obeyed the time-temperature superposition, suggesting that all PI chains in the blend felt the same frictional environment. This result was in contrast to the failure of the superposition previously observed for the same PI chains in a 8/2 miscible blend with a higher-M PtBS (M = 69.5×103). This difference was attributed to a difference of the lifetime of the dynamic heterogeneity due to the concentration fluctuation of PtBS. In the blend with high-M PtBS, the terminal relaxation of PtBS was slower than that of PI and thus the concentration fluctuation was effectively frozen and the PtBS chains behaved as non-uniformly distributed frictional objects during the terminal relaxation of the PI chains. Then all PI chains could not feel the same segmental friction, which naturally resulted in the failure of the time temperature superposition. In contrast, in the blend with low-M PtBS examined in this study, the terminal relaxation was slower for PI than for PtBS. For this case, PtBS behaved as uniformly distributed frictional objects during the terminal relaxation of PI thereby allowing the PI chains to obey the superposition.

Dynamic Tube Dilation in Branched Polymers

In the tube model for entangled polymer chains, the topological constraint for a given probe chain imposed by surrounding matrix chains is represented as a tube confining the probe. Most of current tube models further assume that the relaxed portions of the probe and matrix chains are equivalent to a simple solvent and thus the tube dilates as the relaxation proceeds with time. for polymers of various architectures, this molecular picture of full dynamic tube dilation (full-DTD) can describe the linear viscoelastic relaxation modulus considerably well. However, recent experiments for polymers having so-called type-A dipoles indicate that the full-DTD picture cannot consistently describe the viscoelastic and dielectric relaxation processes of star-branched and multi-branched polymers because of inconsistent coarse-graining of length and time scales incorporated in this picture. This article presents a brief review of these experimental results and explains the molecular picture of partial-DTD in which the length and time scales are consistently coarse-grained on the basis of the constraint release (CR) mechanism.

Rheological and Dielectric Behavior of Dipole-Inverted (SIS)p-Type Multiblock Copolymers: Estimates of Bridge/Loop Fractions for Respective I Blocks and Effect of Loops on High Extensibility of Bridges

A series of symmetric styrene− (S−) cis-isoprene (I) multiblock copolymers of (SIS)p-type (p = 1, 2, 3, and 5 corresponding to tri-, penta-, hepta-, and undecablock) was synthesized with an anion-coupling method and their rheological and dielectric behavior was examined in n-tetradecane (C14), a solvent dissolving the I block and precipitating the S block. The molecular weights of the constituent blocks were almost identical for these copolymers, and a particular I block(s) of respective copolymers had symmetrically once-inverted type-A dipole while the remaining I blocks had noninverted dipoles. At 20 °C, the (SIS)p/C14 systems with the (SIS)p concentration of 40 wt % formed a bcc lattice of glassy, spherical S domains (as confirmed from SAXS) and exhibited the gel-like elasticity. This elasticity was sustained mainly by the bridge-type I blocks connecting the S domains and partly by the coexisting loop-type I blocks. The dielectric loss (e‘ ‘) data exclusively detected the fluctuation of the midpoint of...

Viscoelastic and Dielectric Behavior of a Polyisoprene/Poly(4-tert-butyl styrene) Miscible Blend

Linear viscoelastic and dielectric measurements were conducted for a blend of polyisoprene (PI, M = 19.9 × 103) and poly(4-tert-butyl styrene) (PtBS, M = 69.5 × 103) with a PI/PtBS composition of 8/2 (w/w). In general, PI and PtBS exhibit the lower-critical-solution-temperature (LCST) type phase behavior. At temperatures examined, T ≤ 70 °C, our PI/PtBS blend was in a statically homogeneous state. The PI chain has the so-called type-A dipoles parallel along the backbone, and its large-scale (global) motion activates prominent dielectric relaxation, while the PtBS chain has no type-A dipoles and its global motion is dielectrically inert. In fact, at angular frequencies ω between 101 s-1 and 105 s-1 and at T ≤ 70 °C, the dielectric signal of the blend was exclusively attributed to the PI chains therein. The time−temperature superposition failed for the dielectric loss e‘ ‘ of the PI chains, despite the fact that the blend was statically homogeneous. This result suggested that the frictional environment for ...

Dielectric Behavior of cis-Polyisoprene in Carbon Dioxide under High Pressure

Dielectric measurement was conducted for cis-polyisoprene (PIP) in carbon dioxide (CO2) at high pressures. CO2 is dissolved in PIP more with increasing pressure, and this dissolution is expected to affect the chain dynamics. In our experimental window, the PIP chains having type-A dipoles parallel along their backbone exhibited the dielectric dispersion reflecting their global motion. This dispersion shifted to higher frequencies with increasing CO2 pressure. Time - CO2 pressure superposition was found to hold well, which suggests that the global motion of the chain is accelerated by CO2 without any heterogeneity in space and along the chain backbone. The vertical shift factor (intensity shift factor) for this superposition gave the CO2 concentration in PIP. The plasticizing capability of CO2 evaluated from the horizontal shift factor (frequency shift factor) was found to be a little larger than that of tetradecane in the same range of concentration. No peculiarity was found for plasticizing ability of CO2 even in the supercritical state (at a pressure of 10 MPa).

Viscoelastic and Dielectric Behavior of Entangled Blends of Linear Polyisoprenes Having Widely Separated Molecular Weights: Test of Tube Dilation Picture

Viscoelastic and dielectric experiments were conducted for entangled binary blends of linear cis-polyisoprenes (PI) having widely separated molecular weights, M1 = 21.4 × 103 ≅ 4Me and M2 = 308 × 103 ≅ 62Me with Me (≅5 × 103) being the entanglement molecular weight. The PI chain had type-A dipoles and its global motion (end-to-end vector fluctuation) was dielectrically active. The volume fraction of the high-M chain, υ2, was varied from 0.005 to 1. The Struglinski-Graessley parameter for the blends, M2Me2/M13 = 0.79, was larger than a threshold value ≅0.5 necessary for the thermal constraint release (CR) mechanism to dominate the relaxation of the dilute high-M chains. Indeed, the Rouse-like CR relaxation was experimentally detected for the blends with small υ2 ≤ 0.01. For large υ2 (≥0.05), the high-M chains were entangled with each other (as well as with the low-M chains) and exhibited solution-like relaxation behavior at long times in their terminal regime. Comparison of viscoelastic and dielectric data...

Subchain Dynamics in Disordered Diblock Copolymer: Poly(isoprene-block-butadiene)

We investigated the dielectric normal mode relaxation on diblock copolymers poly(isoprene-block-butadiene) (I-B) with several polyisoprene (PI)/polybutadiene (PB) compositions. Through the dielectric measurements on I-B, we can obtain information about the dynamics of the PI subchain since the PI block is labeled with type-A dipole but PB is not. At the same time, we carried out viscoelastic measurements on the same I-B samples to obtain information of the whole chain motion, especially the longest relaxation times and the plateau moduli. From these viscoelastic and dielectric data, we can directly compare the relaxation spectra of subchains with those predicted by the tube model. From such comparison, we have found that the end part of the chain relaxes faster than the theoretical prediction suggesting extra relaxation mechanisms other than reptation in the dynamics of chain ends.