type-A Dipoles Research Articles

Rheo-dielectrics in oligomeric and polymeric fluids: a review of recentfindings

This paper gives a brief review of recent results of rheo-dielectricstudies for oligo-styrene (OS) and cis-polyisoprene (PI). OS has type-Bdipoles perpendicular to the backbone, and its dielectric αrelaxation (glassy mode relaxation) is accelerated under the shear flow evenat rates much smaller than the equilibrium relaxation frequency. Thisacceleration, resulting in the decrease of the viscosity (thinning) observed atthose rates, is related to flow-induced reduction of the cooperativity of thesegmental motion. For PI chains, having type-A dipoles parallel to thebackbone, the dielectric relaxation detects the global chain motion. For wellentangled PI chains, this relaxation is only moderately accelerated and itsintensity is only mildly reduced even under fast flow in the non-Newtonianthinning regime. This result is related to a flow-induced orientationalcross-correlation of entanglement segments. Within the context of thetube model for entangled chains, this cross-correlation can be related tothe dynamic tube dilation induced by the convective constraint release.

Rheodielectric Behavior of Entangled cis-Polyisoprene under Fast Shear

For entangled solutions of linear and star-branched cis-polyisoprene (PI) chains, rheodielectric tests were conducted to examine the nonequilibrium chain dynamics under steady shear. The PI chains had the type-A dipoles parallel along their backbone, and the observed rheodielectric behavior reflected the dynamics (fluctuation) of the end-to-end vector of the linear chain and/or the star arm in the shear gradient direction. This behavior changed only slightly, in both relaxation time and intensity, with the shear rate γ even in the significantly thinning regime at 1/τ i < γ < 1/τ Rouse , with τ 1 = terminal relaxation time and τ Rouse = Rouse relaxation time for the chain length equilibration. Comparison of the γ-insensitive rheodielectric intensity data and the non-Newtonian viscosity/normal stress data indicated that an isochronal orientational cross-correlation emerged over some number (β) of entanglement segments under fast shear. This result was analyzed on the basis of the molecular picture of dynamic tube dilation (DTD) induced by the convective constraint release (CCR). The analysis suggested β ≅ 1.8 and ≅ 1.2 for the linear and star chains at the largest γ examined. The CCR-DTD picture was consistent also with the observed γ-insensitivity of the rheodielectric relaxation time. Furthermore, the current CCR models for the linear chain were examined for the rheodielectric data. It turned out that the observed γ-insensitivity of the relaxation time was not straightforwardly deduced from the models.

Dielectric Relaxation of Type-A Polymers in Melts and Solutions

This article describes the dielectric relaxation behavior of flexible polymer chains having the so-called type-A dipoles parallel along the chain backbone. This behavior reflects the global chain motion. Viscoelastically well known features of this motion, such as the power-law relationship between the relaxation time and molecular weight of entangled linear chains (τ1 ∝ M3.5), are also observed dielectrically. More importantly, the dielectric behavior of linear chains having once-inverted type-A dipoles enables us to find some detailed dynamic features such as changes in the eigenfunctions fp of a local correlation function with the chain concentration in solutions. These changes are discussed in relation to motional coupling of concentrated chains. The dielectric properties detect the orientational correlation of two submolecules in the chain at two separate times, while the viscoelastic properties reflect the isochronal orientational anisotropy of individual submolecules. Thus the chain motion is differently averaged in the dielectric and viscoelastic properties, and comparison of these properties enables us to find novel dynamic features. Specifically, this comparison reveals the validity of the tube dilation molecular picture for entangled linear chains and weakening of the short-time coherence of the submolecule motion due to the constraint release mechanism. Moreover, the dielectric method enables us to investigate the chain dynamics under strong flow and/or in a molecularly narrow space. In particular, the retarded dielectric relaxation found for homopolymers and block copolymers in such narrow spaces (in the microdomains for the latter) indicates important effects of the spatial and thermodynamic constraints on the global chain motion. All the above results in turn demonstrate the importance of the dielectric method in investigations of the polymer dynamics.

Concentration Dependence of Loop Fraction in Styrene−Isoprene−Styrene Triblock Copolymer Solutions and Corresponding Changes in Equilibrium Elasticity

Dielectric behavior was examined for solutions of a styrene-isoprene-styrene (SIIS) triblock and SI diblock copolymers in an I-selective solvent, n-tetradecane (C14). The SI copolymer had noninverted type-A dipoles in the I block while the SIIS copolymer, a head-to-head coupled dimer of SI, had once-inverted dipoles in the I block. At a low temperature (5 °C) where the S blocks formed glassy, spherical microdomains, the I blocks of SIIS had either the bridge or loop configurations. The loop fraction φl in these I blocks was estimated from the dielectric losses of the SIIS and SI solutions at low frequencies. The φl was found to increase (from 0.6 to 0.8) with decreasing SIIS concentration (from 50 to 20 wt %). This increase of φl was attributed to stretching and destabilization of the bridge configuration on dilution. The equilibrium elasticities of the bridge and dangling loop, estimated from the φl values and rheological data of the concentrated SIIS/C14 solutions, were comparable in magnitude. This sig...

Tube dilation process in star‐branched cis ‐polyisoprenes

In current tube models for entanglement, the tube representing the topological constraint is considered to move with time. This tube motion results in the constraint release (CR) as well as the dynamic tube dilation (DTD), and an importance of DTD has been argued for entangled star chains. Under these backgrounds, this article examines the validity of the DTD molecular picture for the star chains. For monodisperse star chains having noninverted type-A (parallel) dipoles in respective arms, the normalized viscoelastic and dielectric relaxation functions μ(t) and Φ(t) were found to obey a relationship μ(t) ≅ [Φ(t)]2 if the tube actually dilates in the time scale of the star relaxation. For 6-arm star cis-polyisoprene (PI) chains (having those type-A dipoles), dielectric and viscoelastic measurements were conducted to test this DTD relationship. Both viscoelastic and dielectric properties exhibited characteristic behavior expected from DTD models (assuming the arm retraction in the dilating tube), the exponential increase of the relaxation time and broadening of the relaxation mode distribution with increasing arm molecular weight Ma. However, in the range of Ma examined, Ma ≤ 8Me (Me = entanglement spacing), the above DTD relationship was not valid for a dominant part of the slow relaxation (and the models failed in this sense). Thus, for star chains at least in this range of Ma, the simple DTD picture assuming very rapid CR motion (rapid equilibration in the dilated tube) did not explain the slow relaxation behavior of star chains. This result in turn suggested the importance of the CR motion in this behavior. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1024–1036, 2000

Comparison of Dielectric and Viscoelastic Relaxation Functions of cis-Polyisoprenes: Test of Tube Dilation Molecular Picture

Within the context of the generalized tube model, the tube representing the entanglement constraint is not necessarily fixed in space but moves with time. This tube motion results in constraint release (CR) as well as dynamic tube dilation (DTD) for the chain trapped in the tube. For monodisperse systems, the DTD molecular picture leads to the normalized relaxation modulus μ(t) (=G(t)/GN) being proportional to square of the surviving fraction of the dilated tube. In contrast, the normalized dielectric relaxation function Φ(t) of the chain having noninverted type-A dipoles is proportional to this fraction. Thus, the viscoelastic and dielectric relaxation functions satisfy a relationship μ(t) = [Φ(t)]2 if the tube dilates in time scales of the chain relaxation. The validity of this relationship was examined for linear cis-polyisoprene (PI) chains having those type-A dipoles. The relationship was approximately valid, and thus, the tube dilated for the PI chains with M/Me = 10−30 in their bulk state, although...

Effects of Spatial Confinementon Dielectric Relaxation of Block Copolymers having Tail, Loop, and Bridge Conformations.

From a simple calculation considering no thermodynamic requirement of maintaining uniform density, we estimated the effects of spatial confinement on the dielectric relaxation of model block copolymer chains having type-A dipoles. The results were utilized to discuss the relative importancc of these requirement and confinement in the block chain dynamics. For a tail (tethered) chain composed of N segments as well as for loop/bridge chains composed of 2N segments, all confined in a lamella of thickness L=N1/2b (b=segmental step length), the terminal relaxation was moderately faster, its mode distribution was slightly broader, and the dielectric intensity was considerably smaller than those of the same chains in free space. These effects of the spatial confinement were identical for the bridge and loop (either in the knotted or unknotted configuration) and nearly the same also for the tail. The dielectric behavior expected from this calculation was quite different from the behavior of actual type-A blocks. This result strongly suggests that the block chain dynamics is affected much moer significantly by the requirement of maintaining uniform density than by the spatial confinement.

Dielectric normal mode relaxation of tethered polyisoprene chains in styrene-isoprene block copolymers

Abstract

Dielectric Relaxation of cis-Polyisoprene Chains in Oligo- and Polybutadiene Matrices: Matrix Effects on Mode Distribution and Relaxation Time

The dielectric behavior of dilute cis-polyisoprenes (PI) chains was examined in matrices of oligo- and polybutadiene (B) chains of various molecular weights MB. The PI chains had type-A dipoles parallel along their contour so that their global motion was dielectrically detected. Specifically, the matrix effects were examined for the dielectric mode distribution as well as for the longest and second longest relaxation times, τ1,e and τ2,e. τ1,e and τ2,e were determined from dielectric loss (e‘‘) peak frequencies for PI chains without and with (symmetrical) inversion of the type-A dipoles. These relaxation times were compared at an isofrictional state: For this purpose, the relaxation times for the PI chains in short matrices of MB 9K. As done by Colby et al. (Macromolecules 1987, 20, 2226), those ζ-correction factors were determine...

Relaxation of Spherical Micellar Systems of Styrene−Isoprene Diblock Copolymers. 1. Linear Viscoelastic and Dielectric Behavior

Linear viscoelastic and dielectric relaxation behavior was examined for blends of styrene−isoprene (SI) diblock copolymers in a nonentangling homopolyisoprene (hI) matrix. The copolymers formed spherical micelles with S cores and I corona. The I blocks had type-A dipoles, and their global motion induced dielectric relaxation. The micelles exhibited fast and slow relaxation processes for both dielectric loss e‘‘ and viscoelastic moduli G*. For the fast process, a nearly universal relationship was found for reduced moduli Gr* = [MbI/cbIRT]G*SI and reduced frequencies ωτ*, where G*SI was the contribution of the SI micelles to G*, MbI and cbI were the molecular weight and concentration for the I block, and τ* was a relaxation time that increased exponentially with cbI for large cbI. Similar behavior was found also for e‘‘SI (SI contribution to e‘‘). These features were qualitatively the same as those for the relaxation of star chains, indicating that the fast process corresponded to starlike relaxation of ind...

Dielectric Relaxation of Dipole-Inverted cis-Polyisoprene Solutions

Dielectric relaxation behavior was examined for solutions of a series of cis-polyisoprene (PI) chains having almost identical molecular weights (M ≃ 48K) but differently inverted type-A dipoles parallel along the chain contour. The solvent used was a dielectrically inert butadiene oligomer of M = 0.7K that was a moderately good solvent for the PI chains. Global motion of the dipole-inverted PI chains induced prominent dielectric relaxation at low frequencies, and the dielectric loss (e) curves changed their shape (frequency dependence) with increasing PI concentration c PI : At c PI smaller than the overlapping threshold c * the e curves were rather sharp and reasonably close to the prediction of the Tschoegl model considering both hydrodynamic and excluded-volume interactions, while for c PI > c * the distribution became considerably broader than that predicted from the Rouse/Zimm/Tschoegl and reptation models. These dielectric changes were quite similar to those found in previous studies for PI solutions in Isopar-G and heptane. The shape of the e curves reflected distribution of both relaxation times and intensities of dielectric modes, while those times and intensities were separately determined by characteristic times τ p and integrated. eigenfunctions F p (n) for eigenmodes of local correlation function, C(n,t ;m) = / , with u(n,t) being the nth bond vector at time t. For detailed examination of the above dielectric changes with c PI , the e data of the dipole-inverted PI chains were analyzed to evaluate F p (n) and τ p (for the eigenmode indexp = 1-3). At c PI ≤ c * , τ p were almost proportional to p -1.65 and F p (n) were nearly sinusoidal with respect to the segment location n. These results were in reasonable agreement with the Tschoegl model. With increasing c PI > c * , τ p became almost proportional to p -2 while F p (n) became nonsinusoidal. This p dependence of τ p was still in close agreement with the Rouse and/or reptation models, but the n dependence of F p (n) was considerably different. This result indicated that the broadening of the e curves with c PI was essentially due to changes in the eigenfunctions, not due to changes in the p dependence of τ p (relaxation time span). Changes of F p (n) with c PI were discussed in relation to coupling of motion of chains being overlapped at c PI > c * .

Dielectric Spectroscopy on Dilute Blends of Polyisoprene/Polybutadiene: Effects of Matrix Polybutadiene on the Dynamics of Probe Polyisoprene

Dielectric normal mode relaxation was studied on blends containing a small amount (∼5 wt %) of probe cis-polyisoprenes (PI) in a series of polybutadienes (PB) of different molecular weights M B . Since the PI chain has Stockmayer's type-A dipoles parallel to the chain contour, while PB chains do not, we can study global motion dynamics of the probe chain under various entanglement conditions between PI and PB chains. The dielectric normal-mode relaxation time τ of PI with molecular weight M I followed a power law relation τM I α with a varying from 2 to 3 depending on M B : For M B 20 000, α=3.0, conforming to the pure reptation model, and in the range 3000 1) was larger than 3 and became 3.7 (observed for monodisperse PI melts) at M I /M B ≃ 2-3. These findings were consistently interpreted with Graessley's constraint release model. The shape of the dielectric loss curves (reflecting the distribution of relaxation times) of the blends agreed rather well with the Rouse model when M I /M B > 10 and M B M eB ) especially in the high-frequency tail, as usually observed in monodisperse PI melts

Dielectric study of subchain dynamics and dimension: butadiene-isoprene block copolymers

Dielectric normal mode relaxation was studied for dilute and semidilute hexane solutions of butadiene (B)-isoprene (I) block copolymers in which the polyisoprene block has the component of dipole moment aligned parallel to the chain contour (Type-A dipole moment) while the polybutadiene block does not. Thus, the fluctuation of the end-to-end vector of a portion of a chain labeled by type-A dipoles was observed. The results indicate that BI diblock copolymers exhibit a single loss peak while BIB triblock copolymers exhibit double peaks. This behavior can be qualitatively explained by the Rouse-Zimm theory. In dilute solutions, the loss maximum frequency and the shape of the loss curve agree well with the Zimm theory. In semidilute solutions, the loss curve broadens more than the theoretical loss curve calculated by either the Rouse theory or the Doi-Edwards theory. The broadening of the loss curve can be explained by the coupling theory proposed by Ngai and his co-workers. The mean square end-to-end distance, 〈 r 2〉, of the PI block was estimated from the relaxation strength, Δϵ. The expansion factor, α, for 〈 r 2〉 agreed approximately with that of homo PI solution in heptane.

Multiple Dielectric Relaxations in Solid Polyorganophosphazenes

Dielectric properties of solid films of poly(dichloro phosphazene) (PCPN), poly(diphenoxy phosphazene) (PPPN), and poly(difluoroethoxy phosphazene) (PFPN) were studied in the frequency range from 0.1 to 100 kHz. PCPN exhibited only one relaxation peak (named as α process), while PPPN and PFPN exhibited two loss maxima (α and β) in the dielectric loss ε″ curve within the temperature range between 90 and 460 K. The α process for the each sample was seen just above its glass transition temperature Tg, while the β relaxation was observed only for PPPN and PFPN in the region far below their Tg. This result indicates that the β process is due to rotation of the side groups. Based on the simplest two site model, we estimated the amplitude of the rotational oscillation of the side groups and the energy difference between the two sites. Besides these α and β relaxations, PPPN and PFPN showed the mesophase transition at 400 and 345 K, respectively, where the dielectric constant increased step-wise. The dielectric constant in the mesophase was partly attributable to the polarization of the type-A dipoles.