Relaxation Mode Distribution Research Articles

Linear viscoelasticity of double associative polymers with varied density of the secondary interaction

This study examines the linear viscoelasticity of double-associative ionomers based on poly(hexyl methacrylate). The ionomer samples are unentangled and contain a fixed number of ionic stickers per chain, fion≅4, but a varied number of hydrogen-bonding stickers per chain, fH = 5.5–27. Increasing fH has distinct effects on the glassy and rubbery dynamics. On the one hand, the glassy relaxation mode distribution broadens, and the glassy-to-rubbery transition region delays significantly with increasing fH. On the other hand, the delay of the ionic dissociation and, accordingly, the terminal relaxation (activated by continuous ionic dissociations) are much weaker. This contrast suggests that the ionic dissociation is not only activated by the segmental motion of the main backbone but is also partly activated by the motion of the side chains that is less dependent on fH.

Linear viscoelastic response and steady shear viscosity of native cellulose in 1-ethyl-3-methylimidazolium methylphosphonate

Oscillatory and steady shear of cellulose in 1-ethyl-3-methylimidazolium methylphosphonate {[EMIm][P(OCH3)(H)O2]} were studied for cellulose concentrations from 0.017 to 10 wt. %, spanning the dilute, semidilute unentangled and entangled regimes. The overlap concentration of our cellulose in [EMIm][P(OCH3)(H)O2] is 0.065 wt. % and the entanglement concentration is 8× larger (0.5 wt. %). The concentration dependences of specific viscosity, relaxation time, and terminal modulus suggest that [EMIm][P(OCH3)(H)O2] is a good solvent for cellulose. Compared with the cellulose/1-butyl-3-methyl imidazolium chloride ([BMIm]Cl) system, this native cellulose in [EMIm][P(OCH3)(H)O2] has lower c* and ce, and much higher extent of entanglement. A significantly wider than expected rubbery plateau for the entangled solutions and failure of the Cox–Merz rule suggest that cellulose in [EMIm][P(OCH3)(H)O2] is not simply a flexible polymer in a good solvent. The relaxation mode distribution in the terminal regime is much broader for cellulose in [EMIm][P(OCH3)(H)O2] compared with the same cellulose in [BMIm]Cl. The delocalized phosphonate anion likely binds to hydroxyl groups on multiple cellulose chains, acting as temporary crosslinks.

The Solidification Rheology of Amorphous Polymers − Vitrification as Compared to Gelation

The liquid‐to‐solid transition of polymeric materials results from the growth of a heterogeneous, percolating internal structure. The increased connectivity reduces the mobility of internal constituents and dominates the macroscopic rheological properties, which often appear to be very similar for gelation and vitrification. An example near the liquid‐to‐solid transition is the diverging shear viscosity, which is accompanied by high elasticity and a diverging relaxation time (critical slow down). Gelation and vitrification are hard to distinguish in this way. A distinctive difference, however, was found in the distribution of relaxation modes. Short relaxation modes dominate gelation since most internal constituents maintain their high mobility while, in comparison, the percolating structure is too weak to significantly contribute to the macroscopic behavior. The opposite is found for vitrification, which originates from large, cooperatively‐moving regions which finally connect into a percolating structure at the glass transition. As a consequence, the long relaxation modes dominate the approach of the glass transition. Surprisingly, the relaxation time spectrum adopts the same format for both phenomena near the transition, except that the relaxation exponent, n, is negative for gelation and positive for vitrification. Mathematically, one is the inverse of the other. The spectrum is cut off by the diverging longest relaxation time. Examples will be shown for these phenomena.

Fundamental Investigation of Polymer Dynamics with Dielectric and Viscoelastic Methods

This paper briefly summarizes two representative examples of investigation of fundamental polymer dynamics with dielectric and viscoelastic methods: 1) Entangled dynamics of flexible polymers: For type-A polymers having the electrical dipoles parallel along the chain backbone, the entanglement dynamics is differently reflected in the dielectric and viscoelastic relaxation functions. A simple relationship between these functions was deduced for the case of full dynamic tube dilation (full-DTD). This full-DTD relationship was found to hold experimentally for monodisperse linear chains, but not for branched (star and Cayley-tree) chains and linear/linear blends. A refined relationship, referred to as partial-DTD, was developed by taking into account the time necessary for constraint release equilibration. This partial-DTD relationship was found to valid for the linear, branched, and blend systems. 2) Effect of carbon dioxide (CO2) on polymer dynamics: Pressurized CO2 dissolves into polymers to exhibit a plasticizing effect. Dielectric tests revealed that the local dynamics of polymer chains was accelerated by pressurized CO2 without changing relaxation mode distribution. This unusual plasticizing effect of pressurized CO2 for the local dynamics was attributed to extraordinary fast diffusion of CO2 compared to the segmental motion of the polymer chain. The concentration fluctuation of the polymers, being responsible for the relaxation mode broadening usually observed for plasticized polymer systems, is smeared by the fast CO2 molecules in the time scale of segmental motion. In contrast, pressurized CO2 behaves just as an ordinary solvent for the slow, global dynamics of polymer chains.

Dielectric and Viscoelastic Investigation of Segmental Dynamics of Polystyrene above Glass Transition Temperature: Cooperative Sequence Length and Relaxation Mode Distribution

Atactic polystyrene (PS) has the type-B dipole perpendicular to the chain backbone so that its local, segmental motion activates the dielectric relaxation. For monodisperse oligostyrene (OS) and PS samples of various molecular weights M, details of this motion were examined at temperatures T well above Tg through comparison of the complex modulus, G* = G′ + iG′′, and the complex dielectric permittivity, e* =e′ – ie′′, measured as functions of the angular frequency ω. For the OS samples, G*(ω) and e*(ω) fully relaxed through the segmental dynamics thereby exhibiting respective terminal relaxation tails (low-frequency tails), G′(ω) ∝ ω2, G′′(ω) ∝ ω, Δe′(ω) ≡ e′(0) – e′(ω)∝ ω2, and e′′(ω) ∝ ω, at ω below the segmental relaxation frequency ωs. For the PS samples, G*(ω) relaxed partly through the segmental dynamics and then exhibited the polymeric full relaxation characterized by the Rouse-like behavior followed by the terminal flow behavior (with/without intermediate entanglement plateau depending on M). In c...

Dielectric Relaxation of Polymer/Carbon Dioxide Systems

In general, pressurized CO2 is soluble in polymers (to a concentration determined by the pressure) and affects the polymer relaxation behavior. Focusing on segmental relaxation, this study conducted dielectric measurements for racemic dl-poly(lactic acid) (PLA) as well as polystyrene (PS) under carbon dioxide (CO2) pressurized up to PCO2 = 3.5 MPa. The dielectrically detected segmental dynamics of PLA and PS was found to be accelerated on the increases of the CO2 pressure PCO2 that resulted in an increase of the CO2 concentration (detected through a decrease of the dielectric intensity). In this sense, the pressurized CO2 behaved as an ordinary solvent. However, the dielectrically detected segmental relaxation mode distribution was quite insensitive to PCO2, which was in strong contrast to the mode broadening induced by ordinary solvents such as di-n-butyl phthalate (DBP) (the broadening was confirmed also in this study for PLA plasticized with DBP). The mode broadening due to ordinary solvents is attribu...

A theoretical analysis of rheodielectric response of type‐A polymer chains

AbstractFor type‐A polymer chains having type‐A dipoles parallel along the chain backbone (such as cis‐polyisoprene), a theoretical analysis was conducted for the rheodielectric response to relate this response to the chain dynamics. The rheodielectric response in the shear gradient direction (y direction) under steady shear was analyzed on the basis of a Langevin equation. It turned out that the relaxation time is exactly the same for the rheodielectric relaxation function and the end‐to‐end vector autocorrelation function defined in the shear gradient direction and that the relaxation mode distribution also coincides for these functions at least up to second order of the shear rate (corresponding to the lowest order of nonlinearities of these functions). Consequently, the Green‐Kubo theorem holds satisfactorily, and the rheodielectric intensity is proportional to the squared chain size in y direction, 〈R〉, averaged over the time‐independent conformational distribution function under steady shear. The situation is more complicated under large amplitude oscillatory strain (LAOS) because the conformational distribution function fLAOS is synchronized with LAOS to oscillate at the LAOS frequency, Ω. The rheodielectric response under LAOS was found to detect this oscillation of fLAOS being coupled with the oscillation of the electric field, E(t) = E0sin ωt, and thus, split into a series of components oscillating at frequencies ω and ω ± βΩ (β = 1, 2, …). Consequently, the rheodielectric intensity under LAOS, evaluated from the component oscillating at ω, is no longer proportional to 〈R〉. However, the relative mode distribution and relaxation time of this component can be directly related to those of the end‐to‐end vector correlation averaged over a nonoscillatory part of fLAOS. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1039–1057, 2009

Constraint Release in Moderately Entangled Monodisperse Star Polyisoprene Systems

For examination of a constraint release (CR) contribution to relaxation in monodisperse systems of moderately entangled six-arm star polyisoprenes (PI), viscoelastic measurements were conducted for blends of these star PI and a high molecular weight (M) linear PI. In the blends, the linear PI was dilute and entangled only with the matrix star chains. The terminal relaxation of this dilute linear probe occurred through competition of reptation and Rouse-type CR, as confirmed from its relaxation mode distribution. The probe relaxation time τprobe measured in the blends was utilized in the following way to elucidate the CR relaxation in the star matrices: Since the CR time τCR of the star matrix is expressed as (2Na)2τlife with 2Na and τlife being the entanglement number per two arms (span length) and the effective entanglement lifetime in the system, τCR can be evaluated if the τlife value is known. For determination of the τlife value, the τprobe data of the linear probe in the star matrices was compared with the previously obtained τprobe data of the same probe in linear PI matrices under a molecular idea that τlife should be the same in a pair of star and linear matrices giving the same τprobe value. The molecular weight ML,mat of the linear matrix paired with each star matrix was thus specified, and the value of τlife in the star matrix was determined by utilizing this ML,mat value in a previously obtained empirical equation of τlife in the linear matrices (τlife = 2.5 × 10-18ML,mat3 s at 40 °C). For the monodisperse systems of the star PI, the τCR (=(2Na)2τlife) thus evaluated was close to the measured relaxation time, indicating that the CR mechanism significantly contributes to the star relaxation. This result was in harmony with the validity of the molecular picture of partial dynamic-tube-dilation (p-DTD) confirmed for the star PI.

Viscoelastic properties of chitosan solutions: Effect of concentration and ionic strength

The dynamic rheological properties of chitosan solutions have been investigated in terms of ionic strength and chitosan concentration for entangled systems. The overlap concentration C* and the entanglement concentration C e have first been determined to identify the dilute, semi-dilute and concentrated entangled regimes. In dilute solutions, the effect of ionic strength ( I) on the intrinsic viscosity ([ η]) has been interpreted in terms of the Debye electrostatic screening length. The intrinsic viscosity, the radius of gyration and the persistence length decreased with increasing ionic strength, due to the screening of the electrostatic charges on the chitosan chains by the salt resulting in increased chain flexibility. For concentrated solutions, dynamic measurements were performed and the relaxation spectra were calculated from the storage ( G′) and loss ( G″) moduli characterized in the linear viscoelastic region. For all chitosan concentrations and ionic strengths, the time-weighted stress relaxation spectra showed only one peak. However, the width of the spectra increased with increasing polymer concentration, indicating a larger distribution of relaxation modes due to more entanglements and interchain interactions. The mean relaxation time ( τ H), related to reptation, and the zero-shear viscosity ( η 0) were found to follow power-law expressions of the chitosan concentration, with τ H ∼ C 3.1 and η 0 ∼ C 4.1, respectively, with the high exponents indicating the associating character of the polymer. The non-Newtonian nature (elastic properties and shear-thinning behavior) of the chitosan solutions increased with increasing chitosan concentration and decreasing ionic strength.

Stimuli‐responsive reversible physical networks. II. Design and properties of homogeneous physical networks consisting of periodic copolymers synthesized by living cationic polymerization

AbstractThe design and precision synthesis of physical networks consisting of copolymers with crystallizable pendant groups are described in this work. Amphiphilic periodic, statistical, and gradient copolymers consisting of octadecyl vinyl ether (ODVE) units were synthesized via living cationic polymerization. The synthesis involved the copolymerization of ODVE and 2‐methoxyethyl vinyl ether (hydrophilic) with an 1‐(isobutoxy)ethyl acetate [CH3CH(OiBu)OCOCH3]/Et1.5AlCl1.5 initiating system in the presence of a weak Lewis base to yield copolymers with very narrow molecular weight distributions (weight‐average molecular weight/number‐average molecular weight ⋍ 1.2). All aqueous solutions of the copolymers behaved as a viscous liquid above 50 °C. When cooled below 25 °C, the solutions turned into transparent, transient physical gels (exhibiting terminal flow), regardless of the sequence distribution. Viscoelastic studies showed that a periodic copolymer gave a hard gel that was more brittle than the gels obtained from the corresponding statistical and gradient copolymers. This difference and the differences in the relaxation time and relaxation mode distribution of the copolymer gels were consistent with the sequence distributions of ODVE in the respective copolymers. These results indicate that the mechanical properties of a physical network can be controlled by the primary polymer structures. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2712‐2722, 2005

Rheological and Structural Characterization of Hydrophobically Modified Polyacrylamide Solutions in the Semidilute Regime

Semidilute solutions of two series of polyacrylamide (AM)-based copolymers containing hydrophobic di-n-propylacrylamide (DPAM) and di-n-octylacrylamide (DOAM) comonomers, namely P(DPAM-co-AM) and P(DOAM-co-AM), have been characterized using rheology and small angle X-ray scattering (SAXS). The relaxation time and plateau modulus obtained from rheology, and the correlation length (ξ) obtained from SAXS are compared for copolymers with different hydrophobe content (f) and hydrophobe block length (NH). Shear rheometry experiments revealed that P(DOAM-co-AM) copolymers formed gels characterized by a broad distribution of relaxation modes. In contrast, solutions of P(DPAM-co-AM) copolymers exhibited a near-Maxwellian response although additional fast modes contribute significantly to the dynamic shear modulus at high frequency. For both copolymers, the dynamic shear moduli obtained at different temperatures could be time−temperature superposed, with a shift factor described by the Williams−Landel−Ferry equation. For P(DPAM-co-AM) solutions, the sticker lifetime (determined from the fitting of the dynamic moduli to a Maxwell model) was found to increase with increasing f but to be insensitive to NH, in the range examined. However, the plateau modulus Go decreases with increasing NH, which is related to the increase in strand length between stickers. Similar to P(DPAM-co-AM) solutions, one relaxation time for the gels of copolymers with longer hydrophobes (in this case determined from the crossover in the elastic moduli) is more sensitive to f than to NH. The SAXS data for the P(DPAM-co-AM) solutions could be modeled using the structure factor for a polymer solution in a good solvent although enhanced fluctuations had to be considered for the polymers with higher hydrophobe content. The correlation length was found to decrease with increasing temperature for P(DPAM-co-AM) solutions, due an improvement of the solvent quality. But ξ did not depend on the temperature for P(DOAM-co-AM) samples, probably due to stronger associations between hydrophobes. Trends of ξ with NH and f are discussed.

Rheology of carbon black suspensions. II. Well dispersed system

Linear viscoelastic properties were investigated for the suspensions of carbon black (CB) particles having covalently-fused aggregate structures of an average diameter a=120 nm. The suspending medium, an alkyd resin (AR), had a high affinity toward the CB particles, and the aggregates of these particles were well dispersed to form no higher-order agglomerates. Consequently, the suspensions obeyed the time-temperature superposition and their Arrhenius-type activation energy was identical to that of the medium. From comparison of the zero shear viscosity η0 for the CB suspensions and hard-sphere silica suspensions, an effective volume fraction φeff of the CB particles was found to be 2.7 times larger than the bare volume fraction of the particles. The CB particles exhibited a slow relaxation process, and the terminal relaxation time of this process was close to the Peclet time (Brownian diffusion time) evaluated from the aggregate size a and a high frequency viscosity. Furthermore, the terminal relaxation mode distribution of the CB suspensions was well scaled with an intensity factor Ht that was evaluated from the φeff in a way utilized for the hard-sphere silica suspensions. These results demonstrated that the slow relaxation in the CB suspensions was dominated by the Brownian diffusion of the CB aggregates, as similar to the situation for the silica suspensions.

Rheology of poly(methyl methacrylate- co -styrene) particles suspended in water: effects of electrostatic surface layer

Linear and nonlinear viscoelastic properties were examined for aqueous suspensions of monodisperse poly(methyl methacrylate-co-styrene) (MS) particles having the radius a 0 =45 nm and the volume fractions φ=0.428−0.448. These particles had surface charges and the resulting electrostatic surface layer (electric double layer) had a thickness of ts=5.7 nm. At low frequencies in the linear viscoelastic regime, the MS particles behaved approximately as the Brownian hard particles having an effective radius a eff=a 0 + ts, and the dependence of their zero-shear viscosity η0 on an effective volume fraction φeff (={a eff/a 0}3φ) agreed with the φ dependence of η0 of ideal hard-core silica suspensions. In a range of φeff < 0.63, this φeff dependence was well described by the Brady theory. However, the φeff dependence of the high-frequency plateau modulus was weaker and the terminal relaxation mode distribution was narrower for the MS suspensions than for the hard-core suspensions. This result suggested that the electrostatic surface layer of the MS particles was soft and penetrable (at high frequencies). In fact, this “softness” was more clearly observed in the nonlinear regime: the nonlinear damping against step strain was weaker and the thinning under steady shear was less significant for the MS suspension than for the hard-core silica suspensions having the same φeff. These weaker nonlinearities of the concentrated MS particles with φeff∼ 0.63 (maximum volume fraction for random packing) suggested that the surface layers of those particles were mutually penetrating to provide the particles with a rather large mobility.

Linear and Nonlinear Viscoelasticity of Semidilute Aqueous Mixtures of a Nonionic Cellulose Derivative and Ionic Surfactants

Linear and nonlinear viscoelasticity of aqueous solutions of ethyl(hydroxyethyl)cellulose (EHEC) in the presence of a surfactant (sodium dodecyl sulfate (SDS) or cetyltrimethylammonium bromide (CTAB)) have been examined over an extended polymer concentration regime at different surfactant-to-polymer ratios (r). By tuning the value of r and the polymer concentration, the strength of the polymer−surfactant associations can be modulated. At moderate levels of surfactant addition, the viscosity enhancement is much more pronounced for the EHEC−SDS system than for the EHEC−CTAB system. The frequency dependencies of the dynamic moduli cannot in general be described by a simple Maxwell model, but the rheological behavior is more complex with a distribution of relaxation modes. For EHEC solutions without surfactant, the polymer concentration dependence of the zero-shear viscosity η0 can above the entanglement concentration be described by a power law (η0 ∼ Cx, with x = 4.1). By addition of CTAB, the main effect is...

Linear viscoelastic behavior of perfluorooctyl sulfonate micelles: effects of counter-ions

Linear viscoelastic behavior was investigated for aqueous solutions of perfluorooctyl sulfonate (C8F17SO− 3; abbreviated as FOS) micelles having a mixture of tetraethylammonium (N+(C2H5)4; TEA) and lithium (Li+) ions as the counter-ions. The solutions had the same FOS concentration (0.1 mol l−1) and various Li+ fractions in the counter-ions, φLi = 0−0.6, and the FOS micelles in these solutions formed threads which further organized into dendritic networks. At T ≤ 15 °C, the terminal relaxation time τ and the viscosity η, governed by thermal scission of the networks, increased with increasing φLi up to 0.55. A further increase of φLi resulted in decreases of τ and η and in broadening of the relaxation mode distribution. These rheological changes are discussed in relation to the role of TEA ions in thermal scission: Previous NMR studies revealed that only a fraction of TEA ions were tightly bound to the FOS micellar surfaces and these bound ions stabilized the thread/network structures. The concentration of non-bound TEA ions, CTEA *, decreased and finally vanished on increasing φLi up to φLi * ≅ 0.6, and the concentration of the bound TEA ions significantly decreased on a further increase of φLi. The non-bound TEA ions appeared to catalyze the thermal scission of the FOS threads, and the observed increases of τ and η for φLi < 0.55 were attributed to the decrease of CTEA *. On the other hand, the decreases of τ and η as well as the broadening of the mode distribution, found for φLi > 0.55 (where CTEA * ≅ 0), were related to destabilization of the FOS threads/networks due to a shortage of the bound TEA ions and to the existence of concentrated Li+ ions. Viscoelastic data of pure FOSTEA and FOSTEA/FOSLi/TEACl solutions lent support to these arguments for the role of TEA ions in the relaxation of FOSTEA/FOSLi solutions.

Linear and nonlinear viscoelastic properties of aqueous solutions of cationic polyacrylamides

Full Paper : Linear and nonlinear viscoelasticity of aqueous solutions of cationic polyacrylamides at different levels of salt addition have been examined over an extended polymer concentration regime. The polymers have different charge density and the molecular weight of the polymers is high. The rheological features of the systems depend on polymer concentration, charge density, and amount of added salt. The frequency dependences of the dynamic moduli cannot be described by a simple Maxwell model, but the rheological behavior is more complex with a distribution of relaxation modes. The power laws, describing the polymer concentration dependences of the longest relaxation time and the zero-shear viscosity, revealed a stronger concentration dependence of these parameters as the salt concentration increased. At sufficiently hight salt concentration, a behavior resembling that of entangled neutral polymers was observed. Nonlinear shear thinning behavior is found for all systems at higher shear rates. The magnititude of this effect depends on polymer concentration, charge density, and level of added salt. Thixotropy is only observed for solutions of the polymer of high charge density in the absence of added salt. Both, the linear and nonlinear rheological properties elucidate the intricate interplay betwen polyelectrolyte effects and entanglements.

Linear and nonlinear viscoelastic properties of aqueous solutions of cationic polyacrylamides

Linear and nonlinear viscoelasticity of aqueous solutions of cationic polyacrylamides at different levels of salt addition have been examined over an extended polymer concentration regime. The polymers have different charge density and the molecular weight of the polymers is high. The rheological features of the systems depend on polymer concentration, charge density, and amount of added salt. The frequency dependences of the dynamic moduli cannot be described by a simple Maxwell model, but the rheological behavior is more complex with a distribution of relaxation modes. The power laws, describing the polymer concentration dependences of the longest relaxation time and the zero-shear viscosity, revealed a stronger concentration dependence of these parameters as the salt concentration increased. At sufficiently high salt concentration, a behavior resembling that of entangled neutral polymers was observed. Nonlinear shear thinning behavior is found for all systems at higher shear rates. The magnitude of this effect depends on polymer concentration, charge density, and level of added salt. Thixotropy is only observed for solutions of the polymer of high charge density in the absence of added salt. Both, the linear and nonlinear rheological properties elucidate the intricate interplay between polyelectrolyte effects and entanglements.

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

Relaxation in the glass transition regime interpreted in terms of the aggregate model

The retardation time spectra in the glass transition range are discussed on hand of multidimensional deuteron NMR experiments, measurements of the dielectric loss and the T 1 -relaxation of proton spins in liquids at different temperatures and different frequencies. The data can be described by applying the model of reversible aggregation. Every liquid is here characterized by a broad aggregate size distribution. Relaxation is interpreted as collective response of intra-aggregate Debye processes running off while the aggregate ensemble fluctuates. The relaxation time increases with the volume of the aggregate so that every relaxation time distribution is strictly related to the aggregate size distribution. The shape of relaxation mode distributions is similar, the width depends on how the molecular mechanisms couple to the stationary dynamics. The coupling changes on heating so that the width of the relaxation mode distribution decreases. A full description of the α-process needs to account for aggregate ensemble fluctuations, a bimodal relaxation mode spectrum and a heterogeneous kinetics.

Dielectric Normal Mode Process of Star-Shaped Polyisoprenes

The dielectric behavior of six-arm star-shaped cis-polyisoprenes (6S-PI) with the arm molecular weight Mp ranging from 3.5×103 to 21×103 was compared with that of corresponding linear cis-polyisoprenes (L-PI) which were precursors for the arms. In the entangled regime, the normal mode relaxation time τn of 6S-PI was longer and its dependence on molecular weight was stronger for 6S-PIs than for L-PIs. However, an exponential increase of τn with Mp which is characteristic of a highly entangled star chains was not clearly observed for the 6S-PIs examined, because Mp was not large enough. In the non-entangled regime, the relaxation time τnζ at an iso-friction state of 6S-PI was close to that of corresponding L-PI, as suggested by the Rouse-Ham theory. However, the relaxation mode distribution for 6S-PI was broader than that of L-PI. A model calculation using Rouse-Ham dynamics suggested that the distribution of arm length could possibly lead to a substantial broadening for the relaxation mode distribution.