Ralph H. Colby

Modeling electrode polarization in dielectric spectroscopy: Ion mobility and mobile ion concentration of single-ion polymer electrolytes

A novel method is presented whereby the parameters quantifying the conductivity of an ionomer can be extracted from the phenomenon of electrode polarization in the dielectric loss and tan delta planes. Mobile ion concentrations and ion mobilities were determined for a poly(ethylene oxide)-based sulfonated ionomer with Li(+), Na(+), and Cs(+) cations. The validity of the model was confirmed by examining the effects of sample thickness and temperature. The Vogel-Fulcher-Tammann (VFT)-type temperature dependence of conductivity was found to arise from the Arrhenius dependence of ion concentration and VFT behavior of mobility. The ion concentration activation energy was found to be 25.2, 23.4, and 22.3+/-0.5 kJmol for ionomers containing Li(+), Na(+), and Cs(+), respectively. The theoretical binding energies were also calculated and found to be approximately 5 kJmol larger than the experimental activation energies, due to stabilization by coordination with polyethylene glycol segments. Surprisingly, the fraction of mobile ions was found to be very small, <0.004% of the cations in the Li(+) ionomer at 20 degrees C.

Diagnosing long-chain branching in polyethylenes

Abstract We propose a novel method for assessing sparse long-chain branching in synthetic polymers such as high-density polyethylene at levels far below the limits of detectability by the usual methods of solution viscometry, size-exclusion chromatography, and NMR spectrometry on solutions. The new method exploits the extreme sensitivity of melt Newtonian viscosity to random branching architecture, along with the systematic phenomenological description thereof developed recently in fundamental studies by Lusignan et al. The method satisfies the only validation criterion presently available to us: it finds long-branch contents in quantitative agreement with stoichiometric yields calculated for several series of linear precursor polyethylenes treated with very low levels of peroxide.

Self‐consistent theory of polydisperse entangled polymers: Linear viscoelasticity of binary blends

The effects of polydispersity on the linear viscoelastic properties of concentrated polymer solutions and melts are analyzed. Existing theories for the dynamics of linear polymers, based on the idea of each polymer confined in a fixed tube, are shown to be incapable of describing observed rheological response of polydisperse polymers. A model is proposed which, in a self‐consistent manner, solves the many chain problem given the solution to the single chain problem. Two types of polymer relaxation are incorporated in the model. The first type is escape of a polymer from its tube by motion of the polymer itself. It includes all dynamic modes available to the single chain in a tube—those due to its reptation—as well as other modes, such as fluctuations in tube length. The second type is relaxation of a polymer chain by the motions of the surrounding polymers forming its tube (constraint release). The relaxation modulus is then the product of two functions μ(t) and R(t). μ(t) is the fraction of tube occupied at time t=0 that has not been evacuated at time t, thereby representing escape of the polymer from its tube (solution to the single chain problem). R(t) represents relaxation by the constraint release process, which is modeled by a Rouse chain with random bead mobilities. The probability distribution of these mobilities is determined, in a self‐consistent way, from the disentanglement rates due to the tube evacuation processes of the surrounding chains. Thus R(t) is calculated from the spectrum of relaxation rates of the μ(t) processes for the surrounding chains. The predictions of the model with some single chain solutions μ(t) from the literature are compared with oscillatory shear data for binary blends of nearly monodisperse polybutadiene, in which both components are well entangled.

Chain Dimensions and Entanglement Spacings

25.1 Chain Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445 25.2 Chain Entanglement and Tube Diameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446 25.3 Critical Molecular Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446 25.4 Temperature Dependence of Chain Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451

Dielectric spectroscopy and conductivity of polyelectrolyte solutions

The dielectric and conductometric properties of aqueous polyelectrolyte solutions present a very complex phenomenology, not yet completely understood, differing from the properties of both neutral macromolecular solutions and of simple electrolytes. Three relaxations are evident in dielectric spectroscopy of aqueous polyelectrolyte solutions. Near 17 GHz, water molecules relax and hence this highest frequency relaxation gives information on the state of water in the solution. At lower frequencies in the MHz range, free counterions respond to the applied field and polarize on the scale of the correlation length. This intermediate frequency relaxation thus provides information about the effective charge on the polyelectrolyte chains, and the fraction of condensed counterions. However, the presence of polar side chains adds a further polarization mechanism that also contributes in this intermediate frequency range. At still lower frequencies, the condensed counterions polarize in a non-uniform way along the polyelectrolyte chain backbone and dielectric spectroscopy in the kHz range may determine the effective friction coefficient of condensed counterions. In this review, we analyse in detail the dielectric and conductometric behaviour of aqueous polyelectrolyte solutions in the light of recent scaling theories for polyelectrolyte conformation and summarize the state-of-the-art in this field.

Concentration fluctuation induced dynamic heterogeneities in polymer blends

The presence of two distinctly different local segmental mobilities found in the case of several phase mixed polymer blends by two‐dimensional 2H‐NMR, dielectric spectroscopy and depolarized dynamic light scattering is rationalized through a simple concentration fluctuation model. Our primary hypothesis is that, although the probability of the occurrence of concentration fluctuations is symmetric about the mean value in a given volume, the ‘‘cooperative volume’’ over which a fluctuation must occur for it to be detected by a dynamic probe is not a constant, but rather depends on the composition of the cooperative volume. Consequently, we suggest that the cooperative volume associated with a concentration fluctuation be determined by the local composition in a self‐consistent manner. In the case of systems with weak interactions and large Tg contrast, these ideas are shown to create a bimodal probability density function for dynamic concentration fluctuations, which has a local maximum corresponding to smal...

Breakdown of time-temperature superposition in miscible polymer blends

Abstract The empirical principle of time-temperature superposition has been found to fail for a miscible blend of 20 weight% poly(ethylene oxide) in poly(methyl methacrylate). Oscillatory shear rheometry data is reported for this blend at four temperatures well above the glass transition temperature of the blend. The longest relaxation time of each component in the blend is obtained from the frequency dependence of the loss modulus. The temperature dependence of the longest relaxation time of each component in the blend is found to obey the empirical WLF equation of the pure component referenced to the glass transition temperature of the blend.

Molecular mobility and Li+ conduction in polyester copolymer ionomers based on poly(ethylene oxide)

We investigate the segmental and local dynamics as well as the transport of Li(+) cations in a series of model poly(ethylene oxide)-based single-ion conductors with varying ion content, using dielectric relaxation spectroscopy. We observe a slowing down of segmental dynamics and an increase in glass transition temperature above a critical ion content, as well as the appearance of an additional relaxation process associated with rotation of ion pairs. Conductivity is strongly coupled to segmental relaxation. For a fixed segmental relaxation frequency, molar conductivity increases with increasing ion content. A physical model of electrode polarization is used to separate ionic conductivity into the contributions of mobile ion concentration and ion mobility, and a model for the conduction mechanism involving transient triple ions is proposed to rationalize the behavior of these quantities as a function of ion content and the measured dielectric constant.

Rheopexy of synovial fluid and protein aggregation.

Bovine synovial fluid and albumin solutions of similar concentration are rheopectic (stress increases with time in steady shear). This unusual flow characteristic is caused by protein aggregation, and the total stress is enhanced by entanglement of this tenuous protein network with the long-chain polysaccharide sodium hyaluronate under physiological conditions. Neutron scattering measurements on albumin solutions demonstrate protein aggregation and all measurements are consistent with a weak dipolar attraction energy (of order 3kT) that is most likely augmented by hydrophobic interactions and/or disulfide bond formation between proteins. Protein aggregation appears to play an important role in the mechanical properties of blood and synovial fluid. We also suggest a connection between the observed rheopexy and the remarkable lubrication properties of synovial fluid.

Thermally Driven Ionic Aggregation in Poly(ethylene oxide)-Based Sulfonate Ionomers

A series of sulfonate polyester ionomers with well-defined poly(ethylene oxide) spacer lengths between phthalates and alkali metal cations as counterions are designed for improved ionic conductivity. Ion conduction in these chemically complex materials is dominated by the polymer mobility and the state of ionic aggregation. While the aggregation decreases dramatically at room temperature as the cation size increases from Li to Na to Cs, the extents of ionic aggregation of these ionomers are comparable at elevated temperatures. Both the Na and Cs ionomers exhibit thermally reversible transformation upon heating from 25 to 120 °C as isolated ion pairs aggregate. This seemingly counterintuitive aggregation of ions on heating is driven by the fact that the dielectric constant of all polar liquids decreases on heating, enhancing Coulomb interactions between ions.