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Polymerized ionic liquids (PILs) with anions of bis(trifluoromethylsulfonyl)imide (TFSI−), hexafluorophosphate (PF6−), and tetrafluoroborate (BF4−); and cations of poly[1-(4-vinylbenzyl)-3-alkyl-imidazolium] P[VBCnIM]+ with alkyl lengths C1, C2, C4 were successfully synthesized and characterized. X-ray scattering showed an increase of backbone-to-backbone spacing (db) by 0.8 Å per CH2 added to the alkyl side chain. Rheological and dielectric measurements were used to measure rates of chain relaxation and ion dissociation/association. The glass transition temperatures Tg follow the trend: PC4-TFSI < PC2-TFSI < PC1-TFSI< PC1-BF4 < PC1-PF6, which correlates well with their dielectric behaviors. However, the fragility mDR from dielectric relaxation increases with decreasing Tg, which is the opposite of the dependence of the fragility mRheo from rheology for both our PILs and of neutral polymers. The dielectric and rheological relaxations of our PIL’s are expected to be influenced by both their anion-cation binding energies and their relative free volumes, while for neutral polymers, only free volume influences relaxation. The increase of fragility of mDR with decreasing Tg, therefore suggests that dielectric relaxation is influenced more by anion-cation binding energy than by free volume, while the reverse is true for mRheo. The plateau modulus GN and entanglement molecular weight Me estimated from rheological measurements agree with predictions of the packing model, using only a small modification of the Flory characteristic ratio C∞ from that of a neutral polymer. Packing lengths of p= 6.0 ~ 9.3 Å and tube diameters dt= 11 ~ 17 nm are found, depending on specific cation and anion structures. 

We review a selection of models for wormlike micelles undergoing reptation and chain sequence rearrangement (e.g. reversible scission) and show that many different assumptions and approximations all produce similar predictions for linear rheology. Therefore, the inverse problem of extracting quantitative microscopic information from linear rheology data alone may be ill-posed without additional supporting data to specify the sequence rearrangement pathway. At the same time, qualitative parameter estimates can be obtained equally well from any of the models in question. Through our study, we also show that the Poisson renewal model can be reformulated as a differential constitutive equation on the tube survival prob- ability distribution function. Using this reformulation, we identify two previously overlooked inconsistencies with Poisson renewal and discuss how these can be resolved by re-interpreting what the model calls a `breaking time'. 

A high-salt phase-separation re-entry is observed in mixtures of poly (diallyldimethyl ammonium chloride) (PDADMAC), a strong polycation, and poly (acrylic acid) (PAA), a partially charged polyanion, within the pH range 4.7 to 5.3. This intriguing phenomenon exclusively occurs at salt concentrations exceeding the critical salt concentration required for dissolving the coacervate formed at low salt concentrations, here named the “Upper Critical Salt Concentration” (UCSaC), and at monomer concentrations exceeding 0.1M for each polymer. The transition from associative phase separation at low salt concentration, to a single solution, and ultimately to segregative separation at high salt concentration called the Lower Critical Salt Concentration (LCSaC), arises from the interplay between electrostatic interactions and the hydrophobicity of neutral PAA monomers in a high-salt solvent. To explain this transition, we use a theory combining short-range ion pairing and counterion condensation with long-range electrostatics using the random phase approximation (RPA), and with hydrophobic interactions between PAA neutral monomers and water. The latter is modeled through a Flory-Huggins χ parameter of around 0.6. Literature observations of a continuous transition from associative to segregative phase transition with increasing salt concentration, without a homogeneous single-phase solution at intermediate salt concentration, are also predicted and discussed. 

The effect of branches on the linear rheology of entangled wormlike micelle solutions is modeled by tracking the diffusion of micellar material through branch points. The model is equivalent to a Kirchhoff circuit model with the sliding of an entangled branch along an entanglement tube due to the constrained diffusion of micellar material analogous to the flux of current in the Kirchhoff circuit model. When combined with our previous mesoscopic pointer algorithm for linear micelles that can both break and fuse, the model adds a branch sprouting process and therefore enables simulation of the dynamics of structural change and stress relaxation in ensembles of micelle clusters of different topologies. Applying this new model to study the relationships between fluid rheology and microstructure of micelles, our results show that branches change the scaling law exponents for viscosity versus micelle strand length. This contrasts with the long-standing hypothesis that branches affect viscosity and relaxation in the same way that micelle ends do. The model also suggests a process for inferring branching density from salt-dependent linear rheology. This is exemplified by mixed surfactant solutions over a range of salt concentrations with flow properties measured using both mechanical rheometry and diffusing wave spectroscopy (DWS). By elucidating the connection between the branching characteristics, such as strand length and branching density, with the nonmonotonic variation of solution viscosity, the above model provides a powerful new tool to help extract branching information from rheology. 

A thorough study is made of the dependences on salt concentration and polymer chain lengths of the low-frequency plateau of coacervates of poly (diallyl dimethyl ammonium chloride), PDADMAC, and poly (sodium 4-styrenesulfonate), PSS. The reliability and reproducibility of these measurements are carefully checked by determining the frequency-dependent stress limits of the rheometer through the use of reference fluids and by repeat experiments with coacervates. Long-time frequency sweeps show that coacervates with less salt are more repeatable than those with higher salt. A low-frequency plateau reliably appears only below a critical salt concentration, and the magnitude of the plateau depends strongly on salt concentration and chain lengths of both polycation and polyanion. It is only present for the molecular weight of the polycation, PDADMAC, higher than 100 kDa, but the magnitude of the plateau is more strongly influenced by the chain length of the polyanion, PSS. Possible causes of the low-frequency plateau are discussed. 

We examine linear and nonlinear shear and extensional rheological properties using a “micelle-slip-spring model” [T. Sato et al., J. Rheol. 64, 1045–1061 (2020)] that incorporates breakage and rejoining events into the slip-spring model originally developed by Likhtman [Macromolecules 38, 6128–6139 (2005)] for unbreakable polymers. We here employ the Fraenkel potential for main chain springs and slip-springs to address the effect of finite extensibility. Moreover, to improve extensional properties under a strong extensional flow, stress-induced micelle breakage (SIMB) is incorporated into the micelle-slip-spring model. Thus, this model is the first model that includes the entanglement constraint, Rouse modes, finite extensibility, breakage and rejoining events, and stress-induced micelle breakage. Computational expense currently limits the model to micellar solutions with moderate numbers of entanglements ([Formula: see text]), but for such solutions, nearly quantitative agreement is attained for the start-up of the shearing flow. The model in the extensional flow cannot yet be tested owing to the lack of data for this entanglement level. The transient and steady shear properties predicted by the micelle-slip-spring model for a moderate shear rate region without significant chain stretch are fit well by the Giesekus model but not by the Phan–Thien/Tanner (PTT) model, which is consistent with the ability of the Giesekus model to match experimental shear data. The extensional viscosities obtained by the micelle-slip-spring model with SIMB show thickening followed by thinning, which is in qualitative agreement with experimental trends. Additionally, the extensional rheological properties of the micelle-slip-spring model with or without SIMB are poorly predicted by both the Giesekus and the PTT models using a single nonlinear parameter. Thus, future work should seek a constitutive model able to capture the behavior of the slip-spring model in shear and extensional flows and so provide an accurate, efficient model of micellar solution rheology.