We investigated the linear viscoelastic behavior of poly(1-ethyl-3-vinylimidazolium bis(trifluoromethanesulfonyl)imide) (PC2-TFSI) while varying its molecular weight to clarify the molecular origin of the unusual zero-shear viscosity scaling, r10 proportional to M1.7, reported in earlier studies for unentangled poly(ionic liquid)s. PC2-TFSI exhibited a broadening of linear viscoelastic spectra in the vicinity of glass transition zone, similar to the shape of spectra observed for other alkyl-substituted vinylimidazolium-based poly(ionic liquid)s. Therefore, we attributed this broadening to cooperative local motions, such as sub-Rouse motion, caused by enhanced intra-chain interactions. By decomposing the complex modulus of PC2-TFSI into three components, the glassy, sub-Rouse, and Rouse components, through the modified stress-optical rule, we found that the relaxation time of the sub-Rouse mode increased as the molecular weight of PC2-TFSI increased. Moreover, the limiting viscosity associated with the sub-Rouse mode followed the scaling of r1lim proportional to M1.1. Since polymer chain relaxation occurs in a hierarchical manner, the obtained scaling exponent for the sub-Rouse mode can account for the gap between the theoretical prediction of r10 proportional to M1.0 and the experimentally observed scaling of zero-shear viscosity of r10 proportional to M1.7. The molecular-weight dependence of local motions is unexpected, but we hypothesize that it arises from the enhancement of the solvent-like behavior of dissociated counterions as the PIL molecular weight increases.
Understanding how reversible interactions influence polymer dynamics is essential for designing advanced functional materials. Host-guest complexes represent a versatile class of reversible interactions owing to their molecular selectivity and tunable bonding strength. Although host-guest complexes have been widely utilized as reversible cross-links in aqueous polymer systems, their role in bulk polymers remains unclear, mainly because direct experimental observation of complex formation in the solid state is challenging. This study addresses whether host-guest complexes can function as effective reversible cross-links in polymers and how they influence chain dynamics. Herein, polymers incorporating host-guest complexes exhibited characteristic changes in linear viscoelasticity that are quantitatively described by the sticky reptation model. The plateau modulus (GN) gradually decreased, while the terminal relaxation time (2d) increased with increasing host-guest content. The GN values are well explained by considering both entanglement dilution and reinforcement by reversible cross-links. The prolonged 2d indicates suppressed chain reptation due to reversible topological constraints. Furthermore, the effective association probability (p) and bonding lifetime (2s) were extracted through model-based analysis, providing indirect yet quantitative evidence of reversible complex formation in polymers. These findings establish rheological analysis for probing supramolecular interactions in polymers and highlight host-guest complexes as tunable modifiers of polymer dynamics.
In this study, we investigated how symmetric and asymmetric slit geometries influenced the flow-induced structure of rod-like micellar solutions in abrupt contraction-expansion flows. Birefringence and stream-pathline measurements were conducted to clarify the relationship between micellar orientation, elastic stresses, and geometric confinement. The results showed that (i) the in-slit birefringence distribution systematically changes with geometry, exhibiting a strongly asymmetric pattern in asymmetric channels, (ii) the characteristic birefringence structure upstream of the slit is strongly affected by channel height, suggesting the contribution of out-of-plane strain, and (iii) the flow field is dominated by elastic effects under all conditions tested, as indicated by large Weissenberg numbers. Temperature variation substantially modified the micellar length and flexibility, leading to enhanced birefringence at low temperature and markedly reduced birefringence at high temperature, where the birefringence was confined inside the slit. These results demonstrated that geometry-dependent strain fields and the degree of spatial constraint jointly governed the formation of flow-induced structures in rod-like micellar solutions.
The influence of geometric scale on the extensional rheology of viscoelastic fluids was systematically investigated using a liquid dripping method. Polyethylene oxide aqueous solutions were tested with seven nozzles of different outer diameters ranging from 0.23 mm to 2.77 mm. The temporal evolution of the filament diameter was analyzed to obtain the extensional relaxation time, extensional viscosity, and maximum Weissenberg number. To quantitatively evaluate the scale effect, a surface-area-to-volume ratio was introduced as a geometric parameter. The results show that as the nozzle diameter increases, both the extensional relaxation time and the maximum Weissenberg number gradually approach asymptotic values. This indicates that when the influence of scale effects is negligible, the measured rheological properties more accurately represent the intrinsic viscoelastic response of the fluid. These findings demonstrate that the geometric scale significantly affects the observed extensional behavior in filament thinning experiments. Furthermore, this study establishes a practical experimental guideline that recommends the use of sufficiently large nozzle diameters to minimize scale effects. The use of large nozzles enables reliable evaluation of the extensional viscosity of complex fluids and contributes to improving the accuracy of rheological measurements in complex flow systems.
This study proposes a simple method for detecting ultrafine bubble (UFB) by utilizing bubble behavior near rough surfaces. UFB, with diameters less than 1 mu m, are widely used in industrial applications, but their detection remains challenging due to their nanoscale size. In this work, a rough wall was placed in water containing UFB, and bubble generation and growth near the surface were observed under controlled flow conditions. The results revealed that bubble generation and growth depend on three factors: UFB presence, flow, and surface roughness. In UFB water, bubbles exhibited significant growth, whereas they shrank and disappeared in deionized water. Furthermore, initial gas cavities trapped in surface cavities acted as nucleation sites, and their removal by degassing suppressed bubble formation even in UFB water. Comparison with classical nucleation theory suggests that local pressure reduction and direct gas supply from UFB enable bubble growth below the theoretical critical radius. This approach provides a practical and low-cost method for evaluating UFB presence without specialized instruments.
Our superposition rheometry is so called a parallel superposition method and was anticipated in the previous paper to be a significant method for the rheology of complex fluids. In this report, as to the analyzation after this method, it is found that the deformation of elastic component, lambda, in a complex fluid is estimated by the Eq. 1. This equation is the addition of elastic and viscous forces and is fit to a three-component rheology model. Dividing value of the deformation by the shear rate, lambda/gamma, is the relaxation time of Maxwell model. The consistency of this relaxation time is confirmed by coincidence with those values by other methods, using an HEUR (C24-hydrophobically modified ethoxylated urethane) aqueous solution which is a Maxwell fluid with single relaxation. As the rigidity modulus and the deformation are measured separately, utilization and understanding of various rheological properties or behaviors related to the deformation are greatly expected to progress.
We investigate steady-state mode I crack propagation in nonlinear elastic solids using the finite element method. The neo-Hookean model yields a parabolic crack opening profile and r(-1/2) strain singularity, where r is the distance ahead of the crack tip, for all crack velocities considered, consistent with linear elastic fracture mechanics despite its nonlinearity. In contrast, Gent-type models exhibit sharper crack opening profiles and strain plateaus near the crack tip. These findings differ from the weakly nonlinear theory, which predicts a sharp, non-parabolic crack profile and r(-1) singularity. Compared to the neo-Hookean case, Gent-type models show weaker stress, strain, and their singularities for the same crack velocity and applied strain, implying that strong nonlinearity may improve toughness.
The flow-induced structure of suspensions of particles exhibiting rheotaxis in a uniform flow was numerically analyzed. A startup flow and a flow with step changes in the flow direction were considered. The particles were self-propelled and rotated in the flow. The computational model for particle rotation includes rotation in the direction opposite to the flow, alignment with the average direction of surrounding particles within an effective region, and random rotation. The effect of the intensity of both rheotaxis and random motion of particles on their orientation in a uniform flow was analyzed. The particles move to orient themselves in the direction opposite to the flow with time, increasing the orientation order of the particle suspension. The orientation order increases as the effect of rheotaxis becomes stronger. Furthermore, it is evident that robustness of the orientational behavior to noise intensifies even for weak rheotaxis. In a flow in which the flow direction changes, the director rotates more slowly for systems exhibiting weaker rheotaxis and the particles rotate in a more synchronized manner when rheotaxis is strong.
To enable practical deployment in multilayer ceramic capacitors, optimization of Ni paste requires urgent attention. Adding ethylcellulose (EC) as a binder to Ni paste can significantly alter the rheological properties of the paste and the resulting dried coated film structure. However, the underlying mechanism remains unclear. In this study, we used commercially available EC samples (STD-10, STD-45, and STD-300) with a degree of substitution of ca. 2.5, weight-averaged absolute molar masses (Mw) of 27, 62, and 107 kg/mol, respectively, and molar mass distributions (Mw/Mn) of 1.6-2.0 to prepare Ni pastes by varying the additive amount of EC (wEC). Subsequently, we investigated the particle adsorption properties, rheological properties of the pastes, and structure of the coated dried films. The amount of EC adsorbed on the particle surface monotonically increased over the wEC range of 0.85-3.4 wt%, indicating a multilayer adsorption picture rather than a single-layer one. Rheological measurements of the pastes demonstrated that the shear viscosity and plateau modulus increased as wEC increased, and their dependence on wEC indicated interactions involving EC, such as interparticle bridging via EC chains and entanglement between EC chains, particularly in pastes containing high molar mass ECs (i.e., STD-45 and STD-300). Flow curve measurements revealed shear thickening in the intermediate shear-rate range combined with shear thinning at high shear rates. The structural evaluation of the dried Ni-paste films revealed that both the overall surface roughness and the aggregation size of the small barium titanate particles present in the gaps between the large Ni particles constitute key parameters contributing to the film properties. Considering these multifaceted measurements, we propose conditions for developing an excellent Ni paste and discuss the role of EC and its related mechanism.
Deriving constitutive models (CMs) from numerical data has been an attractive approach as a systematic CM building method. One recent study is Rheo-SINDy, which extended the sparse identification of nonlinear dynamics (SINDy) method to rheology. Although the Rheo-SINDy framework discovered an approximate CM from numerical data under shear flow, its versatility has not been investigated. To clarify its applicability to other types of flows, this study applied Rheo-SINDy to numerically generated data under extensional flow conditions. As baseline tests for extensional flow, we considered two problems: (i) whether the Rheo-SINDy framework can reproduce the famous Giesekus model from data generated by that model, and (ii) whether it can derive an approximate CM from data generated by a dumbbell model with a finite extensible nonlinear elastic (FENE) spring. For problem (i), we confirmed that Rheo-SINDy can identify the exact expression of the Giesekus model under extensional flow. For problem (ii), the Rheo-SINDy framework discovered a relatively simple expression of the approximate CM by manually designing the library matrix based on rheological knowledge. The identified approximate CM can reasonably predict extensional rheological properties of the FENE dumbbell model, including an extrapolation region. These findings demonstrate the fundamental validity of using Rheo-SINDy under extensional flow.
We investigate extensional viscosity and polymer conformation in dilute polymer solutions under uniaxial extensional flow using dissipative particle dynamics simulations. At high extension rates, polymers are significantly stretched by extensional flows, and the extensional viscosity growth function exhibits strain hardening. To reveal their quantitative relation, we adopt an analysis method based on the Rouse-type model. We demonstrate that the extensional viscosity growth function is determined by the instantaneous gyration radii in the parallel and perpendicular directions to the extensional direction and their time derivatives. Our approach also provides a framework to describe the steady-state extensional viscosity of dilute polymer solutions for various chain lengths and concentrations in terms of the polymer gyration radius.
The rheological behavior of polymer melts is strongly influenced by parameters such as chain length, chain stiffness, and architecture. In particular, shear thinning, characterized by a power-law decrease in shear viscosity with increasing shear rate, has been widely investigated through molecular dynamics simulations. A central question is the connection between molecular conformation under steady flow and the resulting shear-thinning response. In this study, we employed coarse-grained molecular dynamics simulations of linear and ring polymers with varying chain stiffness to examine this relationship, with chain conformations quantified by the gyration tensor. We identified a strong correlation between the velocity-gradient direction component of the gyration tensor and shear viscosity, which exhibits a clear scaling relationship. This indicates that chain extension along the velocity-gradient direction governs the effective frictional force. Notably, this behavior emerges as a general feature, independent of chain architecture and chain stiffness. In addition, shear viscosity was found to correlate with the component of the gyration tensor corresponding to the direction that is not directly influenced by advective effects of shear flow. Because advection is absent in the direction, polymer chains can be regarded as diffusing freely, and the extent of this diffusion appears to be controlled by the shear viscosity.
The viscoelastic relaxation mechanisms of cellulose nanocrystals (CNCs) and individualized cellulose nanofibers (iC-NFs) in the dilute and semi-dilute regions were investigated. The dynamic viscoelasticity and dynamic birefringence of CNCs and iCNFs were measured and compared with the viscoelastic theory for semiflexible polymers (Shankar-Pasquali-Morse theory). We first developed a high-sensitive apparatus capable of measuring minute dynamic birefringence of dilute CNC and iCNF suspensions. Thanks to the apparatus, we were able to distinguish the respective modes contributing to the viscoelastic relaxation of CNCs and iCNFs, particularly CNCs. The viscoelastic relaxation of CNCs was well explained by Shankar-Pasquali-Morse theory. We first found that CNCs behaved as ideal semiflexible rods in fluids. In contrast, iCNFs showed specific viscoelastic relaxation behaviors. Shankar-Pasquali-Morse theory couldn't fully describe the viscoelastic relaxation of the iCNFs at high angular frequencies, and the existence of additional relaxation modes were indicated. These results were found regardless of average lengths and solvents of iCNFs. Furthermore, the rotational relaxation times of iC-NFs showed significantly stronger concentration dependencies than those of CNCs and other semiflexible polymers.
