Linear Viscoelasticity of ABA-type Vitrimer Based on Dioxaborolane Metathesis

In this study,we synthesized a series of ABA-type vitrimers by crosslinking the short A moieties of precursors with a bifunctional crosslinker and evaporating the small molecular byproduct.The vitrimer samples thus prepared exhibit linear viscoelasticity dependent on the length of A moiety as well as the content of the crosslinks.When the average number of A monomers per end moiety m=1.1,the crosslinker can only extend the chain but not crosslink the chain.When m becomes 2.8 or higher,introducing a crosslinker first leads to the gelation,whereas excess in crosslinker molecules leads opening of the crosslinking sites and accordingly reentry into the sol regime.Surprisingly,a further increase in the length of the A moieties increases the relaxation time much weaker than the exponential increase seen for the physically crosslinked ABAtype ionomers.We attribute this difference to the distinct relaxation mechanisms:the relaxation of the vitrimer samples is based on relatively independent exchange reactions,which contrasts with the ABA-type ionomers that relax through the collective hopping of connected ionic groups from one ion aggregate to another.

Statics,Dynamics and Linear Viscoelasticity from Dissipative Particle Dynamics Simulation of Entangled Linear Polymer Melts

Dissipative particle dynamics(DPD)with bond uncrossability shows a great potential in studying entangled polymers,however relatively little is known of applicability range of entangled DPD model to be use as a model for ideal chains and properly describe the full dynamics of entangled melts.Therefore,we perform a comprehensive study on structure,dynamics and linear viscoelasticity of a typical DPD entangled model system,semiflexible linear polymer melt.These polymers obey Flory's ideality hypothesis in chain dimensions,but their local structure exhibits nonideal behavior due to weak correlated hole effect.Both monomer motion and viscoelasticity relaxation reproduce the full pictures as predicted by reptation theory.The stronger chain length dependent diffusion coefficient and relaxation time as well as dynamic moduli are in close agreement with predictions of modern tube model that accounts for additional relaxation mechanisms besides chain reptation.However,an anomalous sub-diffusive center of mass motion is observed both before and after the intermediate reptation regime and the cross-correlation between chains is not negligible even these polymers obey stress-optical law,indicating limitations of the reptation theory.Hence semiflexible linear entangled DPD model can correctly describe statics and dynamics of entangled polymer melts.

The Effectiveness of the Havriliak-Negami Model in Predicting the Master Curves of the Asphalt Blends with SBS Triblock Copolymer and Organic-Montmorillonite at Different Temperatures and Frequencies

The dynamic viscoelastic properties of asphalt AC-20 and its composites with Organic-Montmorillonite clay (OMMt) and SBS were modeled using the empirical Havriliak-Negami (HN) model, based on linear viscoelastic theory (LVE). The HN parameters, α, β, G0, G∞and τHN were determined by solving the HN equation across various temperatures and frequencies. The HN model successfully predicted the rheological behavior of the asphalt and its blends within the temperature range of 25˚C - 40˚C. However, deviations occurred between 40˚C - 75˚C, where the glass transition temperature Tg of the asphalt components and the SBS polymer are located, rendering the HN model ineffective for predicting the dynamic viscoelastic properties of composites containing OMMt under these conditions. Yet, the prediction error of the HN model dropped to 2.28% - 2.81% for asphalt and its mixtures at 100˚C, a temperature exceeding the Tg values of both polymer and asphalt, where the mixtures exhibited a liquid-like behavior. The exponent α and the relaxation time increased with temperature across all systems. Incorporating OMMt clay into the asphalt blends significantly enhanced the relaxation dynamics of the resulting composites.

Nonlinear dynamic characteristics of piles embedded in rock

The nonlinear dynamic characteristics of a pile embedded in a rock were investigated. Suppose that both the materials of the pile and the soil around the pile obey nonlinear elastic and linear viscoelastic constitutive relations. The nonlinear partial differential equation governing the dynamic characteristics of the pile was first derived. The Galerkin method was used to simplify the equation and to obtain a nonlinear ordinary differential equation. The methods in nonlinear dynamics were employed to solve the simplified dynamical system, and the time-path curves, phase-trajectory diagrams, power spectrum, Poincare sections and bifurcation and chaos diagrams of the motion of the pile were obtained. The effects of parameters on the dynamic characteristics of the system were also considered in detail.

ANALYTICAL SOLUTION FOR MODE Ⅲ DYNAMIC RUPTURE OF STANDARD LINEAR VISCOELASTIC SOLID WITH NONLINEAR DAMPING

Introducing the nonlinear Rayleigh damping into the governing equation of the Mode Ⅲ dynamic rupture for standard viscoelastic solid, this equation is a partial differential and integral equation. First, eliminating the integral term, a PDE of third_order is obtained. Then, applying the small parameter expansion method, linearized asymptotic governing equation for each order of the small parameter is obtained. Dividing the third_order PDE into an elastic part with known solution, the rest part pertains to viscous effect which is neither a Mathieu equation nor a Hill one. The WKBJ method is still adopted to solve it analytically.

A revisit of strain-rate frequency superposition of dense colloidal suspensions under oscillatory shears

Strain-rate frequency superposition(SRFS) is often employed to probe the low-frequency behavior of soft solids under oscillatory shear in anticipated linear response. However, physical interpretation of an apparently well-overlapped master curve generated by SRFS has to combine with nonlinear analysis techniques such as Fourier transform rheology and stress decomposition method. The benefit of SRFS is discarded when some inconsistencies of the shifted master curves with the canonical linear response are observed. In this work, instead of evaluating the SRFS in full master curves, two criteria were proposed to decompose the original SRFS data and to delete the bad experimental data. Application to Carabopol suspensions indicates that good master curves could be constructed based upon the modified data and the high-frequency deviations often observed in original SRFS master curves are eliminated. The modified SRFS data also enable a better quantitative description and the evaluation of the apparent structural relaxation time by the two-mode fractional Maxwell model.

Correlation of Two Coupled Particles in Viscoelastic Medium

Considering the viscoelastic memory effect, we study the correlated motion of two hydrodynamically coupled colloidal particles, each of which confined in a harmonic potential well, in a Kelvin-type and Maxwell-type viscoelastic medium. We find that viscoelastic relaxation plays a significant role in modifying the correlation, particularly the cross correlation. We also find that both the real and imaginary parts of the response function are significantly different from the viscous medium case. In particular there is a phase shift between the vanishing imaginary part and the maximal real part of the response function in a viscoelastic medium. In addition imaginary part of the cross correlation response function exhibits a net energy loss （gain） behavior when the elasticity parameter of the medium is larger （smaller） than the critical value for Kelvin （Maxwell） viscoelastic fluid. Some implication of our results and their connection with previous works are discussed.

Study on Rheology and Release Kinetics of Chuanqi Ophthalmic Microemulsion in situ Gel

[Objectives] To study the rheology and release kinetics of Chuanqi ophthalmic microemulsion in situ gel,so as to provide references for its future study and development. [Methods]The fluid properties and linear viscoelastic regions of this preparation were investigated by MCR 102 rheometer. The release kinetics of Chuanqi ophthalmic microemulsion in situ gel was evaluated by modified Franz diffusion cell method,the ligustrazine and ligustilide were selected as the indictors,and semi-permeable membrane was used as a barrier,sampling time point was 0. 5,1,2,4,6,and 8 h respectively. [Results]Chuanqi ophthalmic microemulsion in situ gel was a pseudoplastic fluid and it had a linear viscoelastic region. Taking the shear stress as the indicator,the linear viscoelastic region was 0-302. 74 Pa; taking the strain as the indicator,the linear viscoelastic region was 0-7. 45%. At the critical point,the storage modulus( G') = the loss modulus( G″) =2 976. 60 Pa,critical shear stress was 302. 74 Pa and critical strain was 7. 45%. The average cumulative release of ligustrazine of 6 samples within 8 h was 33. 71 μg,the average cumulative release rate reached 90. 08%,and the release kinetics followed Higuchi equation. The average cumulative release of ligustilide of 6 samples within 8 h was 68. 46 μg,the average cumulative release rate reached 84. 32%,and the release kinetics followed the zero-order kinetics equation. [Conclusions] Chuanqi ophthalmic microemulsion in situ gel has excellent viscoelasticity and its strain is reversible in a certain range. The release kinetics of ligustrazine is the result from synergistic effect of its physicochemical properties and matrix skeleton,while the release kinetics of ligustilide is mainly affected by its physicochemical properties.

Rheological Behaviour for Polymer Melts and Concentrated Solutions Part Ⅲ: A New Multiple Entanglement Model to Predict the Dependence of Linear Viscoelastic Function (η_0, Ψ_(10)~0,η_(ext)~0) on the Ranges of Primary Molecular Weights and the Species of Polymers

It is shown theoretically that the viscoelasticity of polymer melts is determined by three combining factorst they are the primary molecular weight and its distribution, the number of entanglement sites on polymer chain and the sequence distribution of constituent chains in entanglement spacings. A unified quantity for the three combing factors is the average constrained dimensional number of constituent chains in the long entanglement spacings (v). A new relation of v to the primary molecular weight and the number of testing polymers were derived from the multiple entanglement and reptation model, and a new method for determining v was proposed. The dependences of linear viscoelastic functions on the primary molecular weight and its distribution were derived by the statistical method. When Mn=6Me to 18 Me, the values of (v) can range from 3.33 to 3.70. Their values are in a good agreement with the experiment data, and it can slightjy vary with the different species of polymers and the different ranges of molecular weight of polymers

Linear Viscoelastic Behaviors of Polybutene-1 Melts with Various Structure Parameters

The effects of weight-average molecular （Mw）, molecular weight distribution （MWD）, and isotacticity on the linear viscoelastic behavior of polybutene-1 melts are studied. It is observed that the linear viscoelastic region becomes slightly narrower with increasing frequency. In frequency sweeps, the transition of the polymer melts flow from Newtonian flow to power-law flow can be observed. The melts with higher Mw and：or broader MWD, as well as higher isotacficity exhibit higher complex viscosity, zero shear viscosity, viscoelasticity moduli, relaxation modulus, broader transition zone, while lower critical shear rate, non-Newtonian index, and the frequency at which elasticity begins to play an important role. The relationship of zero shear viscosity on Mw has been established, which agrees with the classical power law. Furthermore, it is found that the cross-over frequency decreases with increasing Mw and the cross-over modulus increases with narrowing MWD.

Hyperbolic Divergence Cleaning in Lattice Boltzmann Magnetohydrodynamics

Magnetohydrodynamics couples the Navier-Stokes and Maxwell’s equations to describe the flow of electrically conducting fluids in magnetic fields.Maxwell’s equations require the divergence of the magnetic field to vanish,but this condition is typically not preserved exactly by numerical algorithms.Solutions can develop artifacts because structural properties of the magnetohydrodynamic equations then fail to hold.Magnetohydrodynamics with hyperbolic divergence cleaning permits a nonzero divergence that evolves under a telegraph equation,designed to both damp the divergence,and propagate it away from any sources,such as poorly resolved regions with large spatial gradients,without significantly increasing the computational cost.We show that existing lattice Boltzmann algorithms for magnetohydrodynamics already incorporate hyperbolic divergence cleaning,though they typically use parameter values for which it reduces to parabolic divergence cleaning under a slowly-varying approximation.We recover hyperbolic divergence cleaning by adjusting the relaxation rate for the trace of the tensor that represents the electric field,and absorb the contribution from the symmetric-traceless part of this tensor using a change of variables.Numerical experiments confirm that the qualitative behaviour changes from parabolic to hyperbolic when the relaxation time for the trace of the electric field tensor is increased.

Analysis of transient viscoelastic response of asphalt concrete using frequency domain approach

The analysis of transient linear viscoelastic response of asphalt concrete （AC） is important for engineering applications. The traditional transient response of AC is analyzed in the time domain by performing complicated convolution integral. The frequency domain approach allows one to determine the transient responses by performing simple multi- plication instead of the complicated convolution integral, and it does not require the time derivative of the input excitation, and thus, the approach could greatly reduce the analysis complexity. This study investigated the frequency domain approach in calculating the transient response by utilizing the discrete Fourier transform technique. The accuracy and effectiveness of the frequency domain approach were verified by comparing the analytical and calculated responses for the standard 3-parameter Maxwell model and by comparing the time and frequency domain solutions for AC. The effect of aliasing of the frequency domain approach can effectively reduce by selecting a small sampling interval for the time domain excitation function. A sampling interval is acceptable as long as the amplitude of the Fourier transformed excitation is close to 0 more than half of the sampling rate. The results show that the frequency domain approach provides a simple and accurate way to perform linear viscoelastic analysis of AC.