Viscoelasticity and rheology in the regimes from dilute to concentrated in cellulose 1-ethyl-3-methylimidazolium acetate solutions

Dynamic rheological behaviors of α-cellulose 1-ethyl-3-methylimidazolium acetate ([Emim]Ac) solutions were investigated in a large range of concentrations (0.1–10 wt %) at 25 °C. On the basis of data from the dynamic viscoelastic test, the exponents of the specific viscosity η _sp versus concentration c were determined as 1.0, 2.0 and 4.7 for dilute, semidilute unentangled and entangled regimes respectively, which were in accordance with the scaling prediction for neutral polymer in θ solvent. The intrinsic viscosity [η] of the solution was determined to be 253 mL/g at 25 °C. The linear viscoelastic response of the dilute and semidilute unentangled solutions could be described successfully by the Zimm and Rouse model (ν = 0.5 for θ solution) respectively, suggesting that the motion of cellulose chain in [Emim]Ac changed from Zimm to Rouse model with increasing concentration. At low concentrations, failure of the Cox–Merz rule with steady shear viscosity larger than complex viscosity was observed. While as the concentration increased, the deviation from the Cox–Merz rule disappeared due to the formation of homogeneous entanglement structure in cellulose solution.     

Dynamics and scaling of polymers in a dilute solution: analytical treatment in two and higher dimensions

We consider the dynamical scaling of a single polymer chain in good solvent. In the case of two-dimensional systems, Shannon and Choy [Phys. Rev. Lett. 79, 1455 (1997)] have suggested that the dynamical scaling for a dilute polymer solution breaks down. Using scaling arguments and analytical calculations based on the Zimm model, we show that the dynamical scaling of a dilute two-dimensional polymer system holds when the relevant dynamical quantities are properly extracted from finite systems. Most important, the polymer diffusion coefficient in two dimensions scales logarithmically with system size, in excellent agreement with our extensive computer simulations. This scaling is the reason for the failure of the previous attempts to resolve the dynamical scaling of dilute two-dimensional polymer systems. In three and higher dimensions our analytic calculations are in agreement with previous results in the literature.     

Non‐Newtonian viscosity in linear and star polymers

We theoretically investigate non‐Newtonian viscosity and coil deformation of linear and (regular) star polymers in dilute solution subject to large shear rates. A bead‐and‐spring model with preaveraged hydrodynamic interaction, accounting also approximately for good‐solvent expansion, is employed within the Rouse‐Zimm approach. We impose a constraint on the average spring lengths, so as to keep constant the average contour length of the arms under shear: this corresponds to assuming that the springs become increasingly stiffer. For any topology and a very large molecular mass, coil deformation modifies the hydrodynamic interaction, that goes to a maximum, and then decreases with a crossover from the Zimm to the Rouse regime with increasing shear rate. Correspondingly, the intrinsic viscosity decreases and then raises above its low‐shear value. This behavior is however much less pronounced under good‐solvent conditions. At very large shear rate, the constraint on the spring lengths becomes the dominant factor. This leads to a decrease of intrinsic viscosity with an asymptotic –2/3 power law for any draining condition. Simultaneously, the strongly elongated coil becomes fully aligned with flow.     

Linear viscoelasticity of poly(acrylonitrile-co-itaconic acid)/1-butyl-3-methylimidazolium chloride extended from dilute to concentrated solutions

The solution rheology of poly(acrylonitrile-co-itaconic acid) (poly(AN-co-IA)) in 1-butyl-3-methylimidazolium chloride ([BMIM]Cl) spanning dilute, semidilute unentangled and entangled regimes were investigated. The exponents in the specific viscosity η_sp ～ overlap parameter c[η] power law were 1, 2 and 4.7 for dilute, semidilute unentangled and entangled regimes, respectively, which were found to be consistent with the scaling prediction for neutral linear polymers in θ-solvent. For dilute solutions (lower than 0.9 wt.%), the linear viscoelastic responses were observed to be in good agreement with the Zimm model (Flory exponent ν = 0.5). While for semidilute unentangled solutions (between 0.9 and 8 wt.%), results obtained had been found to be consistent with Rouse model. Considering Flory exponent ν = 0.5 and the concentration dependences of the specific viscosity and relaxation time, it had been evaluated that poly(AN-co-IA) in [BMIM]Cl behaves as a neutral polymer in θ-solvent. It had also been suggested that according to the unusual deviation of Cox-Merz rule, poly(AN-co-IA)/[BMIM]Cl solutions are typical neutral polymeric liquids for the concentrated solutions but have shown a more complicated behavior at high deformation rates.     

Scaling of the viscosity of the Lennard-Jones chain fluid model, argon, and some normal alkanes

In this work, we have tested the efficiency of two scaling approaches aiming at relating shear viscosity to a single thermodynamic quantity in dense fluids, namely the excess entropy and the thermodynamic scaling methods. Using accurate databases, we have applied these approaches first to a model fluid, the flexible Lennard-Jones chain fluid (from the monomer to the hexadecamer), then to real fluids, such as argon and normal alkanes. To enlarge noticeably the range of thermodynamics conditions for which these scaling methods are applicable, we have shown that the use of the residual viscosity instead of the total viscosity is preferable in the scaling procedures. It has been found that both approaches, using the adequate scaling, are suitable for the Lennard-Jones chain fluid model for a wide range of thermodynamic conditions whatever the chain length when scaling law exponents and prefactors are adjusted for each chain length. Furthermore, these results were found to be well respected by the corresponding real fluids.     

高分子动力学的单链模型

高分子单链模型是高分子稀溶液理论研究的基本模型.对其进行深入地分析,不仅有助于解决高分子稀溶液体系中溶液黏度和分子链扩散等基本问题,而且能够增进人们对高分子链结构与溶液性质间关联性的理解.虽然基于经典连续性介质力学的流体动力学理论可以定性,甚至半定量地获得稀溶液的一些重要性质,但是,随着科学技术的发展,人们从分子水平上建立了许多描述高分子稀溶液性质的模型和理论,期望能够定量地描述高分子稀溶液的性质.本文以高分子稀溶液中3个典型的单链模型为例(包括:不含流体力学相互作用的Rouse模型、含二体流体力学相互作用的Zimm模型和含多体流体力学相互作用的部分穿透球模型),综述高分子稀溶液的重要性质,并详细地给出其动力学方程的推导过程及其重要的研究进展.特别是,对于Rouse模型,本文还将其预言结果拓展到了短链高分子流体体系;此外,还介绍了这一领域的关键科学问题、发展前景和研究方向.     

An exact enumeration study on adsorption transition of a tethered chain at an adsorbing surface

<正>The number of configurations,c(n,m),of a single chain with length n attached to a flat surface with m monomers contacting the surface is exactly enumerated.A function of c(n,m) about m and n is obtained.From the function,a scaling law for mean energy of chain is derived,and we estimate the critical pointε_c = 0.276 and the crossover exponentφ= 0.5.The free energy difference between tethered chain and free chain in dilute solution is also studied,which shows the critical adsorption point is about 0.272 for infinite long chain with φ= 0.5.     

Critical exponents and self-similarity for sol-gel transition in aqueous alginate systems induced by in situ release of calcium cations

The sol-gel transition in aqueous alginate systems induced by in situ released calcium cations was monitored with rheology methods. Four alginate samples with different molecular weights and M/G ratios were used over the concentration C(Alg) of 2 approximately 6 wt % with different mole ratios f of Ca2+ to the alginate repeat unit. The scaling for the zero shear viscosity eta(0) before the gel point and the equilibrium modulus Ge after the gel point was described as eta(0) approximately epsilon(-k) and Ge approximately epsilon(z), respectively, where the relative distance to the gel point f(gel) was epsilon = (/f-f(gel)/)/f(gel). The relaxation critical exponent n was determined with Winter's criterion, and the critical exponents k and z estimated respectively from independent measurements of eta(0) and Ge gave n from z/(k + z). Before the gel point, the storage and loss moduli G' and G' obtained at various epsilon can be superposed fairly well to form the master curve. The critical exponents n, k, and z were also evaluated from the shift factors and the structure self-similarity was found in the critical gel. The critical exponents evaluated with different methods agreed well with each other, suggesting two categories of the gelation as growth and cross-link. For the alginate with lower molecular weight, the critical exponents were almost independent of alginate concentration and close to the percolation prediction. For the alginate with higher molecular weight, the critical exponents, however, changed with alginate sample and concentration. The relative alginate concentration C(Alg)/C(Alg)* was found to serve as a criterion to divide these two transitions.     

Hybrid method coupling fluctuating hydrodynamics and molecular dynamics for the simulation of macromolecules

We present a hybrid computational method for simulating the dynamics of macromolecules in solution which couples a mesoscale solver for the fluctuating hydrodynamics (FH) equations with molecular dynamics to describe the macromolecule. The two models interact through a dissipative Stokesian term first introduced by Ahlrichs and Dunweg [J. Chem. Phys. 111, 8225 (1999)]. We show that our method correctly captures the static and dynamical properties of polymer chains as predicted by the Zimm model. In particular, we show that the static conformations are best described when the ratio sigma/b=0.6, where sigma is the Lennard-Jones length parameter and b is the monomer bond length. We also find that the decay of the Rouse modes' autocorrelation function is better described with an analytical correction suggested by Ahlrichs and Dunweg. Our FH solver permits us to treat the fluid equation of state and transport parameters as direct simulation parameters. The expected independence of the chain dynamics on various choices of fluid equation of state and bulk viscosity is recovered, while excellent agreement is found for the temperature and shear viscosity dependence of center of mass diffusion between simulation results and predictions of the Zimm model. We find that Zimm model approximations start to fail when the Schmidt number Sc < or approximately 30. Finally, we investigate the importance of fluid fluctuations and show that using the preaveraged approximation for the hydrodynamic tensor leads to around 3% error in the diffusion coefficient for a polymer chain when the fluid discretization size is greater than 50 A.     

Celluloses in an ionic liquid: the rheological properties of the solutions spanning the dilute and semidilute regimes

The ionic liquid of 1-allyl-3-methylimidazolium chloride ([amim]Cl) was used as the good solvent to dissolve celluloses. Cellulose concentration covers the range of 0.1-3.0 wt %, spanning both the dilute and semidilute regimes. The rheological properties of the cellulose ionic liquid solutions have been investigated by steady shear and oscillatory shear measurements in this study. In the steady shear measurements, all the cellulose solutions show a shear thinning behavior at high shear rates; however, the dilute cellulose solutions show another shear thinning region at low shear rates, which may reflect the characteristics of the [amim]Cl solvent. In the oscillatory shear measurements, for the dilute regime, the reduced dimensionless moduli are obtained by extrapolation of the viscoelastic measurements for the dilute solutions to infinite dilution. The frequency dependences of the reduced dimensionless moduli are intermediate between the predictions from the Zimm model and elongated rodlike model theories, while the fitting by using a hybrid model combining these two model theories agrees well with the experimental results. For the semidilute regime, the frequency dependences of moduli change from the Zimm-like behavior to the Rouse-like behavior with increasing cellulose concentration. In the studied concentration range, the effects of molecular weight and temperature on solution viscoelasticities and the relationship between steady shear viscosity and dynamic shear viscosity are presented. Results show that the solution viscoelasticity greatly depends on the molecular weight of cellulose; the empirical time-temperature superposition principle holds true at the experimental temperatures, while the Cox-Merz rule fails for the solutions investigated in this study.     

A NOVEL INTERPRETATION OF CONCENTRATION DEPENDENCE OF VISCOSITY OF DILUTE POLYMER SOLUTION*

The concentration dependence of the reduced viscosity of dilute polymer solution is interpreted in the light of anew concept of the self-association of polymer chains in dilute solution. The apparent self-association constant is defined asthe molar association constant divided by the molar mass of individual polymer chain and is numerically interconvertiblewith the Huggins coefficient. The molar association constant is directly proportional to the effective hydrodynamic volume ofthe polymer chain in solution and is irrespective of the chain architecture. The effective hydrodynamic volume accounts forthe non-spherical conformation of a short polymer chain in solution and is a product of a shape factor and hydrodynamicvolume. The observed enhancement of Huggins coefficient for short chain and branched polymer is satisfactorily interpretedby the concept of self-association. The concept of self-association allows us to predict the existence of a boundaryconcentration C_s (dynamic contact concentration) which divides the dilute polymer solution into two regions.     

Static and dynamic critical behavior of a symmetrical binary fluid: a computer simulation

A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination of semi-grand-canonical Monte Carlo (SGMC) and molecular dynamics (MD) methods near a liquid-liquid critical temperature T(c). Choosing equal chemical potentials for the two species, the SGMC switches identities (A-->B-->A) to generate well-equilibrated configurations of the system on the coexistence curve for TT(c). A finite-size scaling analysis of the concentration susceptibility above T(c) and of the order parameter below T(c) is performed, varying the number of particles from N=400 to 12 800. The data are fully compatible with the expected critical exponents of the three-dimensional Ising universality class. The equilibrium configurations from the SGMC runs are used as initial states for microcanonical MD runs, from which transport coefficients are extracted. Self-diffusion coefficients are obtained from the Einstein relation, while the interdiffusion coefficient and the shear viscosity are estimated from Green-Kubo expressions. As expected, the self-diffusion constant does not display a detectable critical anomaly. With appropriate finite-size scaling analysis, we show that the simulation data for the shear viscosity and the mutual diffusion constant are quite consistent both with the theoretically predicted behavior, including the critical exponents and amplitudes, and with the most accurate experimental evidence.     

End-monomer Dynamics in Semiflexible Polymers

Spurred by an experimental controversy in the literature, we investigate the end-monomer dynamics of semiflexible polymers through Brownian hydrodynamic simulations and dynamic mean-field theory. Precise experimental observations over the last few years of end-monomer dynamics in the diffusion of double-stranded DNA have given conflicting results: one study indicated an unexpected Rouse-like scaling of the mean squared displacement (MSD) ?r(2)(t)? ~ t(1/2) at intermediate times, corresponding to fluctuations at length scales larger than the persistence length but smaller than the coil size; another study claimed the more conventional Zimm scaling ?r(2)(t)? ~ t(2/3) in the same time range. Using hydrodynamic simulations, analytical and scaling theories, we find a novel intermediate dynamical regime where the effective local exponent of the end-monomer MSD, α(t) = d log?r(2)(t)?/d log t, drops below the Zimm value of 2/3 for sufficiently long chains. The deviation from the Zimm prediction increases with chain length, though it does not reach the Rouse limit of 1/2. The qualitative features of this intermediate regime, found in simulations and in an improved mean-field theory for semiflexible polymers, in particular the variation of α(t) with chain and persistence lengths, can be reproduced through a heuristic scaling argument. Anomalously low values of the effective exponent α are explained by hydrodynamic effects related to the slow crossover from dynamics on length scales smaller than the persistence length to dynamics on larger length scales.     

Dynamics of fluids near the consolute critical point: a molecular-dynamics study of the Widom-Rowlinson mixture

Molecular-dynamics simulations are presented for the dynamic behavior of the Widom-Rowlinson mixture [B. Widom, and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970)] at its critical point. This model consists of two components where like species do not interact and unlike species interact via a hard-core potential. Critical exponents are obtained from a finite-size scaling analysis. The self-diffusion coefficient shows no anomalous behavior near the critical point. The shear viscosity and thermal conductivity show no divergent behavior for the system sizes considered, although there is a significant critical enhancement. The mutual diffusion coefficient, D(AB), vanishes as D(AB) approximately xi(-1.26 +/- 0.08), where xi is the correlation length. This is different from the renormalization-group (D(AB) approximately xi(-1.065)) mode coupling theory (D(AB) approximately xi(-1)) predictions. The theories and simulations can be reconciled if we assume that logarithmic corrections to scaling are important.     

Density scaling of the transport properties of molecular and ionic liquids

Casalini and Roland [Phys. Rev. E 69, 062501 (2004); J. Non-Cryst. Solids 353, 3936 (2007)] and other authors have found that both the dielectric relaxation times and the viscosity, η, of liquids can be expressed solely as functions of the group (TV?(γ)), where T is the temperature, V is the molar volume, and γ a state-independent scaling exponent. Here we report scaling exponents γ, for the viscosities of 46 compounds, including 11 ionic liquids. A generalization of this thermodynamic scaling to other transport properties, namely, the self-diffusion coefficients for ionic and molecular liquids and the electrical conductivity for ionic liquids is examined. Scaling exponents, γ, for the electrical conductivities of six ionic liquids for which viscosity data are available, are found to be quite close to those obtained from viscosities. Using the scaling exponents obtained from viscosities it was possible to correlate molar conductivity over broad ranges of temperature and pressure. However, application of the same procedures to the self-diffusion coefficients, D, of six ionic and 13 molecular liquids leads to superpositioning of poorer quality, as the scaling yields different exponents from those obtained with viscosities and, in the case of the ionic liquids, slightly different values for the anion and the cation. This situation can be improved by using the ratio (D∕T), consistent with the Stokes-Einstein relation, yielding γ values closer to those of viscosity.     

Normal stress and shear stress in a viscoelastic liquid under steady shear flow: Effect of molecular weight heterogeneity

Under steady shear flow, the normal stress and the shear stress in both dilute and concentrated solutions of monodisperse poly-α-methylstyrenes and their blends were measured. It was confirmed that the molecular theories of Rouse and Zimm extended to concentrated solutions can explain the relation between the zero-shear normal stress coefficient and the zero-shear steady-flow viscosity for both monodisperse and polydisperse systems. Shear-rate dependence of steady-flow viscosity can be understood fairly well by the molecular entanglement concept proposed by Graessley so long as the polymer is monodisperse or the amount of the higher molecular weight component is high. However, zero-shear viscosity of blended systems cannot be explained quantitatively by the theory of Graessley. The shear-rate dependence of steady-state compliance of blended systems was also observed, and it can well be explained by the theory of Tanaka, Yamamoto, and Takano which interpreted the shear rate-dependent steady-state compliance in terms of the relaxation time spectrum and its variation with shear rate.     

Hydrodynamic interaction in polymer solutions simulated with dissipative particle dynamics

The authors analyzed extensively the dynamics of polymer chains in solutions simulated with dissipative particle dynamics (DPD), with a special focus on the potential influence of a low Schmidt number of a typical DPD fluid on the simulated polymer dynamics. It has been argued that a low Schmidt number in a DPD fluid can lead to underdevelopment of the hydrodynamic interaction in polymer solutions. The authors' analyses reveal that equilibrium polymer dynamics in dilute solution, under typical DPD simulation conditions, obey the Zimm [J. Chem. Phys. 24, 269 (1956)] model very well. With a further reduction in the Schmidt number, a deviation from the Zimm model to the Rouse model is observed. This implies that the hydrodynamic interaction between monomers is reasonably developed under typical conditions of a DPD simulation. Only when the Schmidt number is further reduced, the hydrodynamic interaction within the chains becomes underdeveloped. The screening of the hydrodynamic interaction and the excluded volume interaction as the polymer volume fraction is increased are well reproduced by the DPD simulations. The use of soft interaction between polymer beads and a low Schmidt number do not produce noticeable problems for the simulated dynamics at high concentrations, except for the entanglement effect which is not captured in the simulations.     

Adsorption behavior of oxyethylated surfactants at the air/water interface

The low-shear viscosity eta(0) of colloidal suspensions of acrylic latex or silica in aqueous gelatin has been measured at a temperature above the sol-gel transition. Measurements were made on dilution of a concentrated suspension with water or a gelatin solution. Thus, either the gelatin : colloid ratio was maintained or it was varied at constant aqueous gelatin concentration. Systems were studied with four lime-processed gelatins of different molecular weights at two concentrations of added salt. In addition, the latex particle size and the thickness of the adsorbed gelatin layer were measured by photon correlation spectroscopy (PCS) under dilute conditions. The dependence of the low-shear viscosity eta(0) on particle concentration was exponential and did not follow the well-established Krieger-Dougherty model for simple hard-sphere suspensions over the concentration range studied. A simple phenomenological model, eta(0)=eta(o)10(phi(e)/phi(s)), was found to predict the behavior well. Here, eta(o) is the viscosity of a gelatin solution of the corresponding solution concentration, phi(e) is proportional to the volume fraction of the particles, and phi(s) is a scaling factor, which was determined to have a value of 0.85. With this value of phi(s), the dimensions determined from PCS could be used to predict the viscosity values.     

Flexible chain molecules in the marginal and concentrated regimes: universal static scaling laws and cross-over predictions

We present predictions for the static scaling exponents and for the cross-over polymer volumetric fractions in the marginal and concentrated solution regimes. Corrections for finite chain length are made. Predictions are based on an analysis of correlated fluctuations in density and chain length, in a semigrand ensemble in which mers and solvent sites exchange identities. Cross-over volumetric fractions are found to be chain length independent to first order, although reciprocal-N corrections are also estimated. Predicted scaling exponents and cross-over regimes are compared with available data from extensive off-lattice Monte Carlo simulations [Karayiannis and Laso, Phys. Rev. Lett. 100, 050602 (2008)] on freely jointed, hard-sphere chains of average lengths from N=12-500 and at packing densities from dilute ones up to the maximally random jammed state.     

树状高分子PPI水溶液性质的研究

树状高分子是一种新型三维合成高分子,由于其分子量分布很窄,分子具有很高的规整性,可作为理论研究的模型,这类分子具有特殊的高度支化结构,内部存在大量的空腔,表面密布大量的官能团,因此存在很多潜在的用途,近十几年来在国内外得到了广泛的重视和研究,由于上述原因,它们的许多都与线性高分子有很大差异,故在溶液性质方面也有很大的区别,程Rong时等最近提出一种用于研究高分子溶液在毛细管中流动行为的新理论－－吸附理论,在线性高分子溶液中得到很好的验证,本文对树状高分子PPI（聚丙撑亚胺）水溶液尤其是在极稀溶液范围内进行了较深入的研究,不仅验证了吸附理论的适用性,还意外地观测到了动态接触浓度。