流变学的前沿方向—液晶高分子流变学

简要叙述液晶高分子的结构,论述液晶分子流变学特征,液晶高分子流体的各类本构方程,其中包括作者发展的液晶高分子流体型本构方程。     

Phase separation effects in the rheology of aqueous solutions of hydroxypropylcellulose

Aqueous solutions of hydroxypropylcellulose (HPC) have been widely used as a model system to study liquid crystalline behavior in polymers. The HPC limiting concentration for mesophase formation in water is about 40% wt, quite independent of molecular weight. Most rheo-optical investigations have been carried out in the concentration range from 50% to 65% wt, on the assumption that only the liquid crystalline phase was present. In this study, by using video-enhanced contrast light microscopy, we show that an isotropic phase in form of tiny droplets is also present at concentrations up to 60% wt, both in quiescent and in sheared samples at room temperature. The isotropic phase can be made to disappear by lowering the temperature. The effects of phase separation on the rheology of the HPC/water system are studied by measuring viscosity as a function of temperature and concentration. A slope of Region I of the viscosity curve close to –0.5 is found only at low temperatures, when the sample is fully anisotropic, whereas an anomalous dependence of the viscosity on temperature is observed when phase separation is significant. This study shows that special care is needed when interpreting experimental results from the HPC/water system in terms of theories for liquid crystalline polymers.     

The rheology of layered liquids: lamellar block copolymers and smectic liquid crystals

The frequency-dependence of the viscoelastic shear modulus at low frequencies in a lamellar polystyrene-polyisoprene block copolymer is qualitatively identical to that measured in small-molecule smectics, namely, the rod-like 4-cyano-4-octylbiphenyl and the flexible n-nonyl-1-O--D-glucopyranoside. All three materials were studied after quenching from the isotropic state, and during and after alignment by large-amplitude oscillatory shearing. The kinetics of aligning, as measured by changes in moduli during shearing, are similar, despite great differences in molecular characteristics. These moduli and the aligning process are evidently controlled by smectic fluctuations and defects, the dynamics of which have universal features.     

Poiseuille flow of Leslie–Ericksen discotic liquid crystals: solution multiplicity, multistability, and non-Newtonian rheology

Computational modeling of the steady capillary Poiseuille flow of flow-aligning discotic nematic liquid crystals (DNLCs) using the Leslie–Ericksen (LE) equations predicts solution multiplicity and multistability. The phenomena are independent of boundary conditions. The steady state solutions are classified into: (a) primary, (b) secondary, and (c) hybrid. Primary solutions exist for all orientation boundary conditions and all flow rates, and are characterized by a flow-alignment angle that is closest to the anchoring angle at the bounding surface. Secondary solutions exist for all orientation boundary conditions and flow rates above a certain critical value. The secondary solutions are characterized by a flow-alignment angle which can be either the nearest neighbor below the primary solution or any multiple of π above. Hybrid solutions interpolate between the primary and the nearest secondary solutions, and hence exhibit two alignment angles. All solutions are stable to planar finite amplitude perturbations. Hybrid solutions are unstable to front propagation and lead to primary or secondary solutions. The non-Newtonian rheology of the primary and secondary solutions is characterized by non-classical shear thinning and thickening apparent viscosity behavior. Well-aligned monodomains can lead to shear thickening, thinning, or a sequence of both. The degree of rheological uncertainty is present for planar and homeotropic anchoring conditions. The non-Newtonian rheology of non-aligned samples leads to shear thinning and lack the uncertainty of well-aligned samples, since the apparent viscosity becomes insensitive to orientation.     

Rheological properties of some biphenyl liquid crystals

Rheological measurements have been carried out using a rotational viscometer with a system of coaxial cylinders on four liquid crystalline substances from the group of cyanobiphenyls. On the basis of results of these investigations it was found that in the investigated range of shear rates the nematic phases exhibited Newtonian flow behaviour, while the smectic phases exhibited non-Newtonian behaviour. For shear rates up to ca. 1000 s^–1 the dependence of the shear stress on shear rate is well described by a power-law model.     

A constitutive equation for a non-Newtonian liquid

The K-BKZ constitutive equation for non-Newtonian liquids usually uses as invariants the coefficients of the characteristic equation of a certain finite strain tensor. We show that the use of the roots of this equation, the squares of the principal stretches, is more efficient. We use a product of the linear relaxation spectrum and a simple sum of powers of the principal stretches as the energy function in the K-BKZ theory. The predictions of this theory agree with Meissner's data to a good approximation over many decades.Dedicated to Professor Arthur S. Lodge on the occasion of his 70th birthday and his retirement from the University of Wisconsin.     

Constitutive equation of co-rotational derivative type for anisotropic-viscoelastic fluid

A constitutive equation theory of Oldroyd fluid B type, i.e. the co-rotational derivative type, is developed for the anisotropic-viscoelastic fluid of liquid crystalline (LC) polymer. Analyzing the influence of the orientational motion on the material behavior and neglecting the influence, the constitutive equation is applied to a simple case for the hydrodynamic motion when the orientational contribution is neglected in it and the anisotropic relaxation, retardation times and anisotropic viscosities are introduced to describe the macroscopic behavior of the anisotropic LC polymer fluid. Using the equation for the shear flow of LC polymer fluid, the analytical expressions of the apparent viscosity and the normal stress differences are given which are in a good agreement with the experimental results of Baek et al. For the fiber spinning flow of the fluid, the analytical expression of the extensional viscosity is given. The project supported by the National Natural Science Foundation of China (19832050 and 10372100)     

液晶高分子-各向异性流体挤出拉伸分岔研究

应用共转导数型本构方程研究了液晶高分子纺丝挤出过程的拉伸黏度,应用计算机符号运算软件 Maple得出解析表达式,拉伸黏度与拉伸率之间关系(随剪切速率变化)表明存在分岔现象,得出拉伸黏度显著高于相应的剪切黏度,解释了液晶高分子熔体挤出时不发生挤出胀大的物理机制．     

The rational mechanics and thermodynamics of polymeric fluids based upon the concept of a variable relaxed state

The conceptual framework of polymer continuum mechanics based upon Eckart's idea of a variable relaxed state is developed. No constitutive models are explicitly used. The theory admits four constitutive functions only, the scalar specific internal energy, the vectorial heat flux, and two tensorial fluxes representing non-elastic stress and flow (slippage). The non-linearity of the constitutive relations includes self-induced anisotropy (Leonov) with Reiner-Rivlin's equation representing a special example for this. — The effectiveness of this non-linear theory is demonstrated by treating elongational flows of polymer melts.     

Theoretical analysis of non-uniform extensional flows in relation to processing rheology and predictions of some constitutive equations

In this paper, a characteristic equation involving the stream function, already given by one of the authors in a previous work for classifying axisymmetric incompressible flows, is re-considered. Non-uniform nearly extensional flows are derived as particular solutions from this equation. Using experimental data in the literature for polymer solutions and melts, it is proved that particular solutions of the characteristic equation lead to kinematics very close to those encountered in the fiber-spinning process. The kinematic equations satisfactorily correlating the fiber-spinning data are used in order to determine the ability of constitutive equations to predict realistic stresses in the flow domain. The rheological parameters of the fluids, obtained from experiments, are used for computation of differential and integral constitutive equations in the spinning conditions. Comparisons with the stress response of adequate constitutive equations are given and discussed.Also affiliated to: Université Joseph Fourier Grenoble I and Institut National Polytechnique de Grenoble, Associé au CNRS (URA 1510)     

扰动本构方程及粘弹流体拉伸流动不稳定性

提出“准衰退记忆”新概念,发展了非牛顿流体扰动本构理论,并研究了粘弹流体拉伸流动的不稳定性规律     

Viscosity of a liquid crystalline polymer solution with a polydomain or a band texture

The viscosity of a main-chain liquid crystalline polymer (anisotropic aqueous solution of hydroxypropylcellulose) is measured in the case where the liquid crystalline polymer presents a band texture and is compared to the case of a polydomain texture.     

Structure and rheology of wormlike micelles

In a semi-dilute aqueous solution under certain conditions, surfactant molecules will self assemble to form wormlike micelles. The micelles are dynamic in structure since they can break and reform, providing an additional mode of relaxation. The viscoelastic properties of the wormlike micelles can be predicted using simple theological models. For many surfactant solutions the mechanical data can be related to the optical data by the stress-optical rule. From the viscoelastic data it is possible to estimate the breaking time of the micelle. The techniques of birefringence and small angle light scattering are used to study the microstructure of a surfactant solution under simple shear and extensional flow. The sample under investigation is a solution of cetyltrimethylammonium bromide and sodium salicylate in water, with a salt to surfactant ratio of 7.7. Below a critical shear rate, the birefringence increases linearly with shear rate and the stress-optical rule is valid. The SALS patterns reveal distinctive butterfly patterns indicating that scattering is a result of concentration fluctuations that moderately couple to the flow. However, above a critical shear rate the birefringence plateaus and the stress-optical rule is no longer valid. SALS patterns show both a bright streak and a butterfly pattern. The bright streak is caused by elongated structures aligned in the direction of the flow. The oriented structures occur when the characteristic time of flow is faster than the breaking time of the micelles.Dedicated to Prof. Dr. J. Meissner on the occasion of his retirement from the chair of Polymer Physics at the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland     

Formation of fibrous crystals in flowing blends of polyethylene melts

Flow induced crystallization of high density polyethylene has been studied in a two-phase flow system using low density polyethylene as the carrier phase. Extensional stresses were generated under slow flow conditions by either of two methods: one involving flow past a stationary seed, the other involving a droplet deformation and bursting mechanism. In both cases, oriented, fibrillar crystallization of the high density phase was observed optically and correlated with calculations indicating the presence of flow-induced extensional gradients. Morphological, thermal, and birefringence data indicate that the crystalline fibers produced are oriented and superheatable, and consist of a multifibrillar substructure. For fibers produced by the droplet bursting process a semi-quantitative agreement was found between fiber melting point and birefringence based on a simplified analysis for the bursting induced extensional flow. These results demonstrate that two-phase flows of crystallizable systems are a convenient means for studying the phenomenon of flow induced crystallization in polymer melts.     

Accurate heat transfer measurements using thermochromic liquid crystal. Part 1: Calibration and characteristics of crystals

Encapsulated thermochromic liquid crystal (TLC) can accurately measure surface temperature in a variety of heat transfer and fluid flow experiments. Narrow-band TLC, where the colour changes over a temperature range of 1 °C, can be used to determine surface temperature within an uncertainty of 0.1 °C. Wide-band TLC, typically active over 5–20 °C, allow the possibility of mapping surface temperature distributions. In part 1 of this two-part paper, an extensive set of calibrations for narrow-band and wide-band TLC is reported. This generic study provides insight into the importance and influence of the various factors governing the colour–temperature relationship. These governing effects include the variation in optical path, the spectrum of the illumination source, the lighting and viewing angles, the differences between cooling or heating cycles (hysteresis), the variation with the number of heating or cooling cycles (aging) and how this varies with TLC film thickness. Two narrow-band crystals are also specifically calibrated for application to experiments on a transparent disc rotating at high speed (5000 rpm). Part 2 of this paper describes how these accurately-calibrated crystals were used to measure the transient surface temperature on, and heat transfer to, a rotating disc.     

Mechanics of polymeric membranes subjected to chemical exposure

The mechanics of polymeric hyperelastic membranes that are subjected to uniform transverse pressure loading are discussed. The paper also focuses on the membrane behaviour when there is loss of hyperelasticity resulting from the removal of plasticizer from the polymeric material as a result of chemical exposure. Constitutive models presented describe the influence of both hyperelasticity and rate-sensitivity on the mechanical behaviour of the polymeric membrane in its natural and chemically exposed states. The constitutive models developed through experimental investigations are implemented in computational techniques to develop solutions to the membrane deformation problems.     

Pulsierende Druckströmung hochpolymerer Schmelzen im kreisförmigen Kanal

Zusammenfassung Es werden theoretische und experimentelle Untersuchungen pulsierender Strömungen viskoelastischer Flüssigkeiten in einem kreisförmigen Kanal durchgeführt. Unter Voraussetzung einer eindimensionalen, isothermen und vollentwickelten Strömung in Anwesenheit sinusförmiger Druckgradientenschwankungen wird für die rheologische Zustandsgleichung von Bird-Carreau eine asymptotische Lösung erzielt. Die Ergebnisse weisen darauf hin, daß sowohl die relative Amplitude der Ausstoßschwankungen als auch die relative Änderung des mittleren Ausstoßes sich in einer allgemeinen Form darstellen läßt, die bezüglich der Temperatur und der relativen Amplitude der Druckgradientenschwankungen invariant ist. Die theoretischen Ergebnisse werden mit experimentellen Daten für ein Polyethylen niederer Dichte verglichen. Dabei wird eine gute Übereinstimmung der Theorie mit dem Experiment festgestellt.

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Theoretical and experimental studies were carried out on the pulsating flow of viscoelastic liquids through a circular channel. By assuming the flow to be one-dimensional, isothermal, and fully developed and the Bird-Carreau constitutive equation to be applicable, an asymptotic solution was found. The results obtained indicate that both the relative amplitude of pulsation of the output and the relative change in the average output may be presented in a generalized form that is independent of the relative amplitude of the pressure pulsations and temperature. The theoretical results were verified experimentally for a low-density polyethylene. Good agreement was found between the theory and the experimental data.

     

The role of transient rheology in polymeric sintering

The initial theory of Frenkel and Eshelby for the coalescence of drops in air (or sintering) of Newtonian fluids, which equated the work of surface tension to the work done by viscous stresses while assuming biaxial extensional flow kinematics, was extended to the case of time-dependent material functions using the Upper Convected Maxwell (UCM) model. A numerical scheme was developed to solve the ordinary differential equations (ODE) for the stresses, which are embedded in the ODE based on the mechanical energy balance. Initial conditions required to solve the set of non-linear ODEs were obtained from visualization experiments of the coalescing drops as the theory for elastic contact gave unrealistically high values of the initial neck radius. The transient model predicted that coalescence was accelerated by increasing the relaxation time, the opposite relationship of what was predicted by the steady-state UCM formulation, and was capable of quantitatively predicting the experimental coalescence rates at times when viscoelasticity was important.     

Director dynamics of uniformly aligned nematic liquid crystals in transient shear flow

We have developed a modular rheo-optical apparatus to study the flow properties of liquid crystals. Its main components are shearing device, strong magnetic field, and optical microscope. We performed experiments on well defined initial morphologies with uniform molecular alignment. The monodomains were achieved with strong magnetic fields (4.7T). Time-resolved conoscopy is the primary optical technique in our investigation. We propose a simple relation between the distribution of alignment angles over the sample thickness and the conoscopically measured angle, to quantitatively measure the alignment angle in shear flow.We followed the relaxation of a shear-induced splay deformation in small molecule model systems (N-(p-methoxybenzylidene) p-butylaniline (MBBA), pentyl-cyano-biphenyl (5 CB) and a commercially available mixture OM14244). We define a rotational director diffusivity (K _s splay elastic constant.i7s splay viscosity) from the relaxation process and devised a model, based on the diffusion equation to determine their values.The director alignment behavior of the small molecule liquid crystals (SMLC's) in shear flow is well described by the two-dimensional Leslie-Ericksen model. The effect of director elasticity can clearly be seen in our experiments, resulting in a decrease of the steady state alignment angle at smaller Ericksen numbers.We found that there is no strain rate dependence of the director vorticity from 0.002/s to 2/s for poly-(-benzyl-D/L-glutamate) (PBG). We determined ₂/₃ = –44 for a 2007o solution of 280000 molecular weight PBG in m-cresol at 20°C. The conoscopic interference pattern vanished after 8 strain units from an initially planar alignment and shearing could be reversed up to 10 strain units to completely recover the initial monodomain.Presented at 4th Meeting of European Rheologists, Sept. 4–9, 1994, Seville, SpainDedicated to Prof. H. Janeschitz-Kriegl at the occasion of his 70th birthday.