Rheological Behavior for Polymer Melts and Concentrated Solutions——Part Ⅶ: A Quantitative Verification for the Molecular Theory of Non-linear Viscoelasticity with Entanglement Constraints in Polymer Melts

Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated, the theoretical relations between. eta((gamma) over dot), psi (10)((gamma) over dot) and shear rate ((gamma) over dot), and topologically constrained dimension number n ' and a were derived. Linear viscoelastic parameters (eta (0) and G(N)(0)) and topologically constrained dimension number (n ' a and <(<upsilon>)over bar>) as a function of the primary molecular weight (M-n), molecular weight between entanglements (M-C) and the entanglement sites sequence distribution in polymer chain were determined. A new method for determination of viscoelastic parameters (eta (0), psi (10), G(N)(0) and J(e)(0)), topologically constrained dimension number (n ', a and v) and molecular weight (M-n, M-c and M-e) from the shear flow measurements was proposed. It was used to determine those parameters and structures of HDPE, making a good agreement between these values and those obtained by other methods. The agreement affords a quantitative verification for the molecular theory of nonlinear viscoelasticity with constrained entanglement in polymer melts.

Rheological Behaviour for Polymer Melts and Concentrated Solutions Part Ⅰ:A New Multiple Reptation Model to Predict the Nonlinear Visco-elasticity with Nagai Chain Constraints in Entangled Polymer Melts

An approach of stochastically statistical mechanics and a unified molecular theory of nonlinear viscoelasticity with constraints of Nagai chain entanglement for polymer melts have been proposed. A multimode model structure for a single polymer chain with n tail segments and N reversible entanglement sites on the test polymer chain is developed. Based on the above model structure and the mechanism of molecular flow by the dynamical reorganization of entanglement sites, the probability distribution function of the end-to-end vectr for a single polymer chain at entangled state and the viscoelastic free energy of deformation for polymer melts are calculated by using the method of the stochastically statistical mechanics. The four types of stress-strain relation and the memory function are derived from this thery. The above theoretical relations are verified by the experimentaf data for various polymer melts. These relations are found to be in good agreement with the experimental results

Rheological Behaviour for Polymer Melts and Concentrated SolutionsPart Ⅱ: Material Function with Nagai Chain Constraints and Determination of Their Parameters from Flow Curves

An integral constitutive equation and a set of material functions for describing the strain history of polymer melts were formulated in terms of the Cauchy-Green and Finger tensors. A simple memory function and the dependence of ηo and τt on M3.4 were derived from the theory of non-linear viscoelasticity with constraints of entanglements for polymer melts and substituted into the Oldroye-Walters-Fredickson constitutive equation. An integral constitutive equation for polymer melts was consequently obtained. Some material functions of the constitutive equation related to certain 'test flow' are examined as follows : (1) simple steady shear flow; (2) steady elongation flow; (3) small-amplitude oscillatory shear flow; (4) stress growth upon the inception of steady shear elongation flow; (5) stress relaxation (modulus and compllance). These theoretical relations for simple steady shear flow were compared with experimental data from our laboratory and references for various polymer melts and concentrated solutions. A good agreement between the theory and experiment was achieved.

MODELING THE CHAIN CONFORMATION OF POLYMER MELTS IN CONTRACTION FLOW

A constitutive model of quasi-Newtonian fluid based on the type of flow is used in abrupt planar contraction now.The numerical results from finite element analysis are consistent with experimental data for stress patterns and velocityprofiles in the flow field. The chain conformations of polymer melts are then investigated in such a planar contraction byusing the phenomenological model with internal parameters proposed by the author. That is, the shape and orientation ofpolymer chain coils are predicted and discussed in different flow regions of the contraction flow field that possess simpleshear flow, extensional flow, vortical flow, and mixed flow respectively.

A RHEOLOGICAL MODEL FOR POLYMER MELTS WITH INTERNAL STRUCTURE IN FLOW FIELDS

Conceptually, an imagined conformation ellipsoid is supposed to represent the shape of a polymer chain for polymer melts in flow fields and to be equivalent to the volume element in a mathematical sense in continuum mechanics. A power law dependence of shear modulus of polymer melts on detC, referred to as envelope volume, is proposed. Based on those assumptions and the non-linear relation of shear modulus, a phenomenological viscoelastic model is derived. The model is tested in simple shear flow, simple elongational flow, oscillatory shear flow, and relaxation process after flow suddenly stopped. The results show that the model works well to predict the change of internal structure and viscoelastic performance of polymer melts in flow fields.

Exploring Nonlinear Rheological Behaviors in Entangled Semi-flexible Polymer Melts

This study utilizes molecular dynamics simulation to investigate the complex dynamics of entangled semi-flexible polymer melts.The investigation reveals a significant stress overshoot phenomenon in the systems,demonstrating the intricate interplay between shear rates,chain orientation,and chain stretching dynamics.Additionally,the identification of metastable states,characterized by a dual-plateau phenomenon in the shear stress-strain curve at specific Rouse-Weissenberg number Wi_(R),showcases the system’s responsiveness to external perturbations and its transition to stable shear banding states.Moreover,the analysis of flow field deviations uncovers a progression of shear bands with increasing Wi_(R),displaying distinct behaviors in the system’s dynamics under different shear rates and chain lengths.These findings challenge established theoretical frameworks and advocate for refined modelling approaches in polymer rheology research.

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.

Shear and extensional rheology of entangled polymer melts: Similarities and differences

This work extends our previous understanding concerning the nonlinear responses of entangled polymer solutions and melts to large external deformation in both simple shear and uniaxial extension. Many similarities have recently been identified for both step strain and startup continuous deformation, including elastic yielding, i.e., chain disentanglement after cessation of shear or extension, and emergence of a yield point during startup deformation that involves a deformation rate in excess of the dominant molecular relaxation rate. At a sufficiently high constant Hencky rate, uniaxial extension of an entangled melt is known to produce window-glass-like rupture. The present study provides evidence against the speculation that chain entanglements tie up into "dead knots" in constant-rate extension because of the exponentially growing chain stretching with time. In particular, it is shown that even Instron-style tensile stretching, i.e., extending a specimen by applying a constant velocity on both ends, results in rupture. Yet, in the same rate range, the same entangled melt only yields in simple shear, and the resulting shear banding is clearly not a characteristic of rupture. Thus, we conclude that chain entanglements respond to simple shear in the manner of yielding whereas uniaxial extension is rather effective in causing some entanglements to lock up, making it impossible for the entanglement network to yield at high rates.

Diffusion and Relaxation Dynamics of Supercooled Polymer Melts

The dynamic properties of polymer melts are investigated in the range of normal liquid regime to the supercooled liquid regime. The polymer is modeled as a coarse-grained bead-spring model with chain length ranging from 5 to 160. The mean squared displacement and non-Gaussian parameter are used to describe the self diffusion of polymer beads. We find slow dynamics with decreasing temperature and increasing chain length. The time evolution of non-Gaussian parameters shows two peaks （or one peak one shoulder） in the a-relaxation time, τa, regime and sub-diffusion time regime, respectively, where the first primary peak indicates the dynamic heterogeneity stemmed from the motion of beads, and the secondary peak is the result of correlated motion along a polymer chain. Moreover, the relaxation of polymer beads shows clear two-step decay in supercooled melts and the dynamics shows growing heterogeneity with decreasing temperature. As chain length is increased, a peak of the dynamic susceptibility occurs, and the peak height, x＊4, increases and then reaches a plateau. The curves of the height of the first peak of a2, a2＊, versus τa and the curves of x＊4 versus τa follow two master curves for different chain lengths. Our results indicate the similarity of dynamic heterogeneity dominated by the motion of single bead even the chain length is different. It is interesting to find that the Stokes-Einstein （SE） relation between ra and diffusion coefficient D, D-rq 1, is highly length-scale dependent. The SE relation breaks down in both normal melts regime and supercooled regime at large magnitude of wave vectors, attributed to the non-Brownian motion arising from the chain connectivity and growing heterogeneity due to supercooling. However, the SE relation is reconstructed when the probing length scale is large （at small magnitude of wave vectors）. Our results show a hierarchical physical picture of the supercooled polymeric dynamics.

Non-isothermal crystallization kinetics of Nylon 10T and Nylon 10T/1010 copolymers:Effect of sebacic acid as a third comonomer

Nylon 10 T and Nylon 10T/1010 samples were synthesized by direct melt polymerization. The non-isothermal crystallization kinetics of Nylon 10 T and Nylon 10T/1010 was investigated by means of differential scanning calorimetry(DSC). Jeziorny equation and Mo equation were applied to describe the non-isothermal crystallization kinetics of the Nylon 10 T and the Nylon 10T/1010. The activation energies for non-isothermal crystallization were obtained by Vyazovkin's method and Friedman's method, respectively. These results showed that Jeziorny equation and Mo equation well described the non-isothermal crystallization kinetics of the Nylon 10 T and the Nylon 10T/1010. It was found that the values of the activation energy for non-isothermal crystallization of the Nylon 10T/1010 were lower than those of the Nylon 10 T at a given temperature or relative crystallinity degree,which revealed that crystallization ability of the Nylon 10T/1010 was higher. The crystal morphology was observed by means of a polarized optical microscope(POM) and X-ray diffraction(XRD). It was found that the addition of sebacic acid comonomer not only did not change the crystal form of the Nylon 10 T, but also significantly increased the number and decreased the size of spherulites. Comparing with the Nylon 10 T, the crystallization rate was increased with the addition of the sebacic acid comonomer.

Isothermal Crystallization Kinetics of Nylon 10T and Nylon 10T/1010 Copolymers:Effect of Sebacic Acid as a Third Comonomer

Nylon 10T and nylon 10T/1010 samples were synthesized by direct melt polymerization.The isothermal crystallization kinetics of nylon 10T and nylon 10T/1010 was investigated by means of differential scanning calorimetry（DSC）.The crystallization kinetics under isothermal condition has been analyzed by the Avrami equation.It was found that the Avrami equation was well-suited to describe the isothermal crystallization kinetics,combined with the results of the Turnbull-Fisher equation.The values of Tm^0 and Kg were obtained by Hoffman-Weeks and Lauritzen-Hoffman equations,respectively.The activation energies for isothermal crystallization of nylon 10T and nylon 10T/1010 were determined using the Arrhenius equation and found to be-123.24 and-81.86 kJ·mol^（-1）,respectively,which reveals that the crystallization ability of nylon 10T/1010was lower than that of nylon 10T during the isothermal crystallization process.The crystal morphology was observed by means of polarized optical microscopy（POM）and X-ray diffraction（XRD）.It was found that the addition of sebacic acid comonomer did not change the crystal form of nylon 10T,but significantly increased the number and decreased the size of spherulites.

Analyses of Dynamic Rheological Behavior of Polymer Melt Based on Novel Experimental Equipment and Procedures

By introducing a vibrating force field into the extrusion process of polymer melt, an experimental equipment of constant velocity type dynamic rheometer of capillary (CVDRC) was designed. A set of experimental procedures was established, by which the dynamic rheological parameters of polymer can be acquired, and a set of data management methods to undergo time-domain or frequency-domain analysis was set up for dynamic rheological data of polymer melt. Meantime, the characterization formula of polymer melt's rheological behavior in a vibrating force field was set up. The instantaneous value of capillary entry pressure, capillary volume flow rate and their phase difference were measured and analyzed, and the melt apparent viscosity, which describes the rheological behavior of polymer melt in a vibrating force field, was obtained.

WHOLLY-AROMATIC THERMOTROPIC LIQUID CRYSTALLINE POLYMER AND ITS BLOCK COPOLYMER

A wholly-aromatic thermotropic liquid crystalline polymer (WATLCP) composed of p-hydroxybenzoic acid (HBA), 4,4'-dihydroxy bisphenyl (BP), terephthalic acid (TPA), m-phthalic acid (MPA) was synthesized. It was symbolized by BP-LCP. Using a similar method, a new copolymer BP-PSF was prepared. BP-PSF has a semi-flexible chain polysulfone and a rigid-rod chain like BP-LCP. By FT-IR, polarizing microscope and DSC technique, the structures and properties of BP-LCP and BP-PSF were studied.

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

CRYSTAL STRUCTURE AND MORPHOLOGY OF NASCENT SAMPLES OF SYMMETRIC AROMATIC POLYESTERS——Ⅰ.POLY(P-PHENYLENE TEREPHTHALATE)

The morphology and crytal structure of poly(p-phenylene terephthalate) (PPT), prepared by confined thin filmmelt (CTFMP) and solution (CTFSP) and bulk solution polymerization, were characterized by transmission electronmicroscopy, electron dimaction and molecular modeling. The unit cell is monoclinic (P2_1/a space group) with parameters a =7.89, b = 5.49, c = 12.65 A, α=γ= 90°, β=100.33°, density = 1.48 g/cm^3, the a, b and β values differing slightly from thosereported previously in the literature. A degree of variation in relative intensities of hk0 reflections in, apparently, untilted[001] ED patterns was observed from a given sample, suggesting some variation in molecular packing. ED evidence wasfound for a second phase, with [001] appearing the same as for phase Ⅱ of the related poly(p-oxybenzoate) (PpOBA)polymer. CTFMP crystals polymerized above 220℃ (up to 370℃) and CTFSP crystals polymerized at 300℃ consisted oflamellae 100-200 A thick.

Synthesis and Characterization of Poly(terephthalic acid-2,5-furandicarboxylic acid-1,8-octanediol) Copolyester

Terephthalic acid,2,5-furandicarboxylic acid and 1,8-octanediol were adopted as monomers and antimony trioxide as catalyst,and poly(terephthalic acid-2,5-furandicarboxylic acid-1,8-octanediol) copolyesters identified as PEOT-x,where x is the mole fraction of furandicarboxylic acid in the samples,were synthesized by direct esterification.The molecular structure of the copolyesters was characterized by FTIR and 1H NMR spectroscopy.Gel permeation chromatography (GPC),differential scanning calorimetry (DSC),and thermogravimetric analysis (TGA) were used to characterize the molecular weight,molar mass dispersity,glass transition temperature,and thermal stability of the copolyesters,respectively.The mechanical properties of the samples were also investigated.The number-average molecular weight (M_(n)) of the samples varies from 9 700-18 800 g/mol,and molar mass dispersity (■=M_(w)/M_(n)) from 2.15-3.34.The initial decomposition temperature of the copolyesters is in the 332-356 ℃ range,with maximum decomposition rates at 390-410 ℃,while the glass transition temperature (Tg) varies from 0-33 ℃.Mechanical test shows that PEOT-10 has the highest tensile strength,while PEOT-90 has the largest tensile modulus and elongation at break.The experimental results show that these copolyesters can be synthesized with relatively high molecular weights,good thermal stability,and fair mechanical properties,which makes them excellent replacements for commercial polyesters,such as PET,and these properties can be tuned through the relative amounts of biomass monomer 2,5-furandicarboxylic acid used in the reactions.

Study of Synthesis of Copoly (lactic acid/glycolic acid) by Direct Melt Polycondensation

A two steps direct copolymerisation process was developed. The first step is to produce oligomer and then the oligomer of lactic acid/glycolic acid (90/10) is polymerized with binary catalyst tin chloride dihydrate/p-toluenesulfonic acid. In this way, the direct synthesis of copoly (lactic acid/glycolic acid) without any organic solvent was investigated. The properties and structures of products were characterized by nuclear magnetic resonance (NMR), differential scanning calorimetry (DSC), X-ray diffraction and so on. The results show that comparatively high molecular weight copolymer of lactic acid and glycolic acid can be prepared by direct processing under appropriate technological conditions.

Degradable Polyesters based on Oxygenated Fatty Acid Monomer

A series of degradable polyesters was synthesized via melt polymerization of 3,6-dioxaoctane-1,8-dioic acid and five different diols,catalyzed by antimony trioxide(Sb_(2)O_(3)).The polymers were characterized by FT-IR and ^(1)H NMR spectroscopy,gel permeation chromatography(GPC)and differential scanning calorimetry(DSC)analysis.The polydispersity index(PDI=M_(w)/M_(n))of the polyesters ranged from 1.55 to 1.99,the weight-average molecular weight(M_(w))from 1.8×10^(4) to 3.2×10^(4) Da,the melting point from 63 to 123℃,and the highest decomposition temperature observed was 363℃.The influence of the structure of the polymer chain on hydrolytic degradability was investigated with tests performed at three different values of pH.The findings obtained provide useful insight for the molecular design and the synthesis of degradable polyesters.

CRYSTAL STRUCTURE AND MORPHOLOGY OF NASCENT SAMPLES OF SYMMETRIC AROMATIC POLYESTERS——Ⅱ. POLY(p-PHENYLENE 2,6-NAPHTHALATE)

Confined thin film melt polymerization (CTFMP) of naphthalene chloride/hydroquinone (NCMQ, 1/1, molar)mixtures at polymerization temperatures (T_p) below ca. 300℃ resulted in relatively thick, elongated crystals. Polymerizationof NC/HQ above 300℃ between glass yielded well-formed lamellar crystals ca. 100 A thick. Phase Ⅰ and Ⅱ [001] EDpatterns were obtained for all T_p, the relative amount of phase Ⅰ increasing with T_p. Polymerization of naphthalenedicarboxylic acid/hydroquinione diacetate 1/1 mixtures at high T_p also yielded lamellar crystals that "curled up" off of thesubstrate. When the high temperature CTFMP polymerization was conducted between mica, aggregates of lamellae on-edgedeveloped but epitaxial growth did not occur. Epitaxial growth of lamellae between mica could be obtained, however, byconfined thin film solution polymerization, with both of the latter samples yielding apparently related ED patterns from adifferent unit cell than phase Ⅰ or Ⅱ. Fiber patterns, obtained from sheared samples, indicated considerably greater crystaldisorder than in the nascent crystals. Refinement of the phase Ⅰ unit cell parameters, based on the [001] and [01 1] EDpatterns, with modeling based on Cerius^2, suggests a monoclinic phase Ⅰ unit cell with a = 7.76, b = 5.71, c = 14.99 A, α = γ= 90°, β= 99.7°, ρ = 1.47 g/cm^3, space group P12_1/al.

Progress in Recrystallized SiC and Its Composites

Recrystallized silicon carbide（ RSi C）,a high purity Si C material sintered by the process of evaporation-condensation without any additives,is one of the most important structural materials in the fields of high temperatures. However,its low density and porous structure caused by the sintering mechanism in the absence of shrinkage,restrict its wide applications in engineering.This paper reviews the research progress and related technologies on the preparation of high-density RSi C and its composites. RSi C with relative high density up to 2. 75g·cm- 3can be obtained by a combination of pretreatment to Si C raw materials such as reshaping,modification and particle size distribution,and appropriate forming method. Post treatments such as cyclic pyrolysis and impregnation- recrystallization,and slurry impregnation- recrystallization are needed for the further density increase of RSi C（ 2. 99 g·cm- 3）. In addition,high performance RSi C- Mo Si2 and RSi C- Al composites obtained by melt infiltration are also reviewed.