Network models of concentrated polymer solutions derived from the yamamoto network theory

Several choices of the functions describing the creation and destruction processes of entanglement junctions in the Yamamoto network theory of concentrated polymer solutions have been examined. These choices are simple functions of the extension of the network segments bridging the entanglement points and it is demonstrated that the moments of the distribution function describing the network conformation can be solved for analytically. This has been done for a wide range of two-dimensional flows, both for the steady state and transient start-up and relaxation problems. The macroscopic stress tensor and flow birefringence are calculated and a variety of nonlinear effects are predicted and discussed.     

Localized flow birefringence of polyethylene oxide solutions in a four roll mill

We report flow birefringence observations of polyethylene oxide solutions in a four roll mill where the flow field in the central region of the mill approximates well to that of pure shearing flow. When flow birefringence is observed it is seen to be highly localized within a region close to the “outgoing” asymptotic plane of flow. The phenomenon can be explained in terms of the flow birefringence corresponding to high extension of some polymer chains where the localization is caused by the chains requiring sufficient time in the flow field to become extended. This explanation has important consequences in all “persistently extensional flows” and can explain the origin of previously published results of localized flow birefringence observed for polyethylene solutions in axial compression and axial extensional flows.     

Shear and extensional rheology of solutions of mixtures of poly(ethylene oxide) and anionic surfactants in ionic environments

Interactions between a high molecular weight poly(ethylene oxide) (PEO) and the anionic surfactant sodium dodecyl benzene sulfonate (SDBS) in aqueous solutions were investigated by shear and extensional rheometry. Results for mixtures between PEO and sodium dodecyl sulfate (SDS) are also presented for comparison purposes. Addition of anionic surfactants to PEO solutions above the critical aggregation concentration (CAC), at which micellar aggregates attach to the polymer chain, results in an increase in shear viscosity due to PEO coil expansion, and a strengthening of interchain interactions. In extensional flows, these interactions result in a decrease of the critical shear rate for the onset of the characteristic extension thickening of the PEO solutions that is due to transient entanglements of polymer molecules. The relaxation times associated with these transient entanglements are not directly proportional to the shear viscosity of the solutions, but rather vary more rapidly with surfactant concentration. In the presence of an electrolyte, coil contraction results in lower shear viscosities and a decrease in the extension thickening effects at surfactant concentrations just beyond the CAC. The relaxation times associated with transient entanglement reach a minimum at the same surfactant concentration as the shear viscosity, which indicates that coil contraction is responsible for the observed effects in both types of flow. However, the increase in extensional-flow entanglement relaxation times is much more abrupt than the decrease in shear viscosity. All these results point to a greater sensitivity of extensional flows on the molecular conformation of PEO/surfactant complexes.     

Flow birefringence studies of a concentrated polystyrene solution in a two-roll mill. I. Steady flow and start-up of steady flow

We have studied a 4.8 volume percent solution of a narrow distribution polystyrene with molecular weight 3.84 × 10⁶ in flows generated by a co-rotating two-roll mill. These flows have a stagnation point at the midpoint between the roller axes. Further, they are linear, two-dimensional, and the magnitudes of the strain-rates are greater than the vorticity. The overall objective of our studies is to explore the dynamics of concentrated polymer solutions which are in the highly deformed state that is generated in the two-roll mill. Birefringence data are presented for both steady flow and start-up of steady flow in the two-roll mill. The steady and transient data are used to analyze the linear and nonlinear viscoelastic regions of material behavior. In the nonlinear regime, the birefringence upon start-up shows an initial overshoot followed by a strong undershoot that is enhanced as the ratio of elongation to rotation is increased (i.e., the flow becomes increasingly extensional in character.) We attribute this undershoot, which does not seem to appear in simple shear flows, or flows close to simple shear flow, to polymer segment stretching following an initial period of segment reorientation. Model studies are currently underway to test this notion. © 1992 John Wiley & Sons, Inc.     

The response of entangled polymer solutions to step changes of shear rate: Signatures of segmental stretch?

Experiments measuring the orientation angle and birefringence in startup and double-step strain rate flows were conducted on a 3.0 wt % 8.42 × 10⁶ molecular weight polystyrene solution in a Couette flow cell. A phase-modulated flow birefringence apparatus was used to noninvasively probe the sample. Upon startup from rest, the orientation angle undershoots its final steady-state value, as seen by earlier investigators. When the shear rate undergoes a step increase from one nonzero value to another, the amplitude of this undershoot is decreased. However, a more significant effect is a shorter time scale overshoot in the orientation angle that is highly counterintuitive in the sense that an increase of shear rate initially produces a rotation of chain segments away from the flow direction. Similarly, a step decrease in shear rate yields an initial transient rotation toward the flow direction. In both cases, the height of the peaks depends upon the magnitude of the shear rate jump, and the width of the peaks is a function of the final shear rate. The longer time transients in the startup and step increase experiments reflect an apparent change in the relaxation time for segment orientation, which we tentatively attribute to a combination of tube dilation and convective constraint release. The shorter time scale over- and undershoots in the orientation angle appear to be qualitatively explained by considering the differences in extension or contraction of segments along the polymer chain. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 265–280, 1998     

Overshoots in stress and free energy change during the flow-induced crystallization of polymeric melt in shear flow

<正>The effect of pre-shear flow on the subsequent crystallization process of polymeric melt was investigated and a flow-induced crystallization(FIC) model based on the conformation tensor incorporating the pre-shear effect was proposed. The model is capable of predicting the overshoot phenomena of the stress and the flow-induced free energy change of the polymeric system at high pre-shear rates.Under the condition of flow,the increase in the activated nuclei number was contributed by the flow-induced free energy change,which showed an overwhelming effect on the nuclei formation during the pre-shear process at high shear rates.The half crystallization time(f_(1/2)) of polypropylene(PP) as functions of pre-shear rate and pre-shear time at different crystallization temperatures was predicted and compared with the experiment data.Both numerical and experimental results showed that t_(1/2) of PP decreased dramatically when the flow started but leveled off at long times.It was found that two transformation stages in t_(1/2) existed within a wide range of shear rates.For the first stage where the melting polymer experienced a relatively weak shear flow,the acceleration of crystallization kinetics was mainly contributed by the steady value of free energy change while in the second stage for high shear rates,strong overshoot in flow-induced free energy change occurred and the crystallization kinetics was thus significantly enhanced.The overshoots in stress and flow-induced free energy change reflected an important role of flow on the primary nucleation especially when the flow was strong enough.     

Chitosan and its derivatives in extensional and shear flows

Allylchitosan and propylchitosan with different degrees of substitution were prepared on the basis of chitosan from shrimp chitin. The dynamics of semidilute electrolytic polymer solutions of chitosan derivatives in acetic acid was studied by measuring birefringence in extensional and shear flows and by means of viscometry. The optical shear coefficient and critical velocity gradients corresponding to the loss of stability of the macromolecular coil in extensional flow were found. The chain relaxation times depending on the polyelectrolyte concentration and ionic strength of solution were determined.     

Network architecture and modulus of miscible heteropolymer blends

The architecture and entanglement density of a multicomponent polymer network composed of miscible, flexible chains is related to the corresponding properties and concentrations of the pure components. It is assumed that the coupling frequency between different chain species is proportional to their fractional participation in the blend and that the entanglement ability of polymers can be affected by the presence of heteropolymer neighbors. The theory, equally applicable to temporary and permanent networks, estimates the molecular weight between entanglements and their total number along a chain in the blend. This information is used in establishing a mixing law for the rubbery plateau modulus of a fluid polymer blend and in deriving a relationship for the equilibrium modulus of an interpenetrating polymer network containing trapped entanglements and dangling segments. The theoretical predictions are compared with experimental results from the literature on several miscible polymer blends.     

Rheo-optical characterization of dilute polymer mixtures under shear flow

Optical properties can estimate morphological changes of polymer chains under flow. This work proposes a rheo-optical procedure to determine turbidity and both flow and form birefringence of diluted polymer mixtures of polystyrene (PS) and polypropylene (PP) during a controlled shear flow, by measuring the transmitted light intensity with and without crossed polarizers via an own built optical sensor. The turbidity in these dilute mixtures decreased with the increase of the shear rate due to deformation of the dispersed phase droplets, which reduces their cross-sections. The presence of PP as the dispersed phase in the PS matrix caused a decrease in the total birefringence measured, whereas PS as the dispersed phase in the PP matrix caused an increase in it. Both effects are associated to the positive contribution of the form birefringence, produced by the shear-induced elongated morphology of the dispersed phase.     

Relaxation characteristics and intrinsic birefringence and viscosity of polystyrene solutions for a wide range of molecular weights

A comparison is made between measurements on polystyrene solutions and the relaxation characteristics and intrinsic birefringence and viscosity given by the theory for the flexible Gaussian chain of variable number of segments and with internal viscosity and internal hydrodynamic interaction. This is done in order to determine the applicability of the theory to polymers over a wide range of molecular weights, including the low molecular weight range in which there may be conflict with the theoretical assumption of chains having a large number of segments. The longest, terminal relaxation time and the number of chain segments are determined from measurements of the frequency dependence of oscillatory flow birefringence while the intrinsic birefringence and viscosity are determined from steady flow measurements. The range of molecular weights studied is from approximately 900 at 10⁶. It is found that the segment weight is approximately 1000 and the number of segments is in direct proportion to the molecular weight for the range from 1 to 1000 segments. The terminal relaxation time has a molecular weight dependence of the type given by the theory but with better agreement for higher molecular weights. While the measured dependences of the intrinsic viscosity and birefringence are in agreement with theory for molecular weights greater than 5 × 10⁴, they deviate significantly for molecular weights below 1 × 10⁴. The ratio of the intrinsic birefringence to intrinsic viscosity, which in theory is a constant independent of molecular weight, is found to change at the lower molecular weights.     

Effect of the functionality of junctions on the elasticity of polymacromonomer networks: Computer simulation

The elastic properties of polymer networks formed via the radical polymerization of macromonomers with two polymerizable end groups are studied via computer simulation. It is shown that variation in the average functionality of network junctions, f _avg, in a wide range (∼5–55) leads to a significant change in the shear modulus of the network. According to experiments with real networks (gels of poly(ethylene oxide) macromonomers), the shear modulus increases as f _avg increases. This effect is not due only to a decrease in the fluctuations of positions of network junctions. The main cause of the increase in the modulus is that the modulus component due to interaction between polymer chains (entanglements) increases as the functionality of junctions in the investigated networks increases. The conclusion is made that these networks gain entanglements during the formation of network junctions with high functionality rather than inherit them from the solution of macromonomer chains.     

Strain hardening of polymer glasses: Effect of entanglement density,temperature, and rate

The strain hardening behavior of model polymer glasses is studied with simulations over a wide range of entanglement densities, temperatures, strain rates, and chain lengths. Entangled polymers deform affinely at scales larger than the entanglement length as assumed in entropic network models of strain hardening. The dependence of strain hardening on strain and entanglement density is also consistent with these models, but the temperature dependence has the opposite trend. The dependence on temperature, rate, and interaction strength can instead be understood as reflecting changes in the flow stress. Microscopic analysis of local rearrangements and the primitive paths between entanglements is used to test models of strain hardening. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3487–3500, 2006     

Supermolecular structures and flow birefringence in polymer solutions

Experimental studies of supermolecular structures and localized flow birefringence in solutions of high-molecular weight polymer are described. Advantage is taken of poly(ethylene oxide) and polyisobutylene. Supermolecular structures are examined with the aid of optical microscopy using freeze-dried samples of the polymer solutions. Birefringence is investigated that arises in planar elongational flow in a cross-slot cell. Flow velocities at which the onset of the localized birefringence occurs are determined. Then these velocities are correlated with viscoelastic characteristics of the solutions. The presence of a liquid-crystalline fibrillar network in the polymer solutions exhibiting flow birefringence is ascertained. The fibrils are birefringent objects. The fibrils are birefringent objects. The localized birefringence phenomenon is explained in term of the orientation of the fibrils in elongational flow. It has been shown that the onset of localized birefringence occurs at a critical Weissenberg number, the value of which is close to unity.     

Synergistic effects in flows of mixtures of wormlike micelles and hydroxyethyl celluloses with or without hydrophobic modifications

This work presents experimental results on simple shear and porous media flow of aqueous solutions of two hydroxyethyl celluloses (HEC) and two hydrophobically modified hydroxyethyl celluloses (HMHEC) with different molecular weights. Mixtures of these polymers with a cationic surfactant, cetyltrimethylammonium p-toluenesulfonate (CTAT) were also studied. Emphasis was given to the range of surfactant concentrations in which wormlike micelles are formed. The presence of hydrophobic groups, the effect of the molecular weight of the polymers, the surfactant and polymer concentrations, and the effect of the flow field type (simple shear versus porous media flow) were the most important variables studied. The results show that the shear viscosity of HEC/CTAT solutions is higher than the viscosities of surfactant and polymer solutions at the same concentrations, but surface tension measurements indicate that no complex formation occurs between CTAT and HEC. On the other hand, a complex driven by hydrophobic interactions was detected by surface tension measurements between CTAT and HMHEC. In this case, the viscosity of the mixture increases significantly more (up to four orders of magnitude at high CTAT concentrations) in comparison with HEC/CTAT aqueous solutions. Increments in the molecular weight of the polymers increase the interaction with CTAT and the shear viscosity of the solution, but make phase separation more feasible. In porous media flow, the polymer/CTAT mixtures exhibited higher apparent viscosities than in simple shear flows. This result suggests that the extensional component of the flow field in porous media flows leads to a stronger interaction between the polymer and the wormlike micelles, probably as a consequence of change of conformation and growth of the micelles.     

The theory of non-linear molecular orientation and stress in polymer fluids

Non-linear stress, and orientation characteristics for polymer fluids (melts, solutions) composed of chain macromolecules of finite length have been derived. Freelyjointed chains with inverse Langevin statistics have been assumed, and their behaviour in potential hydrodynamic fields analyzed. Numerical calculations have been performed for uniaxial extensional flow in a wide range of flow rates (and stresses). In the range of small stresses, orientation is a linear function of stress. At higher stresses, orientation factor levels off, asymptotically approaching unity.Flow orientation characteristics significantly differ from those derived from affine deformation of polymer networks. This difference is a natural consequence of constraints imposed by network junctions on chain deformation.This work is dedicated to Professor Hanns-Georg Kilian on his 60th birthday in appreciation of his contribution to Polymer Physics.     

The Rheology of Linear and Long-chain Branched Polymer Melts

By generalising the Doi-Edwards tube model to the Molecular Stress Function theory, the non-linear rheology of polymer melts can be described quantitatively. The strain-hardening of linear polymer melts in extensional flows can be accounted for by a strain energy function, which reflects the increase of strain energy due to tube squeeze. In comparison to linear polymer melts, long-chain branched polymer melts show enhanced strain-hardening. This is due to the fact that while the backbone of the branched macromolecule is stretched by deformation, side chains are compressed. It is demonstrated that the experimentally observed slope of the elongational viscosity after inception of strain-hardening depends on the ratio β of total molar mass to backbone molar mass as predicted by the model. The steady-state (plateau) value of the elongational viscosity depends on the maximum relative stretch, , which can be supported by chain segments and which represents the maximum elastic energy storable in the polymeric system.     

EFFECT OF INTERNAL VISCOSITY OF POLYMERIC FLUIDS UNDER STRONG EXTENSIONAL FLOWS

The dumbbell model with internal viscosity for a dilute polymer solution is investigated based on a balance of viscous drag and restoring Brownian forces.An approximate method is used to obtain the solution of extensional stress in closed form in the case of steady flow.For different internal viscosities,this parametric study shows different asymptotic regimes of the extensional viscosity as a function of strain rate.This analysis may explain the attenuation of pressure drop in strong flows from a phenom...     

Sequential semi-interpenetrating polymer networks based on polyurethane and polystyrene

The formation of microheterogeneous sequential semi-interpenetrating polymer networks based on network polyurethanes with different molecular masses of chain segments between crosslinks and a linear polystyrene has been studied by DSC and small-angle X-ray scattering. It has been shown that variation in the molecular mass of polymer segments between polyurethane network junctions affects the formation of the linear component of semi-interpenetrating polymer networks. As a result, the material structure may change in a wide range from a nearly single-phase system to a two-phase one. SAXS measurements indicate that there is a cymbate dependence between the degree of segregation of components of sequential semi-interpenetrating polymer networks and their microheterogeneous structure on the internetwork space. Two hierarchical heterogeneity levels are found to exist in polymer networks, and the features of each of these levels are analyzed.     

Electrostatic fiber spinning from polymer melts. II. Examination of the flow field in an electrically driven jet

The flow field in an electrically driven jet has been examined and quantitatively analyzed. Using a model fluid, the nature of the streamlines and magnitude of the stream velocities were investigated with the aid of tracer particle photography. It was found that the velocity field is not purely extensional, but contains rotational components as well. Furthermore, the only portion of the jet completely free of any rotational component is the region about the symmetry axis. The extensional strain rate along the symmetry axis increases rapidly with the applied electric field intensity and can attain values in excess of 50 sec^?1. This suggests that it might be possible to draw continuous oriented fibers from polymer melts by this technique if the jet can be operated at sufficiently high electric field intensity.