Uniaxial elongational behavior of poly(vinyl chloride) physical gel

A poly(vinyl chloride) (PVC,  M_w = 102×10³)(\mbox{PVC,}\;{\rm M}_{\rm w} =102\times 10^3) di-octyl phthalate (DOP) gel with PVC content of 20 wt.% was prepared by a solvent evaporation method. The dynamic viscoelsticity and elongational viscosity of the PVC/DOP gel were measured at various temperatures. The gel exhibited a typical sol–gel transition behavior with elevating temperature. The critical gel temperature (T_gel) characterized with a power–law relationship between the storage and loss moduli, G^′ and G^″, and frequency ω, G￠=G^￠￠/tan  ( np/2 ) μ wⁿ{G}^\prime={G}^{\prime\prime}{\rm /tan}\;\left( {{n}\pi {\rm /2}} \right)\propto \omega ^{n}, was observed to be 152°C. The elongational viscosity of the gel was measured below the T_gel. The gel exhibited strong strain hardening. Elongational viscosity against strain plot was independent of strain rate. This finding is different from the elongational viscosity behavior of linear polymer solutions and melts. The stress–strain relations were expressed by the neo-Hookean model at high temperature (135°C) near the T_gel. However, the stress–strain curves were deviated from the neo-Hookean model at smaller strain with decreasing temperature. These results indicated that this physical gel behaves as the neo-Hookean model at low cross-linking point, and is deviated from the neo-Hookean model with increasing of the PVC crystallites worked as the cross-linking junctions.     

Rheology of SiO2/(acrylic polymer/epoxy) suspensions. I. Linear viscoelasticity

Linear viscoelastic properties of SiO₂/(AP/EP) suspension with various SiO₂ volume fractions (ϕ) in a blend of acrylic polymer (AP) and epoxy (EP) were investigated at various temperatures (T). The AP/EP contained 70 vol.% of EP. The SiO₂ particles were treated with epoxy silane coupling agent. The effects of the SiO₂ particles are more pronounced in the terminal zone: a transition from viscoelastic liquid (ϕ ≤ 30 vol.%) to viscoelastic solid (ϕ ≥ 40 vol.%) was observed which can be interpreted as a critical gelation occurring at a critical particle content and critical gel temperature. The SiO₂/(AP/EP) systems exhibited a critical gel behavior at ϕ ≅ 35 vol.% and T ≅ 100°C characterized with a power–law relationship between the storage and loss moduli (G ^′ and G ^″) and frequency (ω); G ^′ = G ^″/tan(nπ/2) ∝ ω ⁿ . The critical gel exponent (n) was estimated to be about 0.45. The gelation occurred with increasing T.     

Viscoelastic properties of dibenzylidene sorbitol (DBS) physical gels at high frequencies

The rheological behavior of Dibenzylidene D-Sorbitol (DBS) gels formed in ethylene glycol, glycerol, mineral oil, ethanol, and chlorobenzene was studied using oscillatory squeezing flow viscometry. The storage (G ^′) and loss (G ^″) moduli were measured as a function of gellant concentration (0.5–2 w/w) and type of solvent. As expected greater values of gel strength (G ^′) were observed for gels containing higher concentrations of DBS. In addition, both storage and loss moduli of 2% systems were mostly frequency independent over the studied range, whereas 0.5% gels did exhibit some degree of dependence. We also found that the solvent plays an important role in the properties of the gels. Among the parameters that affect the viscoelastic properties of DBS gels, the solvent polarity and its ability to form hydrogen bonding may have significant effects on the gel rheology.     

Rheological properties of poly(vinyl chloride)/plasticizer systems—relation between sol–gel transition and elongational viscosity

Poly(vinyl chloride) (PVC)/di-isononyl phthalate systems with PVC content of 45.5 (PVC8) and 70.4 wt% (PVC6) were prepared by a hot roller at 150 °C and press molded at 180 °C. The dynamic viscoelasticity and elongational viscosity of PVC8 and PVC6 were measured in the temperature range from 150 to 220 °C. We have found that the storage and loss shear moduli, G′ and G″, of PVC8 and PVC6 exhibited the power-law dependence on the angular frequency ω at 190 and 210 °C, respectively. Correspondingly, the tan δ values did not depend on ω. These temperatures indicate the critical gel temperature T _gel of each system. The critical relaxation exponent n obtained from these data was 0.75 irrespective of PVC content, which was in agreement with the n values reported previously for the low PVC concentration samples. These results suggest that the PVC gels of different plasticizer content have a similar fractal structure. Below T _gel, the gradual melting of the PVC crystallites takes place with elevating temperature, and above T _gel, a densely connected network throughout the whole system disappears. Correspondingly, the elongational viscosity behavior of PVC8 and PVC6 exhibited strong strain hardening below T _gel, although it did not show any strain hardening above T _gel. These changes in rheological behavior are attributed to the gradual melting of the PVC crystallites worked as the cross-linking domains in this physical gel, thereby inapplicability of the of time–temperature superposition for PVC/plasticizer systems.     

Viscoelastic behavior of polymerizing systems

Experimental data of the dynamic viscoelastic properties, storage modulus (G′), loss modulus (G′′), and phase shift (δ) as well as of the viscosity, η, are reported for the polymerization of a free radical polymerization system (methyl methacrylate) which exhibits the Trommsdorff effect. A rheometer-reactor assembly developed in our laboratory is used for this purpose. It is observed that in the early stages of reaction, data lie in the terminal zone. As the polymerization progresses, the Trommsdorff effect leads to a sharp increase in both the polymer concentration and the weight average molecular weight, and the viscoelastic properties then lie in the entanglement zone. A modulus crossover point (when G′ = G′′) is identified that could be used as an identification of the point where the Trommsdorff effect starts assuming significance. Received: 17 September 1998 Accepted: 9 December 1998     

Three views of viscoelasticity for Cox–Merz materials

A slight rearrangement of the classical Cox and Merz rule suggests that the shear stress value of steady shear flow, , and complex modulus value of small amplitude oscillatory shear, G^∗(ω) = (G^′2 + G^″2)^1/2, are equivalent in many respects. Small changes of material structure, which express themselves most sensitively in the steady shear stress, τ, show equally pronounced in linear viscoelastic data when plotting these with G^∗ as one of the variables. An example is given to demonstrate this phenomenon: viscosity data that cover about three decades in frequency get stretched out over about nine decades in G^∗ while maintaining steep gradients in a transition region. This suggests a more effective way of exploiting the Cox–Merz rule when it is valid and exploring reasons for lack of validity when it is not. The τ −G^∗ equivalence could also further the understanding of the steady shear normal stress function as proposed by Laun.     

Evolution of viscosities and morphology for the two-phase system polyethylene oxide/poly(dimethylsiloxane)

Shear viscosities and oscillatory viscosities were measured for the two-phase system polyethylene oxide/poly(dimethylsiloxane) at 70 °C as a function of composition. This blend exhibits the usual droplet/matrix structures in the vicinity of the pure components and a region of co-continuity within which two droplet/matrix structures coexist. A stepwise reduction in the shear rate, , leads to a rapid increase in viscosity followed by a much slower exponential decay; plots of the corresponding rate constants as a function of composition exhibit two discontinuities marking the boundaries of co-continuity; a similar dependence is obtained for the time independent final viscosities . Keeping the blend composition constant and determining as a function of yields a curve that passes a distinct maximum, where the viscosities are very close to that of the less viscous pure component on both ends of this dependence. The dynamic mechanical measurements of the blends yield at low frequencies storage moduli G′ that are orders of magnitude larger than that of the components because of the deformation of the interfaces. At high frequencies, the loss moduli G″ reflect the increasing alignment of the drops suspended in the matrix phases. The composition dependencies of G′ and of the complex viscosities can again be used to determine the limits of co-continuity.     

High-frequency viscoelasticity of crosslinked actin filament networks measured by diffusing wave spectroscopy

We study the short-time relaxation dynamics of crosslinked and uncrosslinked networks of semi-flexible polymers using diffusing wave spectroscopy (DWS). The networks consist of concentrated solutions of actin filaments, crosslinked with increasing amounts of α-actinin. Actin filaments (F-actin) are long semi-flexible polymers with a contour length 1–100μm and a persistence length of 5–15μm; α-actinin is a small 200kDa homodimer with two actin-binding sites. Using the large bandwidth of DWS, we measure the mean-square-displacement of 0.96μm diameter microspheres imbedded in the polymer network, from which we extract the frequency-dependent viscoelastic moduli via a generalized Langevin equation. DWS measurements yield, in a single measurement, viscoelastic moduli at frequencies up to 10⁵Hz, almost three decades higher in frequency than probed by conventional mechanical rheology. Our measurements show that the magnitude of the small-frequency plateau modulus of F-actin is greatly enhanced in the presence of α-actinin, and that the frequency dependence of the viscoelastic moduli is much stronger at intermediate frequencies. However, the frequency-dependence of loss and storage moduli become similar for both crosslinked and uncrosslinked networks at large frequencies, G′(ω)∝G′′(ω)∝ω^0.75±0.08. This high-frequency behavior is due to the small-amplitude, large-frequency lateral fluctuations of actin filaments between entanglements. Received: 20 January 1998 Accepted: 12 February 1998     

Stability and boundedness results for certain nonlinear vector differential equations of the fourth order

We consider the equation X ⁽⁴⁾ + Φ(X″)X‴ + F(X,X′)X″ + G(X′) + H(X) = P(t,X,X′,X″,X‴) in two cases: P ≡ 0 and P ≠ 0. In the case P ≡ 0, the asymptotic stability of the zero solution X = 0 of the equation is investigated; in the case P ≠ 0, the boundedness of all solutions of the equation is proved. Published in Neliniini Kolyvannya, Vol. 9, No. 4, pp. 548–563, October–December, 2006.     

Grafting of polyamide 6 on a styrene–acrylonitrile maleic anhydride terpolymer: melt rheology at the critical gel state

In this work, we studied the melt rheology of multigraft copolymers with a styrene–acrylonitrile maleic anhydride (SANMA) terpolymer backbone and randomly grafted polyamide 6 (PA 6) chains. The multi-grafted chains were formed by interfacial reactions between the maleic anhydride groups of SANMA and the amino end groups of PA 6 during melt blending. Because of the phase separation of SANMA and PA 6, the grafted SANMA backbones formed nearly circular domains which were embedded in the PA 6 melt with a diameter in the order of 20 to 40 nm. The linear viscoelastic behaviour of PA 6/SANMA blends at a sufficiently large SANMA concentration displayed the characteristics of the critical gel state, i.e. the power relations G′ ∝ G′′ ∝ ω ^0.5. In elongation, the PA 6/SANMA blend at the critical gel state showed a non-linear strain hardening behaviour already at a very small Hencky strain. In contrast to neat PA 6, the elasticity of the PA 6/SANMA blends was strongly pronounced, which was demonstrated by recovery experiments. Rheotens tests agreed with the linear viscoelastic shear oscillations and the measurements using the elongational rheometer RME. Increasing the SANMA concentration led to a larger melt strength and a reduced drawability. The occurrence of the critical gel state can be interpreted by the cooperative motion of molecules which develops between the grafted PA 6 chains of neighbouring micelle-like SANMA domains.     

Relaxation patterns of long,linear, flexible,monodisperse polymers: BSW spectrum revisited

Theoretical predictions for the dynamic moduli of long, linear, flexible, monodisperse polymers are summarized and compared with experimental observations. Surprisingly, the predicted 1/2 power scaling of the long-time modes of the relaxation spectrum is not found in the experiments. Instead, scaling with a power of about 1/4 extends all the way up to the longest relaxation times near τ/τ _max = 1. This is expressed in the empirical relaxation time spectrum of Baumgaertel-Schausberger-Winter, denoted as “BSW spectrum,” and justifies a closer look at the properties of the BSW spectrum. Working with the BSW spectrum, however, is made difficult by the fact that hypergeometric functions occur naturally in BSW-based rheological material functions. BSW provides no explicit solutions for the dynamic moduli, G ^′(ω), G ^″(ω), or the relaxation modulus G(t). To overcome this problem, close approximations of simple analytical form are shown for these moduli. With these approximations, analysis of linear viscoelastic data allows the direct determination of BSW parameters.     

Elasticity and dynamics of particle gels in non-Newtonian melts

We investigate the relation between the structure and the viscoelastic behavior of a model polymer nanocomposite system based on a mixture of titanium dioxide (TiO₂) nanoparticles and polypropylene. Above a critical volume fraction, Φ _c, the elasticity of the hybrids dramatically increases, and the frequency dependence of the elastic and viscous moduli reflects the superposition of the independent responses of the suspending polymer melt and of an elastic particle network. In addition, the elasticity of the hybrids shows critical behavior around Φ _c. We interpret these observations by hypothesizing the formation of a transient network, which forms due to crowding of particle clusters. Consistent with this interpretation, we find a long-time, Φ-dependent, structural relaxation, which emphasizes the transient character of the structure formed by the particle clusters. For times below this characteristic relaxation time, the elasticity of the network is Φ-independent and reminiscent of glassy behavior, with the elastic modulus, G^′, scaling with frequency, ω, as G^′∼ω ^0.3. We expect that our analysis will be useful for understanding the behavior of other complex fluids where the elasticity of the components could be superimposed.     

Gelation behavior of polysaccharide-based interpenetrating polymer network (IPN) hydrogels

We report the preparation and rheological characterization of interpenetrating polymer network (IPN) hydrogels made from alginate and hydrophobically modified ethyl hydroxyl ethyl cellulose (HMEHEC). To our knowledge, there have been no studies of the gelation behavior of IPNs. We found that the rheology of these systems can be easily tuned, with the elastic modulus of the IPN strongly dependent on the relative ratio of HMEHEC to alginate. The sol–gel transition of these systems was found to satisfy the Winter–Chambon criterion for gelation at various crosslinker densities. From the power law relationship of the dynamic moduli (G ^′ ~G ^″ ~ω ⁿ), the exponent n appears to be dependent on both the crosslinker density and relative amount of two polymers. The value of n was found to be ~0.5 for all samples for stoichiometric amounts of crosslinker. The effect of molecular weight of HMEHEC on the gel point and viscoelastic exponent has also been reported. Alginate seems to dominate the kinetics of the process but the effect of high molecular weight HMEHEC on the gel point, especially at lower proportion was also evident.     

On the dynamic response of viscoelastic fluids

Summary To define the dynamic shear behaviour of a viscoelastic fluid we require two functions — one elastic and one viscous. There are two simple alternatives based on the Voigt and Maxwell concepts which are mathematically interrelated. Current practice interprets the dynamic response of fluids as a function of angular frequency () in terms of the storage (G) and loss (G) moduli: the loss function is commonly converted to a viscosity = G/. As is well known the parameters andG are the elements of a Voigt model whereas it is near universal practice to interpret steady flow in terms of the Maxwell model. This paper shows how the interpretation of dynamic experiments on fluids in terms of the apparent Maxwell parameters is more simple, more sensitive, more consistent with steady flow behaviour, and physically more realistic.

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Zusammenfassung Zur Festlegung des dynamischen Scherverhaltens einer viskoelastischen Flüssigkeit benötigt man zwei Funktionen, eine für das elastische und eine für das viskose Verhalten. Dafür gibt es zwei einfache, mathematisch miteinander verknüpfte Alternativen, die entweder auf dem Voigtschen oder dem Maxwellschen Konzept gründen. Die übliche Praxis beschreibt das dynamische Verhalten der Flüssigkeiten als Funktion der Winkelgeschwindigkeit durch den SpeichermodulG und den VerlustmodulG bzw. die zugeordnete Viskosität = G/. Die Parameter undG sind bekanntlich die Elemente eines Voigt-Modells, wohingegen es nahezu allgemein üblich ist, das stationäre Fließen durch ein Maxwell-Modell zu beschreiben. Diese Arbeit zeigt nun, daß die Beschreibung dynamischer Versuche mit Hilfe von apparenten Maxwell-Parametern einfacher, empfindlicher, mit dem stationären Verhalten konsistenter und in physikalischer Hinsicht realistischer ist.

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Paper presented at British Society of Rheology conference. Rheometry: Methods of measurement and analysis of results, Shrivenham, April 8–11, 1975.

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With 13 figures and 2 tables     

Oscillatory measurements of silicone oils —Loss and storage modulus master curves

The work describes a way to obtain loss modulus and storage modulus master curves from oscillatory measurements of silicone oils.The loss modulus master curve represents the dependence of the viscous flow behavior on · ₀ ^* and the storage modulus master curve — the dependence of the elastic flow behavior on · ₀ ^* .The relation between the values of the loss modulus and storage modulus master curves (at a certain frequency) is a measurement of the viscoelastic behavior of a system. The G/G-ratio depends on · ₀ ^* which leads to a viscoelastic master curve. The viscoelastic master curve represents the relation between the elastic and viscous oscillatory flow behavior.     

Relations between steady flow and oscillatory shear measurements

Summary Results are given of a comparison between dynamic oscillatory and steady shear flow measurements with some polymer melts. Comparison of the steady shear flow viscosity,, with the absolute value of the dynamic viscosity, ¦¦, at equal values of the shear rate,q, and the circular frequency,, has shown the relation thatCox andHerz had found empirically to be substantially correct.Further, the coefficients of the normal stress differences obtained by streaming birefringence techniques have been compared with 2G () · ^{– 2} in the same range of shear rates as covered by the viscosity measurements (G is the real part of the dynamic shear modulus). Two polystyrenes with narrow molecular weight distribution showed the same shift factor along the orq axis for the normal stress coefficients with respect to 2G () · ^{– 2} and the steady shear flow viscosities with respect to the real part of the dynamic viscosity,. For two polyethylenes the results are not so conclusive owing to the smallness of the shift factor found. An empirical equation is proposed predicting the main normal stress difference from dynamic measurements only.

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Zusammenfassung Die Ergebnisse von Messungen unter erzwungenen Schwingungen und stationärer Scherströmung an einigen Polymerschmelzen werden miteinander verglichen. Der Vergleich der stationären Viskosität mit der absoluten dynamischen Viskosität ¦¦ bei gleichen Werten des Strömungsgradientenq und der Kreisfrequenz zeigt die Gültigkeit der empirischen Beziehung vonCox undHerz.Weiter wurden die Koeffizienten der Normalspannungsdifferenzen, welche durch Messung der Strömungsdoppelbrechung erhalten wurden, mit 2G() · ^–2 verglichen, und zwar wiederum bei gleichen Werten vonq und, wobeiG die Speicherkomponente des dynamischen Schubmoduls ist. Zwei Polystyrole mit enger Molekulargewichtsverteilung zeigen die gleiche Verschiebung entlang der-oderq-Achse für die Normalspannungskoeffizienten in bezug auf2G()· ^–2 und für die stationären Scherviskositäten in bezug auf den Realteil der dynamischen Viskosität. Für zwei Polyäthylene sind die Ergebnisse weniger signifikant, da die entsprechenden Verschiebungen zu klein waren. Eine empirische Beziehung zwischen den Hauptnormalspannungsdifferenzen und den dynamischen Meßwerten wird vorgeschlagen.

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Paper presented at the British Society of Rheology Conference, held at Shrivenham, from 9th–12th September, 1968.     

Viskoelastisches Verhalten von ABS-Polymeren in der Schmelze

Zusammenfassung Mit Hilfe eines Schwingungsviskosimeters mit konzentrischen Zylindern wurde der komplexe SchubmodulG +iG von ABS-Polymeren bei Frequenzen zwischen 10^–3 und 50 Hz und Temperaturen zwischen 130 und 250 °C gemessen. Bei hohen Frequenzen ergeben sich keine wesentlichen Unterschiede im Verlauf der Modulkurven, verglichen mit homogenen Schmelzen. Das viskoelastische Verhalten wird hier vor allem durch das Verschlaufungsnetzwerk der kohärenten Phase bestimmt. Bei tiefen Frequenzen verhalten sich ABS-Polymere in der Schmelze dagegen ähnlich wie vernetzte Kautschuke:G wird frequenzunabhängig, steigt proportional zu ·T an und nimmt wesentlich größere Werte an alsG. Es überwiegen also die elastischen Eigenschaften, während die Schmelzen homogener Polymerer bei tiefen Frequenzen vorwiegend viskos sind. Dieses gummielastische Verhalten ist um so ausgeprägter, je höher der Kautschukgehalt, der Pfropfungsgrad der Kautschukteilchen und, bei gleichem Kautschukgehalt, die Teilchenzahl ist.AusG und G läßt sich die komplexe Schwingungsviskosität ^* berechnen, deren Betrag ¦^*¦ bei vielen Kunststoffschmelzen mit der Viskositätsfunktion () bei stationären Scherströmungen übereinstimmt. Bei ABS-Polymeren wird ¦^*¦ bei tiefen Frequenzen nicht konstant, sondern steigt mit abnehmender Frequenz stark an. Es existiert also offensichtlich keine konstante Nullviskosität ₀ wie bei homogenen Schmelzen.Ein ähnliches viskoelastisches Verhalten wie ABS-Polymere, wenn auch schwächer ausgeprägt, zeigen Kunststoffe mit anorganischen Füllstoffen wie TiO₂.

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Summary The complex shear moduliG +iG of ABS-polymers were measured by means of a dynamic viscometer with concentric cylinders at frequencies between 10^–3 and 50 cps and temperatures between 130 and 250 °C. At high frequencies there are no remarkable differences in the shape of the modulus curves compared with homogeneous melts. The viscoelastic behaviour is here mainly determined by the entanglement network of the coherent phase.At low frequencies molten ABS-Polymers behave like crosslinked rubbers:G becomes independent of frequency, is proportional to ·T and has much greater values thanG. That means that the elastic properties are prevailing, whereas the melts of homogeneous polymers are mainly viscous at low frequencies. This rubberlike behaviour is the more marked, the higher the rubber contents, the degree of grafting of the rubber particles and, with equal rubber contents, the number of particles.FromG andG the complex dynamic viscosity ^* can be evaluated. For many polymer melts the absolute value ¦^*¦ corresponds to the steady-state viscosity (). For ABS-polymers ¦^*¦ does not become constant at low frequencies but rises to much higher values with decreasing frequency. Obviously there is no constant zero — shear viscosity as there is for homogeneous melts.A similar viscoelastic behaviour as shown by ABS-polymers, though less marked, is shown by plastics with anorganic fillers like TiO₂.

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Den Herren Dr.Haaf, Dr.Heinz und Dr.Stein danke ich für die Herstellung der Proben.     

Solidification behavior of the theta system 2-propanol/poly(n-butyl methacrylate)

Thermoreversible gelation of the system 2-propanol/poly (n-butyl methacrylate) — as detected by D'SC or dielectric experiments — does not manifest itself in a straightforward manner in the dynamic-mechanical properties. Its occurrence can, however, be seen in many ways: i) For constant composition of the system and a reference temperature lower than T _gel, the storage modulus G is larger than the loss modulus G in the glass transition zone of the master curve and both vary in an almost parallel manner with the angular frequency over almost two decades (whereas this feature is normally found for other gelling systems within the rubber plateau or the flow region). ii) The entanglement molecular weight obtained from G_max is markedly less max than the entanglement molecular weight in the melt divided by ₂, the volume fraction of the polymer. iii) The temperature influences change from WLF like to Arrhenius-like behavior as T is lowered in the case of highly concentrated polymer solutions; analogous considerations hold true as ₂ is increased at constant T. iv) For sufficiently low temperatures, the activation energy of flow exhibits a maximum in the concentration range where the gelation is — according to DSC experiments — most pronounced. Like with ordinary non-gelling systems it is possible to construct master curves. On the basis of Graessley's theory identical dependencies are obtained for the variation of the entanglement parts of the stationary viscosity with shear rate and for the dependence of the entanglement part of the complex viscosity on the frequency of oscillation. Zero shear viscosity and limiting value of the complex viscosity for vanishing as a function of ₂ match smoothly and exhibit two points of inflection.     

Microstructure and viscoelasticity in thermotropic copolyesters: the influence of monomer concentration

This research investigates the influence of monomer composition on the thermal transitions, mi crostructure, and viscoelastic properties of thermotro pic liquid crystalline polymers (LCPs) based on 1, 4-hydroxy-benzoic acid (B) and 2,6-hydroxy-naphthoic acid (N). Compositions B–N of 1:1, 1:3, 3:1, and 2:1 mol% were studied. The solid-to-nematic transition T _s→n was greatly influenced by the monomer composition, ranging from 230 to 280 °C. However, the decomposition temperature T _dec was independent of composition, all the materials degrading at T _dec = 509 °C. Polarized optical microscopy showed a threaded texture in the nematic phase. Fiber X-ray diffraction showed aperiodic meridional maxima for all LCPs, the number of maxima depended on composition. B–N 3:1 and 1:3 mol% favor the orthorhombic crystallographic phase whereas the 1:1 and 2:1 mol% crystallized in a pseudohexagonal phase. Dynamic time sweeps showed that the nematic phases are stable at the temperatures studied. Strain sweeps showed the existence of a linear viscoelastic (LVE) regime. The LVE properties ranged from predominantly viscous (G^′ < G^″) for the 1:1 mol% composition to predominantly elastic (G^′ > G^″) and with a well-defined rubber-like regime for the 1:3 mol% composition, resembling the rheology of flexible polymer melts. The persistence length q appears to be the parameter driving the rheological behavior.

Comparison of a new internal viscosity model with other constrained-connector theories of dilute polymer solution rheology

Complex viscosity ^* = -i predictions of the Dasbach-Manke-Williams (DMW) internal viscosity (IV) model for dilute polymer solutions, which employs a mathematically rigorous formulation of the IV forces, are examined in the limit of infinite IV over the full range of frequency number of submolecules N, and hydrodynamic interaction h ^*. Although the DMW model employs linear entropic spring forces, infinite IV makes the submolecules rigid by suppressing spring deformations, thereby emulating the dynamics of a freely jointed chain of rigid links. The DMW () and () predictions are in close agreement with results for true freely jointed chain models obtained by Hassager (1974) and Fixman and Kovac (1974 a, b) with far more complicated formalisms. The infinite-frequency dynamic viscosity predicted by the DMW infinite-IV model is also found to be in remarkable agreement with the calculations of Doi et al. (1975). In contrast to the other freely jointed chain models cited above, however, the DMW model yields a simple closed-form solution for complex viscosity expressed in terms of Rouse-Zimm relaxation times.