Zero-shear viscosity of dilute to moderately concentrated solutions of cellulose acetate phthalate

The zero-shear viscosities of dilute to moderately concentrated cellulose acetate phthalate solutions in DMF were measured at different temperatures and the viscosity data were analyzed in terms of Martin's and Fedor's relationships. The [η] values obtained due to the relationships of Martin and Fedor were found to be in very good agreement. The viscosity-concentration data were also generalized in terms of reduced variables. The temperature dependence of viscosities was expressed by the Frenkel-Eiring equation and the free energy of activation (ΔG_v), heat of activation (ΔH_v), and entropy of activation (ΔS_v) of the viscous flow of polymer solutions were calculated. It has been observed that the activation energy for viscous flow increases and the activation entropy decreases with concentration of polymer solutions.     

Measurement and prediction of LDPE/CO2 solution viscosity

When CO₂ is dissolved into a polymer, the viscosity of the polymer is drastically reduced. In this paper, the melt viscosities of low‐density polyethylene (LDPE)/supercritical CO₂ solutions were measured with a capillary rheometer equipped at a foaming extruder, where CO₂ was injected into a middle of its barrel and dissolved into the molten LDPE. The viscosity measurements were performed by varying the content of CO₂ in the range of 0 to 5.0 wt% and temperature in the range of 150°C to 175°C, while monitoring the dissolved CO₂ concentration on‐line by Near Infrared spectroscopy. Pressures in the capillary tube were maintained higher than an equilibrium saturation pressure so as to prevent foaming in the tube and to realize single‐phase polymer/CO₂ solutions. By measuring the pressure drop and flow rate of polymer running through the tube, the melt viscosities were calculated. The experimental results indicated that the viscosity of LDPE/CO₂ solution was reduced to 30% of the neat polymer by dissolving CO₂ up to 5.0 wt% at temperature 150°C. A mathematical model was proposed to predict viscosity reduction owing to CO₂ dissolution. The model was developed by combining the Cross‐Carreau model with Doolittle's equation in terms of the free volume concept. With the Sanchez‐Lacombe equation of state and the solubility data measured by a magnetic suspension balance, the free volume fractions of LDPE/CO₂ solutions were calculated to accommodate the effects of temperature, pressure and CO₂ content. The developed model can successfully predict the viscosity of LDPE/CO₂ solutions from PVT data of the neat polymer and CO₂ solubility data.     

Viscosity of polystyrene solutions expanded with carbon dioxide

The viscosity of solutions of polystyrene (PS) in decahydronaphthalene (DHN) was measured in the presence of carbon dioxide (CO₂) with a moving‐piston viscometer. The effects of the CO₂ pressure (0–21 MPa), polymer concentration (1–15 wt %), temperature (306–423 K), and polymer molecular weight (126 and 412 kDa) on the viscosity were investigated. In the absence of CO₂, the increase in the viscosity with increasing polymer concentration was approximately exponential in concentration and was well described by the Martin equation. All the data fell on a single line when the relative viscosity was plotted against cM^0.50 (where c is the concentration of the polymer in solution and M is the molecular weight of the polymer). The viscosity of the polymer solution decreased with increasing CO₂ pressure under otherwise constant conditions. For a given CO₂ pressure, the viscosity reduction was greatest when the relative viscosity was high in the absence of CO₂, that is, for high‐molecular‐weight polymer, high polymer concentrations, and low temperatures. Reductions in the relative viscosity of almost 2 orders of magnitude were observed in some cases. The viscosity of solutions of PS in DHN also was measured in the presence of sulfur hexafluoride (SF₆). At a given pressure, SF₆ was about as effective as CO₂ in reducing the solution viscosity. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 99: 540–549, 2006     

Temperature dependence of unperturbed dimension and interaction parameters of polyester resin in solvents

The flow behaviour of a polyester in various solvents was studied at temperatures ranging from 10 to 80°C. The practical data obtained from the temperature dependence of limiting viscosity number [η] were used to calculate unperturbed dimensions and interaction parameters of the polyester resin in poor, moderate and good solvents. The data provided information regarding conformational transitions in the polymer chains in terms of exothermic or endothermic local ordering of solvents on resin segments and their fixation on polymer coils. The temperature dependence of unperturbed dimensions K_e, Flory–Huggins interaction parameter χ₁₂, the second virial coefficient A₂, entropy parameter U₁, enthalpy parameter K₁, and viscosity expansion factor α_n, has been used to estimate the solvent quality for the resin.     

Rheological behaviour of some amphiphilic β‐cyclodextrin‐based azo aromatic polyurethanes in N,N‐dimethylformamide solutions

Amphiphilic β‐cyclodextrin‐based azo aromatic poly(ether urethane)s with different soft segment lengths have been synthesized and characterized. Hydrogen bonding in these systems was demonstrated by Fourier transform infrared spectroscopy analysis (carbonyl stretching region). A rheological study was performed on solutions of the synthesized poly(ether urethane)s in N,N‐dimethylformamide at various concentrations and temperatures by employing parallel plate geometry, and a comparative evaluation of the influence of the structural components on the viscometric responses was performed. The rheological behaviour was found to be strongly dependent on the chemical composition of the synthesized polyurethanes which promotes self‐assembly and structuring in solution. Hard segment content and polymer concentration influence pseudoplastic shear‐thinning flow behaviour. The rheology can be interpreted in terms of hydrophobic associations and chain entanglements and a hydrogen bonding network occurring in solution. The start‐up flow of the polymer solutions is determined by the lifetime of the associative polymer segments. Shear stress plateaux indicative of ‘shear banding’ behaviour explained by the structuring of the polymer solutions at increased temperatures were obtained. The studied amphiphilic polyurethane solutions are thermoresponsive systems exhibiting viscosity increase with increasing temperature contrary to the usual Arrhenius thermo‐thinning behaviour. At constant shear rate viscosity was found to increase with increasing temperature due to thermo‐association. © 2014 Society of Chemical Industry     

Viscoelastic properties of polyamic acid solutions—precursors of polyimides

The rheology of polyamic acid (PAA) solutions, precursors of polyimides used in microelectronic device applications, has been investigated by dynamic (oscillatory) shear flow measurements. Frequency dependent storage and loss moduli and dynamic viscosity were measured in the frequency range 10^?1 to 10³ rad/s at 23°C. The storage modulus G′ (ω) and loss modulus G″ (ω) exhibited quadratic and linear dependence in frequency at low frequencies respectively, the viscoelastic fluid behavior commonly predicted for polymer solutions from many molecular theories. At high frequencies both dynamic moduli become proportional to ω^2/3. The results show that PAA solutions are very high loss viscoelastic fluids, judging from the loss tangent values which far exceed unity. It is suggested that dynamic viscoelastic properties could be used to monitor the degree of imidization since there is a gradual change from viscoelastic fluids to soft viscoelastic solids to hard viscoelastic solids as PAA is converted to polyimides. Onset of non-Newtonian flow as shown on the frequency dependent dynamic viscosity was in the range 30 to 200 rad/s. The viscoelastic constants, zero-shear rate viscosity η_o and steady-state compliance J_e⁰, where also determined from the dynamic data and compared to previous steady shear flow results.     

Rheology of polymeric solutions I. Zero shear conditions

Based on kinetic considerations, the following equation, connecting the zero‐shear viscosity of polymeric solutions with temperature and the molecular weight and concentration of the polymer was derived: RTln η_R = KBφMⁿ /(1 + BφMⁿ), where η_R is relative viscosity (i.e., the ratio of the solution viscosity to the solvent viscosity); K represents a change in enthalpy of viscous flow from a pure solvent to a pure polymer at the same temperature or from a polymer of low molecular weight (M) to one of higher molecular weight, and has the dimensions of energy (e.g., J/mol) because the ratio BφMⁿ/(1 + BφMⁿ) is dimensionless; φ is the volume or molar fraction of a polymer in solution (concentration units can be used in dilute solutions); B is a constant related to the stiffness of the chains of the polymer in a given solvent; and at BφMⁿ >> 1, ln η_R = K/RT. The equation describes published data on the zero‐shear viscosity of four polar and nonpolar polymers in nine solvents with R² > 0.98. This approach allows the use of solutions of moderate concentrations for the characterization of polymers and opens a way for a single‐point degree of polymerization (DP) determination of polymers at moderate concentrations if constants K, B, and n of the equation are known. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 85: 2064–2073, 2002     

A novel determination technique of polymer viscosity-average molecular weights with flow piezoelectric quartz crystal viscosity sensing

A new method for the determination of polymer viscosity-average molecular weights was developed with flow piezoelectric quartz crystal (PQC) viscosity sensing. The experimental setup with a 9 MHz AT-cut quartz crystal and a flow detection cell was constructed and shown to be able to give highly reproducible data under the temperature of 25 ± 0.1°C and the fluid flow rate of 1.3–1.6 mL/min. A response model for PQC in contact with dilute polymer solutions (concentration <0.01 g/mL) was proposed in which the frequency change from the pure solvent, Δf_s, follows Δf_s = −k₆η_l^1/2 + k₇, where η_l is the absolute viscosity of dilute polymer solution and k₆ and k₇ are the proportionality constants. This model was examined with poly(ethylene glycol) samples (PEG-20000 and PEG-10000) under the aforementioned experimental conditions using water as solvent. The result was Δf_s = −1587η_l^1/2 + 1443. Based on this model, the method for the determination of polymer viscosity-average molecular weights, M_η, by flow PQC viscosity sensing was described and examined with an unknown poly(vinyl alcohol) (PVAL) sample. The new method proved to be an attractive and promising alternative for the determination of polymer molecular weights based on the good agreement between the molecular weight determined by the new method (M_η = 58600) for the unknown PVAL sample with that determined by the conventional capillary viscosity method. The new method has some advantages over the conventional viscosity method; for examples, operation is simpler and more rapid; the instruments required are cheaper and portable; the needed sample quantity is smaller; and the experimental setup constructed can be used in continuous measurement. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 63–69, 2001     

PVC/PBA random copolymers obtained by SET–DTLRP: Pressure effect on glass transition,rheology, and processing

A study of the effect of pressure on the glass transition and viscosity of poly(vinyl chloride) (PVC)–poly(butyl acrylate) random copolymers prepared by Single Electron Transfer–Degenerative Chain Transfer Living Radical Polymerization and able to act as self‐plasticized PVCs, is presented. The research has a dual purpose, as it focuses on polymer physics, as well as on applied polymer processing. Results of dynamic mechanical thermal analysis, pressure–volume–temperature (PVT), and extrusion capillary tests were combined, to analyze the additivity of the free volume and the effect of frequency and pressure on the glass transition of the copolymers, T_g. Free volume additivity, which is on the basis of self‐plasticization, was revealed by T_g and activation energy of flow, E_a, results. dT_g/dP results were linked to the number of segments involved in the glass transition temperature. Using an ad hoc model, which involves parameters obtained by PVT and the activation energy of flow, the pressure‐viscosity coefficient was determined. This allowed estimating the viscosity as a function of the shear rate, the temperature and the pressure, offering suitable data to be employed in virtual injection molding. J. VINYL ADDIT. TECHNOL., 25:76–84, 2019. © 2018 Society of Plastics Engineers     

Temperature dependence of viscosity of polyurethane polyol solutions: Application of rheological models

Polyurethane polyols were synthesized by reacting the diols with polyisocyanates. Viscosity of their 50% (w/w) solutions in various solvents has been determined at different temperatures by using Haake Roto Visco RV12 Rotational Viscometer. The temperature dependence of viscosity data was solved by Levenberg Marquardt's algorithm by using nonlinear regression models based on WLF, Vogel, and Arrhenius equations. The T_g values obtained from WLF and Vogel equation are comparable to each other and these equations can be satisfactorily used for the analysis of temperature dependence of viscosity data of oligomer solutions. The residuals are random and the absolute average percentage error in analyzing the viscosity data by these equations is minimum. The values of constants in WLF equation are found to be system dependent and adjustable parameters. The predicted In η values obtained from WLF and Vogel equations fit well with the plots of experimental In η values as a function of temperature. © 1996 John Wiley & Sons, Inc.     

Physical and Mechanical Behavior of Polymer Glasses. VI. the Role of Free Volume

Abstract

For various polymer glasses, the temperature-induced recovery of residual deformation was studied. The ratio between the low-temperature and high-temperature recovery components is controlled by the difference between deformation temperature and glass transition temperature T _g of polymer samples independently of their chemical structure. This ratio correlates with polymer macroscopic mechanical characteristics such as elastic modulus and yield stress. Experimental results were treated in terms of the dynamics of segmental mobility within different structural sublevels with different packing densities. To correlate this mechanical response with the structural state of glassy polymers, positron annihilation lifetime spectroscopy (PALS) was used. For different polymer glasses, the microscopic segmental mobility and resultant macroscopic mechanical properties were shown to be controlled only by the development of the adequate free volume content which depends on the difference between testing temperature and T _g . These results allowed us to propose the general correlation between microstructure, microscopic molecular mobility, and Macroscopic mechanical behavior of polymer glasses.     

High‐pressure viscosity of polystyrene solutions in toluene + carbon dioxide binary mixtures

High‐pressure viscosity of polystyrene (M_w = 50,000, M_w/M_n ≤ 1.06) solutions in toluene and in mixtures of toluene + carbon dioxide was measured using a falling cylinder‐type viscometer at 320, 340, and 360 K, and up to 35 MPa. Solutions with polystyrene concentrations of 3, 5, and 7 wt % were investigated. Carbon dioxide levels in the range from 0 to 14.7 wt % were evaluated. Viscosity was observed to vary linearly with pressure at the temperatures and polymer concentrations investigated. Viscosity of the polymer solutions decreased as the concentration of carbon dioxide in the mixture was increased. The largest viscosity reduction was observed at the lowest temperature and at the highest concentration of polymer. The viscosity of the solutions was correlated with the solution density for different compositions. It was found that solutions of the same density have different viscosities, depending upon the carbon dioxide concentration in the mixture. The solutions with the higher carbon dioxide content display the lower viscosities at a given density. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 75: 306–315, 2000     

Nucleophilic Displacement Polymerlzation of N,N'-BIS(p-Chlorobenzylidine)-4, 4'-Diaminodiphenyl Ether with Sodium Sulfide

A novel poly(Schiff-base sulfide) polymer was synthesized by nucle-ophilic displacement polymerization of N,N'-bis(p-chlorobenzylidine)-4, 4'-diaminodiphenyl ether with sodium sulfide in anhydrous condition. The resulting polymer was soluble in some aprotic solvents having inherent viscosity of 0.18 dL/g in dimethylacetamide at 30°C. The monomer and the polymer were characterized by elemental analysis, infrared, and ¹H NMR (nuclear magnetic resonance) spectroscopy. The thermal characteristics of the polymer were also studied by thermo-gravimetric analysis and differential scanning calorimetry. The temperature of 10% weight loss, glass transition temperature (T _g). and crystalline melting point (T _m) of the polymer were found to be 420, 91.89, and 38575°C respectively.     

Plasticating single-screw extrusion of amorphous polymers: Development of a mathematical model and comparison with experiment

A mathematical model was developed for plasticating single-screw extrusion of amorphous polymers. We considered a standard metering screw design. By introducing a ‘critical flow temperature’ (T_cf), below which an amorphous polymer may be regarded as a ‘rubber-like’ solid, we modified the Lee-Han melting model, which had been developed earlier for the extrusion of crystalline polymers, to model the flow of an amorphous polymer in the screw channel. T_cf is de facto a temperature equivalent to the melting point of a crystalline polymer. The introduction of T_cf was necessary for defining the interface between the solid bed and the melt pool, and between the solid bed and thin melt films surrounding the solid bed. We found from numerical simulations that (1) when the T_cf was assumed to be close to its glass transition temperature (T_g), the viscosity of the polymer became so high that no numerical solutions of the system of equations could be obtained, and (2) when the value of T_cf was assumed to be much higher than T_g, the extrusion pressure did not develop inside the screw channel. Thus, an optimum modeling value of T_cf appears to exist, enabling us to predict pressure profiles along the extruder axis. We found that for both polystyrene and polycarbonate, T_cf lies about 55°C above their respective T_gs. In carrying out the numerical simulation we employed (1) the WLF equation to describe the temperature dependence of the shear modulus of the bulk solid bed at temperatures between T_g and T_cf, (2) the WLF equation to describe the temperature dependence of the viscosity of molten polymer at temperatures between T_cf and T_g + 100°C, (3) the Arrhenius relationship to describe the temperature dependence of the viscosity of molten polymer at temperatures above T_g + 100°C, and (4) the truncated power-law model to describe the shear-rate dependence of the viscosity of molten polymer. We have shown that the T_g of an amorphous polymer cannot be regarded as being equal to the T_m of a crystalline polymer, because the viscosities of an amorphous polymer at or near its T_g are too large to flow like a crystalline polymer above its T_m. Also conducted was an experimental study for polystyrene and polycarbonate, using both a standard metering screw and a barrier screw design having a length-to-diameter ratio of 24. For the study, nine pressure transducers were mounted on the barrel along the extruder axis, and the pressure signal patterns and axial pressure profiles were measured at various screw speeds, throughputs, and head pressures. In addition to significantly higher rates, we found that the barrier screw design gives rise to much more stable pressure signals, thus minimizing surging, than the metering screw design. The experimentally measured axial pressure profiles were compared with prediction.     

Water-soluble copolymers. VI. Dilute solution viscosity studies of random copolymers of acrylamide with sulfonated comonomers

Dilute solution viscosity of a series of random copolymers of acrylamide (AM) with sodium-2-acrylamido-2-methylpropane sulfonate (NaAMPS) and with sodium-2-sulfoethylmethacrylate (NaSEM) has been studied using a four-bulb shear dilution capillary viscometer. The hydrodynamic volume of the copolymers in aqueous media was determined as a function of salt concentration, temperature, shear rate, and time. A linear relationship was observed between the intrinsic viscosity [η]₀ and the reciprocal of the square root of ionic strength in sodium chloride solutions, with salt concentrations varying from 0.043M to 0.257M. Negative temperature coefficients for [η]₀ indicate a decrease in the hydrodynamic volume of the ionic polymer molecules with increasing temperature. The relative zero-shear-intrinsic-viscosity change in distilled water to 0.257M sodium chloride aqueous media is used to elucidate viscosity–structure relationships. A maximum value is reached for this parameter at a composition of about 30 mol % of ionic comonomers for AM–NaAMPS and AM–NaSEM copolymer series.     

Viscosity of polypropylene oxide solutions over the entire concentration range

An empirical equation is presented which describes polymer solution viscosity, η, over the entire concentration range from a knowledge of intrinsic viscosity, [η], Huggins constant, k′, and bulk flow viscosity of polymer, η₀. The equation is: \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{\eta _{sp}}}{{C[\eta]}} = \exp \left\{{\frac{{{\rm k'[}\eta {\rm]C}}}{{1 - bC}}} \right\} $\end{document} where solution viscosity, η, is contained in η_sp. No arbitrary parameters are invoked since b can be evaluated at bulk polymer (C = polymer density) where everything else is known. The equation accurately portrays the viscosity of polypropylene oxide (PPG 2025) from infinite dilution to bulk polymer in a very good solvent (benzene) and in a somewhat poorer (～ θ) solvent (methylcyclohexane). The hydrodynamic consequences of the thermodynamic interactions between polymer and solvent are reflected in the constants. This equation should be applicable to other polymer/solvent systems, and thus be immediately useful to those working with concentrated polymer solutions.     

Melt Flow Properties During Capillary Extrusion of Linear Low-Density Polyethylene

Abstract

The melt flow properties of a linear low-density polyethylene (LLDPE) were measured by means of a capillary rheometer under the experimental conditions of temperatures from 220° to 260°C and apparent shear rates varying from 12 to 120 s^?1. The end pressure drop (ΔP _end) was determined by employing the Bagley's plotting method. The results showed that ΔP _end increased nonlinearly with increasing shear stress. The end pressure fluctuation phenomenon was observed at lower shear stress level, and several plateau regions were generated in the end pressure drop-shear stress curves, suggesting onset of the wall-slip phenomenon during die extrusion of the resin melt. The critical shear stress with onset end pressure fluctuation phenomenon increased with a rise of temperature. Furthermore, the melt shear flow did not strictly obey the power law. The melt shear viscosity decreased nonlinearly with increasing shear stress and with a rise of temperature, whereas the dependence of the melt shear viscosity on the test temperature accorded with a formula similar to the Arrhenius expression.     

Evidences of solvent‐induced miscibility in polychloroprene‐co‐ethylene‐propene diene terpolymer blends

Solvent dependent changes in the compatibility behavior of Polychloroprene/Ethylene–propylene–diene terpolymer blends (CR/EPDM) have been investigated using dilute solution viscometry and solvent permeability analysis. To predict the compatibility of rubber blends of different compositions in solvents of different cohesive energy densities, Huggins interaction parameter (ΔB), hydrodynamic interaction (Δη) and Sun's parameter (α) were evaluated from the analysis of the specific and reduced viscosity data of two and three‐component polymer solutions. Miscibility criteria were not satisfied for CR/EPDM blends over the entire composition range in toluene, xylene, and carbon tetrachloride (CCl₄), however, a narrow miscibility domain was observed in chloroform (CHCl₃) for CR/EPDM/CHCl₃ system. These results were further corroborated with the analysis of heat of mixing (ΔH_m) and polymer–polymer interaction parameter (χ₁₂), for all rubber blend compositions. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Polymeric and non-crosslinked acid self-thickening agent based on hydrophobically associating water-soluble polymer during the acid rock reaction

Different from traditional crosslinked polymer diverting agents, a polymeric and non-crosslinked acid self-thickening agent (ZPAM) based on hydrophobically associating water-soluble polymer of acrylamide (AM), [2-(methacryloyloxy)ethyl]trimethylammonium chloride (DMC) and N,N′-dimethyl octadecyl allyl ammonium chloride (DOAC) was synthesized. The apparent viscosity variation of ZPAM acid solutions in acid rock reaction and rheological properties of ZPAM spent acid solutions were studied. Results showed that ZPAM acid solutions demonstrated good uninterruptedly thickening ability from low apparent viscosity to high apparent viscosity during the acid rock reaction. Meanwhile, ZPAM spent acid solutions showed good shear resistance, viscoelasticity and high temperature resistance. The thickening mechanism of ZPAM acid solutions during the acid rock reaction was explained by apparent viscosity change, rheological properties of simulative ZPAM acid solutions, and ZPAM aqueous solutions with different concentrations of CaCl₂. The results showed increasing calcium chloride concentration enhanced the hydrophobic association strength of the thickener solution, resulting in increasing solution viscosity, in other words, the self-thickening agent showed excellent salt resistance and acid resistance. In addition, the change of association strength of ZPAM acid solutions during the acid rock reaction was further confirmed via environmental scanning electron micrographs and UV spectrum. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47907.     

A generalized correlation for the viscosity of dextrans in aqueous solutions as a function of temperature,concentration, and molecular weight at low shear rates

An expression relating the viscosity of dextran solutions to polymer concentration (c), molecular weight (M), and temperature (T) has been derived from experimental data in the following ranges: 5 < c < 25% (wt/wt), 298.2 < T < 363.2 K, and 71,500 < M < 531,000 g/mol. The experimental work was based on capillary viscosimeters. Thermodynamic data (entropy and energy of activation for the viscous flow of a Newtonian fluid) are also presented as a function of polymer concentration for the three molecular weights studied. This thermodynamic analysis suggests that dextrans in aqueous solutions behave as flexible polymers. Application of our expression to existing viscosity data for ethylene/vinylacetate copolymers in paraffin has resulted in improved goodness of fit with respect to established correlations.