Viscosity Of Dilute Polymer Solutions Research Articles

Drop breakup dynamics of dilute polymer solutions: Effect of molecular weight, concentration, and viscosity

The large extensional viscosity of dilute polymer solutions has been shown to dramatically delay the breakup of jets into drops. For low shear viscosity solutions, the jet breakup is initially governed by a balance of inertial and capillary stresses before transitioning to a balance of viscoelastic and capillary stresses at later times. This transition occurs at a critical time when the radius decay dynamics shift from a 2/3 power law to an exponential decay as the increasing deformation rate imposed on the fluid filament results in large molecular deformations and rapid crossover into the elasto-capillary regime. By experimental fits of the elasto-capillary thinning diameter data, a relaxation time of less than 100 μs has been successfully measured. In this paper, we show that, with a better understanding of the transition from the inertia-capillary to the elasto-capillary breakup regime, relaxation times close to 10 μs can be measured with the relaxation time resolution limited only by the frame rate and spatial resolution of the high speed camera. In this paper, the dynamics of drop formation and pinch-off are presented using dripping onto substrate capillary breakup extensional rheometry (CaBER-DoS) for a series of dilute solutions of polyethylene oxide (PEO) in water and in a viscosified water and glycerin mixture. Four different molecular weights between 100 k and 1 M g/mol were studied with varying solution viscosities between 1 and 22 mPa s and at concentrations between 0.004 and 0.5 times the overlap concentration, c*. The dependence of the relaxation time and extensional viscosity on these varying parameters was studied and compared to the predictions of dilute solution theory while simultaneously searching for the lower limit in solution elasticity that can be detected. For PEO in water, this limit was found to be a fluid with a relaxation time of roughly 20 μs. These results confirm that CaBER-DoS can be a powerful technique characterizing the rheology of a notoriously difficult material to quantify, namely, low viscosity inkjet printer inks.

Intrinsic viscosities of polyelectrolytes in the absence and in the presence of extra salt: Consequences of the stepwise conversion of dextran into a polycation.

Viscosities of dilute polymer solutions were measured in capillary viscometers for samples varying in their fraction f of charged units from 0.00 to 0.90. The dependence of the logarithm of the relative viscosity on polymer concentration c is in all cases reproduced quantitatively by three characteristic parameters: [η], the intrinsic viscosity; B, a viscometric interaction parameter (related to the Huggins constant); [η], a parameter required only for polyelectrolytes at low concentrations of extra salt. In pure water [η] increases more than 80 times as the fraction f rises from zero to 0.90 and [η] starts from zero and goes up to ≈71mL/g. Upon the addition of NaCl [η] decreases by at least one order of magnitude (depending on the value of f). The observed dependences of log [η] on logcsalt can be modeled quantitatively by Boltzmann sigmoids.

Thermodynamics and viscosities of dilute polymer solutions in binary solvents

Experiments aimed at comparison of calculated and experimental intrinsic viscosities of PS and PMMA in some binary solvents used as eluents in chromatography are performed. The intrinsic viscosities are determined in mixed solvents of different thermodynamic qualities, including a θ solvent, in a wide composition range. The analysis of the thermodynamic and rheological theoretical equations for ternary systems allowed the interpretation of anomalies observed on the experimental curves of intrinsic viscosity versus solvent composition.

Effect of a controlled pre-deformation history on extensional viscosity of dilute polymer solutions

We use a modified filament stretching rheometer to quantify the influence of a known controlled pre-shear history on the transient extensional viscosity of a dilute polymer solution. Two different types of pre-deformation are explored; both influence the subsequent stretching significantly, albeit in opposite ways. Small-amplitude oscillatory straining parallel to the direction of stretching enhances strain hardening and accelerates the tensile stress growth toward the steady-state value. Conversely, steady torsional shearing orthogonal to the direction of stretching retards strain hardening and results in a delayed approach to steady-state elongational flow. In both cases, the final steady-state extensional viscosity is the same as that observed with no pre-shearing. Calculations using a finitely extensible nonlinear elastic Peterlin dumbbell model qualitatively capture the trends observed in experiments, enabling interpretation of these observations in terms of the degree of polymer chain stretching imposed by the flow before extensional stretching.

Non-Newtonian Viscosity of Dilute Polymer Solutions

The non-Newtonian behavior of dilute polymer solutions is investigated by computer simulation of a bead-and-spring model, using the Brownian dynamics technique to evaluate the shear rate dependence of the intrinsic viscosity. This behavior is a consequence of the combined effects of hydrodynamic interaction, excluded volume, and finite extensibility. The simulations allow the study of the influence of each effect separately. When all the effects are considered, the simulation results can be compared to experimental data of solution viscosities, which are available just in the region of moderately small shear rates. Data from molecular architecture and other solution properties are obtained to parametrize the bead-and-spring model, with emphasis in the description of the chain extensibility. Comparison of simulation and experimental results is presented for both highly flexible vinyl polymers and locally stiff cellulose chains.

How to obtain the elongational viscosity of dilute polymer solutions?

Measurement of the resistance to a stretching motion, the so-called elongational viscosity η e, has proven to be difficult for dilute polymer solutions, although it is important for a large number of applications. We attempt to deduce η e of dilute solutions of flexible polymers in two different ways. First, η e can be inferred from measurements of the shear viscosity η and the first normal stress difference N 1, invoking an appropriate constitutive equation. Second, it is measured in the opposing jet elongational viscometer. Although the results of the latter method have been much debated they agree reasonably well with those from the first method. The combination of the two methods thus allows to obtain the correct order of magnitude of η e.

Shear Viscosity of Dilute Polymer Solutions Compared and Contrasted with Mechanical Properties of Nylon Plus Plasticizer

Both the shear viscosity η(c) of dilute polymer solutions and Young's modulus Y(c) of nylon plus plasticizer with concentration c are assumed to be expressible as a power series in concentration. Scaling arguments are then presented which reveal an intimate relation between the coefficients of O(c) and O(c2) terms in both η(c) and Y(c) The coefficient of the O(2) term is predicted always to be positive, while that of the O(c) term can in principle have either sign. Comparison with experiment is made for η(C) and Y(c) Some further experiments are proposed for both Y(c) and η(c)

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

AbstractA 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, Δfs, follows Δfs = −k6ηl1/2 + k7, where ηl 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 Δfs = −1587ηl1/2 + 1443. Based on this model, the method for the determination of polymer viscosity‐average molecular weights, Mη, 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 (Mη = 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

Viscometric properties of viscosity index improvers in lubricant base oil over a wide temperature range. Part I: Group II base oil

AbstractCapillary viscometry has been employed to measure the viscosities of dilute polymer solutions over the temperature range ‐10 to 150 °C. A Group II base oil containing 95% saturates was used as solvent for an olefin copolymer (OCP), a hydrogenated diene copolymer (HDP), and a polymethacrylate (PMA). These three polymers represent the three major families of viscosity index (VI) improvers used nowadays in lubricant formulations. Intrinsic viscosities and Huggins' constants were also determined. The thickening effects of the olefin copolymer and the hydrogenated diene copolymer were found to be higher at low temperatures (e.g., 40 °C) than at higher ones (e.g., 100 °C), which phenomenon was attributed to stronger intermolecular hydrodynamic interactions at low temperatures, as indicated by the Huggins constants. For the hydrogenated diene copolymer and the polymethacrylate polymer, the viscosity increased abruptly when the temperature went below 10 °C. This unusual observation was attributed to the crystallisation of a small fraction of the base oil. Based on the intrinsic viscosity data, it was concluded that at temperatures between 10 and 150 °C, the polymer coil dimension remains a constant for the olefin copolymer and the hydrogenated diene copolymer VI improvers, but increases with increasing temperature for the polymethacrylate VI improver.

Synthesis and antimicrobial activity of polymeric guanidine and biguanidine salts

Polyhexamethylene guanidine hydrochloride and polyhexamethylene biguanidine hydrochloride were polycondensated in the melt of monomers. The intrinsic viscosity and M ̄ n were determined by the viscosity of dilute polymer solution and VPO, respectively. Polyhexamethylene guanidine stearate and polyhexamethylene biguanidine stearate were synthesized using the precipitation reaction for the first time. NMR, FTIR, XPS and element analysis were used to analyze the chemical structure and element composition. The structure of the resultant polymers is coincident with the theoretic structure. The minimal inhibition concentration (MIC) was measured to characterize the antimicrobial activity of the products. The MIC is not larger than 200 μg ml −1. The polymeric guanidine and biguanidine are effective in controlling bacteria and fungi. The TG test shows that the resultant polymers are stable to heat.

Effect of adsorption on the viscosity of dilute polymer solution

Measurements of the dilute solution viscosities of polyethylene glycol and polyvinyl alcohol in water were carried out. The reduced viscosities of both polymer solutions show an upward turning of curvature at the extremely dilute concentration region and this is similar to the phenomena observed for many polymer solutions in the early 1950s. Upon the changes of the flow time of pure water and the wall surface wettability of the viscometer after measuring solution viscosity, a judgement was formed that the observed viscosity abnormality at the extremely dilute concentration region is solely due to the effect of adsorption of polymer chains on the viscometer wall surface. A theory of the adsorption effect based on the Langmuir isotherms was proposed and a mathematical analysis for data treatment was performed. The theory could adequately describe the existing viscosity data. It seems necessary to correct the viscosity of a dilute polymer solution measured by a glass capillary viscometer for effect of adsorption in all cases.

Apparent elongational viscosity of dilute polymer solutions

Apparent elongational viscosity studies were made on dilute solutions of high molecular weight polymers using a fiber spinning apparatus designed for low shear viscosity liquids with substantial elongational effects. The experimental method involved the flow of solutions of polyacrylamide and poly(ethylene oxide) from a tube into an evacuated vessel. Experimental results showed that the apparent elongational viscosity obtained from the jet shape increased linearly with the stretch rate.

MEASUREMENT OF EXTENSIONAL VISCOSITY OF POLYMER SOLUTIONS AND ITS EFFECTS ON ATOMIZATION FROM A SPRAY NOZZLE

A simple method is described for the evaluation of the extensional viscosity of dilute polymer solutions typically used as drift control adjuvants in agricultural sprays. Extensional viscosity characteristics were determined for a wide range of polymer types and molecular weights, by measurements of the flow of solutions through a packed bed of screens over a range of pressure. The polymer types are classified according to their extensional viscosity-strain rate response characteristics. The effects of molecular weight, concentration, and polymer type are discussed. A correlation is demonstrated for all the polymer solutions tested relating the extensional viscosity at strain rates occurring in agricultural spray processes with the droplet size distribution. Shear viscosity and polymer concentration also affect the median droplet size, but no correlation exists over all polymers.

Shear‐rate dependent viscosity of dilute polymer solutions

Shear‐thinning viscosities have been investigated for dilute solutions (c<c*) of high‐molecular weight polymers, namely, poly(ethylene oxide) (PEO) and polyacrilamide in water and polyisobutylene in kerosene. Measurements have been performed using capillary viscometers and a Zimm–Crothers viscometer with rotors having angular velocities of different magnitude. Shear rate was varied within the range of 0.1–3000 s−1. This made it possible to obtain full curves of viscosity versus shear rate. Owing to a high measurement accuracy, significant data were obtained using concentrations as low as 5 ppm. For the PEO solutions, the shear‐rate dependence of viscosity was investigated as a function of concentration and temperature of the solution as well as molecular weight of the dissolved polymer. The data were compared with theoretical predictions based on the idea of molecular dispersion of the polymer in the solution at low concentrations. Experimental results were found to deviate significantly from the theory and this is explained by supermolecular organization characteristics of the high‐polymer solutions even at low concentrations. A parameter was introduced: the relative amplitude of the shear‐thinning viscosity. This parameter is important for describing hydrodynamic behavior of the polymer solutions.

Evaluation of Apparent Elongational Viscosity of Dilute Polymer Solution Measured with a Spinline Rheometer

Evaluation of Apparent Elongational Viscosity of Dilute Polymer Solution Measured with a Spinline Rheometer

High-pressure viscosity of dilute polymer solutions in good solvents

The high-pressure viscosities of four dilute, good-solvent polymer solutions [polystyrene (PS) in tetrahydrofuran (THF) and chloroform, polyisobutylene (PIB) in THF, and partially hydrolyzed polyacrylamide (HPAM) in 2% NaCl-water] were measured in a new diamond-anvil cell viscometer at pressures up to 20 kbar. The viscosity of these polymer solutions rises faster with increasing pressure than the viscosity of the solvents in the absence of the polymers. The specific viscosity, η sp , was calculated at high pressure by obtaining the ratio of solution to solvent viscosity at each pressure

Effect of Crosslinks on the Viscosity of Dilute Polymer Solutions

Abstract The effect of junction points between macromolecular chains in a dilute polymer solution, in the viscosity of the solution, has been studied for the case of a state laminar flow. An attractive interaction potential energy has been used for the effect of cross-linking. The strength of this potential has been evaluated by considering limiting cases. The viscosity has been found to be proportional to the square of the molecular units of the chain and to depend on the position of the junction point.

Effect of polydispersity on the shear rate dependence of the intrinsic viscosity of flexible linear polymers

A multiple-bulb viscometer has been developed enabling the measurement of the specific viscosity of dilute polymer solutions over a shear rate range from 4.8 s −1 to nearly 4000 s −1 . Polyethylene samples with polydispersities of about 2 and between 5 and 7 are studied. In the Newtonian range at low shear rates the intrinsic viscosity of these samples varies from 31.8 to 5.2 dL/g. The degree of non-Newtonian behavior increases with molecular weight as well as with polydispersity. A method of analyzing the data is derived which describes these effects for polymers with logarithmic normal molecular weight distributions

The influence of pre-shearing on the elongational behaviour of dilute polymer and surfactant solutions

Experimental results are presented which provide information about the elongational behaviour of pre-sheared dilute polymer and surfactant solutions. The viscosity behaviour of these pre-sheared solutions is explained on the basis of molecular data and by flow visualization. A rotational viscometer was modified in such a way that the sheared test fluid left the gap of the viscometer through an orifice in the outer cylinder. The flow-rate at a constant pressure drop through the orifice is related to the elongational viscosity of the fluid. The elongational viscosity of dilute polymer solutions increases when a critical shear gradient is exceeded. The critical shear gradient was found to be independent of the polymer concentration. It could be lowered by increasing the molecular weight of the polymer. Visualization of the orifice flows were done in a rectangular channel. A sudden increase of the apparent elongational viscosity, which is found for poly(isobutene) solutions when a certain Deborah number is exceeded, and an increase of the elongational viscosity, which for poly(acrylamide) solutions is independent of the pre-shearing deformation, can both be related to entrance vortices and instabilities of the entrance flow in the orifice. This was confirmed by flow visualization. The surfactant solutions which were used exhibit a sudden increase of the shear viscosity due to the formation of a shear-induced state (SIS) when a critical shear rate is exceeded. In the SIS their elongational viscosity is also increased. However, the Trouton ratio remains at a value of three which is characteristic for Newtonian fluids.

High temperature capillary viscometer

A new high-temperature capillary viscometer for measuring the viscosity of dilute polymer solutions has been designed, constructed, and extensively tested. The viscometer has combined several valuable capabilities: high-temperature operation (potentially to 280 °C and tested up to 250 °C), high precision (∼10−3 s with a temperature control of ±0.001 °C), variable shear rates (by changing the orientation of the capillary), and differential measurements (by using a twin viscometer arrangement). A description of the high-temperature viscometer and tests of its capabilities are presented.