Langmuir 2003, 19, 559-565
559
Dilute Polyacrylamide Solutions under Uniaxial Extensional Flow Eric Pelletier, Christer Viebke, John Meadows, and Peter A. Williams* Centre for Water Soluble Polymers, North East Wales Institute, PP 21, Plas Coch, Wrexham LL11 2AW, U.K. Received June 7, 2002. In Final Form: October 23, 2002 The shear and extensional viscosities, dynamic viscosities, and normal forces of a series of polyacrylamide solutions of varying molar mass have been determined in a Boger fluid at varying concentrations. The critical strain rate under extensional flow that can be defined from the departure from Newtonian behavior, ˘ c, was found to be independent of the concentration and varied in the same way as the critical coil-stretch strain rate with the molar mass. A quantitative comparison indicated that ˘ c is a decade lower than the strain rate predicted to characterize the coil-stretch transition. This difference indicates that ˘ c reflects the average deformation of the chains over the range of strain rates.
Introduction Water-soluble polyacrylamides are important industrial polymers. They are employed in a wide range of applications such as water treatment, paper manufacturing, food processing, and agriculture. Polyacrylamides are used to flocculate both organic and mineral substances. The rheological behavior, adsorption on solid-liquid interfaces, and molar mass distribution of polyacrylamides have been widely studied.1-5 However the departure from Newtonian behavior for dilute solutions of polyacrylamide has not been systematically studied. In this paper we present results of a mechanical study covering a range of molar masses. The relevant parameters are mechanically and independently measured using a range of rheological techniques. The rheological properties of polymer solutions are strongly dependent upon the concentration regime of the polymer under study. In semidilute and concentrated systems, entanglement effects can have a predominant role in defining the behavior of the system. In dilute solutions the rheological properties of the system are a reflection of the mechanical properties of the individual polymer chains and the number of chains in the bulk solution. However, even in such dilute systems, the mechanical properties of the individual chains and, hence, the bulk solution are strongly dependent on the type of flow to which the system is subjected. In shear flow, the mechanical properties change gradually with the shear rate while in elongational flow the variations can be relatively sharp.6-8 Close to the critical strain rate, a coil stretch transition occurs where the coil quickly reaches its fully stretched state. Such stretching significantly * Corresponding author. E-mail:
[email protected]. (1) Kislenko, V. N.; Verlinskaya, R. M. J. Colloid Interface Sci. 2001, 244, 405. (2) Pefferkorn, E. J. Colloid Interface Sci. 1999, 216, 197. (3) Ghannam, M. T.; Esmail, M. N. J. Appl. Polym. Sci. 1998, 69, 1587. (4) Swerin, A. Colloid Surf., A 133, 279. (5) Hecker, R.; Fawell, P. D.; Jefferson, A.; Farrow, J. B. J. Chromatogr., A 1999, 837, 139. (6) Larson, R. G. The structure and rheology of complex fluids; Oxford University Press: New York, 1999. (7) Rabin, Y. Polymer-flow interaction; American Institute of Physics: New York, 1985. (8) Nguyen, T. Q., Kausch, H. H, Eds. Flexible polymer chain dynamics in elongational flow; Springer: Berlin, 1999.
increases the hydrodynamic volume of the polymer chain, which leads to an increase in the extensional viscosity of the solution. This transition was theoretically predicted by de Gennes9 who proposed a quantitative relationship between the critical elongation rate (˘ c) and the longest relaxation time (τ1) of the polymer chain, ˘ cτ1 ) B. The exact value of B has been under discussion for a long time. De Gennes predicted B ) 1 albeit through use of a very simple model. Subsequent more sophisticated theories10 for Gaussian chains, without hydrodynamic interactions (HI) predict B ) 0.5 and, from more elaborated calculations11 incorporating HI that B = 0.53. These theories are supported by numerical calculations showing that if ˘ c and τ1 are strongly dependent on HI, their product is practically independent10 of HI. The model for free draining chains (Rouse-like) without HI predicts for long polymer chains: ˘ c ∝ N-2 and τ1 ∝ N2. The incorporation of HI leads to ˘ c ∝ N-1.5 and τ1 ∝ N-2, where N is the number of segments of the chain. Rabin12 noted that the variations of ˘ c and τ1 with N could be different in a good solvent, leading to ˘ c ∝ N-1.6 and τ1 ∝ N1.8 and B ∝ N0.2. Recently, Monte Carlo simulations13 have even predicted ˘ c ∝ N-2 in a good solvent. From an experimental point of view, the coil-stretch transition has mainly been studied by measuring birefringence intensity against strain rate in a well-defined extensional field.14-21 Light scattering has also been used to determine the stretching of polymer chains in opposed (9) de Gennes, P. G. J. Chem. Phys. 1974, 60, 5030. (10) Hermandez Cifre, J. G.; Gracia de la Torre, J. J. Rheol. 1999, 43, 339. (11) Magda, J.; Larson, R.; Mackay, E. J. Chem. Phys. 1988, 89, 2504. (12) Rabin, Y.; Henyey, F. S.; Pathria, R. K. Phys. Rev. Lett. 1985, 55, 201. (13) Andrews, N. C.; Doufas, A. K.; McHugh, A. J. Macromolecules 1998, 31, 3104. (14) Guozhu, Y.; Nguyen, T. Q.; Kausch, H. H. J. Polym. Sci. 1998, 36, 1483. (15) Farrell, C.; Keller, A.; Miles, M.; Pope, D. Polymer 1980, 21, 1292. (16) Fuller, G.; Leal, G. Rheol. Acta 1980, 19, 580. (17) Odell, J.; Keller, A.; Miles, M. Polymer 1985, 26, 1219. (18) Atkins, E.; Attwool, P.; Miles, M. Bristol conference on macromolecular flexibility and Behaviour in solution (U.K.), 1986. (19) Brestkin, Y.; Saddikov, I.; Granova, S.; Baranov, Y.; Frenkel, S. Polym. Bull. (Berlin) 1986, 15, 147. (20) Narh, K.; Odell, J.; Keller, A. J. Polym. Phys. 1992, 30, 335. (21) Nguyen, T.; Yu, G.; Kausch, H. H. Macromolecules 1995, 28, 4851.
10.1021/la0205304 CCC: $25.00 © 2003 American Chemical Society Published on Web 01/07/2003
560
Langmuir, Vol. 19, No. 3, 2003
Pelletier et al.
Table 1. Name of the Samples, Mw, Weight Average Molar Mass, P, Polydispersity Index, τeff, Effective Relaxation Time, A1 and A2, Parameters Used to Adjust the Nondimensional Viscosity Ratio with a Power Law, E3c, Critical Strain Rate, τ0, Characteristic Relaxation Time Defined from the Intrinsic Viscosity and Comparison between the Different Relaxation Times Where τ1fr and τ1fz Are the Longest Relaxation Time Defined from τeff by Using the Rouse and the Zimm-like Model (theta solvent) name
Mw (×106 g‚mol-1)
PAM-A PAM-B PAM-C PAM-D PAM-E PAM-F
3.18 1. 56 1.54 1.38 0.94 0.38
P (Mw/Mn)
1.2 1.2 1.46 1.25
τeff (s)
A1
B1
˘ c (s-1)
τ0 (s)
τeff/τ0
τ1fr ˘ c
τ1fz ˘ c
0.063 0.040 0.0077 0.0096 0.0049
4.89 3.46
0.60 0.56
0.44 0.77
0.057 0.063
0.58 0.48 0.34
2.66 3.93 29.7
0.76 1.42 0.28 0.41 0.38
0.042 0.047
1.69 1.55 0.94
0.081 0.028 0.027 0.023 0.013 0.0032
0.039 0.029
0.052 0.039
jet conformation. It has been22 claimed that ˘ c values determined by light scattering are in agreement with birefringence measurements. It should be noted that this conclusion was based on a comparison of a few data points at low strain rates. A more recent study23 shows that molecular deformation following the main axes occurs for ˘ τ1 much lower than 0.5. Direct visualization using fluorescence microscopy24,25 has also been employed to probe the stretching of DNA chains in a stagnation point flow device. By analysis of the subset of molecules that reached steady extension during their residence time, a very sharp critical transition was obtained for B ) 0.4. When the extension was averaged over all the data, a smoother behavior was displayed and extension to zero led to a much lower value of B. Experimental Section Materials. A series of samples of the linear, flexible nonionic polymer (polyacrylamide) covering a range of molar masses were kindly supplied by CIBA Specialty Chemicals (Bradford, U.K.). The weight average molar mass of the various polyacrylamide samples was determined by gel permeation chromatography coupled to a DAWN multiangle laser light scattering detector (Wyatt Instruments Inc., USA). The chosen nomenclature, the weight average molar mass, Mw, and the polydispersity of the various polyacrylamides used in this study are given in Table 1. The polydispersity index could be accurately determined only for the samples of lower molar mass. It was necessary to use a Boger solvent in order to increase the solution viscosity to suppress inertial effects and be within the measurement range of the RFX extensional rheometer. The chosen solvent was 1/5 (w/w) of distilled water/glycerol. The glycerol used was AnalarR grade (BDH Ltd., U.K.) and had a density of 1200 kg‚m-3. The polymer samples were first dissolved in distilled water to give 0.5% w/w solutions, before being mixed with a 5-fold weight of glycerol. The resulting samples for rheological analysis were thus 0.083% solutions of polyacrylamide in 1/5 (w/w) water/ glycerol mixed solvent. To check for concentration effects, solutions covering a range of concentrations from 0.02% to 0.16% w/w in the Boger solvent were prepared for one sample of polyacrylamide, PAM-E. The solutions were used within 24 h after being made. All the results have been obtained at a temperature of 25 °C. Methods. The uniaxial extensional viscosity characteristics of the various polymer solutions were determined by using the RFX fluids analyzer (Rheometrics Inc., New Jersey, USA). The instrument has been described in detail elsewhere,26 and only a brief description of the experimental setup and data treatment is given. The instrument utilizes the principle of opposing jets, creating a flow field that can be considered as uniaxial extension when the solution is drawn into the jets. The position of the jets (22) Menasveta, M.; Hoagland, D. Macromolecules 1992, 25, 7060. (23) Lee, E. C.; Muller, S. J. Macromolecules 1999, 32, 3295. (24) Perkins, T. T.; Smith, D. E.; Chu, J. Science 1997, 276, 2017. (25) Perkins, T. T.; Smith, D. E.; Chu, J. Flexible polymer chain dynamics in elongational flow; Springer: Berlin, 1999; Chapter 10. (26) Meadows, J.; Williams, P. A.; Kennedy, J. C. Macromolecules 1995, 28, 2683.
is held constant while the force acting on one jet is measured. Different jet sizes can be used, making it possible to measure the rheological characteristics of the samples over approximately 4 decades of extensional strain rate. The sample temperature can be controlled to (0.1°C within the investigated temperature range. The software supplied with the instrument has been used to automate data collection. However, a strip chart recorder was connected to the output of the torque transducer in order to monitor its response and detect any flow instabilities It has previously been shown27,28 that the use of the RFX instrument to determine the extensional flow characteristics of relatively low viscosity fluids (e.g.,
