Ind. Eng. Chem. Fundam. 1984, 2 3 , 316-319
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Flow Behavior of Dilute Polyacrylamide Solutions through Porous Media. 2. Indirect Determination of Extremely High Molecular Weights and Some Aspects of Viscosity Decrease over Long Time Intervals Ralmund Haas+ Sonderforschungsbereich80, Universitat Karisruhe, 7500 Karisruhe, FRG
Werner-Michael Kullcke Institut fur Technische Chemie, Technische Universlt Braunschweig, 3300 Braunschweig, FRG
Flow of dilute solutions of high molecular weight polymers through porous media yields, above critical flow rates, a large pressure-drop increase. This viscoelastic flow phenomenon c a n be explained as an extensional viscosity increase which levels off to a maximum value. Both the onset of the sudden viscosity increase and its maximum value are primarily dependent on the molecular weight of the polymer sample used. This effect is proposed as a new method of determining extremely high molecular weights. In addition, from a theoretical approach a stretching parameter can be estimated which gives an idea about the amount of deformation of flexible macromolecules under strong flow. Also discussed are some results about the unusual long-time-dependent viscosity behavior of aqueous polyacrylamide solutions which indicate that chain scission will not occur at least in a period of less than about 30 days.
1. Introduction
The size and conformation of high molecular weight polymer molecules in solution are mainly responsible for the viscoelastic flow phenomenon observed with polymer solutions in shear and elongational flow. The absolute molecular weight of the polymer molecules is the most important molecular parameter for characterization of linear polymers. Several techniques for molecular weight determination have been used; however, problems occur in the analytical techniques when the molecular weight is high, especially in case of aqueous polymer solutions. One widely used technique for molecular weight determination of polymer molecules in solution is light scattering. As shown by Kulicke and Kniewske (1980), the contamination of polymer solutions is a major problem in light scattering. Especially the purification of aqueous polymer solutions from dust, fibers, and particlesaccumulated throughout the preparation is extermely difficult. This problem is enhanced when commercial polymer samples have to be characterized by molecular weight just before use of these products in technical applications, such as chemical flooding operations in enhanced oil recovery, flocculation, or paper making. To increase the efficiency of several processes in industry, polymers with extremely high molecular weights have been prepared by the available methods. This problem will now be described briefly. Theoretically, molecular weight values up to infinity could be measured by light scattering. It involves projecting a beam of light through the polymer solution and measuring the intensity of scattered light at a specific angle 6. The scattering intensity, Rg,is plotted in the form of K.c/Ro as a function of polymer concentration, c, as shown in Hoechst AG, Abt. Angewandte Physik, 6230 FrankfurtIMain 80. FRG. 0196-4313/84/ 1023-0316$01.50/0
Figure 1. Data are taken from polyacrylamide (PAAm) samples as used in part 1 (Kulicke and Haas, 1984). The intercept of a straight line through the experimental data with they axis (c = 0) is l/Mw. At K - c / R o= 0, the value of M, goes to infinity, thereby explaining the theoretically applicable molecular weight range of this light-scattering technique. However, above a molecular weight of 5 X lo6 g/mol, the possible error becomes very significant. The reason is that the molecular weight M , increase hyperbolically as K-c/RBdecreases as can be seen by the right ordinate in Figure 1. Other absolute determination methods for detecting high molecular weights yield similar problems; see Kulicke et al. (1982). Therefore, the normal method for determination of these high molecular weights is by extrapolation of the Mark-Houwink relationship
[ v ] = K*M"
(1)
where K and a depend on the selected polymer-solventtemperature system. The Mark-Houwink relationship found in polymer handbooks, e.g., see Brandrup and Immergut (1975), is limited in most cases to the determination of absolute molecular weights lower than 2 X lo6 g/mol. In the case of PAAm, an [?]-A4 relation exists up to M , = 9 X lo6 g/mol. In order to determine higher molecular weights, one must extrapolate the values as depicted in Figure 2a, where measured data of the system PAAm in 0.1 M Na2S04,used in part 1 are shown. Viscosity measurements of the same polymer-solvent system at T = 25 "C are given in Figure 2b. A nonlinear relationship between q,,/c results from this graph due to intermolecular interactions between polymer molecules for molecular weights larger than lo6 g/mol. Using eq 3 of part 1 and the measured radius of gyration, (RG'), for the different PAAm samples in 0.1 M Na2S04,the critical concentration, c*, can be calculated, which is also shown in Figure 2b as the dotted line. The dashed line represents 0 1984 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 23, No. 3, 1984 loc c
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Figure 1. Light-scattering results of polyacrylamide in 0.1 M NazSO, solution at 25 "C. (Laser-light-scattering photometer, A, = 633 nm, angle region 6-7', samples from part 1). Note: at K.c/R8 = 0 the molecular weight should be M = by definition. -
317
critical concentration C * 1000
2000 c I ippml
Figure 2. (a) Double logarithmic plot of intrinsic viscosity [ q ] vs. molecular weight M, of polyacrylamide in 0.01 M NazSOl solution; PAAm samples as used in part 1. (b) Dependence of the reduced specific viscosity vEP/con concentration c for the same polymer system.
the condition: [qlc = 0.481, which results from the Flory-Fox relationship when combined with eq 3 of part 1. One clearly can see from Figure 2b that no reliable viscosity measurements could be performed at concentrations lower than c*. As reported by Munk et al. (1980) and Kulicke et al. (1982) and their cited references, additional difficulties arise in the [q] determination of PAAm solutions when the molecular weight is higher than about lo7g/mol. This is manifested in the fact that the spread of data in repeated experiments was typically about 10% but occasionally (for the high molecular weights up to 1 X lo7 g/mol) even 25% and reproducibility was found to be much worse for solutions in water than for saline solutions. We have shown in part 1 that dilute PAAm solutions with concentrations far below c* produce dramatic viscoelastic flow phenomena when flowing through porous media at flow rates above onset condition. This behavior is observed in Figure 2, part 1. It becomes more pronounced as the molecular weight increases. At extremely high molecular weights, differeneces in molecular weight can be detected at much lower polymer concentrations by the porous media flow than by any other technique. The porous media flow technique is especially sensitive to molecular weight. Therefore we would like to introduce it as a new way of measuring molecular weights. 2. Determination of Molecular Weight As was shown in part 1, dilute high molecular weight polymer solutions reveal a pronounced onset and saturation behavior of viscoelastic flow phenomenon during flow through porous media. For molecular weight determination of a polymer sample, either the onset of viscoelasticity
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(onset Reynolds number, Re,) or the maximum value of resistance coefficient, A,,, can be used. The method requires that, for the selected polymer-solvent-temperature system, the Mark-Houwink relationships are known and valid for the stated molecular weight range. This is no fundamental requirement, since the parameters (a, K ) can, on principle, be determined by the proposed new method. 2.1. M , Determination by Measurement of Onset Condition. The important relationship between M , and Re, is given by eq 16, part 1. For a selected polymersolvent system and a randomly packed bed (d, n),the onset Reynolds number depends only on M , and c. We obtain from eq 16/I
Re,4sp/vs).Mw1+a= B1
(2) where the factor (@/qs) replaces (1+ [qlqc) in eq 16/I and accounts for the dependence of Re on concentration. Therefore, for a given polymer solution, the molecular weight of the polymer sample can be determined by one measurement of the onset Reynolds number. The precision of eq 2 was shown in Figure 5, part 1, where a good correlation of experimentally determined Re, value to the predicted value, Re,,* = Bl/[M,l+a-(qp/qs)],can be seen. Equation 2 cannot only be used for M , determination of ultrahigh molecular weights, but also for determination of the Mark-Houwink exponent, a, of homologous series of polymer samples. When log [Re,.(qp/qs))is plotted vs. log M,, a linear relationship is obtained with slope -(1+ a). In Figure 3 data are shown for dilute PAAm solutions with solvent ethylene glycol. This system yields a slope of -1.54 and therefore an a = 0.54. This value is the same as was found for the system PAAm/ethylene glycol by Kulicke et al. (1982). 2.2. M , Determination by Measurement of Extensional Viscosity Increase. As was described in part 1, the maximum value of the resistance coefficient, Ap,", expressed in terms of the reduced extensional viscosity, ij*,+,,, can be used as a direct measure of the molecular weight, M,, of the PAAm samples. For calculation of the resistance coefficient, the determination of the pressure drop, Ap, should be performed over a length, hL, so that the number of flow constrictions is constant. This means that AL, has to be adjusted to the sphere diameter, d, of the porous media. Therefore, in this study an entrance length of 5d and hL = 15d was chosen for each porous matrix with different sphere diameters. From the theoretical approach in part 1, section 2, we know that for
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Ind. Eng. Chem. Fundam., Vol. 23, No. 3, 1984
Table I. Characteristic Data for Molecular Weight Determination of PAAm Samples
M, x g mol-' 18.2
c, ppm 50 25 50 100 100 50 100 200
9.2
4.3
-
solvent ethylene glycol 0.5 M NaCl 0.5 M NaCl ethylene glycol 0.5 M NaCl 0.5 M NaCl 0.1 M Na,SO, ethylene glycol
'7 *e,max
190 145 121 130 70 80 79 60
N'
M', x g mol-'
Re/R,,
N 21817 11962 11962 11329 6815 6875 7140
11271 13180 11000 11817 6363 7212 7181
14.3 20.5 16.5 9.7 8.4 9.9 8.8
6.6 7.8 7 .i 7.6 7.1 1.6 I .4
5319
5454
4.4
I .5
%
purely elongational flow of dilute polymer solutions, the following relationship is valid 2N = 2/33(R,2/(R2)) (3) where qm* is the high limiting value of the reduced extensional viscosity and N the number of statistical segments defined in eq 1O/I. ( R 2 )is the mean square endto-end distance of the macromolecule at rest and R, the completely stretched molecule length in its zig-zag conformation. From experiments in porous meida flow, we obtain values for the effective reduced extensional viscosity at the maximum; see part 1, Figure 3 ijm* =
(4) Ne represents the effective number of statistical segments and Re the mean end-to-end distance for the partly or completely stretched macromolecules in porous media flow. From combination of eq 3 and 4 the following relationships can be proposed ij*e,mar N; Re/Ro = [ij*e,max/2"I1" (5) The value Re/R, gives an idea to which minimum extent flexible macromoleculesare stretched in porous media flow at flow conditions above the onset Reynolds number. We now use the data shown in Figures 2 and 3 of part 1 to verify eq 5. The data are summarized in Table I. With knowledge of the Mark-Houwink relationship (eq 1)the number of statistical segments, N , can be computed for the polyacrylamide/solvent systems used. These values are listed in Table I in the fifth column. From experimental data, A = f ( R e ) ,and with eq 13/1, the maximum value, ij*ew, of the effective reduced extensional viscosity can also be calculated for the different polymer-solvent systems. The proportionality between N and v*~,, is shown in Figure 4. This relationship should be valid for M , values much higher than the highest value (M, = 18.2 X lo6 g/mol) used here. We can now use Figure 4 to determine the molecular weight of a PAAm sample. The procedure would be the following. A polymer solution with this sample is prepared, for which the Mark-Houwink relationship is known. The polymer concentration, c, should be of such order than the shear viscosity ratio is vp/vs r 1.05-1.15, respectively, [71] c = 0.05-0.15 to aswe a highly diluted solution. Only under this condition is the maximum value, v*~,-, independent of the polymer conhas to be measured in a porous-media centration, c. flow test. As the maximum value has been shown to be independent of the sphere diameter of the randomly packed bed (Figure 2c, part l),the porous media test can be performed in a test section having sphere diameters slightly different than those given in Figure 4. From if*eFigure 4,given the number of statistical segments for the corresponding molecular weight, is obtained by the following formula
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0
Data for Salt Solution Data for Ethylene Glycol
I t
Calculated value N
Ind. Eng. Chem. Fundam., Vol. 23, No. 3, 1984 319 ,100
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Figure 5. Intrinsic viscosity [7] and the experimentally determined numbers of statistical segments Ne as a function of storage time of polyacrylamide in 0.5 M NaCl solution.
stored at room temperature, in the dark, and without the influence of mechanical degradation effects. No viscosity loss is observed in organic solvents like formamide and ethylene glycol, in salt solution (0.5 M NaCl), or in aqueous solutions to which 2 vol % 2-propanol had been added. The viscosity loss measured from experimental results was attributed to conformational transitions within single polymer chains which are controlled by intramolecular hydrogen bonds. Chain scission of the polymer molecules was excluded. Also other aqueous polymer systems show the unusual viscosity decrease with time, like polyacrylamide-co-acrylate. Chain scission could be excluded and a conformational change seems the most likely mechanism also for this polymer system; see Kulicke and Kniewske (1981). However, the highly non-Newtonian flow behavior of dilute polymer solutions through porous media may be used to give some additional information on unusual time-dependent viscosity behavior expressed by changes of onset and saturation effects of viscoelasticity as recently shown by Haas (1982). A master solution of concentration c = 500 ppm was prepared with the technical polymer product (M,= 18.2 X lo6 g/mol) in 0.5 M NaCl and stored in a closed, light-permeable container for several weeks. In accordance with previous procedures, 5 days was allowed to dissolve the polymer before [ q ] of the solution was measured, and the measurements were repeated after 10,25,75, and 135 days. The results are shown in Figure 5 (upper curve), where an abnormal intrinsic viscosity decrease with storage time can be observed. [o] decreases rapidly to the 30th day, followed by a very weak, linear decrease up to the 135th day. The explanation for this unusual time-dependent viscosity behavior may be given as follows: up to the 30th day, the macromolecules undergo mainly a conformational change, which resulta in more tightly coiled macromolecules with increasing storage time. The weaker decrease of [a] from the 30th day up to the 135th day results from a slow chain scission, initiated perhaps by light and by impurities in the technical product. This explanation can be supported by measurement of the viscoelastic flow behavior the corresponding solutions during flow through porous media. A t the same time when [q] was measured, a dilute PAAm solution of c = 50 ppm was prepared from the master solution and forced through a porous medium consisting of the glass beads having a diameter d = 392 pm. The resulting A-Re plots are shown in Figure 6. Both an onset change and a change of the maximum resistance increase could not be detected through the 11th day, although the intrinsic viscosity had changed to a lower value. This observed decrease in the intrinsic viscosity was not attributed to the lower molecular weight of the sample
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loo
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Figure 6. Time-dependent flow behavior of dilute polymer solutions through porous media.
because of a lower M, would always result in lower values of Re, and ij*e,max. Thus, a conformational change of the macromolecules must be the explanation, which means a lower a exponent and a higher K value. The slow [ 9 ] decrease above the 30th day seems to be coupled with a molecular weight decrease, which is indicated in Figure 6 by an onset shift to higher Re values and a decrease of Ap," with increasing storage time. To demonstrate the complete time-dependent behavior, in Figure 5 (lower curve) the experimental value Ne = TJ*~"/~ is plotted vs. the storage time. The increasing value Ne up to the 30th day indicates a more flexible macromolecule and thus, a conformational change, whereas for higher storage times the steadily decreasing Ne value corresponding to chain scission or a molecular weight decrease.
Conclusions The non-Newtonian aspects of the rheological response of dilute polyacrylamide solutions in porous media flow were found to be suitable for determination of extremely high molecular weights. To improve the proposed method standardized porous beds such as sintered disks with narrow-fractionated spherical particles should be used in further investigations. Calibration curves as shown in Figure 4 can be evaluated for polymer-solvent-temperature systems of interest. Additionally, the onset condition, given in eq 2 and in eq 16, part 1, was developed to be used in conjunction with the molecular weight determination and with determination of the Mark-Houwink exponent, a, for a homologous series of polymer samples. On the other hand, the viscoelastic flow behavior of dilute polymer solutions through porous media may be used to characterize such polymer systems with respect to mechanical and thermal stability, conformational change of macromolecules in solution, or solvent thermodynamic quality. Registry No. Polyacylamide (homopolymer), 9003-05-8.
Literature Cited Brandrup, J.; Immergut, E. H. "Polymer Handbook", 2nd Ed., 1975. Haas, R. Dissertation, University of Karlsruhe, F.R.G., 1982. Kullcke. W.-M.; Haas, R. I n d . Eng. Chem. Fundam. 1984, preceding article in thls issue. Kullcke, W.-M.; Knlewske, R. Mekromol. Chem. 1980, I , 719. Kullcke, W.-M.; Knlewske, R.; Klein, J. Prog. folym. Sci. 1982, 8, 373. Kullcke. W.-M.; Kniewske, R. Mekromol. Chem. 1981, 782, 2277. Munk, P.; Aminabhavi, T. M.; Wllllams, P.; Hoffmann, D. E.; Chmelir, M. Macromolecules 1980, 13, 873.
The support of this work by the Deutsche Forschungsgemeinschaft (DFG) and Fonds der Chemischen Industrie (FCI) is gratefully acknowledged.
