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High-precision viscosity measurements
High-Precision Viscosity Measurements I. Aqueous Solutions of Alkali Chlorides 1,2 ROBERT DORDICK, L A W R E N C E KORSON, AND W. DROST-HANSEN 3 Laboratory f o r Water Research, D e p a r t m e n t o f Chemistry, University o f Miami, Coral Gables, Florida 33124
Received November 14, 1978; accepted March 1, 1979 High-precision viscosity measurements at 25°C of aqueous solutions of the alkali chlorides-LiCI, NaC1, KCI, RbC1, C s C l - - h a v e yielded new sets of Jones-Dole coefficients for A (0.0063, 0.0062, 0.0057, 0.0047, and 0.0062, respectively) and B (+0.1400, +0.0802, -0.0147, -0.0360, and -0.0511, respectively) based on the standard equation "Or = "O/"O0= 1 + A C lj2 + B ' C . With the apparent exception of LiC1, systematic deviations from the Jones-Dole "limiting law" behavior have been observed for all the salts investigated. It appears that the anomalies are introduced by some spurious effect, most likely caused by structurally modified layers of solution, with different viscosities, at the glass (viscometer)/solution interface. INTRODUCTION
Parts of this study were presented at the 176th American Chemical Society National Meeting, September 11-15, 1978, Miami Beach, Fla. 2 Contribution No. 18, Laboratory for Water Research. To whom correspondence should be addressed. 4 The traditional reference for the Jones-Dole formulation (2) expresses the empirically derived relationship in terms of the relative fluidity qSr 4~r = 1 - A C v2 + B ' C .
- 1 + AC1/2 + B'C. [1] r/0 The coefficient A is a unique constant for each electrolyte which may be calculated from equilibrium theory as demonstrated by Falkenhagen (4, 5). ~ The coefficient B is an empirical constant, qualitatively correlating ion-solvent interactions characteristic for each electrolyte. One of the objectives of the present study was to determine as accurately as possible, within the limits of the best currently available techniques, the A and B coefficients in the Jones-Dole equation for the alkali chlorides. The results presented in this paper are a composite of two independent studies performed over a 6-year period. 9r-
An approximate linear dependence of viscosity (or fluidity) on concentration is observed in the dilute concentration range for aqueous solutions of strong electrolytes. However, at very high dilutions, a departure from linearity--i.e., a characteristic negative curvature--was reported by Grtineisen (1) for all salts irrespective of whether the net effect of the salt is to increase or decrease the viscosity. Jones and Dole (2), extending the Debye-Hiickel theory of interionic attraction, empirically accounted for the linear viscosity-concentration dependence with their formulation (3): 4
[2]
The formulation "Or = 1 + A C 112 + B .C was first pre-
sented by Jones and Talley (3). The equivalency of the two formulations is demonstrated by taking the reciprocal of Eq. [2]. Expressing the equation in terms of the (relative) viscosity, the coefficient A is positive for all salts and B may have either positive or negative values depending on the salt and the temperature. 5 A limiting law, "Or = 1 + A C 112, was derived with application only in the limit of extreme dilution. The coefficient A is identical with the A of the Jones-Dole formulation.
206 0021-9797/79/140206-09502.00/0 Copyright © 1979 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
HIGH-PRECISION VISCOSITY MEASUREMENTS EXPERIMENTAL
1. Reagents
207
i.e., the amounts of water for the stock solut i o n s - w e r e weighed on a Voland 2-kg balance requiring one set of weights, while the weighing of the salt was done on a Mettler balance using standard class S weights.
Two different classes of salts were used for this work. The salts--NaC1, KC1, RbC1, C s C l - - o f analytical grade were recrystallized and oven dried at 120°C for several hours. Also, Suprapur salts (EM Laboratories, E. Merck, Darmstadt, G e r m a n y ) - NaC1, KC1, C s C l - - w e r e used without further purification. The LiC1 used was of analytical grade and, prior to use, was gently heated in a desiccator. The water used in the earlier parts of these investigations was obtained from two sources: a Millipore Super-Q ion-exchange system and a Barnstead still. In the more recent work, the water was obtained from a WS-2 continuous water still modified by attaching an AG-1 Corning Pyrex distillation apparatus directly to the output of the first still. Prior to use, all water was filtered through a Flotronics membrane filter, 1.2tzm pore diameter. No differences could be detected between the flow times for the water resulting from any of the water preparations; thus the results (relative viscosity) have been freely compared. Similarly, no differences in the relative viscosity resulted from using the same salt obtained from different sources. For each salt investigated, stock solutions were prepared by weight with all calculated quantities corrected to vacuum. All other solutions were prepared by dilution (by weighing) of the stock. Corrections were made for buoyancy in air on the weighings of the salts and on the weights of water under the specified conditions of room temperature, relative humidity, absolute barometric pressure on that day, and water vapor pressure. Allowance was also made in the calculations 6 for the differences in the specific densities of the different sets of weights used for weighing. Large m a s s e s - -
Cannon-Ubbelohde suspended meniscus overflow viscometers (constructed of Pyrex glass) with dilution chambers were used for all measurements. The viscometers were slightly modified by providing all access ports with ground glass joints. The positioning of the viscometer was made possible by means of a steel rod to which the viscometer was firmly clamped. Tapered at both ends, the steel rod pivoted in two counter sunk depressions; one being a metal block epoxied to the bottom of the bath, and the other mounted on a heavy swing arm securely rotating around a 2-in.-diameter aluminum post. Vertical alignment of the viscometer was accomplished with a specially machined brass rod equipped with a spirit level which fit into the fill arm of the viscometer. The viscometer was placed in a constant temperature bath with a 5-gallon capacity. 7 The bath was completely insulated with 2 in. of polystyrene foam. Two windows were cut in the insulation for inspection purposes; these windows could be closed if necessary. A lid which securely fit and sealed the top of the bath was fashioned from a polystyrofoam plate (about 1 in. thick). Holes were drilled through the lid to accommodate the connection tubes, stirrer, sensors, cooling coil ports, etc. The stirrer used was a constant high-speed, nearly vibration-free device provided with two sets of horizontal blades. The temperature of the bath was controlled with a Hallikainen Thermotrol. The thermoregulator provided a proportional heat input to offset a constant cool-
6 The detailed calculational procedure is available upon request from the senior author (W.D-H.).
7 For a schematicdrawingof the viscometermounted in the bath, the reader is referred to (6, Fig. 1).
2. Apparatus
Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
208
DORDICK, KORSON, AND DROST-HANSEN
.0600 I
.0500 nr-I
.0400
.0300
.0200
.0100
.,6o
'
.260
.360
'
.460
FIG. ]. J o n e s - D o l e plot for LiCI in the concentration range 5.63 x 10-4 to 1.39 x 10-1 M .
ing load produced by circulating a coolant, maintained at a relatively constant temperature by a Blue M Refrigeration Unit (Model PCC-24A-2) with a cooling coil in a 5-gallon ethylene glycol reservoir. The temperature of the bath was measured with a Quartz Crystal Thermometer (Dymec; HewlettPackard, Model 260A) to 0.0001°C. An electrical-optical system (HewlettPackard) was used to measure flow times. Two light sources and photocells were mounted on the viscometer close to the original fiducial marks. The light sources were mounted on clear plastic spacers which separated the light source from the capillary by approximately 1 cm. This minimized direct and indirect heating effects on the liquid in the capillary. Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
The photocells were operated on a regulated voltage (6 V) from a power supply (Power Designs Inc., Model 2005). The start and stop pulses were fed into HewlettPackard electronic counters, Model 5245L, which functioned as millisecond timers.
3. Methodology The viscometer was cleaned prior to each set of runs with a concentrated sulfuric acid-potassium permanganate solution. The viscometer was filled with the cleaning solution and heated very carefully under the hot water faucet for about 10 min. The viscometer was next rinsed thoroughly with water, then with a dilute hydrochloric acid-hydrogen peroxide solution (to re-
HIGH-PRECISION VISCOSITY MEASUREMENTS
209
.0400 nr-I
JF .0300
.0200
,0100
'
.,6o
'
.zb0
.360
'
.460
F1G. 2. J o n e s - D o l e plot for NaC1 in the concentration range 1.77 x 10 4 to 1.49 x 10-1 M.
move any trace amounts of manganese dioxide), and finally with the (prepared) distilled water. The viscometer was dried via suction, the stream of air going through the viscometer having first passed through a Nucleopore Filter, 1.2-/zm average pore diameter. To initiate a run, the cleaned and dried viscometer was placed in the bath by means of the mounting devices described above. Long-stemmed specially fabricated and calibrated delivery pipets (cleaned in the same manner as the viscometer and initially wetted with the solution of interest) were used to deliver the initial water charge to the viscometer, the amount of which was determined by weighing. Once thermal equilibrium was achieved, the efflux bulb was filled by pressurizing
the filling arm of the viscometer. This was accomplished by blowing air through an Ascarite filter, provided with a glass-wool plug and a porous, fritted disk (to prevent transfer of particulate matter). The air stream was next passed through traps maintained in the same bath as the viscometer. Each trap was lined with filter paper, soaked with water (or, for more concentrated solutions, with the same solution as in the viscometer) to insure water vapor equilibration to minimize concentration changes due to evaporation or condensation. The liquid level in the viscometer was raised to the designated height (the center of the upper viscometer bulb), 8 and the 8 The choice and implications of the "designated height" were fully discussed in Ref. (6, p. 36). Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
210
DORDICK, KORSON, AND DROST-HANSEN
KCI 4-.0100nr-I
+.0050
-.005C
'
.~6o
,zbo
'
.3bo
'
,4bo
F1G. 3. J o n e s - D o l e plot for KC1 in the concentration range 3.37 x 10-4 to 1.34 x 10-1 M.
liquid permitted to fall. The meniscus passed the points at which the light sources and photocells were located, and each cell, in turn, delivered the required start/stop pulses to the counter. After the flow time for pure water (calibration runs) was determined, a predetermined amount of one of the stock solutions was added to the water in the viscometer. The transfer of stock solution to the water in the viscometer was accomplished in the following manner. The pipet was rinsed with a sample of solution 1, for example. It was allowed to drain in a rigidly specified manner: Thirty seconds after the end of discharge, the pipet tip was touched to the meniscus of the liquid rapidly three times. The pipet was charged from a second flask containing stock solution 1. The second flask of stock solution 1 was weighed before and after an approximate amount of liquid Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
had been removed by means of the wetted pipet. The pipet, after having discharged its contents into the reservoir of the viscometer, was lightly touched to the meniscus of the solution in the viscometer three times to reproduce the discharge method used in the first washing with stock solution 1--to ensure the same amount of liquid was retained due to drainage and surface tension effects in the capillary part of the pipet. After equilibration, the solution was raised to the designated level in the upper viscometer bulb and the flow time measured. All subsequent dilutions and runs were performed in an identical manner. RESULTS
Flow times were measured for aqueous solutions of alkali chlorides over the approximate concentration range 10-4 to 10-1
HIGH-PRECISION VISCOSITY MEASUREMENTS
211
straight lines for the J o n e s - D o l e plot (Fig. 2) over the concentration range 1.77 × 10-4 to 1.49 × 10-' M. In this range, the n r -] . calculated B-coefficient, +0.0802, and the ~J A-coefficient, +0.0062, are in good agree0 ment with the literature. H o w e v e r , below the concentration of 5.1 × 10-4 M, a slight, but notable, negative curvature is observed. The data points for potassium chloride, -.005C rubidium chloride, and cesium chloride are depicted graphically in Figs. 3, 4, and 5, respectively. The trends observed are essentially identical for all three salts: Over - .OIOC the concentration range 10-3 to 10-1 M, a linear region is evident. F o r the concentra\ \ \@ tion range below 4 × 10-3 M, a distinct \\ negative deviation is observed from the J o n e s - D o l e limiting law behavior for all .260 .4bo .6oo ,/zthree salts. The A and B coefficients were calculated with only the data points in the FIG. 4. Jones-Dole plot for RbC1 in the concentra- linear region and are summarized in Table I. tion range 6.25 x 10.4 to 2.5 × 10-t M. N o t e that the onset of the systematic deviations increases toward higher concentraM. In order to obtain data as reliable as tion in the sequence NaC1, KC1, RbC1, and possible, experimental techniques were CsC1 as summarized in Table II. designed to optimize temperature constancy DISCUSSION and flow time measurement and reproduciThe precise and highly reproducible bility. The result was that during a given r u n - - a p p r o x i m a t e l y 250 s e c - - t h e flow time experimental techniques of this study have variation was usually within +0.002 sec and yielded new sets of J o n e s - D o l e coefficients the temperature variation within _+0.0003% as summarized in Table I. The effects of surface tension, localized The viscosity data are presented graphiheating, and kinetic energy on the precision cally in Figs. 1 through 5 in classical J o n e s and accuracy of the viscosity data reported Dole plots: ('0r - 1)/C 1/2 vs C 1/2. The coefherein have been examined in detail. N o ficients A and B, the intercept, and the corrections were made for surface tension slope, respectively, of a J o n e s - D o l e plot, effects on the effective pressure head. For were calculated via least-squares analysis very dilute aqueous solutions of electroof the data. lytes, the surface tensions vary so slightly F o r lithium chloride (Fig. 1) the data in that the correction can be neglected (7, p. the concentration range 4.74 × 10-4 to 1.39 19). Furthermore, the use of overflow visx 10 -1 M lie on a straight line with neglicometers is already assumed to minimize gible scatter. The resultant B-coefficient, +0.1400, and A-coefficient, +0.0063, are in the need for a surface tension correction. good agreement with the literature values. 9 H o w e v e r , trace amounts of organic conThe data for sodium chloride result in a taminants might cause measurable surface tension changes in the solution. Noting the extreme care in handling and cleaning the 9 Throughout this article, the literature data referred to are taken from the text of(7), unless otherwise noted. reagents and the apparatus and noting the RbCl
•0050 t
Journal of Colloid and Interface Science, VoL 72, No. 2, November 1979
212
DORDICK, KORSON, AND DROST-HANSEN
+.0500
CsCl qr-1
O
-.0050
-.0100
-.0150
'
'
.2+o
'
'
.4+o
FIG. 5. J o n e s - D o l e plot for CsCI in the c o n c e n t r a t i o n ra nge 2.11 x 1O-a to 1.51 x 10-1 M.
resultant high degree of reproducibility, the possibility of spurious contamination seems unlikely. A possible source of error in viscosity determinations using a photoelectric timing method is radiant and conductive heating from the light sources. No information has been published in the literature pertaining to this problem. To investigate the effects of local heating, a number of runs were made with pure water in which we varied the total time that the light was on. The results are shown in Fig. 6. With increasing "percent time o n , " the flow time decreases and this is attributed to the local heating in the capillary. The maximum difference between "100% light on" and the extrapolated value for "0% light" amounts to 0.038%. The minimal deviations from linearity i n the graph suggest that the changes in flow time Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
are directly proportional to the amount of heating. However, while a decrease of 0.038% is highly significant, both the calibration and actual runs were performed in an identical manner. Therefore, assuming that the heat absorption, heat capacity, etc. of the water and the very dilute solutions are essentially identical, the differences in flow times due to local heating must be negligible. A specific effort was made to test if differences in viscosity could be obtained when including a correction for kinetic energy. This correction utilizes the equation employed in an earlier paper on the viscosity of water as a function of temperature (6, Eq. (4), p. 38). However, it was found that no significant difference resulted from the two procedures (namely, calculations with and without the kinetic energy correction) and
213
HIGH-PRECISION VISCOSITY MEASUREMENTS
TABLE I J o n e s - D o l e Coefficients Experimental
LiC1 NaC1 KCI RbC] CsCI
Literature
A
B
A
B
0,0063 0,0062 ~ 0,0057 a 0.0047 ° 0,0062 a
0.1400 0.0802 -0.0147 -0.0360 -0.0511
0.0065 0.0062 0.0052 0.0049 b 0.0049 b
0.143 0.0793 -0.0140 -0.037 -0.052
E x t r a p o l a t e d from the linear portion of the graph. b C a l c u l a t e d with the equation derived by Falkenhagen and V e r n o n (5).
thus, the majority of the data have been used without corrections. Furthermore, it would seem that as all measurements are relative and made on solutions, the viscosities of which are almost identical in the dilute range studied, this correction ought to be negligible. With the apparent exception of LiC1, highly significant systematic deviations from the Jones-Dole limiting law behavior have been observed for all the salts investigated. It appears that the anomalies are introduced by some spurious effect, most likely caused by structurally modified layers of solution, with different viscosities, at the glass (viscometer)/solution interface. It appears most unlikely that the deviations result from either a failure of the JonesDole equation or from a yet undiscovered property of bulk electrolyte solutions. There exists ample evidence that water proximate to solid interfaces (vicinal water) is structured differently from ordinary bulk water (8). This vicinal water has significantly different solvent properties. For example, Wiggins' (9) results from a study of ion distribution in narrow pores (silica gel), recently extended by Hurtado and DrostHansen (10), reveal highly notable ion-discriminating effects. In a mixture of sodium and potassium chloride, the potassium ions--structure breakers--were selectively accepted by the vicinal water (the water in the pores of the silica gel) over the sodium
ions--structure makers. Also, Home and Young (11), with a series of elution studies, using 80- to 120-mesh silica, on 0.10 M solutions of the alkali chlorides, show a correlation between viscosity B-coefficients and the extent of exclusion of the cations. The structure makers-- Li + and Na + - were found to be more concentrated in the initial eluant samples. These ions are presumably excluded to a greater extent from the vicinal water surrounding the solid particles. A similar B-coefficient correlation with exclusion of the alkali-metal cations from silica gel was reported by Maatman (12). It is evident that the deviations from limiting law behavior tend to increase toward higher concentration (Table II) in the sequence down the group Li + to Cs +. The Cs + ion, having the least charge density and being the least likely to have its own hydration sphere, shows the deviation in viscosity at the highest concentration. Ion partitioning by the vicinal water, which tends to increase the relative concentration of the structure breakers in the vicinal layer, offers a reasonable explanation of the phenomenon observed. It appears that changes in the properties of water may occur over distances of at least one-hundredth, and perhaps as much as several tenths, of a micrometer from an interface. Thus, in the "extreme" case of greatly enhanced viscosity occurring in an annulus of thickness 0.2/zm, the effective radius of the capillary would have decreased from 125 (the approximate radius of the viscometer capillary in this study) to 124.8 T A B L E II C o n c e n t r a t i o n at Which D e v i a t i o n from " L i m i t i n g L a w " B e h a v i o r is O b s e r v e d E (M)
C'/2 LiC1 NaCI KCI RbCI CsC1
0.0225 0.060 0.090 0.095
No deviation 5.1 3.6 8.1 9.0
× × × ×
10 -4 10 -3 10 -3 10-~
Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
214
DORDICK, KORSON, AND DROST-HANSEN
.56'
.54'
"G
~
0.001
UJ k--
T
%
0.01%
256.
0 _] LL
2. Instrumental techniques have been perfected for rapid, high-precision, semiautomatic, and reproducible measurements of viscosities of aqueous electrolyte solutions. The technique permits accurate measurements to be carried out with highly dilute solutions (approximately 10 -4 M). 3. Systematic deviations from JonesDole limiting law behavior were observed for NaC1, KC1, RbC1, and CsC1 in the dilute concentration regime. 4. The deviations most likely result from an interfacial phenomenon, namely, the existence of structurally modified layers of solutions, with different viscosities, at the glass (viscometer)/solution interface. ACKNOWLEDGMENT
256.45 20
40
60
80
I00
The senior author (W. D-H.) wishes to thank the U. S. Environmental Protection Agency for its support of his studies of aqueous interfacial phenomena (EPA Grant R-803826-02).
% of time on
FIG. 6. Effect of "percent light on" (of the light sources for the detectors) on flow time for pure water.
/zm. The ratio of these numbers to the fourth p o w e r - - t h e Poiseuille d e p e n d e n c e - - i s 1.0064. This is a very notable effect compared to the high precision (of the order of one part in 10~ or better) with which the relative viscosity measurements were made in the present study. It is not surprising that very high precision viscosity measurements, using a standard capillary of relatively small radius, should exhibit some spurious effects due to the interfacial properties of the capillary. Therefore, until and unless some additional evidence is obtained, we suggest that the systematic deviations from the Jones-Dole formulation reported in this paper are most likely explained by surface effects. SUMMARY
1. High-precision viscosity measurements at 25°C have yielded new sets of A and B coefficients in the J o n e s - D o l e equation. Journal o f ColloM and Interface Science, Vol. 72, No. 2, N o v e m b e r 1979
REFERENCES 1. Griineisen, E., Wiss. Abh. Phys. Tech. Reichsans. 4, 151,237 (1905). 2. Jones, G., and Dole, M., J. Amer. Chem. Soc. 51, 2950 (1929). 3. Jones, G., and Talley, S., J. Amer. Chem. Soc. 55, 624 (1933). 4. Falkenhagen, H., "Elektrolyte," 2nd ed., Hirzel, Leipzig, 1953; "Theorie der Elektrolyte," Hirzel, Leipzig, 1971. 5. Falkenhagen, H., and Dole, M., Z. Phys. Chem. Abt. B 6, 159 (1929); Phys. Z. 30, 611 (1929); Falkenhagen, H., Phys. Z. 32, 745 (1931); Falkenhagen, H., and Vernon, E. L., Phil. Mag. 14, 537 (1932); Phys. Z. 33, 140 (1932).. 6. Korson, L., Drost-Hansen, W., and Millero, F. J., J. Phys, Chem. 73(1), 35 (1969). 7. Stokes, R. H., and Mills, R., "Viscosity of Electrolytes and Related Properties," Pergamon, Oxford, 1965. 8. Drost-Hansen, W., Ind. Eng. Chem. 61(11), 10 (1969); Geophys. Res. 77, 5132 (1972). 9. Wiggins, P. M., Biophys. J. 13, 385 (1973); Clin. Exp. Pharmacol Physiol. 2, 171 (1975). 10. Hurtado, R., and Drost-Hansen, W., "CellAssociated Water," (W. Drost-Hansen and J. S. Clegg, Eds.) Chap. 4. Academic Press, New York, 1979. 11. Home, R. A., and Young, R. P., Electrochim. Acta. 17, 763 (1972). 12. Maatman, R. W., J. Phys. Chem. 71,778 (1967).
Received November 14, 1978; accepted March 1, 1979 High-precision viscosity measurements at 25°C of aqueous solutions of the alkali chlorides-LiCI, NaC1, KCI, RbC1, C s C l - - h a v e yielded new sets of Jones-Dole coefficients for A (0.0063, 0.0062, 0.0057, 0.0047, and 0.0062, respectively) and B (+0.1400, +0.0802, -0.0147, -0.0360, and -0.0511, respectively) based on the standard equation "Or = "O/"O0= 1 + A C lj2 + B ' C . With the apparent exception of LiC1, systematic deviations from the Jones-Dole "limiting law" behavior have been observed for all the salts investigated. It appears that the anomalies are introduced by some spurious effect, most likely caused by structurally modified layers of solution, with different viscosities, at the glass (viscometer)/solution interface. INTRODUCTION
Parts of this study were presented at the 176th American Chemical Society National Meeting, September 11-15, 1978, Miami Beach, Fla. 2 Contribution No. 18, Laboratory for Water Research. To whom correspondence should be addressed. 4 The traditional reference for the Jones-Dole formulation (2) expresses the empirically derived relationship in terms of the relative fluidity qSr 4~r = 1 - A C v2 + B ' C .
- 1 + AC1/2 + B'C. [1] r/0 The coefficient A is a unique constant for each electrolyte which may be calculated from equilibrium theory as demonstrated by Falkenhagen (4, 5). ~ The coefficient B is an empirical constant, qualitatively correlating ion-solvent interactions characteristic for each electrolyte. One of the objectives of the present study was to determine as accurately as possible, within the limits of the best currently available techniques, the A and B coefficients in the Jones-Dole equation for the alkali chlorides. The results presented in this paper are a composite of two independent studies performed over a 6-year period. 9r-
An approximate linear dependence of viscosity (or fluidity) on concentration is observed in the dilute concentration range for aqueous solutions of strong electrolytes. However, at very high dilutions, a departure from linearity--i.e., a characteristic negative curvature--was reported by Grtineisen (1) for all salts irrespective of whether the net effect of the salt is to increase or decrease the viscosity. Jones and Dole (2), extending the Debye-Hiickel theory of interionic attraction, empirically accounted for the linear viscosity-concentration dependence with their formulation (3): 4
[2]
The formulation "Or = 1 + A C 112 + B .C was first pre-
sented by Jones and Talley (3). The equivalency of the two formulations is demonstrated by taking the reciprocal of Eq. [2]. Expressing the equation in terms of the (relative) viscosity, the coefficient A is positive for all salts and B may have either positive or negative values depending on the salt and the temperature. 5 A limiting law, "Or = 1 + A C 112, was derived with application only in the limit of extreme dilution. The coefficient A is identical with the A of the Jones-Dole formulation.
206 0021-9797/79/140206-09502.00/0 Copyright © 1979 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
HIGH-PRECISION VISCOSITY MEASUREMENTS EXPERIMENTAL
1. Reagents
207
i.e., the amounts of water for the stock solut i o n s - w e r e weighed on a Voland 2-kg balance requiring one set of weights, while the weighing of the salt was done on a Mettler balance using standard class S weights.
Two different classes of salts were used for this work. The salts--NaC1, KC1, RbC1, C s C l - - o f analytical grade were recrystallized and oven dried at 120°C for several hours. Also, Suprapur salts (EM Laboratories, E. Merck, Darmstadt, G e r m a n y ) - NaC1, KC1, C s C l - - w e r e used without further purification. The LiC1 used was of analytical grade and, prior to use, was gently heated in a desiccator. The water used in the earlier parts of these investigations was obtained from two sources: a Millipore Super-Q ion-exchange system and a Barnstead still. In the more recent work, the water was obtained from a WS-2 continuous water still modified by attaching an AG-1 Corning Pyrex distillation apparatus directly to the output of the first still. Prior to use, all water was filtered through a Flotronics membrane filter, 1.2tzm pore diameter. No differences could be detected between the flow times for the water resulting from any of the water preparations; thus the results (relative viscosity) have been freely compared. Similarly, no differences in the relative viscosity resulted from using the same salt obtained from different sources. For each salt investigated, stock solutions were prepared by weight with all calculated quantities corrected to vacuum. All other solutions were prepared by dilution (by weighing) of the stock. Corrections were made for buoyancy in air on the weighings of the salts and on the weights of water under the specified conditions of room temperature, relative humidity, absolute barometric pressure on that day, and water vapor pressure. Allowance was also made in the calculations 6 for the differences in the specific densities of the different sets of weights used for weighing. Large m a s s e s - -
Cannon-Ubbelohde suspended meniscus overflow viscometers (constructed of Pyrex glass) with dilution chambers were used for all measurements. The viscometers were slightly modified by providing all access ports with ground glass joints. The positioning of the viscometer was made possible by means of a steel rod to which the viscometer was firmly clamped. Tapered at both ends, the steel rod pivoted in two counter sunk depressions; one being a metal block epoxied to the bottom of the bath, and the other mounted on a heavy swing arm securely rotating around a 2-in.-diameter aluminum post. Vertical alignment of the viscometer was accomplished with a specially machined brass rod equipped with a spirit level which fit into the fill arm of the viscometer. The viscometer was placed in a constant temperature bath with a 5-gallon capacity. 7 The bath was completely insulated with 2 in. of polystyrene foam. Two windows were cut in the insulation for inspection purposes; these windows could be closed if necessary. A lid which securely fit and sealed the top of the bath was fashioned from a polystyrofoam plate (about 1 in. thick). Holes were drilled through the lid to accommodate the connection tubes, stirrer, sensors, cooling coil ports, etc. The stirrer used was a constant high-speed, nearly vibration-free device provided with two sets of horizontal blades. The temperature of the bath was controlled with a Hallikainen Thermotrol. The thermoregulator provided a proportional heat input to offset a constant cool-
6 The detailed calculational procedure is available upon request from the senior author (W.D-H.).
7 For a schematicdrawingof the viscometermounted in the bath, the reader is referred to (6, Fig. 1).
2. Apparatus
Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
208
DORDICK, KORSON, AND DROST-HANSEN
.0600 I
.0500 nr-I
.0400
.0300
.0200
.0100
.,6o
'
.260
.360
'
.460
FIG. ]. J o n e s - D o l e plot for LiCI in the concentration range 5.63 x 10-4 to 1.39 x 10-1 M .
ing load produced by circulating a coolant, maintained at a relatively constant temperature by a Blue M Refrigeration Unit (Model PCC-24A-2) with a cooling coil in a 5-gallon ethylene glycol reservoir. The temperature of the bath was measured with a Quartz Crystal Thermometer (Dymec; HewlettPackard, Model 260A) to 0.0001°C. An electrical-optical system (HewlettPackard) was used to measure flow times. Two light sources and photocells were mounted on the viscometer close to the original fiducial marks. The light sources were mounted on clear plastic spacers which separated the light source from the capillary by approximately 1 cm. This minimized direct and indirect heating effects on the liquid in the capillary. Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
The photocells were operated on a regulated voltage (6 V) from a power supply (Power Designs Inc., Model 2005). The start and stop pulses were fed into HewlettPackard electronic counters, Model 5245L, which functioned as millisecond timers.
3. Methodology The viscometer was cleaned prior to each set of runs with a concentrated sulfuric acid-potassium permanganate solution. The viscometer was filled with the cleaning solution and heated very carefully under the hot water faucet for about 10 min. The viscometer was next rinsed thoroughly with water, then with a dilute hydrochloric acid-hydrogen peroxide solution (to re-
HIGH-PRECISION VISCOSITY MEASUREMENTS
209
.0400 nr-I
JF .0300
.0200
,0100
'
.,6o
'
.zb0
.360
'
.460
F1G. 2. J o n e s - D o l e plot for NaC1 in the concentration range 1.77 x 10 4 to 1.49 x 10-1 M.
move any trace amounts of manganese dioxide), and finally with the (prepared) distilled water. The viscometer was dried via suction, the stream of air going through the viscometer having first passed through a Nucleopore Filter, 1.2-/zm average pore diameter. To initiate a run, the cleaned and dried viscometer was placed in the bath by means of the mounting devices described above. Long-stemmed specially fabricated and calibrated delivery pipets (cleaned in the same manner as the viscometer and initially wetted with the solution of interest) were used to deliver the initial water charge to the viscometer, the amount of which was determined by weighing. Once thermal equilibrium was achieved, the efflux bulb was filled by pressurizing
the filling arm of the viscometer. This was accomplished by blowing air through an Ascarite filter, provided with a glass-wool plug and a porous, fritted disk (to prevent transfer of particulate matter). The air stream was next passed through traps maintained in the same bath as the viscometer. Each trap was lined with filter paper, soaked with water (or, for more concentrated solutions, with the same solution as in the viscometer) to insure water vapor equilibration to minimize concentration changes due to evaporation or condensation. The liquid level in the viscometer was raised to the designated height (the center of the upper viscometer bulb), 8 and the 8 The choice and implications of the "designated height" were fully discussed in Ref. (6, p. 36). Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
210
DORDICK, KORSON, AND DROST-HANSEN
KCI 4-.0100nr-I
+.0050
-.005C
'
.~6o
,zbo
'
.3bo
'
,4bo
F1G. 3. J o n e s - D o l e plot for KC1 in the concentration range 3.37 x 10-4 to 1.34 x 10-1 M.
liquid permitted to fall. The meniscus passed the points at which the light sources and photocells were located, and each cell, in turn, delivered the required start/stop pulses to the counter. After the flow time for pure water (calibration runs) was determined, a predetermined amount of one of the stock solutions was added to the water in the viscometer. The transfer of stock solution to the water in the viscometer was accomplished in the following manner. The pipet was rinsed with a sample of solution 1, for example. It was allowed to drain in a rigidly specified manner: Thirty seconds after the end of discharge, the pipet tip was touched to the meniscus of the liquid rapidly three times. The pipet was charged from a second flask containing stock solution 1. The second flask of stock solution 1 was weighed before and after an approximate amount of liquid Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
had been removed by means of the wetted pipet. The pipet, after having discharged its contents into the reservoir of the viscometer, was lightly touched to the meniscus of the solution in the viscometer three times to reproduce the discharge method used in the first washing with stock solution 1--to ensure the same amount of liquid was retained due to drainage and surface tension effects in the capillary part of the pipet. After equilibration, the solution was raised to the designated level in the upper viscometer bulb and the flow time measured. All subsequent dilutions and runs were performed in an identical manner. RESULTS
Flow times were measured for aqueous solutions of alkali chlorides over the approximate concentration range 10-4 to 10-1
HIGH-PRECISION VISCOSITY MEASUREMENTS
211
straight lines for the J o n e s - D o l e plot (Fig. 2) over the concentration range 1.77 × 10-4 to 1.49 × 10-' M. In this range, the n r -] . calculated B-coefficient, +0.0802, and the ~J A-coefficient, +0.0062, are in good agree0 ment with the literature. H o w e v e r , below the concentration of 5.1 × 10-4 M, a slight, but notable, negative curvature is observed. The data points for potassium chloride, -.005C rubidium chloride, and cesium chloride are depicted graphically in Figs. 3, 4, and 5, respectively. The trends observed are essentially identical for all three salts: Over - .OIOC the concentration range 10-3 to 10-1 M, a linear region is evident. F o r the concentra\ \ \@ tion range below 4 × 10-3 M, a distinct \\ negative deviation is observed from the J o n e s - D o l e limiting law behavior for all .260 .4bo .6oo ,/zthree salts. The A and B coefficients were calculated with only the data points in the FIG. 4. Jones-Dole plot for RbC1 in the concentra- linear region and are summarized in Table I. tion range 6.25 x 10.4 to 2.5 × 10-t M. N o t e that the onset of the systematic deviations increases toward higher concentraM. In order to obtain data as reliable as tion in the sequence NaC1, KC1, RbC1, and possible, experimental techniques were CsC1 as summarized in Table II. designed to optimize temperature constancy DISCUSSION and flow time measurement and reproduciThe precise and highly reproducible bility. The result was that during a given r u n - - a p p r o x i m a t e l y 250 s e c - - t h e flow time experimental techniques of this study have variation was usually within +0.002 sec and yielded new sets of J o n e s - D o l e coefficients the temperature variation within _+0.0003% as summarized in Table I. The effects of surface tension, localized The viscosity data are presented graphiheating, and kinetic energy on the precision cally in Figs. 1 through 5 in classical J o n e s and accuracy of the viscosity data reported Dole plots: ('0r - 1)/C 1/2 vs C 1/2. The coefherein have been examined in detail. N o ficients A and B, the intercept, and the corrections were made for surface tension slope, respectively, of a J o n e s - D o l e plot, effects on the effective pressure head. For were calculated via least-squares analysis very dilute aqueous solutions of electroof the data. lytes, the surface tensions vary so slightly F o r lithium chloride (Fig. 1) the data in that the correction can be neglected (7, p. the concentration range 4.74 × 10-4 to 1.39 19). Furthermore, the use of overflow visx 10 -1 M lie on a straight line with neglicometers is already assumed to minimize gible scatter. The resultant B-coefficient, +0.1400, and A-coefficient, +0.0063, are in the need for a surface tension correction. good agreement with the literature values. 9 H o w e v e r , trace amounts of organic conThe data for sodium chloride result in a taminants might cause measurable surface tension changes in the solution. Noting the extreme care in handling and cleaning the 9 Throughout this article, the literature data referred to are taken from the text of(7), unless otherwise noted. reagents and the apparatus and noting the RbCl
•0050 t
Journal of Colloid and Interface Science, VoL 72, No. 2, November 1979
212
DORDICK, KORSON, AND DROST-HANSEN
+.0500
CsCl qr-1
O
-.0050
-.0100
-.0150
'
'
.2+o
'
'
.4+o
FIG. 5. J o n e s - D o l e plot for CsCI in the c o n c e n t r a t i o n ra nge 2.11 x 1O-a to 1.51 x 10-1 M.
resultant high degree of reproducibility, the possibility of spurious contamination seems unlikely. A possible source of error in viscosity determinations using a photoelectric timing method is radiant and conductive heating from the light sources. No information has been published in the literature pertaining to this problem. To investigate the effects of local heating, a number of runs were made with pure water in which we varied the total time that the light was on. The results are shown in Fig. 6. With increasing "percent time o n , " the flow time decreases and this is attributed to the local heating in the capillary. The maximum difference between "100% light on" and the extrapolated value for "0% light" amounts to 0.038%. The minimal deviations from linearity i n the graph suggest that the changes in flow time Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
are directly proportional to the amount of heating. However, while a decrease of 0.038% is highly significant, both the calibration and actual runs were performed in an identical manner. Therefore, assuming that the heat absorption, heat capacity, etc. of the water and the very dilute solutions are essentially identical, the differences in flow times due to local heating must be negligible. A specific effort was made to test if differences in viscosity could be obtained when including a correction for kinetic energy. This correction utilizes the equation employed in an earlier paper on the viscosity of water as a function of temperature (6, Eq. (4), p. 38). However, it was found that no significant difference resulted from the two procedures (namely, calculations with and without the kinetic energy correction) and
213
HIGH-PRECISION VISCOSITY MEASUREMENTS
TABLE I J o n e s - D o l e Coefficients Experimental
LiC1 NaC1 KCI RbC] CsCI
Literature
A
B
A
B
0,0063 0,0062 ~ 0,0057 a 0.0047 ° 0,0062 a
0.1400 0.0802 -0.0147 -0.0360 -0.0511
0.0065 0.0062 0.0052 0.0049 b 0.0049 b
0.143 0.0793 -0.0140 -0.037 -0.052
E x t r a p o l a t e d from the linear portion of the graph. b C a l c u l a t e d with the equation derived by Falkenhagen and V e r n o n (5).
thus, the majority of the data have been used without corrections. Furthermore, it would seem that as all measurements are relative and made on solutions, the viscosities of which are almost identical in the dilute range studied, this correction ought to be negligible. With the apparent exception of LiC1, highly significant systematic deviations from the Jones-Dole limiting law behavior have been observed for all the salts investigated. It appears that the anomalies are introduced by some spurious effect, most likely caused by structurally modified layers of solution, with different viscosities, at the glass (viscometer)/solution interface. It appears most unlikely that the deviations result from either a failure of the JonesDole equation or from a yet undiscovered property of bulk electrolyte solutions. There exists ample evidence that water proximate to solid interfaces (vicinal water) is structured differently from ordinary bulk water (8). This vicinal water has significantly different solvent properties. For example, Wiggins' (9) results from a study of ion distribution in narrow pores (silica gel), recently extended by Hurtado and DrostHansen (10), reveal highly notable ion-discriminating effects. In a mixture of sodium and potassium chloride, the potassium ions--structure breakers--were selectively accepted by the vicinal water (the water in the pores of the silica gel) over the sodium
ions--structure makers. Also, Home and Young (11), with a series of elution studies, using 80- to 120-mesh silica, on 0.10 M solutions of the alkali chlorides, show a correlation between viscosity B-coefficients and the extent of exclusion of the cations. The structure makers-- Li + and Na + - were found to be more concentrated in the initial eluant samples. These ions are presumably excluded to a greater extent from the vicinal water surrounding the solid particles. A similar B-coefficient correlation with exclusion of the alkali-metal cations from silica gel was reported by Maatman (12). It is evident that the deviations from limiting law behavior tend to increase toward higher concentration (Table II) in the sequence down the group Li + to Cs +. The Cs + ion, having the least charge density and being the least likely to have its own hydration sphere, shows the deviation in viscosity at the highest concentration. Ion partitioning by the vicinal water, which tends to increase the relative concentration of the structure breakers in the vicinal layer, offers a reasonable explanation of the phenomenon observed. It appears that changes in the properties of water may occur over distances of at least one-hundredth, and perhaps as much as several tenths, of a micrometer from an interface. Thus, in the "extreme" case of greatly enhanced viscosity occurring in an annulus of thickness 0.2/zm, the effective radius of the capillary would have decreased from 125 (the approximate radius of the viscometer capillary in this study) to 124.8 T A B L E II C o n c e n t r a t i o n at Which D e v i a t i o n from " L i m i t i n g L a w " B e h a v i o r is O b s e r v e d E (M)
C'/2 LiC1 NaCI KCI RbCI CsC1
0.0225 0.060 0.090 0.095
No deviation 5.1 3.6 8.1 9.0
× × × ×
10 -4 10 -3 10 -3 10-~
Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
214
DORDICK, KORSON, AND DROST-HANSEN
.56'
.54'
"G
~
0.001
UJ k--
T
%
0.01%
256.
0 _] LL
2. Instrumental techniques have been perfected for rapid, high-precision, semiautomatic, and reproducible measurements of viscosities of aqueous electrolyte solutions. The technique permits accurate measurements to be carried out with highly dilute solutions (approximately 10 -4 M). 3. Systematic deviations from JonesDole limiting law behavior were observed for NaC1, KC1, RbC1, and CsC1 in the dilute concentration regime. 4. The deviations most likely result from an interfacial phenomenon, namely, the existence of structurally modified layers of solutions, with different viscosities, at the glass (viscometer)/solution interface. ACKNOWLEDGMENT
256.45 20
40
60
80
I00
The senior author (W. D-H.) wishes to thank the U. S. Environmental Protection Agency for its support of his studies of aqueous interfacial phenomena (EPA Grant R-803826-02).
% of time on
FIG. 6. Effect of "percent light on" (of the light sources for the detectors) on flow time for pure water.
/zm. The ratio of these numbers to the fourth p o w e r - - t h e Poiseuille d e p e n d e n c e - - i s 1.0064. This is a very notable effect compared to the high precision (of the order of one part in 10~ or better) with which the relative viscosity measurements were made in the present study. It is not surprising that very high precision viscosity measurements, using a standard capillary of relatively small radius, should exhibit some spurious effects due to the interfacial properties of the capillary. Therefore, until and unless some additional evidence is obtained, we suggest that the systematic deviations from the Jones-Dole formulation reported in this paper are most likely explained by surface effects. SUMMARY
1. High-precision viscosity measurements at 25°C have yielded new sets of A and B coefficients in the J o n e s - D o l e equation. Journal o f ColloM and Interface Science, Vol. 72, No. 2, N o v e m b e r 1979
REFERENCES 1. Griineisen, E., Wiss. Abh. Phys. Tech. Reichsans. 4, 151,237 (1905). 2. Jones, G., and Dole, M., J. Amer. Chem. Soc. 51, 2950 (1929). 3. Jones, G., and Talley, S., J. Amer. Chem. Soc. 55, 624 (1933). 4. Falkenhagen, H., "Elektrolyte," 2nd ed., Hirzel, Leipzig, 1953; "Theorie der Elektrolyte," Hirzel, Leipzig, 1971. 5. Falkenhagen, H., and Dole, M., Z. Phys. Chem. Abt. B 6, 159 (1929); Phys. Z. 30, 611 (1929); Falkenhagen, H., Phys. Z. 32, 745 (1931); Falkenhagen, H., and Vernon, E. L., Phil. Mag. 14, 537 (1932); Phys. Z. 33, 140 (1932).. 6. Korson, L., Drost-Hansen, W., and Millero, F. J., J. Phys, Chem. 73(1), 35 (1969). 7. Stokes, R. H., and Mills, R., "Viscosity of Electrolytes and Related Properties," Pergamon, Oxford, 1965. 8. Drost-Hansen, W., Ind. Eng. Chem. 61(11), 10 (1969); Geophys. Res. 77, 5132 (1972). 9. Wiggins, P. M., Biophys. J. 13, 385 (1973); Clin. Exp. Pharmacol Physiol. 2, 171 (1975). 10. Hurtado, R., and Drost-Hansen, W., "CellAssociated Water," (W. Drost-Hansen and J. S. Clegg, Eds.) Chap. 4. Academic Press, New York, 1979. 11. Home, R. A., and Young, R. P., Electrochim. Acta. 17, 763 (1972). 12. Maatman, R. W., J. Phys. Chem. 71,778 (1967).