Microrheology of thickened suspensions

Microrheology of Thickened Suspensions1 J. A. DAVIDSON AND E. A. COLLINS B. F. Goodrich Chemical Company, Technical Center, Avon Lake, Ohio 44012

Received May 16, 1975; accepted September 12, 1975 The viscosity of the continuous phase of Carbopol 934 (Carboxy polymethylene polymer; B. F. Goodrich Chemical Co.) suspensions has been measured by recording the diffusion coefficient of codispersed monosized polystyrene latex. The Brownian motion of the latex particles are recorded on cine films from which the mean square of the displacement for a given time interval is obtained by single frame analysis. The viscosity of the suspending media is then calculated using the Einstein equation. Measurements are also reported for water and for aqueous dextrose solutions. INTRODUCTION

Carbopol2 is a unique synthetic carboxymethylene hydrophilic polymer having unusual thickening properties. It has been used widely as a food thickener, in cosmetic formulations, printing inks and pastes, and numerous coating applications. The flow behavior of neutralized Carbopol 934 is described as shear rate thinning with a high yield value. Typical flow curves are shown in Fig. 1 (0.5 and 1.0% by weight C 934 neutralized with NaOH). In general the high viscosity that one obtains with Carbopol or other synthetic and natural hydrophilic polymers has been qualitatively explained by one or more of several potential mechanisms which include electrostatic repulsions of hydrophilic groups along the chain backbone, network formation, or physical entanglement of rigid chains. Very few morphological studies have been reported on this class of materials. This work was undertaken to establish the mechanism of thickening of Carbopol 934. The concentration dependence of the viscosity of Carbopol 934 previously reported (1)

shows a rapid drop in viscosity when a critical concentration is reached upon dilution of a 1% muscilage. This is consistent with a two phase system suggested by Bagley (2). One phase, the continuous phase, is believed to be mostly water, and the second or discontinuous phase is believed to be a highly swollen gel. Figure 2 shows a dark field micrograph of a Carbopol suspension before and after neutralization, illustrating the microstructure of the swollen gel. The measurement of the viscosity 1750

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1050 875 r Lt.~W CURVE FOR CARBOPOL 9 3 4 NEUTRALIZED WITH NoOH

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1 Presented at the 49th National Colloid Symposium, Potsdam, New York, June 15-18, 1975. Registered trade mark B. F. Goodrich Chemical Company.

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Copyright O 1976 by Academic Press, Inc. All rights of reproduction in any form reserved.

Journal of Colloid and Interface Science, Vol. 55, No. 1, April 1976

164

DAVIDSON AND COLLINS

Carbopol Suspension pH = 7.4

.1%

Carbopol Suspension pH -- 2.5

.1%

FIG. 2. Dark field photomicrographs of Carbopol 934 suspensions.

of the continuous phase was accomplished by direct measurement of the diffusion coefficient Of spherical polystyrene latex particles suspended in a Carbopol muscilage. HISTORICAL

In 1826 Brown (3, 4) noted through the microscope the irregular motion of pollen grains suspended in water. This irregular motion is due to the impingement of water molecules against the pollen grains and is known as Brownian motion. In 1906, Eilastei n (5) showed that spherical particles of' radius (r) suspended in a media of viscosity (7) obeyed the following relationship RT A, ~ = 2Dr =-N

where sional (sec); stant;

t ,

[17

31r~r

A2-----mean square of the one-dimendisplacement (cm~) in time interval, t D = diffusion constant; R = gas conT = absolute temperature; N = Avo-

Journal of Colloid and Znlcr/nce 5cience, VoL 55. No. 1, April 1976

gadro's number; ~ = viscosity, poise; and r -- particle radius, cm. The validity of this expression has been experimentally verified by a number of investigators (6-9). Clearly, if the size of the particle is known, then a measure of A,2 will yield the viscosity of the media. In 1925, Kraemer (10, 11) measured the Brownian motion of gel suspended 200-250 #m mercury particles, to study the structure of clarified gelatin gel. He also investigated dibenzoyl cystine gel. He concluded that Brownfan motion in gelatin gels was prevented above 0.5% but did exist in gels as concentrated as 0.3%. The dibenzoyl cystine gel had a fibrous structure with the viscosity of the media between the fibers being the same as before gel formation. Early investigations (10-12) were hampered by a lack of adequate particle size data on the suspended particles and a lack of high speed photographic films for recording the Brownian motion. The last decade has seen the development and characterization of the Dow mono-

MICRORHEOLOGY OF SUSPENSIONS disperse polystyrene latices and the marketing of the high speed cine films needed to carry out investigations of this type. Recently Vados et al. (13) made extensive cine-micrographic studies of the microrheology of 2/zm latex spheres in Poiseville flow using a novel microtube device. The flow using particles in capillaries as small as 50 #m was studied using their apparatus. This work demonstrates the practicability of the study of individual colloid particles and their interactions with the surrounding media. EXPERIMENTAL The general procedure employed in this study was to (1) make up a C-934 suspension containing a small amount of monodisperse polystyrene latex; (2) photograph at 48 fps on 16 mm black and white film the Brownian motion of the latex particles; (3) double print the black and white originals on color stock. The result of this double printing was that each particle on the print was represented twice, once in red and once in green, with the displacement of the red and green images representing a fixed time interval; (4) measure the displacement between the red and green image on each frame for a large number of particles to enable one to compute A2 in Eq. [1~; and (5) solve Eq. [1~ for the viscosity of the media. In addition to measuring X displacement, the maximum displacement in any direction also can be computed. This maximum displacement was often larger and thus easier to measure than X. As was mentioned previously, a latex or colloid of accurately known particle size is required for use in studies of this type. The Dow Monodisperse latex LS-061-A was chosen for this work because its particle size has been measured in a number of laboratories, and also, it was large enough to be easily photographed on Kodak 4X cine film using readily available cine-micrographic apparatus. A number of different determinations of the particle size of the latex used is listed in Table I.

165

TABLE I Particle Size of Dow LS-061-ALatex by Various Investigators Method

av diam

Investigator

"(D~v /*m)

Electron microscope Electron microscope Light scattering Optical arrays

0.365 0.336 0.339 0.343

Dow B.F. Goodrich Dezelic (14) Davidson and Collins (15)

For this study a value of 0.340 /~m was employed. Carbopol 934 suspensions were prepared in the normal manner (15) and the pH adjusted to about 9.0 with ammonia. Since the viscosity of a Carbopol suspension is nearly independent of pH over the range of about 7-11, no special precautions were taken. A small amount of Dow LS-061-A polystyrene latex was transferred on the tip of a needle and mixed with about 1 cm 3 of the Carbopol muscilage. A small portion of this muscilage was then transferred to a specially cleaned microscope slide covered with a No. 1½ coverslip, and the preparation was then sealed with asphaltum. The amount of latex added to the Carbopol suspension was just sufficient to give a field containing perhaps 25-100 particles at the magnification employed. The latex particles were photographed using dark field illumination. A Bausch and L o m b Cardioid Condenser was employed in conjunction with either a Bausch and Lomb 47.5X 0.95 NA or a Zeiss 60X 1.00 NA Apochromat. The use of a 5X eyepiece gave magnification of the 16 mm film of 57X and 72X, respectively. The magnification was determined exactly using a stage micrometer. An Airiflex 16-S 16 mm camera (180 ° shutter) was employed to record the Brownian motion on Kodak 4 X reversal cine film. This fihn, with an ASA speed of 320, enabled the use of a 60 W lamp for the microscope light source. The use of as low a wattage lamp as is practical is recommended to minimize heating effects. Films were shot Journal oJ Colloid and Interface Science, Vol. 55, No. 1, April 1976

166

DAVIDSON AND COLLINS

at 45 to 48 fps, the exact framing rate being noted on the tachometer on the camera. After processing, the films were double printed on color stock. In this procedure the film was first printed using red light. The original was then advanced a specified number of frames (usually 20) and printed again using green light. The result was a color print that represented each particle twice, once in red and once in green as it appeared 20 frames later. Thus, by merely measuring the distance between red and green images, the movement in unit time could be computed. A check of a stationary object, such as the stage micrometer, indicated that there was no printing misalignment. The displacements on the film were measured using a filar micrometer and a magnification of 100>(. Usually about 100 different displacements representing perhaps 25-50 particles were measured. Only single latex spheres were measured with no other latex or Carbopol gel particles in the vicinity. Dark Field Resolution It is impossible to make a statement about the resolution of any optical system without making or assuming some statement with respect to image contrast. Furthermore, the measured object must be relevant to the problem at hand. Thus, resolution criteria derived for ruled gratings would not be applicable in the case of latex particles. A submicron latex particle viewed in dark field may be considered a self-luminous point giving rise to a diffraction disc in the image plane (17). If we consider two equal size latex particle and choose a distance of separation equal to the diffraction disc diameter arising from each, the "resolution" by this criteria is: 1.22k Do =

,

[-2]

NA where N A = numerical aperature of the objective and Do --- diameter of diffraction disc. For the optics employed in this study, Do = 0.6100/am (k = 0.5000 #m). Journal of Colloid and Interface Science. Vol. 55, No. I, April 1976

A more generally accepted contrast criteria is that resolution is still possible when the diffraction discs overlap to the extent that the intensity maximum of one disc falls on the first minimum of the adjacent disc. The resolution in this case is: 1.22k

e = --, 2NA

I-3]

where R = resolution = radius of diffraction disc, or ~0.3000 for the optics employed in this study. However, this analysis makes no attempt to include how the photographic film will record the theoretically calculated intensities. The size of an Airy point recorded on photographic film reflects the intensity of light from that source. This effect has been used to measure the size of submicron latex particles by dark field microscopy since a dark field microscope may also be considered a single particle photometer and its response calculated from light scattering theory (18). Thus, by measuring the size of the Airy points as recorded on photographic film, it is possible to relate this quantity to the particle size of the individual colloid particle as viewed in the dark field microscope. By the use of the double color printing technique here described, it is possible to detect and measure movements of particles well below the lower limits as predicted by Eqs. 2 and 3 since these equations do not provide for the contrast enhancement mechanism of double printing. Thus, displacements as small as 0.1 #m can be measured easily. The dark field microscope can simultaneously give information about particle size and very small displacements of individual colloid particles. RESULTS

1. Dextrose Solutions To check the validity of this method, the viscosity of a number of dextrose solutions was measured. The same dispersion technique described for Carbopol was used.

MICRORHEOLOGY OF SUSPENSIONS TABLE II

1.5

Diffusion Coefficient (cm~/sec) of 0.350 #m Latex Spheres In Dextrose Solutions at 24°C

1.4

Dextrose (wt%)

Viscositya (poise)

Measured diffusionb coefficient (cm2/sec)

0 9.11 X 10-3 1.357 >( 10-8 9.67 11.9 X i0 -3 1.151 X 10-8 27.08 22.9 X 10-~ 0.715 X 10-8 0.377 X 10-8 42.33 54.1 X i0 -~ 0.473 X 10-s 49.33 91.7 X 10-3 0.222 X 10 -8

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2 .4 a Extrapolated to 24°C from NBS data (19). b This work. I n Table II, the values of the diffusion coefficient obtained experimentally are presented. In Fig. 3, a plot of diffusion coefficient versus (viscosity) -1 is presented along with a line predicted by the Einstein equation for a particle 0.340 #m in diameter. As can be seen, except for water, all of the experimental values tend to be larger than predicted by the Einstein equation. An obvious answer to this lies in the rather steep decrease in the viscosity of dextrose solutions with temperature. At a concentration of 42%, an increase of 10°C would reduce the viscosity by about 26%. However, the differences are still larger than can be accounted for on this basis. I t was found that a plot of log maximum displacement versus viscosity yields a straight line (Fig. 4). This curve was used as a calibration curve in the empirical method.

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LS-061-A. These authors obtained a value of 1.344-0.004 X 10-s cm~/sec by employing laser heterodyne beat spectroscopy. While the viscosity of water calculated with Eq. [ 1 ] for both our data and that of Dubin is slightly higher than the accepted literature value, the agreement is really quite good considering the difficulty of making measurements at very low shear rates (ca. 1.4 X 10--a sec-1) and the differences in the two techniques employed.

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AVERAGE MEAN MAXIMUM DISPLACEMENT VERSUS VISCOSITY DEXTROSE SOLUTIONS, 24"C

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The repeatibility of the method can be seen from the determination of the viscosity of water shown in Table I I I . The average value of our results for the viscosity of water lies slightly above the accepted literature values. Also of interest is the determination of the diffusion constant by Dubin et at. (20) of a "monodisperse polystyrene latex" of a diameter of 0.366 #m, which is probably D o w

to

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Journal of Colloid and Interface Science, VoL $5, No. 1, April 1976

168

DAVIDSON AND COLLINS TABLE I I I

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Viscosity of Water as Determined by the Diffusion of Latex Spheres~

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t /

35

Trial No.

Diffusion constant (cm2/see)

~ calc f r o m Einstein Eq. m p b

Operator

.~Z5 CARBOPOL 934 CONCENTRATION

~ 20

1 2 3 4

1.592 )< 10-8 1.358 X 10-s 1.125 )< 10-a 1.338 X 10-8 av = 1.353 >( 10-s =0.19 )<10 - s

8.06 9.45 11.41 9.60 av = 9.6 .= 1.4

1 2 2 2

0

N

The viscosities of the aqueous phase of neutralized Carbopol 934 suspensions are given in Table IV. T h e y are plotted in Fig. 5 versus concentration. Also listed in Table I V are the mucilage viscosities (7 Bulk) for the Carbopols a t the concentration listed. T h e empirical m e t h o d was based on a direct comparison of the m a x i m u m mean displacem e n t with Fig. 4. As can be seen, the water phase viscosity accounts for only a small fraction of the total observed viscosity. This small increase over the viscosity of pure water is p r o b a b l y due to the presence of some slight a m o u n t of t r u l y

A

VERSUS VISCOSITY OF THE A Q U E O U S PHASE

I0 . 3 ~ C- 934 - 94.26 mp I A

I .2

I .3 CARBOL~31_ CONCENTRATION

FIGURE 5

Latex particle size D = 0.340 tzm. Dow LS-061-A polystyrene latex 24°C. b ~ H20 (NBS) std = 9.11 mp 24°C. 3. Carbopol 934

[3 TRIAL 2

/

EMPIRICAL CALC FROM EINSTEIN THEORY CALC FROM EINSTEIN THEORY

soluble polymer. However, the viscosity of a carbopol muscilage is due p r i m a r i l y to the discontinuous or dispersed phase. A plot of viscosity of the continuous phase versus concentration is shown in Fig. 5. As can be seen, there is an increase in aqueous phase viscosity with concentration. T h e v e r y high value obtained at a concentration of 0.3% is p r o b a b l y due to physical trapping of the latex particles r a t h e r t h a n a n y increase in the continuous phase viscosity. Thus, at about 0.3%, the swollen particles appear to be physically in contact with little or no free space between them. ACKNOWLEDGMENT The authors wish to express their thanks to B. Y. Goodrich Chemical Company for permission to publish this work.

TABLE IV Carbopol Viscosities at 24°Ca

REFERENCES Concentration

Brookfield viscosity No. 2 spindles (5 r p m p H = 7-8)

0.05 0.10 0.10 0.20 0.20 0.20 0.30

108 1200 1200 108 000 108 000 108 000 368 000

Aqueous phase

11.4 19.0b 16.5 25.0 b 17.8 27.8 94.2

Operator

2 2 1 2 2

Computed from Einstein Eq. except where noted (mp). b Empirical method based on dextrose solution viscosities (see Figure 4). Journal of Colloid and Interface Science, Vol. 55, No. 1, April 1976

1. MEYER, R. J. AI~D COHEN, L., J. Soc. Cosmeli, Chem. 10, 143 (1959). 2. TAYLOR, N. W. AND BAGLE¥, E. G., J. Appl. Polym. Sci. 18, 2747 (1974). 3. BROWN,R., Philos. Mag. 4, 101 (1826). 4. BROWN,R., Philos. Meg. 6, 161 (1829). 5. EINSTEIN, A., Investigations on the Theory of Brownian Movement (R. Furth, Ed.) Dover, New York, 1956. 6. PERRII%J., J. Phys. Paris 9, 5 (1910). 7. DE BROGLIE, C. R. Acad. Sci. Paris 148, 1315

(1909). 8. FLETCHER,I-I., Phys. Re*. 4, 440 (1914). 9. WESTGREI'r,A., Z. Anorg. Allgem. Chem. 93, 231 (1915).

MICRORHEOLOGY OF SUSPENSIONS 10. KRAEMER, E. 0., Y. Phys. Chem. 29, 1523 (1925). 11. KRAEm'ER, E. O., 2nd Colloid Symposium Monograph, p. 70. American Chemical Society, 1925. 12. LtrcAs, F. F., Ind. Eng. Chem. 34, 1371 (1942). 13. VADOS, E. B., GOLDSMITH, H. L., AND MASON, S. G., J. Colloid Interface Sci. 43, 630 (1973). 14. DEZELIC, G., DEZELIC, N., AND TEZAK, B., J. Colloid Sci. 18, 882 (1963). 15. DAVIDSON, J. A. AND COLLINS, E. A., J. Colloid Sci. 40, 437 (1972).

169

16. Carbopol Service Bulletin GC-36, B. F. Goodrich Chemical Company. 17. ZmLER, H. W., "The Optical Performance of the Light Microscope," Microscope Publications, Chicago, Illinois, 1973. 18. DAVIDSON, J. A. AIqD HALLER, S., J. Colloid Interface Sci. to appear. 19. International Critical Tables 5, 10 (1929). 20. DUBIN, S. B., LUNACEK, J. H., AND BENEDEK, G. B., Proc. Nat. Acad. Sci. U.S.A. 57, 1164 (1967).

Journal of Colloid and Interface Science, Vol. 55, No. 1, April 1976