Oct., 1962
ADSORPTION-FLOCCULATION REACTIONS OF A
POLYMER
1835
THE ADSORPTION-FLOCCULATION REACTIONS OF A POLYhIER WITH AN AQUEOUS COLLOIDAL DISPERSION BY THOMAS W. HEALY AND VICTOR K. LA MER Depurtnaent of Chemistry, Colunabia Un,iversity, A-ew York, N . Y . Received March 6,1968
The theoretical equations for the stability of suspensions in the prefience of polymer flocculaiits have been extended to include two variables previously held constant, viz., the number of segments per polymer molecule, T , and the number of these which adsorb and cover surface sites, p. The “extended segment” model of polymer adsorption, together with the “bridging” model of polymer flocculation, is described in terms of an adsorption parameter and in terms of p and ( T - p ) , where ( T - p ) is the number of extended segments per polymer molecule. The solid-polymer aqueous system studied was calcium phosphate-polyacrylamide and variables examined were polymer concentration, polymer molecular weight, and the time of agitation.
Introduction The phlenomenon of polymer flocculation can best be analyzed in terms of: 1, the adsorption process, and 2, the flocculation process. The theoretical and experimental work on the adsorption process, e.g.lI2is a t present of a preliminary nature, particularly for the case of aqueous systems. It seems probable that when a polymer molecule concentrates at a solid-liquid interface, only a fraction of the total segments per molecule adsorb and cover surface sites. The remainder of the molecule protrudes into the surrounding medium a s an extended ~ e g m e n t . There ~ ~ ~ is an obvious simplification involved in this description, since the polymer molecule is more or less coiled a t the interface, and contact between the polymer molecule and the surface can be made at any number of points along the molecule. Nevertheless, the description in terms of extended segments does allow 11s to explain much of the second topic above, uiz., the flocculation process, e,g.hs6. Since the work of Smellie and La Mer on the filtration of slimes flocculated with was ~ummarized,~ little new work has been reported on the mechanism of the flocculation process. I n the present paper we extend the work of Smellie and La Mer8 to include certain important variables previously held constant, vix., molecular weight of the polymer and the conditions of agitation of the suspension. Theoretical In their treatment of the adsorption process in the flocculation of suspensions, Smellie and La Mer proposed that the decrease in bulk concentration of polymer due to adsorption is equal to the number of solid surface sites covered, (eq. 2, ref. 8). This is true only if every segment per polymer molecule covers a surface site. As pointed out in the introduction, it, is probable that only a fraction of the segments per molecule adsorb and cover surface (1) R. Simha, H. L. rrlsch, and F. R. E m r h , J . Phys. Chem., 67, 584 (1953). (2) R. Perkel and R Ullman, J. Polymer Scz., 64, 127 (1961). (3) S. Elleraitoin and R. Ullman, abzd., 66, 123 (I9Gl). (4) B. J. Fontana and J. R. Thomas, J. Phys. Chem., 66, 480 (1961). ( 5 ) W. E’. Llnke and R. B. Booth, Trans. A I M B , 217, 364 (1960). (6) T. W. Healy, J . CoZZozdSci., 16, 609 (1961). (7) V. K. La Mer, R. H. Smellie, Jr., and P. K. Lee, ibnd., 12, 230 (1957). (8) R. H. Smellie, Jr., and V. K. La Mer, Tbzd., 13, 5S9 (1958). (9) V. K. La Mer and R. H. Smellie, Jr., “Proc. 2nd. Internation,tl Conference,” Geneva, 1958, p. 178; 888 also Clays Clay Mzneralr, 9 , 295 (1062).
sites. For later purposes, it is necessary to include the parameter p in deriving the filtration equations, where p is the number of segments that adsorb per molecule of polymer. Suppose (Po .- P ) moles of polymer concentrate a t the interface, where Po is the initial or added concentration of polymer, and P is the residual polymer concen trakion in solution after adsorption. Then (Po - P ) N molecules concentrate at the interface, where N is Avogadro’s number. Since each polymer has T segments, then (Po - P ) N T segments concentrate a t the interface. If a fraction P / T absorb and cover surface sites, then P(P0 -
= number of surface sites covered
7
$.e,,
-
SS”
‘)Iv
L=
e
= fraction of surface covered
where s is the number of sites/unit area of surface, and Sois the surface area of solid. Note that it has been assumed that a surface site is equal in area to a polymer segment (see e.g., ref. 1). Rearranging
whcrc sso 1‘ = --
N Equation 1 above may be compared to eq. 2 of Smellie and La Mer.* The subsequent equations of ref. 8 may then be modified to include p. For example, eq. 21, ref. 8 becomes
where (3)
THOXAS 'CV. HEALY - 4 m VICTOR K. LA MER
1836
where C is a constant. Similarly by setting dQ/ dPo = 0, a t Po = P, as in ref. 8
__ (1 -
+ bVPIZ b
(6)
'O
Experimental An assembly similar t o that previously describedl0 was used to obtain filtration rates. A technique of mixing the polymer solution with the suspension, agitation of the suspension, and filtration, was developed, such that identical suspensions did not differ in filtration rate by more than 3y0. .4gitation of the suspension was carried out with a magnetic stirrer assembly set a t a fixed degree of intensity for all the results reported. Fresh calcium phosphate suvpensions of 3% by weight of solids in distilled water were used to obtain each individual filtration rate. The calcium phosphate (tribasic) was Fisher A.R. grade reagent and the particles had an average radius of approximately 10 p. We are indebted to the Cyanamid Co. for furnishing samples of polyacrylamide having molecular weights, determined by viscosity measurements, of 0.5 X 106, 1.0 X loe, 3.0 X lo6, and 5.3 X IOe.
Vol. 66
r--t
8 n
a" I
4
Smin. in.
4,
2min.
\
2-
Results The curves for filtration rate vs. concentration of polymer were of the same type previously obI c ~ e r v e da, ~ typical set being shown in Fig. 1. These 20 40 60 ao PO . curves may be characterized by Qm, the maximum Fig. 1.-Variation of filtration rate (& - Qo)in cc./sec. filtration rate for a given set of conditions, and P m , the concentration of polymer to attain that as a function of polymer concentration (Po), expressed as x 10-1o/g. solid for 3% Cas(P04)zsuspension in the maximum filtration rate. Both Q m and P , mole presence of polyacrylamide (mol. wt. = 1 X lo6). change with the following variables : molecular weight of the polymer ( M ) , time of agitation (t), intensity of agitation ( A ) ,and the surface area of the solids (SO). I n this discussion we restrict ourselves to a consideration of the effect of molecular weight and time of agitation. The effect of surface area has been well discussed.11 Intensity of agitation is an important variable, but one that is difficult to specify precisely. It should be referred to the shear stress at the site or sites of polymer-solid contact. It has been suggested6 that for a polymer molecule to remain attached at the surface, a critical number of polymer segments must be adsorbed, and the extent to which this is achieved depends on the shearing forces at the solid-liquid interface. I n general, for a given initial or added concentration of polymer, the amount adsorbed after a given time decreases as the intensity of agitation increases.E The variation of Pm,the optimum concentra,tion of polymer, with molecular weight and time of agitation is shown in Table I. I n Fig. 2 the value of Qm is plotted as a function of the molecular weight for three times of agitation. It is obvious from these results that the variation of P m and Qm with ill is a complex process. It is thought that a more meaningful analysis of the data can be obtained from eq. 2 and 3. The applicability of these equations is shown in Fig. 3 where the quanI - Qo)'/*is plotted as a function of tity Po'/%/(& M. 4 6 I
(10) V. K. La Mer and R. H. Smellie, Jr., J. Collozd Sci., 11, 710 (1956). (11) V. K. La Mer, R. H. Smellie, Jr., and P. K. Lee, zbzd., 12, 566 (1957).
Fig. 2.--Variation of the optimum filtration rate (cc./sec.) as a function of molecular weight ( X 10-9 a t three times of agitation, 2 min., 5 min., and 10 min.
Oct., 1962
ADSORPTION-FLOCCULATIOS REACTIONS OF
2b
oo-
60
40
I
80
P.
Fig. 3.-Liiicar plot of eq. 2 for a t h e of agitation of 5 min. for polyacrylamide samples of molecular weight 5.3, 3, I, .0.5 million, respectively ( P o 5 mole X lO-lO/g. of solid).
Po,for four values of M and at a fixed timc of agitation. Similar sets of curves are obtained a t other times of agitation. The values of the intercept AM of eq. 4 are listed in Table 11. VARIATIONOF P ,
WITH
TABLE I MOLECULAR WEIGHTAND TINEOB AGITATION
M ( X 10-9
0.5 1.0 3.0 5.3
VARIATION CISA , x
M (10-6)
0.5 1.0 3.0 5.3
7 -
2
100 25 4.7 1.o WITH
t (min.)
7
5
10
66 22 6 1.1
160 31 8 3.3
TABLZ I1 MOLECULAR WEIGHTAND TIMEOF AGITATION r___-
2
3.9 2.8 1.5 0.4
t (min.)----6
3 4 1.5 1.0 0.3
10
5.0 2.9 1.2 0.4
Preliminary adsorption measuremenis for this present system12have provided the following information. (1) Adsorption follows the Langmuir relationship. (2) The b value of the Langmuir equation decreases with increase in molecular weight ( M ) of the polymer and with increasing time of agitation (t). (3) The adsorption measurements were not sufficiently accurate to check the change in p with change in M and t. However, these changes in p were generally small compared to the change in b. Discussion Effect of Polymer Concentration.-The optimum effect shown in Fig. 1 has been considered by several workers and is best understood in terms of a model of polymer flocculation involving “bridging” between adjacent solid particles by extended poly-. mer segments. As a first approximation the bridging hypothesis has proved useful. I n brief, it is postulated that the degree of flocculation (as measured by the filtration rate in this paper) at (12) L. Jankovioa, Ph.D. Dissertation, Columbia University, 1961.
A
POLYMER
1837
any particular concentration of polymer depends on: (a) the length and number of extended segments, and (b) the available surface onto which extended segments can bridge. As polymer adsorbs, the number of extended segments increases, but at the same time the free surface area is decreasing. I n terms of the parameters 7, the total segments per polymer molecule, and p, the number that adsorb and cover surface sites, it is further proposed that as more and more polymer is adsorbed, each incoming molecule finds progressively less and less surface onto which it can attach; Le., as Po increases, for a given molecular weight, p will decrease to a constant value determined by the conditions of agitation. The constant value may be thought of as that critical number of segments per molecule that must be attached, under a given condition of shear, for the polymer molecule to stay adsorbed.6 Effect of Molecular Weight.-The Qm - M behavior of Fig. 2 may also be a result of two competing processes. From the data of Jankovics,12 b decreases with increasing molecular weight. As a first approximation, and by analogy to the Langmuir treatment, b is proportional to the ratio of the forward to reverse reaction rate constants for adsorption. For the present system, high molecular weight polymer reacts less extensively with the surface than does low molecular weight polymer. On the other hand, since p is changing only slightly, (7 - p) must be increasing rapidly with increase in M . The situation described previously as “steric” stabilization may thus result.la The extended segments in the case of the high molecular weight polymers may reduce the distance of closest approach between adjacent particles to an extent where their thermal energy may be in excess of their negative potential energy.14 The maximum in Q m with increasing M , Fig. 2, can be described in terms of an increase in ( 7 - p), which a t first favors bridging (Qm increases), but which at high M leads to “steric” stabilization and consequently a decrease in Qm. Effect of Time of Agitation.-Consider a floc linked together by polymer bridges. It has been suggested that with prolonged time of agitation extended segments can curl back, adsorb on solid sites, and cause a contraction oi the floc (contraction). Due to the reduction in bridge lengths in this process, the floc is less resistant to shear and will begin to break up. At the break-up of flocs, new surface is exposed, allowing further adsorption of polymer (redispersion). A third effect of time may be termed a redistribution reaction. Upon addition of the initial polymer solution to the dispersion, there may be regions of local excess coiicentration. Improved flocculation will result from distributing these local excesses. The redistribution, contraction, and redispersion reactions, as defined above, may be thought to have the following independent effects. 1. Redistribution: KO change in b or p but an increase in (& -- Q0) due to more efficient floc formation. (13) W.Heller and T. L. Puph, J . Chom. Phys., 24, 1107 (1956). (14) W. Heller and T . L. Pugh, J . Polymer Sci., 47, 203 (1980).
1838
THOMAS W. HEALYAND VICTORK. LA MER
2. Contraction: Increase in b and p, decrease in 0)and hence decrease in floc size and filtration rate. The increase in b also reduces bridging, 3. Redispersion: Increase in b, probably no change in p. As more surface is covered (Q - Qo) will decrease. The appearance of an optimum time of agitation can be understood in terms of these reactions. With prolonged time of agitation, contraction follows redistribution, and redispersion then follows contraction, so that Qm first increases, passes through a maximum determined by the molecular weight and the intensity of agitation, and then finally decreases. The variation of filtration rate with Po, 1111, and t is thus a three-dimensional surface with sections of the form of Fig. 2, the maximum filtration rate and hence the maximum flocculation for the system being determined by Po, M , and t, or formally: maximum in (Q - Qo) for the system occurs a t Po = P m for M = M o and ~ t = top. I n view of the complex nature of polymer adsorption-flocculation phenomena, it is felt that a more meaningful approach can be found by the use of eq. 2 (see Fig. 3). Sets of data in the form of Fig. 3 have been reproduced and except for the low concentration region, the equation has been found to have wide applicability. Variation of Pm with M and $.--The effect of change in molecular weight and time of agitation on the optimum concentration of polymer is considerable. In eq. 6 (7
-
since b decreases with increase in molecular weight,12 the numerator of the equation must decrease to a greater extent than b decreases with increase in molecular weight. This may be controlled by both b and p in the numerator, and to explain the P , - M dependence dp/dill must be positive, It is probable that the factors of redistribution, contraction, and redispersion affect P m in much the same way as they affect (Q - Qo). Further analysis of Pm in terms of b, p, and ( T - p) is in progress. Concluding Remarks It has been inferred that b is related to the ratio of rate constants for adsorption of polymer. At present this is an oversimplification, for it is not certain which reaction of polymer at the interface is described by this ratio. This question has been examined recently by Peterson and Kwei1l5 who like several other groups of workers found agreement of experiment with the Langmuir equation for polymer adsorption. Nevertheless, b can be thought of in terms of an extent of adsorption o i polymer a t the solid-liquid interface. We have endeavored to point out that the adsorption reaction parameter, b, the number of segments adsorbed per polymer molecule p, and the number of extended segments per adsorbed molecule (. - p) are the coritrolling factors in determin(18)
C. Peterson and T.I
