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Mechanical and surface coagulation
Mechanical and SurFace Coagulation IV. Prevention of Mechanical Coagulation by Surface-Active Additives WILFRIED
H E L L E R AND J A M E S P E T E R S t
Department of Chemistry, Wayne State University, Detroit, Michigan 48202
Received June 29, 1970; accepted September 23, 1970 Previous investigations had established that a colloidal solution of hydrophobic particles becomes subject to mechanical coagulation if its stability--as measured by its behavior towards coagulating electrolyte~is reduced sufficiently. It is now shown that the reverse applies also, i.e., a sol, subject to mechanical coagulation, cannot be coagulated by stirring, shaking, or by gas bubbles if its natural stability is increased sufficiently. The increase is brought about, in the present work, by the addition of moderately surface-active agents. If the latter promote foam formation, mechanical coagulation will be inhibited only at higher stabilizer concentration, whereas, at low ones, the effect of an increase in the water-air interface predominates and leads to a promotion of mechanical coagulation. An increase in sol stability is not the only possible method for preventing mechanical coagulation. Additives which reduce the population density of the colloid in the water-air interface also produce immunity to mechanical coagulation. An example is given. Moreover, the various possibilities of explanation existing for both the latter and former type stabilization against mechanical coagulation are discussed. I. INTRODUCTION Evidence has been accumulated in a series of papers (1) to the effect t h a t mechanical coagulation produced by conventional stirring or shaking or b y bubbling gases through a suitable colloidal solution represents a surface coagulation if, in absence of these treatments, the systems exhibit a considerable shelflife. Since a coagulation at the water-air surface is necessarily sensitive to the state of the surface and to changes occurring in it, complications in mechanical coagulation can be anticipated in the presence of additives which affect the state of this surface a n d / o r the distribution of the colloid between bulk and surface. One can therefore anticipate t h a t mechanical coagulation m a y be either promoted or hindered b y suitable additives, if present in the p r o p e r conceniration, even in those cases where they m a y Present address: The Dow Chemical Com,pany, Midland, Michigan.
not affect significantly the bulk stability of the system. The present paper represents an exploratory investigation of these effects, considering the simplest possible case, viz., t h a t of addition of nonionogenic substances. lI. EXPERIMENTAL The System Investigated. A single colloidal solution of a - F e O O H was used for the entire investigation. I t had already been used previously (sol C) (1 (a)). A few of the pertinent characteristics m a y be repeated here: colloid concentration 370 mg Fc/1, p H 6.5, coagulation value, "y: 3-4 mmoles of K C ] / I of sol (2 hours, room temperature). The Additives Used. One of tile surfaceactive additives used was N , N - d i m e t h y l - n dodecylamine oxide, to be referred to as D D A 0 . I t was selected because a dilute solution does not lead to foam formation on stirring. Therefore, complications of a foam-produced increase in the air-liquid surface area b y stirring relative to t h e
Journal of Colloidand Inter'faceScience,Vol.35, No. 2, February197I 3OO
MECHANICAL AND SURFACE COAGULATION. IV surface area generated in absence of the additive were excluded. A stock solution of D D A O , having a concentration of 0.2 g m / 100 ml of double distilled water, or volumetric dilutions of it were used. The concentration of D D A O in the sol samples was varied b y adding to 5 ml of colloidal solution both a D D A O sohltion of suitable concentration and double distilled water, so as to bring the total volume of the sample up to 6.0 ml? The second surface-active additive used was polyethylene glycol of molecular weight 9,0002 This additive will be referred to as P E G . I n order to remove impurities, the polymer was dissolved in reagent grade acetone, filtered, repreeipitated with redistilled hexane, then washed with redistilled ether, and, finally, an aqueous solution of this purified polymer was dialyzed for 70 hours in a high-efficiency dialyzing apparatus. 4 The aqueous solution thus obtained exhibited a conductance of 1.74 × 10-~ a - t em -~, at a concentration of 1.986 gm P E G / 1 0 0 mh The excess of this conductance over t h a t of conductance water was too small to be of significance for the present work. ~
Determination of the Concentration of Colloid and Additives. The concentration of the colloid was determined as in the preced2 The crystals of DDAO used in the present work were kindly provided by Dr. N. A. LaBel of the Chemistry Department of Wayne State University. 3 This material was kindly provided by the Dow Chemical Company, Midland, Michigan. 4 The rabio (sol-membrane interface area/sol volume) for the thin layer of sol contained between two circular cellophane membranes clamped, together with rubber gaskets, onto two fast rotating horizontal metal rings, was approximately 25 em-L 5 In contradistinction, the concentration of impurities left in the aqueous solution of the polymer prior to dialysis was still too large to make use of the compound possible. At that stage of purification, the conductance was 1.5 X 10-%2-~ cm-1 at a concentration of 2.538 gm PEG/100 ml. The (apparently ionogenic) impurity still present at that stage, although small, was still large enough to produce a well measurable sensitization of the colloidal solution using the coagulation value as a criterion.
301
ing investigations (1 (a)) by means of the o-phenanthroline method. The concentration of D D A O was determined in the prim a r y stock solution b y simple gravimetric procedure. The concentration of P E G , finally, was determined in its aqueous solution with a dipping refraetometer following the simple procedure described b y T. L.
Pugh (2). Method of Mechanical Coagulation. Mechanical coagulation was brought about b y means of rapid shaking. For the experiments with D D A O as the additive, a b a t t e r y of test tubes containing 6-ml samples of a mixture of the colloidal system with a D D A O solution of varied concentration and with water, were agitated for 1 hour. I n the case of P E G addition, a b a t t e r y of test tubes containing 5 ml each of a mixture of the sol and of aqueous solutions of suitable concentrations of P E G , were shaken for 10 rain. I n both cases, identical Pyrex test tubes of 12-ml capacity each were used. After cessation of shaking, all samples were centrifuged for 20 rain at 225g, and the concentration of Fe in the supernatant liquid was determined by means of the colorimetric method referred to above. The shaking of the samples was carried out with a machine which generated vertical shaking with a frequency of 6 seconds -1 and simultaneous horizontal shaking with a frequency of 1 second-*. The amplitudes of the test tube displacements were 3.5 and 0.2 cm respectively. III. RESULTS OBTAINED WITH DDAO Figure 1 shows the effect Of D D A O on coagulation by shaking of the a - F e O O H sol. Up to a concentration of about 0:05 ~rnoles of DDAO/1 sol, the degree of coagulation is, within the limits of the overall experimental error, the same as t h a t of the sol to which no D D A O had been added. On the other hand, from a D D A O concentration of about 0.05 pmole up to 1 pmole per liter sol, a rapid increase in inhibition of mechanical coagulation with increasing D D A O concentration is observed. The degree of coagulation decreases within this range from more than 60 % to less than 5 %. On still further increase of the D D A O concentration, the
Journal of Colloid and Interface Science, ¥ol. 35, No. 2, February 1971
302
HELLER AND PETERS
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FIG. 1: Effect of addition of DDAO on mechanical coagulation produced by one hour shaking of ~Fe'OOtt-sols. c~: Residual sol concentration in percentage of original concentration. attainable degree of coagulation asymptotically approaches 0. Practically complete stabilization, under the specified experimental conditions of mechanical treatment, is obtained at a DDAO concentration of 60 t~moles/liter sol since the degree of coagulation achieved is then only about 2 %. Starting with the now quite secure premise that mechanical coagulation of an a-FeOOH sol of the type used is, at least for the type of mechanical treatment applied, a surface coagulation (1 (b)), one has a priori four possibilities for explaining the stabilizing effect of nonionogenie additives, in general, and of DDAO in particular. The first is that DDAO may compete with the colloidal particles for the liquid-air surface, and therefore reduce their adsorbability. The second possibility is that DDAO, although not materially affecting the adsorbability of the colloidal crystals in the liquid-air surface, may, by virtue of its presence in the liquid-air surface, alter the physical characteristics of the surface (dielectric constant, Debye-Htickel constant) enough to increase the value of the potential energy maximum decisive for coagulation in the surface. The third possibility is that DDAO by adsorption at the surface of the colloidal crystals makes them more hydrophilic so that, for this reason alone, their adsorbability in the liquid-air surface may be significantly reduced. A fourth possibility would be that the additive increases the bulk stability of the colloid which, in line with findings re-
ported earlier (1 (c)), would be accompanied by an increase in its resistance to mechanical coagulation. In the present instance, a more hydrophilic character of the DDAO coated particles would be the most likely reason if such a bulk stabilization were observed. The last possibility could be tested most easily of all. To that effect, the coagulation values V were determined, using NaC1 and the standard contact time of 2 hours. ~ They were 2.9-4.3, 2.9-4.3, and 0.7-1.4 mmoles NaC]/1 at DDAO concentrations of 0, 7.0 × 10-5 and 3.1 X 10-~ moles/l, respectively. The resistance of the collOidal particles towards coagulation by electrolyte, in the absence of mechanical treatment, had therefore not been altered at all within the concentration range where DDAO brings about almost complete immunity towards mechanical coagulation. The fourth possible reason for the stabilizing action of DDAO is therefore excluded. Surface tension was practically the same in distilled water and in the colloidal solution if the DDAO concentration did not exceed 4.36 X 10-6 moles/l, i.e., it did not vary significantly over the entire range covered by Fig. 1. In addition, a check on the effect of DDAO on the foam development and foam life in water showed no difference between pure double distilled 6 The coagulation value is here again the concentration of electrolyte, here in millimoles of NaC1/1 sol, which, 2 hours after addition of electrolyte, just leads to the formation of a waterclear layer below the meniscus of the sol sample.
Journal of Colloid and Interface Science, Vol. 35, No. 2, February 1971
M E C H A N I C A L AND S U R F A C E C O A G U L A T I O N . IV
water and an aqueous solution of DDAO, as long as its concentration was not in excess of 4.4 × 10-7 moles/1J These results do not support the second possibility named above, i.e., the assumption that adsorption of DDAO at the liquid-air surface changed its physical properties sufficiently to account for the stabilization effect observed. In order to check on the third possibility named, the surface area was calculated which one molecule of DDAO would have available if all DDAO molecules were adsorbed at the surface of the colloidal crystals. For this calculation, the surface area derived from electronmieroscopic determination of the size and shape distribution of these crystals was used (see Figure 2 in reference 1 (a)). The result is that 2.4 X 103 (A)2/DDAO molecule would be available at a concentration of 3.6 × 10-~ moles of DDAO/1 sol, that is, at a concentration where the system has already acquired almost complete immunity towards mechanical coagulation. The surface area covered would therefore amount to only about 1%, at the most, of that which one would expect in the case of close packing of DDAO molecules in the surface of the crystals. This low surface coverage makes it unlikely--although one cannot conclusively rule out this possibility - - t h a t adsorption of DDAO at the colloidal crystals made them significantly more hydrophilie and therefore reduced their adsorbability in the air-sol surface. Pending a more definite test of this possibility, s the only remaining possibility for explaining the o
7 At a c o n c e n t r a t i o n of 4.4 X 10-G moles/l, which corresponded to t h e highest D D A O conc e n t r a t i o n considered in Fig. 1, vigorous s h a k i n g p r o d u c e d a few foam b u b b l e s which h a d a lifetime of 5 sec. Only at still higher DDAO concentrations is foaminess very pronounced. T h u s , at c o n c e n t r a t i o n s of 4.4 X 10-5, 4.4 X 10 -~, and 8.7 X 10-3 moles/1 DDAO, the foam life was 20 sec, 2 min, and in excess of 10 min, respectively. s To t h a t effect, it is i n t e n d e d to d e t e r m i n e w h e t h e r or n o t the values of the c o n s t a n t s K1 a n d K2 in the surface coagulation e q u a t i o n (l(a)) v a r y w i t h the c o n c e n t r a t i o n of DDAO. This should allow one to m a k e a definite, t h o u g h indirect, d e t e r m i n a t i o n of t h e effect of D D A O on t h e a d s o r b a b i l i t y of the colloidal crystals at t h e sol-air interface.
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stabilizing effect of DDAO is that named first, namely, reduction of the adsorption of the colloid at the sol-air interface, due to competitive adsorption, at this interface, of DDAO. Incidentally, the low surface coverage of the colloidal crystals by DDAO makes it understandable why the natural stability of the system toward electrolyte had hardly been affected. IV. R E S U L T S O B T A I N E D W I T H POLYETHYLENE GLYCOL
1. Effect of Polyethylene Glycol upon the Bulk Stability of the Colloidal System,. The stabilization produced by the low molecular weight DDAO, against mechanical coagulation of the a-FeOOH sol, represents the simplest possible situation because this (nonionogenic) compound did not, at the concentrations of interest, affect the bulk stability of the sol. The situation becomes more complicated if nonionogenic additives affect not only the ability of the systems to coagulate by mechanical treatment but also their bulk stability. Nonionogenie macromolecules of moderate molecular weight represent this alternate type of substances because they are apt to produce "steric" stabilization (2) of the bulk. For the present work, polyethylene glycol, to be abbreviated to PEG, was selected. These compounds had been found (3) to increase the resistance of Au-sols against coagulation by electrolyte, even at molecular weights as low as 6,000, but particularly at molecular weights 10,000. 9 In the preliminary study to be discussed here, only one sample of PEG of molecular weight 9,000 was used. At this relatively low molecular weight, the risk of formation of real or quasi polymer bridges is excluded. With the coagulation value again used as 9 At very h i g h molecular weights, however, nonionogenic macromolecules m a y actually produce the inverse effect owing e i t h e r to the formation of polymer bridges between t h e colloidal particles or to e n m e s h m c n t of the colloidal particles in an i n t e r m o l e c u l a r n e t w o r k of polymer molecules ( " q u a s i " polymer bridges) (see references 2, 3 and results b y T. W. Healy and V. K. LaMer, J . P h y s . Chem. 67, 2417 (1963) a n d l a t e r papers by L a M e r a n d coworkers.
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HELLER AND PETERS
E ,:= 25
it is well known that even at these relatively low molecular weights, the rate at which adsorption equilibrium is reached is quite slow (4).
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2. Effect of PEG upon Mechanical Coagulation. Figure 3 shows the effect of P E G upon
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FIG. 2. Effect of addition of PEG 9,000 on stability of a-FeOOH-sol against coagulation by electrolyte addition. For definition of coagulation value, see footnote 6. Curve I: Contact time = 5 rain. Curve II: Contact time = 24 hours. Contact time is the time interval between addition of PEG and subsequent addition of electrolyte. Horizontal dashed line: Coagulation value in absence of PEG. a criterion, it follows from Fig. 2 that P E G , as anticipated, increases the bulk stability of the a - F e O O H sol used. Stabihzation becomes noticeable at a concentration of 44 micromoles P E G / l , and it increases rapidly with further increase in polymer concentration. I t is noteworthy that, at a given P E G concentration, the stabilization effect is appreciably smaller here than that exerted by the same compound on gold sols. 1° Just as in the case of the Au-sols referred to (3), the degree of bulk stabilization achieved increases ~4th the time elapsed after addition of the polymer. This clearly indicates t h a t the stabilization is, here also, the result of adsorption of the polymer molecules at the surface of the colloidal crystals, since 10The difference in the stabilizing effect compared to that found for gold sols could be due to the difference in the adsorption constants, or, more simply, to the probably very large difference in surface area of the two types of colloid, the particles in red gold sols having generally an equivalent radius of not in excess of 30-50 m#. Therefore, the surface area in the present instance is at least 10 times larger, and the surface coverage, by PEG, at a given PEG concentration, at least 10 times smaller even on assuming a comparable Langmuir affinity constant.
mechanical coagulation of the a - F e O O H sol used. For the sake of easy reference, the residual concentration of the sol coagulated mechanically in absence of P E G (about 80%), under the conditions specified in Section II, is indicated b y the dotted straight line. Considering first the "equilibr i u m " curve I I , and using the degree of coagulation in absence of P E G as the reference, one sees t h a t mechanical coagulation is more extensive at sufficiently low P E G concentrations but much less extensive at higher polymer concentrations. Comparison with Fig. 2 shows that, in the latter case, stabilization of the system against mechanical coagulation begins at the same P E G concentration (less than 100 micromoles/1) at which one finds stabilization of the same system, at rest, against coagulation by electrolyte. The stabilization against mechanical coagulation b y P E G can therefore be explained simply as a result of an increase in bulk stability, which, as stated (1 (e)) should in general be accompanied by an increase in colloid stability in the water-air interface. The increase in bulk stability is, as stated I00
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FIG. 3. Effect of addition of PEG 9,000 on mechanical stability of ~-FeOOH-sol. Curve I: Contact time = 5 rain. Curve II: Contact time = 24 hours. Horizontal dashed line: c~ in absence of PEG. Time of shaking: i0 rain. Contact time is here the time interval between addition of PEG and start of shaking.
Journal of Colloid a~d Interface Science, VoI. 35, N o . 2, F e b r u a r y 1971
MECHANICAL AND SURFACE COAGULATION. IV above, due to adsorption of PEG at the surface of the colloidal crystals. The slowness with which the adsorption equilibrium of macromolecular solutes is approached (4) is reflected here in the gradual increase, with the "contact time" elapsed after the addition of PEG, in the stability of the sol towards electrolyte (Fig. 2) and in its resistance to mechanical coagulation (Fig. 3): In the ease of curves I, of these figures, electrolyte was added to the sol at rest (Fig. 2) and shaking started without deetrolyte addition, respectively (Fig. 3), 5 rain after PEG addition; in the ease of curves II, 24 hours had elapsed after addition of PEG before the bulk stability (Fig. 2) and mechanical stability (Fig. 3), respectively, were tested by addition of electrolyte and by shaking respectively. Granting that adsorption of PEG and the resulting increase in bulk stabitity arc the cause of mechanical stabilization of the sol, there is an additional factor that may play a role also, viz., a shift upon PEG adsorption, in the distribution equilibrium of the colloidal particles between the bulk and the ai>water interface in favor of the former phase. This would require that PEG adsorption make the colloid surface distinctly more hydrophilie. According to recent experiments in this laboratory, 11 such a shift, if it exists, can, however, be only modest because of a rather low affinity of PEG to H20-vapor. The promotion of mechanical coagulation at a sufficiently low concentration of PEG is interesting but not surprising, since the addition of PEG to the colloidal solution produces foam, in an amount that rises with the PEG concentration. Table I shows the variation of foam height as a function of PEG concentration, shortly (3~-71/~ min) and 24 hours, respectively, after addition of the polymer. It is seen that the foaming capacity of the sol in presence of polymer begins to differ distinctly from that of the polymer free sol from a polymer concentration of less than 2 m~moles/1 on, and it increases steadily with further increase in n Experiments on tt20 sorption by PEG carried out by W. A. Crozier, in this laboratory.
305
TABLE I HEIGHT
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PRODUCED
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2.09 2.09 2.09 6.62 2.09 6.62 2,09 6.62 2.09 6.62
0.0 X 10 -9 X 10-.8 X 10 -7 X 10 -7 X 10-6 X 10 -6 X 10 -5 X 10 -5 X 10-~ X 10 -~
Foam height (cm) after contact time of: ~--7}t rain
24 hours
0,0 0,1 0.1 0.2 0.3 0.4 0.7 0.9 1.4 1.6 2.0
0,0 0,1 0.1 0.2 0.3 0.5 0.7 1.1 1.3 1.7 2.1
C o n t a c t t i m e : t i m e e l a p s e d a f t e r a d d i t i o n of P E G to sol s a m p l e ; f o a m h e i g h t w a s d e t e r m i n e d i m m e d i a t e l y a f t e r t e r m i n a t i o n of 10-rain s h a k i n g of s a m p l e s .
polymer concentration, m The promotion of mechanical coagulation by PEG, at low polymer concentrations, is therefore simply the result of an extensive increase in surface area, by foaming in the shaken samples the colloid stability of which remains, according to Fig. 2, essentially unchanged. The complex effect illustrated by Fig. 3 can therefore be explained readily by the antagonistic influence of two effects of PEG addition: at low PEG concentrations where the stability of the solution is not measurably affected, the promotion of foam Ieads to a steadily increasing surface area, and. therefore to a steadily increasing rate of surface coagulation. On the other hand, at relatively high PEG concentration, the resistance of the colloidal solution towards electrolyte and, therefore, towards shaking has been enhanced so much that further appreciable increase in water-Mr surface area is no longer effective in promoting surface coagulation. 12The foam height given in Table I is, throughout, that determined after termination of the 10min shaking period. The foam life was so large that the small difference which elapsed after conclusion of the shaking, before the foam height. was determined in all samples, did not matter.
Journal of Colloid and Interface Science, VM. 35, No. 2, February 1971
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HELLER AND PETERS V. C O N C L U D I N G R E M A R K S
The results obtained with DDAO and P E G show that the addition of nonelectrolytes to colloidal solutions which are subject to mechanical (surface) coagulation, may lead to their stabilization towards mechanical treatment, there being, as outlined in Section III, a priori several (4) possible reasons for it. In the case of PEG, the stabilization was recognized as being due most likely to the "steric" protection of the colloidal particles in the bulk which would and did reflect itself in a stabilization of the material in thc water-air surface. In the case of DDAO, bulk stabilization was not involved. Here, the most likely or primary reason, among two possible ones, was the competition of this compound for the water-air surface. The resulting shift in the colloid distribution between bulk and waterair surface, in favor of the bulk phase, would result in a correspondingly lower rate of surface coagallation and, in the case of extreme shifts, in a practically complete cessation of surface coagulation. There are two possible antagonistic effects which may complicate the actual situation. (1) Promotion of foam formation by nonionogenic substances will accelerate mechanical coagulation (whenever it represents a surface coagulation), a factor which complicated the results obtained on adding P E G to the colloidal solution; (2) formation of polymer bridges or mechanical entanglement of colloidal particles in a network of polymer molecules of sufficiently high molecular weight. The resulting separation of the colloidal system representing either a true or pseudo coagulation should be accompanied, in the former instance (polymer bridges), by an increased susceptibility to mechanical coagulation whereas, in the latter case, the effect of mechanical treatment should be expected to be the same as in absence of the macromoleeular material. There is no experimental record as yet on the reality and actual role of this second possibility of antagonistic effects. If the additive is ionogenic, its effect upon the bulk stability of a sol can be more varied than in the case of a nonionogenic additive. This will, again, reflect itself in the behavior
of the system towards mechanical treatment. Of particular interest are the following two cases: (1) If the additive is a simple electrolyte, then bulk stability (and the correlated resistance to mechanical coagulation) may be either promoted or reduced, the latter being the more common case. The consequences of the latter effect upon the mechanical stability of a colloidal solution have already been discussed (1 (c)). A detailed investigation of the former effect will be published shortly. 13 (2) If the additive is a long-chain ion or a polyion associated with a microgegenion, then the bulk stability may, as is well known, be increased or reduced by the additive, depending on whether polyion and colloidal particles have the same or opposite sign of charge, and depending also on the concentration of the polyion. This will, again, be reflected in an increase or reduction of the susceptibility of a system to undergo mechanical coagulation. Although, therefore, the basic phenomenon involved in mechanical coagulation has been recognized as being relatively simple, the coagulation taking place primarily or exclusively in the air-water surface, if turbulence effects can be neglected, it is seen that the question as to whether or not a ~ v e n compound will promote or inhibit mechanical coagulation cannot be answered without evaluating the degree of pertinence, in a given instance, of the various possibilities enumerated above. Failure to do so can easily lead to misconceptions on the nature of mechanical coagulation (5). ACKNOWLEDGMENT Mr. Mason Turner, enrolled in the 1964 NSF sponsored Summer program for research participation of high school teachers at Wayne State University, vigorously and efficiently participated in the phase of the work concerned with PEG addition to the systems. REFERENCES 1. (a) HELL,R, W., AND PETERS, J., J. Colloid Interface Sci., 32,592 (1970). (b) PETERS, J., AND HELLER, W . , J . Colloid Interface Sci., 13 Work by William B. DeLauder, carried out in this laboratory.
Journal of Colloid and In~erfaceScience, Vol. 35, No. 2, February 1971
MECHANICAL AND SURFACE COAGULATION. IV 33, 578 (1970). (c) I~ELLER, W., AND D~LAuDER, WM. B. J. Colloid Interface Sei., in press. 2. HELLER, W., AND PUGH, T. L., J. Polymer Sci. 47, 203 (1960). 3. HELLER, W., AND PIyGI:[,T. L,, see reference 2 and also HELLER, W., AND PUGH, T. L.,
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J. Chem. Phys. 22, 1778 (1954); HELLER,W., Pure Appl. Chem. 12, 249 (1966). 4. HnLLna, W., Pure Appl. Chem. 12, 249 (1966); HELLER, W., AND TANAKA, W., Phys. Rev. 82, 302 (1951). 5. See, e.g., P. STAMBERGER,J. Phys. Chem. 62, 127 (1957).
Journal of Colloidand InterfaceScience,VoL 35, No. 2, February1971
H E L L E R AND J A M E S P E T E R S t
Department of Chemistry, Wayne State University, Detroit, Michigan 48202
Received June 29, 1970; accepted September 23, 1970 Previous investigations had established that a colloidal solution of hydrophobic particles becomes subject to mechanical coagulation if its stability--as measured by its behavior towards coagulating electrolyte~is reduced sufficiently. It is now shown that the reverse applies also, i.e., a sol, subject to mechanical coagulation, cannot be coagulated by stirring, shaking, or by gas bubbles if its natural stability is increased sufficiently. The increase is brought about, in the present work, by the addition of moderately surface-active agents. If the latter promote foam formation, mechanical coagulation will be inhibited only at higher stabilizer concentration, whereas, at low ones, the effect of an increase in the water-air interface predominates and leads to a promotion of mechanical coagulation. An increase in sol stability is not the only possible method for preventing mechanical coagulation. Additives which reduce the population density of the colloid in the water-air interface also produce immunity to mechanical coagulation. An example is given. Moreover, the various possibilities of explanation existing for both the latter and former type stabilization against mechanical coagulation are discussed. I. INTRODUCTION Evidence has been accumulated in a series of papers (1) to the effect t h a t mechanical coagulation produced by conventional stirring or shaking or b y bubbling gases through a suitable colloidal solution represents a surface coagulation if, in absence of these treatments, the systems exhibit a considerable shelflife. Since a coagulation at the water-air surface is necessarily sensitive to the state of the surface and to changes occurring in it, complications in mechanical coagulation can be anticipated in the presence of additives which affect the state of this surface a n d / o r the distribution of the colloid between bulk and surface. One can therefore anticipate t h a t mechanical coagulation m a y be either promoted or hindered b y suitable additives, if present in the p r o p e r conceniration, even in those cases where they m a y Present address: The Dow Chemical Com,pany, Midland, Michigan.
not affect significantly the bulk stability of the system. The present paper represents an exploratory investigation of these effects, considering the simplest possible case, viz., t h a t of addition of nonionogenic substances. lI. EXPERIMENTAL The System Investigated. A single colloidal solution of a - F e O O H was used for the entire investigation. I t had already been used previously (sol C) (1 (a)). A few of the pertinent characteristics m a y be repeated here: colloid concentration 370 mg Fc/1, p H 6.5, coagulation value, "y: 3-4 mmoles of K C ] / I of sol (2 hours, room temperature). The Additives Used. One of tile surfaceactive additives used was N , N - d i m e t h y l - n dodecylamine oxide, to be referred to as D D A 0 . I t was selected because a dilute solution does not lead to foam formation on stirring. Therefore, complications of a foam-produced increase in the air-liquid surface area b y stirring relative to t h e
Journal of Colloidand Inter'faceScience,Vol.35, No. 2, February197I 3OO
MECHANICAL AND SURFACE COAGULATION. IV surface area generated in absence of the additive were excluded. A stock solution of D D A O , having a concentration of 0.2 g m / 100 ml of double distilled water, or volumetric dilutions of it were used. The concentration of D D A O in the sol samples was varied b y adding to 5 ml of colloidal solution both a D D A O sohltion of suitable concentration and double distilled water, so as to bring the total volume of the sample up to 6.0 ml? The second surface-active additive used was polyethylene glycol of molecular weight 9,0002 This additive will be referred to as P E G . I n order to remove impurities, the polymer was dissolved in reagent grade acetone, filtered, repreeipitated with redistilled hexane, then washed with redistilled ether, and, finally, an aqueous solution of this purified polymer was dialyzed for 70 hours in a high-efficiency dialyzing apparatus. 4 The aqueous solution thus obtained exhibited a conductance of 1.74 × 10-~ a - t em -~, at a concentration of 1.986 gm P E G / 1 0 0 mh The excess of this conductance over t h a t of conductance water was too small to be of significance for the present work. ~
Determination of the Concentration of Colloid and Additives. The concentration of the colloid was determined as in the preced2 The crystals of DDAO used in the present work were kindly provided by Dr. N. A. LaBel of the Chemistry Department of Wayne State University. 3 This material was kindly provided by the Dow Chemical Company, Midland, Michigan. 4 The rabio (sol-membrane interface area/sol volume) for the thin layer of sol contained between two circular cellophane membranes clamped, together with rubber gaskets, onto two fast rotating horizontal metal rings, was approximately 25 em-L 5 In contradistinction, the concentration of impurities left in the aqueous solution of the polymer prior to dialysis was still too large to make use of the compound possible. At that stage of purification, the conductance was 1.5 X 10-%2-~ cm-1 at a concentration of 2.538 gm PEG/100 ml. The (apparently ionogenic) impurity still present at that stage, although small, was still large enough to produce a well measurable sensitization of the colloidal solution using the coagulation value as a criterion.
301
ing investigations (1 (a)) by means of the o-phenanthroline method. The concentration of D D A O was determined in the prim a r y stock solution b y simple gravimetric procedure. The concentration of P E G , finally, was determined in its aqueous solution with a dipping refraetometer following the simple procedure described b y T. L.
Pugh (2). Method of Mechanical Coagulation. Mechanical coagulation was brought about b y means of rapid shaking. For the experiments with D D A O as the additive, a b a t t e r y of test tubes containing 6-ml samples of a mixture of the colloidal system with a D D A O solution of varied concentration and with water, were agitated for 1 hour. I n the case of P E G addition, a b a t t e r y of test tubes containing 5 ml each of a mixture of the sol and of aqueous solutions of suitable concentrations of P E G , were shaken for 10 rain. I n both cases, identical Pyrex test tubes of 12-ml capacity each were used. After cessation of shaking, all samples were centrifuged for 20 rain at 225g, and the concentration of Fe in the supernatant liquid was determined by means of the colorimetric method referred to above. The shaking of the samples was carried out with a machine which generated vertical shaking with a frequency of 6 seconds -1 and simultaneous horizontal shaking with a frequency of 1 second-*. The amplitudes of the test tube displacements were 3.5 and 0.2 cm respectively. III. RESULTS OBTAINED WITH DDAO Figure 1 shows the effect Of D D A O on coagulation by shaking of the a - F e O O H sol. Up to a concentration of about 0:05 ~rnoles of DDAO/1 sol, the degree of coagulation is, within the limits of the overall experimental error, the same as t h a t of the sol to which no D D A O had been added. On the other hand, from a D D A O concentration of about 0.05 pmole up to 1 pmole per liter sol, a rapid increase in inhibition of mechanical coagulation with increasing D D A O concentration is observed. The degree of coagulation decreases within this range from more than 60 % to less than 5 %. On still further increase of the D D A O concentration, the
Journal of Colloid and Interface Science, ¥ol. 35, No. 2, February 1971
302
HELLER AND PETERS
L.-3 I 0 0 z v
so co LL 0
60
0 '-r 40 rr LIJ I..U.. 2O
o ~ NO
DD~O I-9
I
I
-8
q
-7 -6 LOG ( MOLES D D A O / I . )
-5
FIG. 1: Effect of addition of DDAO on mechanical coagulation produced by one hour shaking of ~Fe'OOtt-sols. c~: Residual sol concentration in percentage of original concentration. attainable degree of coagulation asymptotically approaches 0. Practically complete stabilization, under the specified experimental conditions of mechanical treatment, is obtained at a DDAO concentration of 60 t~moles/liter sol since the degree of coagulation achieved is then only about 2 %. Starting with the now quite secure premise that mechanical coagulation of an a-FeOOH sol of the type used is, at least for the type of mechanical treatment applied, a surface coagulation (1 (b)), one has a priori four possibilities for explaining the stabilizing effect of nonionogenie additives, in general, and of DDAO in particular. The first is that DDAO may compete with the colloidal particles for the liquid-air surface, and therefore reduce their adsorbability. The second possibility is that DDAO, although not materially affecting the adsorbability of the colloidal crystals in the liquid-air surface, may, by virtue of its presence in the liquid-air surface, alter the physical characteristics of the surface (dielectric constant, Debye-Htickel constant) enough to increase the value of the potential energy maximum decisive for coagulation in the surface. The third possibility is that DDAO by adsorption at the surface of the colloidal crystals makes them more hydrophilic so that, for this reason alone, their adsorbability in the liquid-air surface may be significantly reduced. A fourth possibility would be that the additive increases the bulk stability of the colloid which, in line with findings re-
ported earlier (1 (c)), would be accompanied by an increase in its resistance to mechanical coagulation. In the present instance, a more hydrophilic character of the DDAO coated particles would be the most likely reason if such a bulk stabilization were observed. The last possibility could be tested most easily of all. To that effect, the coagulation values V were determined, using NaC1 and the standard contact time of 2 hours. ~ They were 2.9-4.3, 2.9-4.3, and 0.7-1.4 mmoles NaC]/1 at DDAO concentrations of 0, 7.0 × 10-5 and 3.1 X 10-~ moles/l, respectively. The resistance of the collOidal particles towards coagulation by electrolyte, in the absence of mechanical treatment, had therefore not been altered at all within the concentration range where DDAO brings about almost complete immunity towards mechanical coagulation. The fourth possible reason for the stabilizing action of DDAO is therefore excluded. Surface tension was practically the same in distilled water and in the colloidal solution if the DDAO concentration did not exceed 4.36 X 10-6 moles/l, i.e., it did not vary significantly over the entire range covered by Fig. 1. In addition, a check on the effect of DDAO on the foam development and foam life in water showed no difference between pure double distilled 6 The coagulation value is here again the concentration of electrolyte, here in millimoles of NaC1/1 sol, which, 2 hours after addition of electrolyte, just leads to the formation of a waterclear layer below the meniscus of the sol sample.
Journal of Colloid and Interface Science, Vol. 35, No. 2, February 1971
M E C H A N I C A L AND S U R F A C E C O A G U L A T I O N . IV
water and an aqueous solution of DDAO, as long as its concentration was not in excess of 4.4 × 10-7 moles/1J These results do not support the second possibility named above, i.e., the assumption that adsorption of DDAO at the liquid-air surface changed its physical properties sufficiently to account for the stabilization effect observed. In order to check on the third possibility named, the surface area was calculated which one molecule of DDAO would have available if all DDAO molecules were adsorbed at the surface of the colloidal crystals. For this calculation, the surface area derived from electronmieroscopic determination of the size and shape distribution of these crystals was used (see Figure 2 in reference 1 (a)). The result is that 2.4 X 103 (A)2/DDAO molecule would be available at a concentration of 3.6 × 10-~ moles of DDAO/1 sol, that is, at a concentration where the system has already acquired almost complete immunity towards mechanical coagulation. The surface area covered would therefore amount to only about 1%, at the most, of that which one would expect in the case of close packing of DDAO molecules in the surface of the crystals. This low surface coverage makes it unlikely--although one cannot conclusively rule out this possibility - - t h a t adsorption of DDAO at the colloidal crystals made them significantly more hydrophilie and therefore reduced their adsorbability in the air-sol surface. Pending a more definite test of this possibility, s the only remaining possibility for explaining the o
7 At a c o n c e n t r a t i o n of 4.4 X 10-G moles/l, which corresponded to t h e highest D D A O conc e n t r a t i o n considered in Fig. 1, vigorous s h a k i n g p r o d u c e d a few foam b u b b l e s which h a d a lifetime of 5 sec. Only at still higher DDAO concentrations is foaminess very pronounced. T h u s , at c o n c e n t r a t i o n s of 4.4 X 10-5, 4.4 X 10 -~, and 8.7 X 10-3 moles/1 DDAO, the foam life was 20 sec, 2 min, and in excess of 10 min, respectively. s To t h a t effect, it is i n t e n d e d to d e t e r m i n e w h e t h e r or n o t the values of the c o n s t a n t s K1 a n d K2 in the surface coagulation e q u a t i o n (l(a)) v a r y w i t h the c o n c e n t r a t i o n of DDAO. This should allow one to m a k e a definite, t h o u g h indirect, d e t e r m i n a t i o n of t h e effect of D D A O on t h e a d s o r b a b i l i t y of the colloidal crystals at t h e sol-air interface.
303
stabilizing effect of DDAO is that named first, namely, reduction of the adsorption of the colloid at the sol-air interface, due to competitive adsorption, at this interface, of DDAO. Incidentally, the low surface coverage of the colloidal crystals by DDAO makes it understandable why the natural stability of the system toward electrolyte had hardly been affected. IV. R E S U L T S O B T A I N E D W I T H POLYETHYLENE GLYCOL
1. Effect of Polyethylene Glycol upon the Bulk Stability of the Colloidal System,. The stabilization produced by the low molecular weight DDAO, against mechanical coagulation of the a-FeOOH sol, represents the simplest possible situation because this (nonionogenic) compound did not, at the concentrations of interest, affect the bulk stability of the sol. The situation becomes more complicated if nonionogenic additives affect not only the ability of the systems to coagulate by mechanical treatment but also their bulk stability. Nonionogenie macromolecules of moderate molecular weight represent this alternate type of substances because they are apt to produce "steric" stabilization (2) of the bulk. For the present work, polyethylene glycol, to be abbreviated to PEG, was selected. These compounds had been found (3) to increase the resistance of Au-sols against coagulation by electrolyte, even at molecular weights as low as 6,000, but particularly at molecular weights 10,000. 9 In the preliminary study to be discussed here, only one sample of PEG of molecular weight 9,000 was used. At this relatively low molecular weight, the risk of formation of real or quasi polymer bridges is excluded. With the coagulation value again used as 9 At very h i g h molecular weights, however, nonionogenic macromolecules m a y actually produce the inverse effect owing e i t h e r to the formation of polymer bridges between t h e colloidal particles or to e n m e s h m c n t of the colloidal particles in an i n t e r m o l e c u l a r n e t w o r k of polymer molecules ( " q u a s i " polymer bridges) (see references 2, 3 and results b y T. W. Healy and V. K. LaMer, J . P h y s . Chem. 67, 2417 (1963) a n d l a t e r papers by L a M e r a n d coworkers.
Journal of Colloid and Interface Science, Vol. 35, No. 2, February 1971
304
HELLER AND PETERS
E ,:= 25
it is well known that even at these relatively low molecular weights, the rate at which adsorption equilibrium is reached is quite slow (4).
~_J 20
2. Effect of PEG upon Mechanical Coagulation. Figure 3 shows the effect of P E G upon
~- 50
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9
-8I
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FIG. 2. Effect of addition of PEG 9,000 on stability of a-FeOOH-sol against coagulation by electrolyte addition. For definition of coagulation value, see footnote 6. Curve I: Contact time = 5 rain. Curve II: Contact time = 24 hours. Contact time is the time interval between addition of PEG and subsequent addition of electrolyte. Horizontal dashed line: Coagulation value in absence of PEG. a criterion, it follows from Fig. 2 that P E G , as anticipated, increases the bulk stability of the a - F e O O H sol used. Stabihzation becomes noticeable at a concentration of 44 micromoles P E G / l , and it increases rapidly with further increase in polymer concentration. I t is noteworthy that, at a given P E G concentration, the stabilization effect is appreciably smaller here than that exerted by the same compound on gold sols. 1° Just as in the case of the Au-sols referred to (3), the degree of bulk stabilization achieved increases ~4th the time elapsed after addition of the polymer. This clearly indicates t h a t the stabilization is, here also, the result of adsorption of the polymer molecules at the surface of the colloidal crystals, since 10The difference in the stabilizing effect compared to that found for gold sols could be due to the difference in the adsorption constants, or, more simply, to the probably very large difference in surface area of the two types of colloid, the particles in red gold sols having generally an equivalent radius of not in excess of 30-50 m#. Therefore, the surface area in the present instance is at least 10 times larger, and the surface coverage, by PEG, at a given PEG concentration, at least 10 times smaller even on assuming a comparable Langmuir affinity constant.
mechanical coagulation of the a - F e O O H sol used. For the sake of easy reference, the residual concentration of the sol coagulated mechanically in absence of P E G (about 80%), under the conditions specified in Section II, is indicated b y the dotted straight line. Considering first the "equilibr i u m " curve I I , and using the degree of coagulation in absence of P E G as the reference, one sees t h a t mechanical coagulation is more extensive at sufficiently low P E G concentrations but much less extensive at higher polymer concentrations. Comparison with Fig. 2 shows that, in the latter case, stabilization of the system against mechanical coagulation begins at the same P E G concentration (less than 100 micromoles/1) at which one finds stabilization of the same system, at rest, against coagulation by electrolyte. The stabilization against mechanical coagulation b y P E G can therefore be explained simply as a result of an increase in bulk stability, which, as stated (1 (e)) should in general be accompanied by an increase in colloid stability in the water-air interface. The increase in bulk stability is, as stated I00
9O
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-7
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-6
I
-5
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FIG. 3. Effect of addition of PEG 9,000 on mechanical stability of ~-FeOOH-sol. Curve I: Contact time = 5 rain. Curve II: Contact time = 24 hours. Horizontal dashed line: c~ in absence of PEG. Time of shaking: i0 rain. Contact time is here the time interval between addition of PEG and start of shaking.
Journal of Colloid a~d Interface Science, VoI. 35, N o . 2, F e b r u a r y 1971
MECHANICAL AND SURFACE COAGULATION. IV above, due to adsorption of PEG at the surface of the colloidal crystals. The slowness with which the adsorption equilibrium of macromolecular solutes is approached (4) is reflected here in the gradual increase, with the "contact time" elapsed after the addition of PEG, in the stability of the sol towards electrolyte (Fig. 2) and in its resistance to mechanical coagulation (Fig. 3): In the ease of curves I, of these figures, electrolyte was added to the sol at rest (Fig. 2) and shaking started without deetrolyte addition, respectively (Fig. 3), 5 rain after PEG addition; in the ease of curves II, 24 hours had elapsed after addition of PEG before the bulk stability (Fig. 2) and mechanical stability (Fig. 3), respectively, were tested by addition of electrolyte and by shaking respectively. Granting that adsorption of PEG and the resulting increase in bulk stabitity arc the cause of mechanical stabilization of the sol, there is an additional factor that may play a role also, viz., a shift upon PEG adsorption, in the distribution equilibrium of the colloidal particles between the bulk and the ai>water interface in favor of the former phase. This would require that PEG adsorption make the colloid surface distinctly more hydrophilie. According to recent experiments in this laboratory, 11 such a shift, if it exists, can, however, be only modest because of a rather low affinity of PEG to H20-vapor. The promotion of mechanical coagulation at a sufficiently low concentration of PEG is interesting but not surprising, since the addition of PEG to the colloidal solution produces foam, in an amount that rises with the PEG concentration. Table I shows the variation of foam height as a function of PEG concentration, shortly (3~-71/~ min) and 24 hours, respectively, after addition of the polymer. It is seen that the foaming capacity of the sol in presence of polymer begins to differ distinctly from that of the polymer free sol from a polymer concentration of less than 2 m~moles/1 on, and it increases steadily with further increase in n Experiments on tt20 sorption by PEG carried out by W. A. Crozier, in this laboratory.
305
TABLE I HEIGHT
OF
FOAM
PRODUCED
BY
SHAKING
OF
a-FeOOH-Sol C As a FUNCTIONOF PEG C O N C E N T R A T I O N - - 1 0 MINIJTES SHAKING PEG concentration (moles~l)
2.09 2.09 2.09 6.62 2.09 6.62 2,09 6.62 2.09 6.62
0.0 X 10 -9 X 10-.8 X 10 -7 X 10 -7 X 10-6 X 10 -6 X 10 -5 X 10 -5 X 10-~ X 10 -~
Foam height (cm) after contact time of: ~--7}t rain
24 hours
0,0 0,1 0.1 0.2 0.3 0.4 0.7 0.9 1.4 1.6 2.0
0,0 0,1 0.1 0.2 0.3 0.5 0.7 1.1 1.3 1.7 2.1
C o n t a c t t i m e : t i m e e l a p s e d a f t e r a d d i t i o n of P E G to sol s a m p l e ; f o a m h e i g h t w a s d e t e r m i n e d i m m e d i a t e l y a f t e r t e r m i n a t i o n of 10-rain s h a k i n g of s a m p l e s .
polymer concentration, m The promotion of mechanical coagulation by PEG, at low polymer concentrations, is therefore simply the result of an extensive increase in surface area, by foaming in the shaken samples the colloid stability of which remains, according to Fig. 2, essentially unchanged. The complex effect illustrated by Fig. 3 can therefore be explained readily by the antagonistic influence of two effects of PEG addition: at low PEG concentrations where the stability of the solution is not measurably affected, the promotion of foam Ieads to a steadily increasing surface area, and. therefore to a steadily increasing rate of surface coagulation. On the other hand, at relatively high PEG concentration, the resistance of the colloidal solution towards electrolyte and, therefore, towards shaking has been enhanced so much that further appreciable increase in water-Mr surface area is no longer effective in promoting surface coagulation. 12The foam height given in Table I is, throughout, that determined after termination of the 10min shaking period. The foam life was so large that the small difference which elapsed after conclusion of the shaking, before the foam height. was determined in all samples, did not matter.
Journal of Colloid and Interface Science, VM. 35, No. 2, February 1971
306
HELLER AND PETERS V. C O N C L U D I N G R E M A R K S
The results obtained with DDAO and P E G show that the addition of nonelectrolytes to colloidal solutions which are subject to mechanical (surface) coagulation, may lead to their stabilization towards mechanical treatment, there being, as outlined in Section III, a priori several (4) possible reasons for it. In the case of PEG, the stabilization was recognized as being due most likely to the "steric" protection of the colloidal particles in the bulk which would and did reflect itself in a stabilization of the material in thc water-air surface. In the case of DDAO, bulk stabilization was not involved. Here, the most likely or primary reason, among two possible ones, was the competition of this compound for the water-air surface. The resulting shift in the colloid distribution between bulk and waterair surface, in favor of the bulk phase, would result in a correspondingly lower rate of surface coagallation and, in the case of extreme shifts, in a practically complete cessation of surface coagulation. There are two possible antagonistic effects which may complicate the actual situation. (1) Promotion of foam formation by nonionogenic substances will accelerate mechanical coagulation (whenever it represents a surface coagulation), a factor which complicated the results obtained on adding P E G to the colloidal solution; (2) formation of polymer bridges or mechanical entanglement of colloidal particles in a network of polymer molecules of sufficiently high molecular weight. The resulting separation of the colloidal system representing either a true or pseudo coagulation should be accompanied, in the former instance (polymer bridges), by an increased susceptibility to mechanical coagulation whereas, in the latter case, the effect of mechanical treatment should be expected to be the same as in absence of the macromoleeular material. There is no experimental record as yet on the reality and actual role of this second possibility of antagonistic effects. If the additive is ionogenic, its effect upon the bulk stability of a sol can be more varied than in the case of a nonionogenic additive. This will, again, reflect itself in the behavior
of the system towards mechanical treatment. Of particular interest are the following two cases: (1) If the additive is a simple electrolyte, then bulk stability (and the correlated resistance to mechanical coagulation) may be either promoted or reduced, the latter being the more common case. The consequences of the latter effect upon the mechanical stability of a colloidal solution have already been discussed (1 (c)). A detailed investigation of the former effect will be published shortly. 13 (2) If the additive is a long-chain ion or a polyion associated with a microgegenion, then the bulk stability may, as is well known, be increased or reduced by the additive, depending on whether polyion and colloidal particles have the same or opposite sign of charge, and depending also on the concentration of the polyion. This will, again, be reflected in an increase or reduction of the susceptibility of a system to undergo mechanical coagulation. Although, therefore, the basic phenomenon involved in mechanical coagulation has been recognized as being relatively simple, the coagulation taking place primarily or exclusively in the air-water surface, if turbulence effects can be neglected, it is seen that the question as to whether or not a ~ v e n compound will promote or inhibit mechanical coagulation cannot be answered without evaluating the degree of pertinence, in a given instance, of the various possibilities enumerated above. Failure to do so can easily lead to misconceptions on the nature of mechanical coagulation (5). ACKNOWLEDGMENT Mr. Mason Turner, enrolled in the 1964 NSF sponsored Summer program for research participation of high school teachers at Wayne State University, vigorously and efficiently participated in the phase of the work concerned with PEG addition to the systems. REFERENCES 1. (a) HELL,R, W., AND PETERS, J., J. Colloid Interface Sci., 32,592 (1970). (b) PETERS, J., AND HELLER, W . , J . Colloid Interface Sci., 13 Work by William B. DeLauder, carried out in this laboratory.
Journal of Colloid and In~erfaceScience, Vol. 35, No. 2, February 1971
MECHANICAL AND SURFACE COAGULATION. IV 33, 578 (1970). (c) I~ELLER, W., AND D~LAuDER, WM. B. J. Colloid Interface Sei., in press. 2. HELLER, W., AND PUGH, T. L., J. Polymer Sci. 47, 203 (1960). 3. HELLER, W., AND PIyGI:[,T. L,, see reference 2 and also HELLER, W., AND PUGH, T. L.,
307
J. Chem. Phys. 22, 1778 (1954); HELLER,W., Pure Appl. Chem. 12, 249 (1966). 4. HnLLna, W., Pure Appl. Chem. 12, 249 (1966); HELLER, W., AND TANAKA, W., Phys. Rev. 82, 302 (1951). 5. See, e.g., P. STAMBERGER,J. Phys. Chem. 62, 127 (1957).
Journal of Colloidand InterfaceScience,VoL 35, No. 2, February1971