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Kinetics of colloidal particle deposition on pulp fibers 1. Deposition of clay on fibers of opposite charge
Colloids and Surfaces, 59 (1991) 265-277 Elsevier Science Publishers B.V., Amsterdam
265
Kinetics of colloidal particle deposition on pulp fibers 1.Deposition of clay on fibers of opposite charge B. Alince, J. Betlicki and T.G.M. van de Ven Pap&an and Department of Chemistry, Pulp and Paper Research Montreal
Centre,
McGill
University,
H3A 2A7, Canada
(Received 12 October 1990; accepted 29 January 1991)
Abstract The rate of deposition of clay particles on oppositely charged fibers was measured in five systems where the negative surface charge of either the fibers or the clay was reversed by adsorption of cationIc polyethylenimine or pII control. A theoretical model of particle deposition kinetics derived fro-m Langmuir analysis is presented, which is also applicab!r to a system containing fewer partic!es than required for full coverage by introducing a new parameter. It is observed that the rate of deposition of dispersed clay particies is considerably slower than the deposition of clay aggregates. The maximum mass coverage of fibers by dispersed clay particles is also less than the coverage by clay aggregates. The experimental rates are comparable to tilose calculated theoretically and thus consistent with Smoluchowski’s kinetics.
INTRODUCTION
When mineral particles are added to an aqueous suspension of fibers for the purpose of producing filled papers, the obvious requirement is their effect.ive retention. However, because both fibers and particles are negatively charged they repel each other and only particles larger than the openings in the fiber web, which is being formed on a screen, can be entrapped mechanically. The probability for particles of common pigments to be retained by this filtration mechanism is small because of their size, which is often in the submicron range. This has been shown both theoretically [ 11 and experimentally [ 2 ] . The way to improve retention is to encourage natural attraction between fibers and particles. This can be achieved by manipulating pH, providing that the surface charge is pH-dependent, or by increasing ionic strength and thus decreasing repulsion. More effective is the introduction of cationic polyelectrolyte, which by adsorbing on the componerrts can cause their heterocoagulation due to a charge modification or heteroklocculation by a bridging mechanism. Under such circumstances the particles may deposit on fibers and be carried into paper.
0166-6622/91/$03.50
0 1991 Elsevier Science Publishers B.V. All rights reserved.
266
Besides the interaction between fibers and particles, at least two other factors must be considered for retention’to be effective. On a modern, fast running paper machine the time available for particle deposition to take place is of the order of seconds, and, because of the high turbulence, the particles should be attached strongly enough to resist removal from fibers by hydrodynamic forces. The focus here is on the process of clay particle deposition on fibers under conditions where they are oppositely charged and, therefore, mutually attractive. For the surface charge mcdifrcation a highly charged cationic polyethylenimine w~is employed. This polymer is believed to destabilize colloidal particles via charge neutralization rather than the bridging rcechanism [3,4 1. The polymer was applied in different modes either to clay particles or to fibers to provide them with a positive charge prior to the addition of the second component. Upon mixing the two components, clay and fibers, the extent of clay deposition was monitored in timed intervals. The emphasis is on the rate of clay particle deposition on fibers and on an attempt to formulate a theoretical model to describe the process. EXPERIMENTAL
Materials Fibers Hardwood bleached kraft pulp was disintegrated in water and washed several times on a 150 mesh screen (openings 100 pm ) in order to remove fiber fines. The average fiber is 2 mm long and 30 pm in diameter. The surface area is estimated to be 0.5-1.5 m2 g-’ [ 51. Polymer Poiyeth :limine POLYMIN P (BASF), believed to be a highly branched polyme lining primary, secondary and tertiary amino groups in the ratio 1:2:1,was Ujed. It has a broad molar mass distribution with &?, = 60 10” (light scattering) and Mn < 3.5= 104 (vapor pressure osmometry ) [ 3 ]. In aqueous solution it behaves as a sphere [ 61 with an average hydrodynamic diameter around 100 nm (quasi-elastic laser light scattering) /3]. Catiortic fibers Pulp fibers were dispersed in an aqueous solution of golyethylenimine containing 10% polymer per fiber mass. After 60 min of slow paddle stirring, the fibers were separated by filtration, redispersed in distilled water and again separated (repeated three times) in order to remove any unadsorbed polymer. ‘Phe amount of adsorbed polymer determined from nitrogen content (Kjeldahl) was 13.5 mg g-l of fiber.
267
Cationic clay A dispersion of clay at 10% solids was admixed into a solution of polyethylenimine containing 10% polymer per clay mass in a Waring Ble;;det. After 60 min the clay was separated by centrifugation and redispersed in distilled water (repeated three times). The amount of adsorbed polymer was 10 mg g-’ of clay. The clay was positively charged in the region of pH 3-9. Methods Investigated systems For the purpose of producing oppositely charged fibers and clay particles the following procedures were used. (i) Cationic fibers or cationic clay, obtained by treatment with an excess of polyethylenimine, were used in combination with the other untreated component. (ii) Polyethylenimine was added, in an amount just sufficient to reverse the charge, to the suspension of either fibers or clay. After 10 min of c Jntinuous mixing a suspension of the other component was introduced. (iii) Suspensions of both fibers and clay were adjusted to a pH at which clay becomes positive and fibers remain negative and mixed together. Clay particle deposition Fibers (1 g) were dispersed in 250 cm3 distilled water, kept suspended by constant paddle stirring at 80 r.p.m. then 250 cm3 of clay suspension with varied concentration added. .4ftcr mixing the two components together, samples of the supernatant were withdrawn, in timed intervals, by means of a pipette equipped with a filter tip to prevent fibers from entering the pipette. The first rehable reading was at 15 sec. The system was at pH = 6 except when pH was used to control the charge. Electrophoretic mobility A Rank Bros. particle electrophoresis apparatus (Cambridge) equipped with a flat cell was used. To obtain the mobility of fibers a small amount of fines, generated from fibers in a Waring Blender, was added. Their mobility was assumed to represent the fibers. THEORETICAL
MODEL
OF PIGMENT
PARTICLES
DEPOSITION
ON FIBERS
The rate of deposition of small particles on solid surfaces can be described by analogy with the Langmuir analysis of gas molecule adsorption [ 7,8]. However, because often there are not enough particles in the system to cover the available surface fully, our intention is to develop a kinetic equation applicable
268
to a situation where the particles are both in an excess and at less than full coverage. The kinetics of particle deposition can be treated as a collision between fibers and clay particles. Initially there are NO particles and Nr fibers per unit volume and the initial collision frequency per unit volume will be given by
r )
f=hJW’&
where k,, is the rate constant. In a system composed of oppositely charged components it is assumed that the clay particles collide only with fibers and upon collision remain attached to the fiber. The number of fibers is invariant with time and, therefore, the number of particles deposited on fibers as a function of time can be described as
(2) where Nd is the number of particles deposited, N, is the number of particles in the supernatant, N,,, is the maximum number of particles that can deposit, and Nr is the number of fibers. All the number concentrations are expressed per unit volume of the system. The equation was extended to include a collision efficiency factor ffO, which depends on the ratio of attractive and shear forces KU* The conservation of the number of particles requires N,=N,,-Nd
(3)
which combined with Eqn (2) gives I
and by dividing with N,,,
(4)
yields
&/-Nmnx represents the fractional surface coverage B and NO/N,,,
= p reflects the ratio between the number of particles present and the maximum number of particles that may deposit on the available surface of the fibers, thus
(6) The parameter p is of particular Lmportance in a system containing fewer particles than can deposit at maximum coverage. It is not included in the Langmtlir analysis, where it is usually assumed that. there is an excess of molecules
269 1.2 5.0
2.5
I
I
1 1.67
1.25
1.0 -
0.6
0
0.4
1
4
7 ‘12
6
a
Fig. 1. Fractional coverage B as a function of square root of dimensionless time 7 (T= LY&JV~) for different values of j.? (ratio of number of particles present, IV,,, and maximum number of particles that can deposit, N,,), shown in the figure.
available for full coverage. It is of interest to note that as t-*0, 8-4 (6 ) reduces to 8= cyO klzN&
and Eqn (7)
The solution of Eqn (6 ) is 8=
~-expI(1-~~~o~12~f~l 1--P-‘exp[(1-_)~oK12Nft]
‘IN
which describes the rate of particle deposition under conditions where the number of particles present exceeds the number that can deposit, ,G> 1, ‘dswell as where there is a shortage, PC 1. In Fig. 1 the fractional coverage 8 is shown for different fl as a function of square root of dimensionless time z in order to emphasize the early stage of deposition. Time z is defined as ~=a,k,,N~t RESULTS Charge
(9)
AND DISCUSSION
modification
Three methods were used for producing oppositely charged fibers and clay particles. The most straightforward is the pretreatment of either fibers or clay with an excess of polymer followed by removal of the unadsorbed polymer. The second method is to exploit the fact that the surface cha.rge on clay particles is
270
pH dependent. As shown in Fig. 2, the clay particles below pH 4.5 become positively charged while the fibers remain negative. Thus by adjusting the system to pH 4, oppositely charged clay particles and fibers are formed. The third method, using a minim1 lm amount of polymer to reverse the charge of either fibers or clay, is probably the most desirable from a practical point of view. Figure 3 shows the change in electrophoretic mobility of both fxbers and clay, measured separately at pH 6, as a function of polyethylenimine (PEI ) addition. The amount of polymer is expressed either per gram of fibers or per 0.2 g of clay dispersed in 500 cm3 of distilled water for the purpose of maintaining conditions comparable to those used for deposition measurements. As seen, the addition of 1 mg is sufficient to reverse the charge of both. This means
Fig. 2. Electrophoretic POLYMER -0’
mobility
and fiber fines as a function
of pH.
TO CLAY
--J
o
0
POLYMER
TO FIBERS
. -
of clay particles
FIBERS CLAY IN
SPNT
0
1
2
3
4
5
mg/g fiber POLYMER
0
1
2 3 4 mgJ0.29 clay
5
ADDITION
Fig. 3. Electrophoretic mobility of clay particles and fiber fines as a function ot’ polyethylenimirx addition at pH 6. Full points-polymer added to either the fibers (1 g 500 cms3) or the clay (O.:!. g 500 cmd3); open points left-clay particles (0.2 g) added to polymer treated fibers (1 g 500 cmA3); open points right-clay particles (0.2 g) treated with polymer and added to untreated fibers (1 g 500 cm-“l).
271
that either component can be treated before the other untreated one is added and thus create a situation where fibers and clay particles are oppositely charged. However, this requires that all the polymer added be adsorbed because if not, then, upon admixing the untreated component, the excess of polymer may adsorb onto it and affect its charge. There is also the possibility that ravenwhen completely adsorbed on one component, the polymer may redistribute upon addition of the second component. Although the limited data from the literature indicate that, polyethylenimine has a high affinity to both cellulcsic fibers and clay [3,4,10 1, the actual adsorption at the addition level of our interest is difficult to estabiish, the reason being that the available methods are not sensitive enough to detect concentrations below 1 ppm. In order to gain some information concerning this problem a simple test was performed. The mobilities of clay particles, after 60 min of mixing with polymer-treated fibers, and of treated clay particles, after mixing with untreated fibers, are shown as open points in Fig. 3. As can be seen, when 1 mg of polymer is used to treat 1 g of fiber, the clay particles remain negative. On the other hand, when 0.2 g of clay is treated with 3. mg of polymer the particles remain positive. Thus it was established that by using 1 mg of polyethylenimine the system should be composed of oppositely charged fibers and clay. The same test could not be performed with fibers because the fiber fines, required for mobility measurements, cannot be distinguished from clay particles and, furthermore, provided they become oppositely charged, heterocoagulation between clay particles and fiber fines will occur. Kinetics
of clay deposition.
The rate of particle deposition on fibers was monitored in all the abovementioned cases intended to produce oppcsitely charged fibers and clay particles, i.e. (i) cationic fibers or cationic clay were mixed with the untreated second component; (ii) polyethylenimine (1 mg) was added to either fibers (1 g;!or clay (0.2 g) prior to the introduction of the second component; or (iii) suspensions of fibers and clay adjusted to pH 4 were mixed together. Figure 4 shows the deposition of cationic clay, added in amount of 50-500 mgg -’ fibers, as a function of time. The data are plotted in mg clay deposited per gram fibers and against the square root of time in order to emphasize the early stage of deposition. It is apparent that the maximum coverage is around 280 mg. Taking the best fit value for CY&~JV~from the experimental points, Eqn (8) was used to calculate the theoretical curves, a&o expressed in mg clay, rather than fractional coverage 6. The curves shown appear t.o be in reasonable agreement with the experimental points.
272 CATIONIC
CLAY
v
200
-A
100
-0
0
1
2
3 t
4 112
5
6
7
50
8
min’/2
Fig. 4. Experimental points and iheoretical curves for deposition, at pH6, of cationic cIay (added in amounts of 50-500 mg) on fibers (1 g) as a function of time. Numbers indicate the amount of clay added. Theoretical curves were calculated by using the best fit vaiue for cx,k,JV, =0.4 min- ’ from the experimental points.
CATIONIC &
.m G 7 F
PUl.P 500
250 20G
-
150
’
_
z5
G s
LL
100
a
100
x
0
1
2
3
4
s
6
7
8
t’h _ n-tin’/2
Fig. 5. Experimental points and theoretical curves for deposition, at pH6, of clay (added in amounts of’fi 500 mg) on cationic fibers (1 g) as a function of time. Numbers indicate the amount of clay L&s~J~.Theoretical curves were calculated by using the best fit value for q,hlPNf= 0.32 min- ’ from the experimental points.
Figure 5 shows the situation when untreated clay deposits on cationic fiber at pH 6. AgaG.+ thy clay addition is 50-500 mg g-’ fibers, and maximum coverage is around 240 mg. The theoretical curves were calculat-ed using the best
273
I
:tron microscopy
at two
was 0.32 min-’
as
xi with the number le. This can be estibe around 1 m2 [5 ]
274
and the size of the clay particles to be equal to the average equivalent spherical diameter of 0.2 pm. The number of closely packed spheres in cubic arrangement is 2 . 5-10” mm2 which represents about 260 mg, a value close to that observed experimentally. This would also indicate that the clay is well dispersed and deposits on the fiber as individual particles. A micrograph in Fig. 6 shows that this indeed is so. Comparison
of experimental
and theoretical rate constants
Ttz theoretical rate constant k,, can be estimated ‘by treating the particle deposition as a collision between unequal spheres. Considering the size of the particles involved, the process in a stirred system is apparently dependent on hydrodynamic shear and therefore is orthokinetic. This can be demonstrated by rrreasuringthe deposition at different rates of mixing. Figure 7 shows that at the same addition of untreated clay (200 mg g-’ of cationic fibers), the rate of deposition is faster when the mixing speed is increased from SO r.p.m. to 300 r.p.m. As seen in Fig. 7, besides affecting the rate of deposition, the hydrodynamic shear appears to prevent complete deposition. This is likely to be due to particle escape at high shear rates. According to Smoluchowski [ 111, the theoretical rate constant for orthokinetic collision of unequal spheres in simple shear is k
12
=$(a,
+a,)3
where G is the velocity gradient or shear rate, and al and a2 are the radii of the particles. In our system the average shear rate at 80 r.p.m. is estimated as 3.0 s-- i and CATIONIC
0
I
I
I
1
2
3
PULP
I
I
4 5 t ‘/2. min’h
I
6
7
8
Fig. 7. Deposition of clay on cationic fibers as a function of time at speeds of mixing of80 and 300 r.p+m. Clay addition was 200 mg g-’ fiber in 500 cm’.
275
the average equivalent spherical radius of clay particles al =O.l jlrn. An effective radius aPeff of rod-like fibers can be estimated from their average length L=2 mm and average radius R= 15 pm. It can be shown [12] that the deposition rate of small spheres on large rod-like collectors is identical to that for the deposition on large spheres, but with the volume of the rod replaced by an effective sphere. Hence qeff= (3/4 R 2L) ‘I3 “N70 pm. The calculated rate constant then is k12=4.5010-12 m3 s-l. From the best theoretical fit through the experimental points in Fig. 5, the value c~&~~N~=O.32 rnin-l was found. The rate constant Jz12can be obtained providing LX~ and Nr are known. The number of f”ibersNf in a unit vclume ( m3) can be estimated from their average length of 2 mm and the mass per unit length, taken as 0.1 mg m-’ [ 121. At the fiber concentration 1 g 500 cm-‘, Nfz 1 lnl" ~~5=10-~~ m7 s-‘. Hence c~~~~0.1, which is . . mm3 which gives cy0Jz12 somewhat high, but not of an lmreasonable magnitude for the orthokinetic capture efficiency between unequal sized particles at G= 10 s- ’ [ 9 1, seeing that the small particles are also subject to Brownian motion. Thus the observed deposition rate is consistent with Smoluchowski’s kinetics. l
Deposition
of clayaggregates
Figure 8 shows deposition of clay, added in an amount of 200 mg g-l of Cbers, with 1 mg of polyethylenirSne being added either in the fibers (1 g) or to the clay (0.2 g j before the okher component was i.ntroduced. The initial rate of deposition is about six times faster than that observed with clay depositing on cationic fibers (Fig. 5 ) 1 which is also shown for comparison. A similar faster deposition occurs when the cla!/ particles were made positive by adjusting the system to pH 4. The .--*r;,sson for the i”asterdeposition is apparently a deposition of clay aggre-
0
A
PEI
TO CLAY
Y
PEt TOFIEERS
:
i$iONtC
_
/ 0
FtBEt
Fig. 8. Deposition of clay on fibers induced by polyethylenimine addition or pH control. Polymer ( 1 mg) added either to the clay (0.2 g) or to the fibers (1 g) prior to admixing the second untreated component.
576
ii
n 600 -
0
1
2
3
A
5
5
7
8
t l/z, min’h
Fig. 9. Deposition of clay (added in amounts of 600-1000 mg) on cationic fibers (1 g) in the presence of 0.2 mg polyethylenimine.
gates instead of single particles. Confirmation that aggregation indeed takes place was obtained by measuring the turbidity of a clay suspension at a given concentration, 0.2 g 500 cma3. The turbidity of dispersed untreated clay was similar to that of clay treated with an excess amount of PEI (cationic clay). Their rates of deposition were also similar, as seen in Figs 4 and 5. Upon adjusting to pH 4 or addinE 1 mg PEI, the turbidity of the clay dispersion decreased, thus indicating destabilization. A similar decrease in turbidity was obser -ledwhen clay was added to a filtrate of fibers treated with 1 mg PEI. The last c~tst!means that not all the PEI adsorbed on the fibers. It is also of interest to note that although the unadsorbed polymer caused destabilization, the amount was not sufficient to reverse the charge, as shown in Fig. 3. Further observation of Fig. 8 shows that in a system adjusted to pH 4, a detachment of clay takes place with prolonged times of mixing. This could. be due to a decrease ~11! iond strength with time or to a variation of the effective shear at different locations in the stirred system. Whatever the case, it indicates that attachment of clay particles to the fiber is weaker than expected when polymer is present [ 14,151. Besides faster deposition of aggregated clay, maximum deposition also increases, as shown in kl’ig.9. When compared with Fig. 5, where the maximum coverage is 240 mg g;-’ of cationic fiber, upon aggregation, 750 mg of clay can deposit. The deposition of aggregated clay was accomplished by following the same procedure as in Fig. 5. However, before the addition of clay to the cationic fibers, a small quantity of PEI, sufficient to destabilize but not enough to reverse the charge of the clay, was introduced. The faster deposition of aggregates (Fig. 8) can be understood by consider-
277
ing t h e initial r a t e of d e p o s i t i o n w h i c h equals (~ok12Nf,6 ( E q n ( 7 ) ) . In t h e case of aggregates, b e c a u s e of i n c r e a s e d size, b o t h t h e collision efficiency, c~o, and, to a m u c h lesser e x t e n t , t h e r a t e c o n s t a n t , k12, i n c r e a s e (also, for aggregates, a l < < a 2 e f f ) - O n t h e o t h e r h a n d , t h e p a r a m e t e r f l ~ 0 . 3 (200 m g / 7 5 0 rag) decreases in c o m p a r i s o n w i t h t h a t for d i s p e r s e d p a r t i c l e s f l ~ 0 . 8 (200 m g / 2 4 0 m g ) . If t h e initial r a t e of a g g r e g a t e d e p o s i t i o n is a b o u t six t i m e s faster, it follows t h a t a0 is a b o u t 15 t i m e s larger t h a n t h a t for t h e d e p o s i t i o n of single clay particles. T h i s m e a n s t h a t ~o is a v e r y s t r o n g f u n c t i o n of t h e c l a y - f i b e r p a r t i c l e size r a t i o a,/R, s i m i l a r to s p h e r e s [9 ]. CONCLUSION
T h e k i n e t i c s of clay p a r t i c l e d e p o s i t i o n on fibers of o p p o s i t e c h a r g e can be described by a model w h i c h t a k e s into a c c o u n t a s i t u a t i o n w h e n a s y s t e m does n o t c o n t a i n a s u f f i c i e n t n u m b e r of p a r t i c l e s for full coverage. In t h e model, derived e s s e n t i a l l y f r o m t h e L a n g m u i r a n a l y s i s of m o l e c u l a r a d s o r p t i o n , a new p a r a m e t e r fl is i n c l u d e d w h i c h reflects t h e r a t i o b e t w e e n t h e n u m b e r of p a r t i cles p r e s e n t a n d t h e m a x i m u m n u m b e r of p a r t i c l e s t h a t m a y deposit. T h e e x p e r i m e n t a l l y o b s e r v e d r a t e s of d e p o s i t i o n of d i s p e r s e d a n i o n i c clay p a r t i c l e s on cationic fibers or c a t i o n i c clay p a r t i c l e s on a n i o n i c fibers are cons i d e r a b l y slower t h a n t h e d e p o s i t i o n of clay aggregates. Also, t h e m a x i m u m m a s s coverage of fibers b y a g g r e g a t e s is l a r g e r t h a n t h a t b y d i s p e r s e d clay p a r ticles. In general, t h e o b s e r v e d r a t e s are c o m p a r a b l e to t h o s e t h e o r e t i c a l l y predicted a n d c o n s i s t e n t w i t h S m o l u c h o w s k i ' s kinetics.
REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
T.G.M. van de Ven, J. Pulp P a p e r Sci., 85 (3) (1984) J57. B. Alince a n d P. Lepoutre, Tappi, 66 (2) (1983) 101. D. H o r n , in E.J. Goethals (Ed.), P o l y m e r i c A m i n e s a n d A m m o n i u m Salts, P e r g a m o n Press, Oxford, 1980, p. 333. R.I.S. Gill a n d T.M. H e r r i n g t o n , Colloids Surfaces, 28 (1987) 41. A.J. Stature, Wood a n d Cellulose Science, R o n a l d Press, NY, 1964, p. 189. R.E. H o s t e t l e r a n d J.W. Swanson, J. Polym. Sci., Polym. Chem. Ed., 12 (1974) 29. M.T. Boughey, R.M. D u c k w o r t h , A. Lips a n d A.L. S m i t h , J. C h e m . Soc., F a r a d a y T r a n s . I, 74 (1978) 2200. B. Vincent, M. Jafelici and P.F. L u c k h a m , J. C h e m . Soc., F a r a d a y T r a n s . I, 76 (1980) 674. T.G.M. van de Ven, Adv. Colloid I n t e r f a c e Sci., 17 (1982) 105. L. Neimo, X X I E U C E P A Int. Conf., Torremolinos, Spain, 1984, Vol. 2, p. 391. M. Smoluchowski, Z. P h y s . Chem., 92 (1917) 129. J. Petlicki and T.G.M. van de Ven, in preparation. G.A. Smook, H a n d b o o k for Pulp a n d P a p e r Technologists, T a p p i Press, Atlanta, GA, 1982, p. 18. M.A. Hubbe, Colloids Surfaces, 25 (1987) 325. R.H. Pelton a n d L.H. Allen, J. Colloid I n t e r f a c e Sci., 99 (2) (1984) 387.
265
Kinetics of colloidal particle deposition on pulp fibers 1.Deposition of clay on fibers of opposite charge B. Alince, J. Betlicki and T.G.M. van de Ven Pap&an and Department of Chemistry, Pulp and Paper Research Montreal
Centre,
McGill
University,
H3A 2A7, Canada
(Received 12 October 1990; accepted 29 January 1991)
Abstract The rate of deposition of clay particles on oppositely charged fibers was measured in five systems where the negative surface charge of either the fibers or the clay was reversed by adsorption of cationIc polyethylenimine or pII control. A theoretical model of particle deposition kinetics derived fro-m Langmuir analysis is presented, which is also applicab!r to a system containing fewer partic!es than required for full coverage by introducing a new parameter. It is observed that the rate of deposition of dispersed clay particies is considerably slower than the deposition of clay aggregates. The maximum mass coverage of fibers by dispersed clay particles is also less than the coverage by clay aggregates. The experimental rates are comparable to tilose calculated theoretically and thus consistent with Smoluchowski’s kinetics.
INTRODUCTION
When mineral particles are added to an aqueous suspension of fibers for the purpose of producing filled papers, the obvious requirement is their effect.ive retention. However, because both fibers and particles are negatively charged they repel each other and only particles larger than the openings in the fiber web, which is being formed on a screen, can be entrapped mechanically. The probability for particles of common pigments to be retained by this filtration mechanism is small because of their size, which is often in the submicron range. This has been shown both theoretically [ 11 and experimentally [ 2 ] . The way to improve retention is to encourage natural attraction between fibers and particles. This can be achieved by manipulating pH, providing that the surface charge is pH-dependent, or by increasing ionic strength and thus decreasing repulsion. More effective is the introduction of cationic polyelectrolyte, which by adsorbing on the componerrts can cause their heterocoagulation due to a charge modification or heteroklocculation by a bridging mechanism. Under such circumstances the particles may deposit on fibers and be carried into paper.
0166-6622/91/$03.50
0 1991 Elsevier Science Publishers B.V. All rights reserved.
266
Besides the interaction between fibers and particles, at least two other factors must be considered for retention’to be effective. On a modern, fast running paper machine the time available for particle deposition to take place is of the order of seconds, and, because of the high turbulence, the particles should be attached strongly enough to resist removal from fibers by hydrodynamic forces. The focus here is on the process of clay particle deposition on fibers under conditions where they are oppositely charged and, therefore, mutually attractive. For the surface charge mcdifrcation a highly charged cationic polyethylenimine w~is employed. This polymer is believed to destabilize colloidal particles via charge neutralization rather than the bridging rcechanism [3,4 1. The polymer was applied in different modes either to clay particles or to fibers to provide them with a positive charge prior to the addition of the second component. Upon mixing the two components, clay and fibers, the extent of clay deposition was monitored in timed intervals. The emphasis is on the rate of clay particle deposition on fibers and on an attempt to formulate a theoretical model to describe the process. EXPERIMENTAL
Materials Fibers Hardwood bleached kraft pulp was disintegrated in water and washed several times on a 150 mesh screen (openings 100 pm ) in order to remove fiber fines. The average fiber is 2 mm long and 30 pm in diameter. The surface area is estimated to be 0.5-1.5 m2 g-’ [ 51. Polymer Poiyeth :limine POLYMIN P (BASF), believed to be a highly branched polyme lining primary, secondary and tertiary amino groups in the ratio 1:2:1,was Ujed. It has a broad molar mass distribution with &?, = 60 10” (light scattering) and Mn < 3.5= 104 (vapor pressure osmometry ) [ 3 ]. In aqueous solution it behaves as a sphere [ 61 with an average hydrodynamic diameter around 100 nm (quasi-elastic laser light scattering) /3]. Catiortic fibers Pulp fibers were dispersed in an aqueous solution of golyethylenimine containing 10% polymer per fiber mass. After 60 min of slow paddle stirring, the fibers were separated by filtration, redispersed in distilled water and again separated (repeated three times) in order to remove any unadsorbed polymer. ‘Phe amount of adsorbed polymer determined from nitrogen content (Kjeldahl) was 13.5 mg g-l of fiber.
267
Cationic clay A dispersion of clay at 10% solids was admixed into a solution of polyethylenimine containing 10% polymer per clay mass in a Waring Ble;;det. After 60 min the clay was separated by centrifugation and redispersed in distilled water (repeated three times). The amount of adsorbed polymer was 10 mg g-’ of clay. The clay was positively charged in the region of pH 3-9. Methods Investigated systems For the purpose of producing oppositely charged fibers and clay particles the following procedures were used. (i) Cationic fibers or cationic clay, obtained by treatment with an excess of polyethylenimine, were used in combination with the other untreated component. (ii) Polyethylenimine was added, in an amount just sufficient to reverse the charge, to the suspension of either fibers or clay. After 10 min of c Jntinuous mixing a suspension of the other component was introduced. (iii) Suspensions of both fibers and clay were adjusted to a pH at which clay becomes positive and fibers remain negative and mixed together. Clay particle deposition Fibers (1 g) were dispersed in 250 cm3 distilled water, kept suspended by constant paddle stirring at 80 r.p.m. then 250 cm3 of clay suspension with varied concentration added. .4ftcr mixing the two components together, samples of the supernatant were withdrawn, in timed intervals, by means of a pipette equipped with a filter tip to prevent fibers from entering the pipette. The first rehable reading was at 15 sec. The system was at pH = 6 except when pH was used to control the charge. Electrophoretic mobility A Rank Bros. particle electrophoresis apparatus (Cambridge) equipped with a flat cell was used. To obtain the mobility of fibers a small amount of fines, generated from fibers in a Waring Blender, was added. Their mobility was assumed to represent the fibers. THEORETICAL
MODEL
OF PIGMENT
PARTICLES
DEPOSITION
ON FIBERS
The rate of deposition of small particles on solid surfaces can be described by analogy with the Langmuir analysis of gas molecule adsorption [ 7,8]. However, because often there are not enough particles in the system to cover the available surface fully, our intention is to develop a kinetic equation applicable
268
to a situation where the particles are both in an excess and at less than full coverage. The kinetics of particle deposition can be treated as a collision between fibers and clay particles. Initially there are NO particles and Nr fibers per unit volume and the initial collision frequency per unit volume will be given by
r )
f=hJW’&
where k,, is the rate constant. In a system composed of oppositely charged components it is assumed that the clay particles collide only with fibers and upon collision remain attached to the fiber. The number of fibers is invariant with time and, therefore, the number of particles deposited on fibers as a function of time can be described as
(2) where Nd is the number of particles deposited, N, is the number of particles in the supernatant, N,,, is the maximum number of particles that can deposit, and Nr is the number of fibers. All the number concentrations are expressed per unit volume of the system. The equation was extended to include a collision efficiency factor ffO, which depends on the ratio of attractive and shear forces KU* The conservation of the number of particles requires N,=N,,-Nd
(3)
which combined with Eqn (2) gives I
and by dividing with N,,,
(4)
yields
&/-Nmnx represents the fractional surface coverage B and NO/N,,,
= p reflects the ratio between the number of particles present and the maximum number of particles that may deposit on the available surface of the fibers, thus
(6) The parameter p is of particular Lmportance in a system containing fewer particles than can deposit at maximum coverage. It is not included in the Langmtlir analysis, where it is usually assumed that. there is an excess of molecules
269 1.2 5.0
2.5
I
I
1 1.67
1.25
1.0 -
0.6
0
0.4
1
4
7 ‘12
6
a
Fig. 1. Fractional coverage B as a function of square root of dimensionless time 7 (T= LY&JV~) for different values of j.? (ratio of number of particles present, IV,,, and maximum number of particles that can deposit, N,,), shown in the figure.
available for full coverage. It is of interest to note that as t-*0, 8-4 (6 ) reduces to 8= cyO klzN&
and Eqn (7)
The solution of Eqn (6 ) is 8=
~-expI(1-~~~o~12~f~l 1--P-‘exp[(1-_)~oK12Nft]
‘IN
which describes the rate of particle deposition under conditions where the number of particles present exceeds the number that can deposit, ,G> 1, ‘dswell as where there is a shortage, PC 1. In Fig. 1 the fractional coverage 8 is shown for different fl as a function of square root of dimensionless time z in order to emphasize the early stage of deposition. Time z is defined as ~=a,k,,N~t RESULTS Charge
(9)
AND DISCUSSION
modification
Three methods were used for producing oppositely charged fibers and clay particles. The most straightforward is the pretreatment of either fibers or clay with an excess of polymer followed by removal of the unadsorbed polymer. The second method is to exploit the fact that the surface cha.rge on clay particles is
270
pH dependent. As shown in Fig. 2, the clay particles below pH 4.5 become positively charged while the fibers remain negative. Thus by adjusting the system to pH 4, oppositely charged clay particles and fibers are formed. The third method, using a minim1 lm amount of polymer to reverse the charge of either fibers or clay, is probably the most desirable from a practical point of view. Figure 3 shows the change in electrophoretic mobility of both fxbers and clay, measured separately at pH 6, as a function of polyethylenimine (PEI ) addition. The amount of polymer is expressed either per gram of fibers or per 0.2 g of clay dispersed in 500 cm3 of distilled water for the purpose of maintaining conditions comparable to those used for deposition measurements. As seen, the addition of 1 mg is sufficient to reverse the charge of both. This means
Fig. 2. Electrophoretic POLYMER -0’
mobility
and fiber fines as a function
of pH.
TO CLAY
--J
o
0
POLYMER
TO FIBERS
. -
of clay particles
FIBERS CLAY IN
SPNT
0
1
2
3
4
5
mg/g fiber POLYMER
0
1
2 3 4 mgJ0.29 clay
5
ADDITION
Fig. 3. Electrophoretic mobility of clay particles and fiber fines as a function ot’ polyethylenimirx addition at pH 6. Full points-polymer added to either the fibers (1 g 500 cms3) or the clay (O.:!. g 500 cmd3); open points left-clay particles (0.2 g) added to polymer treated fibers (1 g 500 cmA3); open points right-clay particles (0.2 g) treated with polymer and added to untreated fibers (1 g 500 cm-“l).
271
that either component can be treated before the other untreated one is added and thus create a situation where fibers and clay particles are oppositely charged. However, this requires that all the polymer added be adsorbed because if not, then, upon admixing the untreated component, the excess of polymer may adsorb onto it and affect its charge. There is also the possibility that ravenwhen completely adsorbed on one component, the polymer may redistribute upon addition of the second component. Although the limited data from the literature indicate that, polyethylenimine has a high affinity to both cellulcsic fibers and clay [3,4,10 1, the actual adsorption at the addition level of our interest is difficult to estabiish, the reason being that the available methods are not sensitive enough to detect concentrations below 1 ppm. In order to gain some information concerning this problem a simple test was performed. The mobilities of clay particles, after 60 min of mixing with polymer-treated fibers, and of treated clay particles, after mixing with untreated fibers, are shown as open points in Fig. 3. As can be seen, when 1 mg of polymer is used to treat 1 g of fiber, the clay particles remain negative. On the other hand, when 0.2 g of clay is treated with 3. mg of polymer the particles remain positive. Thus it was established that by using 1 mg of polyethylenimine the system should be composed of oppositely charged fibers and clay. The same test could not be performed with fibers because the fiber fines, required for mobility measurements, cannot be distinguished from clay particles and, furthermore, provided they become oppositely charged, heterocoagulation between clay particles and fiber fines will occur. Kinetics
of clay deposition.
The rate of particle deposition on fibers was monitored in all the abovementioned cases intended to produce oppcsitely charged fibers and clay particles, i.e. (i) cationic fibers or cationic clay were mixed with the untreated second component; (ii) polyethylenimine (1 mg) was added to either fibers (1 g;!or clay (0.2 g) prior to the introduction of the second component; or (iii) suspensions of fibers and clay adjusted to pH 4 were mixed together. Figure 4 shows the deposition of cationic clay, added in amount of 50-500 mgg -’ fibers, as a function of time. The data are plotted in mg clay deposited per gram fibers and against the square root of time in order to emphasize the early stage of deposition. It is apparent that the maximum coverage is around 280 mg. Taking the best fit value for CY&~JV~from the experimental points, Eqn (8) was used to calculate the theoretical curves, a&o expressed in mg clay, rather than fractional coverage 6. The curves shown appear t.o be in reasonable agreement with the experimental points.
272 CATIONIC
CLAY
v
200
-A
100
-0
0
1
2
3 t
4 112
5
6
7
50
8
min’/2
Fig. 4. Experimental points and iheoretical curves for deposition, at pH6, of cationic cIay (added in amounts of 50-500 mg) on fibers (1 g) as a function of time. Numbers indicate the amount of clay added. Theoretical curves were calculated by using the best fit vaiue for cx,k,JV, =0.4 min- ’ from the experimental points.
CATIONIC &
.m G 7 F
PUl.P 500
250 20G
-
150
’
_
z5
G s
LL
100
a
100
x
0
1
2
3
4
s
6
7
8
t’h _ n-tin’/2
Fig. 5. Experimental points and theoretical curves for deposition, at pH6, of clay (added in amounts of’fi 500 mg) on cationic fibers (1 g) as a function of time. Numbers indicate the amount of clay L&s~J~.Theoretical curves were calculated by using the best fit value for q,hlPNf= 0.32 min- ’ from the experimental points.
Figure 5 shows the situation when untreated clay deposits on cationic fiber at pH 6. AgaG.+ thy clay addition is 50-500 mg g-’ fibers, and maximum coverage is around 240 mg. The theoretical curves were calculat-ed using the best
273
I
:tron microscopy
at two
was 0.32 min-’
as
xi with the number le. This can be estibe around 1 m2 [5 ]
274
and the size of the clay particles to be equal to the average equivalent spherical diameter of 0.2 pm. The number of closely packed spheres in cubic arrangement is 2 . 5-10” mm2 which represents about 260 mg, a value close to that observed experimentally. This would also indicate that the clay is well dispersed and deposits on the fiber as individual particles. A micrograph in Fig. 6 shows that this indeed is so. Comparison
of experimental
and theoretical rate constants
Ttz theoretical rate constant k,, can be estimated ‘by treating the particle deposition as a collision between unequal spheres. Considering the size of the particles involved, the process in a stirred system is apparently dependent on hydrodynamic shear and therefore is orthokinetic. This can be demonstrated by rrreasuringthe deposition at different rates of mixing. Figure 7 shows that at the same addition of untreated clay (200 mg g-’ of cationic fibers), the rate of deposition is faster when the mixing speed is increased from SO r.p.m. to 300 r.p.m. As seen in Fig. 7, besides affecting the rate of deposition, the hydrodynamic shear appears to prevent complete deposition. This is likely to be due to particle escape at high shear rates. According to Smoluchowski [ 111, the theoretical rate constant for orthokinetic collision of unequal spheres in simple shear is k
12
=$(a,
+a,)3
where G is the velocity gradient or shear rate, and al and a2 are the radii of the particles. In our system the average shear rate at 80 r.p.m. is estimated as 3.0 s-- i and CATIONIC
0
I
I
I
1
2
3
PULP
I
I
4 5 t ‘/2. min’h
I
6
7
8
Fig. 7. Deposition of clay on cationic fibers as a function of time at speeds of mixing of80 and 300 r.p+m. Clay addition was 200 mg g-’ fiber in 500 cm’.
275
the average equivalent spherical radius of clay particles al =O.l jlrn. An effective radius aPeff of rod-like fibers can be estimated from their average length L=2 mm and average radius R= 15 pm. It can be shown [12] that the deposition rate of small spheres on large rod-like collectors is identical to that for the deposition on large spheres, but with the volume of the rod replaced by an effective sphere. Hence qeff= (3/4 R 2L) ‘I3 “N70 pm. The calculated rate constant then is k12=4.5010-12 m3 s-l. From the best theoretical fit through the experimental points in Fig. 5, the value c~&~~N~=O.32 rnin-l was found. The rate constant Jz12can be obtained providing LX~ and Nr are known. The number of f”ibersNf in a unit vclume ( m3) can be estimated from their average length of 2 mm and the mass per unit length, taken as 0.1 mg m-’ [ 121. At the fiber concentration 1 g 500 cm-‘, Nfz 1 lnl" ~~5=10-~~ m7 s-‘. Hence c~~~~0.1, which is . . mm3 which gives cy0Jz12 somewhat high, but not of an lmreasonable magnitude for the orthokinetic capture efficiency between unequal sized particles at G= 10 s- ’ [ 9 1, seeing that the small particles are also subject to Brownian motion. Thus the observed deposition rate is consistent with Smoluchowski’s kinetics. l
Deposition
of clayaggregates
Figure 8 shows deposition of clay, added in an amount of 200 mg g-l of Cbers, with 1 mg of polyethylenirSne being added either in the fibers (1 g) or to the clay (0.2 g j before the okher component was i.ntroduced. The initial rate of deposition is about six times faster than that observed with clay depositing on cationic fibers (Fig. 5 ) 1 which is also shown for comparison. A similar faster deposition occurs when the cla!/ particles were made positive by adjusting the system to pH 4. The .--*r;,sson for the i”asterdeposition is apparently a deposition of clay aggre-
0
A
PEI
TO CLAY
Y
PEt TOFIEERS
:
i$iONtC
_
/ 0
FtBEt
Fig. 8. Deposition of clay on fibers induced by polyethylenimine addition or pH control. Polymer ( 1 mg) added either to the clay (0.2 g) or to the fibers (1 g) prior to admixing the second untreated component.
576
ii
n 600 -
0
1
2
3
A
5
5
7
8
t l/z, min’h
Fig. 9. Deposition of clay (added in amounts of 600-1000 mg) on cationic fibers (1 g) in the presence of 0.2 mg polyethylenimine.
gates instead of single particles. Confirmation that aggregation indeed takes place was obtained by measuring the turbidity of a clay suspension at a given concentration, 0.2 g 500 cma3. The turbidity of dispersed untreated clay was similar to that of clay treated with an excess amount of PEI (cationic clay). Their rates of deposition were also similar, as seen in Figs 4 and 5. Upon adjusting to pH 4 or addinE 1 mg PEI, the turbidity of the clay dispersion decreased, thus indicating destabilization. A similar decrease in turbidity was obser -ledwhen clay was added to a filtrate of fibers treated with 1 mg PEI. The last c~tst!means that not all the PEI adsorbed on the fibers. It is also of interest to note that although the unadsorbed polymer caused destabilization, the amount was not sufficient to reverse the charge, as shown in Fig. 3. Further observation of Fig. 8 shows that in a system adjusted to pH 4, a detachment of clay takes place with prolonged times of mixing. This could. be due to a decrease ~11! iond strength with time or to a variation of the effective shear at different locations in the stirred system. Whatever the case, it indicates that attachment of clay particles to the fiber is weaker than expected when polymer is present [ 14,151. Besides faster deposition of aggregated clay, maximum deposition also increases, as shown in kl’ig.9. When compared with Fig. 5, where the maximum coverage is 240 mg g;-’ of cationic fiber, upon aggregation, 750 mg of clay can deposit. The deposition of aggregated clay was accomplished by following the same procedure as in Fig. 5. However, before the addition of clay to the cationic fibers, a small quantity of PEI, sufficient to destabilize but not enough to reverse the charge of the clay, was introduced. The faster deposition of aggregates (Fig. 8) can be understood by consider-
277
ing t h e initial r a t e of d e p o s i t i o n w h i c h equals (~ok12Nf,6 ( E q n ( 7 ) ) . In t h e case of aggregates, b e c a u s e of i n c r e a s e d size, b o t h t h e collision efficiency, c~o, and, to a m u c h lesser e x t e n t , t h e r a t e c o n s t a n t , k12, i n c r e a s e (also, for aggregates, a l < < a 2 e f f ) - O n t h e o t h e r h a n d , t h e p a r a m e t e r f l ~ 0 . 3 (200 m g / 7 5 0 rag) decreases in c o m p a r i s o n w i t h t h a t for d i s p e r s e d p a r t i c l e s f l ~ 0 . 8 (200 m g / 2 4 0 m g ) . If t h e initial r a t e of a g g r e g a t e d e p o s i t i o n is a b o u t six t i m e s faster, it follows t h a t a0 is a b o u t 15 t i m e s larger t h a n t h a t for t h e d e p o s i t i o n of single clay particles. T h i s m e a n s t h a t ~o is a v e r y s t r o n g f u n c t i o n of t h e c l a y - f i b e r p a r t i c l e size r a t i o a,/R, s i m i l a r to s p h e r e s [9 ]. CONCLUSION
T h e k i n e t i c s of clay p a r t i c l e d e p o s i t i o n on fibers of o p p o s i t e c h a r g e can be described by a model w h i c h t a k e s into a c c o u n t a s i t u a t i o n w h e n a s y s t e m does n o t c o n t a i n a s u f f i c i e n t n u m b e r of p a r t i c l e s for full coverage. In t h e model, derived e s s e n t i a l l y f r o m t h e L a n g m u i r a n a l y s i s of m o l e c u l a r a d s o r p t i o n , a new p a r a m e t e r fl is i n c l u d e d w h i c h reflects t h e r a t i o b e t w e e n t h e n u m b e r of p a r t i cles p r e s e n t a n d t h e m a x i m u m n u m b e r of p a r t i c l e s t h a t m a y deposit. T h e e x p e r i m e n t a l l y o b s e r v e d r a t e s of d e p o s i t i o n of d i s p e r s e d a n i o n i c clay p a r t i c l e s on cationic fibers or c a t i o n i c clay p a r t i c l e s on a n i o n i c fibers are cons i d e r a b l y slower t h a n t h e d e p o s i t i o n of clay aggregates. Also, t h e m a x i m u m m a s s coverage of fibers b y a g g r e g a t e s is l a r g e r t h a n t h a t b y d i s p e r s e d clay p a r ticles. In general, t h e o b s e r v e d r a t e s are c o m p a r a b l e to t h o s e t h e o r e t i c a l l y predicted a n d c o n s i s t e n t w i t h S m o l u c h o w s k i ' s kinetics.
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T.G.M. van de Ven, J. Pulp P a p e r Sci., 85 (3) (1984) J57. B. Alince a n d P. Lepoutre, Tappi, 66 (2) (1983) 101. D. H o r n , in E.J. Goethals (Ed.), P o l y m e r i c A m i n e s a n d A m m o n i u m Salts, P e r g a m o n Press, Oxford, 1980, p. 333. R.I.S. Gill a n d T.M. H e r r i n g t o n , Colloids Surfaces, 28 (1987) 41. A.J. Stature, Wood a n d Cellulose Science, R o n a l d Press, NY, 1964, p. 189. R.E. H o s t e t l e r a n d J.W. Swanson, J. Polym. Sci., Polym. Chem. Ed., 12 (1974) 29. M.T. Boughey, R.M. D u c k w o r t h , A. Lips a n d A.L. S m i t h , J. C h e m . Soc., F a r a d a y T r a n s . I, 74 (1978) 2200. B. Vincent, M. Jafelici and P.F. L u c k h a m , J. C h e m . Soc., F a r a d a y T r a n s . I, 76 (1980) 674. T.G.M. van de Ven, Adv. Colloid I n t e r f a c e Sci., 17 (1982) 105. L. Neimo, X X I E U C E P A Int. Conf., Torremolinos, Spain, 1984, Vol. 2, p. 391. M. Smoluchowski, Z. P h y s . Chem., 92 (1917) 129. J. Petlicki and T.G.M. van de Ven, in preparation. G.A. Smook, H a n d b o o k for Pulp a n d P a p e r Technologists, T a p p i Press, Atlanta, GA, 1982, p. 18. M.A. Hubbe, Colloids Surfaces, 25 (1987) 325. R.H. Pelton a n d L.H. Allen, J. Colloid I n t e r f a c e Sci., 99 (2) (1984) 387.