Kinetics of Polyelectrolyte Adsorption on Cellulosic Fibers - Langmuir

Andrew T. Horvath , A. Elisabet Horvath , Tom Lindström and Lars Wågberg ... Lorna L. Kettle, Avinash P. Manian, John D. Payne, and Stephen J. Russe...
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Langmuir 2001, 17, 1096-1103

Kinetics of Polyelectrolyte Adsorption on Cellulosic Fibers Lars Wågberg*,† and Rickard Ha¨gglund‡ Department Chemistry and Process Technology, MidSweden University, 85170 Sundsvall, Sweden, and SCA Packaging Research, Box 3054, 85003 Sundsvall, Sweden Received May 2, 2000. In Final Form: November 28, 2000 The present investigation has been focused on studying the adsorption of three different molecular mass fractions of a polydimethyldiallylammonium chloride (DMDAAC) (8750 (LMw), 48 000 (MMw), and 1 200 000 (HMw)) on bleached chemical fibers. Both kinetics of adsorption and equilibrium adsorption measurements have been conducted, and the adsorption has been measured by polyelectrolyte titration. The results show that the LMw polymer can reach all the charges in the fiber wall whereas the MMw and HMw can only reach the charges on the external surfaces of the fibers. It is also shown that the kinetics of adsorption of the LMw polymer is not at all affected by the presence of a saturated layer of HMw polymer on the surface of the fibers. Finally the results from the investigation show that it is possible to have a full coverage of the external surface of the fibers by a high molecular mass polymer and a full coverage of the internal surface of the fibers with a low molecular mass polymer provided that the high molecular mass polymer is adsorbed before addition of the low molecular mass polymer. This is true if the polymers are adsorbed to the same type of groups on the fibers. A simplistic model for describing ployelectrolyte adsorption in turbulent flow also shows good agreement with measured values for the low molecular mass polyelectrolyte whereas the agreement for the high molecular polyelectrolyte is not as good. For the high molecular mass polyelectrolyte a more sophisticated model is needed.

Background Cationic polyelectrolytes have been used for many years in the paper industry to improve retention of fine material from the fibers or from added mineral fillers in the produced paper or to improve the strength properties of the paper. The polymers used for these different purposes are naturally different regarding reactive groups, molecular structure, and molecular mass, but they have one thing in common and that is the cationic charge. This charge is necessary for a good adsorption, to the fibers, since it will create a good interaction with the fibers, which carry negative charges. These charges, of the fibers, emanate from some hemicelluloses, which are anionic in their native form or from oxidation of cellulose or lignin during cooking and bleaching of the fibers.1 Earlier works have shown that the adsorption of cationic polyelectrolytes can be looked upon as an ion-exchange process where there is a close 1:1 matching between the charges on the polymer and charges on the fibers.2-4 Since the cellulosic fibers have a porous structure with micropores ranging from 1 to 30 nm and a rough surface, it is also well documented that the molecular mass of the polymer is very important for the adsorbed amount.5-8 This makes it difficult to interpret results from polyelectrolyte adsorption measurements on cellulosic fibers since † ‡

MidSweden University. SCA Packaging Research.

(1) Wågberg, L.; Annergren, G. Fundamentals of Papermaking, Transactions of the 11th Research Symposium held at Cambridge; Baker, C. F., Ed.; Pira International: Leatherhead, U.K., 1997; p 1. (2) Winter, L.; Wågberg, L.; O ¨ dberg, L.; Lindstro¨m, L. J. Colloid Interface Sci. 1986, 111, 537. (3) Wågberg, L.; Winter, L.; O ¨ dberg, L.; Lindstro¨m, L. Colloids Surf. 1987, 27, 163. (4) Wågberg, L.; O ¨ dberg, L.; Lindstro¨m, L.; Aksberg, R. J. Colloid Interface Sci. 1988, 123, 287. (5) Stone, J.E.; Scallan, A. M. Pulp Paper Mag. Can. 1968, 69, T288. (6) Ha¨ggkvist, M.; Li, T.-Q.; O ¨ dberg, L. Cellulose 1998, 5, 33. (7) Alince, B. J. Appl. Polym. Sci. 1990, 39, 355. (8) van de Ven, T. G. M.; Alince, B. Fundamentals of Papermaking, Transactions of the 11th Research Symposium held at Cambridge; Baker, C. F., Ed.; Pira International: Leatherhead, U.K., 1997; p 771.

so many different processes have to be kept in mind. As outlined earlier,9 the following processes occur during adsorption: transport of the polyelectrolytes from the solution to the fiber surface (the definition of the available fiber surface is dependent on the molecular mass of the polyelectrolyte); attachment of the polyelectrolytes on the fibers surface; reconformation of the polyelectrolyte on the fiber surface; detachment of the polyelectrolyte from the surface. Furthermore all these factors become very important when the kinetics of adsorption is discussed. The general understanding, at present, is that the polymers collide with the fibers either through Brownian motion or through turbulent transport.9,10 It has also been found that the initial conformation of the polymers on the fiber surface is similar to the conformation in solution and that the reconformation of high molecular mass cationic polyacrylamides is around 60 s.4,10 For other types of polyelectrolytes, such as polyethyleneimine, the rearrangement is much slower and time scales of the order of days have been suggested.9,11 It is well-known that the desorption of polylectrolytes from cellulosic fibers is a very slow process at least in deionized water.8,9,11 However, in the presence of other adsorbing molecules, of higher molecular mass, and at higher salt concentrations there is definitely a desorption taking place.12 The time scales for the desorption process is though of the order of days, naturally depending on the conditions in solution and the properties of the adsorbing and desorbing species. A fairly recent investigation has also demonstrated this behavior on other types of substrates.13 These authors found that at higher salt concentrations (larger than 0.5 M NaCl) there can be a fairly complete exchange of low molecular mass poly(9) van de Ven, T. G. M. Adv. Colloid Interface Sci. 1994, 48, 121. (10) Falk, M.; O ¨ dberg, L.; Wågberg, L.; Risinger, G. Colloids Surf. 1989, 40, 115. (11) Petlicki, J.; van de Ven, T. G. M. Colloids Surf. 1994, 83, 9. (12) Tanaka, H.; O ¨ dberg, L.; Wågberg, L.; Lindstro¨m, T. J. Colloid Interface Sci. 1990, 134, 229. (13) Sukhishvili, S.; Granick, S. J. Chem. Phys. 1998, 109,16, 6869.

10.1021/la000629f CCC: $20.00 © 2001 American Chemical Society Published on Web 01/20/2001

Polyelectrolyte Adsorption on Cellulosic Fibers Table 1. Summary of the Molecular Mass (Weight Averages) of the PolyDMDAAC Polymers Used in the Experiments type of polymer

molecular mass

LMw HMw HMw

8.75 × 103 4.8 × 104 1.2 × 106

electrolytes for higher molecular mass polyelectrolytes of the time scale of 30 h. Another factor, which is not resolved, is how the polymers will migrate into the pores of the fibers. The polyelectrolytes might penetrate the fiber wall either through a reptation process4 or through a simple diffusion process where the polyelectrolytes simply diffuse through the fiber wall until all available surfaces are saturated. Apart from being of purely academic interest, an understanding of this latter process might be very important when polyelectrolytes are added both to bind the internal structure of the fiber wall and to enhance the binding between two adjacent fibers. The purpose of the present work was hence to study how two different molecular mass fractions of the same type of polyelectrolyte, a polydimethyldiallylammonium chloride (polyDMDAAC), are adsorbed to cellulosic fibers depending on the condition under which they are adsorbed. Experimental Section Material. Cellulosic Fibers. The fibers used in the experiment were from an ECF (elementary chlorine free) bleached chemical softwood reference pulp from SCA Graphic Sundsvall, O ¨ strand Mill, Sweden. The fibers were delivered in dry lap form, and before use, the fibers were disintegrated according to a standard procedure (SCANC18). Following this, the fibers were beaten in an EscherWyss refiner, R 1L, at an edgeload of 0.5 Ws/m until a desired beating result (i.e., 23 SR) was reached. Polymers. Three different types of polyDMDAAC were used in the experiments. A high molecular mass (HMw), a medium molecular mass (MMw), and a low molecular mass (LMw) polymer. The MMw and LMw polymers were delivered by Allied Colloids Ltd, Bradford, U.K., as powders and used without further purification, whereas the HMw polymer was prepared through a special ultrafiltration procedure. To remove the low molecular mass fraction of this polymer, it was subjected to ultrafiltration14 and the ultrafiltration cell was fitted with a filter with a molecular mass cutoff of 300 000. The molecular mass of the polymers was determined by size exclusion chromatography,15 and the results are summarized in Table 1. The charge of the polymers was determined with polyelectrolyte titration16,17 and the HMw was found to have a charge of 6.19 mequiv/g, the MMw had a charge of 5.8 mequiv/g, and the LMw had a charge of 4.9 mequiv/g. The deviation from the theoretical charge of 6.19 mequiv/g for the MMw and the LMw is not understood, but it might due to presence of high concentrations of salt in these dry polymers. This was not checked further, and the measured charge was used to evaluate the charge of the fibers at different structural levels. If the presence of salt should be the reason for the measured deviation, the values of adsorbed amounts in mg/g would be too high whereas the charge of the fibers as estimated from the adsorbed amounts would be correct. (14) Wågberg, L.; O ¨ dberg, L.; Glad-Nordmark, G. Nord. Pulp Paper Res. J. 1989, 4, 71. (15) Swerin, A.; Wågberg, L Nord. Pulp Paper Res. J 1994, 9, 1, 18. (16) Terayama, H. J. Polym. Sci. 1952, 8, 243. (17) Horn, D. Prog. Colloid Polym. Sci. 1978, 65, 251.

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In the polyelectrolyte titrations an anionic polymer, potassium polyvinyl sulfate (KPVS), from Wako Pure Chem. Ltd., Japan, was used together with a cationic indicator, Ortotholuine Blue (OTB), from Kebo AB, Stockholm, Sweden. Other Chemicals. The NaCl, HCl, and NaOH used in the experiments were all of analytical grade. Methods. Fiber Treatment and Fiber Fractionation. To remove all fine material from the fibers below 76 µm a Britt Dynamic Drainage Jar18 (BDDJ) fitted with a 125 P screen (hole opening of 76 µm) was used. The pulp was diluted in distilled water to a concentration of approximately 0.5%. In the fractionation procedure 1 L of this fiber suspension was poured into the BDDJ and the stirrer rate was preset to 1000 rpm. The suspension was allowed to drain, and the material left in the BDDJ was washed with 3 L of distilled water and then defined as long fibers. After the fractionation, the pulp was diluted in distilled water to a concentration of 3% and washed by adjusting the pH to 2 by using HCl and kept at this pH for 30 min. Following this the fibers were washed with distilled water several times until the pH was around 4.5-5. The fibers were then treated with a 10-3 M NaHCO3 solution and the pH was adjusted to 9 by addition of NaOH and kept at this pH for another 30 min. This latter treatment was conducted to convert the carboxyl groups of the fibers to their sodium form. After 30 min the fibers were dewatered and washed with deionized water until the conductivity of the water was lower than 2 µS/cm. The surface charge of the fibers was determined by the polyelectrolyte adsorption technique14 to 11.5 µequiv/g and the total charge by conductometric tiration19 to 44 µequiv/ g. The treated fibers were stored in refrigerator at a concentration of 20% until further use. Adsorption Measurements. In the adsorption measurements, the fibers were diluted with distilled water, and in the experiments where the adsorption from solutions with different ionic strength the fiber dispersions were treated with NaCl addition to final salt concentrations of 10-3 and 10-2 M NaCl. The fiber concentration was 0.5% in all measurements, and the pH was adjusted to 8. Polymer was then added, the mixture was stirred on a magnetic stirrer for a predetermined time, and then the fibers were then separated from the water phase by filtration. The amount of polymer still in the solution was measured by polyelectrolyte titration in equipment similar to that described by Horn.17 The amount of adsorbed polymer was then calculated as the difference between the added amount of polymer and the amount of polymer remaining in the solution. From these measurements, adsorption isotherms, i.e., the adsorbed amount as a function of the equilibrium concentration of polymer in solution, were constructed for the different adsorption times. By extrapolation of the isotherms to zero polymer concentration, a plateau level in the isotherms could be estimated for each adsorption time. The adsorption times investigated were 5, 10, 30, and 120 min in distilled water and 5, 10, and 120 min in dispersions with different NaCl concentrations. In one set of the experiments, the fibers were pretreated with LMw polymer, in an exact amount of around 75% of maximum adsorption, for 5 min. Then the suspension was filtered and a small amount of distilled water was added to displace remaining polymer in the water phase in the fiber pad. To check if the polymer migrated into the fibers, (18) Britt, K. W. Tappi 1973, 56,3, 83. (19) Katz, S.; Beatson, R. P.; Scallan, A. M. Sven. Papperstidn. 1984, 6, R48-R53.

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the fibers were stirred for 25 min in deionized water before the second adsorption experiment was started. A new isotherm was made with the LMw polymer with an adsorption time of 5 min. In a separate set of experiments the adsorption kinetics of the LMw polymer onto fibers precovered with a saturated layer of HMw was investigated. In these experiments the HMw polymer was adsorbed to saturation for 120 min and the fiber dispersion was then dewatered to remove excess of HMw polymer in solution. The fibers were then washed with a small amount of water and then again redispersed in deionized water, and the LMw polymer was then added and allowed to adsorb for different times. All these latter experiments were conducted only in deionized water. In a final set of experiments the fibers were pretreated with HMw for 120 min and then, after dewatering and washing, the adsorption of LMw for 30 min was measured. For the sake of completeness these experiments were also repeated but with the LMw added first. Only deionized water was used in these measurements. Experiments with Equipment Designed for Adsorption Measurements at Very Short Contact Times. To be able to detect polylectrolyte adsorption at very short contact times, special equipment as described by Winter et al. was utilized.2 With this equipment it is possible to collect fiberfree samples after very short contact times, i.e., from 10 s and upward. The Jar has six outputs, each with an arrangement with a filter, a filter holder, and a 10-mL syringe in which to collect the sample. Each set of filters can be used twice in each experiment, if the syringe is exchanged, so that the total number of samples corresponding to different contact times is 12 for each trial. The washed and fractionated pulp was diluted in distilled water to a concentration of 0.5%, and the pH was adjusted to 8 by NaOH addition. 1 L of the pulp suspension was added to the Kinetic Jar (KJ), with the stirrer preset to 500 rpm. The amount of polymer was added and samples were collected after different adsorption times, from 10 s to 120 min. The amount of unadsorbed polymer could then be measured as described earlier, and the amount of adsorbed polymer could then be calculated. To control the mixing in the KJ, some experiments with addition of a nonadsorbing dye were conducted. In these experiments the dye was added to the jar and the samples were collected after different times. Measurements after 10 s, i.e., the shortest time used, showed a perfect mixing between the fiber sample and the added dye. Results Adsorption of Polymers with Different Molecular Mass. Initially it was considered important to investigate the saturation adsorption of the different polymers on the cellulosic fibers. To do this the adsorption isotherms for the polymers at 120 min in deionized water were collected. The results from these measurements are shown in Figure 1. As can be seen from these figures there is as expected a large difference in adsorption between the different polymers. It is clear that the LMw polymer can penetrate the fiber wall whereas the MMw and HMw polymers obviously cannot. By use of the saturation adsorption of the LMw polymer (i.e., 10 mg/g) to estimate the charge of the fibers, a value of 49 µequiv/g is achieved and this is very close to the value as determined with the conductometric titration which was 44 µequiv/g. It hence seems likely that the LMw polymer can penetrate the fiber wall completely provided the charges are evenly distributed

Wågberg and Ha¨ gglund

Figure 1. Adsorption of polyDMDAAC with different molecular mass on the cellulosic fibers. The pH during the experiments was kept constant at 8 and the fiber concentration was 5 g/L in all measurements. All these measurements were conducted with the use of deionized water. Table 2. Summary of the Molecular Characteristics of the PolyDMDAAC Used in the Investigation Including the Radius of Gyration (According to Burkhardt et al., 1987)a type of polymer molecular mass (wt av) radius of gyration (Å)b LMw MMw HMw

8.75 × 103 4.8 × 104 1.2 × 106

86 166 722

a The salt concentration used for the determination of the radius of gyration was 1 M NaCl. b From Burkhardt 1987.

throughout the fiber wall. From an earlier work20 it is possible to evaluate the radius of gyration of the polymers used in the present investigation and the results in Table 2 were achieved. By comparison of these data with the earlier published data on the pore structure of the fibers, it is obvious that the MMw cannot reach into the fiber wall despite the relatively small radius of gyration of this polymer. One reason for this can be the fact that the dimensions of the MMw were determined in a 1 M NaCl solution, and in more dilute solutions this polymer will be more extended due to electrostatic repulsion between the charged segments of the polymer. From this it might be concluded that the HMw and the MMw polymers are larger than the largest pores of the fibers, which according to earlier work are around 30 nm, whereas the LMw polymer can penetrate the fiber wall completely.5,8 This latter information is in accordance with the data by van de Ven and Alince 19978 and do not correlate with the data by Stone and Scallan 19685 where it was found that there are a lot of pores in the range between 1 and 20 nm. It should also be stated that this is an area under large debate, and it is not the purpose of the present work to resolve the issues in this debate. Kinetics of Adsorption of Polymers with Different Molecular Mass, Batch Experiments. The adsorption measurements described in the previous section was repeated for different adsorption times for the LMw and the HMw and for different salt concentrations for the LMw whereas the HMw polymer was only tested in different (20) Burkhardt, C. W.; McCarthy, K. J.; Parazak, D. P. J. Appl. Polym. Sci. 1987, 25.

Polyelectrolyte Adsorption on Cellulosic Fibers

Figure 2. Plateau adsorption of polyDMDAAC with different molecular mass on cellulosic fibers at different times and at different salt concentrations. The pH during the experiments was kept constant at 8 and the fiber concentration was 5 g/L in all measurements. The ionic media used during the experiments are specified in the figure.

salt solutions at 120 min. From the adsorption isotherms the plateau level of the adsorption was determined and the achieved results are summarized in Figure 2. It is seen in this figure that adsorption does not change particularly much with time for the HMw polymer. For the LMw polymer there is a significant increase in adsorption when the adsorption time is increased, i.e., from 8 to around 9.5 mg/g. This indicates that this latter polymer has a dimension which is just on the limit of having full accessibility to the interior of the fiber wall and that the polymer needs some time to move into the fiber wall. In turn this follows the discussions in conjunction with Figure 1. With an increase in salt concentration, the adsorption is first increased for both the LMw and the HMw polymer, going from deionized water to 1 mM NaCl, and then to a decrease upon further increase in salt concentration to 10 mM NaCl. The initial increase can be caused by a decreased size of polymer molecules upon increasing salt concentration or due to a decreased interaction between the adsorbed molecules. Since the LMw polymer already has full accessibility for all the charges already in deionized water, it seems likely that the second explanation is the most probable explanation. The decrease in adsorption upon further increase in salt concentration is explained by a decreased interaction between the charges on the polymer and the charges on the fibers. This is also in full accordance with theoretical predictions by van de Steeg et al.21 Kinetics of LMw and HMw Polymer Adsorption on Cellulosic Fibers, Kinetic Jar Experiments. As was discussed in the Introduction the kinetics of polyelectrolyte adsorption is very important from an application point of view since most polyelectrolytes are expected to have their effect shortly after their introduction. Despite this there are not that many papers devoted to measuring and modeling the kinetics of polyelectrolyte adsorption on different substrates. It was therefore considered important to investigate how the polymers adsorb on the fibers at very short contact times. The results from these measurements are shown in Figure 3 and Figure 4. (21) van de Steeg, H. G. M.; Cohen Stuart, M. A.; de Keizer, A.; Bijsterbosch, B. H. Langmuir 1992, 8, 2538.

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Figure 3. Kinetics of adsorption of the LMw polymer on cellulosic fibers. In the figure, experiments from both the kinetic jar and the batch experiments are included. The concentration during adsorption was 5 g/L in all experiments and the pH was 8. For comparison the saturation adsorption (max adsorption) values for this polymer have also been included.

Figure 4. Kinetics of adsorption of the HMw polymer on cellulosic fibers. In the figure, experiments from both the kinetic jar and the batch experiments are included. The concentration during adsorption was 5 g/L in all experiments and the pH was 8. For comparison the saturation adsorption (max adsorption) values for this polymer have also been included.

As can be seen there is first of all a very good agreement in the results from the batch experiments and the kinetic jar experiments for the LMw polymer whereas there is a difference in the results for the HMw polymer. The exact reason for this difference between batch and kinetic jar experiments is not known, but it might be assumed that the less intense mixing in the batch experiments can cause an incomplete distribution of the polymer and therefore some fibers might be saturated by polymer and no longer susceptible to further polymer adsorption. This would yield a lower initial adsorption but a similar final adsorption. If the experimental results for the kinetic jar experiments are compared with the final level of adsorption in the batch experiments, there is a very good agreement between the different types of measurements. This indicates that the mixing during addition of high molecular mass polyelec-

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Wågberg and Ha¨ gglund

trolytes is very important, and for industrial applications it is definitely recommended to study this further more in detail. From the results in Figure 3 it is also clear that the adsorption of this low molecular mass polyelectrolyte is very rapid and it is a bit surprising to note that the saturation adsorption is reached already after 10 min at an addition of 12 mg/g of polymer. From the discussion in the previous section it is then also clear that this polymer can diffuse into all the pores of the fibers at these short contact times. Again this indicates that the diffusion of the polymer is not hindered at all. This will also be further discussed later when the adsorption of polymer pretreated fibers will be discussed. For the HMw polymer the situation is different. For this polymer the adsorption is not as rapid as that for the LMw polymer, and there is a significant difference in the saturation adsorption value and the adsorption reached at 2 h for an addition level of 6 mg/g. This difference might be explained by at least two different mechanisms. First of all the polymer molecules will be more coiled up when the concentration in the solution is increased as it will be when the saturation adsorption is determined. This will in turn lead to a more compact conformation of the polymers on the surface and a larger number of polymer molecules can adsorb before the charges on the surface are fully neutralized. In turn this will also lead to an overcompensation of the charges on the surface of the fibers by the polyelectrolyte. Another explanation could be that when the polymers will be more coiled, i.e., at higher polymer concentrations, they will have a larger access to the interior of the fibers. To find out which of these two explanations that is most probable, experiments with adsorption on flat surfaces, as described by Wågberg and Nygren22 with the relevant polymer concentrations in this report, should be conducted. On inspection of the data in Figures 3 and 4, it is obvious that it should be possible to model the kinetics of the adsorption since there is a clear pattern for the different results. One approach to model these kind of data, based on Langmuir kinetics, has been described by Kindler and Swanson23 and van de Ven.9 Since the collisions between the polymer molecules and the fibers are brought about by the turbulence in the suspension, the approach in the present work is based on the work by Saffman and Turner.24 Since earlier work12 has shown that desorption is very slow in deionized water, it was considered safe to neglect the desorption term in the model defined by van de Ven.8 According to Saffman and Turner 24 the collision frequency between different particles in turbulent flow can be described by the following equation

N12 ) 1.294(a1 + a2)3Gn1n2

the less probable is it that a colliding molecule will adsorb on the fibers. By doing this, the kinetics of polyelectrolyte adsorption can be written as 3 dΓ 1.294(a1 + a2) Gn1(t)n2(1 - θ)RMw ) dt NACf

where dΓ/dt is the rate of adsorption ((g of polymer/g of fiber)/s), (1 - θ) is the degree of surface saturation from the adsorption data (θ is the degree of surface coverage from Γ/Γmax and Γmax is the saturation adsorption of the polymer in question), R is the collision efficiency factor, Mw is the molecular mass of the polymer, NA is Avogadro’s number, and Cf is the concentration of fibers (g/m3). In this equation the change of concentration of polymer in solution with time is not known explicitly, but by using the adsorption data in Figures 3 and 4, an indirect way of testing the validity of the general equation and to estimate the collision efficiency factor can be achieved. To do this the following equation must be used

n1(t) ) n10 -

(22) Wågberg, L.; Nygren, I. Colloids Surf., A 1999, 159, 3. (23) Kindler, W. A.; Swanson, J. W. J. Polym. Sci., Part A-2 1971, 9, 853. (24) Saffman, P. G.; Turner, J. S. J. Fluid Mech. 1956, 1, 16.

ΓCf NA Mw

(3)

where n10 is the initial polymer concentration and Γ is the adsorbed amount (g of polymer/g of fiber) at time t. By substituting eq 3 into eq 4 the following relation is obtained

(

)

1.294(a1 + a2)3Gn2Mw ΓCf NA dΓ )R n10 (1 - θ) dt NACf Mw (4) By dividing both sides of eq 4 with Γmax, the rate of surface coverage can be written as

(

)

1.294(a1 + a2)3Gn2Mw n10 Cf NA dθ )R θ (1 - θ) dt NACf Γmax Mw (5) Furthermore, by defining positive constants according to

1.294(a1 + a2)3Gn2Mw kI ) NACf

(1)

where N12 is the collision frequency (m-3 s-1), a1 and a2 are the radii of the polymers and the fibers, respectively (m), n1 and n2 are the number concentrations of the fibers and the polymers (m-3), and G is the average shear field in the dispersion (s-1). When this equation is used to describe an adsorption process, it has to be combined with collision efficiency factor R and a surface saturation factor, i.e., a factor describing that the more saturated the surface becomes

(2)

β1 )

n10 Γmax

β2 )

C f NA Mw

eq 5 can be written as

dθ ) R k1(β1 - β2θ)(1 - θ) dt

(6)

Fortunately, eq 6 is a separable equation and can, in this case, easily be solved analytically. Thus, by assuming that θ(0) ) 0, the equation can be solved for θ to yield

θ(t) )

1 - e(1-(β2/β1))k1Rβ1t β2 1 - e(1-(β2/β1))k1Rβ1t β1

(7)

Polyelectrolyte Adsorption on Cellulosic Fibers

Langmuir, Vol. 17, No. 4, 2001 1101 Table 3. Parameter Identification Results from the Fit of Equation 7 to the Experimental Results in Figures 3 and 4

Figure 5. Surface coverage as a function of time for the polymer having low molecular weight. The solid lines represent the theoretical fit of eq 7 to the experimental results in Figure 3 by finding a best fit to the factor R. The value of R achieved in this way is 0.25.

Figure 6. Surface coverage as a function of time for the polymer having high molecular weight. The solid lines represent the theoretical fit of eq 7 to the experimental results in Figure 4 by finding a best fit to the factor R. The value of R achieved in this way is 0.09.

The collision efficiency factor R is determined by fitting eq 7 to experimental data with respect to R in the leastsquares sense. This approach is also much simpler and less complicated than the approach described by van de Ven.9 In this study a numerical routine based on the Gauss-Newton method is used. The fitting procedure is, for each polymer molecular weight, performed on all adsorption curves simultaneously, i.e., one value of R is obtained for each polymer type. These theoretical results together with the experimental results, plotted as θ are shown in Figures 5 and 6. As can be seen from these data there is a good fit between the theoretical prediction and the measured results for the low molecular mass polyelectrolyte whereas the agreement is rather poor for the high molecular mass polymer. The collision efficiency factors for the simulations are given in Table 3. Obviously the proposed model for adsorption fits very well for the low molecular mass polyelectrolyte and it might hence be used to predict adsorption in similar systems as the one described here. For the high molecular mass polyelectrolyte, the agreement is not as good. This can naturally be explained in many different ways, but the most obvious explanation is that for this high molecular

type of polymer

molecular mass

radius of gyration (Å)

R start value

R optimal fit

LMw HMw

8.75 × 103 1.2 × 106

86 722

0.03 0.03

0.2505 0.0914

mass polymer the adsorption has to be described by a more elaborate model. First of all there is an initial adsorption of the molecules to the fiber surface and then there is a reconformation of the polymer on the surface to a flat conformation.4 This probably has to be taken into account in the model to give a better fit to the data. The direct reason for this is that the polyelectrolyte in its initial conformation will not be totally neutralized and will hence act against further adsorption from simple electrostatic reasons. To take this into account a reconformation factor has to be introduced and furthermore more data for this process has to be produced in order to test the new model. This is beyond the scope of the present work. Another factor which might be considered is a desorption term which describes the possibility for the polyelectrolyte to escape the surface once it has been adsorbed. However, since the desorption from the cellulose surfaces is a very slow process, this factor has been considered less important in the present work. Kinetics of LMw Polymer Adsorption on Fresh Fibers and Fibers Precovered with HMw Polymer, Kinetic Jar and Batch Experiments. To check how a preadsorption of the HMw polymer affects the adsorption of subsequently added LMw polymer, a number of experiments on adsorption kinetics were conducted. First the adsorption kinetics on nontreated fibers were conducted with the aid of batch measurements. Following these experiments another series was conducted where the fibers were first saturated with HMw polymer for 120 min and then the excess polymer was removed by filtration. The polymer-covered fibers were then redispersed and the adsorption of LMw polymer was then measured with the aid of the kinetic jar equipment to enable a better detection at shorter contact times. The results from these measurements are shown in Figure 7. Somewhat surprisingly the presence of a saturated layer of HMw polymer does not affect the kinetics of adsorption of the LMw polymer at all. This strongly indicates that the adsorption of the LMw polymer is a “pure” diffusion of polymer into the fiber wall and not a reptation of the polymer on the internal surfaces of the fiber. Considering the dimension of the polymer and the dimension of the pores of the fiber wall, as described by van de Ven,8 this is may be not so surprising since the pores they found in the fibers were of the order of 20 nm. The reason to the lack of influence of the HMw polymer is probably due to the fact that the adsorption of the polyDMDAAC can be considered to be an ion-exchange process,2 and this means that the polymer has a flat conformation on the surface with all the charges neutralized. Once adsorbed the polyDMDAAC molecule takes up a very limited space compared with the size of the pores of the fibers, and hence the adsorbed molecules will not obstruct the fresh LMw polymer molecules, which diffuse into the fiber wall. As discussed by van de Ven and Alince,8 a three-dimensional preadsorbed polymer might result in thicker adsorbed layers and a larger obstruction toward further adsorption. A close check of the data in Figure 7 shows that the adsorption of polymer at the 6 mg/g addition level shows a larger curvature for the presaturated fibers. According to Cohen Stuart et al. this might be due to a build up of

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Figure 7. Kinetics of adsorption of LMw polymer on fresh fibers and fibers precovered with HMw polymer. The measurements with fresh fibers were conducted with batch experiments where different amounts of polymer were added to the fibers whereas the experiments with precovered fibers were conducted with the aid of the kinetic jar equipment. The fiber concentration was 5 g/L and the pH ) 8 in all measurements

an electrostatic repulsive layer by the adsorbing LMw polymer at this higher addition.25 At longer times the polymers will have enough time to reconform, and therefore the final adsorption ends on the same level as for the fresh fibers. To further investigate if a migration of the polymer on the surface of the fibers could be a possible adsorption mechanism, an experiment was conducted where the fibers were first exposed to LMw polymer for 5 min and the excess polymer was then removed. The fibers were then redispersed in deionized water for 25 min before further polymer was added, and the adsorption was measured after an adsorption time of 5 min. These measurements were then compared with adsorption measurements after 5 min on nonpretreated fibers. As can be seen in Figure 8 there is no difference at all between the different types of experiments, and therefore it seems very unlikely that polymer reptation on the fiber surface is important for the adsorption of this type of polymer on cellulosic fibers. Comparison of Equilibrium Polymer Adsorption on Fresh and Polymer Presaturated Fibers. To further test how a preadsorption of the polymers of different molecular mass will affect the subsequent adsorption of the other polymer, a number of equilibrium adsorption measurements were conducted. In these measurements the fibers were first presaturated with the HMw or the LMw polymer for 120 min after which the fiber slurry was dewatered and the excess polymer removed. After a mild wash of the fiber pad in the filtration funnel, the fibers were redispersed and the adsorption of the other polymer was measured at an adsorption time of 30 min. The results from these measurements are shown in Figures 9 and 10. As can be seen in Figure 9 the adsorption of the LMw polymer is only slightly hindered even if the fibers have been presaturated with the HMw polymer. This is in accordance with the results in Figure 7 and indicates that there is a “simple” diffusion of the LMw polymer into the (25) Cohen Stuart, M. A.; Hoogendam, C. W.; de Keizer, A. J. Phys.: Condens. Matter 1997, 9, 7767.

Wågberg and Ha¨ gglund

Figure 8. Equilibrium adsorption of LMw polyDMDAAC on fibers, which have been pretreated with LMw polymer to an adsorption level of 6 mg/g and on fresh fibers. The pretreated fibers were, after washing and redispersing, left for 25 min before the second adsorption was started. The adsorption times were 5 min, and the fiber concentration was 5 g/L in both measurements. pH ) 8 in all experiments.

Figure 9. Equilibrium adsorption of LMw polyDMDAAC on fresh fibers and on fibers which have been presaturated with HMw polyDMDAAC for 120 min. The fiber concentration during the mesasurements was 5 g/L, and pH ) 8 in all experiments.

porous fiber wall. The importance of the charges in the fiber wall is also once again demonstrated since the total number of adsorbed charges is the same irrespective if some of the polymer is of high molecular mass or low molecular mass, at least with this order of polymer adsorption. If the order of polymer adsorption is reversed, see Figure 10, it is clear that the low molecular mass polymer totally will occupy the charges on the fiber surface and will hence block a subsequent adsorption of the high molecular mass polymer. It was also necessary to choose a level of preadsorption lower than the saturation adsorption in order to get any adsorption of the high molecular mass at all. All these measurements hence give strong indications that if a modification of the interior of the fibers should be combined with a specific surface modification of the

Polyelectrolyte Adsorption on Cellulosic Fibers

Figure 10. Equilibrium adsorption of HMw polyDMDAAC on fresh fibers and on fibers which have been presaturated with LMw polyDMDAAC for 120 min. The fiber concentration during the mesasurements was 5 g/L, and the pH ) 8 in all experiments. In the figure both the saturation isotherm for the LMw polymer and the adsorption level chosen for the presaturation have been included.

fibers, by polymeric molecules, the high molecular mass polymer should be adsorbed first followed by an adsorption of the low molecular mass polymer. This is true provided that the polymeric molecules adsorb to the same types of groups on the fibers. Conclusions The present investigation has shown the following: The LMw polymer used in this investigation can reach all the charges in the fiber wall whereas the HMw and

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MMw polymers are restricted to the external surfaces of the fibers. These results are in accordance with earlier data8 which indicate that once the polymer is smaller than a certain size (around 9 nm in the present work) the polymer has full accessibility for all the charges in the fiber wall. Kinetics of adsorption of the LMw polymer is not affected by the presence of a saturated layer of the HMw polymer on the surface of the fibers. If a modification of the interior of the fibers should be combined with a specific surface modification of the fibers, by polymeric molecules, the high molecular mass polymer should be adsorbed first followed by an adsorption of the low molecular mass polymer. A simplistic theory for the kinetics of polyelectrolyte adsorption can give good agreement with the measured values for the low molecular mass polyelectrolyte. This approach can hence be used to predict polyelectrolyte adsorption in more practical systems. For the high molecular mass polyelectrolyte, a more sophisticated model for the adsorption has to be developed where the adsorption and reconformation processes have to be taken into account. This is not easily done since this model has to contain the changeover from a repulsive to an attractive system as the polyelectrolyte reconforms and much more experimental data are needed to test such a model. Acknowledgment. Ms. Anna-Karin Sjo¨lund is gratefully acknowledged for her skilful experimental assistance, Dr. John Kettle is thanked for linguistic revision of the manuscript, and SCA is thanked for allowing the publication of the data. LA000629F