Adsorption Kinetics of Cationic Polyelectrolytes Studied with

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Adsorption Kinetics of Cationic Polyelectrolytes Studied with Stagnation Point Adsorption Reflectometry and Quartz Crystal Microgravimetry Lars-Erik Enarsson* and Lars Wågberg Royal Institute of Technology, Department of Fibre and Polymer Technology, Teknikringen 58, SE-100 44 Stockholm, Sweden ReceiVed January 21, 2008. ReVised Manuscript ReceiVed April 18, 2008 The effects of charge density, pH, and salt concentration on polyelectrolyte adsorption onto the oxidized surface of silicon wafers were studied using stagnation point adsorption reflectometry and quartz crystal microgravimetry. Five different polyelectrolytesscationic polyacrylamides of four charge densities and one cationic dextranswere examined. The adsorption kinetics was characterized using each technique, and the adsorption kinetics observed was in line with the impinging jet theory and the theory for one-dimensional diffusion, respectively. The polyelectrolyte adsorption increased with pH as an effect of the increased silica surface charge. A maximum in the saturation adsorption for both types of polyelectrolytes was found at 10 mM NaCl concentration. A significant adsorption also occurred at 1 M NaCl, which indicated a significant nonionic contribution to the adsorption mechanism. The fraction of solvent in the adsorbed layer was determined to be 70-80% by combining the two analysis techniques. This indicated a loose structure of the adsorbed layer and an extended conformation at the surface, favoring loops and tails. However, considering the solution structure with a hydrodynamic diameter larger than 100 nm for the CPAM and a thickness of the adsorbed layer on the order of 10 nm, the results showed that the adsorption is accompanied by a drastic change in polymer conformation. Furthermore, this conformation change takes place on a time scale far shorter than seconds.

Introduction Polyelectrolyte adsorption onto oppositely charged surfaces is used in many applications, for both stabilizing and flocculating colloid dispersions.1,2 Examples include dispersion agents in paint and cosmetics, as well as flocculants in wastewater treatment and protein separation. In papermaking, as an example, polyelectrolytes are extensively used in order to enhance paper strength, retain filler colloids, flocculate extractives, improve sheet formation, and increase the dewatering capacity.3 In all these applications, the polyelectrolytes are adsorbed onto the colloidal surfaces and their action is controlled by several kinetic processes involving (a) the mass transport to the surface, (b) reconformation at the surface, (c) desorption of weakly attached chains, and (d) the collision frequency between colloids bearing adsorbed polyelectrolytes.4,5 The speed of flocculation processes implies that the polyelectrolyte-induced flocculation is accomplished long before the polyelectrolytes have reached their equilibrium conformation on the surface. Despite this, most studies and theories deal with adsorption equilibrium.6–8 There are exceptions9–12 that all show that the adsorption kinetics as well * Corresponding author. E-mail: [email protected]. (1) Farinato, R. S.; Huang, S.-Y.; Hawkins, P. Polyelectrolyte-assisted dewatering. In Colloid-Polymer Interactions: From Fundamentals to Practice, 1st ed.; Farinato, R. S.; Dubin, P. L., Eds.; Wiley: New York, 1999; p 3. (2) La Mer, V. K.; Healy, T. W. ReV. Pure Appl. Chem. 1963, 13, 112. (3) Eklund, D.; Lindstro¨m, T. Paper Chemistry: An Introduction, 1st ed.; DT Paper Science: Grankulla , 1991. (4) Pelssers, E. G. M.; Cohen Stuart, M. A.; Fleer, G. J. Colloids Surf. 1989, 38, 15. (5) Gregory, J. Colloids Surf. 1988, 31, 231. (6) Fleer, G. J., Cohen Stuart, M. A., Scheutjens, J. M. H. M., Cosgrove, T., Vincent, B., Polymers at Interfaces, 1st ed.; Chapman and Hall: New York, 1993. (7) Chatellier, X.; Joanny, J. F. J. Phys. II 1996, 6, 1669. (8) Dobrynin, A. V.; Rubinstein, M. Prog. Polym. Sci. 2005, 30, 1049. (9) Shulga, A.; Widmaier, J.; Pefferkorn, E.; Champ, S.; Auweter, H. J. Colloid Interface Sci. 2003, 258, 219. ¨ dberg, L.; Wågberg, L.; Risinger, G. Colloids Surf. 1989, 40, (10) Falk, M.; O 115. (11) Cohen Stuart, M. A.; Hoogendam, C. W.; deKeizer, A. J. Phys.: Condens. Matter 1997, 9, 7767.

as the reconformation process will influence both the adsorbed amount and the structure of the polyelectrolyte layers. However, the reported time scales of these dynamic phenomena show a considerable span in magnitude and thus seem highly system dependent, which motivates further studies on the adsorption kinetics of polyelectrolytes. For adsorption of cationic polyacrylamides (CPAM) on cellulose fibers, time constants for reconformation are in the range of 5-30 s,13–15 and similar kinetics is also seen in the hydrodynamic layer thickness of CPAM when adsorbed onto polystyrene latex particles.16 The effect of reconformation appears in these cases as a temporary blocking of the surface, since the saturation adsorption at short contact times of 1-8 s is significantly lower than at 30 min.10,12 Experiments on polyvinylpyridines on polystyrene latexes have on the other hand indicated very slow reconformation processes on the order of 2000 min.17 Slow reconformation processes are also reported for protein adsorption in the area of biochemistry. As reported for titania substrates, the time scales for reconformation varies from minutes for fibronectin and albumin18 to hours for fibrinogen adsorption.19 The saturation adsorption of these proteins shows a reverse time dependence, since the adsorption is reduced at slow adsorption rates, which is interpreted as a slow lateral spreading of adsorbed proteins, blocking free surface sites for adsorption.20,21 In many (12) Solberg, D.; Wågberg, L. Nord. Pulp Pap. Res. J. 2003, 18, 51. ¨ dberg, L. Nordic Pulp Pap. Res. J. 1990, 5, 168. (13) Aksberg, R.; O ¨ dberg, L.; Lindstro¨m, T.; Aksberg, R. J. Colloid Interface (14) Wågberg, L.; O Sci. 1988, 123, 287. ¨ dberg, L.; Berg, J. C. Colloids Surf. 1991, (15) Einarson, M.; Aksberg, R.; O 53, 183. ¨ dberg, L. Langmuir 1991, 7, 43. (16) Aksberg, R.; Einarson, M.; Berg, J.; O (17) Elaissari, A.; Pefferkorn, E. J. Colloid Interface Sci. 1991, 143, 85. (18) Calonder, C.; Van Tassel, P. R. Langmuir 2001, 17, 4392. (19) Santore, M. M.; Wertz, C. F. Langmuir 2005, 21, 10172. (20) van der Veen, M.; Stuart, M. C.; Norde, W. Colloids Surf., B 2007, 54, 136. (21) Wahlgren, M.; Arnebrant, T.; Lundstro¨m, I. J. Colloid Interface Sci. 1995, 175, 506.

10.1021/la800198e CCC: $40.75  2008 American Chemical Society Published on Web 06/14/2008

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Enarsson and Wågberg

Table 1. Properties of the Cationic Polyelectrolytes Included in the Present Study CPAM1 molecular weight (Da) polydispersity index, Mw/Mna charge density (mequiv/g) degree of substitution, DSc refractive index increment (mL/g)

4.6 × 10 4.1 0.50 0.038 0.174

6a

CPAM2 5.2 × 4.6 1.01 0.083 0.187

106 a

CPAM3 5.2 × 3.9 1.60 0.15 0.178

106 a

a Determined using gel permeation chromatography according to a previously described method.28 cationic derivatization. c Degree of substitution defined as the fraction of charged monomer units.

cases, the adsorption of proteins appears to be slower than the mass transport rate to the surface, which has been attributed to energy barriers or reversible adsorption at the surface.22,23 The present study further investigates the layer formation of CPAM at the silica surface so as to determine adsorption kinetics of CPAM, the maximum adsorbed amount, and the layer structure, including the water content in the film. A deeper knowledge concerning these parameters is essential for the better understanding of the flocculation performance from a structural perspective. The adsorbed layer structures of four CPAMs with different charge densities have been studied with the combination of reflectometry and QCM-D. One sample of cationic dextran was added to test whether the results could be generalized for other polyelectrolytes. For the study on adsorption kinetics, one CPAM sample was analyzed more closely in two well-defined mass transport systems, the stagnation point flow geometry,24 which is implemented in the stagnation point adsorption reflectometer (SPAR), and the one-dimensional model for diffusion through a stagnant fluid25 as obtained with the QCMD. Both of these systems allow the mass transport to be calculated from basic parameters, including concentration, bulk viscosity, diffusion constant, jet velocity, and cell geometry. It has previously been reported26 that the SPAR technique allows detection of dynamic adsorption effects at time scales between 1 and 10 000 s, an interval that includes several of the cited dynamic phenomena. This motivates the use of SPAR and QCM-D in studies on the adsorption kinetics of CPAM.

Experimental Section Materials. The four cationic polyacrylamides (CPAM 1-4) were copolymers of acrylamide (AM) and (3-acrylamidopropyl)trimethylammonium chloride (APTAC), kindly provided by Prof. H. Tanaka, Faculty of Agriculture, Kyushu University, Fukuoka, Japan. The charge density was controlled by altering the composition of APTAC. In order to achieve a random distribution of the APTAC monomers in the copolymer chains and a desired composition of the copolymers, the degree of conversion of the added monomers was only 10% in the polymerization. Cationic dextran (Cdextran) was kindly provided by A. Horvath, Department of Fiber and Polymer Technology, KTH, Sweden. It was prepared by adding (2,3epoxypropyl)trimethylammonium chloride to native dextran (2 × 106 Da; Sigma-Aldrich) according to the synthesis described by Zhang et al.27 The charge density, degree of substitution, and molecular weight were characterized for all polyelectrolytes, and the results appear in Table 1. Polyelectrolyte solutions were prepared in a concentration range of 1-200 mg/L. Milli-Q water with a resistivity of 18.2 MΩ/cm was used throughout the work. The pH was adjusted to 7, if not otherwise stated, by additions of HCl (aq) or NaOH (aq) in the presence of (22) Weaver, D. R.; Pitt, W. G. Biomaterials 1992, 13, 577. (23) Jung, L. S.; Campbell, C. T. J. Phys. Chem. B 2000, 104, 11168. (24) Dabros, T.; van de Ven, T. G. M. Colloid Polym. Sci. 1983, 261, 694. (25) Crank, J. The Mathematics of Diffusion, 2nd ed.; Clarendon Press: Oxford, 1975. (26) van Eijk, M. C. P.; Cohen Stuart, M. A. Langmuir 1997, 13, 5447. (27) Zhang, J.; Pelton, R.; Wågberg, L.; Rundlo¨f, M. J. Pulp Pap. Sci. 2001, 27, 145. (28) Swerin, A.; Wågberg, L. Nord. Pulp Pap. Res. J. 1994, 9, 18.

b

CPAM4 3.8 × 5.1 2.36 0.24 0.173

106 a

C-dextran 2.0 × 106 b 5.2 0.50 0.088 0.158

Molecular weight according to the supplier before

a 10-5 M NaHCO3 buffer. The background electrolyte concentration ranged between 10-5 and 1 M. A combination of NaCl plus 10-5 M NaHCO3 buffer was used for salt additions down to 10-3 M salt. Only NaHCO3 was used at salt concentrations of 10-4 and 10-5 M. Methods. Polyelectrolyte Titration. The charge densities of the CPAM samples were determined by means of polyelectrolyte titration according to the method of Terayama,29 but with an addition of 10-5 M NaHCO3. The present experimental setup used colorimetric end point detection following the method of Horn.30 Cationic polyelectrolytes were titrated with potassium polyvinyl sulfate (KPVS; Wako Pure Chemical Industries, Osaka, Japan) using orthotoulidine blue (OTB; VWR) as an indicator. The charge density of the Cdextran was measured by polyelectrolyte titration against sodium polyethylene sulfonate. The end-point was detected with the streaming potential technique using a particle charge detector (Mu¨tek, Herrsching, Germany). RefractiVe Index Increment Determination. An Abbe refractometer from Carl Zeiss (Oberkochen, Germany) was used for determining the refraction index increment (dn/dc) in white light for each polyelectrolyte at 1 and 100 mM NaCl. Preparation of Silica Substrates for Reflectometry. Surface substrates of polished silicon wafers (p-doped with boron) were purchased from MEMC Electronic Materials SpA (Novara, Italy). The wafers were oxidized for 3 h at 1000 °C, targeting an oxide layer thickness of approximately 90 nm. The wafers were cleaned by rinsing with a water/ethanol/water sequence immediately before use. The surface was then hydrophilized by treatment with 10 wt % NaOH(aq) for 30 s, followed by 30 s treatment in 10 W plasma (Model PDC-002, Harrick Scientific Corp., Ossining NY) under reduced air pressure. The surface was rinsed with Milli-Q water between each treatment. The oxide layer thickness was measured for each substrate by means of null ellipsometry using a model 43702-200E thin film ellipsometer from Rudolph Research (Flanders, NJ) equipped with a mercury lamp and an optical wavelength filter for determinations at 546 nm. Preparation of Silica Substrates for QCM. AT-cut quartz crystals (5 MHz resonant frequency), with an active surface of sputtered silica, were supplied by Q-Sense AB (Va¨stra Fro¨lunda). The active surface was cleaned immediately before use with a piranha solution (concentrated H2SO4:30% H2O2, 3:1 v/v) for 1 min and extensively rinsed in Milli-Q water. Caution: Piranha is highly corrosiVe and may react Violently in contact with organic materials. The crystal was further treated in 10 W plasma for 150 s, followed by rinsing in Milli-Q water. Stagnation Point Adsorption Reflectometry. The stagnation point adsorption reflectometer (SPAR) was supplied by the Laboratory of Physical Chemistry and Colloidal Science, Wageningen University, Wageningen, The Netherlands. It was equipped with an HeNe laser light source operating at 632.8 nm. The principle of the instrument has been described in detail elsewhere.31,32 Solutions were injected at approximately 1 mL/min; the actual flow rate was determined volumetrically during the kinetic experiments. Each adsorption step was followed by rinsing with a salt solution adjusted to the same salt concentration and pH. (29) Terayama, H. J. Polym. Sci. 1952, 8, 243. (30) Horn, D. Prog. Colloid Polym. Sci. 1978, 65, 251. (31) Dijt, J. C.; Cohen Stuart, M. A.; Hofman, J. E.; Fleer, G. J. Colloids Surf. 1990, 51, 141. (32) Dijt, J. C.; Stuart, M. A. C.; Fleer, G. J. AdV. Colloid Interface Sci. 1994, 50, 79.

Adsorption Kinetics of Cationic Polyelectrolytes

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A four-layer optical model32 was used to determine the adsorbed amount, and the calculations were conducted using the “Prof. Huygens” software (Dullware). A polyelectrolyte layer thickness of 5 nm was assumed in the model, and the refractive index increments were set according to Table 1. Kinetic Modeling of SPAR Data. The mass flux, J, approaching the surface at the stagnation point was calculated according to the impinging jet mass transport model derived numerically by Dabros and van de Ven24 and later restated by Adamczyk et al.:33

( )

J ) 0.776

D2R¯ U R2

{

C

1.78 + 0.186Re + 0.034Re2 Re < 10 Re g 10 -8.414 + 4.96Re0.5

(2)

∂Γ ) Jβ ∂t

(3)

This efficiency factor was added on empirical grounds and accounted for situations where only a fraction of the incoming flux accumulates at the surface. It should not be mistaken for the sticking probability, which relates the number of adsorbed molecules to the number of collisions at the surface.22 Quartz Crystal MicrograVimetry. A quartz crystal microbalance model QCM D300 from Q-Sense AB (Va¨stra Fro¨lunda) was used. The adsorption was operated in a discontinuous flow mode, in which the cell volume (∼80 µL) was exchanged in approximately 15 s of flow, after which the flow was stopped. Each experiment started by equilibrating the system with a buffer containing the same salt concentration and pH as those of the polyelectrolyte sample. Adsorption was initiated by replacing the cell contents with a polyelectrolyte solution. The adsorption process was monitored until saturation, followed by a final rinsing step. For thin, rigid films, the adsorbed mass, ∆m, is proportional to the frequency shift, ∆f, as obtained from a modified form of the Sauerbrey relationship35

∆f n

(4)

where n is the overtone number and CSauerbrey is a proportionality factor that equals -0.177 mg m-2 Hz-1 for this type of quartz crystal, as derived by Edvardsson et al.36 Kinetic Modeling of QCM Data. Mass transport in the absence of flow was modeled as a process of one-dimensional diffusion to (33) Adamczyk, Z.; Siwek, B.; Warszynski, P.; Musial, E. J. Colloid Interface Sci. 2001, 242, 14. (34) McCormick, C. L.; Blackmon, K. P.; Elliott, D. L. Polymer 1986, 27, 1976. (35) Sauerbrey, G. Z. Phys. 1959, 155, 206. (36) Edvardsson, M.; Rodahl, M.; Kasemo, B.; Ho¨o¨k, F. Anal. Chem. 2005, 77, 4918.

(5)

where C0 is the bulk concentration, D is the diffusion coefficient, and t is time. Applying the same efficiency factor as in eq 3 and differentiating with respect to t1/2 gave a corresponding expression for the adsorption rate in QCM:

Dπ

(1)

Re was estimated on the basis of a specific viscosity of 137 dL/g, as reported for a similar CPAM sample in deionized water.34 A simple model for relating the initial adsorption kinetics, ∂Γ/∂t, to the mass flux, J, was obtained through a dimensionless efficiency factor, β:

∆m ) CSauerbrey

∫t J(t) ) 2C0 Dt π

1⁄3

The stagnation point flow was characterized using an inlet tube radius, R, of 0.5 mm and a surface distance to radius ratio, h/R, of 1.7. The diffusion coefficient, D, was determined to be 5 × 10-12 m2/s in water for CPAM1 by means of dynamic light scattering using a Zetasizer Nano ZS particle analyzer (Malvern Instruments, Malvern, UK). The flow velocity, U, and the sample bulk concentration, C, were experimentally determined. The polyelectrolyte concentration at the surface was approximated to be zero, assuming an infinite sink condition. The flow intensity parameter, R, given as a function of the Reynolds number (Re), was calculated from the numerical solution presented by Adamczyk et al.:33

R)

the surface. The accumulated mass transfer to the surface under these conditions is given by25

∂Γ ) 2βC0 ∂ √t

(6)

The adsorption rate of net polyelectrolyte in QCM was modeled as

∂Γ CSauerbrey Pfrac ∂f(t) ) n ∂ √t ∂ √t

(7)

where ∂f/∂t1/2 is calculated from the frequency data of the third overtone, and Pfrac is the fraction of polyelectrolyte in the adsorbed layer. Assuming Pfrac to be constant during the adsorption process, it was calculated from experimental saturation adsorption data, obtained using SPAR and QCM, according to

Pfrac )

ΓSPAR(sat) ΓQCM(sat)

(8)

Results Effects of Salt, pH, and Charge Density on Saturation Adsorption. Influence of Charge Density on the Adsorbed Amount of Polyelectrolyte. The adsorbed amount was determined for the four CPAM samples of different charge densities at a 1 mM of salt and pH 7. Figure 1 presents the adsorbed amounts as determined using SPAR and QCM, respectively. Both methods showed that the adsorbed amount decreased with increasing charge density of the polyelectrolyte, as qualitatively expected assuming a charge compensation mechanism.6 The methods were complementary, since SPAR was sensitive to the net amount of adsorbed polyelectrolytes, while QCM determined the total adsorbed amount, including the water contained in the adsorbed layer. The amount of water in the adsorbed layer was estimated from the difference in adsorbed amount as calculated by the two techniques; the calculated solvent fractions are given in Table 2. All the adsorbed layers appeared to contain mostly water, but the fraction of water was slightly reduced with increasing charge density of the CPAM. When comparing Cdextran and CPAM of equal charge density, it was found that the adsorbed amount of polyelectrolytes was similar, while the Cdextran layer contained less water. Influence of Salt and pH on the Adsorbed Amount of Polyelectrolyte. The effect of salt on polyelectrolyte adsorption was studied using CPAM1 and Cdextran, which have equal charge densities. Figure 2 shows the results obtained with the SPAR, corresponding to the adsorbed amount of polyelectrolyte. The salt effects at pH 7 were found to be very similar for both polyelectrolytes, and the adsorption followed a parabolic function with a maximum at approximately 0.01 M salt. The adsorption decreased gradually at higher additions of sodium chloride, but was still significant at 1 M salt, which represents the electrostatic screening regime. Additional experiments with CPAM at pH 3, corresponding to a lower surface charge of silica near the isoelectric point37 located at pH 2, indicated that the adsorption was significantly lower at 1 mM salt, in line with the lower surface charge density, but increased at higher NaCl concentrations. At the highest studied concentration of 1 M salt, the adsorbed

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Figure 1. Influence of charge density on the adsorbed amount on silica of four CPAM samples (diamonds) and one Cdextran sample (squares). Filled symbols refer to QCM determinations, open symbols refer to SPAR. Data were obtained at 1 mM NaCl and pH 7.

Figure 3. Adsorption of CPAM1 and Cdextran studied with QCM-D as a function of the salt concentration at pH 7. The results refer to the saturation adsorption after rinsing with salt buffer. (A) Adsorbed mass according to the Sauerbrey relationship calculated from the third overtone frequency shift. (B) Dissipation shift for the third overtone. Diamonds, CPAM1; squares, Cdextran. Lines are drawn as a guide to the eye.

Figure 2. Saturation adsorption of CPAM1 and Cdextran studied using reflectometry as a function of salt concentration: diamonds, CPAM1 at pH 7; triangles, CPAM1 at pH 3; squares, Cdextran at pH 7. Lines are drawn as a guide to the eye. Table 2. Calculated Fraction of Water in the Adsorbed Layer polyelectrolyte

charge density (mequiv/g)

fraction of solvent

Cdextran CPAM1 CPAM2 CPAM3 CPAM4

0.50 0.50 1.01 1.60 2.36

0.74 0.80 0.82 0.77 0.68

amount of CPAM was found to be the same at both pH levels. The effect of salt on the polyelectrolyte adsorption was further studied with QCM. Under the assumption of a constant adsorbed layer density, the mass obtained with QCM that includes both polyelectrolyte and water constitutes an indirect measure of the adsorbed layer thickness. Figure 3 shows the adsorption of CPAM1 and Cdextran at pH 7 as a function of the salt concentration, depicted as the Sauerbrey mass and the dissipation shift. Both parameters showed an increase with salt concentration, with the largest change at the transition between 1 and 10 mM NaCl. CPAM1 adsorption generally resulted in a larger Sauerbrey mass compared to Cdextran over the investigated range in salt concentration. As the net adsorbed amount of these polyelectrolytes were the same at equal salt concentration according to SPAR (Figure 2), the difference in Sauerbrey mass was interpreted as a variation in the water content in the adsorbed layer, indicating a more water-rich and extended conformation of the CPAM

layer compared to Cdextran. This interpretation was further supported by the higher dissipation shift observed for CPAM1, which indicated a less rigid layer that led to more viscous losses in comparison to Cdextran. Adsorption Kinetics. Determination of CPAM1 Adsorption Kinetics Using SPAR. Data on the adsorption kinetics were obtained from each SPAR measurement. Figure 4 exemplifies the results of two experiments conducted at the lowest and highest concentrations of CPAM1 investigated. The adsorption is here represented by the ratio ∆S/S0, where ∆S is the change in the output signal due to adsorption and S0 is the nominal signal at the start of the experiment. The principal phases of the adsorption kinetics experiments are shown in the figure: (a) baseline equilibration, (b) the injection point of polyelectrolyte, (c) the constant initial adsorption rate which was maintained during most of the adsorption process, (d) a retardation point in the curve near the saturation plateau, and (e) a change in the plateau when the flow was switched from polyelectrolyte sample to solvent. The initial adsorption rate was dependent on the sample concentration, in accordance with the linear dependence predicted in the mass transport equation for the stagnation point in eq 1. The correlation between the initial adsorption rate and the sample concentration is shown in Figure 5. Each concentration level was run twice, with one experiment conducted at a low flow rate (0.2-0.4 mL/min) and another at a high flow rate (0.9-2.0 mL/ min). Although the adsorption rate was influenced by the flow rate, it was nonetheless well approximated by a linear function of the sample concentration for each particular flow rate interval. The mass transport model was also applied to predict the mass transport rates to the surface over the stagnation point. These rates are compared with the experimental adsorption rates in


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Figure 4. Adsorption kinetics as determined with the SPAR equipment for two sample concentrations of CPAM1 as evaluated from the reflectometer signal. The comparison illustrates the influence of polyelectrolyte concentration on the adsorption kinetics. Triangles, 1 mg/L; circles, 100 mg/L. Data were obtained at 1 mM NaCl and pH 7. Principal phases during each experiment: (a) baseline equilibration, (b) polyelectrolyte addition, (c) constant adsorption rate regime, (d) retardation point prior to saturation, and (e) plateau change due to rinsing.

Figure 6. Comparison between the experimentally observed adsorption rates and the calculated mass transport rates toward the surface over the stagnation point in the SPAR equipment. Diamonds correspond to low flow rates between 0.2 and 0.4 mL/min, while squares correspond to high flow rates between 0.9 and 2.0 mL/min. The dotted line represents an efficiency factor of unity. The dash-dotted line illustrates a linear regression of the data obtained at low flow rates with a correlation coefficient of 0.42. Data were obtained at 1 mM NaCl and pH 7.

Figure 5. Dependence of the polyelectrolyte concentration on the experimental adsorption rates determined from the initial slope of Γ versus t, as determined from SPAR experiments: diamonds, low flow rate regime 0.2-0.4 mL/min; squares, high flow rate regime 0.9-2.0 mL/min. Lines are fitted with linear regression. Data were obtained at 1 mM NaCl and pH 7.

between 7 and 100 mg/L as examined using QCM is presented in Figure 7, based on the frequency and dissipation data of the third overtone. Unlike the constant adsorption rate observed with SPAR, the adsorption rate observed with QCM decreased over time, since it was operated under flow-free conditions except during sample exchange. The adsorption phases could be distinguished as follows: (a) a rapid adsorption phase when polyelectrolyte solution is flowing through the cell, (b) a second, slower adsorption phase when the flow is stopped, (c) a retardation point in the adsorption rate leading to a slow third phase of adsorption, (d) a saturation plateau, and (e) a modified saturation plateau after rinsing. Notably, the adsorption kinetics was significantly slower in QCM than in SPAR after the flow was stopped. Figure 8 presents a graph of the frequency shift occurring during the first hour of adsorption, plotted as a function of the square root of time. This was done to visualize the presence of possible diffusion-limited adsorption kinetics in the QCM data, which appeared to establish within a few seconds after that the flow was stopped. A simple empirical model of the form ∆f(t) ) A + Bt1/2 was fitted to the linear parts in Figure 8, as evaluated by visual inspection. The fit of the model is depicted in the figure by thick lines. The constant term, A, accounts for the initial adsorption that occurred during flow; this contribution was found to be dominant at concentrations above 50 mg/L. The net adsorption rate of CPAM1 during diffusion-limited mass transport was calculated by applying eq 7 to the empirical regression models, using a polyelectrolyte fraction of 0.20 based on the previous results. Figure 9 presents the obtained adsorption rates as a function of the sample concentration, the linear relationship being obvious at concentrations up to 50 mg/L, in agreement with the theoretical diffusion model, eq 6. Higher sample concentrations typically reached the retardation point in the frequency curve during flow mode and were therefore not applied in this comparison. The final evaluation of the kinetic model for QCM was done by calculating the diffusion coefficient from the QCM data, by inserting the experimentally determined adsorption rate into eq 6. For the simplest case the efficiency factor was set to unity, giving a diffusion coefficient of 1.1 × 10-12 m2/s, approximately

Figure 6. A linear correlation between adsorption rates and mass transport rates was observed for experiments conducted at low flow rates, but the correlation coefficient of 0.42 was clearly lower than unity. This difference between observed and predicted adsorption rates was accounted for in the adsorption model by adjusting the efficiency factor to this value. For experiments conducted at high flow rates, the samples with concentrations up to 50 mg/L gave the same correlation coefficient. This indicated that the flow rate dependence seen in Figure 5 could be accounted for in the mass transport model of the stagnation point at lower concentrations. The experimental adsorption rates for the two highest sample concentrations (100 and 200 mg/L) at high flow rates were, however, found to be higher than expected from the linear correlation model derived for low flow rates. This indicated that the mass transport model did not apply under these conditions. Determination of CPAM1 Adsorption Kinetics Using QCM. The adsorption kinetics of CPAM samples with concentrations

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Figure 8. Adsorption kinetics observed using QCM, showing the frequency shift plotted as a function of t1/2 for the first hour of adsorption. Thick lines represent the least-squares fit of the kinetic model ∆f ) A + Bt1/2 to data of the initial diffusion-limited regime after the flow had stopped. Data from the third overtone obtained at 1 mM NaCl and pH 7.

Figure 7. Adsorption kinetics for CPAM1 in QCM as a function of sample concentration, determined from the third over tone. (A) Data showing the frequency shifts. (B) Data showing the dissipation shifts. Triangles, 7 mg/L; diamonds, 14 mg/L; circles, 30 mg/L; squares, 50 mg/L; filled hexagons, 100 mg/L. Data were obtained at 1 mM NaCl and pH 7. The different adsorption regimes are marked by letters: (a) polyelectrolyte injection under flow, (b) diffusion-limited adsorption, (c) retardation point leading to a slow adsorption phase, (d) adsorption plateau, and (e) modified plateau after rinsing.

5 times lower than the diffusion coefficient obtained using dynamic light scattering, though still in the same range. Compensation for an efficiency factor of 0.42, as obtained from the SPAR analysis, increased the calculated diffusion coefficient to be half the value obtained with dynamic light scattering. Influence of Sample Concentration on the Adsorbed Amount. Figure 10 depicts the influence of the polyelectrolyte concentration on the adsorption plateau for CPAM1 at 1 mM NaCl and pH 7 as determined with SPAR. The plateau was found to be constant over a wide range of concentrations down to 1 mg/L, indicating that CPAM has a high affinity for adsorption on silica and that the net adsorbed amount of polyelectrolyte remains constant. At low concentrations up to 15 mg/L there was a weak indication that the adsorption plateau was dependent on the flow rate, high flow rates giving higher adsorption plateaus. This effect was, however, on the same order of magnitude as the experimental error, and a more sensitive analysis technique would be necessary to test the hypothesis further. Complementary analyses with QCM based on the data in Figure 7 indicated, on the other hand, that the structure of the adsorbed layer was affected by the sample concentration. The maximum absolute frequency shift, which is proportional to the Sauerbrey mass, was observed for the intermediate CPAM1 concentrations of 15 and 30 mg/L. Lower total adsorbed amounts were indicated

Figure 9. Calculated adsorption rates for CPAM1 using QCM as evaluated for the diffusion-limited regime. The observed frequency derivative with respect to t1/2 is shown on the left ordinate, and the calculated net adsorption rate of CPAM, defined by eq 7, is shown on the right ordinate. Data were obtained at 1 mM NaCl and pH 7 using the third overtone.

both at the lower feed concentration (7 mg/L) and higher concentrations (50 and 100 mg/L). Considering that the reflectometer results suggested a constant net amount of polyelectrolyte, the QCM results indicated that the amount of water in the adsorbed layer, and thus the layer thickness, changed with the polyelectrolyte concentration. Also the dissipation shift observed at saturation adsorption appeared to be a function of the CPAM1 concentration. The lowest sample concentration (7 mg/L) clearly gave a smaller dissipation shift compared to the sample concentrations between 15 and 50 mg/L. The highest dissipation shift was observed for the 100 mg/L sample, but this high level decreased during the subsequent rinsing step. Furthermore, large transients in dissipation were observed for the intermediate sample concentrations during the rinsing step, followed by a slower relaxation of the dissipation shift after the flow was stopped.

Discussion Structure of Adsorbed Layers. The difference between the adsorbed amounts determined with SPAR and QCM gave an


Figure 10. The plateau in adsorbed amount after rinsing determined with SPAR as a function of the polyelectrolyte sample concentration. Diamonds: low flow rate regime 0.2-0.4 mL/min; squares: high flow rate regime 0.9-2.0 mL/min. Data were obtained at 1 mM NaCl and pH 7.

indication of the amount of coupled solvent in the adsorbed layer, and the present results indicated that the adsorbed layers were water rich. These data were in line with an earlier QCM-D study by Plunkett el al.38 that found a solvent fraction of 70% for a CPAM sample with DS ) 0.05, which is similar in composition to CPAM1. A decrease in the coupled solvent fraction with increasing charge density of CPAM was noted in both studies, and this trend is expected from the fact that the adsorbed layer becomes thinner with the increased charge density of the polyelectrolyte according to Plunkett et al. When comparing the adsorbed amounts of CPAM1 and Cdextran of equal charge density, the SPAR results were very similar, suggesting that electrostatics controlled the maximum adsorbed amount. The two samples differed, however, in the adsorbed layer structure, as the adsorbed Cdextran layer included less water than CPAM1. This was thought to be an effect of the relative chain stiffness of the two polyelectrolytes, as discussed below in terms of persistence lengths. The validity of the Sauerbrey model in determinations of the adsorbed mass with QCM was tested by applying the viscoelastic model of Johannsmann et al.39 and calculating the “true” sensed mass. As later illustrated by Naderi et al.,40 the true sensed mass is obtained from a series of overtones by plotting the determined mass as a function of the squared resonance frequency, where extrapolation to zero frequency yields a better estimation of the actual mass adsorbed to the substrate. These calculations were performed for the overtones n ) 3, 5, 7, showing that the true sensed mass was about 3% higher than the Sauerbrey masses reported in Figure 3A, based on the third overtone. It indicated that the underestimation of the adsorbed mass with the Sauerbrey model was small and practically insignificant in this case. Effect of Salt on Polyelectrolyte Adsorption. Moderate additions of sodium chloride at pH 7 increased the adsorption of both CPAM1 and Cdextran on silica, as seen in Figure 2. A maximum in adsorbed amount was noted at 10 mM salt, but significant adsorption was still found at salt concentrations up to 1 M. The screening-enhanced adsorption at salt concentrations (37) Bolt, G. H. J. Phys. Chem. 1957, 61, 1166. (38) Plunkett, M. A.; Claesson, P. M.; Ernstsson, M.; Rutland, M. W. Langmuir 2003, 19, 4673. (39) Johannsmann, D.; Mathauer, K.; Wegner, G.; Knoll, W. Phys. ReV. B 1992, 46, 7808. (40) Naderi, A.; Claesson, P. M. Langmuir 2006, 22, 7639.

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up to 10 mM was probably related to a reduced repulsion between polyelectrolyte segments, while the screening-reduced adsorption above 10 mM salt could be related to a reduced electrostatic attraction between the polyelectrolyte and the surface. Especially interesting were the results obtained for the low surface charge at pH 3, which indicated that the adsorption increased with the addition of salt up to a level of 0.7 mg/m2 in 1 M salt. The same amount was also reached for 1 M salt at pH 7, and this common, nonzero, level indicated that nonionic interactions contributed significantly to the adsorption in the electrostatic screening regime. The presence of this contribution was further supported by a comparison with the case of pure electrosorption,41 where the mean field model predicts no adsorption above 0.1 M salt concentration. Regarding this nonionic interaction, it is known that nonionic acrylamide can adsorb on silica,42 and some authors have suggested that this affinity originates from hydrogen bonding between acrylamide and silica,43,44 although the current opinion seems to be split.45 Generally, an entropic driving force for polymer adsorption at mineral interfaces comes from the release of water from the surface,46 and this effect is probably an important contribution to the adsorption mechanism also for this system. The effect of salt on the adsorbed layer structure was evaluated from QCM-D data presented in Figure 3. An increase in both the Sauerbrey mass and the dissipation indicated that the layer thickness was expanded for NaCl additions up to 100 mM. The increase in dissipation was here interpreted as increased viscous losses due to a redistribution of polyelectrolyte segments, which changed from train configuration at low salt concentrations to loop and tail configurations at higher salt concentrations. Such a transition has already been suggested in SCF modeling of polyelectrolyte adsorption.47 The Cdextran layer generally had a lower Sauerbrey mass than CPAM1 and thus appeared to form a thinner adsorbed layer. It also appeared more rigid, as the QCM data were constant for salt additions up to 1 mM NaCl and showed the maximum dissipation and Sauerbrey mass at the high salt concentration of 100 mM NaCl. The most evident difference between the polyelectrolytes was the smaller dissipation shifts observed for Cdextran, which might arise from its lower molecular weight, since the shorter polyelectrolyte chains would limit the maximum length of loops and tails. The lower dissipation shift of the Cdextran layer might also be attributed to the rigidity of the Cdextran chain, expressed as a longer persistence length along the molecular chain that would limit the formation of extended configurations of the adsorbed polyelectrolyte. Literature data on the intrinsic persistence length of similar carbohydrates report 5-15 nm for carboxymethyl cellulose48 and starch,49 which is clearly larger than the reported figures for acrylamide and its derivatives, which are about 2 nm.50,51 Also the electrostatic contribution to the persistence length is proposed to be slightly (41) van de Steeg, H. G. M.; Cohen Stuart, M. A.; Dekeizer, A.; Bijsterbosch, B. H. Langmuir 1992, 8, 2538. (42) Lecourtier, J.; Lee, L. T.; Chauveteau, G. Colloids Surf. 1990, 47, 219. (43) Griot, O.; Kitchener, J. A. T. Faraday Soc. 1965, 61, 1026. (44) Pefferkorn, E. J. Colloid Interface Sci. 1999, 216, 197. (45) Samoshina, Y.; Diaz, A.; Becker, Y.; Nylander, T.; Lindman, B. Colloids Surf. A 2003, 231, 195. (46) Theng, B. K. G. DeVelopments in Soil Science, Vol. 9: Formation and Properties of Clay-Polymer Complexes, 1st ed.; Elsevier: Amsterdam, 1979; p 84. (47) Shubin, V.; Linse, P. J. Phys. Chem. 1995, 99, 1285. (48) Hoogendam, C. W.; de Keizer, A.; Stuart, M. A. C.; Bijsterbosch, B. H.; Smit, J. A. M.; van Dijk, J.; van der Horst, P. M.; Batelaan, J. C. Macromolecules 1998, 31, 6297. (49) Carriere, C. J.; Bagley, E. B. J. Rheol. 1999, 43, 753. (50) Mattison, K. W.; Dubin, P. L.; Brittain, I. J. J. Phys. Chem. B 1998, 102, 3830. (51) Huang, S.-Y.; Lipp, D. W.; Farinato, R. S. Acrylamide polymers. In Kirk-Othmer Encyclopedia of Chemical Technology, 5th ed.; Wiley: New York, 2004; p 304.

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greater for Cdextran, due to a shorter distance between the charges in the polyelectrolyte chain in comparison to CPAM1. The average linear charge densities of the polyelectrolytes were calculated to be 0.18 equiv/nm for Cdextran and 0.15 equiv/nm for CPAM1, by forming the ratio DS/b, where b is the length of the monomer backbones, assumed to be 0.5 nm for Cdextran and 0.26 nm for CPAM1. Adsorption Kinetics Observed Using SPAR and QCM. The well-characterized mass transport conditions for the stagnation point setup, in combination with the continuous flow, gave SPAR certain advantages over QCM in kinetic experiments. These included constant adsorption rates as long as the surface acted as an infinite sink31 and controlled mass transport rates for the full duration of the experiment. In comparison, the discontinuous flow mode of QCM complicated the mass transport analysis, since the first part of the adsorption occurred in lesscharacterized forced convection mode. The second phase in the absence of flow was preferred for kinetic analyses, since hydrodynamic disturbances impaired the frequency determination in the first phase. The presence of a third, slower adsorption phase in QCM should also be noted. The onset of this phase appeared as a preliminary point of saturation, after which the adsorption rate dropped well below the diffusion rate to the surface. This could possibly be related to charge reversal of the surface, which would alter the adsorption mechanism and cancel the infinite sink assumption. The corresponding retardation point in SPAR data would be the transition between the linear region and the slow residual saturation, even if this latter contribution to the adsorbed mass was much smaller with SPAR. Detailed analysis of the CPAM1 adsorption kinetics using SPAR showed that the net adsorbed amount at saturation was essentially independent of the sample concentration and thus independent of the adsorption rate (Figure 7). The examined rate interval included adsorption processes between 100 and 2000 s until saturation was reached. This indicated that electrostatics controlled the saturation adsorption and that no significant lateral surface spreading of polyelectrolytes occurred over time, in contrast to the slow reconformation effects reported for proteins. On the other hand, QCM-D analysis indicated that the polyelectrolyte conformation in the adsorbed layer depended somewhat on the sample concentration, as seen in both frequency and dissipation shifts. Dynamic effects thus seemed to control the structure and water content of the adsorbed polyelectrolyte layer, but not the adsorbed amount. The maximum Sauerbrey mass was found at the intermediate sample concentrations of 14 and 30 mg/L, while the 7 mg/L sample gave the thinnest adsorbed layer, as indicated both in frequency and dissipation. The relatively low Sauerbrey mass observed at high polyelectrolyte concentrations of 50 and 100 mg/L seemed to be correlated with a smaller contribution from the third, slowest adsorption phase. As these adsorbed layers predominantly were formed during the flow transient and at a fast adsorption rate, this might have resulted in a layer of interlocked polyelectrolytes that were less accessible for secondary adsorption or reconformation over time, which possibly limited adsorption in the third kinetic phase. Another fundamental conclusion that could be drawn from QCM data was that a fast reconformation process occurred instantly upon adsorption. The dynamics of the reconformation process were too fast to be observed experimentally, but the effect of reconformation appeared as considerable dimension change of the polyelectrolyte before and after adsorption. Dynamic light scattering was used to determine hydrodynamic diameter in dissolved state, which was 100 ( 6 nm for CPAM1, while the average adsorbed layer thickness calculated from the


Sauerbrey mass was less than 10 nm for CPAM1 at 1 mM salt, assuming the adsorbed layer to have a homogeneous composition and a density of 1000 kg/m3. The 10-fold decrease in polyelectrolyte conformation indicated a considerable initial reconformation, much larger than the small variation in Sauerbrey mass at saturation as a function of the sample concentration. Although the kinetics of the fast reconformation process remain to be determined, comparison can be made with simulations by Ka¨llrot and Linse52 that report time scales for reconformation of uncharged polymers on the order of 100 ns. Their calculations indicate that the reconformation process, i.e. a distortion process, is very fast compared to the relatively slow mass transport obtained in the present study. Evaluation of Mass Transport Models. The impinging jet theory was shown to handle the variations in concentration and flow rate on a relative basis when applied to the SPAR results, but the predicted mass transport rates were systematically higher than the observed adsorption kinetics, resulting in an apparent efficiency factor lower than unity. Errors in the calculations should primarily be considered. It is noted that the current mass transport modelfortheimpingingjet24 isbasedontheSmoluchowski-Levich approximation, neglecting the interactions between the polyelectrolyte and the surface at close distances, which makes it an approximate model for charged systems. In the present form of the mass transport model, the diffusion coefficient was the most critical parameter, determined by dynamic light scattering (DLS) to be 5 × 10-12 m2/s. When assuming infinite sink conditions (β ) 1), the overpredictions of the mass transport model compared to the observed adsorption kinetics might indicate that this diffusion coefficient was too high. Alternatively, the infinite sink condition should be modified, in order to account for the apparent efficiency factor of 0.42. Apart from protein studies, some polymer literature supports efficiency factors lower than unity, as found for dendrimer adsorption onto glass by van Duijvenbode et al.53 Their results indicate that the efficiency factor is dependent on the dendrimer concentration and can be as low as β ) 3% when long-term self-diffusion coefficients from NMR are applied in the mass transport model. In the present study, the efficiency factor appeared to be constant for all experiments except the two highest concentrations, 100 and 200 mg/L CPAM1 conducted at high flow rates. The reason why the mass transport model did not apply to these samples was unclear, but it may be suggested that these samples corresponded to overlap concentration, at which long-ranged shear forces in combination with high flow rates interfered with the diffusion-limited mass transport over the stagnation point. Indirect support for such a viscosity increase was found in the higher dissipation shift for 100 mg/L CPAM1 sample in QCM, compared to the other sample concentrations. Also, the mass transport calculations based on QCM data indicated a lower diffusion coefficient that maximally differed by a factor of 5 from the DLS measurements. The determination of diffusion coefficients in QCM data relied on the precision in determining the adsorbed amounts with both SPAR and QCM, as well as on the assumption that the fraction of coupled water is constant in the adsorbed layer for all surface coverages up to saturation. As a first approximation, the same efficiency factor was applied in the mass transport models for SPAR and QCM. In contrast to the observed order in the present study, Plunkett et al.54 have instead found the diffusion coefficient as determined from QCM measurements to be overestimated by a factor of 3 (52) Ka¨llrot, N.; Linse, P. Macromolecules 2007, 40, 4669. (53) van Duijvenbode, R. C.; Rietveld, I. B.; Koper, G. J. M. Langmuir 2000, 16, 7720. (54) Plunkett, M. A.; Claesson, P. M.; Rutland, M. W. Langmuir 2002, 18, 1274.


when compared to DLS data. They have suggested that the adsorption of a polydisperse sample in QCM will lead to an initial enrichment of polyelectrolytes of low molecular weight at the surface that show a larger diffusion coefficient compared to the average diffusion coefficient determined using DLS. Final Remarks. On the basis of the present results, the formation of an adsorbed layer of CPAM1 at constant pH and salt concentration was found to be independent of the adsorption kinetics, at least over a time scale of seconds. This stands in marked contrast to the previously reported dynamics of a layer of CPAM adsorbed onto cellulosic fibers.10,12 Reconformation is probably present in both these systems, but in order to see dynamic effects on the saturation adsorption, it is here suggested that the kinetics of the reconformation process must be slow enough, i.e. of the same magnitude as the kinetics of the mass transport to the surface. The reconformation kinetics of CPAM on silica wafers seem to be much faster compared to the cited systems of CPAM on fibers and proteins on mineral surfaces. At present, the difference between silica and cellulosic fibers as a surface substrate for CPAM adsorption is discussed in terms of surface morphology. The polished silica wafers are smooth, hard surfaces with an rms surface roughness below 0.5 nm, while the rough fiber surfaces consist of a deep three-dimensional network of fibril aggregates, each having a diameter of about 20 nm.55 Polyelectrolyte adsorption on fibers will likely include an extra mass transport term of diffusion in order to redistribute the chains and access charges within this comparably large network. It can furthermore be suggested that this process probably proceeds slower than the reconformation on a flat surface, since the polyelectrolytes interact with the fibrils during their movement within the network. This hypothesis naturally remains to be tested in further studies, preferably in a model system that allows the adsorption to be followed in real time.

Conclusions Combining the SPAR and QCM techniques, it was shown that the charge density of CPAM affected both the adsorbed amount (55) Fahlen, J.; Salmen, L. Biomacromolecules 2005, 6, 433.

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and the adsorbed layer thickness of CPAM, expressed as the water content in the adsorbed layer. The effect of salt addition on adsorption was studied for two polyelectrolytes, Cdextran and CPAM1, having similar charge densities. The adsorbed amounts were generally similar for the two polyelectrolytes, showing an increase at salt additions up to 10 mM while decreasing at higher salt concentrations. Effective adsorption at a 1 M salt concentration indicated the presence of a significant nonionic interaction with silica for both polyelectrolytes. The difference between the polyelectrolytes mainly concerned the adsorbed layer structure, as CPAM formed thicker layers that gave higher dissipation shifts compared to Cdextran. The adsorption kinetics of CPAM on silica in the stagnation point flow indicated that the mass transport equation could be used to predict the adsorption rate of CPAM at flow rates up to 2 mL/min, provided that the sample concentration did not exceed 50 mg/L. At lower flow rates up to 1 mL/min, the mass transport model was found to be valid for sample concentrations of up to 200 mg/L. Adsorption kinetics determined using QCM were found to be in line with the mass transport model for one-dimensional diffusion, and the technique was shown to be applicable for estimating the diffusion coefficient of CPAM. The adsorbed amount of polyelectrolytes according to SPAR was not affected by the adsorption kinetics within the studied time interval, while the structure of the adsorbed layer showed a weak dependence on the adsorption kinetics, as indicated by QCM-D data. A comparison between the hydrodynamic diameter of CPAM in solution and the thickness of the adsorbed layer indicated a significant reconformation of the polyelectrolyte during adsorption, but the kinetics of this process was faster than could be measured with the applied techniques. Acknowledgment. The authors thank Prof. Hiroo Tanaka for providing the CPAM samples and Andrew Horvath for providing the Cdextran sample. The Swedish Research Council (VR) is acknowledged for financial support. LA800198E

Adsorption Kinetics of Cationic Polyelectrolytes Studied with

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