Langmuir 2008, 24, 10797-10806
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Diffusion of Cationic Polyelectrolytes into Cellulosic Fibers Andrew T. Horvath,‡ A. Elisabet Horvath,‡ Tom Lindstro¨m,† and Lars Wågberg* Royal Institute of Technology, Department of Fibre and Polymer Technology, SE-100 44 Stockholm, Sweden ReceiVed March 3, 2008. ReVised Manuscript ReceiVed May 22, 2008 The penetration of cationic polyelectrolytes into anionic cellulosic fibers was evaluated with fluorescent imaging techniques in order to clarify the mechanism and time scales for the diffusion process. The bulk charge of the cellulosic fibers indirectly creates a driving force for diffusion into the porous fiber wall, which is entropic in nature due to a release of counterions as the polyelectrolyte adsorbs. The individual bulk charges in the fiber cell wall also interact with the diffusing polyelectrolyte, such that the polyelectrolyte diffuses to the first available charge and consequently adsorbs and remains fixed. Thus, subsequent polyelectrolyte chains must first diffuse through the adsorbed polyelectrolyte layer before adsorbing to the next available bulk charges. This behavior differs from earlier suggested diffusion mechanisms, by which polyelectrolytes were assumed to first adsorb to the outermost surface and then reptate into the pore structure. The time scales for polyelectrolyte diffusion were highly dependent on the flexibility of the chain, which was estimated from calculations of the persistence length. The persistence length ultimately depended on the charge density and electrolyte concentration. The charge density of the polyelectrolyte had a greater influence on the time scales for diffusion. High charge density polyelectrolytes were observed to diffuse on a time scale of months, whereas the diffusion of low charge density polyelectrolytes was measured on the order of hours. An influence of the chain length, that is, steric interactions due the persistence length of the polyelectrolyte and to the tortuosity of the porous structure of the fiber wall, could only be noted for low charge density polyelectrolytes. Increasing the electrolyte concentration increased the chain flexibility by screening the electrostatic contribution to the persistence length, in turn inducing a faster diffusion process. However, a significant change in the diffusion behavior was observed at high electrolyte concentrations, at which the interaction between the polyelectrolyte charges and the fiber charges was almost completely screened.
Introduction The underlying molecular mechanisms are generally unclear regarding the diffusion of polyelectrolytes in an oppositely charged porous media. Whereas both a reptation mechanism1,2 and scaling arguments3-5 have been extended to the diffusion of polymers in porous media, the electrostatic interactions inherent for polyelectrolyte diffusion lead to an entirely different molecular mechanism. This mechanism becomes rather complex, as the electrostatic interactions both promote and hinder the diffusion process. While the diffusion of polymers in porous media is driven by concentration gradients, polyelectrolyte diffusion is entropic in nature due to the release of counterions needed to maintain a neutral electrostatic charge within the material.6 Although this entropic driving force is not electrostatic, it is nonetheless a consequence of the electrostatic charges from the substrate and the polyelectrolyte. At the same time that the electrostatic charges promote diffusion, it is expected that the same charges will also act to limit diffusion. For simple polymer diffusion, it has been documented that the time scale for diffusion in a porous media is dependent on the molecular structure of the diffusing * To whom correspondence should be addressed. † STFI-Packforsk AB, Box 5604, SE-114 86 Stockholm, Sweden. ‡ Current address: Mondi Frantschach GmbH, 9413 St. Gertraud, Austria.
(1) Teraoka, I.; Langley, K.; Karasz, F. Macromolcules 1992, 25, 6106. (2) Cule, D.; Hwa, T. Phys. ReV. Lett. 1998, 80, 3145. (3) de Gennes, P. G. J. Chem. Phys. 1971, 55, 572. (4) Muthukmar, M.; Baumga¨rtner, A. Macromolecules 1989, 22, 1941. (5) Honeycutt, J. D.; Thirumalai, D.; Klimov, D. K. J. Phys. A: Math. Gen. 1989, 22, L169. (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: London, U.K., 1993.
polymer.1,7-9 If this holds true for polyelectrolytes, which are unique in the fact that the molecular structure is controlled by electrostatic repulsions between charges along the backbone, then it would be expected that the charge density and electrolyte concentration dictate the diffusion process. These repulsions add a large electrostatic contribution to the persistence length, thereby limiting the movement of the polyelectrolyte chain in a tortuous pore. The rigid molecular structure ultimately leads to more hydrodynamic interactions with the pores, which slows the diffusion process. Aside from steric interactions with the pores, it is expected that polyelectrolytes will also have specific electrostatic interactions with the oppositely charged pore walls. However, the influence that these interactions have on the molecular level for diffusion is unclear. Kabanov et al.10 first suggested that two possible mechanisms should be considered. The first mechanism assumed that the interactions with the pore wall are strong enough to adsorb or fix the polyelectrolyte from diffusing further. The polyelectrolyte would therefore diffuse through a previously adsorbed layer to the first available charge and become fixed. The second proposed mechanism was that polyelectrolytes diffuse through a so-called “relay race” mechanism, in which the polyelectrolyte diffuses between charges from the periphery into the pore structure. Kabanov et al. concluded the latter mechanism existed for the diffusion of oppositely charged polyelectrolytes in swollen polyelectrolyte gel networks. (7) Bishop, M. T.; Langley, K. H.; Karasz, F. E. Phys. ReV. Lett. 1986, 57, 1741. (8) Bishop, M. T.; Langley, K. H.; Karasz, F. E. Macromolecules 1989, 22, 1220. (9) Guo, Y.; Langley, K. H.; Karasz, F. E. J. Chem. Phys. 1990, 93, 7457. (10) Kabanov, V. A.; Zezin, A. B.; Rogacheva, V. B. Macromol. Chem. Phys. 1989, 190, 2211.
10.1021/la800669d CCC: $40.75 2008 American Chemical Society Published on Web 08/30/2008
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Cellulosic fibers, which are made porous during pulping processes, are an abundant material commonly tailored using cationic polyelectrolytes. Although the individual fibers are somewhat heterogeneous in nature, techniques exist to wellcharacterize the pore structure11 and the distribution of charges.12 Recent work has shown that cationic polyelectrolytes can penetrate into the porous wall of anionic cellulosic fibers, although the time scales for this are strongly influenced by the polyelectrolyte charge density and the electrolyte concentration.13,14 Fluorescent labeling techniques have been used to investigate the extent to which a polyelectrolyte penetrated into a porous cellulose substrate, and much of the adsorption behavior can be explained by the polyelectrolyte’s availability to access the pore structure. However, little experimental evidence has been reported regarding the behavior of polyelectrolytes in a porous material, much less the time scales or mechanisms for the macroscopic diffusion process. Although the mechanism for diffusion had not previously been studied in detail, it was inferred that diffusion did not necessarily follow the “relay race” mechanism. It is therefore of interest to clarify the prevailing mechanism for the diffusion of both high and low charge density polyelectrolytes as well as to determine the relative time scale for which the diffusion occurs.
Materials and Methods Pulp. Initial experiments for the adsorption of polydiallyldimethylammonium chloride (pDADMAC) were made using cellulosic fibers from a never-dried, unbeaten softwood (spruce) kraft pulp (M-real, Husum, Sweden). The pulp was elementary chlorine free (ECF), bleached according to an ODQPDP sequence. A Cellecofilter with 100 µm screening slots was used to remove the cellulose fines (20-25%), such that only intact fibers remained. The pulp was washed into its sodium form through a standard procedure, such that all the counterions to the carboxyl groups on the fiber were exchanged to sodium ions.15 The surface charge of the pulp was measured by polyelectrolyte titration to be 1.7 µequiv/g.16 The total charge of the pulp was measured by conductometric titration to be 37 µequiv/g.17 Fluorescent labeled polyelectrolytes were adsorbed onto the fibers of a never-dried, semibleached kraft pulp (Stora Enso, Skoghall, Sweden) that was oxygen delignified to have a κ number of 18 and refined to a drainage resistance of 22° Shopper-Riegler. Fine material was removed with a Cellecofilter having 100 µm screening slots, and the pulp was likewise washed into its sodium form. The total charge of the pulp was measured to be 91 µequiv/g, and the surface charge was measured to be 3.7 µequiv/g by the same methods previously stated. Polyelectrolytes. A commercial polydiallyldimethylammonium chloride (pDADMAC) (Ciba, Yorkshire, U.K.) was fractionated by ultrafiltration using a regenerated cellulose membrane having a molecular mass cutoff of 5 × 105 Da. The high molecular mass fraction was used for the adsorption experiments. Cationic dextran, which served as a model low charge density polyelectrolyte, was prepared as previously described.14 Acrylamide (AM) and diallyldimethylammonium chloride (DADMAC) were copolymerized to form poly(AM-co-DADMAC),13 which served as a model high charge density polyelectrolyte. The polyelectrolytes were fluorescent labeled with sulforhodamine B acid chloride following a general protocol for labeling biological macromolecules.18 The polyelectrolytes were first dissolved at a concentration of 2 mg/mL in a 0.1 (11) Andreasson, B.; Forsstro¨m, J.; Wågberg, L. Cellulose 2003, 10, 111. (12) Horvath, A. E.; Lindstro¨m, T.; Laine, J. Langmuir 2006, 22, 824. (13) Horvath, A. T.; Horvath, A. E.; Lindstro¨m, T.; Wågberg, L. Langmuir 2008, 24, 7857. (14) Horvath, A. T.; Horvath, A. E.; Wågberg, L. Langmuir 2008, 24, 6585. (15) Wågberg, L.; Bjo¨rklund, M. Nord. Pulp Pap. Res. J. 1993, 8, 399. ¨ dberg, L.; Glad-Nordmark, G. Nord. Pulp Pap. Res. J. (16) Wågberg, L.; O 1989, 4, 71. (17) Katz, S.; Beatson, R. P.; Scallan, A. M. SVen. Papperstidn. 1984, 87, R48. (18) Hermanson, G. T. Bioconjugate Techniques, 1st ed.; Academic Press: San Diego, CA, 1996.
HorVath et al. M sodium carbonate/bicarbonate buffer and adjusted to pH 9. Sulforhodamine B acid chloride was dissolved separately in N,Ndimethylformamide (DMF) at a concentration of 2 mg/mL, constantly being protected from light. In darkened conditions, the sulforhodamine B acid chloride solution was slowly added to the polyelectrolyte solution at room temperature with gentle mixing. A ratio of 1 fluorophore to 150 glucose units was used for cationic dextran. A ratio of one fluorescent label per 20 AM monomer units was targeted for the poly(AM-co-DADMAC). The reaction was terminated by dilution with deionized water after 1 h. The solution was then dialyzed to remove any excess fluorescent label and freezedried. It should be noted that ester formation of sulfonyl chlorides with alcohols are subject to nucleophilic displacement, such that care must be taken to ensure that amine containing molecules are not present.19 Polyelectrolyte Characterization. Molecular mass distributions were measured for all polyelectrolytes before fluorescent labeling using size exclusion chromatography (SEC). Measurements were taken at room temperature using a Progel-TSK column. A buffer of 0.3 M acetic acid and 0.3 M sodium acetate was used as the eluent in order to screen electrostatic interactions between the polyelectrolytes and the column. The buffer also acts to screen electrostatic repulsions along the polyelectrolyte backbone, eliminating the electrostatic contribution to the molecular conformation. Molecular mass distributions were obtained from fairly monodisperse polyethylene oxide standards (Tosoh Corp., Japan) using broad molecular mass calibration standard methods.20 The charge density was determined from polyelectrolyte titrations using a Mu¨tek particle charge detector (PCD 03, Mu¨tek Analytical, Germany). Based on streaming current measurements, a standard polyethylene sodium sulfonate (Pes-Na) solution (BTG Mu¨tek GmbH, Herrsching, Germany) was used to titrate a solution of a cationic polyelectrolyte to the charge equivalence point. As the charge density of the Pes-Na solution was known, the charge density of the polyelectrolyte could be calculated from the consumption of the titrant. Dynamic light scattering measurements were made on a Nano-ZS zetasizer (Malvern Instruments, U.K.) for the unlabeled polyelectrolytes in order to determine the hydrodynamic diameter, DH. Adsorption to Untreated Fibers. Adsorption measurements were conducted analogous to a standard procedure developed by Winter et al.21 The pulp was diluted to a consistency of 5 g/L in the desired electrolyte solution. NaHCO3 (Merck KGaA, Darmstadt) served as the electrolyte for all experiments and also acted to keep the pH at ∼7.2. An excess of the fluorescent labeled polyelectrolyte was then added to the pulp suspension. The excess amount was determined by polyelectrolyte titration22,23 from the mass adsorbed at 30 min, which had previously been measured for all the polyelectrolytes in each electrolyte concentration.13,14 For long adsorption times (i.e., t > 2 h), the suspension was vigorously shaken for 30 min, which had been shown to be sufficient for reaching pseudoequilibrium for high molecular mass polyelectrolytes,24,25 and then set in a dark closet to avoid bleaching of the fluorescent tag. For short adsorption times (i.e., t e 2 h), the suspension was shaken for the duration of the adsorption time. The fibers were eventually filtered from the suspension and washed with 1 L of the appropriate electrolyte concentration to remove any unbound polyelectrolyte from the fiber surface. The fiber fraction was then immediately freeze-dried. Adsorption to Pretreated Fibers. Adsorption experiments to pretreated fibers were made in a two-step procedure. The polyelectrolyte used to pretreat the fiber was adsorbed according to a method similar to that previously described. Rather than dosing in excess, the polyelectrolyte was dosed on a basis of the mass needed (19) Scouten, W. H.; van den Tweel, W.; Delhaes, D.; Kranenberg, H.; Dekker, M. J. Chromatogr. 1986, 76, 289. (20) Swerin, A.; Wågberg, L. Nord. Pulp Pap. Res. J. 1994, 9, 18. ¨ dberg, L.; Lindstro¨m, T. J. Colloid Interface (21) Winter, L.; Wågberg, L.; O Sci. 1986, 111, 537. (22) Terayama, H. J. Polym. Sci. 1952, 8, 243. (23) Horn, D. Prog. Colloid Polym. Sci. 1978, 65, 251. (24) Lindstro¨m, T. C. J. Colloid Interface Sci. 1976, 55, 305. ¨ dberg, L.; Lindstro¨m, T. Colloids Surf. 1987, (25) Wågberg, L.; Winter, L.; O 27, 305.
Diffusion of Cationic Polyelectrolytes to compensate 50% of the total fiber charge, which ultimately depended on the polyelectrolyte charge density. Therefore, the thickness of the pretreated layer would not penetrate throughout the entire fiber wall. Also, the polyelectrolyte adsorbed first was always labeled with fluorescein isothiocyanate. After adsorption for 30 min, the fiber fraction was thoroughly rinsed with deionized water and diluted again to a consistency of 5 g/L. A second polyelectrolyte was then adsorbed using the same procedure. The second polyelectrolyte was labeled with sulforhodamine B acid chloride in order to distinguish each individual polyelectrolyte. The fibers were again filtered from solution, rinsed, and then freeze-dried for imaging. Microscopy. Fluorescent confocal laser scanning microscope (CLSM) images were taken with a Bio-Rad Radiance 2000 confocal system mounted on a Nikon Eclipse 800 microscope. Freeze-dried fibers were placed on a glass slide in a few drops of immersion oil. The fibers were covered with a glass coverslip, and the immersion oil was allowed to settle overnight, such that the oil would penetrate the pore structure. Images of the fibers were taken using a 100× N.A. 1.4 oil-immersion lens (Nikon, Japan). A krypton-argon laser was used for excitation, and images were taken simultaneously at 488 and 568 nm. Thus, the intensity from each fluorescent label can be detected separately and combined to create a composite image. The sheer number of fibers contained within a single pulp sample (0.5 g) make it difficult to present an accurate representation of the entire fiber population. The fibers themselves are heterogeneous, and structural differences exist between fibers and even along a single fiber. A large sample size (∼50) would be necessary to provide statistically accurate data, making a complete analysis expensive and time-consuming. Some objectivity was needed to select fibers that were representative of the entire population. Broken fibers were not imaged, as the localized adsorption behavior around the break was not indicative of the overall behavior. Latewood fibers were preferred as they possess thicker walls. Several fibers were first selected at random. Although these fibers were not imaged, they were used to provide an initial distribution in the adsorption behavior. Several more fibers (three to five) were then selected at random to be imaged. Images along the length direction were produced from thin optical sections near the center of the fiber. Cross-sectional images were constructed at several points by scanning in the radial direction. Thus, several images were taken for each fiber in multiple directions. Assessing the Diffusion Length. Profiles of the fluorescent intensity, I, were taken from the individual images at several positions to account for the heterogeneous nature of the single pulp fiber. The residual lignin contained in the fiber wall only fluoresces to a small extent, such that the fiber wall can easily be distinguished.13 The change in the intensity due to the cationic polyelectrolyte depends on the amount of labeling and the adsorbed mass. However, the intensity increase was significant to distinguish the fluorescence from the lignin and the cationic polyelectrolyte. To account for the fluorescence from the lignin, each profile was adjusted by setting a common baseline to the intensity of the bare fiber. Thus, only fluorescence from the diffusing polyelectrolytes was accounted for. The profile was then normalized to the maximum fluorescent intensity Io, which always existed at the outermost fiber surface, to account for differences in the degree of the fluorescent labeling of each polyelectrolyte. The mean-square displacement of the diffusing polyelectrolyte has been calculated from the intensity profile similar to a method previously outlined for the diffusion of fluorescent labeled polyelectrolytes.26 The intensity profiles at each side of the fiber wall have been treated separately as a one-dimensional unsteady diffusion problem. As the labeled polyelectrolytes are not initially present inside the fiber wall, the conditions c(x, t ) 0) ) co for x ) 0 and c(x, t ) 0) ) 0 for x > 0 can be applied. As the polyelectrolyte solution contains excess polyelectrolyte, the concentration can be considered to remain constant during the diffusion process and the additional boundary condition c(x ) 0, t) ) co can be applied. Taking (26) Nazaran, P.; Bosio, W.; Jaeger, W.; Anghel, D. F.; Klitzing, R. v. J. Phys. Chem. B 2007, 111, 8572.
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Figure 1. Fluorescent intensity profiles for the diffusion of copolymer 1 in 10-1 M NaHCO3 at 7 days and 108 days. The profiles have been normalized to the intensity at the fiber surface (x ) 0), and the lines correspond to fits made using eq 1.
into account that the fluorescent intensity I is proportional to the concentration of the polyelectrolyte, c(x, t), the solution to the diffusion problem can thus be written as
(√ )
I(x, t) ) erf c Io
x
2〈∆x2 〉
(1)
where x is the spatial coordinate through the fiber wall, t is time, I(x, t) is the fluorescent intensity at points within the fiber cell wall, Io is the fluorescent intensity at the fiber surface, and 〈∆x2〉 is the mean-square displacement. A value for 〈∆x2〉 can therefore be obtained by fitting eq 1 to the intensity profile, as seen in Figure 1. An effective diffusion coefficient, Deff, can be determined from the mean-square displacement using the simple relationship:
〈∆x2〉 ) (2Deff)t
(2)
Due to the electrostatic nature of polyelectrolyte diffusion, pure Fickian diffusion can most likely be disregarded. The charge gradient in the fiber wall causes the polyelectrolyte to move into the fiber bulk, although the diffusion is expected to be hindered by steric and electrostatic forces between the polyelectrolyte and the pore wall. Deff is considered to be an effective measure of this hindered movement.
Results Polyelectrolyte Properties. Fluorescent labeled polyelectrolytes were used to investigate the kinetics of adsorption to determine if the polyelectrolytes are diffusing into the pore structure of the fibers. pDADMAC does not readily form covalent bonds with typical fluorescent labels; therefore, acrylamide (AM) was copolymerized with diallyldimethylammonium chloride (DADMAC), as the resulting poly(AM-co-DADMAC) could be fluorescent labeled. Moreover, the charge density can be controlled by adjusting the AM composition of the copolymer, as AM is nonionic. This approach was used to synthesize several highly charged poly(AM-co-DADMAC) samples. Cationic dextran was prepared as a low charge density polyelectrolyte and likewise fluorescent labeled. The properties of both polyelectrolytes are presented in Table 1. Two molecular fractions of a native dextran were also fluorescent labeled to investigate the adsorption behavior of an uncharged polymer. Adsorption Kinetics. The kinetics for the adsorption of pDADMAC was initially investigated using only the polyelectrolyte titration technique. The original premise was to determine the appropriate adsorption time for measuring the surface charge of cellulosic fibers using high molecular mass pDADMAC. A bleached kraft pulp was therefore used to be consistent with previous surface charge measurements.12 Whereas an adsorption time of 30 min has become standard for laboratory measurements,
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Table 1. Properties of the Cationic Polylectrolytes diffusion charge density (mequiv/g) constant molecular polydispersity (×109 cm2/ before after labeling labeling s)c polyelectrolyte mass (Da) indexb pDADMAC copolymer 1 copolymer 2 copolymer 3 copolymer 4 Cat Dex A Cat Dex B Cat Dex C native dex D native dex E
4.5 × 105b 1.1 × 105b 4.8 × 105b 4.2 × 105b 2.6 × 105b 2.0 × 106a 5.0 × 105a 1.0 × 104a 2.0 × 106a 1.0 × 104a
2.47 1.8 5.75 2.10 3.52 3.85 2.23 1.41 6.32 1.48
2.1 1.2 4.6 1.7 1.3 2.0 60.6 5.7 83.9
5.90 3.37 5.75 1.95 3.52 0.50 0.53 0.56
3.31 5.72 1.80 3.47 0.50 0.49 0.53
a Supplied by the manufacturer. b Measured by size exclusion chromatography, PD ) MW/MN. c Measured by dynamic light scattering in 10-1 M NaHCO3 before fluorescent labeling.
Figure 3. Effect of polyelectrolyte addition on the kinetics for the adsorption of pDADMAC at pH 7.2 onto a bleached kraft pulp in 10-1 M NaHCO3. The pDADMAC had a molecular mass of 4.5 × 105 Da and a charge density of 6.19 mequiv/g.
Figure 2. Kinetics for the adsorption of pDADMAC onto cellulose fibers from a bleached kraft pulp. The adsorbed mass is presented as the saturation adsorption in both deionized water and in 0.1 M NaHCO3 at pH 7.2. The pDADMAC had a molecular mass of 4.5 × 105 Da and was dosed at ∼5.3 mg/g of fiber.
the adsorption behavior has not been reported in great detail at longer adsorption times. The adsorption of pDADMAC was therefore measured at long adsorption times, and the results are reported in Figure 2 at two electrolyte concentrations. The adsorption behavior of pDADMAC is dramatically affected by the presence of an electrolyte. The adsorbed mass remains relatively constant in deionized water, supporting the notion that a pseudoequilibrium exists for the adsorption of high molecular mass polyelectrolytes to cellulosic fibers.24,25 The adsorption at longer times also has to be considered as a psuedoequilibrium as the adsorbed mass did increase with time, albeit very slowly. The adsorbed mass likewise increased with time at high electrolyte concentrations, although the increase was more dramatic. A larger mass of pDADMAC initially adsorbs in 10-1 M NaHCO3, which can be attributed to screening of the electrostatic interactions within and between the pDADMAC chains. The adsorbed mass increased monotonically with time until the excess pDADMAC was completely adsorbed. Although the driving force is entropic, in this case, both due to release of counterions and due to a concentration gradient of the polyelectrolyte, adsorption is electrostatic in nature. Therefore, the pDADMAC completely adsorbs in an attempt to compensate the fiber charges. However, it is unclear as to whether the increase in the adsorbed mass with time is due to a kinetic reconformation process on the outermost surface or the consequence of the pDADMAC being able to penetrate into the pore structure in order to compensate the charges located within the bulk. Different dosages of pDADMAC were therefore used to determine the adsorption capacity of the fibers and to ensure that the pDADMAC does not completely adsorb. It is also of interest to determine how the concentration of the
excess pDADMAC affects the kinetics for adsorption in 10-1 M NaHCO3. The results are presented in Figure 3. A large difference can be seen in the adsorbed mass for each addition. Although these differences exist, the kinetics for adsorption in 10-1 M NaHCO3 are rather similar for each addition. Despite the differences in the concentration of the excess pDADMAC over time, the adsorption increased at a constant rate. Moreover, this rate was also independent of the dosage. It is difficult to interpret the nature of the time dependence from simple adsorption values, but it is evident from the results in Figure 3 that such a process does indeed occur and it does not appear to be dominated by pure Fickian diffusion, that is, concentration dependent. Adsorption of Poly(AM-co-DADMAC). The fluorescent labeled copolymers were adsorbed to the unbleached kraft pulp to determine the underlying molecular mechanism of the kinetic process for highly charged polyelectrolytes. The unbleached kraft pulp was used to be consistent with previous adsorption measurements for the fluorescent labeled polyelectrolytes.13 Each copolymer was adsorbed at several electrolyte concentrations for times ranging from 1 day to 96 days. Fluorescent CLSM images were then taken to determine the extent to which the poly(AM-co-DADMAC) penetrated into the porous wall. Figure 4 contains CLSM images of copolymer 1 adsorbed in 10-1 M NaHCO3 for various times. Figure 4 indicates that copolymer 1 gradually diffused through the fiber wall. Whereas the adsorption was initially restricted to the outermost surface, the thickness of the fluorescent layer begins to noticeably increase around a time of 59 days. At 96 days, copolymer 1 has diffused throughout the fiber wall, although a gradient can still be seen in the fluorescent intensity profile. This diffusion process nonetheless offers a partial explanation to the kinetic adsorption behavior seen in Figures 2 and 3, despite the differences in the molecular structure of the polyelectrolytes. It can also be seen in Figure 2 that the electrolyte concentration influenced the adsorption behavior of pDADMAC. Whereas the adsorption in deionized water reached a psuedoequilibrium, the adsorbed mass continued to increase with time in 10-1 M NaHCO3. In order to investigate the influence of the ionic strength on the adsorption of the copolymers, a fluorescent labeled poly(AM-co-DADMAC) was then adsorbed in various electrolyte concentrations to observe how the electrolyte concentration influenced the adsorption behavior. The mean-square displacement, 〈∆x2〉, was determined by fitting eq 1 to the intensity profiles
Diffusion of Cationic Polyelectrolytes
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Figure 4. Fluorescent CLSM images showing the adsorption behavior of copolymer 1 for long adsorption times. Adsorption measurements were made in 10-1 M NaHCO3 at pH ∼ 7.2 onto the unbleached kraft pulp. Copolymer 1 had a molecular mass of 1.1 × 105 Da and a charge density of 3.37 mequiv/g.
Figure 5. Mean-square displacement for the diffusion of copolymer 1, having a molecular mass of 1.1 × 105 Da and a charge density of 3.37 mequiv/g, at various electrolyte concentrations. The adsorption measurements were made on the unbleached kraft pulp at pH ∼ 7.2.
taken from the CLSM images. The mean-square displacement is plotted in Figure 5 for the adsorption of copolymer 1 in several electrolyte concentrations. At “short” times, copolymer 1 was restricted to the outermost fiber surface regardless of the electrolyte concentration. The fact that copolymer 1 slightly penetrated into the fiber wall can be attributed to a slight mechanical treatment to which the fibers have been subjected to during the sample preparation. However, the diffusion of copolymer 1 at longer times is notably different for each electrolyte concentration. At 10-5 M NaHCO3, diffusion occurred slowly and copolymer 1 did not penetrate much further into the fiber wall over the course of 108 days. Although diffusion occurred slightly faster at 10-2 M NaHCO3, it was not until 10-1 M NaHCO3 that copolymer 1 appreciably diffused into the fiber wall. Thus, a transition appears to exist around 10-1 M NaHCO3 where the diffusion process is less hindered, possibly due to a more complete screening of electrostatic interactions. This behavior is similar to what has previously been observed for the adsorption of pDADMAC at 30 min, for which a maximum in the adsorbed mass coincided at 10-1 M NaHCO3.12 It should also be noted that the adsorbed mass decreased at higher electrolyte concentrations and eventually no adsorption occurred above 10-1 M NaHCO3. This behavior at high electrolyte concentrations
collaborates with the notion that electrostatic interactions control the diffusion process. The molecular structure of the polyelectrolyte is also expected to influence diffusion into the pore structure. Electrostatic interactions between cationic charges along the polyelectrolyte backbone also play an important role in determining the molecular structure. Several fluorescent labeled poly(AM-co-DADMAC) varying in charge density were therefore adsorbed in moderate electrolyte concentrations to investigate the influence of the charge density on the diffusion process. The molecular mass of the poly(AM-co-DADMAC) was also varied to clarify its relative influence on the diffusion of high charge density polyelectrolytes. The fluorescent CLSM images are presented in Figure 6 for the adsorption in 10-3 M NaHCO3 at 96 days. Despite the differences in charge density, the adsorption of each poly(AM-co-DADMAC) was restricted to the outermost surface at 10-3 M NaHCO3. Thus, the electrostatic interactions between the highly charged poly(AMco-DADMAC) and the anionic fibers were sufficient to limit the diffusion process, unless the electrolyte concentration was high. Adsorption of Cationic Dextran. The range in polyelectrolyte charge density was expanded by studying the adsorption behavior of low charge density cationic dextrans. Cationic dextran is similar to poly(AM-co-DADMAC), as it is linear and the nonionic interactions with cellulose are negligible, that is, χs ≈ 0.6 High molecular mass fractions were chosen, as they have been shown to not adsorb into the pores at short times (t < 30 min),14 and therefore,the diffusion process would not be too rapid. The kinetics for the diffusion process were observed at low electrolyte concentrations using fluorescent labeled cationic dextran. Fluorescent CLSM images are given in Figure 7 for the adsorption of Cat Dex B at 10-5 M NaHCO3. Whereas the diffusion of poly(AM-co-DADAMC) was measured over several months, the diffusion of cationic dextran occurred over several hours. Moreover, the diffusion process into the porous fiber wall occurred at low electrolyte concentrations. Although the mechanism cannot be distinguished from the CLSM images alone, several features can be noted in the diffusion process. The cationic dextran initially adsorbed to the outermost surface, similar to the case of poly(AM-co-DADMAC). However, the diffusion of the cationic dextran was unique due to the fact that it occurred rather uniformly. The fluorescent intensity profiles for the diffusion of poly(AM-co-DADMAC) typically showed a stronger intensity at the outermost surface and a lower intensity
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Figure 6. Fluorescent CLSM images for the adsorption of poly(AM-co-DADMAC) having a different charge density at 96 days. Adsorption measurements were made on the unbleached kraft fibers at pH ∼ 7.2 in 10-3 M NaHCO3. Images: (a) copolymer 1 (molecular mass ) 1.1 × 105 Da and ε ) 3.37 mequiv/g), (b) copolymer 2 (molecular mass ) 4.8 × 105 Da and ε ) 5.75 mequiv/g), (c) copolymer 3 (molecular mass ) 4.2 × 105 Da and ε ) 1.95 mequiv/g), and (d) copolymer 4 (molecular mass ) 2.6 × 105 Da and ε ) 3.52 mequiv/g).
Figure 7. Fluorescent CLSM images for the adsorption of Cat Dex B, having a molecular mass of 5 × 105 Da and a charge density of 0.53 mequiv/g, in 10-5 M NaHCO3 as a function of time. The cationic dextran was adsorbed onto the unbleached kraft fibers at pH ∼ 7.2.
within the pore structure, indicating that most of the adsorption occurred on the surface. On the other hand, the images in Figure 7 indicate that fluorescent intensity within the adsorbed layer remained uniform as the thickness of the layer increased. The diffusion process was also studied in regards to the electrolyte concentration and properties of the cationic dextran, namely, the molecular mass. The mean-square displacement, 〈∆x2〉, for the diffusion of Cat Dex A and Cat Dex B are presented in Figure 8 at various times. The change of 〈∆x2〉 with time was linear in nature for the cationic dextran, regardless of the electrolyte concentration or molecular mass. An effect of the molecular mass and electrolyte concentration can be seen in the rate at which the cationic dextran diffused into the pores. Despite having a similar charge density, Cat Dex B diffused at a faster rate that Cat Dex A regardless of the electrolyte concentration, presumably due to its lower molecular mass. This effect was not observed for the diffusion of the high charge density poly(AM-coDADMAC), and thus, it seems plausible that steric effects become more important as electrostatic interactions are reduced. The electrolyte concentration also influenced the rate of diffusion. Both cationic dextran fractions diffused faster in higher electrolyte
concentrations, although the rate of diffusion was affected more by the molecular mass.
Discussion Kinetics for Diffusion. The kinetics for polyelectrolyte diffusion is very much dependent on the accessibility of the adsorbing polyelectrolyte to the fiber cell wall. Polyelectrolytes initially adsorb to the outermost fiber surface through an electrosorptive process to compensate the surface charges through the release of counterions associated to both the polyelectrolyte and surface charges. To compensate the charges located in the bulk, that is, the internal parts of the fiber wall, polyelectrolytes strive to diffuse into the pore structure. Thus, diffusion will occur if the electrostatic driving force can overcome the entropic loss associated with the polyelectrolyte being confined in the pore volume. Polyelectrolytes are unique, as their molecular structure is often a consequence of electrostatic contributions to the persistence length, namely, through the charge density and electrolyte concentration. Therefore, the accessibility of a polyelectrolyte to the fiber cell wall is governed to a large extent by the charge density. In this respect, it is not surprising that low
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Figure 9. Fluorescent CLSM images for the adsorption of cationic and native dextran onto the unbleached kraft fibers. The adsorption was conducted for 30 min in deionized water adjusted to pH 7.2: (a) native dextran E having a molecular mass of 1.0 × 104 Da, (b) native dextran D having a molecular mass of 2.0 × 106 Da, and (c) native dextran D having a molecular mass of 1.0 × 104 Da adsorbed to fibers pretreated with Cat Dex A (having a molecular mass of 2 × 106 Da and ε ) 0.50 mequiv/g).
Figure 8. Mean-square displacement, 〈∆x2〉, for the adsorption of Cat Dex A (molecular mass ) 2 × 106 Da and ε ) 0.50 mequiv/g) and Cat Dex B (molecular mass ) 5 × 105 Da and ε ) 0.53 mequiv/g) in 10-5 M and 10-3 M NaHCO3 onto the unbleached kraft fibers at pH ∼7.2.
charge density polyelectrolytes penetrate into cellulosic fibers in a manner different from that of high charge density polyelectrolytes. The kinetics of polyelectrolyte adsorption can be rationalized through the extent to which the polyelectrolyte penetrates into the cell wall. For example, Figure 6 shows that high charge density poly(AM-co-DADMAC) does not penetrate into the pore structure in moderate electrolyte concentrations. This fact is also reflected in Figure 2 for the adsorption of pDADMAC in water. The molecular conformation of the pDADMAC restricts adsorption to the outermost surface, such that the adsorbed mass cannot increase with time once the outermost surface is saturated. Therefore, the adsorption reaches a psuedoequilibrium, which cannot be considered a pure equilibrium as the diffusion process only occurs at an extremely slow rate. This fact is further supported by the adsorption behavior at high electrolyte concentrations. Figure 2 indicates that the adsorbed mass of pDADMAC increased with time in 10-1 M NaHCO3. Although it is evident from Figure 4 that the adsorption was initially restricted to the outermost surface, the poly(AM-co-DADMAC) nonetheless penetrated into the fiber wall as time progressed. As both the adsorbed mass and 〈∆x2〉 increased with time, it appears feasible to correlate the rate of increase in the adsorbed mass to the diffusion into the fiber wall, as opposed to a reconformation process at the outermost surface. The pore structure should influence the penetration of the cationic polyelectrolytes into the fiber cell wall. Cellulosic fibers contain a distribution of pore sizes, ranging from large pores that have been shown to be on the order of 80 nm27 to nanopores on that are approximately 5-15 nm in size.11,28 The distribution of pore sizes throughout the fiber cell wall is relatively unknown, although a recent model has suggested that the larger pores occur only at the fiber surface.29 This model also proposed that the pores are connected, and the fact that the cationic dextran (27) van de Ven, T. G. M. Nord. Pulp Pap. Res. J. 2000, 15, 494. (28) Stone, J. E.; Scallan, A. M. Pulp Pap. Mag. Can. 1968, 69, T288. (29) Hubbe, M. A.; Rojas, O. J.; Lucia, L. A.; Jung, T. M. Cellulose 2007, 14, 655.
penetrates throughout the entire fiber wall would appear to support this notion. However, cellulosic fibers act as polyelectrolyte gels, such that the bulk charge and the electrolyte concentration affect the swelling behavior. Cations diffuse into the fiber cell wall to neutralize the bulk charge, in effect creating a Donnan equilibrium that causes the fiber to swell.30 The swelling capacity of the fiber is reduced at high electrolyte concentration, as the imbalance in the counterion concentration is less. This reduction in swelling would be expected to lower the pore size, although Andreasson et al. have shown that the smaller pores are not affected by a high electrolyte concentration.11 This suggests that any change in the pore size would occur for the larger pores, which is logical as a reduction in the size of the smaller pores would further hinder the diffusion process. The fact that the rate of diffusion into the cell wall increased at high electrolyte concentration would suggest that the changes in the polyelectrolyte properties have a greater influence on the diffusion process. A deswelling of the fibers could also occur as the cationic polyelectrolytes penetrate into the pores, although the steady penetration over time suggests that this effect is minimal. However, the effect of the cationic polyelectrolyte on the pore size remains to be proven and is a topic of future research. Diffusion Mechanisms. Whereas the behavior of uncharged polymers in a porous material has been given some attention,7,9,31,32 the behavior of polyelectrolytes in a porous media has proven more difficult to investigate. Therefore, the diffusion of polymers in porous media serves as a useful starting point for investigating the behavior of polyelectrolytes. The original scaling approach of de Gennes3 and the reptation model of Doi and Edwards33-36 provided an understanding for the diffusion of linear polymers in melts and gels. This approach has also been applied to describe the behavior of polymers in porous and disordered media,2,5 in which the wriggling motions of the polymer are confined by the pore wall. The macroscopic diffusion of fluorescent labeled native dextran into a cellulosic fiber can be seen in images (a)-(c) of Figure 9. Images (a) and (b) indicate that the diffusion of native dextran depended on the molecular mass, as the 2.0 × 106 Da dextran did not penetrate throughout the entire fiber wall in 30 min. As it is generally accepted that polymers diffuse in a porous media (30) Scallan, A. M.; Grignon, J. SVen. Papperstidn. 1979, 82, 40. (31) Kislenko, V. N.; Berlin, Ad. A.; Kawaguchi, M.; Kato, T. Langmuir 1996, 12, 768. (32) Langley, K. H.; Teraoka, I.; Karasz, F. E. Prog. Colloid Polym. Sci. 1993, 91, 153. (33) Doi, M.; Edwards, S. F. J. Chem. Soc., Faraday Trans. 2 1978, 74, 1789. (34) Doi, M.; Edwards, S. F. J. Chem. Soc., Faraday Trans. 2 1978, 74, 1802. (35) Doi, M.; Edwards, S. F. J. Chem. Soc., Faraday Trans. 2 1978, 74, 1818. (36) Doi, M.; Edwards, S. F. J. Chem. Soc., Faraday Trans. 2 1978, 75, 38.
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Figure 10. Fluorescent CLSM images for the diffusion of Cat Dex C (molecular mass ) 1 × 104 Da and ε ) 0.56 mequiv/g), labeled with sulforhodamine B acid chloride to fluoresce red, after 30 min in deionized water at pH ∼ 7.2 onto surfaces pretreated with various polyelectrolytes, labeled with fluorescein isothiocyanate to fluoresce green: (a) Cat Dex C (molecular mass ) 1 × 104 Da and ε ) 0.56 mequiv/g), (b) Cat Dex A (molecular mass ) 2 × 106 Da and ε ) 0.50 mequiv/g), and (c) copolymer 2 (molecular mass ) 4.8 × 105 Da and ε ) 5.75 mequiv/g).
through a reptation-like process, the dependence of diffusion on the molecular mass can be attributed to hydrodynamic interactions with the pore wall due to the chain length. The diffusion mechanism was further investigated by trying to adsorb the native dextran to a fiber surface saturated with Cat Dex A. The outermost surface was first saturated by adsorbing a high molecular mass cationic dextran, labeled with fluorescein isothiocyanate to fluoresce green in the CLSM images. The low molecular mass native dextran, labeled with sulforhodamine B acid chloride to fluoresce red, was subsequently added, and a CLSM image of the diffusion process after 30 min is presented in image (c). The absence of red fluorescence in image (c) of Figure 9 indicates that native dextran could no longer diffuse into the pores when the outermost surface was blocked. The layer of cationic dextran presumably acted as a high concentration barrier localized at the outermost surface, ultimately eliminating any driving force for Fickian diffusion. Therefore, it appears as though the native dextran must access the outermost surface in order to reptate into the fiber wall. Whereas the driving force for polymer diffusion is Fickian in nature, the time scales would be dictated by a reptation mechanism due to the constraint of the pore walls. In the absence of specific interactions, as native dextran possesses neither nonelectrostatic nor electrostatic interactions with the cellulose, the native dextran does not physically adsorb to the pore wall. Therefore, it seems plausible that the native dextran simply diffused from the outermost surface into the pore structure as a propagating wave to even out the concentration gradient that existed between the solution and the fiber wall. The fact that the cationic dextran remained fixed to the outermost surface, as opposed to being forced into the pores by the native dextran, suggests that polyelectrolyte diffusion differs from that of polymers. However, it is difficult to assess from only image (c) of Figure 9 if the reptation process is simply retarded due to the cationic dextran being less flexible or if the cationic dextran has electrostatically been fixed to the cellulose. The methodology of using two distinguishable fluorescent labels was also used to investigate the mechanism for diffusion into cellulosic fibers. The effects of a blocked surface on the diffusion of a low molecular mass cationic dextran can be seen in Figure 10. In essence, only the cationic charge of the low molecular mass dextran, again labeled with sulforhodamine B acid chloride to fluoresce red, separates these images from those in Figure 9. Nonetheless, a completely different behavior was observed for the low molecular mass cationic dextran, which was able to diffuse into the fiber wall. Already the importance of the electrostatic charges is apparent, in this case indirectly promoting the diffusion process through the release of counterions.
HorVath et al.
Another feature seen in Figure 10 is that the initially adsorbed layer, regardless of the polyelectrolyte, remained fixed to the outer parts of the fiber wall during the diffusion of the subsequent polyelectrolyte, that is, Cat Dex C. This in itself is notable, as it opposes the so-called “relay-race” mechanism previously proposed by Kabanov et al.,10 for which it was argued that the second polyelectrolyte would push the initial polyelectrolyte further into the pore structure as opposed to adsorbing through a fixed initial layer. The images in Figure 10 therefore suggest another mechanism, for which the first polyelectrolyte becomes fixed to pore wall such that subsequent chains further access the pore structure by diffusion through the layer of initially adsorbed polyelectrolytes. In fact, Kabanov et al. surmised this as a possible mechanism, although their limited data suggested that this was not valid for polyelectrolyte diffusion into an oppositely charged polyelectrolyte gel. Nonetheless, it is apparent in Figure 10 that polyelectrolytes diffusing into cellulose fibers interact with the pore walls enough to become fixed. This would expectedly influence the mechanism for diffusion. In regards to the polyelectrolytes becoming fixed, the cationic charges of the polyelectrolyte predominantly interact with disassociated carboxyl groups in the fiber wall. Considering that the polyelectrolytes are composed of many electrostatic charges, each polyelectrolyte charge will presumably interact with an anionic charge in the confinement of the pore. Thereby, the transport process will be either severely hindered or effectively ceased by electrostatic interactions with the anionic charges in the pore wall. Although it has been evident that the rate of diffusion, seen as the increase in 〈∆x2〉 with time, depends on the molecular structure of the polyelectrolyte, Figure 10 indicates that the each polyelectrolyte became fixed regardless of the molecular structure. Even though the two fractions of Cat Dex C used in image (a) diffuse at the same rate, the electrostatic interactions with the pore wall were enough to fix the initial fraction of Cat Dex C to the outermost pores. Moreover, the sharp boundary between the polyelectrolytes suggests that these interactions were sufficient to effectively cease the diffusion of the initial polyelectrolyte, as opposed to only decreasing the rate of diffusion such that the layers would blend together at the interface. Despite the initial polyelectrolytes becoming fixed to the pores, the driving force for diffusion still exists for the unbound polyelectrolyte chains. Subsequent polyelectrolyte chains are thus driven through the immobilized polyelectrolyte layer until they also become fixed to available anionic charges located further in the pore structure. While reptation remains a viable molecular mechanism for the diffusion of polyelectrolytes within the pore, it is not only the pore walls that restrict the molecular movements. Instead of the geometry of the pore, it can be suggested that the interactions of the diffusing polyelectrolyte with the polyelectrolyte already fixed to the pore wall actually govern the diffusion process. This is a subtle difference, but would limit the importance of how the polyelectrolyte interacts with the anionic charges of the pore wall. At low electrolyte concentrations these electrostatic interactions would be expected to fix the cationic polyelectrolyte to the pore wall. Subsequent chains therefore diffuse through the coated pores and may not interact until diffusing to a bare portion of the pore wall. At high electrolyte concentrations, these interactions may be partially screened. However, either case would suggest the movement of the polyelectrolyte in the pore would be more important than the interactions with the pore wall. Electrostatic Contribution to the Rate of Diffusion. Despite the longer time scales, it is plausible that a reptation process still occurs for polyelectrolyte diffusion within a confining pore,
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regardless of whether the pore wall contains an electrostatically fixed polyelectrolyte. Although the mechanism for diffusion has been shown to differ between polymers and polyelectrolytes, the molecular dynamics for diffusion within the pore could therefore be quite similar. Langley et al.32 have previously shown that the diffusion of semirigid polymers is dominated by quite different mechanisms, compared to flexible polymers, if the persistence length (LP) of the polymer is comparable or larger than the pore size. Due to the high molecular mass, the chain size of the poly(AM-co-DADMAC)13 and the cationic dextran14 is generally larger than the size of the smaller pores in the fiber wall. Although LP is a local measure of the chain properties, the polyelectrolyte chain cannot maintain its solution conformation within the pores. The movement of the polyelectrolyte chain within the pore therefore is more dependent on the local chain behavior. Furthermore, polyelectrolytes are unique, as there is a significant electrostatic contribution to the persistence length, which is a consequence of the charge density and the electrolyte concentration. For a polyelectrolyte, the persistence length comprises an intrinsic persistence length, LPo, and an electrostatic persistence length, LPe:37
LP ) LP0 + LPe 38
(3)
39
Odijk, and Skolnick and Fixman developed a theory to calculate the electrostatic contribution to the persistence length based on so-called equivalent parameters:
LPe )
λBλD2
(4)
4b2εM2
where λB is the Bjerrum length, λD is the Debye length, b is the distance between the charges along the polyelectrolyte backbone, and εM ) 1 for b > λB. At low electrolyte concentrations the counterions contained by the polyelectrolyte must be considered, such that the Debye length can be described as
λD )
(
8πλB NS +
NP 2
)
(5)
where NS is the number of ions from the electrolyte and NP is the number of counterions contributed from the polyelectrolyte charges. At high electrolyte concentrations, the counterions become negligible. The Debye length for a 1:1 electrolyte at 25 °C becomes a simple function of the electrolyte concentration, Cel:40
λD )
0.304
√Cel
(6)
Using LP as a measure of the flexibility, Figure 11 shows that the flexibility of the polyelectrolyte greatly influenced the Deff value. More significantly, the Deff value for each polyelectrolyte in various electrolyte concentrations collapsed onto a common curve, showing two distinct types of behavior. The Deff was generally much smaller for polyelectrolytes having a high charge density, that is, poly(AM-co-DADMAC). Similar values for Deff have also been noted for other high charge density polyelectrolytes in multilayers.26,41 The high charge density leads (37) Dautzenberg, H.; Jaeger, W. J.; Philipp, B.; Seidel, Ch.; Stscherbina, D. Polyelectrolytes: Formation, Characterization and Application; Hanser Publisher: Munich, Germany, 1994. (38) Odijk, T. J. Polym. Sci., Polym. Phys. Ed. 1977, 15, 477. (39) Skolnick, J.; Fixman, M. Macromolecules 1977, 10, 944. (40) Israelachvili, J. N. Intramolecular and Surface Forces; Academic Press: London, U.K., 1992.
Figure 11. Effect of the persistence length on the effective diffusion coefficient for each polyelectrolyte in the fiber wall in various electrolyte concentrations at pH 7.2.
to a significant electrostatic contribution to the persistence length. This in turn caused the chain to be locally stiff and to diffuse slowly. The higher charge density would also lead to stronger interactions with the pore wall, which may hinder the diffusion process. The electrostatic repulsions that cause the chain to be stiff and the interactions with the pore wall both can be screened by increasing the electrolyte concentration. A slight increase in the Deff value can be seen at moderate electrolyte concentrations as the LP value decreases with increasing electrolyte concentration. A noticeable transition occurred for the poly(AM-co-DADMAC) when the electrolyte concentration approaches 10-1 M, which is particularly evident in the diffusion behavior of copolymer 1. Although LP is only slightly reduced by increasing the electrolyte concentration from 10-2 to 10-1 M, a larger increase is observed in Deff. A similar transition corresponds to behavior previously observed in the hydrodynamic diameter, as the molecular conformation of the poly(AM-co-DADMAC) was similar to that of an uncharged polymer at 10-1 M NaHCO3 due to the electrolyte completely screening the electrostatic contribution to the persistence length.13 The electrostatic interactions with the fiber charges may also become screened, such that the reptation process would not be hindered by electrostatic interactions with the pore wall. This transition in the diffusion behavior was further observed for the cationic dextran. However, the diffusion of the cationic dextran was measured at 10-5 and 10-3 M, at which the electrolyte does not completely screen the electrostatic interactions. Therefore, the interactions with the pore wall are not the only explanation for the transition in the diffusion behavior. The low charge density leads to a weaker electrostatic contribution to the persistence length, and the cationic dextran is more flexible than the poly(AM-co-DADMAC). The cationic dextran also has a larger hydrodynamic radius than the poly(AM-co-DADMAC) due to the larger molecular mass,13,14 and we believe that it is the flexibility that has a larger influence on the diffusion process. Thus, the effect of the LP value becomes significant below a critical value, such that the Deff value increased by orders of magnitude by slightly reducing the LP value. Steric Contribution to Diffusion. Because polyelectrolyte dynamics is dominated by forces created by the electrostatic charges in low and medium concentration electrolyte solutions, it is difficult to interpret steric effects due to the molecular size of the polyelectrolyte chain. Steric interactions occur with the confining pore and slow down the diffusion process, and further
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Conclusions
Figure 12. Effective diffusion coefficient for various polyelectrolytes in the fiber wall versus the ratio for the polyelectrolyte persistence length to the contour length.
restrictions to the diffusion process should occur when the length of the diffusing polyelectrolyte becomes on the order of the pore length. These steric effects are not evident in Figure 11, as the persistence length is a measure of flexibility rather than the overall size. A closer inspection of Figure 8 reveals that the higher molecular mass cationic dextran, Cat Dex A, diffused slower than the lower molecular mass fraction, Cat Dex B, despite having essentially the same charge density. It is therefore important to account for the overall size of the polyelectrolyte chain, which can be done by scaling LP by the contour length (LC) of the polyelectrolyte. Figure 12 presents Deff as a function of LP/LC in order to account for these steric effects. Although steric effects influence the rate of diffusion, the importance of the steric effects becomes negligible for the diffusion of stiff molecules. Presumably, the large persistence length restricts the wriggling motion within the confinement of the pore structure. In essence, the diffusion process is sufficiently slow to not be impeded by the length of the chain in regards to the pore length. A transition in the diffusion behavior occurs as the flexibility of the chain increases, by either reducing the charge density or increasing the electrolyte concentration. The more flexible chains are able to move more freely within the confinement of the pores, such that they diffuse at a faster rate. Steric effects become predominant as the overall length of the chain restricts the motion in the bends of the tortuous pores in the fiber wall. Therefore, Deff was somewhat lower for the higher molecular mass cationic dextran. Although steric effects are appreciable for the diffusion of flexible polyelectrolytes, the overall flexibility of the diffusing chain has the largest influence on Deff. However, the polydispersity of the polyelectrolytes also becomes relevant for flexible polyelectrolytes. Although fractionated polyelectrolytes were used, it can be seen in Table 1 that the high molecular mass polyelectrolytes are still polydisperse. This will particularly affect the determination of mean-square displacement into the fiber wall using eq 1, as the decay of the fluorescent intensity in the cell wall could be due to the lower molecular mass chains diffusing further than the higher molecular mass chains. Therefore, the importance of the molecular mass, that is, contour length, would be better observed using polyelectrolytes having lower polydispersity. (41) Dubas, S. T.; Schlenoff, J. B. Langmuir 2001, 17, 7725.
Cationic polyelectrolytes have been shown to diffuse into cellulosic fibers, leading to an increase in the adsorbed mass over time. The rate of diffusion has been shown to occur on the order of hours for low charge density cationic dextran and on the order of months for high charge density poly(AM-coDADMAC). The rate of diffusion is primarily governed by the electrostatic interactions, rather than the molecular size. The cationic dextran diffused faster than the poly(AM-co-DADMAC) despite having the largest molecular mass. The low charge density leads to weaker interactions between the polyelectrolyte charges and with the pore wall. The weak electrostatic interactions between charges along the polyelectrolyte backbone allow the chain to be more flexible, better facilitating local movements in the pore volume. This can also be used to explain the slower diffusion of the high charge density poly(AM-co-DADMAC), which would also interact strongly with the pore wall at low electrolyte concentrations. The electrolyte concentration also affects the rate of diffusion, such that increasing the electrolyte concentration results in a faster diffusion process. This can be attributed to the polyelectrolyte chains becoming more flexible and having weaker interactions with the oppositely charged pore wall at higher electrolyte concentrations. It was also observed that the molecular mass can affect the diffusion of flexible chains, due to increased hydrodynamic interaction with the pore wall. However, this effect was not exhibited by high charge density polyelectrolytes, presumably as the electrostatic interactions are dominant. Polyelectrolytes diffuse into cellulosic fibers through a complex process. The diffusion process is entropic in nature, driven by the release of counterions within the porous fiber wall. This entropic gain must offset an accompanying loss of entropy associated with the polyelectrolyte being confined in the pore. While electrostatic interactions promote diffusion, these same electrostatic interactions also hinder the diffusion process. Electrostatic interactions between the diffusing cationic polyelectrolytes and the anionic charges in the pores acted to fix the polyelectrolytes. Thus, polyelectrolytes do not appear to diffuse as a propagating wave or by a “relay race” mechanism. Rather, they diffuse through a layer of “fixed” polyelectrolyte to available anionic charges located deeper in the fiber wall. The effective diffusion coefficients measured were similar to those reported for polyelectrolytes in multilayers. Whereas the initial penetration into the fiber wall is believed to correlate to the molecular size of the cationic polyelectrolyte, the effective diffusion coefficient was correlated to the persistence length of the chains, which appears to be an appropriate measure for the local chain movements in the pore volume. Acknowledgment. The authors would like to thank Mrs. Anni Hagberg for her services with the fluorescent confocal laser scanning microscopy. Mr. Lars-Erik Enarsson and Mr. Mangus Gimåker are thanked for their helpful discussions. Mr. Per Larsson is also thanked for helping with the fitting of the fluorescent intensity profiles. Financial support from the Biofibre Material Centre (BiMaC), the Royal Institute of Technology (KTH), and STFI-Packforsk AB is gratefully acknowledged. LA800669D
