Adsorption of a Cationic Polyelectrolyte on Escherichia c oli Bacteria

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Adsorption of a Cationic Polyelectrolyte on Escherichia coli Bacteria: 2. Interactions between the Bacterial Surfaces Covered with the Polymer Xavier Chaˆtellier,*,† Jean-Yves Bottero,† and Jean Le Petit‡ CEREGE, Europoˆ le de l’Arbois, 13545 Aix-en-Provence Cedex 04, France, and Laboratoire de microbiologie, Faculte´ des Sciences de Saint-Je´ roˆ me, 13397 Marseille Cedex 20, France Received January 31, 2001. In Final Form: February 2, 2001 Quaternized polyvinylpyridine (PVPQ) was used as a cationic polymer to destabilize an Escherichia coli bacterial suspension. The optical density and the fraction of free cells, obtained by light scattering measurements, were recorded as a function of the introduced polymer amount, as a way to monitor the stability of the suspension. The flocculation was almost complete for polymer dosages ranging from about 28 to 47 mg of carbon of PVPQ per dry g of bacteria. These dosages correspond to still negatively charged cells, as shown by ζ potential measurements. At low polymer coverages, a less efficient flocculation is observed. At higher dosages, the suspension restabilizes. We interpret these results using our previous study on the adsorption of the polymer chains. We argue that the flocculation at low dosages is rendered possible by the strong inhomogeneities of charge on the bacterial surfaces because of the self-similar configuration of the adsorbed polymer layer and that the restabilization at large dosages is due to the small mesh size of the polymer network on the surface as well as to the Coulombic repulsion between the cells. The properties of the bacterial aggregates were investigated by light scattering. Destabilized suspensions produce aggregates with sizes decreasing as the quantity of adsorbed polymer increases. At the optimum of flocculation, the polydispersity of the aggregates is low, suggesting a diffusion-limited aggregation mechanism (DLA). The presence of the characteristic self-similar structure of DLA aggregates, with a fractal dimension on the order of 1.9, is suggested by some of the light diffusion experiments. On the other hand, at low coverages, that is, when only some regions on the surfaces are covered with polymers, the flocculation seems to obey a reaction-limited aggregation, with a large polydispersity in the size of the aggregates.

1. Introduction In the last few decades, the understanding of interaction forces between surfaces has improved dramatically. Originally, it was proposed that the force between two similar surfaces could be modeled as the sum of attractive van der Waals forces and repulsive electrostatic forces.1,2 This is known as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, which predicts that the attraction will overcome the repulsion, provided that the electrostatic repulsion is sufficiently screened, that is, provided that the ionic strength is large enough. Although the DLVO theory proved to be useful in a number of cases, for instance, by predicting the destabilization of some colloidal suspensions by addition of a salt, this simple picture can be used only for simple types of planar surfaces and solvents, that can be modeled as continuous and homogeneous media. The roles of the solvent and of the dissolved molecules that it contains, in particular, are crucial and can seriously modify the DLVO scheme in several ways. Some of the dissolved species may adsorb on the surface and consequently modify its properties. In particular, their adsorption on the surfaces may lead to chemical and surface charge heterogeneities.3,4 The adsorption on * Corresponding author. Present address: Department of Earth Sciences, University of Ottawa, Ottawa ON K1N 6N5, Canada. E-mail: [email protected]. † CEREGE, Europo ˆ le de l’Arbois. ‡ Laboratoire de microbiologie, Faculte ´ des Sciences de SaintJe´roˆme. (1) Verwey, E. J. W.; Overbeek, J. T. G. Theory of stability of lyophobic colloids; Elsevier: Amsterdam, 1948. (2) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: London, 1985. (3) Kekicheff, P.; Spalla, O. Phys. Rev. Lett. 1995, 75, 1851-1854.

surfaces of macromolecular species is also known to correspond to many possible behaviors.5 Recent research is increasingly suggesting that the correlations between the spatial fluctuations of charge in the solvent may not always be negligible and that the mean-field treatment of the electrostatic interactions of the DLVO theory is thus not always adequate. In particular, when the surfaces are highly charged and the ions of the solvent are multivalent the fluctuations may lead to an attractive electrostatic interaction instead of a repulsive one.6 Although the science of surface forces has reached a certain maturity, it is surprising that it has been concerned almost solely with abiotic systems. It is true that biological interfaces have complex structures and present additional difficulties and challenges. However, the many interfacial processes of importance involving microorganisms justify some additional research effort in that direction. In particular, the surface properties of bacterial cells are determinants for their mobility in porous soils, which has some consequences on their efficiency in bioremediation processes or in the transport of various attached contaminants. They also play an important role in the formation of biofilms and in the processes of aggregation occurring in conventional biological wastewater treatment. In this paper, we consider the effect of a strongly charged synthetic cationic polymer on a Gram-negative bacterial suspension. By adsorbing on the bacterial surfaces, the polymer may induce a destabilization of the suspension. (4) Gregory, J. J. Colloid Interface Sci. 1973, 42, 448-456. (5) Guyot, A.; Audebert, R.; Botet, R.; Cabane, B.; Lafuma, F.; Jullien, R.; Pefferkorn, E.; Pichot, C.; Revillon, A.; Varoqui, R. J. Chim. Phys. 1990, 87, 1859-1899. (6) Stevens, M. J.; Robbins, M. O. Europhys. Lett. 1990, 12, 81-86.

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This simple study is a preliminary work aimed at demonstrating that modern concepts and methods of colloidal science can successfully be applied to biological interfaces. It also has direct implications for wastewater treatment, because we examine the effect of a macromolecular flocculant on a bacterial suspension. A similar approach was used in the 1960s, when Stumm et al. and a few other workers examined the flocculation properties of various bacterial suspensions upon the addition of various additives.7-9 They showed that the classical phenomena of restabilization and charge inversion of the cells can occur at high dosages of added polymers and justified in this way the designation of “biocolloids” for bacterial cells. We present here for the first time a complete study of the effect of a strongly charged cationic polymer on a bacterial suspension. The first part of this study, presented in the preceding paper, investigates how the polymer adsorbs on the bacterial surfaces.10 The second part, presented here, examines the consequences of the adsorption of the polymer, which modifies the interfacial properties of the cell walls by adsorbing on them and may induce a destabilization of the suspension. In addition to the determination of the extent of the flocculation as a function of the introduced polymer amount, we consider the characteristics of the bacterial aggregates by a light scattering technique. These aggregates are thought to be best described as self-similar structures, with a fractal dimension df. We recall that the fractal dimension df of an aggregate is defined by M ∝ Rdf, where M is the mass of the aggregate contained in any sphere of radius R contained within the limits of the aggregate. For a compact aggregate, df ) 3. For a rodlike “aggregate”, df ) 1. “Typical” fractal aggregates have a fractal dimension somewhere between 1.7 (low fractal dimension) and 2.5 (high fractal dimension, quite compact fractal aggregates).11-14 2. Materials and Methods The samples were prepared as explained in part 1 of our study.10 We used quaternized polyvinylpyridine (PVPQ) as a flocculant for the bacterial suspensions. The degree of quaternization of the PVPQ chains was equal to 0.8 ( 0.1, and their degree of polymerization was on the order of 7000. In this paper, the concentration of the polymer is expressed in mgC/L, that is, in mg of carbon of PVPQ per L. The properties of the pure PVPQ solution and of the pure bacterial suspension were discussed in section 4 of ref 10. The experiment was carried out by mixing Escherichia coli cells at 4 °C for 21 h with PVPQ solutions of increasing concentrations. The hydrodynamic agitation during the mixing period was controlled by putting the samples on a rotor turning at a speed of 60 rpm. For each analysis described below, fresh samples were prepared. The ζ potential measurements were performed as explained in ref 10. 2.1. Flocculation. At the end of the mixing period, the tubes were left to rest for 1 h at 4 °C, which allowed sedimentation of the aggregates. The rate of flocculation was determined by a measurement of the optical density A at 450 nm of the (7) Tenney, M. W.; Stumm, W. J.sWater Pollut. Control Fed. 1965, 37, 1370-1388. (8) Busch, P. L.; Stumm, W. Environ. Sci. Technol. 1968, 2, 49-53. (9) Dixon, J. K.; Zielyk, M. W. Environ. Sci. Technol. 1969, 3, 551558. (10) Chaˆtellier, X.; Bottero, J. Y.; Le Petit, J. Langmuir 2001, 17, 2782. (11) Lin, M. Y.; Lindsay, H. M.; Weitz, D. A.; Ball, R. C.; Klein, R.; Meakin, P. Nature 1989, 339, 360-362. (12) Guan, J.; Waite, T. D.; Amal, R. Environ. Sci. Technol. 1988, 32, 3735-3742. (13) Li, D.; Ganczarczyk, J. Environ. Sci. Technol. 1989, 23, 13851389. (14) Serra, T.; Logan, B. E. Environ. Sci. Technol. 1999, 33, 22472251.

Chaˆ tellier et al. supernatants. The result is presented as the ratio A/A0, where A0 is the value of A for the witness sample, where no polymer was added. 2.2. Light Scattering. To investigate the size distribution and the structural properties of the bacterial aggregates, we delicately diluted the samples at the end of the mixing period in 80 mL of salted water (NaCl 4 × 10-3 M) and analyzed them with a granulometer (Malvern Mastersizer S). In this experiment, a He-Ne laser beam (632.8 nm) propagating horizontally is scattered by the suspension. The beam is vertically polarized. The scattered intensity I is recorded for various scattering vectors q by a set of detectors on a vertical axis located at various scattering angles θ, where q is related to θ by the relation q ≡ (4π/λ) sin(θ/2). A characteristic size 2π/q can be associated with each wavevector q. The detectors are lying at angles varying from θ = 0.03° to θ = 50°. The range of sizes covered extends thus from about 0.5 µm to 1000 µm ) 1 mm. The interpretation of the scattering data is a complex challenge. A first difficulty arises from the shape of the E. coli bacterial cells, which is close to that of cylinders with a length about twice as large as their diameter. Few theories exist for systems where the scattering particles are not spherical.15,16 We shall neglect here the fact that the E. coli bacterial cells do not have a spherical shape. Because there is only a factor of about 2 between the diameter and the length, the error associated with this assumption is unlikely to modify the qualitative and the semiquantitative findings of our work. A first way of analyzing a suspension of bacterial aggregates is to model it as a polydisperse suspension of spheres, as is done by the software provided with the Malvern granulometer. This method is based on the Mie theory, which predicts the intensity scattered by a spherical particle15,16 and allows a quantitative estimation of the size distribution of the aggregates in the suspension. For a stable E. coli suspension, such an analysis yields a size distribution centered around a peak at 1.14 µm with a tail ending at about 3 µm. For a destabilized suspension, the volumic fraction τ of “spheres” in the size fractions lower than 3 µm can be easily computed. τ may be thought of as an estimation of the fraction of free bacteria, that is, of bacteria that did not aggregate, and can be compared to the results of the flocculation experiments mentioned previously. The mean diameter Dv of the aggregates can also be estimated easily by considering the mass distribution in size of the fraction 1 - τ of the aggregated cells. Although the Mie theory allows a quick and quantitative way of estimating the fraction of aggregated cells and the average size of the aggregates, its assumption that the aggregates can be described as spheres is unlikely to be correct. We have thus registered the value of the wavevector q at the point where the slope of the scattering curve is the steepest. The associated size 2π/q may be thought of as a rough indication of the size of the aggregates, which can be compared with Dv, in particular when the polydispersity is not too large. At smaller length scales, the internal structure of the aggregates is tested, whereas at larger length scales the Guinier regime is approached and the slope of the scattering curve decreases to zero. To extract structural information about colloidal aggregates in a suspension, the Rayleigh (-Debye-Gans) theory is in general invoked.12 For a monodisperse suspension of aggregates made up of small spherical scattering particles, it predicts that15,16

I(q) ∝ F(q) S(q)

(1)

where F(q) is the form factor, that is, the intensity scattered by a single sphere, and S(q) is the structure factor of the aggregates. F(q) is easily obtained by measuring the intensity scattered by a stable suspension of the scattering particles. The scattered intensity of an E. coli suspension is displayed in Figure 1 and is such that F(q) tends to a constant F(0) when log(q) < 0, that is, when (2π/q) > 6 µm. In the case where the aggregates have a self-similar structure with a fractal dimension df, the structure factor is proportional to q-df. The slope of log(I(q)/F(q)) as a function of log(q) thus displays a plateau over a range of sizes (15) Klein, R.; D’Aguanno, B. Light Scattering: Principles and Development; W. Brown: Oxford, 1996. (16) Kerker, M. The scattering of light and other electromagnetic radiation; Academic Press: London, 1969.

Adsorption of Cationic Polyelectrolyte on E. coli

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Figure 1. Intensity scattered by an E. coli suspension versus scattering vector. corresponding to that where the structure of the aggregates is self-similar. In section 3, several plots of the slope of log(I(q)/ F(q)) versus log(q) are displayed. The Rayleigh theory has been developed for small particles such as

4πrp np | - 1| , 1 λ ns

(2)

where λ is the wavelength of the beam and rp, np, and ns are the radius of the particles, their refractive index, and the refractive index of the solvent, respectively. For bacterial cells, np = 1.39, and for water ns ) 1.33.17 The size of a cell is on the order of 1 µm, and the Rayleigh condition (eq 2) is thus poorly satisfied. Recent theories have been developed to extend the Mie theory to aggregates of spheres of arbitrary size.18-21 In particular, Botet and co-workers have developed a mean-field approximation, focusing on the average properties of the aggregates by considering that the light scattered by any given sphere does not depend on its position within the aggregate and thus being particularly suited for the investigation of the role of the fractal dimension on the scattered intensity.20 A beautiful result of this approach is that eq 1 can be generalized, except that F(q) has to be replaced by another term Fmf(q). The mean-field “form factor” Fmf(q) has a mathematical form which is very similar to that of a single spherical scatterer, but it depends on the fractal dimension df as well as, if df > 2, on the size of the aggregates. The interpretation of the results of the mean-field approximation in terms of predictions for the scattered intensity plots as a function of the fractal dimension and of the aggregates’ size and polydispersity can in principle be performed numerically. Unfortunately, such work is not completely straightforward and has not been performed yet, although there were some recent attempts in that direction.21 Like previous workers,12 we have thus restricted ourselves to the Rayleigh theory as a base to interpret our scattering data in terms of structural properties for the aggregates, as described above. Although this remains to be demonstrated, we believe that this approach is reasonable when the fractal dimension of the aggregates is lower than 2. When the fractal dimension df of an aggregate is lower than 2, its projection on a plane is not space-filling; the probability that a beam of light propagating through the aggregate will hit a particle is thus on the order of N1-2/df and tends to zero when N f ∞.22 Hence, multiple scattering is a local phenomenon when df < 2. At length scales much larger than the cell size, we thus expect that Fb(q) f Fb(0) and that the scattered intensity is, as in the Rayleigh theory, proportional to the structure factor. On the other hand, when df > 2, the larger the aggregate, the more numerous the scatterings. Multiple (17) Latimer, P.; Wamble, F. Appl. Opt. 1982, 21, 2447-2455. (18) Mackowski, D. W. Proc. R. Soc. London, Ser. A 1991, 433, 599614. (19) Xu, Y. L. Appl. Opt. 1995, 34, 4573-4588. (20) Botet, R.; Rannou, P.; Cabane, M. Appl. Opt. 1997, 36, 87918797. (21) Lambert, S.; Thill, A.; Ginestet, P.; Audic, J. M.; Bottero, J. Y. Langmuir 2000, 228, 379-385. (22) We thank R. Botet for sharing with us this qualitative argument.

Figure 2. Relative optical density A/A0 at 450 nm after sedimentation as a function of the amount of polymer introduced in mgC of polymer per g of bacteria. Three regimes are distinguished: poor flocculation (1), optimum of flocculation (2), and restabilization (3). scattering is then a nonlocal phenomenon, and the Rayleigh theory is likely to become more inaccurate. Finally, we would like to underline that eq 1 describes the dependence of the Rayleigh scattered intensity on the wavevector by a dilute monodisperse suspension of aggregates. For a polydisperse suspension, the linear dependence of log(I(q)) with log(q) is valid only for values of q-1 . rp that are much smaller than the size of the smallest aggregates. At larger length scales, the slope of the intensity plot log(I(q)) is decreased by the polydispersity of the suspension.23 It is thus smaller than the fractal dimension df and unlikely to be constant when q varies.

3. Results 3.1. Flocculation of the Bacterial Suspension. By adsorbing on the bacterial cell walls, the polymer modifies the surface properties of the bacteria and may induce a destabilization of the suspension. Figure 2 shows that we obtain the three usual regimes of flocculation, which were already observed with abiotic colloids as well as with bacteria.7,9,24 At low dosages in PVPQ, the flocculation of the suspension is poor, and its extent increases with the amount of PVPQ introduced (regime 1 in Figure 2). Between about 28 and 47 mgC of PVPQ per dry g of bacteria, the flocculation of the suspension is almost complete. This is the regime of the optimum of flocculation (regime 2). For a larger amount of introduced PVPQ, the suspension is readily restabilized (regime 3). Compared to other systems, our mixed PVPQ/E. coli samples display a quite wide regime of optimal flocculation and a very narrow transition between optimal flocculation and restabilization. These results are confirmed by the measurements of the fraction of free cells, presented in Figure 3. These measurements suggest in addition that even at low polymer dosages only a relatively small fraction of the cells are free. It is thus likely that in the regime of poor flocculation most of the cells take part in small aggregates of at most a few cells, which are not large enough to sediment over the few cm of the sample tubes in 1 h. 3.2. Electrophoretic Mobilities of the Cells Covered with PVPQ. The electrophoretic mobilities of the cells, in terms of their ζ potential, were presented in Figure 2 in ref 10 according to the usual convention, that is, as (23) This can be easily understood by considering the example of a bimodal distribution of sizes for the aggregates and adding the intensities scattered by each class of aggregates. (24) Mabire, F.; Audebert, R.; Quivoron, C. J. Colloid Interface Sci. 1984, 97, 120-136.

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Figure 3. Fraction of nonaggregated bacteria as a function of the amount of polymer introduced in mgC of polymer per g of bacteria. The three regimes of Figure 2 are shown.

Figure 4. The ζ potential as a function of the introduced polymer amount. The dotted line suggests the true values corresponding to flocculated cells. The three regimes of Figure 2 are shown.

Figure 5. The ζ potential as a function of the adsorbed polymer amount. The dotted line suggests the true values corresponding to flocculated cells. The three regimes of Figure 2 are shown.

a function of the introduced amount of polymer. This figure is redrawn here for convenience of the reader and is denoted as Figure 4. In ref 10, the introduced polymer amount was related to the adsorbed polymer amount by the adsorption isotherm, presented in Figure 1 of ref 10. This allows us to present here, in Figure 5, the ζ potential as a function of the adsorbed polymer amount. This representation will be useful for the discussion of the electrostatic properties of the bacterial cells covered with various quantities of polymer. The precision of the values

Chaˆ tellier et al.

shown in Figures 4 and 5 is on the order of (5 mV for the ζ potential and (2 mgC/g for the polymer adsorbed amount. Figure 4 shows that the bare cells are negatively charged but that they become less negative, neutral, and then positive as more PVPQ is added to the suspension. An interesting feature of Figure 4 is that the ζ potential of the cells seems to be independent of the introduced polymer amount, for PVPQ dosages ranging from about 28 to 47 mgC/g, that is, within the regime of the optimum of flocculation. It should be kept in mind, however, that the electrophoretic mobility is measured for the free bacteria, that is, for the cells which do not flocculate. The values which are obtained by a ζ potential measurement thus cover a range which corresponds mainly to “stable” cells. In the regime of the optimum of flocculation, almost all the cells are scavenged during the sedimentation of the suspension. The few cells that remain in the suspension for the electrophoretic mobility measurements are thus probably not very representative. It is indeed interesting to see in Figure 4 that no cells with a ζ potential between about -20 and -5 mV are observed. We believe that this shows that the bacterial cells are unstable when they have such a negative ζ potential. Such behavior has already been observed for various systems, including polystyrene latex suspensions and clays.25 The true value of the ζ potential in Figure 4, in the regime of the optimum of flocculation, is hence probably better represented by the dotted line than by the experimental points. Taking this into account, the increase of the ζ potential as a function of the introduced polymer amount appears in Figure 4 as quite regular. In Figure 5, the points corresponding to the regime of optimal flocculation have been omitted, and we have instead added a dotted line, which suggests the true position of the missing points. Three regimes are observed in Figure 5: For small polymer dosages, the ζ potential sharply increases. At intermediate PVPQ concentrations, the increase of the ζ potential is slow, and in the regime of restabilization, the ζ potential increases sharply again. Note that the first two regimes here do not correspond to the regime of poor flocculation (regime 1) and to the regime of the optimum of flocculation (regime 2). A better correspondence can indeed be established with the different regimes of the adsorption isotherm, shown in Figure 1a,b in ref 10. Figures 4 and 5 suggest that the isoelectric point, where the ζ potential of the cells is zero, corresponds to a dosage of PVPQ of about 50 mgC/g and to an adsorbed amount of PVPQ of about 17 mgC/g. 3.3. Properties of the Bacterial Aggregates. Direct eye observation of the bacterial aggregates showed that two regimes can be distinguished, which correspond to the regime of the optimum of flocculation and to the regime of poor flocculation, at low amounts of adsorbed polymer. In the regime of the optimum of flocculation, the aggregates are visible but small, on the order of at most 100 µm. Their size distribution seemed to have a small polydispersity. On the other hand, in the regime of poor flocculation a large polydispersity is observed, with some free cells and aggregates of various sizes. Most of the aggregated cells seem to belong to a few large aggregates, having sizes which can reach hundreds of µm. These direct observations were confirmed by the light scattering experiments. Examples of the scattered intensity log(I(q)) versus log(q) for various amounts of added polymer are plotted in Figure 6. All scattering curves (25) Black, A. P.; Vilaret, M. R. J.sAm. Water Works Assoc. 1969, 61, 209-214.


Figure 6. Scattered intensity versus wavevector for various amounts of added polymer: 0 (2), 6.9 (O), 15.7 (b), 27.7 (0), 46.3 (9), and 50.2 mgC/g (4).

Figure 7. Characteristic size for the aggregates, as obtained by the Malvern software (O) and by the maximal slope method (0).

mingle at large wavevectors log(q) g 0, that is, (2π/q) e 6 µm. At such wavevectors, the plot corresponds to single scattering by isolated cells. All curves also reach a plateau at low wavevectors, corresponding to the Guinier regime. The various plots differ by their slopes at intermediate wavevectors. Only relatively minor changes in the scattered intensity are observed when the amount of added polymer increases from about 5 to 19 mgC/g, that is, within the regime of poor flocculation. A similar observation is made in the regime of the optimum of flocculation, when the added amount varies from about 22 to 47 mgC/g, except for the position of the plateau at low wavevectors. However, the plots change quickly between 18 and 23 mgC/g or between 47 and 50 mgC/g. The scattered intensity in the regime of restabilization is not exactly the same as in the case where no polymer is added. This may be a kinetic effect due to the presence of a few remaining aggregates, and we shall not discuss it further in this paper. As we mentioned in section 2, it is not easy to determine quantitatively the size distribution of the aggregates in the flocculated suspension. However, a clear feature of Figure 6 is that the width of the plateau at low wavevectors increases with the amount of polymer added. This means that the size of the largest aggregates decreases as the amount of polymer added increases. The two methods mentioned in section 2 to estimate the average size of the aggregates are displayed in Figure 7. The good overall agreement between the two methods may be a sign in favor of their semiquantitative validity. Figure 7 confirms that the average size of the aggregates decreases when the quantity of added polymer increases. The restabilization regime occurs when it becomes on the same order

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Figure 8. Slope of the scattered intensity curve for an added amount of polymer equal to 15.7 mgC/g. The full line represents a polynomial fit of order 9.

of magnitude as the size of the cells. In the regime of poor flocculation, the mean size of the aggregates reaches hundreds of µm. Some of the aggregates were visually observed to be larger than a mm. Because this large size happens in correlation with a large fraction of unaggregated cells, we conclude that the polydispersity in size of the suspension is very large in the regime of poor flocculation, that is, when little polymer is adsorbed on the cells. In contrast, the mean size of the aggregates in the regime of the optimum of flocculation is on the order of at most 100-150 µm. At the same time, the fraction of unaggregated bacteria is very low. This shows that the polydispersity of the aggregates is much smaller than in the regime of poor flocculation. The distribution of sizes calculated by the Malvern software suggested indeed that in this regime the sizes of all the aggregates present in the suspension were on the same order of magnitude. To obtain some information on the internal structure of the aggregates, we have plotted in Figures 8-10 the slope of the scattered intensity log(I(q)/Fb(q)) versus log(q), where Fb(q) is the intensity scattered by a suspension of free E. coli cells, without any added polymer. This procedure enhances the differences between the various scattering curves. At large and at low wavevectors, the slope of log(I(q)/Fb(q)) tends to zero. At intermediate wavevectors, it contains the information on the characteristics of the size distribution of the aggregates and of their structure at a given length scale. The large wavevectors, where the slope tends to zero, are not shown in Figures 8-10. The results are presented for wavevectors ranging from log(q) ) -2 to log(q) ) 0. This corresponds to sizes ranging from about 600 down to 7 µm. We define the range of intermediate wavevectors from log(q) ) -1.2 to log(q) ) -0.2, corresponding to sizes between 10 and 100 µm. This is the range of sizes where the internal structure of the aggregates is likely to be tested. In the regime of poor flocculation, a typical slope curve is shown in Figure 8. Because of the large polydispersity of the suspension, the slope of the scattering curve cannot be accurately interpreted in terms of the compactness of the structure of the aggregates. In addition, multiple scattering may affect the form factor, which then cannot be properly approximated by Fb(q). We have not attempted to extract all the information contained in the slope plots, as in the one of Figure 8. However, at intermediate wavevectors the low value of the slope seems to confirm that the polydispersity of the suspension is large. In contrast, the high value of the slope at its minimum, which was between about 2.5 and 3, suggests the presence of a compact structure, at least at large length scales, from about 100 µm. The slope curve for an added polymer amount of 22.3 mgC/g, at the onset of the optimum of flocculation, is shown

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Figure 9. Slope of the scattered intensity curve for an added amount of polymer equal to 22.3 mgC/g. The full line represents a polynomial fit of order 9.

Figure 10. Slope of the scattered intensity curve for an added amount of polymer equal to 22.3 (O), 31.8 (0), and 46.3 mgC/g (4). Polynomial fits of order 9 are shown as a full, a dashed, and a dotted line, respectively.

in Figure 9. Its main feature is a plateau for wavevectors between log(q) ) -0.4 and log(q) ) -0.9, corresponding to sizes ranging from about 15 to 50 µm. The slope at the plateau is equal to 1.9. At larger length scales, above 60 µm, the slope reaches a maximum value, suggesting a denser organization of the large-scale structures. Finally, the evolution of the slope curve in the regime of the optimum of flocculation for various amounts of added polymer is displayed in Figure 10. 4. Model and Discussion 4.1. A Model for the Electrostatic Properties of the Cells. The role of PVPQ as a flocculant for the bacterial suspension can be understood if we take into account the results concerning the adsorption of the polymer chains on the cell surfaces, which are presented in ref 10. We have shown in ref 10 that the polymers adsorb on the bacterial surfaces in a very flat configuration and that they do not have loops extending into the solution, outside of the lipopolysaccharidic layer. They are thus unlikely to induce flocculation by making bridges between different cell walls, as has been already understood for a long time.5,24 This means that Figures 2 and 3 can be interpreted on the basis of electrostatic arguments only. It is usually found that the flocculation is optimal at the isoelectric point, where the electrostatic repulsion between the particles of the suspension disappears. The attraction between the particles leading to flocculation is generally believed to be due to the inhomogeneities of charge on the surfaces, the negative regions sticking to the positive ones, and to the van der Waals forces.5,24 In our case, the optimal flocculation occurs when the cells are still negatively charged, with a ζ potential typically


between -20 and -5 mV, as we explained in section 3.2. The restabilization of the suspension occurs close to the isoelectric point. To understand why cells that are still quite negatively charged can aggregate, we need to develop a precise description of the electrostatic properties of the cells as a function of the quantity of polymer adsorbed. Such a description can be based on Figure 5. The bare bacterial cells have a ζ potential equal to about -47 mV. This can be translated into a surface charge density. E. coli cells have a lipopolysaccharidic brush on the outer membrane which is likely to displace the position of the shear plane, where the ζ potential is defined. Assuming that the distance between the shear plane and the Stern layer is on the order of 2 nm, we have estimated previously from the ζ potential of the bare cells that the effective charge density of their surfaces outside the Stern layer is roughly σeff = 1.6 × 10-2 C m-2.10 The positive groups on the bacterial surfaces are outnumbered by the negative sites, and we can neglect them and estimate roughly the average distance between the negative sites as being on the order of 3 nm.10 It should be remembered, however, that there are much more potential negative sites and that most of these potential sites are neutralized by counterions which condense on the surface in the Stern layer. We have indeed discussed in ref 10 that the polymer adsorbs on the bacterial surfaces mainly by a cation-exchange mechanism, that is, by replacing the cations that are condensed on the outer membrane of the cell walls. This suggests that the average distance between the sites that can potentially carry a negative charge on the cells is on the order of the size of a monomer, that is, on the order of 0.3 nm. The actual average distance may be slightly larger, because the bilayers are bidimensional liquids, and each lipopolysaccharidic molecule may adjust its exact position and configuration in order to minimize the distance between its negative sites and the positive charges of the polymer chains. Three regimes are observed in Figure 5, as the quantity of adsorbed PVPQ increases. In the first regime, little polymer is adsorbed on the bacterial surfaces. However, the ζ potential increases quickly and is divided by a factor of 2 for an adsorbed amount on the order of 2 mgC/g. If the charged monomers would only adsorb on the surface by replacing some of the cations of the Stern layer and have no other effect, the ζ potential would not change. However, because of steric constraints, such as for instance the crossing points between the polymer chains, there are some “defects” leading to non-neutralized positive charges on the chains and to a decrease of the effective surface charge density of the cells. Figure 5 suggests that the number of positively charged defects is equal to half the number of negative sites when the adsorbed amount is only about 2 mgC/g. Because this amount corresponds to an adsorbed polymer charge density of about 5 × 10-2 C m-2, we may conclude that about one-fifth of the quaternized monomers are defects. However, this estimation neglects a possibly important phenomenon: polycations have been known, in some instances, to disturb the outer membrane of Gram-negative cells.26-28 The exact mechanism and the conditions of action of the polymers are still partly mysterious, and we did not focus in this paper on the antibiotic effect of PVPQ on bacteria. However, we performed preliminary measurements of the organic (26) Schindler, P. R. G.; Teuber, M. Antimicrob. Agents Chemother. 1975, 8, 95-104. (27) Vaara, M.; Vaara, T. Antimicrob. Agents Chemother. 1983, 24, 107-113, 114-122. (28) Nikaido, H.; Vaara, M. Microbiol. Rev. 1985, 49, 1-32.


matter released by the cells during the experiment. They are presented in the Appendix of ref 10. A more complete examination of their properties and of the relation of their release with the polymer adsorption will be presented in a future work. Meanwhile, we have observed a significant release of organic carbon of biological origin in the samples with little PVPQ introduced. If this organic matter is composed primarily of lipopolysaccharidic molecules, as other studies suggest,27,28 the quick decrease of the ζ potential at low amounts of adsorbed PVPQ may be related to a “loss” of negative sites to the solution more than to defects in the polymer adsorption. The relative intensity of both effects on the ζ potential cannot be assessed at this stage. In the regime of adsorption below the isoelectric point, the slope of the ζ potential versus the adsorbed amount seems to decrease markedly. In this regime, we have discussed in ref 10 that the polymer forms a network on the surface, with a mesh size on the order of a few nanometers. On the other hand, we have mentioned that the distance between unhidden negative sites on the surface was likely to be on the order of 3 nm. In the concentrated regime, the positive defects thus become sufficiently numerous to affect the electrostatic field close to each potentially negative site. This may decrease the efficiency of the counterion condensation on the surface and lead to an increase in the number of unhidden negative sites, which would explain the decrease in the slope in Figure 5. A quantitative understanding of this possible phenomenon remains to be worked out. However, if we admit that the defects still correspond to about one-fifth of the charged monomers in this regime, we find that the surficial density of positive as well as of negative unhidden sites is equal to about 8 × 10-2 C m-2, that is, to a typical distance between equally charged sites on the order of 1.5 nm. Finally, an increase in the slope of Figure 5 above the isoelectric point may be attributed to an important increase in the number of defects. In this regime, the steric constraints and the electrostatic repulsions between the charged monomers are likely to make it difficult for additional monomers to find their way to the surface. In this regime, it would be possible to form small loops. In conclusion, we have proposed a tentative description of the electrostatic properties of the surfaces, which takes into account the condensation of the counterions in the Stern layer. 4.2. Flocculation of the Suspension. To understand qualitatively and semiquantitatively the properties of flocculation of the suspension, we consider the simplified model where the surfaces covered by bidimensional polymer solutions in the concentrated regime are described as bare surfaces, with a surface charge density σeff, covered by some positive charges distributed on the polymer network. We have discussed previously that the distance between the unhidden negative sites on the surface is likely to be on the order of 1.5-3 nm. The positive sites are separated by distances on the order of 1-1.5 nm along the polymer chains. At length scales smaller than their persistence length lp, the chains are rodlike. We have estimated that lp is on the order of a few nanometers.10 The “rods” form a network with a mesh size ξs which decreases as the quantity of adsorbed polymer increases. Using this representation, we may now discuss at a more fundamental level the results of our flocculation experiments. Because of the presence of the lipopolysaccharidic layers and because of the roughness of the bacterial surfaces, two adjacent cells cannot approach at distances smaller than a few nanometers; the van der

Langmuir, Vol. 17, No. 9, 2001 2797

Waals forces are thus unlikely to be responsible for flocculation. On the other hand, the distance separating two adjacent surfaces is at most on the order of the screening length. We may hence model the force of interaction between two bacterial surfaces as a purely classical electrostatic force. If we would model the surfaces as homogeneous, we would only have to consider their overall charge. Within the framework of a mean-field theory, namely, the Poisson-Boltzmann theory, the force between them would always be repulsive, except at the isoelectric point where it would cancel. The effects of the correlations between the fluctuations of charge in the solution are still a matter of current research.3,6,29 They are known to reduce the repulsion and even possibly to induce an attraction between like charged surfaces at short separation distances and high surface charge densities. However, this effect is believed to be negligible for monovalent ions, because, as the Bjerrum length lB is on the order of magnitude of the size of an ion, the steric repulsion between two neighboring ions prevents their electrostatic energy of interaction from being noticeably larger than the thermal energy kBT.6 We thus believe that the nonideality of the surfaces is a determinant for the flocculation of the bacterial cells; there are some positive sites and some negative sites, that is, in the language of statistical physicists, the surfaces are “disordered”. There are two extreme opposite types of disorder: If the inhomogeneities are spatially frozen, the disorder is said to be “quenched”. Two similarly electrostatically charged quenched disordered surfaces, coming into contact with an area of contact which is much larger than the largest length scale of the disorder, repel each other in much the same way as ideal homogeneous surfaces. There may be small regions where some negative sites are facing positive sites, inducing a locally attractive force, but there are more numerous regions where likewise charges induce a repulsive force. Because they are quenched, the surfaces cannot shift their positions with respect to each other in a way that would optimize their free energy and lead to an attractive force. The opposite case of disorder, which is called “annealed” disorder, corresponds to inhomogeneities whose spatial configuration can be considered as a thermodynamic variable. When two similarly charged annealed surfaces face each other, configurations of the positive and negative charges on both surfaces which minimize the free energy are thus favored, resulting in an attractive force between the surfaces. The difference between the two types of disorder can be understood qualitatively on a simple case by a very simple model. Let us consider two bidimensional lattices facing each other, with one charge either positive or negative at each vertex. Let us assume here that each vertex of one lattice is facing a vertex of the second lattice and that the screening length is much smaller than the lattice mesh size but much larger than the spacing between the two lattice planes. The force between the two planes is thus the sum of the forces corresponding to pairs of vertexes facing each other. We denote the number of positive and of negative sites by n+ and n-, respectively. Considering that the surfaces are disordered in the quenched way, the probability that a positive site is facing a negative site is n-/(n- + n+). The force corresponding to all positive sites is thus proportional to n+(n+ - n-)/(n+ + n-), and the force between the two planes is proportional to (n+ - n-)2, as would have been predicted by modeling the planes as ideal (29) Barnes, C. J.; Davies, B. J. Chem. Soc. Faraday Trans. 2 1975, 71, 1667-1689.

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homogeneous surfaces with a surface charge proportional to (n+ - n-). If, on the other hand, the lattices are annealed, we may neglect in a first approximation the fluctuations of configurations around the most favored ones and follow the mean-field theory. If we admit, without any loss of generality, that n+ < n-, the probability for a positive site to face a negative site is 1, and the probability for a negative site to face a positive one is n+/n-. The force between the two planes is hence proportional to n- - 3n+, showing that a number of positive sites amounting to between 1/3 and 3 times that of the negative sites leads to an attractive interaction between the two lattice planes. In our case of a cationic homopolyelectrolyte adsorbing on a negative bacterial surface, we believe that the disorder is best described as annealed. The defects leading to positive charges along the adsorbed polymer chains may have little mobility, but the location of the negative sites can probably adjust itself quite easily: A negative site is a negatively charged group surrounded by other negatively charged groups neutralized by condensed cations. Because the Bjerrum length lB is not much larger than the size of a cation and than the distance between charged groups, the energy barrier for a cation to hop to a neighboring free charged group is probably at most on the order of kBT, and the move is thus relatively easy. This may be the reason the polymer chains are successful in removing the condensed cations during their adsorption process. We think that the annealed disorder is the cause of the attractions between the bacterial surfaces. At low polymer surface coverages, the probability that two positively charged sites come in front of each other is quite low. Negative sites thus face most of the positive sites. The crude lattice model presented above shows that the bacterial surfaces can stick to each other, even when they are still quite strongly negatively charged. When the adsorbed amount increases, the correlation length ξs becomes smaller than the distance between the surfaces; each positive charge thus “sees” on the adjacent surface some positive charges as well as some negative ones, and the intensity of the attractive force drops quickly. This transition seems to have been observed for neutral glass surfaces covered by adsorbed cationic surfactants by Kekicheff and Spalla.3 We believe that this effect may explain why the redispersion occurs close to the isoelectric point, where the correlation length ξs is on the order of 2 nm. A small positive overall charge is then sufficient to restabilize the cells. The attractive electrostatic force is ineffective at high polymer surface coverage for the same reason that the van der Waals forces can be neglected. The van der Waals forces, which also somehow correspond to transverse annealed charge fluctuations, become similarly ineffective at separations larger than the typical length scale of these fluctuations, that is, a few angstroms. Having discussed the restabilization transition, let us consider the regimes where the adsorbed amount of polymer is lower. When the correlation length ξs is larger than the separation between adjacent surfaces but smaller than the persistence length lp of the polymer chains, the simple mathematical model that we have presented above predicts that the force between two adjacent planes is attractive as soon as n+ > n-/3. Using a charged density of negative sites equal to 16 × 10-3 C m-2 and a number of positive defects equal to one-fifth of the adsorbed monomers, this corresponds to an adsorbed amount on the order of 1 mgC/g. The actual minimal value of the adsorbed amount for an attractive force may indeed be even smaller because the crude model that we have presented above does not take into account the possibility that the negative charges are not exactly facing each other.


We believe that these arguments explain why the cells flocculate efficiently, even at the onset of the concentrated regime,10 when the adsorbed amount is as low as 1 or 2 mgC/g. For even lower amounts of adsorbed PVPQ, the bidimensional polymer solution is semidilute or even dilute; that is, the persistence length of the chains is smaller than the correlation length ξs, which increases very quickly up to the critical length ξcs and then slightly more slowly as the adsorbed amount decreases.10 Figures 2 and 3 show that although the flocculation of the suspension is much less efficient there is still a large fraction of the cells that do aggregate. The possible flocculation of the cells is probably rendered possible by the large-scale inhomogeneities that develop on the bacterial surfaces at low polymer coverages. As we discussed in ref 10, the adsorbed polymer layer displays a fractal structure in the directions parallel to the surface for length scales between the critical length ξcs and the correlation length ξs. It is difficult to estimate directly the value of ξcs, but we proposed that it was reasonable to consider that it is in our case on the order of a few tenths of a nanometer. The important point is that in contrast to ξs, the critical length ξcs is independent of the adsorbed amount. The regions where there is no polymer adsorbed are homogeneously negatively charged and thus cannot be responsible for the flocculation. On the other hand, the regions where the polymer is adsorbed are made up of domains of size ξcs, where the local concentration of polymer is that of the semidilute Gaussian regime, that is, large enough to induce a flocculation of the cells.10 If the area of contact between two adjacent cells has a characteristic size lower than the critical size ξcs, it is thus understandable that these two cells may flocculate, provided that the regions in contact are regions where some polymer is adsorbed. Flocculation may also occur in asymmetric situations where one of the surfaces is locally uncovered with polymer but the other one has some polymer coverage. To evaluate the area of contact between two adjacent cells, let us model each cell as a cylinder with a length equal to l ) 2 µm and a diameter equal to D ) 1 µm. The area of contact may be defined as corresponding to the regions of the cells separated by a distance smaller than the Debye length κ-1. The value of the area of contact depends on the relative positions of the two cylinders when they meet. If at least one of the cells hits the other one by one of its tips, it can be modeled as a sphere having a diameter D and the area of contact is equal to Dκ-1 = 5000 nm2. In the more general case where the cylinders come into contact by their sides, the area of contact depends on the angle between the long axes of the cylinders. When they are perpendicular, it is also on the order of Dκ-1, but when the cylinders lie side by side, the area of contact can be as large as 2lxDκ-1 = 0.3 µm2. In comparison, we have mentioned that the regions covered with the polymer have an area on the order of ξc2 s , which is likely to be very roughly on the order of 103 nm2. This suggests that two cells can aggregate, but only when they hit each other in a way that minimizes their area of contact and if the regions of contact are both covered with polymers. When the adsorbed amount decreases, the probability that the regions in the contact area are covered with polymers decreases, and the probability that two cells aggregate also decreases, which explains why the fraction of free cells gradually increases, as obtained in Figures 4 and 5. In conclusion, we have proposed in this section a model in agreement with our experimental results describing


how the adsorbed polymer layer modifies the electrostatic properties of the bacterial cells and affects the stability of the suspension. We have shown that even at very low polymer surface coverage, flocculation of the cells may occur, although it becomes more and more unlikely as the adsorbed amount decreases. In the concentrated regime of adsorption where the cells are still negatively charged, the surfaces stick easily to each other, and the suspension flocculates optimally. However, close to the saturation point the correlation length ξs becomes smaller than the distance between the cell walls, and the inhomogeneities of charge become ineffective in producing an attractive force. A small overall charge is then sufficient to restabilize the cells, and the restabilization occurs indeed close to the isoelectric point. 4.3. Properties of the Bacterial Aggregates. We have shown that the interfacial properties of the bacterial cells are profoundly modified by the adsorption of the polymer chains. When the suspension is destabilized, it is interesting to investigate how the characteristics of the bacterial aggregates depend on the amount of adsorbed polymer. The relation that we obtain between the interfacial properties of the bacterial cells and the characteristics of the size distribution of the aggregates that they form is in agreement with former results of colloid science. The regime of poor flocculation can be related to the socalled reaction-limited aggregation process (RLA). In this mode of aggregation, the probability that two cells stick to each other is not very high. Hence, the association between large aggregates is favored, because of the large number of cells that they contain and because of their smaller mobility. This leads to a large polydispersity.30 On the other hand, the regime of the optimum of flocculation can be associated with the diffusion-limited aggregation process (DLA). The probability that two colliding cells aggregate is then close to unity. The aggregation process depends only on the mobility of the cells and of the aggregates. Because the free cells and the small aggregates have a much larger mobility than the large aggregates, they quickly meet other cells or aggregates and merge with them. The process thus leads to a size distribution with a well-defined characteristic size and a relatively small polydispersity.31 Apart from the size distribution of the flocs, the RLA and the DLA processes differ by leading to aggregates with a different internal structure. Self-similarity was predicted and observed in both cases, but with different fractal dimensions.11 In the case of DLA, relatively tenuous structures are expected, with a fractal dimension lower than 2, whereas in the case of RLA denser structures are found, with a fractal dimension larger than 2. The qualitative reason for this difference between the two processes is that in the case of RLA a given particle has more time to diffuse within an aggregate before it becomes attached to the aggregate, because it can collide several times with other particles before attachment occurs. On the other hand, in the case of DLA a particle becomes attached as soon as it meets an aggregate and thus remains at the periphery of the aggregate, which leads to a tenuous structure. In the regime of the optimum of flocculation, we expect the aggregates to be the product of a DLA process and thus to be more tenuous. Multiple scattering is then a local phenomenon, which affects the scattering curve only at wavevectors corresponding to length scales on the order (30) Von Schultess, G. K.; Benedek, G. B.; De Blois, R. W. Macromolecules 1980, 13, 939-945. (31) Meakin, P.; Vicsek, T.; Family, F. Phys. Rev. B 1985, 31, 564569.

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of a few micrometers. On the other hand, we have mentioned that the polydispersity of the suspension is much smaller than in the regime of poor flocculation. There may thus be in the DLA regime a range in the diffusion curve, corresponding to length scales larger than the size of the cells but smaller than the size of the smallest aggregates, where the data is influenced only by the internal structure of the aggregates. In the case where the plot of the slope of the scattering curve displays a plateau over a large range of length scales, it is thus probably correct to interpret the plateau value as a fractal dimension for the aggregates. Figure 9 displays such a plateau, with a value of the slope on the plateau equal to 1.9. This result compares favorably with previous work on DLA. For instance, Wong et al. obtained a fractal dimension of 1.9 for aggregates of silica spheres made by using a highly cationic polyelectrolyte.32 Figure 9 thus strongly suggests that the aggregates in the regime of the optimum of flocculation have a fractal dimension equal to about 1.9, in agreement with the easy aggregation process that we predicted. This assertion should be tempered, however, by the fact that the range of length scales over which the plateau is observed is rather narrow. In addition, the slope plots corresponding to amounts of added polymers larger than that of Figure 9 did not display such a clear plateau. As the added amount increased, the plateau tended to disappear, as appears in Figure 10. A reason may be that the size of the aggregates becomes too small to allow for a large range of length scales where the self-similar structure can be displayed. The complete understanding of Figure 10 probably requires the full use of recent scattering theories20 and their extension to polydisperse suspensions of aggregates. In conclusion, we have observed that the characteristics of the aggregates and their size distribution can be related to the properties of the adsorption of the polymers. When little polymer is adsorbed, the flocculation is poor, and the aggregates are formed by a RLA process, leading to a large polydispersity. In the regime of the optimum of flocculation, the aggregation between the cells is easy and can be described as a DLA process, leading to a small polydispersity and, likely, to a fractal dimension of 1.9. However, our results concerning the compactness of the aggregates need to be confirmed by a thorough investigation of the scattering properties of the suspension of the aggregates, using the recent theory of Botet et al.20 This will be the subject of a future work. 5. Conclusion In this investigation, we have discussed how the interfacial properties of an E. coli bacterial suspension are modified by the adsorption of quaternized polyvinylpyridine and how this affects the stability of the suspension. We have also observed the properties of the aggregates in the suspension, when it is destabilized, and related them to the configuration of the adsorbed chains. We have observed the three usual regimes of flocculation, depending on the quantity of polymer adsorbed on the bacterial cells. When a lot of polymer is added to the suspension, the overall surface charge of the cells is inverted and the suspension is restabilized by the electrostatic repulsions. At intermediate amounts of polymer, the suspension is destabilized. The overall surface charge of the cells remains negative. Adhesion between the cells is rendered possible by the heterogeneities of charge on the surfaces, the length scale of which is larger than the (32) Wong, K.; Cabane, B.; Duplessis, R. J. Colloid Interface Sci. 1988, 123, 466-481.

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minimum distance between two adjacent surfaces but smaller than their area of contact. Adhesion between the cells is easy, and this leads to a monodisperse suspension of aggregates formed according to a diffusion-limited aggregation process. Finally, for small quantities of polymers the surfaces are undersaturated. The bidimensional self-similar structure of the chains on the surface leads to the presence of large-scale heterogeneities of surface charge, and two adjacent cells can aggregate only if their surface regions facing each other in the area of contact are covered by enough polymer chains. In this situation, the flocculation is less efficient; this leads to a very polydisperse suspension, with some free cells as well as some large aggregates, formed according to a reactionlimited aggregation process. Our findings and interpretations need to be confirmed by additional experiments. The exact consequences of the possible disturbance of the cell walls by the polycations need to be assessed in more detail, for instance, by analyzing the organic matter released by the cells and by observing the outer membranes by electronic microscopy. Some future work should also focus on a more refined and rigorous interpretation of the light scattering experiments, to investigate the properties of the bacterial aggregates, when the suspension is destabilized. This should in principle be possible, with some numerical effort, using the mean-field theory of Botet et al.20 The experimental conditions should also be modified to test whether our model has to be modified or if it can be extended. For instance, the ionic strength should be varied, to tune the


strength of the electrostatic interactions. The modification of the degree of quaternization of the chain, from about 0.3 to 1, would demonstrate whether the distance between two charges on the chains affects the number of positive defects in the adsorbed chains. Apart from the polymer and solution properties, it would also be interesting to investigate with our method the properties of other bacterial suspensions. For instance, we could compare the properties of the strains E. coli K12 D21 and E. coli K12 D21f2, which differ only by the length of the lipopolysaccharidic brush.33 These two strains have already been found recently to have strikingly different interfacial properties.34 Future extensions of this work could also deal with other types of polymers, including weakly charged polyelectrolytes, which can develop structures in the direction perpendicular to the surfaces. Acknowledgment. We are grateful to E. Pefferkorn and J. Widmaier, from the Institut Charles Sadron in Strasbourg, for providing us with the PVPQ. The society Picosil and A. Vernet from the INRA at Montpellier are thanked for giving us access to their zetameter. We also acknowledge useful discussions with E. Pefferkorn, J. Widmaier, and F. Lafuma from the ESPCI in Paris as well as technical help from S. Moustier and F. Albert at the CEREGE. LA010171X (33) Boman, H. G.; Moner, D. A. J. Bacteriol. 1975, 121, 455-464. (34) Ong, Y. L.; Razatos, A.; Georgiou, G.; Sharma, M. M. Langmuir 1999, 15, 2719-2725.

Adsorption of a Cationic Polyelectrolyte on Escherichia c oli Bacteria

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