Journal of Colloid and Interface Science 417 (2014) 346–355

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Dendrimer induced interaction forces between colloidal particles revealed by direct force and aggregation measurements Marco Finessi, Istvan Szilagyi ⇑, Plinio Maroni ⇑ Department of Inorganic and Analytical Chemistry, University of Geneva, 30 Quai Ernest-Ansermet, 1205 Geneva, Switzerland

a r t i c l e

i n f o

Article history: Received 30 September 2013 Accepted 22 November 2013 Available online 1 December 2013 Keywords: PAMAM dendrimer Colloid particle Atomic force microscopy Light scattering Aggregation

a b s t r a c t Interaction forces and aggregation rates were determined in order to characterize colloid stability of negative carboxyl latex particles in the presence of oppositely charged poly(amido amine) (PAMAM) dendrimers of three different generations G4, G7 and G10. The force profiles were measured by the atomic force microscopy (AFM) based on multi-particle colloidal probe technique. Close to the isoelectric point, the measured force profiles were more attractive than the pure van der Waals interactions. This behavior was rationalized in term of an additional electrostatic patch–charge contribution whose magnitude increases by increasing the dendrimer generation. The aggregation rates were calculated from these results using the classical theory developed by Derjaguin, Landau, Verwey and Overbeek (DLVO) as well as including the additional attractive term and a radially symmetric force field. The calculated aggregation rates were compared to the ones obtained directly from time-resolved dynamic light scattering (DLS) measurements using exactly the same latex particles as in the AFM study. The results from these two methods were in good agreement in the case of dendrimers of lower generation, while at higher generation, significant differences were found. In the latter case, the stability ratio in the slow aggregation regime extracted from direct force measurements was much higher than the one measured experimentally by DLS. Despite the fact that the additional attractive term was included in the calculation, the discrepancy between the two different stability ratios suggests that the assumption of radial symmetric interaction is weak. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction The classical theory developed by Derjaguin, Landau, Verwey and Overbeek (DLVO) [1,2] constitutes the milestone in describing the stability of a colloidal system which is governed by the interplay between repulsive double layer and attractive van der Waals interactions. For a homogeneously charged surface, the DLVO theory has been verified with different techniques such as total internal reflection microscopy [3,4], colloidal probe [5,6] and surface force apparatus [7,8]. At the beginning of the 70s, Kasper [9] and Gregory [10] suggested that polyelectrolytes might adsorb on oppositely charged surfaces in a heterogeneous way creating a patchy charge distribution. The basic idea was that even if the overall charge of the surfaces is neutral, it is unlikely that each surface charged site can be neutralized by the polymer segments. Consequently, although the surface may have an overall charge close to neutrality, there are ‘‘patches’’ or ‘‘islands’’ of opposite charge between regions of uncoated substrate [11]. From these patch interactions, ⇑ Corresponding authors. Fax: +41 22 3796069. E-mail addresses: [email protected] (I. Szilagyi), [email protected] (P. Maroni). 0021-9797/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jcis.2013.11.060

an additional attractive force of electrostatic origin was originated [12,13]. Intuitively, when two patchy surfaces approach to each other, the patches formed by the polymer segments adsorbed on one of the surfaces experience an attractive force with the corresponding uncoated portions present on the other surface. Dynamic light scattering (DLS) experiments aiming to study the stability of colloidal suspensions of particles covered with polyelectrolyte showed stability ratios smaller than unity in the fast aggregation regime at low ionic strength. An additional attractive patch–charge interaction was suggested to be responsible for the acceleration of the aggregation processes in this case [14–17]. Direct evidence of such interaction was observed with multi-particle colloidal probe technique based on atomic force microscope (AFM) for amidine latex and sulfate latex particles coated with polystyrene sulfonate (PSS) and poly(amido amine) dendrimers (PAMAM) respectively [18–23]. Although the importance of surface charge heterogeneities originating from the adsorption process were emphasized with these two different techniques, the results could not been compared directly since the size of the particles used for AFM measurements was more than 10-times higher than the ones applied in the DLS experiments. Direct comparison of forces and aggregation rates was not possible earlier, because of the different size of particles

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as well as the different geometry in the force measurements. We have recently reported for the first time direct comparison of stability ratios determined with DLS and AFM individually using the same colloidal polystyrene latex particles in the presence of multivalent ions [24,25]. As a compromise between the two methods, a particle size of around one micrometer in diameter was suitable to use them in both types of experiments. PAMAM dendrimers are highly branched macromolecules with an ethylenediamine core and they attract significant interest due to the growing number of applications in fields such as medicinal chemistry, materials science and catalysis [26]. Accordingly, they have been in focus of various kinds of investigations by several research groups worldwide [27–31]. Due to their particular molecular structure and monodispersity, they are perfect candidate to form patchy surface by their adsorption as it has been shown previously by AFM images [32,33]. In the present study, interaction forces measured by the multi-particle colloidal probe technique based on AFM [34] were determined in the system containing negatively charged carboxyl latex particles with a diameter of 1 lm covered with PAMAM dendrimers of different generations. Aggregation rates were calculated from the obtained force profiles and compared to the ones determined in time-resolved light scattering measurements. Using the same particles in both study allowed us to discover the origin of the interaction forces responsible for particle aggregation in the present systems. 2. Materials and methods 2.1. Materials Poly(amido amine) (PAMAM) dendrimers of generations G4, G7 and G10 were purchased from Dendritech (Midland, USA) and used without further purification. Their concentrations were verified by total organic carbon and nitrogen analysis (TOC-V, Shimadzu, Japan). Carboxylated polystyrene latex particles were purchased from Interfacial Dynamics Corporation (Portland, USA). The data sheet provided by the manufacturer showed the following characteristics: diameter of 1 lm, surface charge density of -127 mC/m2 obtained by conductometry and a polydispersity of 4.5% determined by transmission electron microscopy. The particles were dialyzed against Milli-Q (Merck Millipore, Billerica, USA) water with a cellulose ester membrane having a molecular mass cutoff of 300 kg/mol (Spectrum Rancho, Dominguez, USA) till the conductivity of the surrounding medium reached the value of the Milli-Q water. The particle concentrations were determined with light scattering by comparing the scattering intensity of an unknown sample with a reference one. All the experiments were carried out at a particle concentration of 80 mg/L, while dendrimer concentrations were varied between 1 and 10 mg/L. The measurements were performed at pH 5.8 adjusted with HCl (Merck, Darmstadt, Germany) or KOH (Sigma–Aldrich, Steinheim, Switzerland) solutions and at an ionic strength of 1 mM by adding appropriate amount of KCl (Acros, Geel, Belgium) solution to the samples. In such conditions, the degree of ionization of the dendrimers due to the protonation of the primary amines is roughly 0.65 [35].

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appropriate amount of KCl solution used to adjust the ionic strength. The sample preparation was finished by the addition of 0.5 mL of the latex stock suspension. The final volume was always 5 mL. The samples were equilibrated overnight and the electrophoretic mobilities were determined in plastic capillary cells (Malvern Instruments, Malvern, UK) by averaging 5 individual measurements. The f -potentials were calculated invoking the standard electrokinetic model developed by O’Brien and White [36]. 2.3. Light scattering Static and dynamic light scattering experiments were performed with a multi-angle goniometer having 8 fiber-optic photomultiplier detectors (ALV/CGS-8, Langen, Germany) and a solid state laser of a wavelength of 532 nm (Verdi V2, Coherent Inc., Santa Clara, USA). Round borosilicate glass cuvettes were used for stability measurements while static light scattering experiments were carried out in quartz cuvettes. Both were cleaned with a mixture of concentrated H2SO4 and H2O2 at a volume ratio of 3:1 (piranha solution) at 80 oC for 3 h and afterwards rinsed thoroughly with Milli-Q water and dried in dust-free environment. The absolute aggregation rate constant of the particles was determined in time-resolved simultaneous static and dynamic light scattering measurements where changes in intensity and hydrodynamic radius were followed with time in an aggregating sample containing 4.5 mg/L latex particle in 1 M KCl solution. Plotting the slopes obtained from intensity versus the ones from hydrodynamic radius measurements, the absolute aggregation rate can be determined from the intercept as detailed elsewehere [37,38]. As published in our previous study carried out with the same particle, an absolute aggregation rate of 2.0  1018 m3/s was obtained for the carboxyl latex particles [25]. Colloid stabilities were investigated in time-resolved dynamic light scattering (DLS) experiments. The total volume of the samples were always 2 mL prepared by mixing calculated amount of KCl and PAMAM denrimer solutions followed by the addition of the particle stock suspension. The aggregation rates k were determined on the basis of calculating the slope of the hydrodynamic radius versus time plots as follows [38].

    1 dRh  sinð2qRÞ Rh;1 1 kn0  ¼ 1þ  Rh;0 dt t¼0 2qR Rh;2

ð1Þ

In the equation above, Rh,0 is the initial hydrodynamic radius, q is the magnitude of the scattering vector, Rh,2/Rh,1 = 1.38 is the ratio of the hydrodynamic radii of the dimer and the monomer, and n0 is the initial particle number concentration. The stability was expressed in stability ratio (W) which is the ratio between the fast or diffusion controlled aggregation rate constant determined in 1 M KCl solution and the aggregation rate obtained in the actual measurement. Note that in case of fast aggregation, the stability ratio is close to unity while it increases when the aggregation slows down. A critical coagulation concentration (which separates the slow and fast aggregation regimes) of 190 mM and a fast aggregation rate of 2.7  1018 m3/s were determined for the carboxyl latex particles in the presence of KCl. The latter value close to the absolute aggregation rate obtained from simultaneous static and dynamic light scattering measurements indicating a good estimate for the optical and structural properties of the particles.

2.2. Electrophoresis 2.4. Direct force measurements The electrophoretic mobilities of the bare particle suspensions as well as in the presence of PAMAM dendrimers were measured with a Zeta Sizer 2000 (Malvern Instruments, Malvern, UK) device in the range of electric fields of 7.5–15 kV/m. In a typical experiment, 0.1–4.0 mL of denrimer stock solution was mixed with

Forces between two colloidal particles were measured with a closed loop atomic force microscope (AFM) (MFP-3D, Asylum Research, Santa Barbara, USA) mounted on an inverted optical microscope (IX70, Olympus, Volketswil, Switzerland). The glass

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plate of the AFM fluid cell was cleaned for 2–3 h with piranha solution at 80 oC and subsequently rinsed with water. Successively, the glass plate was dried with nitrogen gas and plasma treated for 20 min (PDC-32G, Harrick, New York, USA) before it was silanized overnight in vacuum with 3-(ethoxydimethylsilyl)propylamine (Sigma–Aldrich, Steinheim, Switzerland). The silanization was verified by measuring the contact angle with a drop of water which was found to be approximately 36°. Once the glass plate was inserted in the fluid cell, roughly 2 ml of the particle suspension was deposited on it for few hours. In this way, the particles were able to adhere to the substrate. In order to remove those ones that did not stick properly, the fluid cell was gently flushed at least five times with an electrolyte solution previously degassed for 2 h and having the same pH and ionic strength as the particle suspension. The use of a degassed solution avoided the formation of nanobubbles around the hydrophobic latex particles. These bubbles indeed would be unavoidable during the process of drying-rewetting step that occurs when the particles are attached in air at the edge of the cantilever by a micromanipulator [39,40]. The tip-less AFM cantilevers (NSC12 and CSC12 Tipless/NoAl, MikorMasch, Tallinn, Estonia) were cleaned in plasma cleaner and then silanized on the same way as the glass plate. A particle was attached at the edge of the cantilever by pressing it against the substrate and successively it was superimposed to another one presents in the fluid cell by means of the interference fringes of an optical microscope. A precise alignment was reached using a horizontal AFM scanner with a precision of 20–50 nm. Deflection triggers toward the surface were set around 20 nm. Interaction forces for each pair of particles were obtained by time-averaging 100–150 approach-retract cycles with a frequency of 0.2 Hz resulting in an approach velocity of 200 nm/s and a data acquisition rate of 10 kHz. Before and after averaging, typical force noises were roughly 80 and 7 pN respectively. The contact point was determined by the onset of the constant compliance region with a precision of 0.2 nm. The final force for each sample was obtained by averaging at least 3–5 particle pairs present in the sample. The cantilever deflection was then transformed into force using the Hook’s law. The spring constant of the cantilever was obtained by using three different independent methods described elsewhere [41–43] and the average of these values was used. These data agreed within an error of 15%. The cantilevers employed have a spring constant between 0.03 and 0.3 N/m. The force was normalized to the effective radius given by

Reff ¼

R1 R2 R1 þ R2

Olympus, Japan) of a nominal tip radius smaller than 9 nm and a resonance frequency of 25–36 kHz in water. The images were taken by going on the top of the particle and using a scan size of 500 nm with a scan rate of 2.0 Hz and free oscillation amplitude (FOA) of 35 nm. The set-point was fixed at 70% of the FOA. The counting of the dendrimers was done automatically on a flatten height image through Gwyddion software freely available at http://gwyddion.net/ by setting a threshold of 2 nm which represents the distance between the highest and the lowest peak for the height of the bare carboxyl latex particles. This kind of threshold was used to take the roughness of the particle into account. Once all the dendrimers were counted, a sum of their projected area gave the total area occupied on the surface. Dividing this result by the surface area of one dendrimer adsorbed on the substrate (assuming a radius of 9.15 nm [44]) the total number of the dendrimers corresponding to a topographic image size of 500  500 nm2 was established. The number of dendrimers was normalized to the area by dividing it by the projected area of the topographic image. This value was found to be 0.274 lm2. Bare carboxyl latex particles were also imaged in air by depositing the sample on mica. Before imaging, the sample was dried with nitrogen gas. Images in air were performed using silicon cantilevers (AC-240 TS, Olympus, Japan) having a resonance frequency of 70 kHz, a spring constant of 2 N/m and a tip radius of 7 nm. The root mean square roughness (RMS) was calculated on the flattened height image by using a polynomial of third order function for four different particles. The final average of RMS was 0.39 ± 0.11 nm indicating that the surface is very smooth compared to other latex particles investigated earlier in our group [19,22]. 2.6. Modeling The stability ratios obtained from light scattering measurements were compared to the ones calculated from the results of the AFM study as follows. The aggregation rate (k) can be described for a particle with a radius of R as [45]



4 3bgR

2.5. AFM imaging In a typical experiment, roughly 100 lL of the suspension contained carboxyl latex particles and PAMAM dendrimers of generation G10 at pH 5.8 and ionic strength of 1 mM was deposited for about 1 h on previously cleaved mica with a dimension of 1  1 cm. The suspension was then flushed with 100 lL of an electrolyte solution having the same pH and ionic strength in order to remove the particles that did not stick properly on the substrate. A drop of the electrolyte solution was put on the edge of the cantilever for keeping the liquid condition. The images were performed in ac-mode with a Cypher instrument (Asylum Research, Santa Barbara, USA) using BioLever Mini cantilevers (BL-AC40TS,

1

ð2R þ hÞ

0

#1

BðhÞ 2

exp½bVðhÞ dh

ð3Þ

where h is the separation between the particle surfaces, g is the viscosity of water, b is the inverse thermal energy, V(h) is the total interaction potential energy and B(h) is the hydrodynamic resistance function

ð2Þ

where R1 and R2 are the radii of the two interacting particles. The value of the radii was taken in accord to that was reported by the manufacturer. After the force measurements, the particle was detached from the cantilever by pressing it against the surface and by sliding it. Another particle then could be attached.

"Z

2

BðhÞ ¼

6ðh=RÞ þ 13ðh=RÞ þ 2 2

6ðh=RÞ þ 4ðh=RÞ

ð4Þ

The total interaction potential energy (V(h)) can be expressed using the modified DLVO theory with the superposition of the repulsive and attractive forces

VðhÞ ¼ V vdW ðhÞ þ V dl ðhÞ þ V p ðhÞ

ð5Þ

where VvdW(h) is the attractive van der Waals, Vdl(h) is the repulsive electrostatic interaction potential energy originating from the DLVO theory and Vp(h) is the additional, non-DLVO patch–charge interaction potential energy which will be discussed in more details in the next section. The van der Waals interaction energy can be calculated as follows [46]

V vdW ðhÞ ¼ 

HR 12h

ð6Þ

where H is the Hamaker constant. The repulsive electrostatic interaction energy was calculated within the Derjaguin approximation by the Poisson–Boltzman theory with superposition approximation [47].

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3. Results and discussion The present work deals with characterization of colloid stability, i.e., aggregation processes in systems contained carboxyl latex particles and PAMAM dendrimers of different generations such as G4, G7 and G10 at pH 5.8 and ionic strength of 1 mM. Under these conditions, the carboxyl latex particles are negatively charged [48] and the PAMAM dendrimers are positive [35]. 3.1. Surface charges PAMAM dendrimers are able to overcharge oppositely charged colloidal particles at sufficiently high concentrations [16,22]. This phenomenon was already observed for similar polyelectrolyteparticle systems investigated with electrophoresis [49–51]. Starting from the bare negative latex and increasing the dendrimer dose, the charge on the surface becomes more positive until it reaches the isoelectric point (IEP) where the entire charge of the particle is completely neutralized. Ion-ion correlation effects [52–61] and hydrophobic interactions [62] promote further adsorption on the surface switching the sign of the charge from negative to positive. The potential increases until the surface saturates at the adsorption plateau. At this point, the potential levels off and it is independent on the dendrimer dose further added, as shown in Fig. 1 for the three generations of dendrimers adsorbed on the latex particles. An interesting feature observed is that the IEPs shift towards higher dose values (1.05, 1.23 and 1.88 mg/g for G4, G7 and G10 respectively) by increasing the dendrimer generation. A similar trend was also observed in previous studies with systems of similar charge balance [16,22,23]. The explanation for this phenomena is that by increasing the generation, a large number of charges on the dendrimer structure is neutralized by the adsorption of the counterions present in the solution [63,64] leading to a substantial decreasing of the effective charge responsible for the neutralization of the surface charge [65]. Accordingly, the effective charge increases more slowly by increasing the generation than the bare charge, thus a higher amount of dendrimer is needed to neutralize the entire surface [44,66]. 3.2. Repulsive and attractive forces As mentioned before, the AFM-based multi-particle colloidal probe technique was used to measure the interaction forces between pairs of particles. Fig. 2 shows the forces normalized to the effective radius as a function of the separation distance for two different G10 doses, defined as mg of PAMAM dendrimers per g of latex particles, and different pairs of particles in the presence of G10. The deviation between the forces measured with different pairs is high at low dose, while it is minimized by increasing the dose. We assume that this behavior can be inferred to the different heterogeneity on the surface. Indeed, increasing the dose, the adsorption of the dendrimers results in a more homogeneous surface and this is reflected in a low variation of the strength of the force profiles. Similar behavior was found in our previous studies carried out with latex particles and oppositely charged ions [24,25]. Force profiles for particles in the presence of different doses of G10 PAMAM dendrimers are shown in Fig. 3. For bare latex particles, the forces are strongly repulsive due to the negative charge of the latex. The origin of this force is the overlap of the diffuse part of the electrical double layer and the fitting describes its strength by invoking the Poisson–Boltzmann theory (PB) rationalized in term of the charge regulation approximation (CR) introducing a regulation parameter (p).

Fig. 1. Potentials determined in electrophoretic and AFM measurements as a function of the dendrimers dose for generations of G4 (a), G7 (b) and G10 (c). The dendrimer dose is expressed as mg of polymer per gram of particle. The solid line is a sigmoidal function used to fit the experimental points extracted from AFM force profiles and used to calculate the stability ratios.



CD CS þ CD

ð7Þ

where CD is the capacity of the diffuse layer and the CS is the capacity of the Stern layer. The regulation parameter (p) is equal to 1 in the case of constant charge (CC) and 0 for constant potential (CP) boundary condition. The p value can become also negative and it varies between 1 and 1 [67]. In the present work, the regulation parameter has been kept fixed for all the fittings at a value of 0.5 for simplicity. The strength of the repulsive interaction is expressed in term of the diffuse layer potential (wD) and its range is defined by the Debye length (j1) which is related to the ionic strength (I).

j1 ¼

2e2 NA I kT ee0

ð8Þ

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Fig. 2. Variation of force curves between different pairs of particles in the presence of PAMAM dendrimers G10 at pH 5.8 and ionic strength of 1 mM at two different doses. (a) Significant variation for different pairs at low dendrimer dose (1.16 mg/g) and (b) good reproducibility at higher dose (2.58 mg/g).

where e is the elementary charge, NA is the Avogadro’s number, k is the Boltzmann’s constant, T is the absolute temperature, e0 is the permittivity in vacuum and e is the permittivity of the medium. In this case, the fit on the forces has been performed by fixing the ionic strength according to the experimental condition of 1 mM. To describe the extra forces originating from the surface charge heterogeneities, an additional attractive term was added to the van der Waals forces and it reads.

F ¼ Aeqp h Reff

ð9Þ

where A is the amplitude of the force and qp is the inverse of the decay length. This strong additional attraction can be explained by the presence of patches formed on the carboxyl latex particles upon adsorption of the dendrimers. This model suggested independently by Kasper [9] and Gregory [10] states that when the charge densities of cationic polyelectrolytes are higher than charge densities of colloidal particles, it is physically not possible to give the overall charge neutrality for each surface charged site to be neutralized by the cationic polyelectrolyte. The reason is that the average distance between two neighbor surface sites is higher than the distance between two consecutive charges in a segment along the polymer chain. It follows that the adsorbed dendrimers on the latex particles lead to an accumulation of positive surface charges which they can be identified like ‘patches’ or ‘islands’ between negatively charges surface. Thus, an additional attractive contribution is then originated from the electrostatic interactions. Quantitatively, this contribution can be explained within the patch–charge model proposed by Miklavic et al. [12]. In this model, the patches are described as a periodic surface lattice distribution having an arbitrary

Fig. 3. Force profiles measured by the multi-particle colloidal probe technique at different doses of PAMAM dendrimers G10 adsorbed on carboxyl latex particles at pH 5.8 and ionic strength of 1 mM. (a) Forces below the IEP (1.88 mg/g) and (b) after the IEP.

unit cell. For a square lattice, the corresponding decay length is defined as

q2p ¼ j2 þ

p2 a

ð10Þ

where j is the inverse of the Debye length related to the experimental ionic strength and 2a is the lattice constant. As discussed earlier, the dendrimers adsorb strongly on the oppositely charged surface leading to charge neutralization at the IEP and subsequent overcharging at higher dendrimer doses [22]. This is reflected in a lower strength of the long-range repulsion and a prominent short-range attraction is getting more pronounced (Fig. 3a). At a dendrimer dose of 1.88 mg/g, the surface is neutralized and the diffuse layer does not exist any longer. By increasing the dose, a reverse charge phenomenon is observed as detailed in Fig. 1. A diffuse layer around the particles set-in again and from its overlap a long-range repulsive force is measured (Fig. 3b). Its strength increases by increasing the added dendrimer dose until the whole surface is saturated. After that point, the potential will be independent on the dendrimers further added to the system [21,22] since they remain dissolved in the solution. Fig. 4a–c shows AFM 3-D height topographic images of G10 PAMAM dendrimers adsorbed on carboxyl latex particles for different doses. Each bump corresponds to one dendrimer adsorbed on the surface and the different size of the bumps in these images is due to aggregation of the adsorbed dendrimers. From the images,

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Fig. 5. Adsorption of PAMAM dendrimers G10 expressed as number density as a function of the dose taking the different polydispersity of the system into account (dashed lines). The oblique solid line represents the theoretical adsorption of the dendrimers on the surface for a certain value of dose, while the horizontal solid line represents the saturation regime.

Fig. 4. AFM 3-D topographic images of G10 PAMAM dendrimers adsorbed on carboxyl latex particles of 1 lm in diameter at doses of 0.77 mg/g (a), 1.55 mg/g (b) and 7.75 mg/g (c).

it is clear that the number of dendrimers increases on the surface by increasing the dose in good agreement with the previous findings. This in turn allowed counting the number of dendrimers and normalizing to the surface area. Fig. 5 shows the number of dendrimers adsorbed per lm2 as a function of G10 dose. The error bars represent the standard deviation obtained from the imaging for at least 5 different immobilized particles. The number of adsorbed dendrimers obtained from an AFM image can be directly converted into the adsorbed mass, since the average molecular mass per dendrimer is known with high precision. The oblique solid line in Fig. 5 represents the surface coverage, which would be expected for a complete adsorption of all PAMAM dendrimers present in the solution. For low and intermediate G10 doses, one finds a scatter of data within the range of the error bars between the experimentally determined number densities and the theoretical values for a complete adsorption of PAMAM dendrimers from the bulk solution. Most likely these deviations originate from the polydispersity of the dendrimer samples. Indeed, calculations including the presence of lower generation dendrimers in different percentage reduce this discrepancy, like it is shown by the dotted and dashed lines. However, for doses larger than approximately 5 mg/g, the maximal coverage is reached and the number density of adsorbed dendrimers does not change

anymore. The horizontal line in Fig. 5 represents this plateau with an approximate value of 663 dendrimers per lm2. Conversely to linear or branched polyelectrolytes, one does not find a complete coverage of the substrate by PAMAM dendrimers [32,33,68]. This behavior can be rationalized in term of a modified Random Sequential Adsorption (RSA) model which includes electrostatic interactions between the adsorbed dendrimers molecules which is expected to be repulsive at this ionic strength leading to limit in the adsorption capacity [20,32,33,44,68,69]. Since in vicinity of the IEP, the electrical double layer repulsion contribution is small, the additional attractive term due to the heterogeneous distribution of charges on the particle surfaces becomes predominant. This is shown in Fig. 6, where forces measured at the IEP for three different dendrimer generations (G4, G7 and G10) are reported. Since experimentally targeting the IEP is extremely difficult, the force profiles measured close to the IEP showed a small repulsion due to the incomplete neutralization of the particles. Thus, in order to determine the purely attractive forces, the experimental force profile was fitted at large distances with the

Fig. 6. Attractive interaction forces for carboxyl latex particles in the presence of three different PAMAM dendrimer generations of G4, G7 and G10. The dashed line shows the pure van der Waals attraction measured for bare carboxyl latex particles at 200 and 300 mM KCl concentrations, the dotted line represents the force originated from the pure patch–charge attraction for G4 while the solid lines are the fits including DLVO forces and the additional patch–charge interactions.

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expected van der Waals and electric double layer forces as described earlier [22]. Subsequently, the electrostatic contribution was subtracted from the experimental curves. The dashed line in Fig. 6 represents the pure van der Waals force which was measured for carboxyl latex particles at an ionic strength between 200 and 300 mM, above the critical coagulation concentration. Under these conditions, the forces are purely attractive due to the screened surface charges. The value of the Hamaker constant H extracted from the direct force measurements was 5  1021 J. This value is in a reasonable agreement with the theoretical one of 9  1021 J determined for polystyrene [70]. The discrepancy between these two values can be due to the surface roughness of the particle. This value has been used to fit all the force profiles in the entire work. One observes that by increasing the dendrimer generation (Fig. 6), the forces are more attractive than the van der Waals force and no more compatible with DLVO theory. The decay length of the patch–charge interactions as determined by fitting Eq. (9) to the experimental force profiles are listed in Table 1 for G4, G7 and G10 together with other characteristic values. The pure patch– charge contribution is also indicated in Fig. 6 with dotted line for G4 and it shows that the van der Waals forces are much smaller than the additional attraction induced by the non-DLVO patch– charge interactions. The third column in Table 1 represents the calculated decay lengths for the different generation by using Eq. (10). The adsorbed number density C is calculated using the polymer doses at the IEP as obtained from Fig. 1, the reported dendrimer molecular mass and assuming particle diameter of 1 lm. The lattice constant is defined as 2a = C1/2. From the values shown in Table 1, we can point out two important aspects. First, the square lattice increases as increasing the dendrimer generation. For high dendrimer generations, the size of the patch is bigger. This bigger size is reflected in a higher value of the amplitude and of the decay length [22,23]. Second, in spite of some deviations, the calculated and fitted decay lengths follow the same trend. Thus, increasing the generation the interaction range increases as well as the patch size. This can be additionally confirmed from Fig. 7a–c where AFM 3D height topographic images of carboxyl latex particles saturated with dendrimers of different generations are shown. It is clear from the images that by increasing the generation of PAMAM dendrimer, the size of the patches increases. From the experimental force profiles fitted with the modified DLVO model within the superposition approximation, the diffuse layer potential, the decay and the amplitude of the additional attractive term shown in Eq. (9) were extracted. To simplify the data treatment, we decided to keep the decay fixed at 2.2 nm throughout all the fitting procedure. This number represents an average of the three generations investigated. The surface potentials obtained in such a way as a function of polymer dose are reported in Fig. 1 together with the f-potentials measured by electrophoresis. As discussed earlier, despite some scatters in the measured data, a good agreement was found between the two different techniques. The amplitude of the additional attractive term for different generations and polymer doses are shown in Fig. 8a–c. Two important features can be rationalized from these data. First, the absolute

Fig. 7. AFM 3-D topographic images of dendrimers G4 (a), G7 (b) and G10 (c) adsorbed on carboxyl latex particles of 1 lm in diameter at saturation of the surface.

value of the amplitude is higher nearby the IEPs for all three generations of the dendrimers. Second, this value increases by increasing the dendrimer generation due to the bigger size of the patches on the surface. Such change in this parameter leads to stronger attraction induced by patch–charge interactions.

3.3. Aggregation rates Fig. 9 shows the calculated (from AFM results) and directly measured (by DLS) stability ratios for the systems contained carboxyl latex particles and G4, G7 and G10 denrimers. A general

Table 1 Characteristic values for the additional attraction term in systems containing carboxyl latex particles and PAMAM dendrimers of three generations at the IEP.

a b

Dendrimer generation

Measured decay length (nm)

a Decay length q1 p (nm)

Lattice constant 2a (nm)

Adsorbed number density C (1/nm2)b

G4 G7 G10

1.8 2.2 2.6

1.7 4.3 7.2

11 30 68

7.82  103 1.12  103 2.13  104

Decay length was calculated using Eq. (10). The adsorbed number density was obtained directly using the dendrimer molecular mass and the adsorbed mass at the IEP determined in electrophoretic measurements.

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Fig. 8. Amplitude of the additional (non-DLVO) attractive forces as a function of the dendrimer dose for G4 (a), G7 (b) and G10 (c).

Fig. 9. Comparison between the stability ratios measured directly by DLS (symbols) and calculated from AFM force curves (solid and dashed lines) as a function of the dendrimers dose for G4 (a), G7 (b) and G10 (c). The dashed lines are the stability ratios calculated with the additional attractive term, while solid lines are the results from the pure DLVO calculations.

trend was observed in all cases which can be described as follows. The particle suspensions are stable at low dendrimer dose due to the negative charge of the bare particles. At these low doses, the carboxyl latex is only partially neutralized by the adsorbed dendrimers and as a consequence, the repulsive electrical double layer forces predominate between the particles leading to stable suspensions. The stability ratio decreases with the concentration and reaches a minimum near the IEPs. Since the particle charge decreases with the dose due to the adsorption process (Fig. 1), the strength of the repulsive double layer forces also decreases and the suspension became less stable corresponding to higher aggregation rates and hence lower stability ratios. The samples are unstable around the IEPs where the overall charge of the particles is close to zero. Due to the neutralized latex, the double layer forces vanish and the remaining attractive interactions lead to fast aggregation of the particles and a stability ratio close to unity. After

further addition of dendrimers to the samples, the stability ratio increases again due to the charge reversal process. As shown in Fig. 1, the dendrimers are able to overcharge the carboxyl latex particles and the double layer interactions stabilize the samples again. Note that the particles are positively charged in this case, so that the counterions are the chlorides from the KCl used to adjust the ionic strength. If one compares the experimental stability graphs in Fig. 9 for the dendrimers of three generations, the following conclusions can be made. The stability values are widened, i.e., the slopes in the slow aggregation regimes are smaller, with increasing the dendrimer generations and the fast aggregation regime is shifted towards higher doses on the same way. The latter effect is due to the shift in the IEP values, since fast aggregation occurs near the IEP. The shallower slopes at low and high doses might be the effect of the surface charge heterogeneities and the subsequent

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patch–charge interactions. As discussed before with the force measurements, if the number of generation increases the patch– charge interaction becomes more pronounced leading to higher aggregation rates and hence, lower stability ratio values. Adsorption of smaller denrimers leads to smaller patch–charge interactions which results in steeper slopes before and after the IEP. A slight acceleration was also observed in the fast aggregation regime in the direction from G4 to G10. This effect again is due to the additional patch–charge attractive forces induced by the adsorbed dendrimers. The decrease in the stability ratio with the generation of the dendrimers in this regime was even better represented in the case of smaller particles which are more suitable for light scattering measurements and therefore, higher accuracy could be reached [16]. The effect of patch–charge interactions on colloidal stability was observed in several systems contained particles and oppositely charged polyelectrolytes [14,50]. Let us now compare the stability ratios obtained from DLS measurements and calculated from the AFM results. The solid and dashed lines shown in Fig. 9 represent the predictions of the stability ratios calculated directly from the AFM force profiles. Accordingly, the experimentally extracted surface potentials as a function of dendrimer doses were fitted with a sigmoidal function shown as solid lines in Fig. 1. The stability ratios were then calculated in two different ways. First, pure DLVO interactions were used (solid lines). Second, an additional attractive term as in Eq. (9) was introduced (dashed lines). In this case, the decay constant q1 was kept fixed at 2.2 nm and the amplitude A was set to its p experimental absolute maximum value (0.02 N/m). Even if the additional attractive term was overestimated, no significant differences in the calculated stability ratios were observed. One can observe that the discrepancy between calculated and experimental stability ratios measured by DLS increases by increasing the generation of PAMAM. Relatively good agreement has been found in the case of G4 and the data were significantly different for G10. The calculated stability ratios fall into a narrow range in all cases as indicated by the steep transition of potentials around the IEP values (Fig. 1). The main reason of the deviation especially in the case of G10 is most likely that a radially symmetric force field is assumed to obtain the rate calculations but this cannot be applied in the case of surface charge heterogeneities. Furthermore, since the particles are attached at the edge of the cantilever in the force measurements, they have lower degree of freedom to adjust their mutual orientation which is reflected in higher stability ratio. However, aggregating particles in a suspension, as in the case of light scattering measurements, will find their preferred orientation to which corresponds to the lowest energy barrier. Thus, lateral charge heterogeneities might be the most likely explanation for the observed discrepancies by increasing the dendrimer generations which can be well detected experimentally by DLS, but not in the AFM measurements due to the fixed position of the particles attached on the cantilever and the substrate. Similar effect was observed in the case of colloidal particles of the same size in the presence of multivalent ions of higher valence [24,25].

4. Conclusions Aggregation rates, i.e. stability ratios, measured by DLS was compared to the one calculated from the interaction force profiles determined by the AFM-based multi-particle colloidal probe technique in systems contained negative carboxyl latex particles and oppositely charged PAMAM dendrimers of different generations from G4 to G10. The dendrimers adsorb strongly on the surface leading to charge neutralization at the IEP and subsequent charge reversal at higher dendrimer doses. The colloid stability of the systems can be described well by the classical DLVO theory

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Dendrimer induced interaction forces between colloidal particles revealed by direct force and aggregation measurements.

Interaction forces and aggregation rates were determined in order to characterize colloid stability of negative carboxyl latex particles in the presen...
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